Author: Калюжный В.В.
Tags: философия психология невероисповедательные формы религии мантика (гадание) масонство оккультизм (спиритизм) антропософия магия пророчества эзотерика нумерология
ISBN: 978-985-16-2774-1
Year: 2009
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npecTon B30wna AHHa oaHoBHa, KOpOHal.4MJI KOTOpO COCTOJl-
naCb 28.04.1730 r., M T. A.
CyAb6oHOCHWe "Mena
Lj...,CI1a H pOnOO1'tecKoft 4>op-
Mynbl 3aK0H8 WHCTBa B pa3-
HblX CO'feTaH...,RX HepeAK npo-
CI1e>K...,BaIOTCR B B8)l(HbiX ,A8Tax
>KM3H..., ..., .o.pyr""x Bbf,QaIO\.1.tYIXCSI
I1...,4HOCTeM, KaK Obi 06beJU'lHRR
...,X cyJJJ:bl B MeTOpillM. npM4eM,
eCI1..., I11OA'" cy e AI1R
cBoeM )t(M3HM ""CI18 38Me'f8J1"" ...,
no B03MO)t(HOCT..., C .....,M..., corna-
COBblB8I1M ceo..., AeMCTB...,R. TO B
3T..., AHt.4 MM OCo6eHHO Be3no.
10
4\.1CJ10 28 6butO CHMSD-
nH4HblM M B cyAb6en.H. TOI1-
CToro. Iles H\.1KOnaeBH4
pOAHncJI 28.08.1828 r. B
AaTe era poJKAeHHJI '4MCJ1a
2 M 8 n08TOpJllOTCJI He-
CKonbKO pa3: ASa>KAbl4HC-
no 2, TpH>KAbi '4HCnO 8 H
ABa pa3a 3TO '4HCJ10 nOSTO-
pfleTCSI 8MecTe - B Ha4a-
ne Mecfll.4a M B KOHl.4e rOAa
po>KJ\eHMJI. IleB HHKonae-
BM'4 3aMeTHn 31Y OCo6eH-
HOCTb M cran K '4Hcny npM-
CMaTpHBaTbCJI. BCKOpe OH
06HapY>KHn, '4T0 BO BceM,
BBe.cteHHe
'ITa CBJl3aHO C 31MM '4HC-
nOM, eMYYAMBHTeJ1bHblM
H He06'bJlCHHMblM 06pa-
30M Be3eT.
YBepoBaB, '4TO '4HCJ10
28 A11J1 Hero C'4aC1J1HBoe.
neB HHKOnaeBH'4 crpe-
MHnCJI CBJl3b1BaTb C HMM
caMbie Ba>KHble MOMeH-
Tbi >KH3HH, YMblwneHHO
nepeHOCKTb Ha 3TO '4HC-
no OTBeTCTseHHble MO-
MeHTbI CBoeM AeJlTenbHOCTH, a TaK>Ke no B03MO>KHOCTM ynoMMHaTb
'4MCJ10 28 B CBOHX npoM3BeAeHMJlx.
npH CJ1}"4ae TonCToM nlO6H11 npoBOAKTb cpaBHeHMe '4MCJ1a csoero
po>KAeHMJI C Ba>KHblMH A11J1 Hero c06b11MJlMM >KM3HH. Tal(, B 1855 r. OH
nHtan T.A. EpronbCKoM: «28-e - AeHb Moero po>KAeHMJI... 6b1J1 A11J1
MeHJI naMRTHbiM H ne'4aJ1bHblM AHeM: B nepBblM pa3 14 neT TOMY Ha3aA
3TO 6b1J1a CMepTb TeTYWKM AneKcaHAPbI HnbHHM'4HbI.. .».
CaM TonCToM TaK 06'bJlCHJtn CKnOHHOCTb K 4MCJ1Y 28: «Sf pOAMncJI
B 28-M roAY, 28-ro MCJ1a, M BCIO MaIO >KM3Hb 28 6b1no AJ1J1 MeHJI
caMbiM C'4aCTnHBblM '4HCJ10M. H BOT HeAaBHO MHe npMwnocb Y3HaTb,
'4TO H B MaTeMaTMKe 28 eCTb oc060e cOBepweHHoe '4HCJ10». To eCTb
'4HcnO CBoero Be3eHMJI neB HMKOnaeBH'4 CBJl3b1BaJ1 MMeHHO co 3Ha-
MeHHeM AaTbi CBoero p0>KAeHHJI.
AeMCTBMe poMaHa «BocKpeceHHe» n.H. TonCTOM npMyp0'4HBaeT K
28-MY '4Hcny (anpenJt). B '4epHOBO BapHaHTe 3TOro poMaHa Ha'4anO
ero AeMCTBMJI npoHCXOAKT B HOJt6pe, HO TO>Ke 28-ro '4MCJ1a - BHMMa-
HMe nHCarenJl nO'4eMY-TO npKTJlrMBaeT MMeHHO 3TO '4HcnO.
CoaepweHHOe 'tMcno
n Jl.H. Toncro-
ro, B KOTOpbIX OH I'1OICman ce&I JCak
TaJ1aHT1UIIBbIM f"IMCaTel1b, 6bu1M KlrWI-
C8HbI B rQD,bI, OKKyl1bTHOe CI1O)ICBtMe
MCeI1 KOTopbIX AaBaOO I.fMCJ1O 2 W1M
8. Hanpw.,1ep, paca<a3 «Ha6er.. HQ-
nMCaH B 1853 r. (= 8), B 31OM)I(S rop,y
H8fl bI noeecTM ,
-1OHocTD» - B 1856 r. (= 2).
11
Bse,lteHHe
no BocnOMMHaHMJlM crapwero CblHa TonCToro - (epreJl nbBO-
BM a, B tieony6nMKoBaHHblX 01pblBKax M3 «KpeMqepoBOM COHaTbI»
neB HMKo.naeBM'4 nMeaJ1: «.R 6b1n TOfAa coaceM MOOOA M BJ1I06neH,
MHe 6b1no 28 neT, JI exaJ1 B ceMblO 6yAYU4eM >KeHbI c.qenaTb npeAJ10-
>KeHMe». B 310M CJ1Y'4ae TonCTOM OKa3aJ1CJ1 aepeH ee6e: B03paCT
era repoJl - 28 neT.
«MHe npMJrnfO, - '4aCTO C03HaBaJ1CJl J1ee HMKanaeBM'I, - MrpiITb qe-
KOM '4aCOB M HaBepTblBaTb ee 28 piu... no '4MCJJy M F"OAY po)l(,QeHMJI».
........................... . .........
: OKa3bIBaeTCA. ASi:1cTBMTenbHo BCTpe IOTCR 'IMCJ18, KOTO- :
· pble C YAHB...TenbHO&II 3aKOHOMepHOCTbIO «nPM8H3aHbl lt K ·
. enOBeKY ... pKTMY ero JtC...3H&.1 ... nep"'OAH'feCKM BMeWMBa- .
· IOTCR B ero cylJP6y. B"'AyanbHbI&II ttyMeponorw.ecKM&II ·
· KOA. no MCCne,p,OBaH"'RM HyMeponOO1M M aCTpOl1OO1M. OOR- .
. 38TenbHO BnneTeH (To Hee - ;38KOAHPOBaH) B MOMeHT :
· po*.Q.eHMR 'fenOBeKa (B W"'POKOM CMblcne - B . .D,eHb, ·
. MecRU,. fOA. B 3HaK 30AMaKa) M ero MMR (<<nnaHEny MMe-
· H..... 4>aMM11MIO, 01'4eOTBO ... caMO MMR. KOTopoe AaIOT eMY ·
· poAKTenM Ka38I1OCb Ob.. COBepweHHO cn ). M B He- ·
. KOTOptlle .Qpyr...e KC'fMCnReMbie nOKa38TenM. C8R38HHble C .
· ero PO*ABHMeM. 3rOT KOA &.1 BMAyaneH, HO. 'fT0 O'feHb ·
. BCVKHO. OH cy.Q.b60HOCeH; Ha npoTRJtCeHMM see&ll )KM3HM e- ·
: nOBeK8 CBR3aH C H8MOOnee BCVKHblMM ,w1R ero IM'fHOCTM :
· COObITMAMM. 3H8R ero. 'fenOBeK BO BpeMR aKTMBHOCTM C80- ·
. ero KOCMM'4ecKoro KOA8 MOJtCeT 6b1Tb oo.nee OCMOTJ>MTenb- .
: HbiM M nocTapaeTCR &.136e>KaTb onaCHbiX «CI1Y'f8MHOCTe&il It . :
· oonbWe oOeperaTb CBoe 3,l\OpoBbe. 6b1Tb YA8'UJMBee B Ae- ·
. nax M 60nee C'iaCTn...Bb&M B JtC&.13HM.
12
Bse,o.eHHe
Ko AnJl ero CTcJTbM «"ITa TaKoe MCI¥=CTBO?» norpe6osanMcb CTH-
XOTBOpeHMJt 4>paHl\Y3CKMX MOAepHMCTOB, neB HMKOJ1aeBM'4 noaynMn
cn MM 06pa30M: M3 BCex nOnaAaBWMXCJI eMY KHMr co CTHxaMM
4>paHl\Y3CKMX 00310B OH m6Mpan TOnbKO Te, KOTopble 6bU1M Ha apa-
HH 28. KaK M3BeCTHO, craTbJl nonY'4MnaCb 3aMe'4aTeJ1WtaJ1!
CbfH Toncroro - CepreM nbBOBH - poAMnCJI TOJKe 28-ro Mcna.
OH BCnOMMHaI1 CJ1OBa. ycJ1b1WaHHble MM aT MaTepH: «j1 poAM/ICJI28 MIOHJI
1863 r. 27-1'0 '4MCJ1a. KO Ha'4anMCb POAbI, 0Tel4 ro pM1I MarepM: -
weHbKa, OOAOJlW1 AD nOnyH M». EMY XOTellOCb, '4TOObi ero craPWHM
CblH POAMI1CR 28-ro: KaK M3BeCTHO, l4H4>py OH C\fMTaJI AnJl ce6J1 C'4a-
cmMBOM» (HayKa M penMrMJI. 1988. N! 12).
nocneAHMM YXOA n.H. TonCToro M3 j1CHOM nOltJlHbI npoM30wen
MMeHHO 28-ro (oKTJl6pS1).
A06aBMM TO, 'fero He 3Han neB HHKOnaeBM'4: "MtIrO 28 BXOAMT B
HYMeponOfM'fecKYIO 4>OPMYny 3aKoHa EAMHCTBa MMpa - 310 '4MC-
no onpeAenReT tyAb6b1 MCTOpMM, a TalOKe pO>KAeHMe 3HaMeHMTblX
nlOAeM M, BepoRTHO, npOAOn>KeHHe MX Aen B >KM3HM. n03TOMY '4MC-
no 28 6b1J1o C'facmMBblM M AnJl nerpa I M 3aTeM BCTpe'faerCJI B co-
6b1TMRX rO<:yAapcTBa POCcMMcKoro no .«HaCJ1eAMIO Aen neTpOBblx»
'4al1\e, M ApyrMe '4MCJ10Bble KOM6MHaLtMM AaT.
06 3TMX M APYJ"MX YAMBMTenblibix '4MCJ1aX '4MTaTenb Y3Haer M3 AaH-
HaM KHMrM.
13
rnABA 1
A3bl HYMEPOnOrMM
Cl)MnococbMSI - L\8PML\8
HYMeponorMM
4 CJ10BaJl acrponOrMJI non}"4aeT 6naronpMJlTHYIO nO'4BY AnJl pa3-
BMTMJI, Mcnonb3YSI B CBoeM OCHOBe HaKonneHHble Ha npOTJI>KeH
MHorMX BeKOB 3HaHMJI npeMMYL14eCTBeHHO ABYX HaYK - HYMepono-
rHM M acrponorHM. Ka>KAaJl M3 3THX ABYX HayK MMeeT CBOH ApeB-
HeMWMe TpaAa4 MM, MeTOAMKH CCJ1eAOBaHMJI M paC'4eTa nporH03a
6YAYL14ero; B Ka>KAOM MO>KHO OTMeTHTb M 3aMe'4aTenbHble nO}"4MTenb-
Hble B3J1eTbi pa3BMTMJI 'H ycnewHoro Hcnonb30BaHHJI B np KTHKe, H
BpeMeHa 3aCTOJl, naAeHMJI K HMM MHTepeca co CTOpOHbI HCCJ1eAOBa-
TeneM M 06 CT8a. OAHaKO npHMe'4aTenbHO TO, '4TO O'4epeAHOe CHM-
>KeHHe aKT BHOQM 3THX HaYK CMeHJlnOCb nepeCMOTpOM 6a3b1 AaH-
HbiX M MeTOAOB MCCJ1eAOBaHHJI, nepeOCMblCJ1eHMeM HaKonneHHblX
3HaHHM, '4TO CTMMynHpOBaJ10 tia 04epeAHbie AecJlTKH (a TO H COTHM)
neT 6YPHblM :nan MX HOBoro pa3BMTHJI H 60nbworo MHTepeca CO CTO-
pOHbI 06L14eCTBa.
cno.hb30BaHMe oc06oM «BOCTO'4HOM» 4>Mnoco4>HH HYMeponorH-
eM H aCTpOnOr eM BbI:JblBaeT nepBOHa'4aJ1bHblM HHTepec, 3aTeM YAMB-
neHMe M3-3a HepeAKo AeMCTBMTenbHo cBepwalOU4HXCft nporH030B
14
A3b1 HYMeponOrJlfH
(npH'Ie... Aa>Ke paCC'IM-
raHHblX ynpOuteHHblMM
MeTOAaMH M HOBM'4KaMH)
M npMBJ1eKaeT HMM HO-
BbiX nOKnOHHHKOB, nOCTe-
neHHO 4>OpMMPYJl H3 HHX
3HaJOKOS :nOM HayKH. Hy-
Meponor - APeBH MWee
eHHe (B nOHJlTHe«HayKa»
aHa c4>opMHpOBaJ1aCb Ha-
MHoro n03>Ke), KOTopoe
npeJ:\wecrsoBaJ10 pa3BMTHIO
MHorHX Hay rpe6YIOU4MX
paC'4eTa H tPoPMyn, B TOM
'4HCJ1e H aCTponorHH. AnJl n}"4wero nOHHMaHMJI Mcnonb3yeMoM B HeM
CMMBonHKH 14H4>p, 6YKB H HHblX 3HaKOB OCTaHOBHMCH Ha pa3BMTMH
HYMeponorHH nOAP06Hee.
OKKYnbTHbie HayKH, K KOTOpblM OTHOCJlT HYMeponorHIO H aCTpo-
norHIO, nOnOnHJlIOT COKpOBHU4H .LtY CBOMX 3HaHMM, H3}"4aJl peanbHble
3aKOHbI >KH3HH 06'beKTMBHbI-
MH, cY6'beKTHBHblMH H «Heo-
C03HaBaeMblMH» MeToAaMH
MccneAoBaHHM (HanpHMep,
MHTyHTHBHblMH, nOAC03Ha-
TenbHblMM). C'4MTaIOT, '4TO OK-
KynbTHbie HaYKH nonY'4HnM
CTMMyn AnJl cBeero pa3BMTMJI
.. Hay'4Hble MeTOAbi AnJl H3Y-
'4eHMJI oKpY>KalOU4ero MMpa
H8 38M8ncy
OAHa if!3 oc66eHHOCTe tiyMe-
po.l1Of11if! if! aCTpc>J1Of\1if! - ifIC-
nol1b3OBaHiI1e <!>101110c0-
<!>if!if! (if!MeHyeMOM acTO «BOC-
T()&.IH "). C ecKorO
BOCnpil1sm1 if! Mif!poeo33peHif! if!
bHbD( MeTOAOB HCcne-
AoaaHif! . OTl1i11'f8. OT
npif!B HbD(,opTO
HaY'<.
M3 rl1y6MHw MKOB
B Al)eBtMe BpeMeHa nepBO
«oOATIif!HHOR H8yKOOIO B EBpo-
ne npif!3HaaanaCb .I1OfHt(a
BTOpoe MeCTO OTBOAHJ1if! Ae-
AytCTif!BHOO reoMeTJ)if!&.1. co-
3A8HHOO EBKJ1&.1AOM Ha OCHO-
BaHif!if! etMst ApiflCTOTel1st.
15
rnasa 1
nOCJ1e aKTMBHoro Hcn011b30Ba-
HMJI ApeBHeM BOCTO HOM 4>H-
noco4>HH. Bee OCHose ne>KHT
KMTaMCKaJt <l>Hnoco4>MJt-
«u,apHu,a HYMeponorHM». KM-
TaMCKaJl 4>WJ10C04>HJI KaK HO-
BbiM 06pa3 MblWneHMJI H n03HaHHJI MHpa no speMeHH, BepOJlTHO,
OKOH'4aTenbHO c4>opMHpoBanacb TorAa, KorAa B ApeBHHX KHTaMc-
KHX PYKonHCJ1X nOJlBHnMCb .. CTanH 06cY>KAaTbCJI 4>Hnoco4>cKHe
nOHJlTMJI M TepMMHbI, - K Ha any I TblCJl eneTHJt AO H. 3. ApeBHe-
HHAHMCKaJl H ApeBHerpe ecKaJl$HJI0co4>HM nOJlBMnMCb n03AHee -
npHMepHO K 1500 r. AO H. 3.
B CBoe BpeMJI TepMHHonorM eCKaJl OLteHKa H AaTa npH3HaBanMCb
MapKCHCTaMH - 06 3TOM 4>aKTe nMCaJ1 B. . neHHH (KoHCneKT KHHrH
f renJl «neKu,HM no HCTOpHH 4>Hnoco4>HH», T. 29). B KHTae «Hay'4-
HbiM MHcrpYMeHToM» MnM n03HaBaTenbHoM MOAenblO (opraHoHoM)
6b1na HYMeponorMJI, onpeAenJleMaJt KaK «4>opMaJ1M30BaHHaJt Teo-
peTH'4eCKaJl CHCTeMa, 3neMeHTaMH KOTOpOft JlSnJlnHCtI '4MCJ10Bble
KOMnneKCbf M reoMeTpH ecKHe crpYKTyPbl. OHM 6b1nM CBJt3aHbI Me>K-
AY C060M rnaSHbiM 06pa30M He no 3aKOHaM MaTeMaTHKH, a CHMBO-
nM'4ecKH, aCCOLtHaTMBHO, MHeMoHM ecKH», - OTMe'4aeT M3BeCTHbiM
CHHonor A. . K063eB B KHHre «Y eHHe a CMMBOl1aX M HCJ1aX B KH-
TaMcKoM KnaCcH ecKOM 4>Hnoco4>HM (1994).
OAHH H3 BeAYU4Mx Y'4eHbIX 3anaAHoM CHHonorHH A>K. HHA3M
(KeM6pMA>KCKMM YHHBepcMTeT) nposen <J>yHA(iMeHTaJ1bHble MCCJ1e-
AOBaHMJI ( Mcnonb30saHMeM 60rareMwero cnekTpa 4>aKTOs: aT 3KO-
nOnt'4eCKHX AO nHHrBHCTH eCKHX. OH nepBblM AOKa3an 3anaAHoMY
MHPY, '4TO Hay'lHble TpaAMLtHH KHTaJl «BO MHorOM COAeMCTSOBaJ1M
Hay'4Ho-TeXHM'4eCKoMY nporpeccy Ha 3anaAe».
CMHOnorM - eHble,
&o13 alO &o1e KYl1bTYPY; <!>&01-
l1OCO<!>HIO, Sl3b1K HAP.
KHTaSl.
16
A3b1 HYMepOnOrnu
B Hay HOM H nOBceAHeBHOM >KH3HH 06U4eCTBO 4aCTO Hcnonb3yeT
CTepeOntnbl MblWneHMJI. npH gTOM He nOOU4pJleTCJI MblwneHHe APY-
r'HMM KaTerOpHJlMM, KOTopble BblXOAJIT «3a paMKH A03BoneHHoro».
Ho HMeHHO nOCJ1eAHHe, KaK H3BeCTHO H3 HCTOpHH, OTpa>KaIOTCJI Ha
n03HaBaTenbHblX cnoc06HOCTJlX enOBeKa H Ha pa3BHTM" HOBOro
HanpaBneHHJI B HaYKe (B.B. HBaHoB, 1994).
AHrnMMcKHe CMHonorM A. rp3M M A>t<. HHA3f04 06paU4aIOT BHHMa-
HMe Ha AOBonbHO n03AHee npHHJlTHe eBponeMcKoM HayKOM TepMHHa
«3aKOH» - B nOCJ1era- . .
l1..neeBCKYIO 3noxy (c
KOHLta xvn B.), AO 3TOro
HcnOnb30BaJ1HCb TaKHe
TepMMHbI, KaK «npo-
nOp14HJI», «n pM H 14M m ,
«paLtHO» H «pa14HO-
HanbHOCTb»: KHTaM14b1
HaXOAMnHCb B 60nee
6narOnpHJlTHOM CH1Ya-
14HM, YaK KaK paHbwe eB-
poneMLteB BBeJ1H B 4>HJ1OC<$HIO «3aKOHOACJTeJIbHylO MeTa4>oPY». 31"0
6b1J1M cnosa, KOTOpblMH yTBep>KAaJ1M 060cHOsaHHOCTb M HeOCnOpMMOCTb
paCcy>KAeHHM, - OHH nOMoranM J1y'4we 4>opMHpoBaTb e,qMHCTBO B3mJl-
AOB B 4>HJ1OCo4>HH H oco6oe MHpo)AaHHe. no Bblpa>KeHHIO f p3Ma, Ha'4M-
HaS! C XI B. HeoKoH aHCTBO «Hai4HOHanH3MpoBaJlO KOCMOC» (T. e.
3TO IUfTaMCKoe HMe rnaBeHCTBOBaJlO B BOCT0'4HOM 4>HJ1OCo4>MH) c no-
MOI4bIO WMpoKOro HCn0J1b30BaHHJI B MOAenM BOCnpHJm1J1 0Kpy>Ka101Ue-
ro MHpa YHHBeptanbHOro nOHJmfJl «I1H».
MYApeLtbi ApeBHOCTM nOHHManM, '4TO AJ1J1 4>Mnoco4>cKoro no-
3HaHHJI MHpa Hero ycrpOMCTBa Tpe6yeTcJI Hel<HM YHMBepcanbHblM
CMHono.... C'tMT8IOT
Ha4HHaA C XI B., no C110BaM A. rpa-
Ma. npH n «111>1- C HTanCA npH-
CYW,HM KIDK,AOMY ABl1eHHIO H Ka)I(-
AOH BeUJ,Jil H OAHQBpeMeHHo 6b1n
Ka'fecTBeHHo eAHHblM A11A Bcex
HHX. OTp8)K8A HX 06w,Y'O cyw.- .
HOCTb.
17
rnasa 1
TepMMH, 4<KaTerOpMJI», KO-
TOpaJl He Y'4MTblBana 6b1
AeTaJlM Ka>KAOM BeU4M HnH
JlBneHMJI, a 6b1na 6b1 06-
U4MM MepMllOM AllJI Bcex
HHX. B OAKOM M3 ApeBHHX
naMJlTHHKOB KHTaMCKOM
4>Mnoco4>HM - «Pe'4ax
LtapcTB», ynoMM alOU4MM-
CJI KMTaMcKMM CMft0l10rOM
ro 10M (1958), 6bU1a c4>opMyflMposaHa nOA06HaJI MAe1t Bbl,qeheHM1I e-
Koero 06U4ero TepMMHa AllJI Beex JlBJ1eHMM H BeU4eM. o nOHJm1e HMe-
no 06UWIO AM Beex JlBneHHM M BeU4eM '4ep1Y H Morna Mcnonb30BaTb-
CJI AnJl 4>MlIOcocJ>cKoro n03HaHMJI MMpa - era npo06pa30M CTaJ10
'4MCJ10.
KHTaMCIOtH 4>H3HK .. HaYKOBeA U.JlHb 83HblOaHb yYBep>KAan,
'4TO Bepw""OM TpaAMLtMOHHOM KMTaMCKOM HayKM CTana MaTeMa-
TH'4eCKall TeopMJI MY3b1KM, a H1! TeOpHJI MarHeTM3Ma, KaK C'4HTaeT
1\>+<. HHA3M. nJlTb TOHOB KMTaMCKOM neHTaTOHMKH cornaCOBaHbI C
nJlTblO 3neMeHTaMM (CTHXMJlMM. - npUH. osm.), COCTaBJ1J1IOU4MMH
CyTb Bcex 4>Mnoco4>cKMX CTpyKTyp H 06DeKTOB MMpa.
Ka>KyU4l4eC1I-COBpeMeHHOMY enOBeKy HaMBHblMM paCcy>KAeHMJI
ApeBHMX MYApe OB AOBonbHO T HO oTpa)l(alOT 3aKOHOMepHble JlB-
neHHJI >KH3HM. 06U4Me CBOMCTBa BeU4eM M IIBneHMM (a He KOHKpeT-
Hble HX Ka'4eCTBa, KOTopble Mbi npMBblKnM 3aMe'4aTb B nep&ylO O'4e-
peAb) B 'paCCY>KAeHHIIX ApeSHMX cl>MlIOC04>OB '4epe3 CMM80nMKy
'4HCen H 3HaKOB YAMBMTel1bHblM 06pa30M comaCOBbiBalOTCJI C OT-
Kpbffi1J1MH COBpeMeHHblX Y'4eHblX. 310 Bbl3b1BaeT YAMBneHMe H npe-
KnOHeHHe nepeA MYAPOCTblO HaWHX npeAKOB.
B .Pe-t8X 1.48pcT11" 0 KaTerOJ)MH
Hcen m1canOCb TaK: ..Bee mo,(U1
H AYXH nocpeACTBOM HCen co-
rnaCOBblB8IOT. a nocpeACTBOM
3Byt<OB npOSiCHRtOT. nocne TorO
KaK Hcna cornaCOB8HbI, a 3BYKH
rapMOHH3HpoBaHbI, CTaHOBMTCR
B03MO)KHblM eAMHeHHe».
18
A3b1 H}'MeponOrHH
HeBonbHO B03HH-
KaeT )f(enaHMe BOC-
KnHKHyTb: «KaK)f(e Mbi
paHbwe He 3aMe'4anH
HnM He MornH nOHJlTb
Te MCTMHbI B MMp03Aa-
HHM, a KOTOpblX HHOCKa3aTenbHO, CUMBOJ1QMU nMcanM ApeBHMe
MYApe bI CBOMM nOTOMKaM, T. e. HaM C BaMH, YBa>KaeMbiM '4HTa-
Tenb?!»
TpHnneTHbiM (TpOMHOM) pHTMM'4AblM KOA 06HapY>KeH B '4MCJ1ax
MaTeMaTM'4ecKoM $>pMynbl reHHOM CnMpaJ1M '4enOBeKa. 4HCJ10B e
pHTMbI, HanpMMep, 4>OpMHPYIOT TalOKe CTpYICTYPY Hawero Jl3b1Ka:
TpMnneTHbiM KOj\ BXOAMT B '4HCJ10BYIO CTpyKTyPY Hawero an4>aBMTa
(A. KHcenb). .
TpHnneTHaJl CHMBonHKa npHBneKaJ1a BHHMaHMe eU4e ApeBHHX
4>Hnoco4>oB H HYMeponoroB. B HaWM AHH Ha eHHoCTb HAeM B
ApeBHMx TpaKTaTaX 06paTHnH BHMMaHMe. COBpeMeHHble Y'4eHble.
Tal<, B.B. BaHoB nHweT, '4TO naypeaT H06eneBcKoM npeMHM no
6HonorHH >KaK06, OTKPblBWHM TPOMHH'4HblM reHeTM'4eCKMM KOA, C
YAHBneHMeM 06-
HaPY>KMn CXOAHY'O
TpMnneTHYIO CHM-
BOOHKY B Aj)eBHe-
KMTaMCKOM «KHMre
nepeMeH» (noA-
p06Hee 06 310M
3araA0'4HOM 1paK-
TaTe CM. nOCJ1eA-
HIOIO masy KHMrM).
KMTaACK8tl1fYIot8POI1OI"' BO MHO-
rOM ttanOMIilHaeT nlllcS>arope"CKoe
}"ieHIiIe 0 «MY3b1Ka11bHO- IIICno
CTpyKType KOCMOCa».
OcHOSW HYM8POIlOnt"
3aKOHOMepHble "f'r'lCnOBbie co eTaHIilA
( IIICl1oBbie CIIIMBOl1b1l1111111 «,D,IiICKpeTHbie
3HeprOpIilTMbI»), BepoATHO,.onpep,el1A-
lOT CTPYKTYPY Bcero cytJ4ero, nOCKOl1bI<Y
OHIII B onpeAel1eHHbIX cO'teTaHIilAX pery-
l1ApHO nOBTopAIOTCA B OKpy*alO eM
Hac Mlilpe B ABl1eHIIIAX III Beuta>(.
19
rnasa 1
VlAeH )f(aK06a 6b1nH pa3B TbI H3BeCTHbiM Jl3b1KOBeAOM POMaHoM
flK06cOHOM, KOTOpblM Mcnonb30Ban TpMnneTHbie CTpyKTypbl AJlJJ
AOKa3aTenbCTBa BnMJlHHJI 3aKOHOB 6HonorMM Ha pa3BHTMe Jl3b1KO-
3HaHHSI. B OpMrHHaJ1bHblX TpYAax a BblJlBneHMH cMMMeTpHM CJ10B B
OpaTOpCKOM HCKytCTBe flK06cOH nOA'4epKHBan 60nbwyIO ponb pa3-
pa60TaHHoro eU4e B ApeBHocTH KHTaMcKHMH HYMeponoraMH y e-
HMJI a cHMMeTpHH '4HCen. Era HAeM nOAAep>KanH naypeaTbi H06e-
neBCKOM npeMHM no 4>H3MKe 11H H flH B CBOHX pa60Tax a Bn JlHMH
Jl3b1KOBbiX CHMBonOB CHMMeTpHH Ha 4>opM poBaHHe Ha HbIX no-
HJlTHM. OHM C03AanH CBoe eHHe 06 oc06b1x CHMMeTpM'4eCKHX OT-
HoweHHitx BeU4eM H JlBneHMM B 4>H3HKe.
Y4eHMe a «'4HCJ10BblX pe30HaHcax» M a 'fMCJ10BOM crpYKType noCT-
poeHHSI OKpy>KalO ero MHpa (B ApeBHet<MTaMCKOM nOHHMaHHH) 3a-
nO>KeHO B pa3pa60TaHHoM COBpeMeHHblMH 4>H3HKaMH npeACTaBne-
HHM 06 YCTpoMcTBe BceneHHOM. TaK, B 60-e rOAbi XX B. 6b1no
pa3pa60TaHo, a B 70-e rOAbi non MJ10 B $13MKe Bce06U4ee npH3Ha-
HHe eHMe rpMHa H WBapLta a TeopHH CsePXcrpYH H cyneprpaBHTa-
i4HH. XapaKTepM3yJ1 OCo6eHHOCT pa3HblX 4>H3H'4eCKMX JlBneHHM, 3TH
TeopMH nO TH nonHOCTblO «COBnaAaIOT C KMTaMCKHMH TeopMflMH He
TonbKO 06U4ero co06pa>KeHMSI a ponH HeKoTopblX '4HCeI1 (B pa3BMTHH
nlO60ro JlBneHMJI HnH npoi4ecca npHpoAbf H BXOARU4HX B HHX 4>H3H-
'4eCKHX <fx>PMYJI. - npUM. osm.), HO H n08TOpJlIOT caMH KOHKpeT-
Hble HCJ1a», - nMWeT B.B. VlBaHOB.
B Hay'fHOM MblwneHMH cOBpeMeHHHKH C'4KTaIOT YHHKaJlbHblM MeTOA
1])aAM4MoHHOro KKTaMCkoro noAXOAi!' K CMMBonaM ('4McnaM, CJ10BeCHbiM
0603Ha'4eMMJlM), KOTOpblM oKa3aJ160nbwoe BJ1HJlHHe Ha pa3BHTHe H npa-
BMnbHOe 4>oPMHpoBaHMe Hay4HbIX B3rn OB Y MHorHX MYAJ)e40 B AJ)e8-
HOCTH. 3r0 >Ke o6crOJrrenbCTBo o6bJ:ICHJleT, nO'4eMY HeJ1b3J1 6e30mJlAH<)
OTBeprm TeopHH ApeBHHX HblX nHWb nOTOMY, '4T0 OHM ( penH»
20
A3b1 HYMepOnOnm
no BpeMeHM M CUJl3(lHbf C HeTpa-
AH14HOHHblMM KnH OKKynbTHbI-
MH HayKaM .
epornM4>H'4eCK M H3b1K.
npoTHBononO>KHO opMeHTHpo-
BaHHblM- no OTHOweHHIO K CHC-
feMe eBponeMCKHX an<PaB.m>a,
cnoco6craosal) HAJ¥OM opHeH-
TaJ.4HM Ape8HetG1TaMCKoM Ky11blY"
pbl(B.B. BaHOB,A. . K063e8).
OAHO H3 nonywapH y enOBeKa AOMHHHpyeT B 3aB.HCHMOCTH aT
BHAa CHIOMMHyTHO peaJ1H3yeMoM AeJlTenbHOCTH. TaK, y npaBweM
3M014HOHaJ1bHO-06pa3Hoe MblwneHHe CBJl3b1BaIOT C 4>YHK14HeM npa-
Bora nonywapHJI, a a6cTpaKTHO-nOrM'4eCKOe - C 4>YHN4MeM neBO-
ro, rAe pacnOnO>KeH pe'4eSOM ueHTp.
Y ApeBHMX rpeKOB Ka>K-
AaH 6yKBa MMena He TOnb-
KO 3BYKOBoe, HO H 4 CJ10-
Boe Bblpa>KeHHe (anbcl>a
0603Ha'4anaCb '4MCnOM 1,
6eTa - 2, raMMa - 3 H
T. A.). nonaralOT, '4TO 3TO
BnHJlnO Ha BOCnpHJlTHe
6yt<B M Hcen M Ha 4>Hno-
co4>cKoe nOH MaHHe x
CHMBOJ1HKM B n03HaHHH 3(1-
KOHOB >KH3HM. AeJl nocr-
poeHMJt rpe'4ecKOro aJ14>a-
BMra 6btna TecHO CBJl3aHa C
Ha 3aM8TKY
B OCHOBe BOCnplitSm1S1 lit Ha-
npaBlleHHOCTlit MblWlleHlitSl
lle>KaT <l>lit3 0110rn KiIte
MexaH 3MbI, nOllywapYISl ro-
110BHOro M03-ra OObl'iHO YH-
KlU'10HlitpyK)T C nonepeMeHHo
cMeHSleMoH aKTlitBHOCTbfO.
3TO H8AO 3H8n.
KlitTaHCKaSl KYllbTypa OCHOBaHa
He Ha aJ1 aB THOM (l1eBonOllY-
wapHOM), a tia liteporn lit'feC-
KOM (npaBonollywapHOM) nplitH-
u,litne MblWneHlitSl, C TaeT aBTO-
p TeTHblH COBeTCKlitH ClitHOll0r,
3aH MalOUl.litHCSI TeopliteH ClitM-
80110B, A. . KOO3eB. B nOAXOAe
K MCllY OHa conOCTaBMMa C
«an aBMTHOH kyllbTypoH rpe-
Koro T na".
21
fnaaa 1
OTKpblTMeM HcnypanbHOro pJWI '4MCeJ1, M3MeHHBWMM npeACTaBl1eHHe
a 'IMCllax. «An4>aBHTHbiM npMHLtMn M CBJl3aHHble C HMM HAeM AMCKpeT-
HbIX eAMHH M3 KOTOpblX COCTORT MMpbl CHMBOJlOB... Hepa3pblBHbI C
M,QeeM Hcnypa11bHOro pJWI» (A. . K063eB).
C OC06eHHOCTblO neBO- M npaBononywapHoro MblWneHHJI pyc-
CKaR penHrMJI CBII3b1BaeT AYXOBHoe COCTOJlHHe H OC06eHHOCTb Be-
poMcnOBeAaHMJI '4enOBeKa (B. KaHAbl6a, 1998). B nCMXM'4eCKOM
AeneJ1bHOCTH BCerAa Y'4aCTBYIOT 06a nonywapHJI - OAHO B 60nb-
weM, APyroe B MeHbweM CTeneHM (B 3aBMCMMOCTH aT BHAa AeJlTeJ1b-
HOCTM M COCTOIIHHJI nCMXMKM). npM 3TOM onpeAeJ1J1IOTCJI '4eTKOCTb
nCMXM'4eCKOM n03MLtMM M B HeKOTopOM Mepe ypaBHoBeweHHOCTb
3MOLtMOHaJ1bHOrO COCTOJlHMJI. npH OTHOCMTenbHO paBHOM Y'4aCTMH
nonywapHoM AeJlTeJ1bHOCTM MO>KeT B03HMKaTb «TpeTbe» COCTOJlHMe,
XapaKTepM3ytOU4eeCJI HeypaBHoBeweHHOCTblO nCHXHKM M 3M0l4HM.
KaHAbl6a C TpeMJI COCTOJlHMJlMH ronoBHoro M03ra CBJl3b1Baer «Tp0-
M'4HOCTb npMpOAbi '4eJ10BeKa», onpeAeJ1J1IOU4Y1O era nOBeAeHMe, BbI-
60p AeJlTeJ1bHOCTM M Bepo.McnOBeAaHHJI - B l4enOM CYAb6y '4eJ10-
BeKa (nOAP06Hee CM. B pa3AeJ1e «B03paCTHOM aHaJ1M3 3HeprMM»).
Bee 06DeKTMBHoe n03HaeTCJI B cpaBHeHHH. Mbi '4aCTO rOBopHM,
'ITa OAH06oKaJl OLteHKa He OTpa>KaeT CYU4HOCTH np06neMbi. BOCTO'4-
HaJl 4>MJ10C04>MJI C ee «npaBonoJlywapHblM» (HepOrJlH4>H'4eCKMM)
MblwneHHeM AaeT .waHC HaweMY npeHMYU4eCTBeHHO «JIeBononywap-
HOMy» (aJ14>aBHTHOMY) MblwneHMIO McnpaBHTb nOnO>KeHHe: OLteHMTb
peaJ1bHyIO >KM3Hb C ABYX CTOpOtt, a He TonbKO «OAHOM nonOBMHOM
rOJlOBHOrO 03ra» M HcnOnb30BaTb CBOM HHTeMeKT' Ha nonHyIO MQU4-
HOCTb. K it M3BeCTHO, BocnpMHMMaTb peaJ1bHOCTb npeAMera MO>KHO
npH pa3HOM era OCBeI14eHMH, npM'4eM 60nbwee '4HCJ10 MCTO HMKOB
6oKOBOM nOACBeTKM C03AaeT eMY J1Y'4wYIO penbe4>HOCTb M peaJ1bHOCTb
BOCnpMJlTHJI.
22
HTe.eeCHO, 4TO eB-
poneMCKaJI H BOC'TO'4HaJ1
4>Hnoco4>HH, npHMe-
HJlJI pa3HbIe npHHl4Hnbl
MblWDeHHJI H aHanM3a"
AOCTMrJlH JlBHblX ne-
XOB B n03HaHMH 3aKO-
HOB >KH3HM H 0Kpy>Ka-
lO ro MHpa. npH eM
nOAXoAHnH paHbwe H
nOAXOAJITTenepb K pe-
weHMIO HacyD4HblXBOn-
pecOS C pa3HblX CTOpOH. Ka)ff;AaJl 4>Mnoco4>MJI C'4MTaeT ce6J1 ripM-
opHTeTHOM M AYU4et4 B HY>KHOM Hanpa neHMM nO) HHJI.
3 CKa3aHHoro BbiTeKaeT, '4TO '4eM rny6)t(e Mhi 6YAeM H3Y'4aTb
4>H110co4>cKMe MeTOAbf APyr APyra M nonHee Hcnonb30BaTb HH-
TenneKTyanbHble B03MO>KHOCTH B n03HaHMM 3aKOHOB >KM3HM TeM
l1Y'4We H CKopee CMO>KeM Mcnonb30BaTb CBoe npeAHa3Ha'4eHMe -
npaBHnbHO H B cornaCMM C npHpOAOM 'npe06pa30BhlBaTb Hawe
OKpY>KeHHe, 60nee C'4aCTnHBO CTpOHTb OTHOWeHMJI B 06U4eCTBe,
ceMbe.
KorAa npHBblKwMe K a6CTpaKTHO-nOrH eCKOMY (neBononywap-
HOMY) MblwneHHIO eeponeMCKMe Y'4eHble Ol4eHHnM ceOH np06neMbi
nocpeACTBOM 3M0l4HOHal1bHo-06pa3Horo (npaBononywapHoro)
MblWneHHJI, TO pe3ynbTaTbi npeB30wnH O>KMAaHMJI HaCTonbKO, 'fTO
HeKOTop e M3 HMX ycOMHMl1MCb B CBoeM BbiCOKOM n03HaBaTenbHOM
cnOC06HOCTM npM Hcno.nb30BaHHH 4<craHAaPTHoro» MblWneHMJI.
KaK eBponeMCKaJl, TaK H COBpeMeHHaft KHTaMCKaJl KnaCCM'4ecKaJl
4>Mnoco4>HJI npOAOn>KaeT pa3BHBaTb }NeHMe a CMMBonax (B TOM 4MC-
A3b/ H}lMepOnOruu
no-rn. KUfA08 MJ oe H8-
npaBII8HMe HCCI1e,A08aHIIM cyLlUiOC-
TH ()bfTMSI KaK 8ocT0Ka, TaK lit 3anB,Aa
8blRBW1O MHOrO'fMCneHHbI6 4!akTbl
yOeAHTenbHbIX noATBePJlKAeHMM CBO-
eM TO'fKM 3petiMSt. KOTopbIe nerJM
B 0CH0ey IIIX )"feHMR. <no AOKa3blBa-
aT. 'fTO 6onbWMHCTBO MeTQAHK 1It3y-
'feHM OKpy*8 ef'O Mlitpa OObeK-
THBHO aTpaQlOT peanbHytO >KK3Hb.
23
rnBSB 1
ne a '4HCJ1ax), '4TO CKa3b1Ba-
eTCJI Ha Ol4eHKe BOCnpHJI-
THJI H n03HaHHJI MHpa.
AanbHeMwHe HCCJ1eAoBa-
HHJI nOKa>KyT npHopHTeT-
HbiM BKnaA Ka>KAOrO H3
3THX Y'4eHHM B HCTopMIO
n03HaHHJI.
AnJl eAMHoro 4>HJ10-
co<l>cKoro nOHHMaHMJI MH-
pa He06xoAHMa eAHHaJl
MeTOAOnOrHJI. B eBponeMcKoM 4>Mnoco4>cKoM TpaAHLtHH ponb Me-
TOAonorMH HrpaJ1a 4>opManbHaJl norHKa, a B IU1TaMcKoM - HYMepO.,
nOrHJI, T. e. oc06aJl TeOpHJI CMMBonM eCKHX nocrpoeHHM crpYK1YP
C nOrM'4ecKHM HCLtHCJ1eHHeM. C'4HTaeT A. . K063eB {1994}. OH nH-
weT: «AHanoroM KHTaMcKoM HYMeponorHM B EBpone 6blna rn14>aro-
peMcKo-nnaTOHM'4eCKa1I apMTMOnOrHJI... AllJI KOTOpOM TalOKe eHT-
panbHblMH 6b1nM KaTeropHH CHMBOJ1a 06pa3a H '4HCna... 6e3
nOHMMaHHlI KHTaMcKoM KnaCCH'4ecKoM 4>Hnoco4>HH rioA06MeM 3a-
raAO Horo c4>HHKca 6YAer OCTaBaTbCJI AllJI Hac BClI Kynbtypa KHTaJI,
nOCKonbKy 4>Hnoco4>HJI B HeM Hrpana ponb 60nee 3Ha HTenbHYIO,
'4eM B KaKOM-n,,60 APyroM Kynbtype. cJ>HJ1OC04>HJI 3AeCb 6blna l4a-
pMl4eM HaYK».
cJ»Mnoco«l>cKoe HaC/leAHe npownoro B caMOM MHorOHaceneHHoM
crpaHe MMpa OCTaeTCJI, no CJ10!laM K063eBa, «AeMCTBHTeJ1bHblM HH-
TenneKljaJ1bHblM CTatjAapTOM». 3HaTb OCHOBHble era npHHLtHnbl, KaK
M OCHOBbf Y'4eHMJI ApeBHMx HYMeponorOB EBponbl, He06xOAMMO A111I
nOHHMaHHJI Y'4eHHM nY'4wHx YMOB HaWHX npeAKOB Ha HCTOpH'4eC-
KOM nyTH n03HaHMJI HMH 3aKOHOB >KH3HH H KOCMoca H ponH OAHO-
CMHOnOrM C'tMTaIOT
AaTopmeTHbll-1 cMHonor 3a
A*. HM,D,3M yraep)K,D,aeT, TO
«<I>Mnoc<><S>clG1e npMH nbl KM-
Tast HaM60nee 6J1M3KM K M,D,eanb-
HOH HaYKe 6y.o.Y11\ero (BCeMMp-
HOH.YHMBepcanbHOH.3 eHM-
l.feCKOH )..
24
A3b1 HYMSponOrHJ1
ro H3 HHcrpYMeHTOB :noro n03HaHHJI - '4HCnOBOM acrponorHM H
HYMeponorHH.
MarMSI M "IMCna.
0611\ee npeACTaBl1eHMe 0 MarMM
B ApeBHHX KHMrax MYAPOCTH a 3aKoHax >KH3H14 '4aCTO Hcnonb30-
BaTlHCb TaK Ha3b1BaeMbie TaMHble 3HaHHJI, a OCHOBHble MblCJ1M HHO-
CKa3aTenbHO 3aWH$pOBblBaJ1HCb B TeKCTe. nMWb 06naAalOU4He 3TH-
MH 3HaHHJlM MornH Ilp04 TaTb «Me>KAY CTpOK» nepeAaBaeMbie
ApeBHHMH MYApeLtaMH MblCJ1H. K TaKMM KHHraM MYAPOCTH OTHOCJlT H
6H6nHIO. «KaHOH» B nepeBOAe C rpe ecKoro 03Ha'4aeT «3aKOH», «npa-
BHna»;a «anOKpH4>H'4eCKHM» - «TaMHbIM», «COKpOBe"HbIM». B 6H6-
nHH ynoMHHaeTCJI B03MO>KHOCTb 3HepreTH4eCKoro 06U4eHHJI '4eno-
seKa C BblCWHMH CHnaMH H cnoc06HOCTb 3THX CHn B03AeMCTBOBaTb
Ha '4enOBeKa '4epe3 CHCTeMY pHTYinOB, KOTopble BK11IO'4aIOT oc06b1e
AeMCTBHJI, 06naAalOU4He «4YAOM», «Mar eM»: '4epe3 3HeprHIO «HanO-
>KeHHJI KpeCTa», '4epe3 HKOHbI, cneu,MaJ1bHble neCI:iOneHMJI H T. A.
COKpOBeHHble (anOKpH4>H'4eCKHe, npH3HaBaeMbie u,epKOBblO KaK
«nOCTopOHHHe») KHHrH 6b1nH H paHbwe, H B HaWH AHH AOCTYnHbI
nHWb H36paHHblM. «He
BblAenMHCb Ha BCe06U4ee
H3Y'4eHHe OHM no o eHb
npocrOM npM'4HHe, - nM- -
WeT A. KHcenb, - 3TH
KHHrH COAep>KanH TaM-
Hble 3HaHHJI. HMeHHO
K 3THM TaMHblM KHHraM
«AnOKpM4»M ecKMe" KHMrM
BeTX 3aBeT 6 6n COCTO T
3 39 KaHOH eCKHX 11 HeKaHO-
HJ.14ecKJ.1X, «anOKpJ.14>J.1 ecKHxlO,
KH r, He BKJ1 eHHblX LtepKOBblO B
KaHOH.
25
rnasa 1
Aocryna-ro MbI, H "te HMe-
eM» (KnaAe3b 6e3AHbI).
6H6nMJI COAep>KMT MHO-
ro LteHHblX CBeAeHHM 06 HC-
TOpH'4eCKMX c06b1THJlx, 3a-
wH<I>PO!aHHblX B pa3Hblx
oKKynbTHbix CMMBonax. B
«TaM HaM AOKTpHHe» EneHa
6naBalCKaJl nMweT: «...HH
OAMH MMcponOnt'4eCKMM pac-
cKa3, HM OAHO TpaAMqMOH-
Hoe C06b1TMe B HapOAHbfX
CKa3aHMJlX HMKOrAa H HH B OAHY 3noxy He 6b1no BblMblCnOM, t<a>KAbiM
H3 TaKHX paCCKa30B HMeeT AeMCTBMTenbHo HCTOpH'4eCKYIO nOAO-
CHOSY» (T. L KH. 2).
YCTaHoBneHo, TO TeKCT 6H6nMM MHOrna HCKa>Ka1lCJ! M COAep>KHT
HenOCJ1eAOltlTenbHble M3nO>KeHMJI MCTOpM'4eCKMX 4>aKTOB. n03TO-
MY HeT HM'4erO YAMBMTeAbHOrO B tOM, '4T0, KpoMe 0606uteHHblx, HH-
TerpHpOBaHHblX 3HaHMM, nOJ1y'4aeMbiX M3 6M6nHM, AononHeHMeM K
HHM AOn)KHbI 6b1Tb TaMHble y-'4eHMJI H3 anoKpM4>H'*!CKHX KHHr, OC-
BeU4alOutMe oTAenbHble np06neMbi n03HaHMJI MHpa.
Eute B AJ>eBHOCTM C'4MTanOCb, '4T0 n03HaHMe TaMHbIX, OKKynbTHbiX
HayK AaeT CK11Y, .HO rpe6yeT 3a1paT HHTeMeKTa M sonH. 4enOBeK KaK
6b1 npoxOAMT HCnblTaKMe Ha AOCTOMHCTBO, Ha npaso BllaAeHHJI TaMHbf-
MM 3HaHMJtMM, npoJlBIIJtJl BOnK> H HaCTO" MBOCTb B MX nOMCKe M ycsee-
HMM, M TEYt caMhiM Kat( 6b1 6pocaer 3epHa 3TMX 3HaHMM B f1O'4By C80MX
cnoc06"OCTeM H nM'4HOCTHbIX B03MO)t(HOCTeM.
P. WraMHep nMcan: «nOCBJluteHHblM 6bU1 Taro MHeHMJI, '4T0 HapoA-
Hoe MHpoB033peHHe OTHOCMJ1OCb K era 3HaHMK>, KaK TbMa K C8e1y, HO
EcnM B8pMTlt OKKYnbTM3M}f,
OT MHOrO HCJ1eHHbIX MHOfOBe-
KOBbiX nepem1CblBaHMH 6116-
I1HH I1IOAbMH, He scefA8 00118-
A81O MH AOCT8TO'fHblMH
3H8HH MH He pel1Mnt03HOM H
OKtcyl1bTHOM ypoBHe, aCTb
TeKCTOB 6b&na HCKIDkeHa W1H
HenpaBHl1bHO nepeBeAeHa.
26
3aTO Ha :nOM TbMe 06HTaeT
HeBHAMMoe C'4aCTbe. MHCTH-
KM C'4HTaJ1H, TO Henb3J1 npe-
CTynHO nOKywaTbCJI Ha 3TO
C'4aCTbe» (XpHCTHaHCTBO KaK
MHCTH'4eCKHM aKT. EpeBaH:
HaM, 1991).
nonY'4alOU4HM TaMHble,
MHCTH'4eCKHe 3HaHHJI Aon-
>KeH 6b1Tb nOAroToBneH K HX
BOCnpMJlTMIO HaCTaBHMKOM.
Y'4eHHKY CJ1eAOBano nepe-
CMOTpeTb CBOH npe>K.H'He.
B3rnJlAbi Ha >KH3Hbi1 ee BOC-
npHJlTHe, H3MeHHTb TO'4KY
3peHHJI Ha B3aMMOOTHowe-
HHJI nIOAeM. nocJ1e MMCTM-
'4eCKOrO nOCBJlU4eHHJI OH AOn>KeH 6b1n MblcnMTb HHbfMH KaTero-
PHJlMH. eHHK nonY'4aJ1 3HaHHJI AllJI Ka'4eCTBeHHO HOBoro ypOBHJI
>KM3HM, He TOnbKO AllJI 3aU4MTbI
ce6J1 aT «3HepreTH'4eCKHX Hana-
AeHHM co CTOpOHbI - KonAOB-
CTBa, crna3a, HarOBopa M T. A.,
..0 H AllJI B03MO>KHOCTH caMoMY
oCYU4eCTBnJlTb 3HepreTM'4ecKoe
HanaAeHMe Ha APyrMx nIOAei4,
KorAa K 3TOMY npMHy>KAaJ1M 06-
CTOJlTenbCTBa». TeM caMbiM OH
Mar BMeWHBaTbCJI B XOA HeKO-
Mant. M peanllHOCTIa
.nlO6bfe 3HaHs.1S1 s.1CKa3s.1Tb
MO)I(HO HaCTOJ1bKO, TO
nOTpe6yeTcSI HeMaJ10 TPY-
1J;J AnSI BblSlBl1eHs.1S1 s.1C1liIHbI.
s.1 C Mars.1e HeJ1b3S1 He s.1-
TaTbCSI, ecn..., OHa 0TPS)KaeT
XOTSI 6b1 AOJ11O peaI1bHOCTs.1.
A3b1 HYMeponorHH
Ta"H'" Hayut
Ta Hble 3HaHs.1S1 LfeJ1oae e-
CTea BcerA8 6b1J1s.1 cnpSlTaHbI
OT W""POKs.1X Macc. HaMOol1ee
nblTJ1s.1BblM nps.1XOAHJ1OCb AO-
6b1BaTb Y'iQHs.1 Mar...,s.1 s.13 CTa-
PblX, Hepe,D.KO pyKons.1CHbiX
s.1CTO<iH...,KOB, s.1MeBW...,XCSl He B
K8)l(,AO KPynHO 6s.16J1s.10Te-
Ke, HO 6epe)I(HO coxpaHSle-
MbiX B KHs.1roxpaHWlM ,
KY1J;J AOCTyn n03BOl1eH J1MWb
M36paHHblM, - B MeHSCTblpc-
IGtX s.1 J1s.1 HblX 6M6nIo1OTeteaX.
27
rnasa 1
TOpbfX c06b1TMM 3eMHOM >KH3HM. np eM nIOAM, KOTOpwe 3TO 803-
AeMCTBHe HCnblTblBanM, He MornM nOHJtTb, nO'4eMY C HIt..M npoMCXo-
AMnH He06'bJlCHMMble, HeJlOnt'4Hble, KaK MM 0 COOTBeTCTBMM C MX
ypoOHeM 3HaHMM Ka3anOCb, c06bfTMJI. n03TOMY RepeAiNa OKKy1IbT-
HbiX 3HaHMM rpe6oBaJla" nOArOTOBKM Y'4eHMKa B MopanbHOM nnaHe,
HeBOCnpHMM'4MBOCTM K c06na3HaM M 06MAaM. CTpOICUI OT8eTCT&eH-
HOCTb 3a Bbl60p }"feHHKa, era BOCmtTaHMe M OOy-fettMe B03Jlara-
naCb Ha HaCTaBHMKa MnH Y'4HTeJ1J1.
no MHeHMIO A. KMCeJ1J1, «B }"feHMKe y6HBaJ1OCb TO, 'teN OH )l(Mn.
TaM OH n03HaBan He'ITO APyroe, 4eMY Her 3KBMBaIIeffTa B peaIIbHOM
>KH3HM. AaoanMCb 3TH 3HaHMJI nMWb TeM, Koro MYAIJeI4W HaXOAMJIM
AOCTaTO'4HO 3penblMH» (KnaAe3b 6e3AHbI, . II).
HaH60nee c mbHoe BnHJlHHe Ha 4>OpMMpOBaHMe esponeMCKOM
CMCTeMbi MarMM M 06U4eCToeHHblX npeACTaBneHMM 0 tteii MMen" rpe-
KO-pHMCKaJl H MYAeMCKaJl t<ynbTYPbl. Y'4eHMK nnaroHa KceHOKpaT
pa3rpaHH4Mn CBepXDeCTeCTBeHHbfM MHp Ha ABa ijapCTBa - 60mB
H AeMOHOB. nepBble Hfo\E!nH oce npMBneKC1IOU4Me 'feJlOBetCa Ka'feCTBa,
BTopble - OlTaJlKMBaIOU4Me. « YAeH AaJ1M HM" Ktul310 TWtbl- (a-
TaHa. epe3 rpe'4ecKMM M naTMHcKHM Jl3b1KH OHO npotfillUlO B espo-
neMcKMe, rAE! CaTaH8 CTaJ1 AbJtBOnOM. 06pa3 CaTaHbI cj)opMtepoaan-
CJI nOCTeneHHO, B Te'4eHMe Aonroro BpeMeHM - C 200 r. I¥J H. 3. H
AO 150 r. H. 3., __ nMWyT BMKTOp H pHHa norcIROBW. - B KOH e
KOH OB Ka>K.qblM -1t6or, M J\b".
Bon - non}"fIlllM CBOe O:
BceBblWHHM - qapc:T80 CseTa,
BnaCTeJ1MH 3na -l.4itpcTBO TbMbI.
CTOpMJI pacn0PJlAllllaCb TaJ(., 'ITa
xpMCTMaHCTBO CTcUIO CMOi, Cblr-
paBweM pewalOlqyIO ponb S cyp.b-
He 38Mency
BeAbM0tt'8H 0bU18 oco-
6eHHO npHC}'U48 nepMoAY
B03PO)I("D,8HH M Pe<I>op-
M8LU-1M - XV-XVI SD.
28
6e MantM... MaJ1lJl,Jl3b14eCKHe penHrMH, wapoAHble BepoBaHMJI CTa-
nH nep6WM111peMJI MCTO'4HMKaMH M COCTaBHblMM '4aCTJlM" eBponeM-
CKoro KOJlA()BCTBa. XpMCTMaHCKMe epeCH... 3aHJlnH 'feTBepToe Me-
CTO» (A36ywa KQllAOBCTBa. M.: HOBOCTH, 1994, c. 4-5).
«K 1300 r. nJM!ACTaBJ1eHMe a KonAoBCTBe B u.enoM c4K>PMMpoBa-
nOOt,. M B TpH C nonoBHHoM BeKa crpax nep4!A BeAbMaMM H
oxara Ha HIIX CTcIIIM HeOTbeMJteMOM '4aCTbIO *H3IiH 06aqeCTBa» (c. 7).
AMepttKaHCKMM MCCJ1eAOBaTenb A>t<.6. PacceJ1, MHOro .neT M3Y-
'4aBWMM MaJ1lIJ M KonAOBCTBO, OTMe'4aJ1, '4TO pacnaA 06tqeCTBeHHblx
CTJ>YICTYP M Be3Ae B nepexoAHble nepMoAbi conpoBO>KAanCJI
B3pYBOM MKTepeca K '4apOAeHcTBY, oKKynbTHbiM HayKaM (acrpo-
nOntM, HytteponorMM, Ka66aJ1MCTH'4eCKMM Y'feHMJlM), K BOCT04HOM
4>MJlOC.M. }ro 6111n onpaB-
AaHHWM MKTepet K MeroAaM,
o6eu¥1BWMM npeACKa3aHMe 6y-
.
de >ICe Kpyf1t, OTOpble 6b1nH
HHMu.HaropaMM OXOTW Ha BeAbM,
nonOJKMJlM eM KOHeU.. 4TO npH-
Me'4aTeAbHO... sepa B MoryU4e-
CTBO MarMM coxpaHMnacb H B
XIX.. M B XX CTOJM!l1UUC» (nOTa-
nOB" B. M M. A36ywa KonAOB-
CTBa, c. 7-8).
Bee, 'ITO 6yAer M3J10>KeHO HH>Ke, OCHooaHO Ha cOBpeMeHHblx H
CTapllOC MCTO'fHMKaX oKKynbTHbix 3HaHMM H npeAnonaraeT, '4TO Ma-
rMJI peanwta. CoBpeMeHHoe KonAOBCTBO OTnH'4aeTCJI aT cpeAHeBe-
KOBoro 60Jtwuei 6naroJKenaTenbHOCTbIO M ryMaHHoM HanpaBneH-
HOCTWO II OOtOBaHO Ha A06poM, 6enOM, MarHH.
A3b1 HYMeponorHH
MCT0p"'f8CK.. cnpaBKa
nOCneAHAA Ka3Hb no 06BH-
HeHHtQ 8 KOn,A08CTBe COCTO-
MaCb: 8 AHrnHH 8 1684 r:,
8 AMepHKe - 8 1692, 8
WOTna H - 8 1727. 80
<!>paHW1111 - 8 1745.8 rep-
MaHHH - 8 1775 r:
29
rnBBB 1
«BOMCTMHY eCTb He'4TO 06eCKYPa>KMBalO ee B TOM MCTOpH'4eC-
KOM TpaeKTOpMM, KOTOPYIO, npoH3MB BpeMeHa H npocrpaHCTBa, onH-
CaJ1a MarMJI, B03BpaTMBWMCb B KOHLte KOHL40B Ha KpyrM CBO$l»,-
nMweT EpeMeM napHOB B «TpoHe nlOL4H4>epa».
4HTaTenb, BepSlU4MM B 3HepronepeHOCbI, T.. e. B B03MO>KHOCTb
nepeAa'4H '4aCTM 3HeprHH aT OAHoro 4>M3H eckoro Tena (BK/lIO'4aH
Teno '4enOBeKa) MnH JlBneHHJI APyroMY Teny HnM JlBneHHIO, a TaK>Ke
npM3HalOU4MM 3aBMCHMOCTb nOBeAeHMJI '4enOBeKa aT CHJ1 npMpOAbi
H B03AeMCTBHJI KOCMM'4eCKOrO Pa3YMa, HaMAeT B :nOM KHHre AO-
nonHMTenbHble TOMY nOATBep>KAeHHJI. 4HTaTenb, KOTOpblM C COM He-
HHeM OTHOCMTCJI K MMCTHKe H MarHH, nonY'4HT nlO60nblTHYlO «nMU4Y»
A/1J1 pa3MblwneHMM, He BCerA'! 06'bJlCHMMYIO C MaTepMaJ1HCTH'4eCKMX
n03H4HM. C OAHOM CTOpOHbI, nonaraeM, \'4TO :310 ero pa3BJ1e'4eT, C
APyroM - 3aCTaBMT 3aAYMaTbCJI HaA crpaHHoM pHTMH'4HOCTblO (MnH
Aa>Ke 3aKoHoMepHoCTblO) npOMCXOAH HX B era >KM3HH 4<CJ1Y'4aMHO-
CTeM» M «ClOpnpH30B».
nOHRTMe 0 pM-ryanaX
B npOJlBneHHH 3araA0'4HblX JlBneHHM H npH «CBepweHHH Ta-
HHCTB» He Bce .MO>KHO 06'bJlCHHTb c n03ML4MH OPTOAOKcanbHOM
HaYKH. EcnH npeAnOJlO>KHTb, '4TO HenOHJlTHbie C MaTepHanMCTH-
'4eCKOM TO KM 3peHHJI JlBneHHJI cYU4ecTBYIOT, TO npH H3Y'4eHHH
MeTOAMK '4McnOBOM actponorMH '4HTaTenlO none3HO nonY'4HTb 06-
ee npeACTaBneHHe a ponH pHryanoB, a TaK>Ke n03HaKOMHTbCSI
C nOHJl1HeM 6enoC1 H '4epHOM MarMH.
eHHe 6enoM, A06poM, MarHH nonY'4Hno HaH60nbwee pacnpocr-
paHeHHe H npOAOn>KaeT Bbl3b1BaTb HHTepec. ABTOp He CTpeMHTCJI 06y-
30
ifMTb 'ifUtcni nJl TaMHblM ...erona....-
6enoM MnH TeM 60nee '4epHOM
MarMH. Era Ltenb - AaTb 06U4He
npeACTaBneHMJI a B03MO>KHOC-
TJlX Ka66anbl '4MCen, paCCKa3aTb
a HeKoTop"'" OCo6eHHOCTJtX OK-
KynbTHbix 3HaHMM, 3aMHTepeco-
BaTh H Bbl3BaTb Y '4KTaTenJt >KenaHMe y>Ke 4eneHanpaBJleHHO, no cne-
4ManbHblM PYKoBoACTBaM, yrny6nJlTb H pa38MBaTb n03HaHMJt B
COOTBeTCTBMH co C80MM MHTepecOM.
npO$ecCHoHanbHoe OBl1CW!HMe TaMHblMM 3HaHHJlMH Tpe6yeT COO -
BeTCTByIOtqeM nepecrpoMKM nM'4HOCT'H, Bblpa60TKH onpeAeneHHblx MO-
panbHblx M B011eBbiX K3'4eCTB, 3a'Tp3T BpeMeHM M HaCToM"IM8OCTM, noc-
11eA0BaTeJ1bHOCTM B BoeHMM 3HaHHM, a 3TO HaeepHSUC3 He 1GUt<A0MY
no CHnaM.
CorJ18CHO Y'f8HMIO
3aH"'MaTbCSI MarneM lVK'
YAOBneTBOpeH"'S1 TonbkO -
HbO< noTpe6HocTeM (BbI .
H",e ceoero 6n", wero 6y-
A}'U4ef'O, BbI60p napTHepa B
Ael1e '" T. A.) ropa3,Q.o n e '"
MaTep....anbHO ,."roAHe8, IfeM
nJ»1HY*.QaTb .qpyroro 'fe11OBe-
Ka nOA&ftltH&o1TbCS1 csoeM BOne
(H8np....Mep. HaCnaTb tta HerO
«I1OP'fy. )
A3b1 HYMepononm
no CII088M Maroa
npo<S>ecCMOHa11bHOO OBna-
AeHHe T8MHblM.... 3HaH -
M.... - 3TO nyTb tlt36p8HHblX
Kon.qyH, Mar, Bonwe6HHK,
BeAYH, npopM b (He 6y-
AeM yrO'4HJtTb pa3/lH'4HJI, no-
CKonbKy MMeeM B BHAY MX 06-
U4Y1O AeRTenbHOCTb) - 3T0
4enOBeK, He TonbKO MHOro
3HaIOU4MM, HO H MHom YMelO-
U4MM. OH cnoco6eH Ha npaK-
TMKe, CBOMMM pyKaMM, M3roTO-
BHib nopoM O'4eHb CJ1O*Hble
«Bonwe6Hwe» aTpM6yt'b1. Mar
CO'feTaeT B ce6e Ka'4eCT8a Te-
opeTHKa M npaKTMKa. Comac-
HO nMTeparype no oKKynbTM3-
31
rnasa 1
MY npownbIX !leT M COBpeMeHHblX H3Ai!HMM, K011AOBCTBO - CJ10)f(Hoe
3aHJm1e, HacblU4eHHoe ManOnOH1fTHOM AflJI HenOCBJlU4eHHoro '4enOBe-
Ka aTpH6yntKOM M HenOrM'4HblMM AeMCTBHJlMH. C OAHOM CTOpoHbI, Ma-
rMJI, Mcnonb3yeMaJI TonbKO B nM4HblX MHTepecax, 06b14HO rpe6yeT Me-
Hee CnO>KHblX M 60nee AeweBbiX no M3rOTOBneHMIO aTpH6yroB
KonAOBCTBa (0 HHX nOMAeT pe'4b HH>Ke). C APyroM CTOpoHbI, TaKaJl Ma-
rHJlOOnee 6e30nacHa AM co6CTBeHHoro 3AOPOBbJl: C4HTaeTCJI, '4T0 «6y-
MepaHr 4epHOM MarHM» B03BpaL1¥leTCJI K nOCJ1aBweMY ee B03BpaaqaJl
eMY He aCTbe.
B MarM'4eCKHX AeMCTBax oc060e 3Ha'4eHMe HMelOT KonAoBC-
KMe pMryanbi ,(\Hana30H HX Hcnonb30BaHHJI caMbiM 06WHpHblM:
aT npOCTblX AO 60nee CJ10>KHblX. npMMep npocToro AeMcTBHJI -
KpeU4eHMe, HnM «HanO>KeHMe Ha Teno KpeCTa nepCTaMM» (y KaTO-
nMKOB - ABYMJI, Y xpHCTHaH - TpeMJI naJ1bl\aMM). 60nee cnO>KHblM
AeMCTBHeM MO>KeT 6b1Tb TeHMe MOnHTBbl. AnJl BCTynneHHJI B CBJl3b C
....... . .............................
. .
· Mar..,R Ha l1I06..,Tel1bCKoM (ynpo eHHoM, Ha4aI1bHoM) ·
. ypooHe. YAOBl1eTBOpRlOlJ.¥iR HeCl1O)KHblM n"' HblM 3anpo- - :
: caM. npo e .., AOCTYf1Hee KIDKAOMY (HanpMMep, BbILII4CJ1e- :
· H..,e nOBopoToB B cBoeill cYAbOO c nOMO blO HYMepol1or..,- ·
. ecK"'X MeTO,D,HK). npo<f>ecC..,OHaI1bHble 3aHRT..,R Mar , .
· cYAR no cne ;' bHoill J1I-1TepaType, Tpe6YIOT He TOl1bKO ·
· MHOr011eTHero YCS<JeH..,R OKKYJ1bTHbIX 3HaH..,iII, HO .., coaep- ·
. weHCTsa sl18AeH..,R co6o . YMeH..,R ynpasl1RTb CSO..,M.., .
· 4>"'3.., ecK"'M"'''' nc..,x.., eCK"'MM, noA ac YH..,KaI1bHblM..,. ·
. cnoc06 OcTRM'" (Hanp..,Mep. Mar AOmtCeH YMeTb Me,D,HT"'- ·
: posaTb).
32
A3b1 H}'MeponOrHH
A06pblMH CHJ1aMM WCUI
MarMJI COBel)leT '4HTaTb,
HanpMMep, «ONe Haw».
epHa MarM.JI; Hanpo-
TMB, cOBeryeT 3T'J >Ke
MonMTBY '4MTaTb Ha-
D60pOT, aT KOH a K Ha-
'4a.AY.. COBepWalOTCJI
TalOKe 60nee CnO>KHble
pMTyanbi C Hcnonb30-
BaHHeM CAenaHHblX
c06CTBeHHbfMH PYKaMH Mara arpH6yTOB, peLtenroB. (Ma01 ecKHM
KpHCTan.A. MarHJI rJ1a3aMH y eHblx H '4apOAeeB (COCT. VI.T. Kaca-
BMH). M.: Pecny6nHKa, 1994.)
B '4epHOM MarHH AorOBop npeAwecreyeT TecHOMY 06U4eHMIO C AbJl-
BonOM. VlMeIOTc pa3Hbie pMTYaJ1b1 BX0>KAeHMJI C HMM B KOHTaKT. 06
OAHOM H3 HHX paccKa.
3blBaeT L10raHH feTe B
MCTOpHM AOKTOpa CJ>ay-
eTa. nepBoe 06U4eHHe
AYxa C cJ»aycrOM npOHC-
XOAHT '4epe3 BcnblX-
HYBwee KpaCHOBaToe
nJ1aMJI, B KOTOpOM no-
JlBnJleTCJI 3noH AYx.
VlHTepeCHO, 4TO feTe
B oKKynbTHoM npeA-
CTaBneHHH 6b1n O'4eHb
'4YBCTBHTeneH K BOC-
MHT8pecHbiM 4»8KT
COBepwafl Tall1HCTBO, Marn roTO-
BflTCfl K BCTp&4e C BblCWIl1MII1 CII1-
naMII1 He TOJlbKO nCII1XOJlOrll1 ecKII1.
OHII1 roTOBflT CBoe TeJlO nocpeA-
CTBOM pa3J1 '4HblX pIl1TYaJ108 cc()till1-
eHlI1fl": He MeHee eM ABYXHe-
AeJlbHOrO rOJlOAfiHlI1fl, '4aCTblX npw
eMOB Aywa 111 T. A.
AnA 1I10603H8TellbHblX
CKJlOHHOCTb feTe K OKKYJlbTII13MY
HYMepoJ10rH BII1ART B er9 ccKOCMII1-
4eCKOM nacnopTe po>K,AeHlI1fl lO
(28 aBrycTa 1749 r.) - B MHoro-
KpaTHOM nOBTopeHlI1111 B ero AfiTe
po>K,AeH R 'U1CeJl 3 <t>OPMYJ1bl 3a-
KOHa EA!I1HcTBa (28 = 4 X 7) 111 ee
KOHCTaHTbI (147) (noAP06Hee 0
<t>oPMYJlax CM. pa3AeJ1 KHlI1rll1 «<3>op-
MYJla 3aKOHa EA!I1HCTBa").
33
rnasa 1
npHJlTHIO 3HeprMM '4HCen opMynbf 3aKoHa EAHHCTBa M ee KOH-
CTaHTW.
EenM '4Mena 4><>pMynbl 3aKoHa EAMHCTBa M ee OKKynbTHOM KOHCTaH-
conocraBMTb C AClTOM PO)f(,QeHMft fere (28 aBrycra 1749 r.). TO y&H-
AMM B HeM pa3HbIe tl3HepreTH'4ecKMe pe30HaHCbI» $>pMynbl M ee KOH-
CTaHTbl. - '4MCJ1a 2, 8, 1, 4 M 7 nOBTOpJlIOTCJI B pa3HblX CO'4eTaHHJOC
B '4MCJ1e pO>KAeHMJI MMeeTCJI «ABOMHOM pe30HaHc» '4MCen 4>op-
Mynbl: 28;
B MecJlLte pO>KAeHMJI oTpa>KeH eAHHH4HblM «'4HC/lOBOO pe30HaHC»
(B nOpJlAKOBOM 'fMCJ1e'MeCJll.ta): 8-M no c'4ety;
OTMe'4aeTCft «rpOAHOM pe30HaHc» '4HCen KottPaHTbI a n.epSbIX
'4HCJ1aX rOAa pO>KAeHMJI: 174 (BonnmqeHMe BceM «CYMto1h1» 4>oPMY-
nbl KOHCTaHTbI).
no MHeHMIO HYMeponoroB, 3TO HecnpoCTa. «We4>CTBo» HaA co-
6b1THJlMH B >KM3HM feTe KaK 6YAYU4eM MCTOpH'4eCKO nH'4HOCTM era
CYAb6a (KOTopylO OTO>KAeCTBnJlIOT C BnHJlHHeM KocMoca HnM Bblc-
wero Pa3YMa) 83J1na BCKOpe nOCJ1e ero p0>KAeHHJI. npoJlBHnOCb 3TO
ynpaBneHMe '4epe3 3aKoHoMepHble CO'4eTaHHJI '4HCen. n03TOMY B
>KM3HM feTe 4HCJ1a 4>opMynbl 3aKOHa EAHHCTBa HnH KOHCTaHTbI '4ac-
TO OOBTOpftnMCb B f) Hble AI1J1 Hero (CYAb6oHoCHble) AHM.
KaK M3BeCTHO, «'4enOBeKy HH'4TO '4enOBe'4ecKoe He '4y>KA0». OK-
KynbTHCTbI KaK .tCTMHHble xpaHMTenM TaMHblX 3HaHHM npOBOAMnM
T1I4arenbHblM 01'601> «nOCBJlt4eHHblX», HCKnlO'4aJl «HH3KHX H HeAOCTOM-
HblX» (no ou.eHKe H3 OKKYnbTHOM nMTepatypbl). OAHaKO HawnHCb H-
TenJl, KOTOpble npeAnO'4J1M HCnonb30BaTb HX B AOCTH>KeHHH nH'4HbI><,
KOPblCTHbiX LteneM. OHM McnOnb30BaJ1M MeTOAbi MarHH AllJI npHHYAH-
TenbHoro B03AeMCTBHJI Ha APyrHx nlOAei1 H ynpaBneHHJI HMH. 4aU4e
Bcero Ltenb HX B03AeMCTBMJI 6b1J1a B YAOBneTBopeHHH HM3KHX CKpbl-
BaeMbiX >KenaHHM H nopOKOB. 3TOMY H<e Hcnon 30BaHHIO cpeACTB
34
A3b1 H}'MeponOrHH
MarMM «HeAOCTOMHble Y'4MTen"» 06Y'4anH CBOMX Y'4eHHKOB. n03TOMY
B HeKOTopblX wKonax TaMHble Y'4eHMJI CaTaHbI (HnM '4epHaJi MarMJI)
3aHMH '4ecro Y'4eHMJI BceBbiWHero (HnH 6enaJl MarHJI).
C'IHTaeTOI, '41'0, BC1YrtaJI B nooosylO 6nH3OCT'I,. MyHNM eHU4HHa
OOABepralOTCSl B11HJ1HMIO «He'fMCTbIX CMn», H pa38MTHe AiiI1bHeMWHX OTHO-
weHHM Me>t<AY HHMM nepexOAKT B pyKM Ab$tBOna. He Ha 3TUT nH pMCK «18-
l1e'4bCJ1 OTC'JYf1HH'4eCT80M» B >KH3HM yKa3b1BaIOT'ttet<bT'opble nOCOOBMl4bI,
HaJ>OAHbIe npHMeTbI M 06pa3-
HIlle cpaSHeHHJI? HanpMMep,
«ce,qMHa B 6oJ)OAY - 6ec B
pe6po», KOf'ACI y 3peno1'O '4e-
noeeKa e,qpyr npocblnaeTCJI
TJlra K npenI060AeJlHMJlM,
MnM TaK noHJlTMJI, KaK «Ha-
CTaBHTb para», «0CTaTbCJI C
poraMM» M T. A-
C AbJiBOnOM He BcerAa
CBJl3aHO 3no HnM HenpMJIT-
HOCTb. AbJlBOn MO>KeT «3aBoeBbiBaTb AYwy» '4epe3 O'4eHb npMJlT-
Hwe AnJl '4enOBeKa 6nara - 3TO MO>KeT 6b1Tb YAOBneTBopeHHe pa3-
nM blX MepKaHTHnbHbI)(, TaMHblx M HM3KMX >KenaHHM. HanpHMep,
'Iepe3 pa3J1H'4Hble «rpeXOBHble YAOBneTBopeHHJI», ceKcyaJ1bHble yTe-
XM (B npOTMBOnOnO>KHOCTb 4»M3H'4ecKOM nlO6BM nnaTOHH'4eCKYlOnlO-
60Bb, MnH «B03BbI!JJeHHYIO», OTHOCJlT K BnaCTM BceBbiWHero). 4e-
nOBeK MO>KeT 6b1Tb "4<nOAKYMeH» He'4MCTbIM '4epe3 ynoeHMe BnBCTblO
HCIA APyrHMH nlOAbMM MnM B03MO)t(HOCTblO YAOBneTBOpJlTb C80M TaM-
Hille >KenaHMJI, KaK AOKTOP cJ»aycr, M 1. A.
fpeXM, 6e3 KOTOpblX '4enOBeK He MO>KeT o6ecne'4HTb npOAJ1eHHe
pOAa H BonnOTHTb Ha 3e;..ne npeAHa3Ha aBwYlOcJI eMY KOCMOCOM
EcnM ..pttTb OuylHtTM3MY.
HHn1MHble H ceKcyanbHble no-
HOCTH'4enOBeKa.ne*8
B HCTOKax SCTeCTBeHHQrO npo-
ABneHHA nlO6BH H npawleHHA
poA8. K8K -rpexoBHble B03nHA-
HHAIO 6b1J1H npll'l HCneHbI K 803-
Ae CTBHIO TeMHblX CHn.
35
rnasa 1
KapMY, LtepKOBblO pa3peWalOTCJI
(HanpMMep, nOnOBaJl 6nH30cTb).
OAHaKo nOCJ1e cOBepWeHMJI rpexa
Heo6xoAMMO nOKaJlTbCJI, BCTynMB
'4epe3 M3BeCTHbiA pMTyaJ1 B 3Hepre-
TH'4ecKYIO CBJl3b C BceBblWHHM AJ1J1
4CO'4HU4eHHJI aT rpexa». «He BCJlKaJl
MonMTBa 60roM 6YAeT ycnblwa-
Ha», - Y'fMT 6H6nHJI, eCJ1H aHa «COTBOpJleTCJI HeMcKpeHHe». A 3Ha-
'4HT, He BCJlKHA rpex 6YAeT npOU4eH.
«HeManbiM BKJ1aA B 4>opMHpoBaHMe 06pa30B, H no ceM' AeHb Ha-
BOAHU4HX Y>Kac Ha nIOAeM, BHeCJ1a penMrH03HaJl 4>MnoCO HJI. 60nb-
WHX OTKPblTHM-OHa He CAeJ1aJ1a, HO pa3pa60TaJ1a Ba>KHble AeTaJ1M...
AelO AorOBopa C AbJlBOnOM peJ1HrM03HaJl 4>Hnoco4>MJI YKpaCHna
06J13aTeJ1bHblM pH1YanOM nonOBoro CHOWeHHJI BeAbM C BnaAblKOM
aAa HnM HHty6aMM - 31Ib1MM AYXaMH-C06na3HHTenJlMM», - nHwyT
B. H . nOTanoBbi -(1994).
«To, 'ITa B OCHOBHOM >KeHU4HHbI 6b1nH npHC11y>KHMLtaMH CaTaHbI,
06'bJlcHJleTCJI KaK 60nbweM nOABep>KeHHOCTbIO >KeHU4HH c06na3HaM M
rpexaM, YaK M reM, \fTO AbJlBOn - naAWHM aHren, a 3Ha'4MT, He HMeeT
nona H MO>KeT nq>KenaHHIO npHHHMaTb H CKOM, M >KeHCKHM OOnHK...
CaTaHa nO'4TH B erAa
nJ>eACTaB1U1eTCJl B OOntt-
Ke MY>K'4MHbI. ECTeCTBeH-
HaM napniepweM KHJl3J1
TbMbI BO BCex MbfCJ1MMbIX
H HeMblC11MMblX npemo-
60AeJlHHJlX 6b1na >KeH-
I4H Ha-KonAYHbJl ».
npo....HM8
no MHeHMIO LteptCBM,
rpeXM OblB8IOT pa3HbIe.
nplll coaepweHlllM He-
KOTOpblX npocTynKoB
B03MO*H0 npo eHllle.
Ha 38M8TJCy
r1l1(),AOM TPYAOB L4epKOBHbtX MblC-
nlllTene CTano OAHO OTKpbITllle:
OK83b19aeTCR.3Ha IIITenbHoe
OOnbWIt1HCTBO npMcnY'KHIIIKOB Ca-
TaHbI... COCTaBl1Rnlll JKeHU.U1HbI.
36
A3b1 HYMeponOrHH
MO>KHO OnMCaTb CJ10>KHble Ae CTBHJI B H8KOTOpblX pMTyaJ1ax Ma-
rHH, KOTopble HenOCBJllijeHHOMY 4eJ1pBeKY nOKa>KyTCJI. CTpBHHblMM
H nOrH'4eCKH lie CBJl3aHHblMH C 4>YHKL4MeM KonAOBCKOM l4enO'4KH.
He 6YAeM cnopHTb a TOM, HaCKonbKO MX penb B MarM4ecKtiX Aei1-
CTBax He3aMeHM14a, - nycrb 06 3TOM CYAJIT caMM MarM, sanwe6HH-
KM, KonAYHbI, '4apOAeH. MO>KHO npeAnOnO>KHTb, '4TO HaBepHJlKa OHM
4<3HepreTH'4eCKH» HY>KHbI, pa3 npHMeHJUOTCR'B MarHH COTHH neT, M
'4TO «cpa6aTbiBaIOT» OHH nY'4we Bcero npM BbinonweHMM MMeHHO B
onpeAeJ1eHHOM nOCJ1eAOBaTeJ1bHOCTH.
. nonaraeM, 4TO '4HTaTenlO, KOTOpblM f10>KenaeT npoBepMTb HeKO-
Topble HYMeponOrH'4eCKMe paC'4eTbi MarHH B AeMCTBM'1, none3HO
3HaT 06 OC06eHHOCTJlX HcnOnHeHHJI pMTyaJ1a. '-IT06b1 OH npeACTa-
BMn, 0 '4eM HAeT pe'4b, npMBeAeM HeCKonbKO yrO'4HeHMM. PHTyaJ1
JlBnfteTCH AaneKO He eAMHCTBeHHbIM, HO 06J13aTeJ1b,HYM ycnOBMeM
npeABapMTeJ1bHOrO «CBJllijeHHOAeMCTBHft» Mara. 0 HeM B. M M. no-
TanOBbi nMwyr: «.. . BcerAa 3TOT pMTyaJ1 COCTOMT H3 Tpex 4acreM: npM-
roTOBJ1eHMJI He06xoAMMOro peKBM3HTa, O'4MU4eHMJI TeJ1a H AYWM, CO-
BepWeHMJI caMara 06pJlAa» (A36YKa KonAoBCTBa).
J.\yxa Bbl3b1BaIOT C LteJ1blO Hcnonb30BaHHJI era A11J1 3HepreTH'4ec-
KMX BOJ.qeMCTBMM Ha '4To-TO MnH Koro-TO. B pHTyane }"4MTblBaIOT Bpe-
MJI f1aAeHHJI Ha 3eMnlO 6naronpH1ITHoro A11Jt MarHH pHTMa 3HeprH
KocMoca - Bce AeMCTBHJI Mara pacc4MTaHbI no MHHyTaM. Tpe6yIOT-
CII AOBonbHO clJyHAaMeHTanbHble 3HaHHJI no MHorHM, '4aCTO caMbiM
HeO>KMAaHHblM AMCLtMnnMHaM, HanpMMep no aaponorMM M Ky3He'4-
HOMY y. Tal(, KMHr H Ca3epneHA nHwyr, '4TO MarM'4ecKMM cepn He-
06xOAMMO AeJ1aTb TonbKO M31¥=Ka HOBOM CTa11M B nepBblM '4ac nocne
BOCXOAa ConH B AeHb MepKypMJI (cpeJW) HY>KHO 3HaTb Tpa oBe-
AeHMe M rOMeonaTMIO: 3HepreTM'4ecKMe KOJ1AOBCKMe peLtenTbl 6b1Ba-
lOT caMblMM He06b1'4HblMM. Heo6xoAMMO 3HaTb npaBHna 06pa60TKH
37
rnasa 1
KaMHeM, HX npeAHa3Ha'4e-
HMe B KonAOBCKHX pHrya-
nax M aTpH6yrax H MHorae
APYroe.OCHOBHOMaTpH6yT
AOn>KeH 6b1Tb BbinonHeH
TonbKO PYKaMH Mara: OH
He AOn>KeH 6b1Tb nOKyn-
HblM, 'fT06b1 H36e>KaTb era
«3HepreTH'4eCKOr03arpJl3-
HeHHJI» '4y>KHMH pyKaMH.
Mar B cOBepweHcTBe
AOn>KeH BnaAeTb MeAMTa-
MeM, KOTOpOM, Me>KAY npO"tMM, 06y alOTcJI HeCKonbKO neT, YMeTb
«3HepreTH eCKH pa3ABaHBaTbCJI» H T. A. (a HeKOTopblX B03MO>KHO-
CTJlX HaWHX 3HepreTH'4eCKHX Ten CM. KH.: 60nbWOM aCTponOrH'4eC-
KMM npaKTHKyM. T. 2. MH.: 3AaTenbcKHM AOM «CHAYMer», 1994.).
Ho «3HepreTM'4ecKoe pa BoeHHe» Tena He Bcerna Hcnonb3YIOT
TonbKO BO BpeA '4enOBeKy, - HM nonb3YIOTCJI COBpeMeHHble 3KCT-
paceHCbI AnJl ne'4eHMJI Ha paCCTOJlHHH 60nbHblX nIOAeM. «KaK npa-
BHno, enMTenb HanpaBnJleT (CBOIO. - npU/rf. oem.) 3HeprHIO '4e-.
pe3 3Be3AY, KOCMOC, XOTJI nOTepJ1 3HepniM npM 3TOM 3Ha'4MTenbHee,
a ne'-fe6HblM 34>cpeKT MeHbwe, - nHweT H3BeCTHbiM YKpaMHCKHM e-
nHTenb A.n. 6a6H'4. - 11 nOCblnalO 3HeprMIO Ha 60nbWHe paCCTOJl-
HM '4al14e Bcero C naAOHeM, conpOBO>KAaJl npOLteAYPY '4TeHHe,.. MO-
nMTBbI. 3HeprHIO HanpaBnJlIO KaK Ha Teno '4enOBeKa, TaK H Ha era
aCTpanbHoe COCTOJlHHe (ABOMHHKa») (4YAeca cpeAH Hac. XapbKOB:
YHHBepcHTeT, 1991).
CamacHo OKKynbTHOM'nHTepaTYpe, B MarM'4eCKHX AeMCTBax Kon-
AYHa nepeAa'4a HanpaBneHHOM 3HeprHM MMeeT rnaBHoe 3HayeHHe.
no CJl08aM MarOB
AnS1 CBoeM A8S1TenbHOCTH Mary
He06xoAHMbI cepbe3Hble no-
3HaHHS1 He TonbKO B COBpeM8H-
HOIf; 6H03Hepren1Ke ( eHHe 0
aKpax loll MepHAHaHax), Ha.o,O
eUl.8 3H8Tb 1f;0ry, BOCTO HYIO
<l>Hnoco<l>HIO H, kOHe HO,
HMeTb rnyOOKHe 3HaHHS1 DO
HYMeponorHH.
38
A3b1 HYMeponOrUu
KOJJAYH YMeeT -KOHLteHTpMpOBaTbCJI 3HepreTH'4eCKH H «H3BneKaTb»
M3 CBOHX KOCMH'4eCKMX Ten HnM BocnpHHHMaTb H3 KOCMoca 3Hep-
rHIO Hy>KHoro eMY Ka'4eCTBa, KOTOpylO OH HanpaBnJleT Ha lJ,eJ1b. B
onpeAeneHHOM CTeneHM Mar AeMOHCTpHpyeT He TonbKO CB9H 3KCT-
paceHcopHble cnoc06HOCTM no BOCnpHJlTHIO, HO H CTaH9BMTCSI re-
HepaTopOM ynpaBnJleMOM 3HeprHH. nOCJ1e TOro KaK Be eCTBO no-
6b1BaJ10 y Hero B PYKax (HanpHMep, eAa, Bo a MnH KaKoe-TO HHoe
Be eCTBO), aHa Bbl3b1BaeT COBepweHHO HHoe B03AeMCTBMe, eM TO,
KOTOpoe CJ1eAOBaJ10 6b1 O>KHAaTb, OCHOBblBaJlCb H H3BeCTHbiX Ha-
YKe era 4>M3M'4eCKHX CBOMCTBax M npMBbI HblX Ka eCTBax.
· B OKKYJ1bT"'3Me "'MeeT 3Ha eH"'e '" TatCO <!>aKT: Y"I"'TblBaS1. ·
. TO aCTb TpaHc<!>opM"'pOBaHHO opraH"'3MO 3Hepr"'''' .
: Mar nepe,o,aeT HaM eHHO eJ1"', OH AOJ1)KeH cosepwaTb :
· 3TO C Ha"'MeHbW"'M'" norpeWHOCTRM"'. n03TOMY OH C8M ·
. AOJ1)KeH "'MeTh 3AOpoByK> '" « "'CTYK>. O 3Hepr"'lO, T. e. He .
· Clp8A8Tb T )KeJ1b1M 3800J1eBaH"'eM, "'Ha e 3Hepr"' Oyp,eT ·
· "'CKa)KaTbC .. nepeA8BaTbC CMewaHHO C He3AopOBO ·
. 3Heprne ero Tena.
.
................................. .....
39
rnasa 1
'1epHaR MarMR M CaTaHMCTbl
Pa3nH'4Hble pel1HrMH M 4>Hnoco$cKHe Y'4eHMJI ApeBHMx H COBpe-
MeHHblX Cne HaJ1HCTOB no <<TaMHblM 3HaHHJlM» yTBep>K.QaIOT, '4TO
'4epHaJl MarMJI C ee cHMBonHKoM H paC'4eTaMH - peanbHoCTb, C KO-
TOpoM He06xoAHMO C'4HTaTbCJI. cnonb3yeMbie elO AeMCTBa HanpaB-
neHHblX «3HepronepeHocoB», KaK C'4HTaIOT, Bbl3b1BaIOT «3HeprOMH-
4>H HpoBaHHe» H OKa3b1BaIOT BpeAHoe BnHJlHHe Ha nCHXH'4ecKoe M
4>H3M'4ecKoe 3AOPOBbe '4enOBeKa, npH'4eM ABycropoHHee - KaK Ha
«npeAMeT», HnM '4eJ10BeKa, nOABeprtiyBwerocJI B03AeMCTBHIO, MnM
«HanaAeHMIO» (npOJlBneHHe BpeAHoro BnHSlHHJI Y HMX MaKCHMaJ1o-
Hoe), TaK M Ha caMara Mara, MnH KonAYHa, nocblnalOU4ero «3Hepro-
HH4>eK HIO» (B MeHbweM Mepe
Bblpa>KeHHoe, HO nOCTeneHHO
HaKannHBaeMoe era OpraHM3-
MOM, H nOTOMY A11J1 Hero 60-
neenary6Hoe).n03ToMYBceM
«HenOCBJlU4eHHblM» H YBne-
KalOU4HMCJI epHoi4 MarMeM
HOBH'4KaM HY)f(HO nOMHHTb,
TO 3HepreTH CKHe AeM-
CTBa - naJ1Ka-o AB.YX KOHLtax.
3Mo HoHanbHo H 3HepreTH-
'4eCKM Hact:"l.qeHHble pHTyanb-
HbienpeACTaBneHHJlHepeAKO
nOTpJlCa.lOT nCHXMKY He06b1'4-
HOCTblO H OCTpOTOH Bne'4aTne-
HHM. He BceM 3TO AocrynHo
PacnnaTa H8MMHyeMa
HeKoTopblX npll1BneKaIOT
npll1eMbi LiepHo Man1I11. Ha-
npaBJ1eHHble Ha nOA II1HeHIite
CBoe Bone .QPyroro enoae-
Ka "111 COBepWeHIite 3na 061i1A-
II1KaM. E e pa npe.o.ynpe)K-
A8eM, TO TaKoe YBne eHlI1e
R8nReTC.fI3a6nY>KAeHlI1eM.3a
KOTOpoe paHO II1nll1 n03AHO
npli1AEnCR pacnna II1B8TbCR.
npll1 eM II1CnpaBII1Tb nonO>Ke-
HlI1e.KaKnpaBlI1no. aaeT
HeB03MO)KHO. ..
40
A3b1 HYMeponorHU
no COCTOJlHHIO 3AOPOBbJl. TaKHe pHyYaJ1b1 MOryr Bbl3b1BaTb He3AO-
pOBoe Ae4>opMMpoBaHHe nCHXMKM H 3AOPOBbJl H Y caMara epHoro
Mara.
npHBeAeM npHMepbl nary6Hhlx nOCJ1eI{CTBHM pMyYaJ108 '4epHOM
MarHH H3 HaweM >KH3HH. 0 HHX nHweT A. naHbI blK B CTatbe «):\eBJI-
TbI 8aJ1 caTaHH3Ma» (ra3eTa «J].eTeKTMB», 1998, MaM). BOT TonbKO
HeKOTopble npHMepbl aKTHBHOM AeJlTeJ1bHOC1H epHblX MarOB H MX
eHHKOB - caTaHMCTOB (B caMOM ra3eTe '4MTaTeJ1b MO>KeT 03HaKO-
MHTbCJI c HMMH nOAP06Hee).
B pa3HblX crpaHax MHpa '4epHaJl MarMJI M caTaHIo43M aKTHBHO pac-
npocrpaHJlIOTCJI KOHKpeTHblMH, 3aMHTepeCOBaHHblMH B HMX ceKTa-
MH H petlHrHJlMM. «A 3TO 03Ha'4aeT, - nHweT naHbt'4b1K, - '4TO ca-
TaHH3M - I<paMHe cepbe3Hoe JlBneHMe, 3a KOTOpblM CTom BnonHe
onpeAeneHHble CHnbl... CYU4eCTBYIOTTaMHbie HJ1M nony:raMHble opra-
HH3aLtHM, nOAAep>KHBaIOU4He AerpaAa HIO nH'4HOCTM. XpMCTHaHCTBo
HMeHyeT HX c06HpaTenbHblM HMeHeM «CblH norM6enH», HCJ1aM >Ke
rOBop 1T 06 «aBIIMH..3w-waMTaH», Hn&4 «CBJlTbiX CaTaHbI». x Ha3b1-
BalOT TaK>Ke « epHblMM MaraMH». fnaBHaJt HX 3aAa'4a - cnoc06-
CTBOBaTb «npHweCTBHIO LtapCTBa AHTHXpHCTa:». He M36e)f(anM «TeM-
HbiX CHn» H crpaHbI{Hr, rAe OTMe'4eH pe3KHM BCnJ1eCK aKTHBHOCTH
'4epHblX MaraB H caTaHMCTOB.
«npaKTM'4e.(KH (OHM) OTKpblTO AetkrnYIOT BO MHOrMX ropoAaX. Tal(, B
MHHcKe 3aAep>KaH caTaHHCT, coeepwaBwHM pH1}'a11bHble y6HMCTBa. 3a-
Aep>KaHHblM He OTpHLtaJ1 CBOOM BHHbI H npH3Hanot, 'frO HeCKOJIbKO neT
roTOBHJ1CJ1 K 3TOMY, y6HBaJI KOTOB. Ko '4HcnO «Ka3HeHHbIX» >KHBOT-
HbIX AOC111mo '4Hcna 666 (B ttyMeponorHH )TO '4MCJ10BOO c eraHMe Ha-
3blBaIOT (<'fHCJ10M 3eepJt». - npUM. osm.), caTaHHCT «BO MMJt cBeero
rocnoAMHa» 3ape3a11 "IenoeeKa. MBA Pecny6nHKH 6enal¥b npH3Hano,
'lTO )TO A(ineKO He nepBblM tny'faM pKTyanbHoro y6HMCTBa».
41
rnasa 1
Ha TeppMTopHH CHf TaKHe CJ1 aH MHOrO'4HCJ1eHHbI. npHseAeM
npHMepbl.
«B TIOMeHcKoM 06naCTM >KMTeJlM npHropoAHoro cena AHTHnHHo
6b1nM nOTpJlCeHbI cepHeM 6ecnpeLteAeHTHbix 3araA0'4HblX cMepTeM.
OAHOro 3a APyrHM H3 neTnH BbiTaCKHBaJ1H nOAPoCTKOB 6e3 JlBHblX
npM3HaKoB HacMnbCTBeHHoM cMepTH. no nepBblM CJ1yxaM, 3TO 6b1nM
caMoy6HMCTBa, HO 4>aKTbI rOBopHnH a APyroM: Bce norH6wHe JlBnll.
nHCb '4neHaMM caTaHHHcKoM CeKTbI H 6b1J1H 3aAYweHbI BO BpeMJI TaM-
Horo pHTyaJ1a nOCBJlI14eHHJI.
npH BcrynneHHH B ceKTy
3aCTasnJlIOT BbinOnHJlTb ca-
Mble a6cYPAHble pMtyanbi.
Tax. B pHTyaJ1e Hcnonb3YlOT
'4epen K03J1a (cMMBon AbJl-
Bona) H '4enOBe'4eCKMe '4e-
pena (CMMBon 4<TeMHblx, no-
TyCTOpOHHM .CHn»), nblOT
KpoBb AeByweK-CeKTaHTOK.
KpOBb A06b1BaIOT H3 HX BeH
WnpHLteM, npeHe6peraJl 3neMeHTapHblMH npaBHnaMH 6e30naCHOC-
TH: '4epe3 KpOBb MO>KHO 3apa3MTbCJI onaCHOM MnH Aa>Ke CMepTeJlb-
HaM 6one3HbIO (HanpHMep, Cm1AoM MnM «6e306HAHOM» 60ne3HbIO
60TKHHa - HcIk LtMOHHblM XpOHM'4ecKMM renaTHTOM).
CYU4eCTBYIOT COBepWeHHp C03HaTeJlbHble M nonHOCTblO OTAalO-
IqMe ce6e OT'4eT B CBOMX AeMCTBHJlX AbJlBOnOn0KJ10HHHKH, «CBJlTbie
CaTaHbI».. 8 CBOHX 330TepH'4eCKMX MCCJ1eAOBaHHJlX OHH AownH AO
onpeAeneHHoM «ABepM», HO 06HapY>KHnM ee 3aKpblTOM AllJI ce6J1
(330Tep"M'4ecKoe Y'4eHMe' HMeeT 4>Mnoco4>cKoe 06ocHoBaHHe, '4TO
rpe6yeT AllJI era nOHHMaHHJI onpeAeneHHoro pa3BHTHJI HHTenneK-
H8 38MeTJCy
no AaHHblM MBA PocCHM.
TOllbKO B MOCKBe .o.e£;CTBY'QT
60llee 30 opraHH30BaHHblX
ynncaTaHHCTOB.HMe
B ooU-'eH CJ10)KHOCTH 01<0110
2 TbICR neHOB.
42
Ta, a 3TO He BeeM « epHbfM MaraM» M eaTaHHCTaM nOA cMny. - npUH.
aem.). OHM 6b1nH Bb>IHy>KAeHbI BepHyTbCJI «Ha3aA», nHWb '4aCTH'4HO
060raT':fB CBOH nCHXH'4eCKHe B03MO>KHOCTH (a B03MO>KHO, '4TO H
HCKa3HB, Ae4>opMHpoBaB HX. - npUH. aem.) M He B03P AHBW Cb
AYXOBHO. 3T0 «'4epHble MarM», HOCMTenH oc06b1x BnHRKMM H cno-
C06HOCTeM. OHM COBepwalOT '4YAeca, TaKMe, KaK «6MonOKa14MJI»,
«J1eB Ta14HJI», HO Mcnonb3YlOT x B LteJ1J1X yc1<OpeHHJI npMxoAa AH-
THxpMcTa. WHpOKO M3BeCTHO H APyroe onpeAeneHHe CaTaHbI KaK
«06e3b1lHbI 60ra».
B npoTMBoBecCY U4HM
ceMH «6narHM» (CBJlTbiM. -
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Hbl. BropaJI - B CYAaHe, B ropHOM paMOHe, HaceneHHOM <<J1HKaHTpOna-
MM», nIOAbMM, KOTOpble MOryr «npeBpalqaTbOl B BonKOB» (0 peanbHOCTM
TaKHX nepeBonnoU4eHM '4eJ10BeKa C nOMOU4blO opHeMOB «'4epHOM "'a-
ntM» Ha HCTOpH'feCKHX npHMepax y6e>tw1er '4HTaTeJ1J1 Haw COBpeMeH-
HMK Mar, ntnHOTM3ep H a eMHK B.M. KaHAbl6a B KHMre «11IOAM H 4>e-
HOMeHbI. YAMBMTe11bHbIe 4>eHOMeHbI pa3HblX crpaH H 3nox». - npUM.
asm.). TpeTWI- B CMpMM, '4eTBepTaJl- B VlpaKe, nJITaJI- B TypKec-
A3b1 HYMeponorHH
. . Y'f8HtM CaraHw
Ha 3eMHOM wape ecTb
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libl - x Koop HaTbi
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<S> 'feCK He cornacoBbI-
8811, HO 'fTO Y B TenbHO,
Ha KapTe X pacnonO)Ke-
t-I e t-IanOM HaeT nOAKOBY.
43
rnaSB ,
TaHe (ecTb CBeAeHMJI, 'fTO B HeM 6b1J1 nOCBJI H B 'fepHylO MarHIO 'OBe-
CTHbiM Mar feoprHM fypA)KMe8). WecraJt - Ha yPane M teAW4aJl- B
3anCWfOM CM6MPM».
>KM3HeHHble HHOCTM, KaK M3BeCTHO, CMeHJlIOTC" aT nOKOneHMJI
K nOKoneHMIO, M 3TO Y'4MTblBaeT '4epHaJi MarHJI. Ee «TaMHble }"4e-
HMJI» nO-HOBOMY npenOAHOCJJTCJI HaeeneHMIO, OC06eHHO AI1J1 Taro,
'fT06b1 3aMHTepecoBaTb MOnOAe>Kb. B CTaTbe AaJ1ee (o06U4aercJI:
«HHTepeCHo, TO 3HaKOMCTBO C CaTaHM3MOM CerOAHJI npoMcxoAHT
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KOHrponMpyeMbiM «'4epHblM PblHOK» BHAeo4>HnbMoB HaCblU4f!H ca-
TaHHtTCKOM cMMBOnMKoM (0 HeM eM. COOTBeTCTBYIOU4MM pa3Aen AaH-
HaM KHMrH. - npUM. Qsm.) M AaeT B03MO>KHOCTb npaKTH'feCKH
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Hble opraHM3al4HH EBponbi. OC06eHHO 3TO KaCaeTCJI H3BeCTHoro
«'4epHoro ra» An CTepa KpoynM. Era C'4MTaJlH CBOHM AYXOBHblM
Y'4MTeJ1eM Api'yp 6paytt, CTMHr M l\3BMA 60YM.
nOA06HoM «06pa60TKe TaMHblMM 3HaHHJlMM» nOABepraJ1HCb He-
KOTopble KMHeMaTOrpa4>MCTbI, HanpMMep KeHHeT 3Hrep.
ny611MKaLtHM B OTKPblToM ne-
'laTH paHee TaMHbIX CBeAEHMM, B
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H3eec bO( poK-rpynn, ya-
KMX ICBK ..Rolling Stones»,
..Led Zeppelin-, ..Psychic
TV» H T. A.
44
A3b1 HYMepononru
AeT (HJlH Y>f(e npoHcxOAHT) ]a
YMbi no.qpacralOaqero nOKone-
HMJI, eM HaWeM CMeHbI M
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CJI B atm1MOpanDHbDC H aHTH06LqeCTBeHHblx HOBKaX.
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BaTenlO: «MHe npHJlTHO OC03HaBaTb, '4TO JI He TaK KaK BC -
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'4epBH, KOTOpblX HaAO TonTaTb]l).
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aqecrsa, B KOTOpoM OHM npo>KHBaIOT, M nOCTpaAaJ1M 3a perynJlpHoe Ha-
pyweHHe 3aKOH08 MOpanM, 'frO npoJlBMOOCb B A$pMaqHM nM&4HOCTH,
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KOM KOpoTKoM) pacnnaTs:tTCR 38 3TM
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45
rnaea 1
roB. 06U4ecTBO 60peTCJI ]a CO HanbHYJO H MeAM HCKyIO nOnHOLteH-
HOCTb. ]a npeBpa HMe caTaHMCTOB B paBHonpaBHblX rpa>KAaH.
K CO>Ka11eHMIO, HanpJl>KeHHe 60pb6b1 «CBeTa H TbMbI» He YMeHb-
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HbiX 3HaHMM» CJ1eAYeT 6b1Tb oc06eHHO OCTOpO>KHblM.
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4>Mryp).
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nO>KeHMJI)( cseTMn M nnaHeT. n03TOMY Mar nepeA AeMCTBOM npOH3-
BOAMT pac\i!TbI HX nOnO>KeHHJI Ha He60CBo e.
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neHHoe nOnO>KeHHe. B H3MeHeHMM nOnO>KeHHJI Tena B npocrpaH-
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A. AasHA-Heanb, MaH11V1 n.
XOM VI , 0e3ycnewHbI;
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46
CTBe (TaKoe nOnO>KeHHe MO>KeT 6b1Tb He06b1'4HblM H TpYAHO ocyiqe-
CTBHMblM caMOCTonenbHO) Mary nOMoraeT era nOMOU4HMK.
«X0'Ol Bbl3b1BaTenbHQM MarMeM (npMBneKalOU4eM K ce6e pa3Hble
3HepreTM'4eCKHe CHnbl M «3HepreTM'4eCKMe MaTpM bI», &,fOM 'fMCJ1e
AYWH YMepWHX. - npU/if. osm.) MO>KHO 3aHMMaTbCJI M. B OAMHO'4-
Ky, - nHweT H3BeCTHbiM aHrnHMCKMM Mar Kp3r, - nbiTalOU4HeCJI
caMH npaKTMKOBaTb Bbl3b1BaTeJlbHYIO MarMIO AOCTMralOT MaJ10 ycne-
xa, eCJ1H A06HBaIOTC era Bo06u&e. He06xoAMM'O,.'4T06b1 80 BpeMJI
Bbl3b1BaH"" PIlAOM C saMM 6b1J1 nOMoU4HMK-1CCMOtpJlU<t14». nM eCJ1M
Bbi caMH co6HpaeTecb AeMCTBoBaTb KaK CMOTpJlU&MM, BaM nOHaAo-
6KToi 'IenOBeK AIlS! cOBepweHHS! Ba>KHblX '4acTeM pHtyaJ1a» (CoBpe-
MeHHBSI MarM", 1991). _.' -
B «cMoTpJlU4Me» cOBe1YlOT Bbl6HpaTb '4eJ10BeKa C onpeAeJleHHblM
MHTenneKTyaJIbHblM ypoBHeM H 06naAalOU4ero HaM60 weM nCHXM-
'4ecKOi4 '4YBCTBMTenbHoCTblO, Bne'4aT1lMTeJlbHOCTbIO. TOfAa 01' 6YAeT
nepeAaBarb npeACKa3aHHJI C nOBblweHHoM TO'4HOCTbIO. «CMOTpJliqMM»
AOn>KeH MMeTb XOPOWYIO naMJlTb Ha acrpanbHble BOCnpMJlTHJI (Ha-
npMMep, '4aU&e ApyrMx .olOAeM BHAeTb BeU&He CHbi H Aonro nOMHMTb
C80H cHoBHAeHHJI, He 3a6b1BaTb MX cpa3y >Ke nOCJ1e cHa). QH AOn>KeH
npaBMJ1bHO BnaAeTb pe'fblO, YMeJlO M '4eTKO OnHCblBaTb CBOH ol4}lU&e-
HMJI. >KeJlaTeJlbHO, '4T06b1 310T
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npM 310M «CMOTpJlU4HM» AOn>KeH
B OCHOBHOM YMeTb KomponHpo-
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BaeMbiM «CYIlt6CTBOM» B
BlII,[te ero 3HepreTW4ecKoro
00pa38 - yxa.
47
rnB88 1
nOA06paTb xopowero
nOMOU4H M Ka-«CMOTpJl ute-
ro», KaK BHAHM, Mary He-
npoCTO. ECTb PJlA M APyrHx
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aKTMBHble eHbI 06U4eCTBa, TaK KaK AOKa3aHO, TO HepeAKo ceKcy-
anbHaJl 3HeprHJI B '4enOBeKe CO'4eTaeTCJI C AenoBo aKTMBHOCTbIO M
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nO>KKTenbHblX Ka'4eCTB Mana: nOMOutHHKy CJ1eAYeT 06naAaTa; eute H
pa3BMTO MHTyM HeM.
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CTBa, C MTaeTi<p3r, 3TO TO, '4TO «CMOTpJlutHM» nOMOutHHK HM ero He
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MOU4HMK «He 06naAaeT aAeKBaTHo pacKpblTbiM nCHXH eCKHM 3pe-
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M3 OKpy>KatOutHX Ha ponb «cMoTpJlU4ero», TO Mary peKOMeHAYeTCJI
onpOCMTb npMCyTCTBYlOutHX Ha npeAMeT TJlrH K MarHM. B Ka eCTBe
MHHHM Jtl,HOrO rpe60BaHHJI OH 06pautaeT BHHMaHHe Ha cnoc06-
HOCTb '4enOBeKa '4aCTO BHAeTb BeutHe CHbI, YBne'4eHHOCTb era «He-
TPaAH HOHHblM" 3HaHHJlMH» MnH B KpaMHeM CJ1Y4ae npHcyTCTBMe y
Hero 60nbworo >KenaHHJt acTBoBaTb B npeACTOJlU4eM 3KcnepHMeH-
So BpeMR 8rM'IecKOro AeA-
CTa8 peKoMeHAyeTcSI pe3KO
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npSl)KeHHe caoero Ten8 H Ten8
«cMOYpSlU4ero lt . 88)1(HO K8'4e-
CTBeHHO M3MeHKTb CBoe C03H8-
HHe H C03H8HHe nOMOU4HMKa.
48
Te. XOPOWO, ecnM 3TM TpM Ka-
eCTBa 6yAY1 npHCyTCTBO-
BaTb B 1.IeJ10BeKe.
AnJl nOBbfWeHHJI 3MO H-
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Mara M «CMOTpJllqero» npH-
MeHJlIOT pa3Hble MeTOAbi.
nO'4TM BCe OHH AnJl perynJl-
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nOnb3YIOT acrpaJ1bHble CBOMCTBa opraHM3Ma - '4YBCTBa, 3MO HM.
310 MO>KeT 6b1Tb 'fYBCTBO HaMBblcwero 6na>KeHCTBa, opra3Ma MnM
CMnbHOM 60J1H.
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HaCJ1a eHHe H YAOBonbCTBHe TonbKO npM CHJ1bHOM 'MO MOHaJ1b-
HaM B036Y>KAeHHH, crpecce. TaKoe COCTOJlHHe MO>KeT B03HHKaTb aT
npH'4HHeHHJI ce6e HecTepnHMoM 60nM (Ma30xHcTbI) HnM npM Ha-
6nIOAeHHH 3a npOJlBneHMeM 3MO MOHaJ1bHOM 6YPH Y napTHepa (Ha-
npMMep, npM ceKcyaJ1bHOM 6nH30CTH).
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HMKa, KOTOpblM OHH B 60nbWMHCTBe CJ1 ae8 C03HaTenbHO ynpaBnJl-
lOT, JlBJ1J1eTCJI eOTheM1ieMbiM ycnOBHeM CBepWeHMJI MarMH. AOCTHl.lb
3MO HOHanbHoro B036y>K,qeHHJI (<<3aBecTH ce6J1») MO>KHO pa3HblMM
cnoco6aMH. OAMH M3 HHX - A06HTbCJI ceKcyanbHoro B036Y>KAeHHJI.
TaKoe B036y>K,qeHHe C'4MTaeTCJI OAHMM H3 caMbiX nerKO Bbl3b1BaeMblx,
yaK KaK HM aT npHpOAbi 06naAaeT 60nbWHHCTBO nIOAeM. CBepWaeTCJI
aHa pe4>1\eKTOpHO B onpeAeneHHblX ycnOBHJlX, Kor a 06b1I.1HO HerpYA-
HO A06HTbCJI HY>KHoro ypOBHJI B036Y>KAeHMJI (oc06eHHO npM YM blX
AeMCTBMJlX napTHepa npOTMBOnOnO>KHOrO nona). n03TOMY ceKcyanb-
H.oe B03 eHMe KaK OAMH H3 BapMaHTOB «3MO MOHanbHoro HaKa-
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nOJ1b3yeMoH B WaMaHCIC )(
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npMMeH IOT caM06H eB8H'-1e.
49
rnasa 1
na» AllJI M3Bne'4eHMJI M3
opraHM3Ma He06xOAM-
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ra3Ma. He06xOAHMY
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renbHoro M 6eCC03HaTenbHoro BOCnpMJlTHJI peanbHOCTH. HanOM-
HHM '4MTaTUIO, '4To.cYU4eCTBOBaHHe B .KOCMoce H4>opMa HOH-
Hare non";.8 KOTOpOM XpaHJlTCJI 3HepreTM'4eCKHe MaTpH bI a
npownOM HaCTOJlU4eM M 6YAYU4eM nnaHeTbi 3eMnJl H a Ka)tij\OM ee
>KHBOM cYU4eCTBe, npM3HaeTCJI cOBpeMeHHoM HaYKoM (CM. pa3Aen
KHMrM «n03BonHTenbHo nM 3HaTb
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I.feCKOO IiIH4>oPMa'-'IiIM.
50
3ro HBAO 3H.n.,
S SOCnpIilSlT\ltM peanbHO-
CT\It OOJ1bWee 3Ha eH\lte
nOny'iaeT noAKOpKa ( YB-
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(Tena,opraHM3Ma) M 3Hep-
reTM'feCKHXou.w eHHM (Ha-
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nocne B03Bpara C03HaHHJI
B peaJ1bHOCTb Mar OCHOB-
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THM (npeMMYU4etTBeHHO ac-
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rOM M era nOMO HMKOM OAHoro nona. n03TOMY Bce MarM CTpeMJlTCJI K
TOMY, '4T06b1 Y HHX 6b1J1M noMO HMKaMH nHI,4a APYroro nona. nOCKonb-
K'J Man4 4aU4e foty>K'4MHbI, TO nOMoU4HMKM Y HMX - >KeH HHbI.
OAHaKo Hcnonb30BaHMe ceKcyaJ1bHOM TeXHMKM B MarM'4ecKHx AeM-
CTBax He BceM MaraM AOCTynHO. Aeno He TonbKO B TOM, '4T06b1 Me>KAY
Y'4aCTHMKaMH 3Toro «MarH'4ecKoro 3KcnepMMeHTa» 6b1J1a B3aMMHaSi
ceKcyanbHaJI Tm-a. OAHOBpeMeHHO AOn>KHbl6bITb OnpeAeneHHblM om 1T
nonoBoM 6nH30CTH (sna,qeHMe TexHMKOM ceKca), xopowee 3AOpoBbe
M aKTMBHblM B03paCT. c<CMOTpJlU4MM» TaK>Ke AOn>KeH MMeTb nepe'4Hc-
neHHble Bblwe Ka'4eCTBa: '4YBCTBeHHOCTb, BOCnpHHM'4MBOCTb, npHsne-
KaTenbHOCTb H T. A.
npOl4MTHpyeM BblCKa3b1BaHMe ()" ceKcyaJ1bHOM TexHMKe B MarMM
TaKara 3HaTOKa OKKynbnt3Ma, KaK AOHaJ1bA Kp3r, M3 era KHMrH «Co-
BpeMeHHaJl MarHJI. OAMHHaAl4CITb YPOKOB Bblcwero MarH'4eCKOrO
MCKyCCTBa» (c. 278-279):
A3b1 H}'MeponOrHH
Ac1'pBnWfWA caKC
CeKcyanbHaR OAHQnOnaA On&>1-
30CTb (*eHCKaA - &>18H-
CTBO &>111&>1 M}')ICCK8A - eK-
cyan&>13M) B MarM&>1 He nP&>13H8eT-
CA IC8K &>1CT &>1K,AnR noI1y'feH&>1R
M ceKcyaJ1bHOM 3HeJ>rM&>1.
B P&>'J1Y811ax MarM'" nP8AflO KTa-
eTCR ecTecTBeHH8A nOOOBaR
CBA3b Me Y pa3HOnOnblM&>1
n8pTHepaM&>1
51
rnasa 1
CTexHMKa n CKa3aHH", Mcnanb3YlOiqaJI ceKcyanbHOCTb, nOAXoAMT
He BCeM. 6oJ1bWHHCTBO He >KenalOT npaKTMKOBaTb ee, M no HopManb-
HO. 0Ha Ha3b1eaerCJI «3poTOKOMaT03HaJI JlCHOCTb». 3rOT PM1Ya11 npeA-
nonaraeT OAHoro «CMOTpJlI14ero» M OKpy>KaIOU4MX nOMOU4HMKOB npoTM-
BOI1QIIO)I(H()ro nana. nOMOU4HMKM Ha'4HHaIOT ceKcyaJ1bHO M3MaTb1BaTb
penyaIIMCTa (<<CMOTpJlU4ero». - npu/rf. osm.) BceMH H3BeCTHblMM MM
cnoco6aI4M. MO>KHO MCnOnb30BaTb nlO6ytO TexHHKY; ecnH KTo-nM60 M3
MKOB er, era 3aMeHJfeT APYrDM.
B KOHLte KOHijOB «CMOTpJllijMM» B pe3ynbTaTe «CBepXMCTo",eHHJI»
CM nOrpy>KaeTCJt B rny60KMM COHo To a Ltenb nOMo",HMKOB MeHJI-
eTCJ1. OHM AOn)KHbI nonbnaTbCJI pc136YAHTb pM1YaJ1MCTa, HO nocPeA-
CT80M ceKcyaJ1bHO CTHMynJl MM. npH nepBblX npM3HaKax npo6y>K-
I¥!HMJI CTMMynJlLtHJI 3aKaH'4HBaeTCJI. OHa 6YAeT n.pOAOn>KaTbCJI AO
rex nop, nOKa pM1YaJ1HCT He OKa>KeTCJI B COCTOJlHHH Me>KAY CHaM H
6oApcrB0BaHMeM, KorAa era (ee) P.Pv oCBo6o>KAeHHblM nonHblM Te-
neatWM M3ttypeHHeM M YAep>KMBaeMbiM aT BXO>KAeHMft B rOpOA CHa,
CQeAMHReTCJI C BceBblWHMM CBJlTbiM rOcnOllHHOM (BXOAHT B «3PO-
TM'teCKMihpaHC». - npUM. osm.).
PwtyaJ1 OKaH'4HBaeTCJI, eCJ1H pKTyaJ1HCT non HOCTblO 3aCblnaeT HnH
npo6yJKAaeTCJI H (nocne) nOCJ1eAHerO opra3Ma (BHOBb) 6e3MJlTe>K-
HO nOrpy>KaeTCJI B COHo nOCJ1e np06Y>KAeHHJI OH AOn>KeH HeMeA-
.netIHO 3anMCaTb.CBOM BocnOMMHaHM" (nOTOM AewM4>pylOT CMM80-
nMKy CHOBMAeHHJI: -' npUM. oem. )>>.
3aMeTMM, '4T0 B MeAM MHe npeACTaB11eHHe a «KaMe» He COOTBer-
crsyer nOHlITHIO a JlCHOM C03HaHHM - 3TO 6ecC03HaTe11bHoe COCTOJl-
HMe C oTqitcmMeM aKTMBHbI TeM 6oJ1ee OC03HaHHbIX, AeMCTBMM, C Ha-
pylRHMeM pJlAa pe4>neKCOB.
cCY11'eCTByeT eU4e OAHa n03M HJI, - nMweT A. Kp3r AaJ1bWe,-
HO OHa All" CHnbHblX nIOAeM: B TaHTpe aHa Ha3b1BaeTCJI n030M «Bopo-
52
Ha». nocne 06 HOM ceKCy-
aI1bHOM CTMMynJl HH MY>K-
'4MHa, BCTaBaJl, nOAHMMaeT
)KeH MHy, craBMT ee BBePx
HoraMM. B 3TO,.. nonO)Ke-
HMM OHM 3aHHMalOTCJI 060-
IOAHblM opanbHblM ceK-
COM. 06b1'4HO >KeH HHa
onneraer HeraMM welO MnH
ronOBY My>K'4MHbI - 3TO
3aBMCMT aT AIIMHbI ee Hor.
M MHa >l<e Aep>KMT >KeH-
U4MHy ](I TalIMIO. EcnH M HHa He CJ1MWKOM CHJ1eH, OH 6b1CTpO -
eT. nepeBepHyraJl BBepX HoraMM-)I(eHU4HHa '4YBCTByeT &nbwoM I1JM-
nMB KpoBM K ronOBe - 3TO BeAeT K npeAcKa3aHHIO» (npM ycnoeMM,
'4T0 npM 3TOM npoHcxoAMT HapyweHMe C03HaHHJI >KeHI14 HbI. - npulf.
Dsm.).
A06aBMM, '4TO «ceKcyaJ1bHblM pMTyan» MarHH B nOCJ1eAHeM IIC-
nonHeHMH n03b1 He6e30naceH KaK AllJI >KeH HHbI H3-3a nepeRaAa
KpOBJIHOrO AaBneHHJI, oc06eHHo B CTOPOHY era YBenH'4eHMJI (no3a
npoBo MpyeT BpeMeHHoe HapyweHHe M03rOBoro KpoBo06paute-
HMJI), TaK M AnJl MY>K'4MHbI, KOTOpblM aT 3MOLtMOHaJ1bHOro II c1JlI3M-
'4eCKOrO nepeHanpJl)KeHMJI MO>KeT nepeHeCTH COtyAHCTblM tq)1I3 II
era ocnO>KHeHHe - HH4>apKT. 0 CJ1Y'4aJlx MH4>apKTa y My>K'''IH 110
apeMJI MX ceKcyaJ1bHOM neperpY3KM npHBOAJITCJI C006U4eHMJlII Me-
AM14MHCKOM nHTepaType. 06 3TOM aBTOp y>Ke nHcan B KHMre ckr-
p0J10rMJI AenOBoro '4enOBeKa. CeMeMHaJl acrponontJl» (1994).
no MHeHMIO Kp3ra, B MarM" AnJl nonY'4eHHJI «3HepreTM'fecmA
CMeCM» «BMeCTO 6ynaBbi H '4aWH Hcnonb3YlOTCJI nonOBbie opraH"»
A3b/ HYMeponorHH
O.ClcynlaTM3M ...epa M c
Me,nIr1 HCKoe nOHRTMe «K0M8-
M OKKYnbTHoe nOHSlTI1e I<J>3.ra
«apoTOKOMaT03HaSl fICff
(ecJ1M nOHIIIMaTb aTO KaK COICpB-
U4eHIlle c aHmlllMcKoro nepeeQAII
CooB «SpoT...mcKast KOMa-)-
H6CpaBHIIIMbie coct'OS1HIIISI. He
SlB1ISlHCb sp8'fOM, Kpar, B03MOIiIC-
HO, ttey.Q8 HO BbIp83111J1CSf.
53
fnasa 1
COOTBeTCTBeHHO MY>K'4HHbI M >KeHI14MHbI. AeJl TaKOBa: MY>KtKaJl
cnepMa H >KeHCKHe BbiAeneHHJI 06naAalOT «eCTeCTBeHHblMM MarM-
'4eCKHMH Ka'4eCTBaMH» (OHH pe3BbI'4aMHO HaCbI eHbI B 3HepreTH-
eCKOM nnaHe. - flpu/rf. oem.) KaK pe3ynbTaT «MeHTaJ1bHOrO BOC-
npHJlTHJI M ceKcyaJ1bHOM CTHMynJl4HH».
o CMMBonHKe 4>oPMbI 6ynaBbI-necTHKa H OBana BXOAa B '4awy no-
3,qHee roBOpMT H 3MrMyHA cJ»peMA CBJl3b1BaJ1 C HHMM HeOC03HaBaeMbie
(noAC03HaTenbHble) ceKcyanbHbIe '4}'BCTBa '4enOBeKa.
TPaAHLtHOHHoe n0110>Ke-
HHe aJ1XHMHH maCMT: npo-
Lteec 3HepreTI1'4eeKoro B03-
AeMCTBMJI MaTepHH 3aBHCMT
aT ee pa30rpeeaHMJI, Ha 'frO
HHOrna YXOAHT MHoro Bpe-
MeHH. AnJl «ceKcyaJ1bHoro
Mara» (Bblpa>KeHHe Kp3ra)
3TO 03Ha'4aeT, '4TO nY'4WHM
cnoc06 pa6arbl C MY>KCKHMH
M >KeHCKHMH $1IOHAClMH-
310 A11HTenbHaJl no,qroTOBKa
C B3aHMHblMH naCKaMH, B03-
MO>KHO HeCKonbKO '4aCOB
(reXHHKa neTTMHra).
nOJlCHMM MexaHM3M Hcnol1b3yeMoro MaraMH ceKcyanbHoro
TpaHca (ynpocrHB OKKyJ'fbTHbie 06b"cHeHHJI). BbiAeneHHe ceKcyanb-
HaM 3HeprMJpe6yeT aKTMBHoro Y'4aCTMJI n04TH Bcex CHCTeM opra-
HM3Ma B pe>KMMe MX MaKCHManbHoro HanpJOKeHHJI, 3M04HOHaJ1bHOM
neperpY3KM M Aa>Ke CTpecca. CTpecc - HblHe MOAHblM B ynoT-
pe6neHHM TepMHH (BnepBble BBeAeH B 1936 r. KaHaAcKHM Y'4eHblM
ComaCHO Y'f8HMIO
..CeKCyanbH}lrO ManflO- B PYKO-
BOACTB8X no 0KKyJ1bn13MY HHor-
1J11 on blealOT no.o. TepM HOM
«B yrpeHH (CeKcyanbHa )
an)(J.1M -. npM'teM I-tHCTPYMeH-
Tap '" aI1XMMMKOB - wa
6ynaea-necTMK AI1 paCT paH
npenapaTOB M noJ1Y'fSH 3Hep-
reTWfeCKoo CMeC - B «CeKcy-
anbHO an)G1M - MeeT onpe-
AeJ1eHtfYK) C MBOnMt<y.
. 54
r. C _be>. -:- rpaKTyeTQJ..B M AH "HCKOM 3H MKJ10neAHH KaK Hecne-
LtH4>H'4eCKaJl peaKLtHJI' opraHM3Ma Ha '4pe3MepHble pa3Apa>KMTenM,
He3aBHCHMO aT Taro, BnJlIOTCJI OHM OTpMLtaTeJ1bHblMM HnH nOnO>KH-
TenbHblMM. CTpeCC xapaKTepM3yeTCJI He06b1'4HOM OTBeTHOM peaK M-
eM H HanpaBneHHoCTblO Ha BOCCTaHosneHHe HOpMaJ1bH YHKi.4HM
opraHH3Ma. no cpaBHeHHIO C APyrHMH BHA M 3aTpaT 3HeprHH no-
TepH ceKcyanbHoM 3HeprHM npM «ceKcyaJ1bHOM crpecce» HaH60-
nee 6b1crpo HCTOU4alOT opraHH3M. nOCJ1e on.pe,4eneHHoro ypOBHJI
TaKHX 3Hepro3a1paT npOAOn>KaIOU4MMcJI ceKC 06edH!'4HSaeTCJI y>Ke
3a C'4eT 3HeprHH APyrHx BHAOB AeJlTenbHOCTM: MHTeJ1neKTyaJ1bHOM,
4>H3H'4eCKOH (HaH60nee aKTMBHO pacrpa'4MBaeMOM npM ceKce) M
caMoH Ba>KHOM - BHyrpeHHeM 3HeprMM, tfanpaSneHHoM tfa noiJiJep-
JKQHUe JKU3HU opraHH3Ma (AblxaHHJI, cepA'4e6MeHMJI, HopManbHoro
KpOBJlHOrO AaBneHHJI H T. A.) (ltBeTbi KMTaMCKOM MYAROCTH).
no MHeHHIO 4>H3HonoroB, sce nepe'4McneHHble 3aTpaTbi 3Hep-
reTM'4eCKorO nOTeHLtHaJ1a opraHH3Ma, KpOMe ceKca, no eKopOCTH
pac.xOAosaHHJI 3HeprHH OCYU4eCTBnJlIOTa MeAlleHHee M 3KOHOMH'4-
Hee. 136b1To'4HaJl nOTepJl 3HeprMH >KH3He06ecne'4MBaIOU4MX CMC-
TeM opraHH3Ma npM neperpY3Ke ceKCOM cnoc06Ha Bbl3BaTb pa3-
nM'4Hble HapyweHHJI AeJlTenbHOCTM - 0CJ1a6neHHe HnH nOTeplO
KOHTpOnJl HaA nCHxH ecKOM,
HHTenneKTyaJ1bHOM AeJJTeJ1b-
HOCTbIO, 3MO HOHaJ1bHyiO He-
CAep>KatniOCTb (HanpHMep,
HenpoM3BonbHble BCKPHKH-
BaHMJI, CTOHbI). 3TO He Bee-
rna ynpaBJIJleMoe COCTOJlHMe
MO>KHO Mcnonb30BaTb no-
pa3HOMY.
A3b1 H}'Meponoruu
31'0 H8AO 3MaTlt
Bcne cTBHe OOJ1bWHX 3aTpaT
«>KH3HeHHbfX CWl- el1.l.e MY.QPe-
UbI ,QpeBHOCTM n...,C8/1"" 0 CYl1.I.e-
CTByK>l1.I.eM pMCKe .QJ1R >KH3H..., B
3aHRTHRX ceKCOM .QJ1R J1Hl4 co
cna6bfM 3,D,OpoBb8M.
55
rnaBa 1
BblC1Ci3b1BaR CBoe MHeHHe
OTHOCHTenbHO 3TH4HOCTH «ceK-
cyaJ1bHOrO pHl)'aJ1a», Kp3r CO Be- .
tyeT: «KaK B03MO>KHO OTAenMTb
AYXOBHOCTb aT penHrHH, MO>KHO
OTAenMTb ceKC aT mo6BH... CeKC
B ceKcyanbHOM MarHH MO>KHO OT-
Aem4Tb aT ceKca B nlO60BHblX
B3aHMOOTHOWeHMJlX. 310 He 03-
Ha'4aeT,4TO MO>KHO MMeTb ceKC
Ha CTOpOHe, H3BHHJUI era MarH-
eM. He06xoAHMO co06U4MTb napTHepy a npeAnonaraeMoM enH CHO-
WeH JI, nonY'4MTb era pa3peweH e. 310 pa3peweHHe He AOn>KHO e-
AHTbCJI CKB03b C>KaTbie ry6b1, Bbl3b1BaTb 3n06y H HeHaBMCTb.
nOMHHTe,410 npaBAHBOCTb >KM3HH He06xOAHMa Mary... nlO60Bb M
YCTaHOBHBWHeCJI OTHOWeHHJI Ba>KHbI B '4enOBe eCKOM >KH3HM»
(c. 280).
CornaCHMCJI c Kp3roM, '4TO >KenaHMe Y'4aCTBOBaTb B «ceKcy-
anbHOM pHryane MarMM» AOn>KHO 6b1Tb 060lOAHblM H A06poBonb-
HbiM. OTMeTHM TaK)f(e, '4TO, HeCMOTJ)JI Ha CBOIO npHBneKaTenbHOCTb-
«3anpeTHoM TeMOM» - «MH-
THMHOM M31O HKOM» (eU4e
rOBOpJlT - «Kl1y6HtJ'4KOM»),
ceKcyaJ1bHblM apecc no MeTO-
AHKe Bbl3b1BaHHJI 6nHH<e He K
'4enOB KOMY, a K >KHBOTHO-
MY Hcnonb30BaHHIO CBOHX
B03MO>KHO M. Ho Aa>Ke >KH-
BOTHbie He AOBOAJIT ce6 AO
B M8rM" ceKcyanWlblM
TPBHC - O H ...,3 MeTOAOB
Bocnp...,stT...,st ...,3MeHeHHblM
C03HaH...,eM cna6b1x KOCM""-
46CK...,X 3Hepr...,'" (MeHTaT1b-
HbIX. aCTp8J1bHbIX ..., /JPY-
niX), KOTopble B HOpMaT1b-
HOM COCTOstH...,..., 06b1 HbI'"
enoBeK He 3aMe'faeT.
CMHOItOnt C'lMT8IOT
Ecn..., Y'faCT...,e B p""ryaT1ax,
8I<1IIO'fast ..., p""ryan ceKCYaT1b-
HO'" Mar...,...,. C03A8eT Tpe ""-
Hbi B OTHoweH...,stX, nY'fwe
Bcero OTKa38TbCst OT BblnOJ1-
HeH...,st TaK...,X p""ryaT10B.
56
A3b1 H}'MeponOrnH
MCTOl14eHM'H. .B.RAHMO, 003T Y AaHHblM MeTOA Bbl3b1BaHMJI TpaHCa B
MarHM Mcnonb3YlOT O'4eHb peAKO.
ACTponorM eCKMe
M reorp8c1»M ecKMe
ccCBSll1.\eHHble» 3H8KM
3HaK Pbl6b1 (pHC. 1, a) Bowen B cHny H CTan Mcnonb30BaTbCJt
B oKKynbTH3Me, KorAa (onH e B CBoeM B03BpaTHOM KOCMM'4eC-
KOM 060pOTe nepeMeCTHnOCb H nepewno M3 C03Be3AHSI OBHa, rAe
aHa AO 3Toro npe6b1BanO, B c03Be3AMe Pbl6. AeHb, KorAa 3TO npo-
H30wno, CTaJ1 Ha'4anOM HOBOM
3.pbl - nepBblM AHeM nepBO-
ro roAa HaweM 3pbl. no nOA-
C'4eTaM ApeBHMx xanAeeB,
nlOAH Aonro 6yAY1 >KHTb B ac-
TponOrH'4ecKYIO 3Py Pbl6 (3a-
TeM ConH e nepeMAeT B APY-
rOM 30AHaKanbHblM 3HaK-
a
OAHMM 3 CaMbQi C8st eH-
HbiX np 3HaHHblX B OK-'
KYl1bT 3Me 3HaKOB, ecJ1 He
caMbiM 3HaMeHHTblM H3
HHX, stBl1steTCst 3HaK Pbl6b1.
C\o1MBO.n KOTOporo H300pa-
>KaeTCst OAH M poc ePKOM.
6
B
z
><:) SL
. I I
t
PUC. 1. «(B1uqeHHble» OKKYllbTHbie 3HaKM
57
rnaBa 1
BOAoneM, H Ha'4HeTCJI 3pa BOaOJfeR, KOT9paJl TO)t(e, QPOAJIh1TCJI
2140 neT).
B AeHb, KOrAa 3TO CJ1Y'4HnOCb, cornaCHO npeAaHMIO, npOH30wno
TaK>Ke 3HaMeHaTeJ1bHoe MCTOpH'4ecKoe c06b1THe: POAHJlCJI Hcyc XPH-
CTOC, 'ITa eU4e 60nbwe YKpenMno 3Ha'4eHHe 3HaKa Pbl6, H 3TOT AeHb
cran Ha'4anOM XpMCT\4aHCKOM 3Pbl. 3HaK Pbl6 C Tex nap CTan H306pa-
>KaTbCJI Ha 3HaMeAax XpHCT\4aH B pa3Hble BeKa.
CHMBon neTnH-Pbl6b1 (a He
Kpyra) H3 ropM30HTaJ1bHOro rpa-
4>M'4eCKOrO HcnOnHeHHJI, '4TO
6nM>Ke K «aCTpOnOrH'4eCKOMY»
opMrHHany, nepeMeCTHnH Bep-
THKaJ1bHO. npH 3TOM H3 neTnH-
Pbl6 nonY'4HnCJI neTneBOM
KpeCT AHKX - OH >Ke Kpyr AH-
caTa, KOTOpblM WHPOKO McnOnb30BaJ1CJI B ApeBHeM En1nTe (pHC. 1,
6 H B).
Kpecr AHKX MMeeT H ceKcyanbHoe COAep>KaHHe: neTnJl CHMBonH-
3HpyeT >KeHCKMM opraH, a BeprHKaJlbHaJI nHHHJI- My>KCKOM. X CO-
BMeCTHoe coeAMHeHHe AaeT
«CMMBon nnoAopoAHJI».
KpeCT AHKX - CHMBon
Be HOM >KM3HM; peHHKapHa-
MM (O'4epeAHoro- TeJteCHoro
BonnO eHMJI 6eCCMepTHOM
AYWH HCi ;3eMJIe) H nepepo>K-
AeHMJI (pHC. 1, z).
KaK B EBpone, TaK M Ha Bo-
CTOKe KpeCT KaK CBJlI14eHHblM
OKKyI1I1TM3M .'tepa
M cerOAHw
APeBHHe X8MeH B "'C-
11W1'" npoAoJaCHTenbHOCTb
3PbI PbI6 - 2140 neT.
MHTepeCH"''' cS»aKT
KpecT AAIOC HCnOI1b3yeTcSI
l<alC C"'MBOI1 Ha OAe)I(,Ae PHM-
CI<HX I<aTOI1HKOB: TaK. CI1}')ICH-
Tel1H ,-,epl<BH H8 eepxHeH
OAe)I(,Ae HOC"'I1H no ABa Kpec-
T8 C OOlJ.LeH neTneH - cnepe-
AlII H C38,D;1.
58
CHMBon MOJlBHnCJI O'4eHb
AaBHO M CHMBOnH3HpOBan
eAMHeHHe ABYX OCHOSHbiX
CMn npHpOAbI: CHn He6a
(BepTHKaJ1b KpeCTa) H CHn
3eMJ1 (rOpH30HTaJ1b KpeC-
Ta). no TpaAHLtHH, npH Ha-
nO>KeHHH Ha ce6J1 KpeCTa
xpMCTMaHHH B rpYAHYIO MH-
HyTy npH3b1BaeT Ha nOMoU4b
CMnbl He6a H 3eMnH.
y ApeBHHX Jl3b1'4HHKOB-esponeMLteB TO>Ke 6bU1M KpecTbI. HaM60nee
nonynJlpHbI 6blnM ABa: COnHe'4HblM KpecT C pa8HbfMM no A11HHe nMHHJI-
MM eepTHKaJlH H ropH30HTa/1M, '4TO 03Ha'4anO ypaBHOBeUleHHOCTb CHJ1
He6a H 3eMJ1H (pMC. 2, a) M n03AHee - C CMMBonOM rnaBeHCTBa CHJ1
He6a HaA CHnaMH 3eMJIH (pHC. 2, 6). BTOpblM no nonynJlpHOCTH 6bU1
KeJ1bTCKHM KpeCT, me CMMBon COnHl¥!- Kpyr - 3aHHMan nepeKpecT
CHJ1 He6a H 3eMJIH, KaK 6b1 perynHpyJl HX 3aHMOCBJl3b (pHC. 2, B HZ).
a
+t
A3b1 HYMeponOrllfH
Ecn. MH8HM8
Cne anMCTbI no OM03Hepre-
TMKe H 3KCTp8ceHCbI C KTaIOT.
TO H8110>KeHMe Ha CeOsf.q>ecT8
pa3rnIDKHBaeT .o.e<l>eKTbI H8weH
aypbl. nocne 3TOro 3HepreTH-
ecKHe o6o KI1 CTaHoBsrrc
YCTOH'4HBeH K «3HapreTH'feC-
KOH HH<l>eK H..
6
8
z
PUC. 2. KpeCTW (onHe'4HW" (a U 6) M KeJlbTCKM" (8 U z)
59
rnasa 1
KpeCT Mar rcuoKe CHMBonH3M-
pOBaTb 3pHTenbHoe BOCnpHJlTHe
'4enOBeKOM npeAMeTOB Ha 60nb-
WOM paCCTOJlHHM. npH 3TOM npeA-
MeTbi BocnpHHHMalOTCJI nnocKo, B
AByxMepHoM M3MepeHMH. B MaTe-
MaTM'4eCKOM nOHJlTMH - no OCH
a6CLtHCC; M 0PAMHaT, KOTOpble CMM-
BonH3HpylOT B3aHMHO nepeceKa-
IOlqMeCH nMHMM KpeCTa. 06'beMHOe HX BOCnpHJlTHe «B3rnJlAOM
Bmy6b» 3aTpYAHeHO.
BepTMKal1b M ropM30HTaI1b KpecTa C 3arHyTblMM KOH MH (pHC. 3, a)
«.nOManMCb» nocpeAMHe. H 3arM6aJ1HCb nOA yrnoM 90° K OCHOBHOM
nMHMM. CepeAMHa KpeCTa BepTMKaJ1blO H ropM30HTaJ1blO TO>Ke nepe-
CeKanaCb nOA yrnoM 90°. KOH W COnHe'4HOrO Kpecra 3arH6aJ1HCb
no xony COEH MJlM '4iCOBOM CTpel1KM. 310T CBJlU!eHHblM - KpeCT B
xonyy 6enoA MarMH.
B Eapone M AMepMK8
WMPOKo a.138eCTeH BH,A
OICJCyI1bTHoro tcpeCT8 C
38fHYTb1MM KOH'-'8MM -
Col1H8'fHt:llM KpecT (Mo-
noT Topa) MnM tcpeCT
cJ>Mn<I>o (cB8cn-nea).
a
6
Puc. 3. MMCTM'tecKalil MCTMHHaR CBaCTMKa 6enoM MarMM (a)
M Hal4MCTCKaR. nepeBepHyraR, CBaCTMKa (6)
60
nb>Ka '4epHOM MarMH B repMaHHH, '4J1eHOM KOTOpoM 6wn rM11lep,
H3MeHHna Ha'4epTaHHe «cBJlU4eHHom KpeCTD Ha aJ1bTePHaTMBHoe.
OHa M306pa3MJ1a em KaK CHMBon-Bblpa3HTe11b eBoeM CMnllf; nepece-
'4eHHe nHHHM cepeAHHbI Kpecra CMelijeHO aT mpM30HTaJlIt.ti Bepnt-
KaIIM nOA yrnoM 45 0 . J10MaHble nMHHM Hal4MCTtKOm KpeCTa (pM(. 3,6)
paCXOWlTCJI B HanpaBJIeHMM, npoTMBOnOnO)f(HOM ABM>KeHMIO (onHqiI
M npoTHB '4aCOBOM crpel1KM. TaKoM KpeCT KaK 6w e8MAeTeJ1bCTBOBa11 a
CMJ1e, KOTOpaJl HAeT HanepeKop 06U4enpM3HaHHblM aH6BKaM, no-
MaJl H Kpywa Bce, 'ITa MewaeT CTopoHHMKaM ee B3m"AOB.
CneAYE!T nOMHMTb. 'ITa pmyanbl, KOTopble cOBepwalOTCJI C KpecTOM
6enOM MnM 'iepHOM MarHeM, He CJ1eJ\YE!T paCCMaTpMBaTb KaK npoJlBJ1e-
HMe KaKOrO-nH60 BepoHcnOBeAaHMJI (HanpMMep,xpHCTHaHeKOM aepw)
HlIH pacM3Ma (HanpMMep,4>a-
wH3Ma). B oKKynbTH3Me-
3TO CMMBon 3neMeHYapHom
B03AE!HCTBHSI CW1 KOCMoca M
o6lijero npMHLtHna (OTBope-
HHJI MHpa.
nJlTb OCHOBHblX 4>Hno-
C<$cKMX 311eMeHTOB, COcraB-
nJlIOU4Hx MHP, - CMJ1b1 CTH-
XMM (OroHb, 3eMnJl, BOAa,
Bo3AYX, MeTaM) HawnM ceoe
oTpa)f(eHHe KaK B nocrpo-
eHMM «MarH'4eCKoro KBaA-
paTa», YaK M B KOHcrpyKLtHH
3Be3A H reKcarpaMM (noA-
po6Hee CM. B COOTBe1CT&yIO-
utHX pa3Aenax KHHrH).
A3b1 HYMeponorMH
M3 rny6MHw MKOB
3 reOMeTP"l.fecKMX CMMBOJ1OB
B AaBHMe BpeMeHa 6011bWOe
pacnpOCTpaHeHMe nOI1Y'iMJIM
TpeyrOl1bHMKM. K8)K,D,bIM yrOl1
MMel1 Q>MI1OC<><l>cKoe 3Ha'e-
HMe, a B uel10M Q>Mrypa nepe-
AaBaI1a 38KOH lpMeAMHCTBa
CMI1 npMpo,Abl - He6a. 3eMnM
LII BocnpMHMMalOU4ero 3'04
CMI1b1 4enoBeKa. B OTI1M M8 OT
Tpeyrol1bHMKa kpeCT nepeAaeT
aI1bTepHaTMBHble CW1b1 B38M-
MOAeMCTBMJI M pa3BMTMJI npt4-
POAbi (MHb-RH).
61
rn8S8 1
CMMBon rpeyronbHMKa Hcnonb3yeTCJI B 0603Ha'4eHHM '4eTbipeX
OCHOBHblX CTMXMM: OrHJI- «(Jl3b1K» nnaMeHH), 3eMnH - (cHMBon
ne3BMJI nonaTbi MJ1M KMpKM), BOAbi - (cHMBon ypoBHJI BOAbi B co-
CYAe) M B03AYXa.
TpeyronbHMKM M reKcarpaMMbI aCTO Mcnonb3YlOTcJI B AeMCTBax
MarMM, HanpMMep npM raAaHHJlX. TaK, 4>Mrypbl, npeACTaBneHHbIe Ha
pMC. 4, iJ M 4, e, COcraBnJtIOT no KapTaM apKaHa Tapa H npM PMTYaJ1e
C03epLtaHMJI Tapa (oAHoro H3 BHAOB «MarM'4eCKOrO AeMCTBa»), MC-
nonb3YlOU4ero MeTOA CJly'4aMHblX Bbl60pOK M3 KapT Tapo H '4MenO-
BbiX MX KOM6MHaLtMit npM 3TOM MarM c06nlOAalOT ycnOBHOCTH HY-
. MeponorM ecKoM Ka66aJ1b1: pMcoBaTb MnM C MTblBaTb nOKa3aTenM
BcerAa Ha'4MHaIOT C BepwMHbI TpeyronbHMKa, Aa>Ke KorAa OH 06-
paU4eH BepwHHoM BHM3 (n03HLtHH 2 Ha pMC. 4, iJ H 1 Ha pMC. 4, e),
a 6 B Z iJ e
A l1.W
\7¥¥Wb
PUC. 4. TpeyronbHMKM (a U 6) M reKcarpaMMbI (B-e). (MMBOllbl
CTMXMM OrHJI (a), 3eMI1M (6) M MX eAMHCTBa (B) B 3Be3Ae
AaBHAa. 3ra 'Be3Aa TalUKe CMMBonM3MpyeT eAMHCTBO
B03AYXa M BOAbi Iz) C Y'feTOM CHMBonMKM >KMpHblX nMHMM,
n03,!OMY 3Be3Aa .QaBMAa - CMMBon eAMHeHMJI Bcex '4eTbipeX
.OCHOBHblX CTMXMM. 3Be3Aa AaBHAa - CHMBOI1 eAMHeHMJI
My>KCKoro M >KeHCKOro Ha'4ana (JIH M HHb), CMMBOJI
nnOAopOAMJI. Mrypbl reKcarpaMM (iJ H e) npH COCTaBJleHMH
HX KapTaMH Tapo
62
a nHHMM BceM 4>Hrypbl pHcy-
lOT npOTHB '4aCOBOM CTpenKM
(pMC. 4,0 M 4, e).
«CBJlU4eHHblx» 3HaKOB M
4>Mryp B HYMeponorMM AOCTa-
TO HO MHoro. 3Ha'4HTenbHoe
KOnM'4eCTBO HX 6b1no n03aMM-
CTBOBaHO M3 O'4epTaHHM oc-
HOBHblX cone3AttM Ha He6e,
HanpMMep CO Be3.AHA OpMoHa. C06CTBeHHO, 8 « MCTOM» HYMepo-
norMM TpYAHO BbijlenHTb «MarM4ecKYIO» 4>MryPY MIIM '4MenO, KOTO-
pee He 6b1no 6b& $Mnoco$:KH cooTHeceHQ C He60M. Tal(, 6b1na yc-
!,(IHOBneHa CBJl3b KpecTa X3 TY M '4MCna 8 C pac00110)f(eHMeM
«maBHblX» 3Be3A C03Be3AMJI OpMoHa.
B KHHre '4MTaTenb n03HaKOMHTCJI C OCHOBHblMM oKKYnbTHblMM
CMMBonaMH, Hcnonb3yeMblMH B 4HCJ10BOM acrponorMM M B « HCTOM»
HYMeponorHH. BbfAenHM H3 HMX HaH60nee AOCToBepHble.
He Bce nOKa3aTenH, C KOTOpblMM npOBOAJIT BbI'4HCJ1eHHJI Y-
MeponorH, HMelOT BbiCOKYIO CTeneHb AocToBepH0cTM. "IMTaTenb
He AOn>KeH BocnpMHHMaTb :no KaK CYU4eCTBeHHblM HeAOCTaTOK.
"fT06b1 HaMTH MCTHHY B HaYKe, He TonbKO AonYCKaeTCJI, HO H-
npM3HaeTCJI none3HblM nonY'4eHMe «HeKoppeKTHblX» M Aa)f(e
nbTep'HaTHBHblX AaHHbfX. Ha OCHOBaHHM MX cpaBHeHMJI npH-
06peTaeTCJI on biT «np06 M OWM60K» B HaXO>KAeHHM npaBMl1b-
tiara nyrH. TaK, B MeAH HHe eCTb AOCTOBepHble M «ManoMH4>op-
MaTMBHble» nOKa3aTenH HccneAOBaHHJI AnJl YCTaHOBneHMJI
AMarHo_3a. KaK anbTepHaTHBHblM npHMep BcnOMHHM M3BeCTHoe
yTBep>KAeHHe, '4TO «OTpM aTenbHblM pe3ynbTaT - 3TO TO>Ke no-
ne3HblM pe3ynbTar».
A3b1 HyMe nOrHH
Ha 3aMenty
TSCHOe CO'feTaH..,e C..,Mson..,-
IG1 a.tCen C rpa<l>..,KoM 3Be3,A
B el1W1O aClpOnont.., ee
<t>W1OC BeTBb - 1ItC-
nOByiO (H eponOnt'ieCKYJO)
aCTponOr\fl().
63
rnaBa 1
KOHe'4HO, MO>KHO paccMoTpeTb MerOAMKM npOBeAeHM 60nee
CnO>KHblX M KOM6HHMpoBaHHblx Bbl4MCJ1eHHM, '4T06b1 Y'iHTblBaTb
BeCb KOMnneKC HYMeponOnt'4eCKHX 3Ha'4eHHM KaK nOnO)f(HTenb-
HblX, TaK H oTpH aTenbHwx '4MCen. 3TO n03BonMno 6b1 OCHOBbI-
BaTb CBOH npOrH03b1 Ha HX «COBMeCTHOM anbTepHaTHBHoM YCH-
nHH», T. e. aHanM3MpoBaTb TY 30HY, KOTOpaJll1e>KMT Me>KAY HHMM,
B nepexoAe aT MHb K JlH. CepeAHHa :310H 30HbI, BepOJlTHO, H 6y-
AeT HMeTb MaKCMManbHYIO AOCTOBepHOCTb H HaM60nbWYIO Bepo-
THOCTb CBepWeHHJI HYMeponOrH'4eCKOrO nporH03a. Ho 3TO, no-
>KanYM, Y>Ke YAen npo4>eccHoHanoB, xopoUJo pa36MpalOutHXCJI B
OCHOBax oKKynbTHblx Bbl4MCJ1eHHM, a He Ha4MtfalOU4Hx HYMepo-
norcB H aCTponoroB, Ha KOTOpblX B nepBYIO O'4epeAb pacc4MTaHa
AaHHaJl KHHra.
n03BOnMTeJ1bHO nM 3H8Tb
CBoe 0YAYlL\ee?
«CrpaHHbIM Bonpoc, - CKa>KeT 4MTaTenb. - MblCJ1MMO nM Tex-
HM'4eCKH 0CYU4eCTBMTb TaKoe? C03AaTb MaWMHY BpeMettM! HaBep-
Hoe, 3TO nOKa HepeaJ1bHO. Ho KaK XO'4eTCJI 3HaTb, '4TO >KAeT Hac Bne-
peAH, 3arnJlHyT-' B CBoe 6YAYutee!» AcrponorH C03AaJ1H ropOCKonbl,
HYMeponorH - a eCKHe» '4HCJlOBble H r.pa4>H4ecKHe cxeMbI.
C03AaHbI ApeBHHe raAaTeJ1bHble cMCTeMbI, HanpHMep KapTbl Tapa, M
MHoroe APyroe. Ho He nycraJl nM 3TO TpaTa BpeMeHM paAM pa3Bne-
'4eHHJI, yiexH?
OKKYl1bTHble HaYKM, K KOTOpblM np HaA11e>KaT HYMeponOrHJI M
aETpOnOrHJI, a Tenepb H COBpeMeHHaJl HaYKa <nocne npOBeAe""
HHJI HK11a HCCJ1eAOBaHHM H BbI'4HCl1eHM ), npH3Ha1OT, qTO nOA06-
64
Hble pa3pa60TKH HMelOT peanb-
HOe OCHOBaH e. np "paBHnb-
HaM BHeApeHHH B npaKTHKY
OHH MOryr AaTb '4enOBeKY LteH-
HYIO HH4>opMa MIO. npH'feM
HCTO'4HMK ee H3BJ1e'4eHMJI CJ1e-
AYeT MCKaTb He Ha 3eMne, a B
KocMoce. He CTonbKO B CrpYK-
Type BeU4eCTBa Hn MaTepHH
KocMoca, B 4>H3M'4eCKOM noCT-
poeHMH He6ecHbix Ten, CKonb-
KO B 3HepzemUlieCKUX npOJlBneHHJlX H 3aKOHOMepHOCTJt . TpYA-
HOCTb COCTm1T B H306peTeH n1 HaAe>KHblX CpeACTB AJ1J1 npaBHnbHO
AewH4>poBKH aCTOTHO-BonHOBOM 3HeprMH, naAalOtijej Ha 3eMnlO
H3 KOCMH'4eCKoro «3HepreTH'4eCKOrO 06naKa», Ha3b1BaeMOro TaK-
me «BbICWHM Pa3YMOM».
Ha '4eM >Ke OCHOBaHO y6e>KAeHHe COBpeMeHHblX Y'4eHblx, TO
HaCTaHeT BpeMJI, KorAa MO>KHO 6YAeT 3apaHee Y3HaBaTb 6YAYtijee,
BHAeTb nocneACTBHJI CBOHX nocrynKOB, Bbl6MpaTb caMbie npaBM b-
Hble AeMCTBHJI? ECTb nH Y>Ke cerOAHJt KaKHe-nH60 H3BeCTHbie HaYKe
AOCTOBepHble CBeAeHHJI, '4T06b1 «nHTaTb HaAe>KAbI»? OKa3b1BaeTCJI,
HaKonHnOCb MHoro KaK m opemu4ecKux pa3pa60TOK, TaK M t/JOK-
mOB, nOATBep>KAeHHblX 3KcnepHMeHTanbHO. OHH CTonb OCHOBaTenb-
HbI, '4TO y eHble nepewnM aT CJ10B It Aeny: CTaJ1M TpaTMTb CBoe Bpe-
MJI M rOCYAaPCTBeHHble AeHbrH (KTO 6b1 n03BonHn MM :310 AenaTb,
eCJ1M 6b1 4>aHTaCTH'4eCKaJl HAeJl He HMena OCHOBaHHJt BOnnOTHTbCJI
B peaJ1bHOCTb!) Ha C03AaHHe MaWHHbI BpeMeHH. YnOMMHaHHe a HeM
(no KpaMHeM Mepe, KaK a TeopeTH'4eCKH B03MO>KHOM 4>aKTe) Tenepb
Y>Ke MO>KHO yn.orpe6nJlTb 6e3 KaBbI'4eK. PaCCMOTpHM nHWb OAHO
A3b1 HYMeponorHH
M8WMHa lIp8MeHM
GKnan n TCTBa 8
OCTaeTCR y enOBel(8 CTOJ1b
BenHK8, TO tf8 npoTR)I(e-
H CBoe... TOp OH
c03A811 MHoro B8pH8HTOB
Ca0e06paeHbIX .M8W H
BpeMeH . nppAOn)K8eT
x COBepWeHCTBOB8Tb.
65
rnaea 1
o4>M14HanbHOe co06U4eHMe, ony6.nMKoBaHHoe B ra3ere «ApryMeHTbI
M 4>aKTbI» PycnaHoM Wep6YKoBblM, B3J1BWMM MHTepBIriO Y PYKOBO-
AMTenJl HK6 «fpaBHTOJi» A.e. Wa4>paHa (AHcJ». 1995. N!! 16).
«nHcaTenM-4>aHTacTbI, KaK npa8HJ10, nMwyr yronHM, - pac-
CKa3b1BaeT A.C. Wa4>paH. - B HaweM nOHHMaHMM (pe'4b MAeT
a c03AaHHM B03MO>lUiorO TeXHM'4eCKOrO BapHaHTa MaWHHbI. -
npUM. osm.) B03MO>KHa HH4>opMaLtMOHHaJl MaWHHa BpeMeHH
(KoTOpaJl n03BonHT nony-
'4MTb OTBeTbi Ha 3aAaBaeMbie
Bonpocw a 6YAYU4eM -
npUJ4. osm.), a He YpaHCnop-
TMpylOU4iUI (T. e. He nepeMe-
U4alOU4aJl 06beKTbI, BKJ1IO'4aJl
'IenOBeKa, B npOCTpaHCT-
Be. - npUM. osm.). AnJl ee
npoeKTMpOeaHHJI AOCTa-
TO'4HO npHHJlTb ABe BeCbMa
peanHCTH'4eCKHe rMnOTe-
3b1 - a cYU4ecTBOBaHHH
HeKoeM MHpOBOM naMJlTM H HeB03MO>KHOCTH MrHoBeHHoM nepe-
Aa'4M MH4>OPM(H4MM M nepeMeI14eHMJI BO BpeMeHM».
cJ»H3MKH C'4HTeIOT, '4TO B crpYK1Ype MblCJ1H 3aJ10>KeHa 3HeprHJI
Menb'4aMWHX MaT@pMajtbHblX '4aCTMLt - MHKponenrOHoB (KCTaTH,
MHKponenToHaM npMnMCblBalOT 06pa30BaHMe 3HepreTH'4eCKHX TeJ1
MaTepMaJ'!b1iblX 06'beKTOB, B TOM '4MCJ1e M '4eJ10BeKa). 3Ta 3HeprHJI
nynbcHp ', a 3Ha'4MT, nOAAaeTCJI Ka'4eCTBeHHOMY H KOnM'4eCTBeH-
HOMY npOC'4eTy. K TOMY >Ke 3HeprHJI MblCJ1H npe06pa3yeTcJI B pa3-
Hble BHAbi (<<MblcnH HOCJlTCJI B B03AYxe, HAeH He YMHpa T»,-
roBopHnH eU4e ApeBHMe $Hnoco4>bI). MHKponenroHbI CTonb Ma.nbl,
CoIIpllM81HIM HayK8 npEWlO-
nar8eT, 'lto IK) BceneHHOO
TByeT.COBOKynHOCTb
nOJ1eM .., 'f8e ycnoBHO Ha
3bfBaeMast MMP080H na-
MRTbIO,. rAe cOAep*KTCSI SCSI
HH4>opMatU1S1 0 SpeMeHH -
lCaK npowbOM. T8K H 6YAY-
liteM.
66
'4TO npOHMKaIOT CKB03b aTOMapHbfe
crpYKTYPbI nlO60ro BeU4ecTBa, '4eM
06'bJlCHJlIOT nepeAa'4Y MbICJ1H Ha
paCCTOJlHHe M BcenpoHHKalOU4ee
CBOMCTBO MblCJ1H.
HYMeponorH C'fHTaIOT, 'frO '4HC-
na M CMMBonbi JlBnJlIOTCJt YHMBep-
canbHblMM MepMJ1aMH 3HeprMH MblC-
nM: C MX nOMoU4blO He TonbKO MOryT
06MeHMBaTbCJI HH$>pMa MblC-
nJlU4He tyU4eCTBa, HO H MOryr n03Ha-
BaTbCJI '4MCJ10Bble 3aKOHOMepHOC-
TM, KOTopble ne>KaT B OCHOBe Bcex
npOJlBneHHM >KH3HH KOCMoca.
Ho 06paTHMcJI K MHeHMIO cne-
LtMaJ1MCTa. A.e. LUa4>paH C'4HTaeT,
'4TO cneAYeT pa3PywMTb 06U4ee
npeACTaBneHHe a TOM, '4TO Mbi ABH-
>KeMCJt BO BpeMeHH BnepeA: «MbI
OCTaeMCJI Ha MeCTe, a BpeMJI HaA-
BHraeTCIi Ha Hac, npoTeKaeT '4epe3 Hac M 3aCTblBaeT B npownoM
npO'4ep'4eHHaJl H3 HaCTOJlU4erO B 6YAYU4ee nHHHJI >KM3HM n1060r
06'beKTa HnH JlBneHMJI- enOBeKa
06lqeCTBa, ropoAa, yparaHa, 3eMne
TpJtceHHJI - npeAonpeAeneHa, JiO B
TO >Ke BpeMJI nOABep>KeHa He60nbwMM
eCTeCTBeHHblM OTKJ10HeHMJlM».
CornacylOTCJI nM 3TH BblCKa3b1Ba-
HMJI CO B3rnJlAaMM OKKYnbTHbiX HayK
143 rny6MHw B8KO.
«\.iMCJ1a npaBRT M -
paM-, - rOBOplr1J1
HyMepoJ10rn t\peB-
He rpe lr1.
A3b1 H}'MeponOrHH
OKKYnlltTM3M
....pa M C8r0AH-
B TOM, o Mblcnb MaTe-
f)HBnbHa. CXOASIT MHe-
HIr1R BCex Y'leHbIX, K8K
npeA TaB_Ir1Tene «OpTO-
AOKC8J1bHb1X-, T8K Ir1 «He-
OPTOAQKcaflbHbIX», OK-
KYJ1bTHbiX H8YK. CJ>Ir1I1OCO-
<l>bI, OCo6eHHO BocTOKa
Oonee TecHO CBR38H
C O J1bllil3MOM, nOJ1a-
ralOT. 'fTO M8R
J1IOAbMir1 MblCnlr1TeJ1bH8R
3HeprMR He Ir1C T, a
HaKanJ1Ir1BaeTCR B npo-
CTpaHCTBe.OCTaBaRCb
TaM M nocne Ir1X CMePlliI.
67
rn8B8 1
Ha >KH3Hb? CornacylOTCJI, TaK KaK
MMp0a8t1 naMt1Tlt A.e. Wa4>paH, npo4>eccHoHan
COBpeMeHH8R HaytCa nPH- CBoero Aena, npM3HaeT, TO CY-
3HaeT C ecTBOB8HMe B U4ecTByeT HeKall npeAonpeAe-
KOCMoce HeKoero 3Hep- neHHOCTb, npeAYrOTOBaHHOCTb
reTWfecKoro OOil8Ka. Ero Te eHHJI )fU13HM Ha 3eMlJe (c He-
npoMCXO)I(.QeH e CBR3b1- KOTOpblMH' ee Kone6aHHJlMH).
BaIOT c Bbl,D.eneH eM B OKKYnbTHble HayKK H BOCTO'4HaJl
npocrpaHCTBO KOCMOCa cJ>Hnoco4>MJI Ha3b1BaIOT :no Kap-
« HTenneK1»aJ1bHOM MOM, nporpaMMOM Bblcwero Pa-
3HepnH ., H8KonneHHoM 3YMa KoCMoca. C'4HTa TCJI, '4TO
'4enOBe'feCtCMM OOlite- '4eJJOBeK 8 He60nbWOM AHana30-
CTBOM peanH3osaHHO He BapMaHTOB C80eM CYAb6b1 MO-
B npocYp8HCTBe B <l><>PMe >KeT COBepWaTb «nOAnpaBKH B
M poBoM n8MRT . nPM- CBOIO nonb3Y». EMY KaK 6b1 Aa-
'4eM Bblpp8eTCA yeepeH- eTCJI B03MO>KHOCTb C03HaTenbHO
HOCTb, 1'0 )?Ke np * 3H 3MeHHTb CBOIO >KH3Hb K nY'4we-
HblHeWHero nOKoneH R MY, nOKa3aTb CBoe COBepweH-
6YAeT C03A(iHO «'4YAO CTBO M CTOMKOCTb B npeoAone-
enoee ecKoM Mblcn....., HHM >KH3HeHHblX npenJlTCTBHM,
T. e. M8w HaepeMeH . '4aCTH'4HO H36e>KaTb «YAapos
CYAb6b1» (:no, HanpHMep, yTBep-
>t<AalOT M acrponorH TlpM COCTasneHHH ropocKona: ero MH4>opMa-
HJI npeAYnpe>Kj\aeT, HO He 06J13b1SaeT).
B03MmKHO, LfTO «4YAO», MaWHHa BpeMeHH, Y>Ke cy eCTByeT, Ha
3TO YK83b1BaeT caMO Ha3BaHHe CTaTbH HC!>>>: «MawHHa peMeHH
Y>Ke CYU4eCTByeT?» C-03AaHHeM TaKOM MaWHHbI BpeMeHH CeH'4aC 3a-
HJlTbi nY'4WHe YMbI eHblX H KOHCTpYKTOpOB pa3HblX CTpaH MHpa ,«s
3aKpblTbiX na60paTopHJlX M 6YHKepax», HaXOAJICb Ha pa3HOM 3Tane
68
ee reXHH'4eCKOM peaJ1H3aLtHM. «BCnOMHHTe HCTOpMIO C aTOMHOM 60M-
60M, - HanOMMHaeT Wa4>paH, - KOTOpaJl TO>Ke AenanaCb BTaMHe
H OAHOBpeMeHHO B pa3HblX crpaHax. He MCKnIO'4eHO, '4TO MaWHHa
BpeMeHM y>+<e cytJ4ecTByen>.
«A cJ» MH4>OpMHpyeT: B03MO>KHOCTH cOBpeMeHHoM HayKH TaKO-
BbI, '410 OHa «BnnOTHYIO nOAowna K TOMY, '4To6bf H HTbCJI C'4HTbI-
BaTb 3T'j MH4>opMa MIO (M3 MMpoBoM naMJI'tM. - npUM. Dsm.) M
paCwM4>poBbiBaTb ee. 3TO 3HaI.fMT, '4TO enOBe'4eCTBO CMO>KeT 6YK'
BaJ1bHO no MHHyTaM npOCJ1eAMTb BCIO CBOIO HCTOpH.IO, Aa M He Tonb-
KO CBOIO, HO H BCIO HCTOpHIO BceneHHOM."B TOM '4HCJ1e M 6 14ee...
cJ»aHTa3HJI CTaHer 6b1nblO!»
B CTa'Tbe YKa3b1BaeTCJI, "'TO AnSI «BXO)f(.QeHMJI B KOHIaKT» C MaWHHOM
BpeMeHM '4eJ10BeKY Heo6xOAHMO npm13Becnt <Bee onQ3HaH.He M nony-
4MTb pa3peweHMe Ha 06U4eHHe. AnJl 3TOro 6YAeT He06XAAMMO BBeCTH
OCOObIM 4<KnIO'4»: npeACTaBMTb eH He CBOIO nH'4HOCTb (no aHanorMM C
$>TOKapTO'4KOM nacnopra) HJ1M ronoc (npH on03HaHHH 3HaKoMoro ro-
noca MbI, HanpMMep, OTKpblsaeM ABepb KBaPTHPb1), a reHeTM'4eCKHM KOC-
MM'Ie<:KMM KOA- CpaBHMTe - HYMeponorH H aCTponorH TO>Ke Ha.qeJ1J1-
lOT '4enOBeKa KOCMHl.fecKHM
KOAOM (0 HeM nOMAeT pel.fb B
COOTBeTCTByIOU4MX pa3Aenax
KHMrM).
B ciaTbe Aa>Ke peKOMeH-
AYeTCJI, eo M36e>KaHMe B
cTpaHe xaoca H Y HTblBaJl
MaCCOBoe npOH3BOACTBO
TaKMX MaWHH B 6YAYU4eM,
BeeCTM B HHX orpaHH HTenb
BpeMeHH - «BpeMeHHYIO
A3b1 H}'Mepononm
Me)I(AY "pG'4MM
nOJ1aralOT, 'frO np\o1 «oOuteH\o1"'.
C MaW"'HO BpeMeH'" 'fenOBeK
AOruKeH CTaB"'Tb nepeA He
KOHKpeTHble '" peanbHbIe BOn-
pocbl, peal1"'3alU'l KOTopbIX
B03MO)I(Ha np'" ero Y'48CT\o1M M
npM ero JOt3HM, npe*Ae acero
B 6nM)K8 wee BpeM .
69
rnaaa 1
3arnywKy» (<<rOpM03 BpeMeHM») - C B03MO>KHOCTblO nporH03a Ha
6nM>KaMWMe 1-2 AHJI.
Ho Aa>Ke npH KpaTKoBpeMeHHoM nporH03e, Bcero Ha HeCKOllbKO
AHeM, HerpyAHO ce6e npeACTaBHTb, KaKMe HeO>KHAaHHble B03MO)K-
HOCTH nOJ1Y'4MT '4enOBeK, 3apaHee 3HalOU4HM nOCJ1eACTBHJI npeAnpH-
HJlTbiX MM AeMCTBMM. ECJ1M npeACTaBHTb, '4TO BcrynalOlijMM C HHM B
06U4eHMe APyroM '4enOBeK 06naAaeT TaKOM >Ke MawHHoM BpeMeHH,
o6ecne'4MBaIOU4eM cBoero X03J1HHa nOA06HOM >Ke. HH4>opMaLtHeM,
TO MX 06U4eHHe, nO>KaJ1yM, 6YAeT HanOMHHaTb waxMaTHYIO Mrpy. B
TaKOM Mrpe, paBHO BnaAeJl MH4>opMaLtHeM M 3Haft B03MO>KHOCTH Ka>K-
Aoro «xoAa» napTHepa, C 60nbweM nO b30M AllJI ce6J1 ee CMO>KeT
Mcnonb30BaTb TOT, KTO 6YAeT HaH60nee TepnenHBblM B nOHCKe
BapMaHTOB, 60nee OCTOpO>KHblM H nOrH'4HblM B AeMCTBHJlX. ECJ1H
>Ke BTOpOM napTHep He HMeeT TaKOM MaWHHbI BpeMeHM, MO>KHO
npeAnOnO>KHTb, '4TO nepBbI
napTHep, 06naAaJl «nyTeBO-
AHTeneM» B pa3BHTHH HX
B3aHMOOTHoweHHM B BHAe
HH4>opMaLtHH H nporH030B,
6YAeT HMeTb HeCOMHeHHoe
npeHMYU4eCTBO. OH nerKO MO-
>KeT A06HTbCJI >KenaeMOro AlII'
ce6J1 pe3ynbTaTa BCTpe'4H,
Bbl6paB He06xOAHMblM BapH-
aHT pa3BHTHJI C06b1THM.
ABTopa CTaTbH B ra3eTe
«AMeS»» CnpaBeAIIHBO 6ecno-
KOMT nOCJ1eAHee. npeABHAft
TaKoe pa3BHTHe C06b1THM,
MaWMgIlp8M8HM
MaWI4Ha BpeMeHI4 no3B0l114T
Y3HaBaTb MHoroe 143 Toro,
TO OObl HO B 06lJ.4eHI4I4
CKPbl88eTCSI, HSnpl4Mep I4C-
KpeHHe 141114 HeT K 88M OTHO-
CI4fCSI APyroo 'fenOBeK, no.o.-
.o.ep)l(l4f 1114 OH Ba TPY.AHYIO
MI4Hyty 141114 nOCT)'flMT Hao6o-
POT, Hl4pyeT 1114 OH Bep-
HYfb 9aM elJ.4b 141114 .o.eHbOt,
1<0TOpble Bbi eMY o.o.Ol1)1(l4nl4,
14 TOM)' no.o.OOHoe.
70
KorAa HHcpopMaLt JI a '4enOBeKe M era TaMHblX nOMblCJ1aX 6YAeT 3a-
paHee npeAonpeAenJlTb nOCJ1eACTBHJI 06U4eHHJI C HMM, aBTOp YCMaT-
pHBaeT B 3TOM 3Ha'4HTenbHble >KHTeMCK e CJ10>KHOCTM. n03TOMY Aa>Ke
KpaTKOBpeMeHHblM nporH63 a CBepweHKK C06b1TKM 6YAeT i4MeTb
pOKOBbie nOCJ1eACTBMJI. BblCKa3b1BaeTCJI MHeHMe, '4TO n.paao Ha Bna-
AeHHe MaW HOM BpeMeH Aa>Ke C KOpOTKMM nporH030M (AO He-
CKonbKHX AHeM) AOn>KHO 6b1Tb pa3peweHO orpaHH eHHOMY '4MCJ1Y
n L\. CKopee Beero 3TO A011>KHbI 6b1Tb PYKO AJI He nHL\a roCYAap-
CTBeHHoro HnH BbiCOKoro 06U4eCTBeHHoro ypOBHJr. Ha4e, C'4HTaeT
aBTOp, 3TO MO>KeT Bbl3BaTb 0CJ10>KHeHHJI B nonMTH4eCKOM, 4>HHaH-
COBOM, BoeHHOM H APyrHx Ba>KHblX c4>epax >KH3HM CTpaHbl.
KCTaTM, KpaTKOBpeMeHHblM nporH03 nOBblwaeT BepOJlTHOCTb em
CBepWeHHJI. HblMH CJ10BaMH, He BCJlKHM nporH03 OKa>KeTCJI AOC-
TOBepHblM. Aa>Ke TaKoe HHTenneKtyaJ1bHoe '4YAO KOH I<TOpOB
Y'4eHbIX, KaK COBpeMeHHaJl MaWHHa BpeMeHH, 6YAeT Aa&aTb «norpew-
, HOCTb» B nporH03e. B CBOMX nporH03ax acrponorH H HYMeponorM Ta-
KHe «norpeWHOCTH» OTHOCJIT K KapMH ecKH 06poBlleHHblM 3aKOHo-
MepHOCTJlM - C11Y'4aMHOCTJlM.
Pa3pa60TaHHble B HaCTOJl ee BpeM" B OKKynbTH3Me BapMaHTbI
«MaWHHbI BpeMeHH , KaK H ee TeXHH'4eCKHM npo06pa3, He 0CYU4e-
CTBnJlIOT MaTepHaJ1bHOrO nepeHoca Tena '4enOeeKa B APyroe M3Me-
peHHe BpeMeHH (KaK 3TO AeMoHCTpH-
PYIOT 4>aHTaCTM'4eCKHe cpHJlbMbI). Ho,
no yTBep>KAeHHIO BOCTO'4HOM 4>Hnoco-
4>MH, OHM nOMoralOT BXOAKTb B 3Hep-
reTH'4eCKMM pHTM KOCMoca M H3Y aTb
era 3aKOHOMepHOCTM, B TOM '4HCJ1e H3-
MeHeHMJI BpeMeHH, C nOMOij4blO '4MCen
H CHMBonOB.
71
A3b1 HYMeponoruu
M3 rny6MHbI BeKOB
JJ.peBHKe $MJ1OC<>4>bI
rOBOpKJ1K, TO HK TO
He (5b1BaeT c a -
tiblM: Bee CJ1Y'ia HOC-
TK - 38KOHOMepHbI.
rn8S8 1
HYMeponorH rTpH3HaIOT,4To HX pa3pa60TKH B npeAcKa3aHMH 6y-
AY ero (cHMBon «HYMeponOf '4eCKOM MaWH.HbI BpeMeHM») nOKa
HeAOCTaTO'4HO cOBepweHHbI, '4T06b16b1Tb HaAe)f(HbiM nOBoAbipeM no
rpone >KM3HH H C HaHMeHbWMMH oWH6KaMH npeAcKa3b1BaTb c06b1-
THJI. C'4HTaIOT Bce >Ke, '4TO nonY'4eHHe TaKOM B03MO>KHOCTM BnonHe
0CYUleCTBMMo, KorAa 6yAYT BHeApeHbI 60nee cOBepweHHble Ka66a-
nMCTH'4eCK e H MarH eCKMe MeTOAHKH (BeAb oKKYnbTHbie HayKH, KaK .
M OPToAoKcanbHble, npOAOn>KalOT cOBepweHCTBOBaTbCJI M pa3BH-
BaTbCJI) .
HeT nH TyT npoTHBope'4MJI B nOHMMaHHH 3aKOHOMepHoCTeM >KH3-
HM? npOTHBOpe MJI HeT. OAHaKo caM 4>aKT OAHOBpeMeHHoro CYU4e-
CTBOBaHMJI npOTHBOpe'4HBblX, aJ1bTepHaTHBHbIX CBOMCTB B pa3J1H HblX
060eKTax H JlB11eHMJlX C'4HTaeTCJI caMbfM pacnpocrpaHeHHblM B npH-
pt) e. nOHHMaHHe B3aHMOCBJl3M
anbtepHaT BHblX CBOMCTB nOMO-
raeT nOHJlTb CY HOCTb Be H
06'beKTa HnH JlBneHHft, nf)eAYra-
AClTb B HHX H3MetfeHHJI H npeA-
CKa3aTb 6YAY ee. KaK 3TO nOHH-
MaTb?
MaTepHanMcraMH onHcaH
3aKOH, camaCHO KOTOPOMY pa3-
BMTMe JlBneHMM M 06beKTOB
npHpOAbi ocy eCTBnJleTCJI '4e-
pe3 npOTHBOpe HJI MX CBOMCTB.
OAHaKO eU4e 4>Hnoco4>bI ApeB-
HOCTH nMcanH B PYKonMCJlX O'Ba>KHOM- ponH npOTHBOpe'4HBblX
CBOMCTB (HHb-JlH camaCHO BOCTO'4HOM 4>HJ10C04>HM) B p03BUmUlJ
JlBneHHM H 06beKTOB. npOTMBOpe'4HBble CBOMCTBa CTHMynHpYIOT
31'0 88JKHO
L-1cTonKOBe.&ilR C&ilMBOl1OB
&II I.j&llcen ,QaIOT He KOHKpeT-
Hble. a l1&i1Wb 06 e peKO-
MeH.A8 &II &II nporH03b1
6Y.Ay ero. KOHKpeTHyJO
&IIHcpopMaUlltIO, BepoRTHO,
6Y.AeT ,AaBaTb nMwb.TeXH&iI-
"IeclOil CKOHCrpY&IIpOBaHHBR
MaW&IIHa BpeMeHM.
72
pa3BMTMe M3MeHeHMM B 06beKTBX M JlBneHHJlX. 310 C03AaeT ycnO-
BHJI A11J1 HaKOnneHHJI HOSOZO Ka'4eCTBa. KOJ1uyecmso M3MeHeHMM,
HaKannHBaJlCb, nepeXOAHT B HOBOe KOyeCmsO MaTepHH 06beKTa
MnH 3HeprHH JlBneHHJI. Ha060pOT, MO>KeT npOHCX()N!1'b nepe-
XOA Ka'4eCTBa B -KOnH'4eCTBO. TaK. B CnOpTe nepexOAY KbnH'4eCTBa
B Ka"teCTBO MO>KeT COAeMCTBOBaTb '4M O ypeHMpOBOK: '4eM 60nb-
we HX KOnH'4eCTBO, TeM CHnbHee Ka'4eCTBetf1lto MeHJleTCJI peaKLtMft
opraHH3Ma cnopTCMeHa Ha ct>H3H'4eCKYIO liarpY3MY, O CTaHOBHT-
CJI Bbl1iOCnHBee.
nepexoA Ka'4ecTBa B KOnM'4eCTBO y cnopTCMeHa MO>KeT npoftBMTb-
Cft B TOM, .'frO CMCTeMaTM'4eCKMe TpeHHpOBKM BHa'4ane nOBbiwalOT
«jJyHKLtHIO - cHny cOKpaaqeHMJI MblW bI, a aKonneHMe 31Oro CBOM-
CTBa B CBOIO O'4epeAb Bbl3b1BaeT M3MeHeHHe crpYKTYPblfl'b1W bI, pa3-
BHTMe B HeM AononHMTenbHblx MblWe'4HblX BonOKOH npOMCXOAHT
YBeJ1H'4eHHe MblWe'4HOM MaCCbI).
AnbTepHaTMBHbIe npH3HaKH H pa3HoHanpasneHHble CBOMCTBa MO>K-
HO 06HapY>KHTb Be]Ae: B 0611eKTaX, Y'4eHHJIX, JlBI1eHHJIX, c06bmU1X, AeJI-
TeIIbHOCTM enOBeKa. Bocr0'4HOM
4>MJ10co4>HeM 3TO onpeAeJ1eHO
KaK KapMH'4eCKH 00y610Bl1eHHoe
M or cBoern 3apo)f(,QeHHJI cy
CTBYIOU4ee (Bpo)l(AeH1ioe) CBOM-
CTBO. ctiHnoco4>bI ern MMeHYIOT
«!fa'4aJ10M HHb-JlH».
npMMepoM aJ1bTepHaTMBHbIX
nOHJlTHM B MeAH MHe MO)f(eT
6b1Tb onpeAeJ1eHMe 3AOPOBbJl
MJ1M 6one3HH, >KH3HM HnH CMep-
1M H T. A.
A3b1 H}'MeponOnfU
AnbTepH8TMB.
npaBHl1bHO i-1CnOI1b3ys1
npoTHBope"tMBble CBOM-
CTBa OAHoro BeU4ecTBa,
MO>KHO n0l1y'u1Tb >KeI18e-
MbI 811bTePH8TI1BHbI pe-
3yJ1bT8T B APyroM OObeKTe
W1H RBl1eHH,"", 3n1 B03-
MO>KHOCT,"" MCnOI1b3yJOTcR,
HanpHMep, B Me,O.Io1l.UitHe.
73
rnaBa 1
AnbTepHaTHBHble CBOM-
CTsa oOHOZO u mozo JKe Be-
U4eCTBa MOryT Bbl3b1BaTb ne-
'Ie6HblM 34>4>eKT. «A03a
pewaeT, 6b1Tb BeU4ecTBY
JlAOM HnH neltapCTBoM», -
MYAPO 3aMeTHn BblAalO-:
I14HMCJI HeMeLtKHM Bpa'4 H
XHMHK 3nOXM B03pO>KAe-
HHJt napal.l.enbC (1493-
1541).
AeMcTBHTenbHo, A03a
JlAa nocne YKYca raAIOKH
MO>KeT OKa3aTbCJI cMep-
TenbHo . OAHaKo pa3Be-
AeHHaJl A03a JlAa 3TOM >Ke
3MeM ycne1lft0 npHMeHJleTCJI AJlJI ne'4eHHJI 60ne3HeM cycTasoB.
MblWI.I" paAMKynHTa (HanpHMep, npenapaTbl «BHnpaToKc», «BHn-
pOKyTaH», «BMnpaKcHH», «BHnpaKTHH» cOAep>KaT JlA aAIOKH).
(nasa napaLtenbCa nOATBep>KAaeT npaKTHKa cOBpeMeHHblx Bpa-
'4eM: O'4eHb Manble A03b1 neKapCTBa Hcnonb3yeT HeTpaAHI.I.MOH-
HaJl MeAMLtMHa (roMeOnaTHJI), a 60nbwHe A03bl neKapcTBa - rpa-
AMI.I.HOHHaJl, MiM «06b1'4HaJl», MeAHLtMHa. npH'4eM Ka>KAaJl H3
nepe'4HCneHHblx l4eA'lI.l.HHCKHX npaKTHK nonb3yeTCJI Y 60nbHblx
'3acnY>KeHHblM YBa>Ke+tMeM, raK KaK B Ka>KAOM cnY'4ae AOCTHra-
eTCJI H3 eHMe! TonbKo HY>KHO 3HaTb, KorAa, npM KaKHX 60ne3-
HJtX, B KitKOM A03e B KaKoM nOCJ1eAO aTenbHoCTH MO>KHO npH-
MeHJlTb AJlJI ne'4eHHJl60nbHOro 3TH anbTepHaTHSHble A03b1 OAHoro
H Taro >Ke BeU4eCTsa.
H8 38M8ny
B K8)t(,IJ.OM RBJ1eH J1 06beK-
Te ecTb «Ha60p anbTepHaT B-
HbiX np 3HaKoB CBO CTB..
KaK n0J10)l(&llTeJ1bHbIX (xeJ1aH-
HblX), TaK OTP"1 TeJ1bHbIX
(He)KeRaHHblx). III BceM 3T M
npoTMBOpe RMcBo cTaeHeH
npo ecc pa3B T R. 3TOT npo-
ecc 06b1 HO HepasHoMepeH.
B I(8)K,D,OM 06beKTe W1 RBJ1e-
HMH npoHCxoART 6opb6a, .KOH-
K}'peHUMR COCTaBJ1RIO X ero
pa3HOHanpaBJ1eHHblX Ka ecTB.
74
A3b1 H}'MeponOrVlVl
nHCaTeJ1b EpeMeM napHoB 06 aJ1bTepHaTHBe nMweT: dlA H 3AO-
pOBbe. ClI.eneHMe '4epe3 CMepTb. 3AeCb TOT >Ke npHHLtMn Bce06-
U4eM CHMnaTH'4eCKOM CBJl3M. 3MeJl 3cKynana, CKJ10HHBWaJlCJI HaA
'4aWeM, rOTOBa 3aMKHyTb aJ1XMMH'4eCKOe KOnbll.O. ApJlXJ1QMY CBHH-
4.Y, MeTanny CarypHa, '4T06b1 B03pOAHTbCJI B CBepKaHHM naTa A/1J1
>KM3HH Be HOM, npeACTOJlno YM.epeTb B 3ane aTaHHOM peTopTe. O'4e-
BMAHO, npaKTMKa A06b1BaHHJt JlAOB, B '4eM oc eHHO npeycneJ1 Ltapb
MHTpHAaT, HanO>KHna Ome'4aTOK M Ha OKKynbTHbie npeACTaBneHHJI».
napHOB OTMe..aeT, ..TO HapOAHbfe 4emnenH MarM'4eCKHMH CBOMCTBa-
MH HaAeJ1J1nH, HanpHMep, Bee paCTeHHe B LteJ10M, a aJ1bTepHaTHBHbI-
MM CBOMCTBaMH - lIoemb 3TOro >Ke paCTeHHJI, HanpHMep MOAbi MnH
KOpHH. «ECJ1H B Jl6nOHe BMAenH HaMeK Ha 3arp06HYlO >KH3Hb, TO
Jl6nOKO - CHMBon nepBopOAHoro rpexa "HenpeMett,ttblH aTpH6yT
CKa30K - 03Ha'4aJ10 HenpeoAonHMblM MHPCKoM"c06naflt» (TpOH nlO-
LtH4>epa. KpHTH'4eCKHe o epKH MarHH H oKKynbTH3Ma, 1991, c. 120).
MaTepHan CTH'4eCKOe yTBep>KAeHMe, '4TO Bce pa3BHBaeTCft '4e-
pe3 npoTHBOpe MJI M npoTHBOpe'4HBble MHeHMJI JlBnJlIOTCJI HCTO'4-
HHKOM pa3BHTMJI 06eMx TO'4eK 3peHHJI, npM3HaeTCJI H oKKynbTH3-
MOM. KaK BHAHM, B HYMeponorHH H B eU4e HeAaBHO BbicrynaBweM
KaK ee onnOHeHT MaTepHanHCTM'4eCKOM Y"feHMH eCTb o6Lque yTBep-
>KAeHHJI. H He TonbKO npHBeAeHHble Bblwe B Ka'4eCTBe npHMepa 3a-
KOHOMepHOCTH. n03TOMY He CJ1eA'jeT 3apaHee OTHOCHTbCJI C npeAY-
6e>KAeHHeM K «HerpaAHlI.HOHHblM» 3HaHMJlM, He 03HaKOMMBwHCb C
OCHOBOM HX «Hay'4HOM nnaT4>oPMbI)I). BepOJlTHO, He CJ1eAYE!T OTMa-
XHBaTbCft, He pa306paBWHCb B caMOM CyTH, aT Y"feHHM BOCTO'4HblX
4>Hnoc04>oB M HYMeponorOB, KOTopble 6blnH no-cBoeMY TaJ1aHTnM-
BblMH H MHTeJ1neKTYanbHO nepeAOBbiMM. Apyroe Aeno, CMO>KeM nM
Mbi CO CBOMX n03HlI.HM, Hcnonb3YJt COBpeMeHHble 3Ha HJI, OTAeJ1HTb
HCTHHHoe aT HaAYMaHHoro, HCKa>KeHHO AOHeceHHoro K HaM epe3
75
rnasa 1
C88A8HM.noo nbTM3MY
MO>KHO socnplllHIiIMaTb no-
pa3HOMy. nonaraeM, 'ITO 3Ta
IIIH<t>oPMa He cpa3Y 1113-
MeHlIIT nplilBbI HYIO T KY
3peHIIIR miTel1R: OJ],HaICO
Kp ecKM OLteHeHHbIe CBe-
AeHMR no HyMepo110rMIIIIII
IIIC110BO aCTpOl1on1l11, B03-
MO>KHO.n03B0l1RT liITaTel1lO
nO-HOBOMY OC03HaTb III 0Lt9-
HMTb caoe M&4poe033peHM9.
MHorMe BeKa. CMO>KeM nH
npMHJlTb K CBeAeHHIO H HC-
nonb30BaTb B >KM3HH 3aKOHO-
MepHOCTM, Ha KOTOpble 06pa-
utanM BHMMaHMe MYApel4b1,
Y'4eHble ApeBHOCTM.
BepOJlTHO, MHeHMe '4HTa-
TeJ1116YAeT 60nee o60cHoBaH-
HblM nHWb nocne Taro, KaK.
OCBOMB 3neMeHTapHble HYMe-
pOnorM'4ecKHe M MHble paC'4e-
TbI, OH CMO>KeT fotHorOKpaTHO
nposepHTb HX B >KH3HH.
"IMcnoBaS1 T8MHa HocTp8AaMyca
KpaTKO 0 npe,qcKB3aHJfflX HOCTPBABMYCB
B pa3HblX crpaHax MHorMe acrponorM H HYMeponorM nblTaJ1HCb
pa3raAaTb HeKHM MHcrpYMeHT, 4>opMynbl paC'4eTOB, n03B0J1HBWHe
HocrpaAaMycy YAHBMTeJ1bHO TO'4HO npeACKa3b1BaTb CBepWeHMe co-
6b1TMM KaK B CBQe BpeMJI, TaK M Ha MHorHe BeKa BnepeA. OAHaKo
MeTOAHKa, MCnOJ1bJye.wt HM AllJI paC'4eTa npeAcKa3aHHM, OCTaBa-
naCb TaMHOM.
BnpO'4eM, HeAapOM roBOpJlT, '4TO Bce TaMHoe paHO HnM n03AHO
CTaHOBMTCtI JlBHblM. MOCKOBCKHM HCCJ1eAOBarenJlM AMHTpMtO H Ha-
Ae>KAe 3'MMa YAaJ10Cb HaMTM npoCToM H n9HJlTHbiM KJ11O'4 K npopO'4e-
CT,aaM HOCTpaAaMyca, paCKpblTb 3awH4>poBaHHYIO enO'4KY era
npeAcKa3aHHM. 06 3TOM nMweT ra3eTa «Bce 060 BceM» B CTaTbe
76
A3b1 H}'Mepon OrHH
«TaMHa HocrpaAaMyca pac-
KPblTa?» (1999, MaM, C. 4).
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3aHHM HOCTpaAaMyca ycnenM
Y>Ke HcnonHMTbCR B T04HOM
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HbiM. PeBOnlOLtMM B POCCMH
H 80 CbpaHl4MM, ABe MMposbie
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AO HeCKonbKHX MeCJlLteB 3a MHOro BeKOB AfJ Taro, KaK Bce 3TH c06b1-
THJI npOH30wnH. TO'4HOCTb npeACKa3aHMM HocrpaAaM npeBblCH-
na 90 OJo. OAHaKo caMbiM ne anbHblM OTKpblTHeM CTaJ10 TO, '4T0 Y>Ke
B HeAaneKOM 6YAYU4eM nepeA '4enOBe'4eCTBOM B,:raHeT np 3pa HO-
BOH MHpOBOH BOMHbI,
HI1H, rOBopR cnoBaMM
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npeACKa3aHMR era
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MeHa B BOMHax Mcnonb-
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77
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Bce CBOM B03MO>KHOCTM. no npeAcKa3aHHIO HOCTpaAaMyca, AllJI Tex.
KTO BbI>KMBeT, HaCTaHeT HOBaJl 3pa C HOBbiM MHpOB033peHMeM H MHO-
>KeCTBOM HOBbiX 3HaHMM.
fopOCKonbl M npeACKa3aHMJI Ha TOM M OCHOBaHbf, anaTOMY
nonb3YIOTCJI nonynJlpHOCTblO, '4TO npeAYnpe)f(AalOT a B03MO>KHblX
nOCJ1eACTBHJlx. nOABOAHblX KaMHJlX CYAb6b1, KOTopble '4enOBeK MO-
>KeT M AOn>KeH 060MTH. «KTO npeAYnpe)f(AeH, TeT Boopy>KeH»,-
rOBopMnM ApeBHMe MYApeLtbi. BO MHO rOM 6b1nM npaBbI...
06paTMMCJI K MHTepecHOM MH4>opMaLtHH, npMBOAHMOM B ynoMJI-
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'4eCKMH 4>aKT: era OCHOBHOM npo4>eccMeH BHa aJ1e 6b1na MeAHLtH-
Ha. OH nonY'4Hn IIIeAMLtMHCKoe 06pa30BaHHe M CTaJ1 Bpa OM. nocne
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BOHn CJ10>KHble MaTeMaTM'4eCKMe pac eTbi ABM>KeHHJI nnaHeT, MX
npoeKl4H Ha 3eMnIO H B3aMMHoro nepeCe'4eHHJI TpaeKTOpHM. '4TO H
Mcnonb309an B CBOMX npeACKa3aHHJlX.
Ho crpaHHO, '4TO B OAHOM H3 era npeAMCJ10BMM K l4eH1Yp"JlM, H3-
BeCTHOM KaK «nOCJ1aHMe feHpMxy», B rna3ax pJl6MT aT HeTO'4HOCTeM
H OWM60K. B TOM '4HCJ1e H 3neMeHTapHblX apHcpMeTMHeCKMX.
78
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caM HOCTp(lAaMyc 06paU4aeT BHHMaHKe Ha TO, '4TO 3TOT KOpOTKMM
TeKCT nHCaJ1CJ1 HM roA C TBepTblO - C MapTa 1557-ro no MIOHb
1558 r. - no HeCKOJ1bt<y CJ10B B AeHb! npM 3TOM npopoK Hb CMnb-
HO MCKa>KaeT TeKCT 6M6nMM. Bne'4aTneHMe TaKoe, '4TO OH rU10xo 3Ha-
eT ee TeKCT, HO 3TO OnJlTb-TaKM HeB03MO>KHO, TaK KaK HocrpaAaMyc
6b1n 06pa30BaHHeMwMM enOBeKOM.
B nOCJ1aHMH npJlMO roBOpMTCJI a KaKOM-TO wM<J>pe, M nOToM}' no-
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KMe M MaTeMaTM'4eCKMe paC'4eTbi. M nOBe3J10, MX He nponan
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TblX H(lABoe, - 11; 11.
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HbiM TalIaHT. Tat(, OH cyMen OCTaHOBHTb pacnpocrpaHeHMe HeCK011bKMX
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npMMep, B nOCJ1aHMH CKa3aHO: «Bee nOCTpoeHHJI H rapMOHHJI npo-
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HM'4ax)>>, npH'4eM nonb30BaTbCJI 3TMM «TpeHO>KHHKOM» CJ1eA}'eT,
«nOMeCTHB MarH cKMM >Ke3J1 (eU4e OAHY eAHHHLtY) Me>KAY era HO>K-
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nOBHM npOBHAe4 nMweT, '4TO «HaCJ1eAHoe CJ10BO npeACKa3aHHJI (T. e.
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nOpJl>KeHMe OKpy>KHTb era rp06 '4eTblpbMJI CBe'4aMH no OAHOMY nHB-
py - no ABe C pa3HblX CTOpOH.
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CpOK, ne>KaU4MM Me>KAY AaToM HanHeaHHJI npOpO'4eCTB - MIOHb
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3TO npMMepHo Hawe BpeMJI)>>. TaKHM 06pa30M, BCIO '4eno'4KY AaT
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MMpoSOM SOMHW?
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reo fopa3Ao HHTepeCHee TO, '4TO npH nOMOU4H HaMAeHHoro K034>$H-
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3 TeKCTOB HocrpaAaMyca MO>KHO nOHJlTb, 'tro HpaKCKHM KPM-
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B paCKpblTOM AMHTpHeM M HaAe>KAOM 3HMa ra6nHLte nOAP06HblX AaT
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weMY BpeMeHH. « 3-3a CBOHX >KeHU4HH OH npep.aCT nlOAeM epHOM
CMepTH. HMKorAa He 6b1no CTonb >KeCToKoro CYU4eCTBa». BepoJlT-
HOCTb oWM6KM npaKTH'4eCKH HCKnIO'4eHa. COBnaAaeT nO'4TM Bce: H
MeCTO AeMCTBHJI- paK, M nOBOA - npen1060AeJlHHe, M Aa>Ke TO,
KaKoe np03BM nonY"lMT KnMHTOH. CeM ac B AMepHKe Aeno KnMH-
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3TOM rOBOpHt HOCTpa,QaMyc: «}f{eHcRoe 6eC'4eCTbe npHAeT K npo-
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KOTOpble He npHHHMalOT Y'4aCTMJI B KOH4>nHKTe, pe3KO B03paCTeT
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CJ1Y'4ae C BbeTHaMOM, '4T06b1 HeMTpanH30BaTb HeAOBonbCTBO CBO-
MX rpa aH, CUtA npMAeTCJI npOAOn>KaTb BoeHHYIO MCTepHIO, a
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nottJrOteM, KaK 60r. B03MO>KHO, HMeHHO 8 POCCHH 3TO A8M>KeHMe H
pa308beTCJI C HaM60nbweM CMJ10M. B CBJl3H C 3TMM HOBaJt 3pa Ha'f-
HeTCJI MMeHHO 3Aecb,1I:0TJI AO 3TOro e e npeACTOMT HcnblT3Tb MHO-
ro nepeApJlr. POCOiJ1 y*e nepe>KHna pe3t<y1O CMeHY nOnHTM'feCKOrO
ttypea. C6.,nHCb YKa3aHHJI HocrpaAaMyca H Ha HeAOBonbCTBO ap-
MMM M Ha "ee ponb B B03MO>KHOM nepeBopOTe. npH'4MHa )f(e O'4eHb
o6I.NHa - «AlIJ1 conAaT He HawnH AeHer». BnpO'4eM, nepeBopoTa
MOrna M He 6blTb, eCJ1H 6b1 npaBHTenbCTBO npoCTO H3MeHMno C80M
tcypC.
84
no HOCTpaAaMYCY, yJl(e B
2000 r. BnaCTb B POCCMM eTa-
HeT cOBepweHHo HeY3Haaae-
MOM. npHAYT HOBbie nl>AM, KG-
Topble n06eAU 'He CMnOM
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naraJ10Cb, 'ITp- B POCCM",
AO 2002 r., HeKHM nMAep :JT'O-
ro ABH>KeHHJI, CKOpee acero,
6YAeT nory6neH (803MO.HO,
y6HT), H HMeHHO 310 MO)l(er
nOCJ1Y>KHTb npM'4MHOM AM Ko-
nOCCaJ1bHOrO 060CTpeHMJI KOH4>nMKTa, AflJI «'4YAOBMiittOro MCTpe6-
neHMJI nlOAeM H >KMBOTHblX». npH'4MHO 3TOro, rOBopHn HoCTpaAa-
MYC, CTaHeT TO, '4TO 3a HeCKonbKO neT, 3a KOTopble Hy>t<HO 6YAf!T
H HTbCR >KHTb nO-HOBOMY, BPJlA nH MHorMe cyMelOT OTKa3a'ThCJI
OT TaKoro '4enOBe'4eCKoro '4YBCTBa, KaK >Ka>KAa MeCTM. He HaMeK JIM
:no Ha M3BeCTHbie C06b1TMJI B e\fHe?
KOHe'4HO, C tpYAOM BepHTCJI B TO, '4TO TaMHa nO'4T\o1 500-nentei
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nMKMM npOBMAe14 onpeAenHJ1 B CBOMX TeKCTax Taro, KOMY
HO CTaTb nepBblM '4enOBeKOM, npO'4MTaBWMM npasAY B era KaT-
p Hax. HOCTpaAaMYC nMweT, eCTeCTBeHHo, B 3awH4>poBaHHOM
BMAe, 'lTO TaMHblM KJ11O ' CnpJlTaHHblM MM B «nOCJ1aHMM feHpuy»,
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Bwwna KHMra «pacwMq>-
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TO 3Ta BepcMR CTaHeT noc-
neAHe M OKoH aTel1bHoM,
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WMe nocl16ACTBMR AIIR
6YAeT OTKpblT 10.97. 4TO H 6b1-
no cAenaHo AMHTpHet04 3HMa
B oKu6pe 1997 r. Ho caMoe
crpaHHoe, '4TO HocTpaAaMYc
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pOAHTCJI B 1966 r.». CnHWKOM
MHoro cOBnaAeHHM, '4T06b1 He
AOBepJlTb TeopH AMHTpHJI H
HaAe>KAbi 3HMa.
rnABA 2
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MarMR nYHHOM opMynbl
OrKyAa B3J1nHCb '4HCJ10Bble eAH-
HMLtbl, ne>KaU4He B OCHOBe KOHcrpYK-
4HH «MarH'4eCKoro» KBaApaTa AIO-
pepa? CnY'4aMHbI nH OHH? HeT, He
cnY'4aMHbI. 4McnOBbie BenM'4HHbI
KBaApaTa AlOpepa CBJl3aHbI C acrpo-
nOrH'4eCKHMH nOHJlTMJlMH, a MMeH-
HO C xapaKTepHCTHKOM 4HKna H 4>a3
nYHbI. 4MCJ10Bble BenH'4HHbI, oTpa-
>KalOU4He aCTponorH4eCKHe nOKa3a-
TenH nYHbl, eU4e ApeBHHe Y'4eHble
Hcnonb30BanH AllJI paC'4eTa TaK Ha-
3b1BaeMOM YHHBepCaJ1bHOM OKKynbT-
HPM 4>opMynbl.
cJ»opMyna BHa'4aJ1e 6b1.na H3BeCT-
Ha KaK «11YHHaJl», nOCKonbKy orpa-
>KaJ1a pa3Hble '4HCJ10Bble napaMeTpbl
HO'4HOrO CBeTHna. Ho Y>Ke nocne
Octto.w ttyMepOIIOntM
1-13 HYMeponQf1't HaM
3BecTeH «Mtfrli/ ec-
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(MKA), COCTOR '" 3
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Hapy>KMnaCb BbiCOKaJl CTeneHb ee AOCTOBepHOCTH B RpeACKa3aHHH
TeKY MX M 6YAYU4MX c06b1TMM. nO:noMY 4>oPMyna nonyYHna 60nee
rpoMKoe HMJI: 6b1na nepeHMeHOBaHa B 4>opMyny «3aKoHa EAHHCTBa
pa3BHTHJt, rapMOHHH M cy eCTBOBaHMJI MHpa». nonHoe ee Ha3Ba-
HHe npHMeHJleTCJI peAKO. 06b1'4HO Hcnonb3YlOT ABa nepBblX cnoBa .8
ee HMeHH.
cJ)opMyna 3aKOHa EAHHCTBa, MnH nYHHaJi 4>opMYJ1a, npeACTaBne-
Ha CJ1eAYlOiqHM ypaBHeHMeM: 28 - 4 x 7.
YAHBHTeJ1bHO, HO '4MCJ1a 4>opMynbl 3aKoHa EAMHCTBa H ee KOH-
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'4eM He3aBHCHMO aT Taro, CO-
sepweHO nH 3TO M3MepeHHe B
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ry, - maBHoe, 'fT06b1 nOJl8H-
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ee KOHCTaHTbI.BnIleTaIOTCRB oc-
HOBHble, HaH60nee Ba>KHble
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nH'4MHbI, HanpHMep xapaKTepH-
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CTOpoH 4>OPMYI1b1 (28 = 2 +
+ 8 = 10 = 1) BMecTe C oc-
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nne'4Y» oKKYnbTH3MY.
He HMeJl Ha ceroAHJlWtU4A AeHb APyrHx 06'bJlCHeHHM M He YMeJl
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ee pa3YMHee Y'4MTblSaTb, nOKa
«o4>HLtHanbHaJl HayKa» He npeA-
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nOJlBJ1eHHe nJlM M3MepeHHM Be-
U4eM, 06beKTOB HJ1H HHblX c06b1THH
)f{H3HM CO'ieTaHHJI 4M$P 4>oPMynbl
HnH ee KOHCTaHTbI nlOAM Aonro
C HTa1IM CJ1Y'4aMHOCTbIO M He 06pa-
HHa'3TOBHMMaH .npHMepoB
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Teu<, B03bMeM npoCToe pa3nO>KeHMe Ha 3neMeHTbI Mcnonb3yeMo-
ro '4enOBe'4eCTBON '4HCJ10BOrO pJlAa. ECJ1H paCnOnO>KHTb B rpM crp04-
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MH) CJ1eBa HanpaBo, KaK Mhi npMBblKJ1H '4MTaTb H nHcaTb. TO non HM
CJ1eAYIO ee (KBaApaT MK):
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fMX pa3AYMHM He npHBneKIla MX BHHMaHHe nYHa... MO>KeT 6b1Tb,
89
fnasa 2
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B 3TO CBeTHno, KOTOpoe '4aU4e APyrHx He6eCHbiX Ten npHBneKaeT
B3rnJlA '4enOBeKa?
HTepeCHO M TO, '4TO nOAC03HaTenbHO nlOAH BbiAenHnM B HanH-
caHMH HMeHHO 3TM '4HCJ1a M3 OCTaJ1bHblX 3neMeHTapHblX 4Hcen. OCO-
6eHHOCTb '4HCen 1,4 H 7 B TOM, '4TO npHHLtHn HX HanHCaHHJI OTnM'4a-
eTCJI aT npHHLtHna HanHCaHMJI OCTanbHblX '4HCen. HeKOTopble
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HMIO, OH AOKa3b1BaeT Hawy nOAC03HaTenbHYlO CBJl3b c KOCMOCOM. B
OKt<ynbTHOM nOHHMaHHH nOAC03HaHHe OTpa>KaeT CBJl3b HaWHX 3Hep.
reTM'4eCKMX Ten C KOCMOCOM. AeMCTBMTenbHO, nO'4eMY He OAHO ('4TO
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HMe M MMeHHO TonbKO '4HCen, BXOAJIU4HX B KOHCTaHTY, 061:1J1CHMTb
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Aowna HX OAHaJl MYAPOCTb: «60r (T. e. B nOHHMaHHH COBpe-
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B HanMcaHMM OCTanbHblX
4Mcen eCTb OBan (2, 3, 5, 6, 8,
9), a B '4HCJ1aX KOHCTaHTbI -
TonbKO oCTpble yrnbl.
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CTaHTbI 3aKOAMp08aHbI 80
Bcex JlBneHHJlX H 06'beKTaX
peanbHoro MHp a'4MHaJl
aT ConH a M KOH'4aJl '4enOBe-
KOM. HanpHMep, AJ1J1 ConH-
ECTb MMeHM.
naBen MYXOpTOB C &IIT8eT.
TO apa6cIC&IIe &IIC118 ICOH-
CT8HTbI n&llwytCR TaK nOTOMY,
TO 3TO He TOI1I;1<O yc110BHoe
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KO -TO HHbI HaM KOCMO-
COM .. p., Ko,a, AB&II>Ke-
H&IIR, B TOM &IIC.ne He6ecHbiX
Tel1 &II Hawe nnaHeTbi.
90
C/)opMyna «HOI/HOM cpeH»
Lta 4>6pM}lJ1a 28 - 4 x 7 MO>KeT 3Ha'4MTb cneAYIOU4ee: 28 - :no
'4HCnO, xapaKTepH3YIOU4ee paCnOIlO>KeHHe ConH4a B KOCMM'4eC-
KOM npOCTpaHCTBe aT 4eH!pa fanaKTHKH (28 000 CBeTOBbiX neT).
Ha nOBepXHOCTH ConH4a YCKopeHMe CHnbl TJI>KeCT .28 pa3
60llbwe, '4eM Ha nOBepxHocTH 3eMnM (Aazaes M.M. .. AP. ACT-
POHOMHJI). 4Hcno 4 - )TO nepHoA peanM3aLtHH BMCOKOCHbiX
(onHe HbIX neT, a 7 - '4",cno AHeM B H en . AnJl '4enOBeKa
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CTBa ce6e nOA06HblX» - HopManbHaJl npOAOn>KHTenbHocTb 6e-
peMeHHocTH 280 AHeH (10 nYHHblx MeCJlLteB). A AJ1J1 3eMnH M
'4enOBeKa '4HCnO 28 03Ha4aeT, HanpHMep, '4MCnO MHnnHOHOB
lIeT, 4epe3 KOTQPble nOBTOpJlIOTCJI MaCCOBbie BblMHpaHMJI >KH-
BOTHblX, 06ycnoBneHHble BHe3eMHblMH C06b1THJlMH (BoULlexos-
CHUU A.H. 3HaHHe. 1990. 7).
npm13BeAeM e(1te OAHY npoBepKY: nonp06yeM OnpeAeJ1HTb, co-
Aep>KHTCJI nH oKKYnbTHoe 3Ha eHHe :noM 4>opMynbl B nYHHblx MeCJI-
4ax. CpaBHHM HX npOAOn>KHTenbHoCTb B AHJlX H npoH3BeAeM Teo-
co4>H'4eCKOe CJ10>KeHHe: .
. cHAepH4ecKHM MeCJll4 - 27,321661 - 28 - 1, T. e. 2 + 8-
- 10 - 1 + 0;
CHHoAM4ecKH MeCJlLt... 29,530588... 40 - 4 (4 + 0);
aHoManH4ecKHM MeCJlLt - 27,554551- 34 - 7 (3 + 4).
BHOBb B xapaKTepHCTHKe nYHbI npOJlBHnHCb '4HCJ1a KOHCTaHTbI -
147. VI TonbKO ApaKoHH4ecKHM MeCJlLt nYHbI HMeeT «'4MCJ10 3BepJl»:
27,212220 II: 18 (6 + 6 + 6).
A. 6poHw:reMH B KHHre «KaK ABH>KeTCJI nYHa?» (M., 1990, c. 51)
nHweT: «no faJ1HnelO, BpeMJI, He06xoAHMoe nYHe, '4T06b1 ynaCTb Ha
3eMnlO, eCJ1M 6b1 aHa nepeCTana Bpa(1taTbCJI, paBHO 8848 (KaK cnpa-
BeAJ1MBO 3aMe'4aeT A. KMcenb, CnO>KeHMe BXOAJlU4MX B 3Ty BeJ1H M-
91
rnaBa 2
HY '4HCen TO>Ke 3HaMeHaTe11tr
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147 MMHYT 28 ceKYHA». 4HC-
na 4>oPMynbi H KOHCTaHTbI
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BceneHHoM, KaK SHAHM, no-
BTOpeHbI nonHOCTbIO.
nonaraeM, TO Aa>Ke ne-
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McnOnb30BaTb KaK MHpOBOM 3TaJ10H H3MepeHMJI.
4Mena 4>opM nbl HYMeponorH, KOHe HO, B KOH e KOHU.OB Mor-
nM 6b1 M3Bne'4b "3 J1Io60ro HHoro.06'heKTa Hl1H JlBneHHJI (pa3
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naraeM, '4TO paHO MnM n03AHO TaK 6b1 H CJ1Y'4HnOCb... OAHaKo
cY>KAeHO 6111no MX nonY'4HTb H3 xapaKTepHCTMK He3eMHoro
06'heKTa - nYHbI. nMWb nocne 3Tore 06HapY>fu1nocb, '4TO MX
«'4MCnOBaR CMMBOl1HKa» YHHBepcanbHa H ee MO>KHO YBM.AeTb B
xapaKTepMCTMKax MHorHX Be eM H JlBneHHM, KaK MaTepHanb-
06l1l'i110 npM3HaK 38KOHOMep-
HOCTM B HBnetU1H M11H oObeKTe
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83HTb AIIH npHMepa Ty )t(e
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AeJ1MTb Ha IJ1)e paBHbIe aCTH H
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HyMepon eCKOMY KOAyan-
<l>asKT8 (MMelOl..4ero nocneAo-
BaTenbHbM c eT 6yJ(B), TO TO>Ke
nOl1Y'M'i' 'Mella; «Jly.-
34. «Ha- - 16. 3m HCJ1a H
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ro KB8,Qp8Ta AK>pepa: 34 - 3TO
cyMM8 'fMC8I1 no J1HHHHM MK,A.
a 16 - 'fMC.I1O KneTOK KB8,D,paTa.
92
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$opMynbl. no MHeHMIO tiYMe-
ponoroB. CBR38HbI C 3alcbHOM
HCTB8 MMpoBOr'O pa38M-
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aIOTCR B RBneH M 06'beKTax
olCpY'K8lO ero Hac MMpa.
cc.nYHHoe '1MCnO» B HaWeM 6MopMTMe
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3HeprHH B opraHM3Me, KOTopble aBJ1HBalOT Haw 3IfCJqUOH(JnbHb/U
CfCI1yC, KaK 3TO B XIX B. AOKa3aJ1 HeMeLV<H Bpa'4 B. cJ»nMCt. MMeIOT nMIUt
BOJIH nOA"beMa H naAeHMJI npoAOJ1>KHTeJ1bHOCTbIO KaK pa3 B 28 AHeM.
nHcc TaK>Ke ycraHoBHn, '4TO Haw opraHH3M MMeeT BonHbI npH-
nMBOB £!JU3uC/ecICUX CHn C nepHOAOM 23-AHeBHoro LtMKJ1a. nOA'beM
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HMe - 60nbWYlO sepOJITHOCTb 3a-
60neBaHHJI, nOBblweHHYIO «paHM-
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ca aBCTpHMCKHM MH>KeHep A. TonbT-
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}To HaM60nee 6narOnpMJlTHoe BpeMJI AllJI TBOp'4eCTBa M 06U4eHMJI,
AII YKpenneHHJI 3AOPOBbJl: nporynoK Ha npMpOAe, 4>H3M'4eCKMX yn-
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aqeCTBeHHo npH caxapHoM AMa6eTe H 60J1e3HM LqMTOBMAHOM >KeJ1e-
3b1) nJ10xae HacrpoeHHe 6b1BaeT '4aLqe, eM npH APYrMX naTOnOrHJlX.
AcrponorH M 3HeprOAMarHOCTbI npHBeAeHHble CBeAeHHJI AononHJlIOT
pe3ynbTaTaMH CBOHX HCCJ1eAOBaHHM: Ha AHH cnaAa 6HOpHTMa 6onb-
Hble nlOAH pearHpylOT nnOXHM HacrpoeHHeM '4aLqe H npOAOJ1>KHTeJ1b-
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96
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6nM>KaTbCJI Apyr K APYry. npH 3TOM B03HMKaeT nM60 npHnMB COOTBeT-
CTBYJOI14eM CHHycOHAbi 3HeprHH (npH COBnaAe!fMH aepxyweK CHHycO-
HA HaA rop 30HTanblO), nM60 pe3KHM cnaA 6H03HeprMM (npH
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lOT C Y'4eTOM AHJI pO eHHJI. CTpOJlT rpa4>MK Kone6aHMf'!6MopHTMOB
Ha AeHb pO>KAeHHJI, a aT Hero npOAneBalOT CHHYCQMAbi BnepeA (AnSI
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MHTepecyeT npH'4HHa era HeYAa'4 B npownOM - HHorAa aHa 06bJlC-
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opraHH3Ma).
npH nOCTpOeHHH rpa4>HKa MTblBaIOT '4MCJ10 enblx CyTOK (365),
a OCTaTOK (0,25 CyTOK) HaKannHBalOT AO 06pa30BaHMJI enoro AH
M '4epe3 4 rOAa nonY'4alOT BHCOKOC-
HblM reA paBHblM 366 AHJlM (OAHH CyT-
KH A06aBnJtlOT K $eBpaJ1lO, n03ToMY B
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97
4>opMyna «HOIiHOa cf>eH»
M388CTHO, 'fTO...
fOAOB<WI plltTM npllt-
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rAe rTeK - TeKyU4MM roA; fpO)t(A - rOA pO)t(AeHMJI; 365 - '4HC-
no AHeM 06b1'4Horo KaneHAaPHoro rOAa; NBMC - '4MCJ10 npO>KHTblX
BMCOKOCHbiX neT.
4MCJ10 np0)f(MTblX BMCOKOCHbiX neT onpeAenJleTCJI TaK:
NBMC - (rTeK - rpO)t(A) : 4,
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rOA.
AnJl npMMepa COCTaBMM rpa4>HK 6HOPHTMPB Ha 1996 r. Ha
HJ1. BaHoBa, pOAMBWerOCft 19 MIOHJI" 1951 r. AnJl npOBeAe-
HMJI paC'4eTOB HaM nOTpe6yeTCJI 3HaTb (Ha. CnY'4aM, ecnM QAHa"
M3 BOJIH 6YAeT Ha'4HHaTbCft C npeAbiAYUlerO MeCJlLta), CKonbK
AHeM BXOAMT B MaM - cornaCHO KaneHAaplQ 31 AeHb. OCTanb-
Hble paC'4eTbi npoBoAMM no npHBeAeHHblM Bblwe 4>opMynaM.
NBMc - (1996 - 1951) : 4 - 11,25.
6epeM enoe '4MenO neT - 11.
A - (1996-1951) x 365 + 11- 16436 AHeM.
YCTaHaBnMBaeM, CKon6KO 3a Bce npO>KMTble BaHoBbiM AHM >KH3-
HH 3aBepwMnocb 6H03HepreTH'4eCKHX LtHKJ10B:
4>H3H'4eCKHX 16 436 : 23 - 714 M B OCTaTKe 14 AHeM,
3MO MOHaJ1bHblX 164 376 : 28 - 587 M B OCTaTKe 0 AHeM,
HHTenneKTyaJ1 HblX 16 436 : 33 - 498 M B OCTaTKe 2 AHJI.
Tenepb HaM n CTO"T onpeAenMTb, C KaKMM BpeMeHHblM CABM-
rOM aT AHft pO)t(AeHHJI eAYE!T Ha'4MHaTb CMHycOMAY Ka)t(AOro 6MO-
pHTMa. 3r0 onpeAenJletcJI nyTeM MHHycOBaHHJI aT '4MCJ1a AHJI PO>K-
AeHMJI ocnrKa AHeM aT AeneHHJI 6M03HepreTH'4eCKOrO HKJ1a (TyT
eCTb oc06eHHOCTb: AeneHMe CJ1eAYE!T npOM3BOAHTb He KanbKynJlTO-
paM, a BPY'4HYIO, TaK KaK KaJ1bKynJlTOp AaeT AeCftTH'4Hble 3HaKH, a
HaM CJ1eAYE!T MMeTb '4HCJ10 Ltenblx AHeM B OCTaTKe). ECJ1H '4HCJ10 AHeM
98
C/)opMyna «HoIIHO" cpeH»
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no AHeM C KOHLLa npeAblAY ero Me-
CJlLLa, T. e. C 31 MaJl.
npOM3BeAeM paC'4eTbi Ha OCHOBe nOnY'4eftHb6< AAHHblX:
19 - 14 - 5 MIOHJI - Ha'4aJ10 ct>H3H'4ecKoro LLHKn8. ECJ1M 6b1 BMeC-
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nY'4MnM 6b1 «-3» AHJI. )To 6b1 03Ha'4aJ10, '4TO C 1 no 19 MIOHJI CM o-
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nonHOCTblO. eU4e - B Hee BXOAJIT TpH nQCJ1eAHHx AHJI MaJl. TaKMM
06pa30M, Ha'4anO LLHK1Ia OTC"IMTblBaJ10Cb 6b1 C 28 MaJl.
19 - 0 - 19 HIOHJI- Ha'4aJ10 3MOLLHOHaJ1bHOro LtKMa,
19 - 2 -17 MIOHJI- Ha'4aJ10 HHTenneKTyanbHoro LLHKna.
YCTaHoBneHHble AHM JlBnJlIOTCJI H '4aJ1bHblMM COOTBeTCTBYIOU4MX
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99
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ycTOC4'4MBOCTb 4>OpM. n03TOMY rapMOHHII BcerAa BxoAMna B cxe-
Mbi nepBblX 4>Mnoco4>cKMX npeACTaBneHMM a CTpoeHHM BceneH-
HaM. no MHeHMIO ApeBHM)(, KpacoTa '4epe3 pa3Ho06pa3He 4>OpM
BocnpMHHMaeTCJI C03HaTenbHO H nOAC03HaTenbHO KaK rapMOHHJI,
npMcy aJl np pOAe '4enOBeKa.
AnJl HYMepanora n0Y'4HTeneH 3Tan $>pMMpoBaHHJI npeACTaBne-
HHJI ApeBHMX.9 KpHTepHJlX H CHMBonax H ynOTpe6n HHJI HX B pac-
cy>KAeHHIIX. aco6eHHO HHTepeceH :nan Mcnonb30BaHMII MMM Ka'4e-
CTBeHHbfX CMMBonOB. nep1sble npeACTaBneHMJI a rapMOHHM MYApe bI
CBJl3b1BaJlH C nOHJlTMeM .Q06pa eU4e AO M306peTeHHJI '4MCen. nOHJlTHe
.Q06pa KaK BapHaHT rapMOHHH
OHW BocnpHHHManH KaK «co-
CTaBHYIO '4aCTb BceneHHOM» H
BBOAMnM .Q06po B cxeMY ee
crpoeHMJI. no HX npeACTaBne-
HMIO, pa3BHTHe ,Q06pa Ha'4HHa-
nOCb CHH3Y, C MaTepHaJ1bHOrO
Ha'4ana, 4<HH3Wero ,Q06pa» 3eM-
nH. A06po BOCXOAHJ10 no Bep-
THKanH - CMMBon ee MOHO-
ABa 1C8'f8CTB8 A06pa
cJ>W1OCO<I>bf H8.AenwM .AYWY
'fenoeeK8 « MM /JtJ6-
pa.. - CMeCbK) «HM3wero. ...
«BbICUJer Ao6Pa., n03TOMy
KTanoCb, 'ITO noeeK coo-
co6eH npostBnSfTb 3n1 AB8
ecraa csoero noOpa.
102
XOPAa - K «BblCWeMY A06py» He6e K AYXY. TaM 3aBepWanaCb BblC-
waJl CTaAHJI pa3BHTMJI A06pa (CM. pHC. 6).
CS>Mnoco4>bI nOnaraJ1M, '4TO Ao6po '4enOBeK BocnpHHMMaeT «c ro-
TOBHOCTblO», oc06eHHo eCTeCTBeHHoe, npHpoAHoe A06po,.KOTOPoe
HaXOAMTCJI B rapMOHM'4HOM «C03BY'4MM» C A06pOM AYW 1{enOBeKa.
To, '4TO enOBeK Ha3b1BaeT 3nOM, C'4HTaJ10C-b AMcrapMOHM'4HblM co-
3BY'4HIO era AYWH. 3no - :310 HCKa>KeHHblM MccoHaHc 3neMeHTOB.
YrBep>KAaJ10Cb, 4TO Bce Bel14H A/1J1 CBoeM O}'4HBOCTH AOn>KHbI
$OpMHpoBaTb B3aHMOOTHOWeHHJI, MCXOAR H3 3aK6HoB A06pa npM-
POAbI, H rapMOHH'4HO CO'4eraTbCJI B >KH3HM. npMMepoM BblcweM rap-
MOHMM npeACTasnJlnOCb nnaHerapHoe nocrpoeHMe KOCMOCa, rAe Bce
AMcrapMOHM'4HOe pa3pywaeTCJI, Aonro He CYl14eCTByeT. rapMOHHJI,
C'4KTaJ1M MYAJ)e bI, ecTb npo-
JlBneHHe BonH Bblcwero
Pa3YMa, Be'4HOrO A06pa.
no npeAaHHIO, 60ry
fepMecy, OCHOBaTenlO HC-
KycCTB, rpe'4eCKHe 4>Hno-
C04>bI npHnHCblBanH KOH-
.CTP1 poBaHHe-nepBoM
nMpbl: A/1Jt nonY'4eHMJt MY-
3b1KanbHOM rapMOHHH OH
HaTJlHyn CTPYHbI Ha naH-
LtMpb '4epenaXM. nlO60e
npe,qaHHe, HAYU4ee K HaM
M3 rny6MHbI BeKOB, nepe-
MewMBaeT npaBAY C BbI-
MblCJ10M, HO 4>aKT peaJ1eH:
I1Mpa - 04eHb ApeBHMM
(/)opMyna ccHOI./Hoff cpe".,»
CMMBonw . 4»M MM
M3HIU1 n. Xonn (1992) OTHOC -
rel1bHO ynorpe()11eH C MB01lO8
B CPW10c0cp n weT: «B M Te'
PMRX l1 pa OfKTanaCb Cet<peT-
HbiM C..wJBOnOM e11OBeKa, Kop-
nyc HCTpyt.4eHTa npe.QCT8B11M
<PM3M'feCKoe Teno, CTPYHbI -
HepBbI, 8 M}'3bIKaHT - AVX. r-
H8 HePB8X, AYX TaKHM 00ps-
30M, COTBOpSU1 rapMOH 1O HOp-
M811bHOH My.3bIIG1, KOTopaR, CA-
H8KO, n TCSI B
AHCrSPMOH IO. ecn np"'po.o.a
LfenOBel<8 pa3BpaU48H8».
103
rnasa 2
My3b1KaJ1bHblM MHCTpyMeHT. TaK. nnaTOH (428-348 rr. AOH. 3.) C'4M-
Tan, 'ITa pMTMM'4Hble neCHM M n033HfI, MCnOnHJleMbie nOA aKKOMna-
HeMeHT nMpbf, 6b1nH Y erHnTJlH no KpaMHeM Mepe eU4e AeCJlTb TblCJI'4
neT Ha3aA, a HCKYCCTBO 6b1no CTonb B03BblweHHblM, TO, KaK eMY
npeACTaB.RMOCb, HMeno He3eMHoe npOHCXO)f(,qeHHe.
C'4HTaIOT, '4TO XaJ1AeM (5000-3000 rr. AO H. 3.) nepBblMH 06pa-
THnH BHHMaHMe Ha TO, '4TO B THWH tfO'4H 3BY'4MT «My3b1Ka c«PeP» M
'4TO He6eCHbie Tena npH nepeABH>KeHHM" no He6y McnonHJtIOT KOC-
MM4eCKMM rHMH. Ho eU4e paHbwe a My3b1KaJ1bHOM rapMOHMH CTpoe-
HMJI MHpa 3aAYMblSaJ1Hd ApeBHHe KHTaMltbi. no yTBep>KAeHMIO KM-
TaMCKoro eHoro B3HblOaHJI, MaTeMaTM'4eCKaM TeopMJt My3b1KH OAHO
BpeMJl6b1na BepWMHOM ApeBHeM TpaAHltHOHHOM KHTaMCKOM HayKM.
nJlTb OCHOBHblX TOHOB KHTaMCKOM neHTaTOHHKM cornaCOBbisanMCb
C nJlTblO 3neMeHTaMM, COCTaSnJlI014MMM CyTb MMp03AaHHJI.
ApeSHerpe'4eCKHe 4>Mnoco4>bI HCTO'4HHK «He6eCHOM MY3b1KH»
CBJl3b1BaJ1H C TeM, '4TO Ka>KAOe H3 He6eCHbiX Ten, HecytqeeCJI c rpo-
MaAHOM CKOtQCTblO CKB03b KOCMM'4eCKOe npOCTpaHCTBO, C03AaeT
cBoe06pa3HbI"M 3BYK. «KonHpYJI MexaHH3M» B03HHKHOSeHHJI 3BYKa
npM paCCe"leHHH npOCTpaHCTBa npyroM HnH ca6neM. B nOCJ1eAHeM
CJ1Y4ae 3BYK YCHnHBaeT pacceKaeMbiM B03AYX, a B nepBOto' - 34>Hp-
Hall nblnb.
B ApeBHeM KHTaMCKOM PYKonHCH - «KaHOHe» - npHBeAeHbI
TaKMe pac eHHII: «OnaHeTbi npH CBoeM spatqeHMM SOKpyr 3eM-
nM npOH3BOAJIT onPeA@neHHble 3BYKH. 3SYKM, OTnH'4alO14HeCJI APyr
aT APyra B 3aBMCMMOCT14 aT SenH\fMHbf, 6b1CTpOTbi ABH)t(eHHJI Ten M
MX yAaneM.,"... CaTyPH, HaM60nee YAaneHHaJl nnaHeTa (B Te AaSHMe
BpeMeHctC MTaJ1H, '4TO ConHe4HytO CHCTeMY COCTaBJ1J1IOT TOnbKO ceMb
nnaHeT. - npUM. asm.), AaBaJ1 caMbiM HH3KHM 3BYK. a JlYHa, 6nM-
>KaMWaJl nnaHeTa, - caMbiM SbiCOKHM 3BYK. 3TO 3BYKH ceMH nnaHeT
104
C/>oP M yn a «HO'IHOH cp eH»
B Ccpepe HenOABM>KHblX 3Be3A» (noA nocneAHMMM nOHMManMCb TaK-
>Ke C03Be3AHJI 30AHaKa. - npUM. OBm.). )
nH<J>arop (580-500 rr. AO H. 3.
He 6b1n MY3b1KaHTO ,HO MMeH-
HO eMY npMnHCblBaIOT:OTKpblTMe
MY3b1Kan HO-'4MCnOBOM AMaTO-
HH'4eCKOH.-'UlKanbl, KOTOpaJl no-
3BonHna eMY Mcponb30BaTb rap-
MOHHIO MyJblKM .KaK MaTpH4Y AnJl
rapMOHM'4HblX pa3AeneHHM Be-
U4eM H flBneHMM.
CamaCHO MCTOP.M'feCKMM AOt<y-
MeHTaM .. °KaK 3TO 6b1BaeT B >KM3HM
(0 '4eM nHwer A. C TMH B cBoeM
KHMre «npeBpaTHoCTH Hay'4HblX HAeM»), OTKpblTHIO n AWeCTBOBaJ1a
CJ1Y'4aMHOCTb. nH4>arop, npoxoAJI MHMO MaCTepCKoM MeAHMKa, yc-
nblwan 3BYKH pa3HOM TOHanbHOCTH. OH 3awen B MaCTepct<y1O H Ka-
Koe-TO BpeMJI Ha6nlOAan 3a
pa60TOM MeAHHKa, o eHHBaJl
rapMoHHIO H AHcrapMOHMIO
3BYKOB aT YAapa no MeTaJ1ny
pa3HblMM no Becy MOnOTO'4-
KaMM. AOMa nH4>arop YKpe-
nHn ABe 6anKM, a Me>KAY
HHMM Ha paBHblX paCCTOJlHH-
JlX HaTJlHyn eTbipe oAMHaKo-
Bble CrpYHbI, npHKpenMB k
HHM COOTBeTCTBeHHO Mono-
T0'4KaM Me,t\HMKa pa3ttble rpy-
&narOA8pt1 p83pa60T-
KaM nM4»8ropa, eBpo-
neHcKaR Ha}'Ka n01T}"u1na
ceMiIIWKaI1bHYIO MY3b1-
Ka1TbHO- iIIC1TOByJO CiIIC-
TeMY. 001Tee coaepwe+i-
HyJO no cpaBHeHilllO c
nRTHWKaI1bHOH KHTaMc-
KOH neHTaTOHIilKoH.
rapMOHMtI BOlCpyr Hac
PeaY1TbTaTbl C80HX HabiCKaHHH
nH4>arop nepeHec Ha OKP}')ICa-
lOl4yJO )KHaHb. Ha ee R8J1 HR H
npeAMeTbl. B noHCKaX B HHX
TatG1X )ICe CO'feTaHHH aCTeM OH
C Y 8J1eHHeM OOHapY*\iI1T. "ITO.
3T..,...c eTaHHR Ha,o.e1TRIOT
npeAMeTbi H RB1TeHHR rapMO-
HWiHblMH C80HCTBaMH
.105
fnasa 2
3bI. K nepBoM crpYHe nM4>arop npMKpenMn rpY3 BeCOM 12 4>YHTOB,
KO BTOpOM - 9, K TpeTbeM - 8 H K '4eTBepToM - 6 4>YHTOB.
3KcnepHMeHTHPYJl co 3BY'4aHHeM crpYH cBaeM My3b1KaJlbHOM KOH-
crpYKl4HH, nH4>arop 06HapY>KMn, TO B03HHKalOU4HM 3BYKaM CBOM-
CTseHHbI '4MenOSbie 3aKoHOMepHoCTH. npM'4eM nMWb TeM CO'4eTa-
HMJlM 3BYKOB, KOTopble 6b1nM rapMOHM'4HbI H npM1ITHbi Ha CJ1yx. Tat<,
cosMeCTHoe 3BY'4aHMe nepBoM H '4eTBepToM crpYH AaBaJ10 rapMo-
HM'4HblM MHTepSan OKTaSbI, nocKonbKY YABoeHHe Beca 6b1no pasHo-
CMnbHO KTY yKopo'4eHHJI crpYHbI HanonoBHHY. nepBaJl crpYHa
6b1J1a HaTJlHyTa BASoe CMnbHee '4eTSepToM - nonY'4aJ10Cb COOTHO-
weHMe 2 : 1, T. e. ABYKpaTHoe. Paccy>KAaJl M 3KcnepHMeHTHpY1I AaJlb-
we, nM4>arop ycraHoBMn, '4TO 3BYKM nepBoM H TpeTbeM crpYH npM
COOTHOWeHMM 3 : 2 AaIOT rapMoHMIO AHaneHAe, HI1H KBHHry. TaKYIO
>Ke rapMoHMIO AHaneHAe AaBaJ10 COBMeCTHoe 3BY'4aHHe BTOpOM H
'4eTBepToM crpYH. nM4>arop ycraHoBHlI H APyrMe 3aKoHoMepHoCTH
'4MCJ10BOM rapMoHMM My3b1KM.
.......... ............... .............
· n 4>arop npOC T8J1 MaTeMaT eCKYIO MOAenb CBoero
. HaMeH TOrO Tea7p8K7JfCa, KOTOpblH CTaJ1 Y rpeKoB Bep- .
: XOBHblM C MBonOM yH BepcanbHblx .C n npOL\eccoB ·
· COAep)k8J1 TeQJ)M1O MaTeMaTM eCKoro np nO)l(eH R K RB-
. neH RM np po.ilb' 'f8CTOT MY3bUC L\BeTa. MOAenb npeA-
· CTaBnRl1a co60H c MBon ecKYIO n paMH,IJ,Y, 06pa30BaH-
. HytO 3 :rO'4eK M nej:JBblx eTblpex '4 ce.A 3neMeHT8pHoro
· ti}'Me 'feCKOrO pR,D,a - 1, 2, 3 4. 3m 'f cna B pa3-
· HbiX CO'feTaH RX A8BaJ1 rapMOHM OKT8BbI, AHaneH,D.e
. AHaTeccapoH.
106
«AnJl nM4>aropa My3b1Ka 6btna npOM3BOAHOM aT 60>KeCTBeHHOM
HayKH MaTeManIKM, ee rapMOHM >KeCTKO KOHTponMpOBaJ1HCb Ma-
TeMaTM eCKHMM nponOPLtHIIMH, - nHweT Xonn. - nHd>aropHMI4b1
yTBep>KAaJ1H, '4TO MaTeMaTMKa AeMOH-
CTpMpyeTT0'4HblM MeTOA, KOTOpblM 60r
ycraHOB n H yTBepAHn BceneHHYIO.
4MCJ1a. CJ1eAOBaTenbHO, npeAweCTBY-
lOT rapMOHMH, TaK KaK HX HeH3MeHHble
3aKOHbI ynpaBnJlIOT BceMH rapMO-
HH'4HblMH npOnOPLtHJlMH. nOCJ1e OT-
KpblTMJI rapMOHM'4HblX COOTHoweHHM
nM<J>arop nOCBJlTMn CBOHX nocneAOBa-
TeJleM B 3TO Y'4eHHe KaK B BblcwyIO TaM-
HY CBOHX MHCTepMM. OH pa3Aenlln
MHO>KeCTBeHHble '4aCTH TBOpeHHII Ha 60nbwoe '4HCJ10 nnocKoCTeM HnH
c4>eP, Ka>KAO H3 KOTOpblX npMnHcan TOH, rapMOHH'4HblM HHTepBan,
HCJ10, MMII, I4BeT H 4>OPMy».
nH4>arop HaCTonbKO pa3BHn CBoe Y'4eHMe, '4TO ycTaHoBHn '4 C-
nOBYIO rapMoHMIO CooTHoweHHM Me)f(,t\y nnaHeTaMM, c03Be3AMJlMH
M 3neMeHTaMH MHpo3AaHH . nH4>aropMMcKall WKona CYU4eCTBoBa-
na cBblwe 200 neT - VI-IV BB. AO H. 3.
B My3b1KaJ1bHO-MaTeMaTM'4ecKoM nnaHe nM4>arop paCCMaTpHBaJ1
BceneHHYIO KaK rpOMaAHeMwylO MOHOXOPAY C CMMBOnM'4ecKoM OA-
HaM crpYHOM, npMKpenneHHOM BepxHHM KOH140M K «a6COnIOTHOMY
A'JX'P He6ec, a HH>KHMM - K TsepAH 3eMnM. TaKMM 06pa30M, Bo06-
pa>KaeMaJl CTpyHa 6b1na HaTJlHyTa Me)f(,t\y He60M M 3eMneM. Cornac- -
HO rapMOHM'4HOMY MY3b1KaJ1bHO-'4MCJ10BOMY CooTHoweHMIO, nM4>a-
rop AenHn MOHOXOPAY Ha 12 '4aCTeM H Ha 3 Cct>ePbl. BepxHJIJI c4>epa
OrpaHH'4HBaJ1aCb-Hf:nOABH>KHblMM 3Be3AaMM c03se3AMM H 6b1na Me-
C/)opMyna «HOI.IHOH cpeH»
He UMeTKy
Y B MY3b1KY leaK
T04HyIO YKY, nH<I> -
rop npMMeHHn H8 -
AeHHbIe MM 38KOHbI
raPM<>HM ecKHX OTHO-
weHH KO BeeM <l>e-
HOMeHaM "PMPOAbi.
107
rnasa 2
Puc. 6. n PM",clW cxeMa Ccl>ePbI MeJKAY He60M M 3eMJ1eM.
npeACTaBJIeH MOHOXOPAOM KaK ABoMHU OKTaaa. nOKa3b1BaIO-
-.aa A8e KpaMHOCTM eCTIOBaHMJI raptllOHMM. (OIlH e.
BwcCNaiauee He60 .. 3eMIt MMelOT oAMHaICoBbiM TOH, pa1J1M"ao-
IIMiCJI.RMWIt no BblCOTe ("3 KHMrM ..nYAAi «3eMHU M}l3b1Ka»)
108
C/)oPMYna «fIocIHoiI cpe..
CTOM 06MTaHMIt «6ecCMeprHblX AYXOB» (pMC. 6). B cpeAHei c4tePe
6W11M Ha60pbl CTMxadi (rpe'feCKMe cI»tJIococl»w BWAeJUUlM 'feT11Ipe
3.neMeHTil MMpo3AaHMJI: O b, Bo3AYX- BoAY M 3eMJIao) M HeT,
CpeAM KOTOpWX COnHL\e KaK 6w 6wno CpeAMHHOM OCWD IOCMIf'IeC-
KOro xopoBoAa nnaHer (nOpItAOK pacnOnO>Ke,.HMIt Matter Ita
xOPAe: Ca1YPH, IOnMTep, Mapc, ConHL\e, BeHe.ea- Mepltypd, J1yHa).
HtOKHlt1t c4>epa COOTBeTCTBOBaJ1a 3JleMeHrcu '3eMMoiil '1'8epAM.
npeACTaBneHMe m. ropMML\eB a MY3WKaJ1bHo- CIIOBOi crpyI(-
'type BceneHHoM nepe,qaeT cxeMa cJ»nYAAa C ero AOOOllHeHtUl.... (pMC.
6 M 7). PMC. 6 AeMOMCtpMP)'eT pa3BMTMe COCTOItHM" 3JIeMetfTOe .
COOTBeTCTBMM C TeOpMeM ytt..BepcanbHoi My3b1KM. B Hei MOttOXop-
Aa C<J>epbl Me*AY He60M M 3eMeM paCCMaIpMBaeTa ICaJC ABOiHaR
OKTasa. nepeAilO1qaIt ABa lCpaMHMX aapMaHTil IUI rap-
MOH"M. COnHL\t!, Bwco'faAwee He60 M 3eMIt B cxeMe ..MeliM DAMita-
KOBbI.. TOH, pa3J1H'4alOU4....CJI nMWb no BbfCOTe. HM)KtfAJI OIffiIBa -
aT Cl»a AO Conb - OXBaTblBaJ1a Ty '4aCTb 8ceJleHHo B Karopoi cy6-
CTaI:fL\MIt npeOOnitAaJ1i HaA 3HeprMei. Ee rapMoHMa npoRBIIJIe1CI
Jtp'le, '4eM B BblCwei OKTaae - aT Conb AO Conb, rAe 3ttepnU1 npe-
06naAaeT HilA cy6craHLtMeM. no MHeHMIO ClJnyAAa, 3B}"IaHMe eepx-
HeM, AYXOBHOM '4aCTM MOHOXOPAbi AaeT Be'4HYIO >KM3Hb, a HMJOtei -
MaTepManbHYIO, BpeMeHttylO.
CamacHo cxeMe ytTpOMCTBa MMpa no tPnyfJJJ.Y, 3neMetmi npMpo-
AbI M nnaHeTW HaxOARTCJI B rapMOHMM He6ecHbiX CU3eM.
Cl»11YAA C'4MTaJ1, 'fTO 3J1eMeHTbI MOHOXC>pAbl MO)l(HO COOTHeCTII C co-
CTOfIHMeM nlO6wx ltB11eHMM M aetqeM. no 4>1MJI1:f, nlO6oM 3IIeMeHT npII
Ka'feCTBeHHOM "3ttepreTM'feCKOM npe06pa308aHMM MC»KeTI1QAHMMiJJ1r
CJI aT HM3we (MaTepMaJlbHOro) AO BblCwero (3HepreT'M'teClCOf'O) co-
CTOItHMIt, npoxOAJl Bee ABa C nonOSMHOM TOHa. 06pa3Yt!MwM npM :JTOM
,qMaTeCCapoH etTb rapMOHM'4ecKMM MHTepeal1 pa3BMTMJI 3IIeMeKTOL
109
rnaB8 2
EenM cl>MoneToBbiM BeT
Tpe6yeT 800 TpMnnMoHoB
BH6paLtMM B CeKYHAY, TO
KpaCHbiM - 400 TpHnnHO-
HOB. KaK BHAHM, C06nIOAaeT-
ell 3aKOHOMepHOCTb YABoe-
HMJI '4aeTOT BH6pa4MM Ha
KOHLtax WKaJ1 KaK 3BYKa, TaK
M 4BeTa. YABoeHMe npOMCXOAMT '4epe3 Ka)I(Abie ceMb «cryneHeM»
WKaJ1b1 aT MCXOAHOM cryneHM. 6e66HT nHweT: «KorAa 3aKaH'4HBa-
eTCJI OAHa MY3b1KaJ1hHaJl OKTaBa H Ha'4MHaeTCJI APyras, C BH6pa-
JlMM B ABa pa3a 6ynbwMMM, He>KenM B npeAblAYU4eM OKTaBe, Ta
>Ke caMaR tiOTa nOBTOpJleTCJI B 60nee TOHKOM WKaJ1e. B TO BpeMR
KaK BMAMMaft '4aCTb cneKTpa 3aBepWaeTCJI 4>HoneToBbiM 4BeTOM,
APyrMe OKTaBbi HeBMAMMblX LtBeTOB C YABoeHHblMH BH6pa4HJlMM
npOAOn>KalO no TOMY >Ke 3aKOHY».
Ka1IrAwA 3 eTbipex OCHOB-
HbiX 3neMeHTOB np POAbi
<J>ny.AA npeACTaBWI KaK TP
nOAP83,O.el1eH A WI AB8
C n0I10B HO MY3b1K811bHblX
TOHa (J»1c. 7).
Ha 38M8Ttcy
3. 6eOO T B KH re «np H -
Obi CBeTa '-'BeTa» np BOAl-1T
CI10Bble COQTHOweH A ceM
HOT '-'BeTOB. TaK.....CI1
ceAbMaA, BblcwaA HOTS C
TpeOyeT A11A Bocnpo 3BeAe-
IoMA 48'a..opa,-, B ceKyH,Ay,
TO HOTS IJ,o - H )I(HAA B WKa-
ne - poBHO nonoB HY-
24 B Opa,-, .
Ha OCHOBe M3Y'4eHMJI 330-
TepM'4eeKOM 4>Hnoeo4>HH "
BOCTO'4HOM CHMBOJ1MKH Ene-
Ha 6J1aBaTeKaJI TO>Ke COOTHo-
CHna LtBeTa C «ceMepHOM
KOHCTpyK4HeM '4eJ10BeKa» M
cera WKanOM BOCnpMJlTMJI.
CeMb rapMOHH'4eCKMX HOT
4>HJ10eo4>bf Mcnonb30B nM
KaK MepHno.
HMeHa rnaBHblX 60roB
TO>Ke 06pa30BblBaJ1M H3
ceMH nJ1aHeT (cenTHHepOB),
110
C/)opMyna «HOI/HOM cPeH»
PUC. 7. nOcrpoeHMJI npMpOAbI e Men0J1b30BaHMeM eTblpex OCHOBHblX
3JIeMeHTOB cxeMbI MOHOXOPAbI. 3J1eMeHTbI pa3AeneHbI Ha ABa
c n0J10BMHOM MY3b1KaJ1bHblX TOHa. Ka>K,qblM 3J1eMeHT AJlJI
AOCTM>KeHMJI rapMoHMM AOJ1>KeH McnblTaTb CMMBOJ1M eCKMe
npe06pa30BaHMJI, npOXOAJI CHM3y BBepx Bee 2,5 TOHa -
AMaTeccapoH (M3 KHMrM J1YAAa «3eMHoM MOHOXOPA»)
111
rnBBB 2
a l4epKOBttyIO My3b1Ky CBJl3b1Ba11H C ceMblO nnaHeTapHblMH rapMOHHJlMM.
Ta enumnte OrpaHH'4HBa11H CBOH CBJI eHHble necHH ceMblO nepBH -
HblMH 3syKaMH, 3anpeU4C!JI npoH3HOCKTb HHbte 3syKH B xpaMe. MHorHe
crpyHHble HHCTpyMeHTbI, Ha'4HHaJI OT ApeBHHX H KOH'4aJ1 cOBpeMeHHblMH,
HMeIOT ceMb CTpyH (HanpHMep, ceMHctpyHHaJI rMTapa).
CeMHWKanbHaJl CHCTeMa Mcnonb30BaHa B «3Be3Ae MarOB» - ce-
MHJ1Y"IeBOM 3Be3Ae, JlBnJlIOU4eMCJI OCHOBOM oKKynbTHbix nocrpoeHHM
cpeAHeBeKoBoM acrponorHH M HYMeponorHH. Ha Ka>KAOM nY'4e «3Be3-
Abi MarOB», KOTOpaJl JlBJ1J1eTc.JI OCHOBOM oKKynbTHbix nocrpoeHHM, ca-
maCHO nM4>aropMMCKOMY My3b1KanbHO-'4HCJ10BOMY Y'4eHHIO, 6b1J1 CO-
OTBeTCTBYIO HM CHMBon HOTbi H nnaHeTbi (pHC. '8). B Te AaBHHe
BpeMeHa COOTHOCHMOCTb LtBeTa, HOT H nnaHeT no ceMHWKanbHOM
WKane 6b1.J1a CJ1eAYIOU4eM:
KpaCHblM, AO - IOnHTep;
OpaH>KeBblM, pe - Mapc;
>KenTblM, M" - COnHl4e;
3eJ1eHblM, a - MepKypHM;
'tMCIIO 7
CeMb HOT CpaBHa.fBaJl.., c
ceMbIO r11aBHblM.., opraHaM..,
enOBe eCKoro opraH..,3Ma,
KOTopble 06ecne aIOT
eMY rapMoH..,1O )K"'3H..,. C
nnaHeT ..,-cenT"'HepaM"'.
c ceMblO OCHOBHblMM eTa-
M.., PaAyr..,. c ceMblO AHRM..,
HeAen.., .., T. A.
rony6oM, conb - BeHepa;
CMHMM, n1l - nYHa;
4>HoneToBblM, CH - CaTYPH.
CpeAM CenTHHepOB 3aAalO-
U4eM nepBblM My3blKanbHblM TOH
nnaHeTOM C'4HTaJ1CJllOnHTep: B
cpeAHeBeKOBOM nH4>aropHMC-
KOM y eHHH a MY3b1KanbHOM
npHHLtHne nOCTpoeHHJI Bce-
neHHoM C IOnHTepa Ha'4MHanaCb
OCHOBHaJl - Ma>KOpHaJl -
raMMa.
B COOTBerCTBHH C ceMH-
wKanbHo" cHcTeMoM pa3Ae-
neHMH BH6pa4HM KpacHbiM
112
BeT, JlBnJlJlCb HaMHH3WHM
TOHOM B LtBeTOBOM WKane, CO-
OTBeTCTByeT nepBOM HaTe MY-
3b1KanbHOM WKanbl-- HCTe
Ao. no aHanorHH COOT BeT-
CTBHJI BeTa H TOHa pacnpe-
AeneHMe HMeeT TaKOM BMA: aT C tt
OpaH>KeBOrO BeTa -- HOTa
Pe M, KaK nepe'4 CnJlnOCb
Bblwe, AO 4>MoneToBoro Be-
fa - CH. BOCbMOM BeTOBOM
TOH, rpe6yeMbiM AJlJI 3aBep-
WeHHJI O eHO'4HOM WKanbl,
AOn>KeH HaxOAHTbCJI B 60nee
BbiCOKOM OKTaBe. TpH 4>YHAa-
MeHTaJ1bHble HOTbi MY3b1KaJ1b-
HaM WKaJ1b1 -- nepBaJl, rpeTbJl H nJlTaJl (Ao, MH H Conb), no npeA-
CTaBneHHIO nM4>aropHMLteB, COOTBeTCTBYIOTTpeM nepBH4HblM LtBeTaM
p rM: KpacHOMY, >KeJ1TOMY H rony6oMY. 3TH nepe'4HCJ1eHHble TOHa
M BeTa OHH C'4MTaJ1M «C.aMblMM COBepweHHblMM».
nOCJ1e OTKpblTHJI OCTanbHblX nllTH nnaHeT COnHe'4HOM CHCTeMbI,
06U4ee '4HCJ10 KOTOpblX (BMeCTe C CenTHHepaMM) cocraBHno 12, npeA-
CTOllno nepepacnpeAenHlb Bon HOBbie COOTHOWeHMJI Ha MY3b1KaJ1b-
HbiX cTyneHJlX WKaJ1b1. AnJl :nOM LtenH 6b1nH H36paHbI raMMbI, HCJ10
KOTOpblX MMeHHO 12 M KOTopble no '4MCJ1Y paHee COOTHOCHnM co 3Ha-
KaMH 30AHaKa. CeMMTOHaJ1bHblM PJlA OLteHO'4Hoi4 WKaJ1b1 oM4>aro-
pMMCKOM MY3b1KanbHO-'4MCJ10BOM CHCTeMbi 6b1n pa3ABMHyT TaK. '4TO-
6b1 Me)l(J\y CenTMHepaMM MornH pa3MeqHTbcJI BHOBb OTKpblTbie
nnaHeTbI: .
t:PopMyna «HO'-lHOH cpau»
ped'
<!>a
I1R »
9 COl1b
PUC. 8. 3Be3Aa MarOB
(My3 KanbHo- HcnOB MarpH4a)
AJ1J1 nOMCKi rapM"''4HblX
COOTHoweHHi4
113
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· An cornac0B8H.... 3H8KOB 3op,11t8K8 co WKanOH Bllt6palU't....
. ,QpeBH....M aCTponoraM .... <S>....noco<l>aM np....WnOCb paCW....- .
: p....Tb eTOByJO WK811Y. KOTopast ....Men8 TaKO" BII\Q,:
· lJ.o - KpacHblH: ""CTO-KP8CHblH eT - OBeH. Y; KpaC- ·
. HO-opaH)KeBblH - Tenelt, b'.
· Pe - OpaH>KeBblH: McTO-OpaH>KeBbiA - 6n....3Heltbi. ]I;
· opaH)KeBO->KenTblH - PaK. €9.
MM - >KenTblM: ""CTO->KemblH - J1ea. Q; >KenTO-3ene-
HblH -lJ.esa. ytp.
. <!>a - 3eneHblH: IItCTo-3811eHblH - Becbl. ; 3eneHO-rO- .
: ny60H - CKopnMOH. T11.,
· Conb - rony60H.
. J1 - C....H....ft: IItCTO-CMHMH - CTpenelt. I; cMHe-cpMone-
· TOBbM - K03epOr, ii5.
· CM - <S>M0!1eTOBblM: CBeTl10-<S>MoneToBblH - BO,Q,oneH. =; ·
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........... ... ... ... ...... ..... .... ...
Me>KAY IOnHTepoM ( ) M MapcoM (d') BCTaJ1 nnyTOH (ffi, t );
Me>KAY ConHLteM (0) M MepKypMeM ( ) - BynKaH, HnM XMpOH;
Me>KAY MeJ>KY1*eM M BeHepoM ( ) - npo3epnMHa, MnH pepa (J!I).
nOCKonbKY, no .reopMM 14Y3b1KH, pOACTBO raMM onpeAenJleTCJI
no KBMHTOBbiM COOTHOWeHHJlM, npMBeAeM KBMHTOBbiM PJlA nna-
HeTapHblX CooTHoweHMM TOHanbHOCTeM no C. utenaHoBcKoM M
B. BeTaw (1991), ymy6neH.Ho M3Y'4aBwMM 3Ty np06neMY (Ta6n. 1).
He TOHaJ1bHOCTM MOryr6blTb Ma>KOPHblMM M MMHopHblMM, 'lTO mpa-
>KaeTCJI Ha MY3b1KanbHOM 3Ha'4eHHM MaHer. Tat<, B Ma>KopHOM Kpyre r1ny-
TOH MO>KeT nonacTb B o6nam Mapca MnM IOnKTepa (eM. Ta6n. 1), a B MK-
114
C/>opMyna «HOI/HOM cpeH»
Ta6nu".a 1
KIIMHTO.we nnaHeTlpHble COOTHOWeHMJI
-COOTHOWeHMJI nnaHeT " HopHble
Ma>KopHble (OilHe'4HOM CMCTeMbi
TOHanbHOCTM l4cnOBOM KOA - nnaiieTa TOHanbHOCTI4
CenTI4HepOB 12-TI4 PI1aH T
Ao 5 ....:. IOnl4Tep .,. - CarypH.
(onb 6 - BeHepa 22 - npo3epn14Ha
Pe 3 - Mape 10 - nnyroH
nJl 2 - nYHa 8 - YpaH
MI4 1 - (onH4e 1 - (on....e MI4
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cJIa 4 - MepKYPMM 4 - MepKYPI4A-.., OIa
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nJl 2 - nYHa 9 - HenTyH J1It"
HOpHOM - T011hKO B c4Jepy IOmfTepa. Pa31IH'4Me Me>KAY Ma>KOpoM M MM-
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BenM K TOMY, o B 12-ayneH'4aroM raMMe JlnymHy COO113eTCTByIOT cpa3y
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115
rnasa 2
M3 MHOf1D( B03MO)l(HWX npMMepoB npMBeAeM OA"H: OKa3blBaeT-
a. aoicrBa MHOI'MX 31IeMeHTOB B pa3JI"'4HWX BeU4«f8aX HaXOAftT-
a II Of1peAeneHHOM "Mcn080M rapMOH...., COOTHOCMMOA C MY3WKaJ1b-
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BOCXONiUteM B 3aBMCMMOCTM OT aTOMapttwx BetOB, TO, no A. HillO-
neHAY, a 'feM ynoMMHaeT M3KnM n. XOM (1992), Ka)l(AwA BOCbMOA
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HOi xMM.... 31'0 MMeHyeTCJI 3QKOHO OKmOBhI.
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yMWIIIIeHHO BWpa)l(aeT My3b1KaJ1bHWM conpo80)t(AeHMeM (npo ce6
MJI. IICJIyX HaneBa MeJ1OAMIO): 310 6paaYPHaJl, Ma OpHaJI My3b1-
COOTBeTCTBYlOl14a YAa'fe M xopoweMY HacrpoeHMIO .nMOO rpyc-
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pOlan HaCTpoeH..e, nOBWCMTb CTOMKOCTb 8 npeOAoneHMM
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3tteprttJl My:uiKaJ1bHblX PMTMOB peryn..pyeT YBCTBa KaK nM'4HOC-
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tta CTaAMOHe), nOMOfaJI 8 3M 0-
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p&3IWIHbI8 CO&teTaHMR lUi8-
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116
4>opMyna «HolIHC:»f cpe.r»
Co3BY'tMe ccMY3blKM KaMHII»
M ccnyttHOM COHaTbl»
no onMcaHMtO ApeBHerpe ecKoro MCTopMKa fel>OA. Ta (484-
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XanAebMM 3MKKYJ)CIT - acrpoHOMM'feCKaJI 6aWtUI 60ra He6a - 8
60pcMnne OOAHMMaTlOt CeMbtO aynettJIMM: KaJICACU' CTyneHIt6wMOIt-
pawetta B qBeT COOTBeTCTBylOU4eM MatteN cenTMttepa.
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COOJJYAIUI$>HTaH M3 ceMM ypoBHei 8 COOTBeTCTBMM C '4MCJ1OM cen-
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4MaJ1ItH...'" KaHanaM, M3ro-
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M nnaHeTaMM CeflTIlHepa. 8
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117
rnasa 2
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Bpa'4, 4>Hnoco4>, aCTpOHOM M aCTponor H6H CHHa (980-1037) pa3-
BMn H HcnOnb30BaJ1 B CBoeM ne'4e6HoM npaKTMKe npeACTaBneHHe
ApeBHMX a «A06poM» M «3J10M» BM6paL(MM BonH LtBeTa, HanpHMep
Mcnonb30BaJ1 KpacHbiM LtBeT npM ne'4eHHM MH4>eKLtHOHHblX 60nb-
HbiX KaK CTMMynJlTOp HMMYHHTeTa M KpOBH: KpaCHYIO OAe>KJJ,y, Kpac-
Hble 3aHaBeCKM Ha OKHax H T. A.
B MYJblKaJ1bHOM rapMOHHM nM4>aropMML(bI OTAaBaJ1H npeAnO'4Te-
HMe CTpYHHboIM MHCTpYMeHTaM no cpaBHeHMIO C AYXOBblMM, C'4MTaJl,
'4TO CTpYHHble MHcrpYMeHTbf 3aTparMBalOT B03Bblwe ble '4aCTH
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AaeT, a cnoK«ti;HaJl MYJblKa CTpYHHblX MHCTpYMeHTOB ycnOKaHBaeT.
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KOTOpblM nbJlHblM nOM HnC1I B AOM CBeeM nOAPyrM H, cropaJl aT peBHO-
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neKO aT :noro MeGl1fH Mrpan S036y>KAaIOUWIO 4>PHrHMCKyIO My:JblKy.
nM<J>arop yroBOpMJ1 cImt,IhMCTa H3MeHMTb MenOAMIO Ha cnOKOMHYIO H
npMJITHyIO, TO OKa3aJ10 ycnOKaHBalOl.qee AeMCTBHe Ha nbJlHOrO 6yJl-
Ha: OH c06pan XBOpoCT H nowen AOMOM.
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TaBWHM, '4T0 My:JblKa, KOTopa" 06naropa>KMBaeT YM, ropa3AO 60nee
BbiCOKHX nOpJlAKOB, He>KenH My:JblKa, anMJ1HpYIOU4aJl K YBCTBaM.
OH CO BeTa Ban MrpaTb 60APble M >KHBble MenOAMH AJlJI My>f<'4MH M
118
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Ae>KH.
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cne MaJ1bHW< 3BYKOBbiX 3anax.
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HepBbI... (nIOAH) CHnbHoor-
paHH'4eHbI CTeHaMM, ccopY-
>KeHHhlMH '4YBCTBeHHblMM
BOCnpMJlTHJlMH. HawH 3HaHMJI
a csere He nonHbl, HO eCTb H
BOBce HeH3BeCTHbie (HaM)
4>OpMbI cseTa, AnJl KOTOpblX
HeT OnTH'4ecKOro 3KBHBaneH-
Ta. 4enO}3eK OKpy>KeH CBepx-
"IYBCTBHTenbHOH BceneHHOM,
TaAHbI HSYKM
ECTb &>1Cl1eHH e (.tBeTa,
KOTOpble Mbi He Mo*eM B eTb;
TaK *e, Kal< &>1 3BYl<H, KOTop e
Mbi He Mo*eM CI1b1WaTb; 3ana-
>G1. KOTopble Mbi He Mo*eM
o6oHRTb;apoMaTbI,KOTopble
He MOfYI- 6b1Tb aM&>1 nonpo6o-
eaH ; cy6cTaHlU1&>1. 1<0TOpble He
MOryT 6b1Tb OIJ..tYll.\8eMbi.
120
B03AeHcrBMJI 3Hepr.... nnaHeT,
BeTa H MY3b1KH. HaH60nee y,qa -
HaJI c creMa OCHOBaHa Ha :laKa-
He OKTaBbI, ycTaHaBnHBalO eM
paMKH BOCnpHJlTHJI. Haw CJ1yx
MMeeT60nee WMpoKMM AMana30H
'faCTOTHbiX BocnpHJtTMM, 4eM 3pe-
HHe.
TaK, yxo MO>KeT perHcTpM-
pOBaTb aT AeBJlTM AO OAHH-
HaA aTM OKTas, TOfAa KaK
rna3 BocnpHHHMaeT TonbKO
ceMb 4>YHAaMeHTanbHblX Be-
TOSbiX TOHOB. OTMentM, '4TO
npaKTH'4eCKaJl AeJlTenbHOCTb
'4enOBeKa B OCHOBHOM nOCT-
poeHa Ha.3pHTenbHOM BOC-
npHJtTHH HH4>opMa MH - AO
80 o H 60nee ee 06lqero no-
TaKa. 4MTaTenb, 8epOJITHO,
06paTHn BHMMaHMe, '4TO '4eno-
BeK 6YAeT HMeTb MOlqHblM- pe-
3epB AnJl CBoero MHTenneKTyanbHoro pa3BHTHJI, ecnH CMO>KeT HC-
nonb30BaTb CBOM cnyx TaK >Ke aKTMBHO, KaK 3peHMe.
C. l!\enaHoBCKafl M B. BeTaw nMWyT: «AcrponorMJt M MY3bfKa -
ABe BeTBH Kynbrypbl, KOTopble HaM60nee flCHE> H HenocpeACTBeHHO
onHCblBalOT Hawy nCMxMKY: MY3b1Ka - KaK HCKycCTBO, acrpono-
rHJt - KaK JiaYKa. n03TOMY MY3b1Ka MO>KeT CJ1Y>KHTb xopoweM MJ1-
nlOCTpa HeM Taro, KaK OTpa>KaIOT AYwy pa3Hble acrponOrM'4eCKHe
CPopMyna «HO'4Hofr cpew
OKKYnIlTM3M
, lI'fepa M ceroAHw
y'4eH....e cp....noeo<S>oB npo-
wl1oro 0 TOM, TO -
Ka/1bHble cOOTHoweH....R
npH110)t(HMbI K nl1 HeT8p-
HOM C&4cteMe nOCTpoeHHR
H pacn0I10)t(etP.11O nnaHeT.
6b1J1o np....HRTO H pa3B&4TO
COBpeMeHHblMH acTpol10-
raMH H HyMepoI10r8M.....
B03HMPlO He06b1'-fHoe Ha-
npaeneHHe aCTp rHH :-
aCTponor.......ecKoo My3b1KO-
BeAeH....e. B OCHOBe KOTopo-
ro ne>KMT K....TaMcKoe H n -
<l>aropHMcKoe eHHe 0
MY3b1KanbHO- ....CI10BOM
rapMOH....H c<I>ep. npHpo,Abl
H KOCMOC8.
121
rnaaa 2
nCMXOTHnbl, KaK OHM BHAJlT, TO'4Hee, CJ1bIW8T ee. AcrpoJ10n'WMO)f(eT
nOMO'4b pa306paTbCJI B TOM, nO'4eMY pa3Hble KOMn03HTOpbl, HCnOJ1-
HMTeJ1H, AHpM>Kepbl M npoCTO nlOAH CJ1b1WaT AYWY HMeHHO TaK» (Ae-
TponorH'4eCKOe MY3b1KOBeAeHHe, c. 116).
3 MB ropocKonbi 57 M3BeCTHbiX KOMn03MTopOB KnaCCH'4eCKOM
MY3b1KH, l1tenaHOBCKaJl H BeTaw (1991) 06paTHJ1M BHHMaHHe Ha TO,
'4TO HaJ1M'4Me B ropocKone onpeAeneHHoro CO'4eTaHMJI nnaHeTap-
HbiX CKonneHMM B 3HaKax 30AMaKa, a TaK>Ke caM 3HaK 30AHaKa, nOA
KOTOpblM pOAMnCJI KOMn03HTOp, OTpa>KaIOTCJI Ha MY3b1KanbHOM TO-
HanbHOCTH ero npOH3BeAeHMM.
HanpHMep, POAHBWHMCJI nOA 3HaKOM Pbl6b1 6anaKHpeB npeAn0'4H-
Tan TOHaI1bHOCTb 3TOro 3HaKa - HOl)' eM. BHBanb,O,M B CBOHX npoH3Be-
AeHMJIX J1I06W1 MCn0J1b30BaTb TOHanbHOCTb Conb, 'ITa CBJl3b1BaIOT C CWlb-
HbiM nOnO>KeHMeM B era ropOCKone BeHepbl, ynpaBnJlIOU4eM 3TMM
My3b1KaT1bHblM TOHOM. B ropocKone Mo pTa CWlbHoe nOnO>KeHHe ]a-
HMMaI1 Map<: - 31MM 06 eHJlIOT TOT $lKT, 'ITa nO'lTM nOJ1OBHHa npoH3-
BEW!HMM seAtbcoro KOMn03KTOpa nocrpoeHa C TOHaI1bHOCTbIO Per «CO-
3By'4HoM» MaHeTe Mapc;'
MHTepecHWM 4»aKT
Korp,a PO)I(JJ.eHOO peOOH-
Ka npoMCxo B MeCTe,.
Ha KOTOpoe B 310 B
npMXO.D.HTCSI npoel<1.4HSI
«MY3bI\CB1IbHOM» nJ18HeTbl,
TOK CW1bf
Cnoco(5cTBYK>T po)I(JJ.e-
H IO KOMnoo opoB.
60nbwe Beero po>KAeHMIO KOM-
n03HTopOB enoc06CTBYlOT 3HaKH:
CTpe.nel4, 3aTeM - Pbl6b1, Ha rpe-
TbeM MeCTe - TeneLt. 3aMe'4eHO,
'4TO caMbie H3BeCTHbie AMpM>Kepbl
poAMnMcb nOA 3HaKOM OBHa (Kapo-
JlH, TOCKaHHHH MAP.). PO>KAeHHIO
AHpH>KepOB 6naronpHJlTCTBYlOT
3HaKH 30AMaKa aT Pbl8 AO nbBa, a
6onbwMHCTBo M3BeCTHbiX neBLtOB
KnaCCH'4eCKoro CTHnJl McnonHeHHSI
122
cJ>opMyna «HO&/HOH cpeH»
.....-................................ .
.
· 6b111a o(5HapY)l(eHa rapMOHHR HCI10BblX COOTHOWeHHH ·
: Me)l(,D,Y MY3b1KOH, L.U5eTOM, 3H8KaMM 30 aK8 H nnaHeT8- .
: ' MM. HTepeCHO, TO oe TaKoe 'fHcnoaoe coo owe- ·
· HHe B OTAenbHOCTM BbI3b1BaeT Y 'fenOBeKa C03BY"....e-'CBOe- ·
. ro 3neMeHTa. HanpHMep, HOT8 Pe Bbl3b1BaeT O eHHe .
· 3HeprHH KpacHoro L.U5eTa; 3HeprMA IOnllJepa - ycW1MBa- ·
· eT BOCnpMRT\1e HOTbi Ao M T. A. npM eM 3Ta ()I:OOeHHOCTb ·
. HaWeH peaKLl.HH Ha «r8pMOHH Hoe HCnO. BpO)l(,D,eHHaA. .
· npMBe.o.eHH8A M3«5MpaTenbHOCTb aocnpHAT\1A 3HeprMH, KaK ·
yrsep)l(,D,alOT tiyMeponOrM I npoABnAeTCA y>Ke C po)t(A8HHA. ·
. CKa3b1BaACb Ha HBWeM BOCnplo1RTHM 101 MblWneH....M.
POAM.nHCb nOA 3HaKaMH 30AMaKa, Ha'4HHaJi aT BOAoneJl M KOH4aJl
IlbBOM (npM ABH>KeHHH no 3HaKaM ropocKona no '4aCOBOM CTpeJIKe).
CpeAH «MY3b1KanbHblX» 3HaKOB 30AMaKa Ol.leHb npHMe'4aTeneH
3HaK Pbl6b1. CTpOnOrH'4eCKHe HCCJ1eAOBaHHJI nOKa3aJ1H, TO nOA
3TMM 3HaKOM pOAMnMCb KOMn03HTopbl, COCTaBHBWHe OCHOBY
MHpOBOM MY3b1KanbHOM KnaCCMKM: BMBanbAM, TeneMaH, feHAenb
M APyrHe.
3HaK Pbl bI 3aBepwaeT 30AHaKaJ1bHblM PJlA «COTBOpeHHJI"IenO-
seKa» BblCWHM Pa3YMOM. B 3aBepweHHM «TBOp'4eCKOrO LtHKJ1a» MC-
nonb3yeTCJI Ha60p nM'4HOCTHbiX '4epT M AOCTOMHCTB, KOTopble He
6b1J'1H BOnnOlijeHbI B nM'4HOCTJlX. POAMBWHXCJI nOA npeAblAYI14MMH
3HaKaMH 30AHaKa. no npeACTasneHMIO aCTponorHM, nepBble ABe
tpeTM3HaKOB30AHaKa«pa36HpaIOT» JlCBOMx«nOAOne'4HblXAYW»
(AYWM, KOTopble 6yAyT peMHKapHMpOBaHbI B Tena AeTeM, POAMBWHXCJI
nOA 3THMH 3HaKaMM) HaH60nee aKTHBHble. «60M OBCKMe» Ka'4eCTBa.
123
rnasa 2
JlocneAHMM 3HaKaM 3oAMaKa, B acTHOCTM Pbl6aM. AocraeTCJI OcraB-
WMb HaOOp MeHee MHMU,Ma BHWX M arpecCMBHbIX AJ1" >KM!HM Ka-
'4ecTB. f103ToMy Pw6w alqe AOBOJlbCfBy1OTCJI reM, 'fro caMO nonw-
eT MM B pyltM, MWByT, KaK pw6 no Te'4eHMIO >KM3HM, MCnonb3YJI
roTCBDe. HO aKTMBHO «nepepa6aTwBaJt» ern. nocne.qHee OHM MOryr
M CoeepwaTb Hb AAJKe YACt'4HO, 06roHJ'" Ha CKPYfblX ooBO-
poTax JKM3HM» HeKOTOpbIX nlOAeM, POAM8WMXCJI nOA 60IIee «arpec-
CM8HblMM .. MHMu,MaTMBHblMM» 3HaKaMM 30AMaKa. n03TOMY po>KAe-
HMe no.q cnepcneKTMBHWM, nOBwweHHO 3Hepre '4ecKMM» 3HaKOM
30AMaKa etqe He npeACKa3WBaeT 06J13aTenbHoro ycnexa B )l(M3HM:
Bce 3aBMCMT aT Taro, KaK 'fenoBeK CMO>KeT MCnOnb30BaTb TO, 'fro
eMY AaHO OT poJKAeHMJI. KaK :no cyMeeT CBJl3aTb C BOCnMTaHMe14
caMoro ce6J1, co CBOMM MHTe.nneKTOM M nOHMMaHMeM M >KM3H...
m KOHttenlJ."R npMJK»KMMa M K KOMn03MTOpaM-Pbt6aM. OrMe'4a1OT,
'lTO MX f4Y3WtW111HOe TBOp'4eCT80 pa3Hoo6pa3HO. HaMOOnbWMX )Ole-
X08 Pw6w IOT RpM 06pa60T1re nony'feHHOf"O 141414 HaC1leAMJl:
opMntH ncHt080MY nepepa60Tas era, HaXONIT HOeOe Hanpaa-
neHMe MIDI CCBeJKMM B3mJlA» Ha npMBbl\fHbIe yaaH08KM. npMBeN!M
npMMepW TBOP'feCT1Ia Pw6-KOMf103MTOpoB M MY3WKaHTOB. PocCMHM,
o606u&M HaKOMeMHWM AO HerO M}'3WKallbHblM onbIT, tyMeJI
wetfCTBOUTIt MTaIWIHCKy10 onepy AO ypoBHR ee BWCtNaMwero pac-
u,BeTa. 6oIoceptttM AOCTMr BWCOKoro MCnonHtfTeJlbCKoro Maaepcnsa M
cran KIIaCXIC)M bHOf'O MCK)«TBa. PMMCKMM-KOpcaK08 3a-
BepWMII piDItMTMe J¥CKOM onepbI. Ooto8onon<»KHMKOM 'feWCKoM KIIaC-
CM'4eCKoi My3WKM cra.n CMeTa a nOJ1bCKOM KnaCCMKM - WoneH.
6pa3MJ1IiCia1M KOMno3MTOp BMJIa J106oc npocnaBM11CJt CBOMMM «6pa-
3MJ1bCKMMM 6axMaHaMM».
C. 1lteniH0BCKaJI M B. Beraw Ha OCHOse CpaBHeHMJI acrponOrM-
ecKMX nOU3aTeJ1eM M AenOBbiX Ka ecTB OTMe'falOT: «XOPOWMMM
124
MC Hlm!JUIM" My:3b1KM' ABJUUOTCR eBpeM, KaK HaL(MR. HaxCWIaqaJl-
a OOA 3HaKOM Pbl6» (c. 124).
C OK¥h1Hb&X 003ML(MM MMeeTcA «3HepreTM'feCKoe c03lJy'tMe» Me)K-
fJtI HOTOit nA, l1yttoM, CMHMM l4BeTOM M MCJ1OM 2. POAMB...a «f1OA
J1yNob, T. e. KO B 80CX0A"aqeM Ha ropM30HTe 3HaKe 30AMaKa B
MOMettT POJW!MMA HaXOAMTCA 3TO CBeTMJ10, npMBlleKaIOT HOTa nA iii
c....... qBeT. KOMn03MTOpbl. poAMBWMeCA «n(fA l1yHoM». -.aCTO Me-
TOtta.IWtOCTb nA KaK B Ma)KOpHblX CBOMX " pO.t38e MJ\)(
(6JlaropQAHO-TOp>tteCTBeHHOM MY3b1Ke yTBep*AeHMA 'H!JI()BeKa B
HOOHM), TaK M B MMHOpe (AYUJeBHwe nepe)l(MBaHM1t, rJ¥:1D).
YJce ynoMMHanOCb 06 cyHMBepcanbHOM», «My:3bIKaJlbHO TpMnM-
KOM» r1nyrOH KOTOp<»otY npMCYU4M Cpa3Y TRM TOHaJlbHOCTM: Pe-6e-
MOIna-Ma)l(Op, Ao-AMe3-Ma)l(0p M nO-AMe3-MMHOp. KOMA03MTOpbl, Y
Koropwx B ropocKone nnyroH, GmM'4aIOTCA oco6oA 'fYBdeMTeJlbHOC-
1WO B MMHOpe M TOP*ecTBe+fHO-BaJKHblMM MY3b1KaJ1bHblMM npoM3Be-
AeMMAMM II Ma*ope. Tal(, OTM eHO MMJlHMe flnyroHa Ha TBop'4eC-
Kyl)AeftTeJ11tHOCTb 6eTXOBeHa - «.11yt1HaJI COHara»; PaxMaHMHOBa -
npelllOAKR Ito-Atfe3-MMHOP; aMKoBCKoro - HOKTlOpHW; WoneHa -
Ko.w6enbHall, BanbCbI M HOK-
T1OpHbI; nMCTa - KOHL(eprHblM
mDA: npoKoct>beBa - 7-11 CMM-
cIJoHMA; CKpR6MHa - npenlO-
AMtI Pe-6eManb-Ma>KOp.
EcnM Bw.qeJ1MTb C.aMbIX Me-
AOTBOpHblX M 3HaMettMTWX KOM-
n03MTopOB, TO OKa3b1BaerCJI,
'4TO HaM60nbwee aCTpo.nont-
eCKoe nOKpOBMTenbCTBO MM
OKa3b1BaIOT CJ1 lOiqMe 3HaKM:
C/)opMyna .HOCIHOii cpeu»
..n,tatwe K OMII03IfI'OpW -
nPMM8PQM «nyHHbIX KOMnO-
3KfOp08» MOryT &iTb 6eT-
XOBeH-7-A .
MeHAe11bCOt1- -
1C8A . 0r'MHcIcMM-
r1011OHe3bI. «J1yHHaA HOTa-.
- caM8SI 00Ry1lAplel
TOH811bHOCTb 1IMpMICM.
125
rnasa 2
Pbl6b1 co CBOMM ynpaBHTeneM HemYHoM;' Crpene", C IOnMTepoM;
6nM3He"'bI C MepKYPHeM.
HanpMMep, eCJ1M npoaHaJ1M3HpoBaTb MCTOpHIO pO>KAeHHJI BHAHblX
KOMn03MTopoB Ha'4MHaJI C xvn B., KaK 3TO CAenaJ1M lllenaHoBCKaJl M
BeTaW, TO nO MM TaKMe nK>60nWTHbie AClHHble. C 1678 no 1685 r.,
Korp.a HemYH npoxOAMJ1 no 3HaKaM BOAoneJl M Pbl6, a «MY3b1KaJ1b-
HaJl» nnaHeTa nnyroH HaxoAMnacb B 4<MY3b1KanbHoM» 3HaKe PaKa, 3a
7 neT POAMJ1MCb TaKMe BbiAClIO-
I14MetJI KOMn03MTopbl: 6ax, BM-
BaJ1hAM( feHAenb, PafotO, CKap-
naTTH M TeneMaH. t 1809 no
1813 r., KOrp.a HemYH npe6b1-
BaJ1 II CrpenbLte, a nnyroH - B
Pbl6ax, 3a 4 roAii POAMJ1MCb 6y-
AYU4Me KOMn03HTOpbl BarHep H
BepAM, nMCT H MeHAenbcoH,
WoneH M WYMaH. C 1.833 no
1844 r., KOl"Aa HemYH BHOBb
npOXOAMJ1 no 3HaKY BOAoneJl,
a nnyTOH npe6b1BaJ1 B TenbLte,
3a 11 neT pOAHnMCb 6YAYU4Me
MY3b1KaJ1bHble CBeTMna: 6ana-
KHpeB, 6M3e, 60POAHH, 6paMc,
.[\enM6, .[\BOp>KaK, fpMr, KIO",
MaCCHe, MycoprcKHM, PMMC-
K.HM-KopcaKOII, CeH-(aHC M
lfaMKOBCKHM. C 1858 no
1865 r., KOrp.a «acrponorH ec-
KHe BHHOBHHKH» pO>KAeHHJI
..Myo3WK&nwtwA no,lUlpot(.
KOCMoca
ECI1M nOnbIT8TbCSI npe.QCKa-
38Tb Cl1eAYIOliU't" «My3b1-
K811bHbI nOAapoKIt KOCMOCa
'feI1088'fecTBy, TO. BeposrrHO.
po)t(,Q6H rpyn-
nbl KOMrl6sKTOPOB cneAOBa-
110 O)l(IIt,D,8Tb npM npoXO)I(,Ae-
HMM HenTyHa B BOAOl1ee B
2000 r. OcT811OCb He TaK y*
MHorO &peMeHM AfI nOA-
TBep*.l\eHMSL nporH038. "fM-
TaTel1b CMO»CElT neosePMTb,
Ae"CTBMTel1bHO 11M npM CO-
BMe eHMM 3n1X «My3b1KaTlb-
HblX lt :lia8HeT M 3H8KOB PO,D,M-
nMCb ocoOo MY3b1K811bHO
OAapeHHble AeTM, 6YAyuu1e
BenMKMe KOMn03MTOPbl XXI B.
126
4>opMyna «HOI./HOH cpeH»
KOMn03MTOpoB BHOBb -CoeAMHHnMCb (HemYH npoxOAMJ1 no 3HaKaM
Pbl6 H OBHa), 3a 7 neT MMp nonY'4Mn po>KAeHHe Mb6eHMCa, Bonh4>a.
Ae6IOCCH, MaJ1epa, n}"4'4MHM M P. WTJ>¥a.
/IyHbIM I
4HCJ10BaJl aCTpOnOrHJI onMpaeTCJI Ha Y'4 H BOCTO'4HOM M-
noco4>MH M oKKynbTM3Ma. no MX npeACTaBneHMtp, B crpYKTYpe,
06eCne'4HBaIOU4eM cy eCTBOBaHMe 06'beKTOB M JlBneHMM npMpo-
Abr M OKPY>KaIOU4erO MMpa, MMeeTC" 3HepreTM'4eCKOe '4aCTOTHO-
BonHOBoe «Ha'4aJ10» M «nepBopOAHaJl (KapMM eCKast) 3HeprMJt».
3Ta 3HeprHJI HeOAHopOAHa M MMeeT Ka'4eCTBeHHble M-KOnM'4eCTBeH-
Hble OTnM'4MJI. B HeMaTt!pHaJ1bHblX H MaTepttaJ1bHblX npoJlBneHMstX
MMpa 3HeprHJI 06eCne'4HBaeT B3aMMOCBJl3b, B3aHMoii;OHMKHOBe-
HMe M pa3BMTHe, 61iarOAapJl '4eMY pa3BMBaeTCJI OAHO CBOMCTBO H3
APyroro: «nepenMBaHHe» Ka'4eCTBa iHeprHH. Tat<. B HeMaTepManb-
HO,. M He>KHBOM .,.Hpe BeTep Bbl3b1BaeT noxonOAaHHe.l '4aCTb CBO-
eM 3HeprMH ynaBwMM npeAMeT (lepeAaeT CTonKHYBweMcJI C HHM
nOBepxHocTH, a OAHO C06b1THe >KM3HM HeMMHyeMo «3anycKaer»
pa3BMTMe APyroro. B >KMBOM MMpe Ocyt1(ecTBnJleTCJI nOAAep>Ka-
HMe >KM3HH Bcero >KHBOrO Ha 3eMne, B TOM '4MCJ1e '4enOBeKa. nona-
ralOT, '4TO 3HeprMst JlBneHMM H C06b1TMM 60nee «TOHKaJl», '4eM 3Hep-
reTM-'4eCKaJl crpYKTYpa MaTepHanbHblX 06'beKTOB.
B «nepBopOAHOM (KapMH'4eCKOM) 3HeprHH» MO>KHO BbiAenMTb
He MeHee Tpex Ba>KHblX npH3HaKoB: 1) «He3eMHoe» npOMCXO>KAe-
HHe H BcenpoHMKalOU4Y1O cnoc06HoCTb - MX CBJl3b1BaIOT C pery-
nJlLtMeM >KH3HM KOCMOCOM, BblCWMM Pa3YMoM; 2) Ka>KAOMY 06beKl)'
HnM JlBne HIO npMcyU4e «CBoe» 3HepreTH'4eCKOe a'4aJ1O, BepOJlT-
Hee Bcero, 3aBHCJlU4ee OT KOM6HHaLl.HM ero COCTaBnstlO Mx, a He
127
rnasa 2
KaK 06pa30BaHHe HOBoro 3HepreTH'4ecKoro Ha'4ana, HHa\fe 6b1 HX
6b1no HeCMeTHoe KOnM'4eCTBO (BPJlA nH np poAa H BblCWMM Pa-
3YM CTonb paCTO'4HTenbHbI); 3) 3HepreTM'4eCKOe Ha'4anO HMeeT
npaBMnbHYIO H nOCTOJlHHYIO nynbCaLt IO, onpeAeneHHblM MJI AaH-
Horo JlBneHHJI MnH 06'beKTa pHTM, KOTOpblM MO>KHO M3MepHTb no
BpeMeHH YCJ10BHblMH eAMHHLtaM 3HeprH - HCJ1a... HX aHa-
noraMM (6YKBaMM, enoBaMH). .
nOA6HpaJl COAep>KaHHe '4MCen H enOB, MO>KHO H3MeHJlTb HX 3Hepre-
TM'4eCKYIO HaCblU4eHHOCTb. Ee, B CBOIO o epeAb, MO>KHO HcnOnb30BaTb
KaK «KpaTHbiM pe30HaHC» A11J1 M3MepeHMJI 3HepreTM'4etKOM BH6pal,4HM
B 06'beKTaX M JlBJ1eHHJlX.
HM>Ke 6yAY1 paccMoTpeHbf 06U4Me nOnO>KeHHJI, npMcYU4Me ne-
pe'4HCneHHblM npOJlBneHHJlM 3HeprHM: 1) BcenpoHHKalOU4ee
CBOMCTBO M 06J13aTeJ1bHoe npM-
cyTCTBHe 3HepreTH'4eCfCOrO Ha-
'4aJ1a oTpa3HT 4>opMyna 3aKo-
Ha EAMHcTBa BceneHHoM, MnM
3aKoHoMepHoe nOBTopeHHe
ee '4HCen; 2) 3HepreTH'4eCKOe
Ha'4anO npOCJ1eAI4M Ha npHMe-
pax Hcnonb30BaHHJI npHeMoB
HYMeponorHM no BblJlBneHHIO
BnO>KeHHOrO B flBneHMJI H
06'beKTbI KOAa 4>opMynbl 3aKo-
Ha EAMHcTBa; 3) M3MepeHHe M
npOC'4eT AHHaMHKH «nepBo-
pOAH'OM KapMH'4eCKOM 3Hep-
rHH» nOKa>KeM Ha npMMepax
Mcnonb30BaHMJI Cnel,4ManbHblx
OcHOBbi ttyMeponOI"MM
Kak H <S>H3t11Ka, HYMepono-
rHSI CLlHT8m, o BOI1HOByK>
3HeprHIO HMeeT 3BYK (Ha-
npHMep,pa3roBop, Te e
BCI1YX). HO B OTnH He OT
<S> 3 KH HYMeponorHSI Ha-
Ael1S1eT 3Hepr eH MblC-
l1eHHoe nporosapHIlaHHe to
C MB0I10B ( c:el1. 6YKB-
BeAb M C11b C HTaeTCSI
MaTep ahbHoH, po lO-
eH 3HeprHIO MHkpol1en-
TOHHblX nepeMeU-\eH H).
128
OKKYnbTHblX MeTOAOB, n03BOnJllOU4MX OnpeAeJ1MTb ee Ka'4eCTBO M
KOnM'4eCTBO B 3aBHCHMOCTH aT BpeMeHH: B npoweAweM, JiaCTOJl-
U4eM M 6YAYU4eM. Oc06eHHO npMBneKaeT noeneAHee, '4TO AaeT 803-
MO>KHOCTb "pOrH03HpOB Tb C06b1THJI 6YAYU4erO no rll OSt9neHMIO
3HeprHH B «HeMaTepHanbHblX» JlBneHHJlX >KM3HM (HaflpHMep, 8
MCTOpM'4eCKHX C06b1THS!X) H KapMM eCKoA 3HeprHM B MaTepManb-
HbiX 06'beKTaX npH HX BonnOU4eHMM (HaijpMfo\fp, B '4eJ10BeKe M
era OKPY>KeHHH).
B '4MCJ10BOM acrponorHH B OCHOBHOM Mcnonb3YIOTCJI -Te >Ke '4HC-
nOBbie AeMCTBHJI, '4TO H B HYMeponorHH, HO npe06pa30BaHK1I Kaca-
IOTCS! npe>KAe Bcero acrponOrH'4eCKHX 06beKTOB H B3aMMOAeMCTBMJI
'4enOBeKa C HMMH. npM 3TOM 6YKBbI, cOCTaBJiJlIOU4He HaHMeHOBaHMJI
nnaHeT M JlBneHHM, HaH60nee ",aCTO nOABepralO T CJ1eaYIOU4MM Ka6-
6anMCTH'4eCKMM npe06pa30BaHHJlM:
· KOAMPYIOT 6YKBbI an4>aBMTa '4HenaMH nocneAOBaTenbHoro
(CKB03HOro) npOC'4eTa: B pycCKOM an4>aBHTe aT 1 AO 33;
· KOAMPYIOT 6YKBbI an4>aBHTa AeBJlTM3Ha'4HblM npOC'4eTOM (aT
1 AO 9), pacnonaraJl HX B CT0J16MK npH Ka>KAOM HOBOM '4MCJ10BOM
KOAHpoBaHHH;
· KOAHPYIOT 6YKBbI_an4>aBHTa.'4HCJ1aMH apKaHoB Tapa (aT 1 AO
_ 9 H '4HCJ1aMH 11 H 22);
· Hcnonb3YIOT reoMeTpH'4eC-
KHe nocTpOeHHJI '4MCJ10BOA
MaHAaJ1b1, OAHMM H3 BapH HToB
JlBnJleTCJI MarH'4eCKHM KBaApaT
AlOpepa;
· npHMeHJlIOT oKKynbTHYIO
4>opMyny H KOHCTaHTy 3aKoHa
EAHHCTBa MHpa. -
(/)opMyna «HO'4HOH cpeH»
CornaCHO '1MCnOSOM
aCTponOntM
lo1Cna OKKYJ1bTHOH q>oPMY-
J1b1 3aJ1o>t<eHbI B 3Heprent-
ecKOH CTPYKTYpe SlBneH H
06beKTOB 3eMHOH np po-
l1bI He6ecHbiX Ten
129
rnasa 2
4HCJ1a OKKynbTHoM 4>opMynbl MO>KHO 06Hapy>KMTb Be3Ae M BO
BceM, '4TO HMeeT pHTM MnH nOAAaeTCJI «HC'4MeneHHIO cBoero Ka-
'4eCTBa». 3Ta 4>opMyna B HYMeponorMM nOKa He MMeeT CTpororo
HCJ3BaHHJI, HO B03MO>KtlOCTb ee Mcnonb30BaHHJI B H3Y'4eHHH 3a-
KOHOM.epHOCTeM npHpOAbi BCJlKHM pa3 nOATBep>KAaeT ee «yHH-
BepcanbHOCTb KaK MHCTpYMeHTa n03HaHHJI». HaM60nee '4aCTO 3Ty
4>opMyny Ha3b1BaIOT4>opMynoM «3aKOHa EAHHCTBa nOCTpoeHMJI Bce-
neHHOM (MHpa}», «nYHHOM 4>opMynOM», 4>opMynoM «n03HaHHJI
MMpa».
Ee npOJlBneHMJI B 3HepreTH eCKMX pMTMax JlBneHHM M 06DeKTOB
MOryr 6b1Tb nonHblMM (B HHX BXOASlT Bce '4MCJ1a 4>opMynbl KOH.-
aHTbI) MJlM '4aCTM'4HblMM ( aCTb '4MCeJ1 4>opMynbl HnM KOHp-aHTbI
3aKOHOMepHO nOBTOpJleTCft B nOKa3aTenJlX 3HepreTH'4eCKOM BH6-
pa MH JlBJleHHM MJlM 06'beKTOB). 4aCTOTt1b1e BM6pa HH 'U1cen 4>op-
MYJ1b1 M ee KOHCTaHTbI MMelOT CBOIO 3aKOHOMepHYlO o epeAHOCTb H
CO'4eTaHHJI, n TOMY. Tpe6YIOT nOJlCHeHMJI, HCXOM H3 CJ1eAYIOU4HX
oKKynbTHbix rtpe06pa30BaHHM:
a) 28 - 4 x 7 - 3TO cpopMyna 3aKOHa EAHHCTBa. npe06pa3YJl
neBYIO '4aCTb 4>opMynbl, Mbi nony aeM HCJ10 1 (2 + 8 -10), a B CO-
eAHHeHMM C npaBoM '4aCTblO 4>opMynbl nony aeM ee oKKynbTHYIO
KOHCTaHTy, MnH npoM3BoAHYIO: 147;
6) «MarH'4eCK '4HCJ1a» 4>opMynbl H KOHCTaHTbI 3aJ10>KeHbI B CyTb
Bcex JlBneHHM H 061ft!I<1iOB. HaH60nee '4aCTO «pe30HMpYIOT» CJ1eAY-
IOtqMe '4HCJ1a 4>opMynbl:147,47,4, 7, 11 (3TocyMMa: 4 + 7), 28,1 (2 +
+ 8 - np JeOco4>H'4eCKOM CJ10>KeHHH «0» He Y'4HTblBaeTCJI) MX
npOH3BO,QKbte (HanpMMep, 19 -1 + 9 -10 - 1). 4aCTo BCTpe'4aeTCJI
YABO HHbI HnH yTpOeHHblM pe30HaHc 3neMeHTapHoro Hcna:
11 (KOA CJ10Ba «(blH»), 111 (<<BceneHHaJl»), 666 (oTHoweHHe '4HC-
nOBbiX KOAOB CJ10Ba <<1lYHa» K CJ10BY «3eMnJl») H T. A.
130
C/JopMyna «HOIiHOH cpeH»
o '4aCTOTe MX '4MCJ10BblX pe30HaHCOB E. 6naBaTCKa" nHWeT B «TaM-
HaM AOKTpMHe»: «Ha6nlOAaeMbie nepHOAbi AOn>KHbI CTaTb OCHOBOM
AllJI acrponorM'4eCKMX BbI'4MCJ1eHHM... Mbi .,.O>KeM yTBep>KAaTb, '4TO
MMeHHO :310T cnoc06 MC'4MCJ1eHMM 6b1n npMMeHeH BC " .HapoAa-
MM» (T. L KH. 2. c. 110). ECTb nM B HayKe 4>opMyna, nOAo6Ha" «no-
3HaHMIO MMpa», KOTOpylO MO>KHO 6b1no 6b1 McnOnb30BaTb B oKt<ynb-
TM3Me AJlJI YHMBepcanbHblx BbI'4MCneHMt? «-HMKaKoM APyroM
4>opMynbl HaM He Ai'CT «aKClAeMM'4eCKaJl HayKa», ..L. C'4MTaeT A. KM-
Cellb. - CneAOBaJ10 6b1 HaM B3J1Tb Kat<yIO-HM6YAb MHYIO 4>oPMyny?
HeT. Bo-nepBblx, npocro Jie cyt1.IeCTByeT, a BO-BTOPblX, 3TOM 4>oP-
MynoM nOnb30BaJ1MCb HaWM npeAKM Ha npOTJI>KeHMM TblCJI'4eneTMM.
AocraBuiMeCJI HaM B HaCJ1eACTBO paC'4eTbi QCHOBaHbI MMeHHO Ha :nOM
4>oPMY1!e» (KnaAe3b 6e3AHbI, . I, c. 12-13). '
C yrsep>KAeHMeM A. KMCelIA MO>KHO nocnopMTb. B poJlTHo, OTAa-
Ba" AOn>KHOe 3Ha'4eHMIO 4>opMynbl 3aKoHa EAMHCTBa, Bce >Ke He
CJ1eAyeT ee nepeo eHMBaTb B paC'4eTaX «HaWMX npeAKOB Ha npoT"-
>KeHMH TblCJI'4eneTMM». HYMeponoraMM H MaTeMaTMKaMH 6b1no pa3-
pa60TaHO MHO>KeCTBO M APyrMx CHCTeM C'4MCJ1eHHJI (He TonbKO 4('4M-
C.TO» '4McnOBblX, HO M reOMeTpM'4eCKMX, TpHrOHOMeTpH'4eCKHX,
norapH4>MH'4eCKHx, C apa6CKOM M pHMCKOH CHCTeMaMM C'4HCJ1eHM"
H T.A.) co CBOMMH 3aKOHaMH H «MarH eCKMMM» 4>opMynaMH. npM-
'4eM OHH TO>Ke 6b1nH BbI'4HCJ1eHbI H3 npaKTHKH M TO>Ke peaJ1bHO
OTpa>KanM onpe)\eneHHble 3aKOHOMepHOCTM npHpOAbI, a 3Ha'4HT.
Ka>KAaJl M3 TaKHX CHCTeM MMeeT npaBO Ha >KH3Hb. C YBa>KeHHeM OT-
HOCJlCb K MHTepeCHbiM M Ba>KHblM HYMeponOrM'4eCKHM HCCJ1eAOBa-
HMJlM A. .KHCelIJI (pe'4b a HMX nOMAeT HH>Ke), 6YAeM t MTaTb, '4TO OH
B AaHHOM CJ1Y'4ae HeYAa'4HO Bblpa3HnCJI.
CamacHo npeACTaB11eHMJlM E. 6naBaTCKOM, A. nOABOAHoro, A. KM-
Cell", KaMpo H ApyrHX 4>Mnoco4>oB H HYMeponoroB, npHMeHJlBWMX
131
rnaBB 2
OKKYJlbTHWe 3HaHMJI M paC'4eTbi
B aCTpOllorMM, topMyna «28 -
- 4 X 7» M ee CKOHCTaHTa 147»
ne)l{aT 8 OCHOBe CMCTeM'" nOCT-
poeHMJI «OT CoJlH&4a AO CBeTnJl'4-
Ka, nOn3a erO II TPaBe» (TaA-
HaJl AOtcrpMHa, T. I, c. 340). 31'0
3Ha'4MT, 'frO IXOMAeHMe 'fMCen
$oPMYJ'W MnM KOHCTaHTbI B nlO-
6b1e M3MepMTenhHbIe BenM'4MHbI
06'heKTa MnM JlBneHMJI o6ecne-
'4MBaeT MM ycTOA'fMBOCTb If rcip-
MOHMIC 83aMMOAeACTBMA C OK-
py*alO'" npMJ)OAoA.
HM>Ke paccMOTpM'" MCOOJ1b3OBatfMJt nepe'fMCJIeHHWX tty-
Mepo1lOO4'teCMtix npeo6pa3OlaHMA AllJI C03AiiHMJI «MafM'feCKOro KQAa».
mn- Ko,q arpaJKaer cyTb MHMDC omeKTOB M JlB11eHttM. npoaHallH3MpyeM
nony'4eHHbM! 3aKOHOMepHOCTM Gtepn1M 'fMCJIOBbIX pe3OHaHCOB» (MnM
«pe30HaHCHbIX 'fMCJK)BbIX CBJl3eM»). 03HaKOMMM 'fMTaTe1Ul C OCH08Hb1-
MM OKKYJ1bTHhlMM '4MCJ1aMM M- CX'eMaMM. npM M31K»«eHMM M rtpMAep-
JKMBa'TbCR 061qef1 MCTOnKOBaHMA TaTOB OKKyJIbTHbIX npe-
06pa30saHMM, npM"JfTbO(. CTaDOi1 M CoepeMeHHOA ttyMepOI100fM.
Cnp.IARI_a C1'1t MHO-
nec M8TeMaTM'f8CKMX M
reoMeTPM'fE'CKMX paC'te-
TOB 8 npM'J1O*eHM" K
MJ1OCOCI>CKMM nOHA-
TMAM M CMMBOI1aM noA-
TB8PAMI1M M8TeM8TMKM C
MMpoBblM MlMeHeM-
raycc. A*. HeneP. Terr-
nop.BeAnb.3Anep.no-
6a'feBCKMM M AP.
CI)opMyna 3aKOHa EAMHCTBa
nOCKoJIl>KY J1yHHaJl4K>pMyna OTpa)KaeT cyTb JlBneHMM MnM 06'h4!M-
TaB, TO aHa npoJlBnJleTCJI B >KM3HM YHMBepCallbHO M aeTCJI npM
caMbiX HeOJKMAilHHblX 06cr0RTeJ1bCT8aX, BblCTaBnJlJl np06neMY B MHOM
CBeTe, 3aCTaBnJlJl nO-HOBOMY OC03HaTb ee ponb B >KH3HM 'IeJ10BeKa.
132
MO>KHO npMSeCTM MHOro
npMMepOB, KorAa 3a.RO)l(eH-
HaJl S CJ10Ba M '4MCJ1a 4>op-
Myna 3aKOHa EAICHCTsa 6b1na
MCT HMKOM CBepweHMJI c.CJJy-
'taMHblX» C06WTld4 B08ce He
enY'faMHO. 06paTMMCJJ K 4>aK-
raM.
TaK, CAaJIHCKaJl a36YKa
KM pMnna M Me4>oAMJI 6wla
C03 a B 863 r. KMpMJUlfj.O
npMHJlTMJI MOHaweCTBa B 869 r
MMen MMpCKOe ICMJI - KoH-
CTaHTMH.
Y'4TeM 310 MJiUI B OKKy.R1tTHWX paC'feTax C o603Ha'4eHMeM CKB03-
HaM nopJlAKOd HYMe M an4>aaMTa:
«KOHCTatmtH» + M» -143 + 84 - 227 -11- 2.
863 - 17 - 8.
CamacHo 3aKOHY CYAA-6w (KaPMW), MMeHHO 3TM ABa 'feIIOBeKa Aon-
>KHI.J' 6bIJIM C03AiJTh cnaBJlHCK)'1O a36yKy M MMeHHO B TOM roP:i, KO
310 AeMCTBMre1IbHO npoM30WJ10.
UteAYJOU4MI4 npMMep. BpeMeHeM OCHOBaHMJI MOCKSW C'4MTaeTCJI
28 Mapra 1147 r. (31M roA MMeeT nonHOe nOBTopeHMe '4MCen KOH-
CTaHTbI - 147, a ralOKe '4MCJ10 28 - neBaJl '4aCTb nYHHOM 4>oPMY-
nbl, 'fTO n03l1on npeNJonO)l(MT..- e 6e3 pac'feTOB tcapMM'4ec-
Koe npeA3HaMeKOBaHMe).
npoM3BeAeM oKKYnbTHbie BW'4McneHMJI:
«MocKBa» - 14 + 16 + 19 +12 + 3 + 1 - 65 - 11 - 2.
28. 03. 1147 - 2 + 8 + 3 + 1 + 1 + 4 + 7 - 26 - 8.
cPoPMyna «Ho'IHOH </)eH»
IIyHH" .0PMYI1.
(28 = 4 x 7) M ee OtCJCynbT-
HaA KOHCT8HT8 147 ( TO C
Hyueponon1 ecK -n03M-
....." 3 MT TO JlCe caMoe)
OTpuca T 38KOHbI eAMH- _
CTsa paah Bcel18HHOM,
noaTOMy 4>oP\fyna -.acTO
T8K M H83b1aaeT : 4>oPMY-
ria 3UOHa pa3SMTMA Bce-
neHHOM, 3aKOH CyAbObI
(KapMw).
133
rnasa 2
nOnY'4aeTCJI, '4TO OCHosaHHe MOCKB 6b1no MCTOpH'4eCKH npe-
AonpeAeneHo, TaK KaK Ha3BaHMe MecTa H SpeMJt nOCeneHHJI AalOT
'4MCJ1a 4>opMynbl 3aKoHa E,qMHCTBa BceneHHOM.
OCHOBaTeneM pocCMMCKOM MOHapXHM JlBnJleTCJI PlOpHK. npOM3Be-
AeM HYMeponOrH'4ecKoe KOAHpoBaHHe M cnO>KeHHe 6YKB era HMeHM:
«PIOPHK» - 18 + 32 + 18 + 10 + 12. Or nepBoM 6YKBbI aJ1«1>aBMTa AO
nepBoM 6YKBbI HMeHH - «p,. - HaC'4MTb1BaeTCJI 17 6YKB, a AO noc-
neAHeM 6YKBbI MMeHM «K» pac"nonO>KeHO 11 6YKB. CYMMa: 11 + 17 -
- 28. He npaBA'J nH, nK>6onbITHbie pe3ynbTaTbI, He! KOTOpble 06paU4a-
eT BHMMaHHe A. KMcenb? MO>KHO Ha 3TOM OCHOBaHHM nOnaraTb, '4TO
He TOJ1bKO MMeHHO PlOpMK KaK nH'4HOCTb 6bU1 npeAHa3Ha'4eH b60M
OCHOBaTb MOHapXMIO, HO H AOn>KHa 6b1na POAHTbCJI (MHKapHMpoBaTb-
CJI) nH'4HOCTb HMeHHO nOA 3TMM HMeHeM H HMeHHO C TaKHMM '4enOBe-
'4ecKHMH Ka'4eCTBaMH, KOTOpble nOMomH eMY npeOAoneTb Bce >KH3-
HeHHble 1It0nnH3MH, '4T06b1 BbinonHMTb npeAHa3Ha'4eHHYIO eMY
MCTop eM pwv,?
CM. Cono B B KHMre « CTOpHJI PoeCMH C ApeBHeMWHX Bpe-
MeH» nMweT, '4TO nepBaJl KHHra no MaTeMaTHKe C Hcnonb30BaHHeM
apa6CKMX I4M4>p (AO 3TOro
'4HCna B POCCHM npHHJlTO
6b1J10 0603Ha'4aTb 6YKsaMH)
6b1na COCTaBneHcrneoHTH-
eM MarHMI4KHM B 1103 it-. H
Ha3b1BaJlaCb aHa «ApH4>Me-
THKa, CHP 'Jb HaYKa '4HC-
nHTeJ1bHa1I ' OpOH3BeAeM
HYMeponOrH'4eCKHe pac-
'4eTbI:
1703 -1 + 7 + 3 -11 - 2.
OcHoa... ttyMeponO....M
Haw MSI cpaMHn SI A8H
HaM He C11Y'f8MHO, OH CBOIltM
3Hepren1 ecta1M plltTMOM OT-
pWICBIOT Hawe COOTBeTCTBlite
TOM ponllt B )l(1It3HIIt, KOTopaSi
OTBeAeH3 HaM lEapMoM. 3Hep-
reTIIt ecKIltM plltTM IItMeHIlt aano-
)l(eH B HawMX .o.enax.
134
CPopMyna tcHO&lHOU cpeU»
«ApM4>MeTHKa, CMpe'4b HaYKa HMCJ1HTenbHaJl» - 8.
3Ha MT, nOJlSneHMe Y4e6HMKa no apM4>MenlKe C HOBbiM CHM-
BonOM 4M4>p 6b1no HCTOpM'4eCKM npeAonpeAeneHo. Ho HHTepec-
HO BblJlCHMTb, AeMCTBHTenbHo nH :3Ta MCTOpM'4eCKafi ponb 6b1na yro-
TOBaHa CYAb60M HMeHHO neoHTHIO MarHH4KoMY:
<<11eoHTMM» + «MarHH4KMM» - «13 + 6 + 16 + 15 + 20 + 10 + 11» +
+ «14 + 1 + 4 + 15 + 10 + 24 + 12 + 10 + 1 - ((4 + 6 + 7 + 6 + 2 +
+ 1 + 2» + «5 + 1 + 4 + 6 + 1 + 6 + 3 + 1 + b - 28 H 29.
TaKMfi4 06pa30M, cornaCHO oKKynbTHOMY BbI'4HcneHMIO, CYAb6a
AeMCTBMTenbHO AaJ1a B03MO>KHOCTb n. MarHM4KOMY 0CYU4eCTBMTb
ero KapMH'4eCKoe. npeAHa3Ha eHHe. BHAHMO, y Hero peaJ1M3aLtHJI
CB.oeM ponH npOXOAMna epe3 TpYAHOCTH, '4epe3 «ayneHb» 60Pb-
6b1- 06 3TOM rOBopHT '4MCJ10 «29», a He.«28», 4To.CJ1eAOBaJlo 6b1
O>KHAaTb no Ka66anMCTH4ecKMM paC'4eTaM. ',.:c
A HMelOTCJI nM 4HCJ10Bble 3aKOHOMepHOCTM (<<'4MCJ10Bble 3Hepre-
TH'4eCKHe pe30HaHcbI») B npHpoAe? 06paTHMCJI K npHMepaM.. KaK
H3BeCTHO, BOAa M npHpoAHble coeAMHeHMJI yrnepoAa HaXOAJITCJI B
MCTOKaX pa3BHTHJI >KM3HM - TaK yTBep>KAaeT OPTOAOKCaJ1bHaJl Ha-
YKa. npoBeAeM oKKynbTHbie pac4eTbi A11J1 npoBepKM, CJly'4aMHbI nM MX
83aMMoAei4crBMfI: «yrnepoA» (21 + 4 + 13 + 6 + 18 + 16 + 5 - 83 ...
- 11 - 2), B COCTaB BOAbi BXOAJIT «BOAOPOA» (3 + 16 + 5 + 16 + 18 +
+ 16 + 5-79-16-7) M «KMCJ10pOA» (12 + 10+ 19 + 13 + 16 + 18 +
+ 16+ 5-109-10-1). CnMJlHMe B BOAe BOAopoAa C KHcnopo-
AOM AaeT 06U4MM KOA 8. nonY'4aeM '4MCnO 2B. Ha OCHosaHMH
MarH'4eCKMX BbI'4HCneHMM 3aKJ1IO'4aeM, 4TO ponb BOAbi M coeAM-
HeHMM yrnepoAa B pa3BMTMM >KM3HM Ha 3eMne KapMH'4eCKH npe-
AonpeAeneHa.
4MCJ10 16 - «npoM3BoAHoe» '4MCen 2 M 8 (-16), cOCTaBnJlIOU4MX
'4MCJ10 28 - neBoM 'laCTH 4>opMynbl 3aKoHa EAMHCTBa. B «Ka66aJ1e
135
rnasa 2
1:IMCel1" ABeccanOM nOABOAHblM
nHweT, '4TO 3HeprOBM6paLtHJI '4HC-
na 16 B oKt<ynbTHbix npe06pa30Ba-
HMSIX 06naAaeT 60nbwHMM B03-
MO>KHOCTJlMM: «Ha ypoBHe 16
oTKpblBaeTCJI npJlMOM KaHan B
MHpoBOM Pa3YM, T. e. HenocpeA-
CTBeHHaJl B03MO>KHOCTb C'4HTbI-
BaTb OTTyAa HH4>opMaLtHIO . 4e-
nOBeK '4epe3 '4MCnO 16 nony aeT AocTyn K TaMHaM npMpoAbi M
KocMoca.
4MCJ1a 16 H 28 HnH HX npoH3BoAHble '4aCTO JlBnJlIOTCJI COCTaB-
HaM '4aCTblO H3MepHTenbHblx BenH'4MH, KOHCTaHT HnH-4>opMyn TO'4-
HbiX HayK. B03bMeMA11J1npHMepacaMbleH3BeCTHbleH3HHx.MC-
nonb3yeMbte A11J1 pac eTa ABM>KeHHJI He6eCHbix TeJ1 B acrpOHOMHH
M acrponorMH, ;- '4HCJ1a n M e.
4MCJ10 n AiMeTCJI '4HCJ10BblM Bblpa>KeHHeM OTHOWeHHJI A11HHbI
OKPY>KHOCTM K AHaMeTpY it 6b1no BBeAeHO Y. A>KOHCOIiI (1706) H
n. 3MnepoM (1736). KaK H '4HCJ10 p, 3HaKOM HHAMBHAYaJ1bHblX 06'beK-
TaB B MaTeMaTHKe JlBnJleTCJI '4HCJ10 e - 3TO OCHOBaHHe HaTypaJ1b-
HbiX norapH4>MoB BnepBble 6b1no BBeAeHO n. 3MnepoM. CpaBHHM
HX '4HCJ10Bble Benld'4MHbI C TO'4HOCTblO AO 16-ro 3HaKa (npoH3BoA-
Horo '4MCJ1a 28; 2 x B -J6):
e - 2,718281828459045 - 2.
n - 3,141592653589193 - 8.
OKKYnltTM3M
.'tepa .. cerOAHtI
B COBpeMeHHOM OKKyl1b-
TH3Me C110 16 ABnAeT-
CA C MB0110M CTPYKTYPbt
«TOHKoro nnaH81t ABne-
HHH OObeKTOB
KaK BMAHM, OTKpblTHe 3TMX '4MCen KaK MaTeMaTH'4eCKOrO HH-
cTpYMeHTa B n03HaHHH MMpa 6b1no BO MHorOM npeAonpeAeneHo.
x BenH MHbI CBJl3aHbI C M3MepeHHeM «'4MCnOBOM CTPYKTypbl»
136
CyrM JlBneHHM M. 06'beK-
TaB npMpOAbI, OTpa)t(alOT
onpeAeneHHble HX 3aKO-
HOMepHOCTH. BepOJlTHO,
npH OAHOBpeMeHHOM MC-
nonb30BaHMH 3TMX ABYX
BenM'4HH 3Ha'4MTenbHO
nOBbiWalOTCJI B03MO>KHO-
CTM OTKpblTMJI H BHeApe-
HMJI B npaKTMKy pa3nH'4-
HbiX JlBneHHM H 06'beKTOB
C03AaHHblX PYK8MH '4e
nOBeKa.
4>opMyna «HO"lHOH cpeu»
Ecn. MH8HM8
no nOBO.o.y y,O,HBMTeI1bHOM pa-
3YMHOCT KOHCTPYKl" U1 B3a -
MOCBfl3 'faCTe MMP03.QBH fI
4> I1oco4> KaHJ BOCKJ1 : «KaK
3TO B03MO)I(H0, 'fTOObI Me>K.D.Y
CTOI1b pa3J1 bI M
CyllteCTBOBa1Ia TatcaR com8CO-
I;!aHHOCTb... npmOM comaco-
BaHHOCTb CTOI1b 60I1bWafl. CTOI1b
.o.aJIeKO .o.Yl1-'8f1 8 ",:0 )tee BpeMfI
CTOI1b T H8R".
rnABA 3
HYMEPOnOrM B An ABMTE
KOAbi ancl»aBMTa
MeAM HHCKHMM HccneAOBaHH MH
paHOBneHO nOTpJlcalOlqe Ba>KH()e 3Ha-
'4eHHe 3BYKOB aJ14>aBKTa H CJ10B B Ha-
weM >KH3HM. HaM Ka>KeTCJI, '4TO HOBO-
pO>KAeHHbIM e "'O>KeT OC03HaBaTb
06palqeHHYIO K HeMY pe'4b, TaK KaK elqe
He nOHMMaeT CJ10B H He YMeeT pa3rOBa- '
pHBaTb.OAHaKonpaKTMKanpenOAHOCHT
YAMBHTenbHble 3araAKH: HOBOpO)t(AeH-
HbiM Hy>KOOemCJI B 06palqeHHOM K HeMY pe'4H MaTepH, ynaBnMBaeT
OTTeHKH ee 3BY'4 MJI.
ECJ1H CTHMynMpoBaKMe nCHXM'4eCKHX npo eCCOB B AaHHOM eny-
ae He npeACTaBnJleTCJI peaJ1bHblM, nOCKonbKY pe b pe6eHOK eU4e
He nOHHMaeT; TO, KaK r10naralOT Cne HaJ1MCTbI no 6H03HepreTMKe,
aKTHBHoe pUBMTMe nCMXMKM pe6eHKa MO>KHO OTHeCTH 3a C'4eT 3Hep-
zemUl/eCHOZO B03AeMCTBHJI 3BYKOB pe'4M. BHAMMO TaKoe B03AeM-
CTBMe 3HeprMM 3BYKOB HOBOpO>KAeH"HbiM BocnpHHHMaeT (AO nep-
BbiX 3BYKOB CaMOCTOJlTenbHoM pe'4H) Ha ypOBHe noOC03HOmeJ1bHOZO.
MHTepecHW" .KT
06pa HH8R K HaM
3HeprlitR 6yKB
CJ10B OKB3b1aaeT
CT MYJ1 p U4ee
B03,D,eMcT8Me Ha
pa3B TMe nC X K .
138
XOTJI nOAC03HaTenbHble
BOCnpHJlTHJI Mbi 06'bJlCHMTb
He MO>KeM (TaK KaK Hawe-
MY 06'bJlcHeHMIO nOAAaeTCJI
nMWb TO, '4TO Mbi OC03HaeM),
04>MLtMaJ1bHaJt HayKa npM-
3HaeT, '4TO nOOC03HOHue-
sXooum 8 MexOHU3M ncu-
XUyeCKOU 4J'yHKLI,UU YeJ10-
8eKO. CCblnaJlCb Ha IOHra,
KOHApaweHKO M .[\OHCKOM
BbiAenJlIOT '4eTbipe OCHOB-
Hble nCHXH'4eCKMe 4>YHK-
4MM: MblwneHHe, '4YBCTBOBaHMe, 0U4YU4eHMe H MtnyMlP!lO. OHM nM-
wyT: «K CO>KaJ1eHMIO, Y '4enOBeKa 3TM '4eTbipe 4>YHK4HH pa3BMTbI
HepaBHOMepHO. 06b1'4HO oAHa H3 HMX AOMMHHpyeT M eU4e oAHa -
conyrCTByeT. OCTaJ1bHble ABe 4>YHKLtHM Bblpa>KeHbI CJ1a60 H Haxo-
A"TCJI B 6ecc03HaTeJ1bHoM» (06U4a" ncMxoTepanHJI. MH.: HayKa H
reXHHKa, 1993, c. 36). BOT M non}"4aeTCJI, '4TO 3BYKM aJ14>aBHTa M
CJ10Ba, pe'4b 3aMbiKalOT «Konb40 HaweM nM'4HOCTM» B lI.enoe Ha YPOB-
He C03HaHHJI M nOAC03HaHMJI.
MO>KHO npeAn0J10>KKTb, 'frO 3HeprerM'4ecKoe 06 eHHe nepeAaeTCJI
pe6eHKY'4epe3 nOAC03HaHHe, a nOAC03HaHHe, KaK H3BecTHO M3 6H03Hep-
rerMKM, 4>opMHpyeTCJI He TonbKO Ha ypoBHe MaTepManbHoro, HO H KaK
3HepTeTH'feCKoe COCTaB1UlIOU,\ee Te11a pe6eHKa. 8a>KHO OTMeTKTb TaK>Ke
caN <J>aKT: C nepBblX HeAeJ1b >KH3HH pe6eHOK ocrpo Hy>K,QaeTCJI He TMb-
KO B naCKe MarepH M B 3HepreTM'4ecKOM 06U4eHHM '4epe3 TellO (MaTepH
none3HO 6parb Ha pyKH pe6eHKa M npM>KHMaTb K ce6e, naCKaJI), HO H B
Jl3b1KOBOM 06U4eHMM '4epe3 3..eprMIO 3eyKOB ee ronoca.
HYMeponorUR B ancpaBUTe
Y M8Tept4, nOCTORHHO pa3ro-
Bap....Ba e co CB<»1M HOBO-
po*AeHHbfM, pe6eHOK paHbWe
H8 ""HaeT rOBop....Tb ....
....HTenReKTy.anbHopa3B....saeT-
CR. eM Y MVep..... KOTOpaR
MOI1 a 06c eT cBoero
HOBopo)l(,D,eHHOro. - 00 3TOM
n....wyr M....HCKHe npo4>eccopa-
B.T. KOH.APaweHKO....
A.I.1. AOHCKO (1993).
139
rnasa 3
AJIcIaaaMT MMeeT crporylO 3HepreTM ecKyIO eM6paltMlO, «nOAAa-
IOU(YIOCJI "MCI10BOMY n . Ko.q, KaK C'4MTCOOT HYMepoJlOrM, B
C8OIO 'fepe3 HyMeponorM'fecKMe AewMcI»paropbl M 4>oPMY-
JIY aBllJN!1'Ol KllIO'40M K pacKpW11410 TaMH npMpoAbi (MaKp0#4Mpa) M
(MMKpoMMpa), KOTOpbl" JUIJ1J1eTCJII ee '4acTblO.
: Ilpt&tAeM 3H8't8HMe 6yKs pyccKoro '" narnHCKoro an<I>a- ;
· BMT0811pM MX 9-3H8'*1OM KOAMJ)OB8HMM (3l1eMeHTapHblM ·
. 'MCIIOIIWM KOAOM) no C.A. BpoHCKOMy (1991):
1 2 3 4 S. 6 7 8
A 6 B r JJ. E £ )t(
M A K It MHO n
C T Y <J> X U "J W
b bI b 3 10 SI
ABC 0 E F
J IS L M N 0
S , v u x y
G
p
Z
9
3
p
W
.
.
H
a
I
R
..................................... .
. . . . . . . . . . . . . . e. . . . . . . . . . . . . . . . . . . . . . . .
: ConIacHo namocy (KaMana. cno, 1910), KOA naTMHCKO- :
· ro 11Y"W8 OOAJ)a3Aensnb T8KMM 06pa3OM;
1 2 34 56 7
A B 40 E U 0
J C J. M N V Z
G R S T X
K
a
y
8
F
H
P
.
.
140
.
........ ..............................
. .JJOnfR B. ".;
. . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
· B ttyMepO.norMM MCnOl1b3y1OT M MHbIe 3H8PI'"eTM't8C1CM9 KG- ·
. AMJ)08aH , HBnpl4Mep K OAMP088HM6 no 22 C1'8pI1»W lip- .
· KaH8 Tapa (n.n. rno6a, 1991):
1234567
A 68 r A E E
11 MHO n p c
W Wb bf b 3
8
)K
T
10
9
3
\I
10 11
H A
CI> X
22.
K
l!
........................... ...........
- .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
: np.1 nopsfAt(osoM, MnM CtCB03HOM, HYMepal4MM a.ncINBna :
: KOA HapacTaeT OT nePBOM (1) AO OOCI18AHM fAo ·
. 'fMCJ1a 33): .
: 1-A 10-111 18-P 26-W :
2-6 11-f1 19-C 27-lU
3-8 12-K 20-1 28-b
4-r 13-11 21-Y 29-bI
5-A 14-M 22-<1> 3O-b
6 - E 15 - H 23 - X 31 - 3
7-E 16-0 24-L\ 32-10
8-)1( 17-n 25- 33-SI
9-3
.
.
.
.
.
.
.
.
........................... ...........
TpMMeTHoe KOAMpoBaHMe MMeeT «'4MCJ1OBOM pe3OHaHO C MCTO-
KaMM >KM3HM, RBnRJlCb OAHMM M3 YaK Ha3b1BaeMWX KoiJoHoB AHK. no
MHeHMIO A. KMCeJ1J1 (1992), «KOA yHMBepcalleH: OAMH (nOAXOAMT. -
npuM. QlJm.) AnR Beex )l(MBytW4X Ha 3eMJ1e cytJ4eCTB. Y 6a rpIf-
6a, 'feJ1OBeKa, Kpa6a, aCTpbl OAHM M Te )l(e TpMMe'TW KOAMpyIOT ONtM
M Te )l(e aMMHOKMcnOTW» (KnaAe3b 6e3AHY, 't. L c. 17).
141
rn888 3
YHHBepcanbHblM KOA nOAXOAMT K '4MC-
naM M 6YKBaM, n03TOMY COBpeMeHHaJl
HYMeponorMJI CTaJ1a WMpOKO MM nonb-
30BaTbCJI. An" nepeBoAa an4>aBMTa 'Ha
3-6YKBeHHblM - TpMnneTHbI" KOA
(KorACl caMall 60nbwaJI BenM MHa KOAa
He npeBblwaeT '4HCJ1a 3) BHa'4aJ1e npoM3-
BOWtT '4MCnoBYIO WM4>POBKY Ka>KAOrO
3Ha eHMJI 6yt<BbI C Mcnonb30BaHMeM LtM4>P CKB03HOM HYMepaLtMM aJ1-
4>aBMTa. nOnY'4aeMbie '4HCJ1a cyMMMpylOT camaCHO npaBMJlaM HYMe-
nepcneKTMBHWM
BapHaHTOM KOAH-
poBaHa.1A arnt>aBKTa
AB11AeTCA a.1CnOnb-
30BaH e TpHnnST-
Horo KOAB.
......... ... .... ....... ...............
· A= 1 = OAHH = 1.
· 6 = 2 = ,D.B8 = 2.
. B = 3 z::: TPM = 3.
· r= 4= "IeTbfpe = 1.
. A=5=ntpb=1.
· E = 6 = w9cTh = 2.
· = 7 = ceMb = 2.
. )K = 8 = BOCeMb = 2.
· 3 = 9 = AeBATb = 2.
· =10=A8CRTb=1.
: 111= 11 = OAHHfla.0A8Tb = 2.
· K = 12 = ABeHaAt\811i = 2.
. 11 = 13 = TPMH8AM811:» = 2.
· M = 14:r: "IeTblpHa.0A8Tb = 1.
· Hz::: 15 nAT Tb= 1.
. 0 = 16 = wecTHa.0A8Tb = 1.
· n = 17 = ceMHa.0A8Tb = 2.
P = 18 = BoceMHa.0A8Tb = 1.
C = 19 = A8BfITHa.0A8Tb = 1.
T=20= Tb=2.
Y=21 = TboAHH=2.
4> = 22 = ABa.0A8Tb ASS = 2.
X = 23 = Tb TpM = 2.
= 24 = Tb eTblpe = 2. ·
Y = 25 = Tb nATb = 2.
W=26= TbwecTb=1. ·
LJ.t = 27 = ABa.0A8Tb ceMb = 1.
b = 28 = ABSAu,sTb BoceMb = 2. .
bI = 29 = AB8AL48Tb AeBRTb = 2. ·
b = 30 = TPMAL4aTb = 2.
3 = 31 = TP Tb OAHH = 3.
10 = 32 = Tp Tb ASS = 2.
S1 = 33 = TPM,D,UaTb TPH = 1.
.... ............ ........ ...... ........
142
ponorHH (meoccxpu&leCl<U AO nony-
'4eHMJI OAH03Ha'4HOM 4M4>Pbl, npH
3TOM HynM He Y'4MTblBaIOT). nony-
eHHoe '4HCJ10 3aMeHJlIOT ero CJ10-
BeCHbiM aHaJlOrOM M CHOBa npOC'4H-
TbiBalOT era '4HCJ10Boe 3Ha'4eHHe no
'4MCJ1aM CKB03HOM HYMepa4HH aJ1-
4>aBHTa, cyMMHPYIOT Teoco4>H ec-
KH, H TaK AO nonY'4eHHJI KOAa C Be-
nM'4HHOM '4HCJ1a He 60nee «rpH».
npMMep nony eHHJI TpHnneTHoro KOAa npH nepeKOAHpOBaHMH
CKB03HOM HYMepa(.tHM aJ14>aBHTa:
A -1- (CJ10BO «OAHH») - 16 of' 5 + 10 +'15 - 46 -10 -1.
I) = 2 = (CJ10BO «ABa») = 5 + 3 + 1- 9 (AeBJlTb) - 5'. 6 + 3 + 33 +
+ 20 + 30 - 97 - 9 + 7 - 16 .. 1 . 6 - 7. 3neMeHTapHoe HCJ10 BHOBb
nepeBoAHM B cnOBO: «ceMb» - 19 + 6 + 14 + 30 - 69 - 15 - 6,
«weCTb» - 26 + 6 + 19 + 20 + 30..101- 2.
B .. 3, «TPM» .. 20 + 18 + 10 - 48 - 12 - 3.
nepe'4MCJleHHble Bblwe HYMeponorM ecKHe KOAbi aJ1(1)aBHTa npo-
BepeHbI HYMeponoraMH M acrponoraMM H KaK 60nee HC!Ae>KHble AllJI
npeAcKa3aHHM peKoMeHAoBaHbI AllJI Hcnonb30BaHHJI.
HYMeponon1R B ancpaBHTe
EcnM eepMTb ouynlt-
TM3My, &.1CnoBbte kO,Abl
B OKkYnbn13Me He npo-
"'3B011bHbI. X c 901n1-
Ka ... paLU1QHaJ1bHOe Ae-
neH no Kon...tfeCTBeH-
HOMY j'I ka'4eCTBeHHOMy
3Ha e..HiM OTpaOOTblBa-
n...Cb CTOnen1 M"'.
"3Heprope30HaHc»6YKB
C "IMCnaMM
VlcCJ1eAOBaHHJlMH MHorMX HYMeponoroB AOKa3aHbI MaTeMaTH ec-
KaJl crpOMHOCTb crpYKTYPbl aJ14>aBMTa, era '4HCJ10BaJl rapMOHHJI H
cHMMeTpHJI. PacnOnO>KeHHe 6YKB B pycCKOM an4>aBHTe nOA HHJleT-
143
rnasa 3
4>oPMyne 3aKOHa EAHHCTBa npHpoAbi M ee KOHCTaHTe. A. KHce-
neM, KaHpa, C. BpOHCKHM H APyrMMH ycTaHOBneHO, TO, 06pa3YJl
CJ10Ba, 6YKBbI HMelOT «'4HCJ10BOM pe30HaHC» C TeMH JlBneHMJlMH H
06'beKTaMH npHpOAbI, B tTPYKTYpe KOTOpblX TO>Ke 3anO>KeHbI 3TH >Ke
KOAbi.
4MCJ1a 147 H 28 B03HMKalOT npH cosepweHHo npoH3BonbHblx npe-
06pa30BaHMJlx H pa3AeneHHJlX 6YKB pyccKoro aJ14>aBHTa. HanpM-
Mep:
a) 06U4aJl cyMMa Bcex nOpJlAKOBbiX HOMepoB napHblx cornaCHbiX
(CM. npeAblAYI14MM pa3Aen) paBHa YHCJ1Y 147: 2 + 17 + 3 + 22 + 4 +
+12+5+20+8+26+9+1
6) cyMMa Bcex nOpJlAKOBbiX HOMepOB 6YKB aJ14>aBHTa (aT «a» AO
«JI»): 1 + 2 + 3 +... + 33 - 561. nepeBeAeM 3TO '4HCJ10 B CJ10BeCHOe
Bblpa>KeHHe M nOC'4HTaeM KOnH'4eCTBO 6YKB B Ka>KAOM cocraBnJlIO-
lijeM era CJ10Be:
nJlTbCOT - 76YKB HnH HCJ10 7;
weCTbAedIT - 10 6YKB -, '4HCJ10 4;
OAMH - 4 6YKBbI - 1tHCJ10 4.
KaK BMAHM, B 3TOM, Ka3anOCb
6b1 CJ1y aMHoM, '4HCJ10BOM BbI-
pa>KeHMH 3aKoAHpoBaHbI YHCJ1a
KOHCTaHTbI - 147;
B) cyMMa nOpJlAKOBbiX HOMe-
pOB Bcex 6YKB: rnaCHbiX - 186,
cornaCHbiX - 375. HanHweM
3TH Bblpa>KeHMJf CJ10BaMH, npo-
HYMepyeM Ka>KAY1O 6YKBY '4HCJ1aMH CKB03HOM HYMepal4HH an4>aBH-
Ta H CJ10>KHM nonY'4eHHble '4HCJ1a: 186 + 375 - (CTO BoceMbAeCJlT
HaM60nee 'faCTO j,1CJ10-
BO pe30HaHC BblSlBJ1S1eTCSI
'Ha KOHCTaHTy1 j,1cno 147)
j,1 Ha "J1eBYIO nonoBMHY-
<l><>PMYJ1b1 38KOH8 H-
CTB8 np"'POAbi ( j,1CJ10 28).
144
HYMeponorUR B ancpaBHTe
WeCTb) + (TpHCTa ceMbAecJlT nJITb) - (1 + 9 + 2) + (7 + 8 + 1) - 28.
nOnY'4eHa neBaJl '4aCTb 4>opMynbl 3aKoHa E,qMHCTBa.
4T06b1 eU4e pa3 nOKa3aTb CKenTHKaM, '4TO n4>aBHT HMeeT CTpo-
ro MaTeMaTH'4eCKOe CTpoet3He M COAep>KMT «'4HCJ10BOM pe oHaHc»
6YKB, npoM3BeAeM HenorH'4HOe npe06pa30BaHMe H TtpCMOTpMM,
H3MeHHT nH :no Y>Ke YCTaHoBneHHYIO B aJ1 aBMTe CTpOMHYK> 3aKO-
HOMepHoCTb:
a) H3 CKB03HOro (nopRoKoBOZO) KOAMpOBaHHJI 6YKB aJ14>aBMTa
BblnHweM Te 6YKBbI, nOpJlAKOBbie HOMepa KOTOpbrx cooTBeTCTBYIOT
Ka)t(,QoMY HCJ1Y KOHCTaHTbl147. 4MCJ1Y «1» cooTBeTCTBYIOT 6YKBbI:
a, H, C, 'b; '4HCJ1Y «4» - r, n, 4>, 3; MCJ1Y «7» - e, 0, ;
6) pa3AeJ1H,.. 6YKBbI an4>aW1Ta Ha rnaCHbie M cornaCHbie M OT-
AenbHO BblnHweM B KonOHKy 3HaKH. Ka)t(.fW1O KonoHKy npoHYMepy-
. eM CKB03HOU HYMepa14MeM..
r.naCHbie 38 M
I-a 6- y
2-e 7-bA
3-e 8- 3
4-" 9- 10
5 - 0 10 - 11
Cor.naCHbie 311
1-6 6- 3 11-H 16-
2 - B 7 - M 12 - n 17 - x
3 - r 8 - K 13 - P 18 - 4
4-A 9- n 14-( 19-
5-)1( 10.- M 15 -I 20- w
21 - lq
3ttaHM
1-1>
2-b
B} maCHbiM H comacHblM, HMelOU4HM KOA«1»,«4», «7» - a. M,e, 'b, r,
n, 4>, 3, e; 0, '4, COOTBeTCTByiOT '4HCJ1a nOCJ1eAHero HYMeponorM eCKoro
npe06pa30BaHHJI: 1,4,14, 1, 3, 9, 16,8,3,5, 19. x cyMMa paBHa «3ep-
KaJ1bHOMY orpa>KeHHIO» '4MCen 4>opMynbl 3aKOHa E,qHHCTBa - 82
(3HaK b, He JlBJ1J1lOl14HMCJI 3BYKOM M HMelOtqMM KOA «1», He Y'4HTblBaJ1-
CJI). HTepecHO M TO, 'ITa HeY'fTeHHblM 3HaK «b» HMeeT B «06b1'4HOM»
145
rnaBa 3
an4>aBHTe nOpJlAKOBbiM HOMep
«28». aMHOCTb?
«lfHCJ10BOA" pe30HaHC» aJ1-
4>aBHTa C '4HCJ1aMM 4>oPMynbl3a-
KOHa HHCTBa yCTaHoBneH, HO
MO>KHO nM BblJlBMTb TaKOM >Ke
3HepreTH'4eCKMM pe30HaHC C
'4MCJ1aMM KOHCTaHTbI, pa3 '4MCJ1a
4>oPMynbl M KOHCTaHTbl B OKKYnb-
THOM npeACTasneHMH - «OAHO
H TO >Ke»? Hey>KenM '4Hcna 4>oP-
MYJ1b1 3anO>KeHbI B crpYKTyPY
«3HepreTM'4eCKHX BM6pa HM»
Bcero, '4TO Hac OKPY>KaeT?
Aa>Ke B an4>aBHT? 8eAb AJ1J1 3TO-
ro AeMCTBMTeJtbHO Hy>KHa YAMBMTeJlbHaJl HCJ10BaJl CTpOMHOCTb, yno-
pJlAO'4eHH «Bcero, C03AaHHoro nOA nYHOM»!
AnJl eU4e COMHeBaIOU4M)(CJI B MaTeMaTH'4eCKOM ynopJlAO'4eHHH aJ1-
$tBMTa A. KMcenb npeAJ1araeT npoAOn>KMTb HYMeponorM4ecKoe HC-
CJ1eAOBaHHe, npoBep,H onepa MIO, 06PaTHYIO HYMepa MM aJ14>aBMTa
nyHKTa «6». BHOBb BblOMweM 6YKBbI, MMelOU4He nOpJlAKOBbie HOMepa
«1», «4» M «7»: I1IjCHbie - a, M, bI, JI; cornaCHble - 6, At M, M, p, 4>, '4.
Bcex 6YKB 11. CYM H)t nOpJlAKOBbiX HOMepoB npH CKB03HOM npo-
c eTe Bcero aJ14>aBHTa: 1... 10 + 29 + 33... 2 + 5 + 11 + 14 + 18 + 22 +
+ 25 - 170. 11 6YKB Aa.oT B oKKYnbTHoM M MCJ1eHHM LtH4>PY «2», a
«170» - «8». BHOBb non eHo MCJ10 3aKoHa HHCTBa - 28.
3anO>KeHHble B aJ14>aBHT '4HCJ1a 4>opMynbl H KOHCTaHTbI 3aKoHa
MHCTBa nOMoralOT BblJlBHTb «'4HCJ10Bble pe30HaHcbI» Me>KAY CJ10-
BaMH H nOHftTHJlMH, AononHJIJI MX CMblCJ10BOe 3Ha'4eHMe HOBbiM YPOB-
H8 38MeTKY
C4....TaIOT, TO '-'8tnp pa3B....-
r..-. M....poB()M Hayl(.... .... KYnb-
rypbI B OYAVU-'8M nepeMec-
r....Tc B POCC....IO (aclpOno-
nt 3TO nOATB8p>KAaIOT no
rpaH3HTaM, T. e. no AB....)I(8.
H....IO nnaHeT), Tal( KaK PYC-
CK.... 3b11( oOna,Qa8T H8....-
6onbUJ....M.... 3HepreT.... ecK....-
M.... B03MO>KHOCT M}1 B
n03HaH........ Ta H M....p8 ....
38KOHOB KapMbI KOCM0C8.
146
H)'MeponOnfR S ancpaSHTe
HeM OKKyJ1bTHOrO nOHMMaHMJI. KaK C'4MTaeT HYMeponorMJI, 6naroAa-
pJl 3TOMY ycTaHaBnHBaeTCJI YHMBepCaJ1bHaJl '4MCJ10BaJt B3aMMOCBJl3b
C OKpY>KaIOU4MM MHpOM,nY'4we nOHMMalOTCJt era KapMM'4ecKHe npeA-
Ha3Ha'4eHMJI H BnHJlHHJI Ha 'IenOBeKa. Ha 3TOM OCHOBa tlfpycCKO-
MY aJ14>aBHTy M Mcnonb3YIOU4eMY ero PyccK9J13b1 HOMY HaceneHMIO
oKKynbTM3M npeACKa3b1BaeT JlpKOe M npoAYItTMBHoe 6YAYU4ee.
Bbl60p MeTOA8
B HYMeponorHM pa3pa60TaHbI pa3Hble MeToAHKM '4MenOBbiX H
rpacl»M'4eCKHX npe06pa30BaHMM. Pa3 MX MHoro, TO He JlBnJteTCJI nM
caM 4>aKT Mcnonb30BaHHJI pa3HblX '4MCJ10Bbix KOAOB TeppeTM'4eCKOM
CJ1a60CTblO H Hepa36epHxoM B HYMeponorMH, Ha,qyMftfHOCTblO BbI-
'4MCJ1eHMM? HeT, He JlBnJleTCJI. cnonb30BaHMe pa3HblX BenH'4Mtt '4MC-
nOBbiX KOAOB HanOMMHaeT npMMeHeHMe B «OPTOAOKCaJ1bHOM HayKe»
'4MCJ10BbIX M3MepeHMM pa3HOM BeJ1M'4MHbI, HO C OAMHaKOBOM LtenblO.
Tat<, npM xapaKTepMCTMKe AflMHbI MO>KHO ee M3MepRTb B CaHTHMerpax,
MeTpaX, KMnoMerpax, MMJ1J1X; npM o eHKe MaCCbI MO>KHO nOnb30BaTbCJI
rpaMMaMH, KHnorpaMMaMM, TOHHaMM - BcerAa pe3ynbT.aTbi 6yAYT
COOTBeTCTBOBaTb HCTHHe, HO C pa3HoM TO'4HOCTblO. C nOA06HoM
LtenblO MO>KHO HcnOnb30BaTb pa3Hble 4MCJ10Bble KOAbI, Ka)t(AbiM M3
KOTOpblX AaCT CBOIO xapaKTepHCTMKy HCCJ1eAYeMoMY JlBneHHIO B TOM
MnH MHOM CTeneHH npM6nM>KeHHJI (HnM, KaK rOBOpJlT, «B '4MCJ16BOM
YBeJ1M'4eHMH»). 4TO KaCaeTCJI npaBOMO'4HOCTM Mcnonb30BaHHJI Taro
HnM MHoro KOAa, TO 06 ngM 6YAeT CKa3aHO HM>Ke.
npHBeAeM npHMep Hcnonb30BaHMJI KOAa npH xapaKTepHCTMKe
Ha3BaHHJI «nYHa». cnonb3yeM MeTOAbi npHBeAeHHoro Bblwe KO-
AMposaHMJI 6YKB aJ14>aBMTa:
47
rnaea 3
,
,.. 9-3HHtOM KO,qMpOBaHMM: «11yHD - 4 + 1 + 6 + 1- 14- 5.
Me no BeJ1M'tMHe craPWMX apKaH08 Tapo: 1 + 9 + 3 +
+1-14-5.
IkwtpoeaHMe CKB03HOM tcyMepaijMei4: «l1yHa» - 13 + 21 + 15 +
+1-50- 5.
... IIIIIAMM, npM npaBMJ1WtOM MCn0l1b30BaHMM pa3Hwe HyMepo-
KOAbi AaIOT OAMH pe3yJlbm.
MeIoAw OICKYJlbTHOro enOJKeHM1I 'tMCen M ynPOll4t!HM" Ma1eMaTM-
'feCDX twpaJ(eHMM MCnOJlb3ONllMCit AO nM ropMMqeB, KO-
TOpwe weHCTBOBaJ1M M pa3BMl1M HYMeponol1NeCKHe MeTO-
AW- JIIo6oe MHOr03Ha'fHoe '4MC11O craHOBMJ1OCb OAH03Ha'{HWM nyreM
'Y"IIIIpOUHMII ero 'tneHOB, 'fT0 3Ha'4MTenbHO ynpo&qaJIo MaHM-
nyJIIItIHI: 64 - 6 + 4 - 10 -1; 1511 - 1 + 5 + 7 + 1 - 18 - 1 + 8 - 9
MT.
. .Qa oqetfKM B03MOJfUfOCTeM OKKY11bTHYX npeo6pa30BaH" M BbI-
"..... MX Hl86W'fHblX CBOHCTB npoM3BeneM CpaBHMTeJIWtWe BIII-
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2, M ero cnpoM3BOAHbfe», 06pa3OlaHHwe npM TeococI*'IeCKOM eno-
JlCeHMM: 11 (1 + 1- 2); 29 (2 + 9-
-11-2); 38 (3 +8-11-2) -3101
"YMeponOrM'4eCKH PIIA MO)l(HO
npoAOmKM1lt:
a) enOJKeHMe:
2 + 2 - 4.
2 + 11' - 13 - 1 + 3 - 4.
2 + 29 - 31 - 3 + 1- 4;
6) BbI'fMTaHMe:
11 - 2 - 9.
0..-.. ..,.........
HIIIyp8nwtbM ..
C8A OJ 11lfJ 9 RBmIeTCfI
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148
H - , ,nOrHR B. ,,;..
29 - 2 - 21- 2 + 1- 9.
38 - 2 - 36 - 3 + 6 - 9;
8) YMHOJKeHMe:
2 x 2 - 4.
11 x 2 - 22 - 2 + 2 - 4.
29 x 2 - 58 - 5 + 8 - 13 - 1 ... 3 - 4;
r) AUeHMe:
2 : 2 - 1.
11; 2 - 5.5 - 5 + 5 -10 -1.
29 : 2 - 14,5 - 1 + 4 + 5 - 10 - 1;
A) BQ3IIeAeHMe B KBaAJ)aT:
Z2-4..
11 2 - 121- 1 + 2 ... 1- 4.
292-841-8+4+ 1-13 -4.
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HMJt paapwBaIOT onpeAeneHHWe ceoMcrBa '4Mcen. OuyIIbTIICIW ..x
McnOJlh3ylOT e HecKOJ1W(O TIIICJI'4 neT.
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BOKVf1HOCTb CAOB - MbiC/UJ, a BOT MWCIIM HecyrCJI B ... M03rY
B MaTe nt'teCKOM nopJlAKe, CorAaCHO KaKMM-TO , M
«KO MW rOBOpMM, TO HaWa MWCJIIIt MMeeT MaTet4ane'leCllli 06-
nMK» (...It c. 62). 3Ha"MT, MWCJIb MO)I(HO IIWpa36m 'f IIftM
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I4Dmuveac awpaeHMe B 'fMCJlax MJlM MX aHanorax (
enoBaX, )l(ecTOllbiX cMMBonax) M Mwenb MO)l(HO BWpa31111t II rpa-
cl»MK TO BlIOIItte peanbHO McnO.ltb30BaHMe KOHTPO.ltJl jt
M OijeHl(M HOJ)J'a.nbHOfO I4b1WJleHU . 3Ty OCo6eHHOCT1t .-e14
neMUKM Mcnonb3YlOT 8 C80MX Mcc.neAoHTenbCKMX TeCTax II(.M-
149
rnSB8 3
xonorM H nCMXMaTpbl. OHH npo-
CJlT HcnblTyeMoro HanMCaTb
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(npocTo '4epTHTb) «B cB060A-
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BaHHM -3aKnIO'4eHMe a COCTOJl-
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npMAaBan 60nbwoe AMarHOC-'
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BMAeHMJI KapTMH, HaAnMceM, cn08 H nMHMM cHoBMAeHHM AnJl
nporH03a 6}IAYU4erO '4enOBeKa, KOTopoe TO>Ke 3aBHCHT aT CO-
CTOJlHMJI ero hCMXMKH._
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06b1'4HO 6b1BaeT C TeM, '4TO 3anO>KeHO B CMblCJ1 CJ10Ba. «HMKOfAa He
n03BOnftnOCb Y'4 HKy M3naraTb KaKMe-nH60 MCTOpH'4eCKHe, penH-
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'4T06b1 CMnbl, CBJl3aHHble C 3THM"C06b1TMeM, He 6b1nH eUL pa3 npH-
Bne'4eHbI ,. - nHweT (neHa 6naBaTCKaJl B «TaMHOM JlOKTPHHe»
(T. L KH.,2",'-'C. 8).
MHorHe penHrHM npM3b1Ba1OT K C<'4MCTblM nOMbicnaM» M 3an-
peU4alOT nnoxo AYMaTb a APyrOf!1 enOBeKe, Aa>Ke a Bpare. C'4H-
TaeTCJI, '4TO C<3HepreTH'4eCKHM 6YMepaHr» MblcnM BcerAa B03Bpa-
OKKYn TM3M .'tepa
M C8r0AHtl
A. I<Mcenb nonaraeT, 'lTO
pycclG1'1 81$8BHT a.1MeeT
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HOe KOCMOCOM MaTeMan1-
'feCKoe nocYpOeHa.1e a.1 ero
C03,D,aHa.1e SfBlmeTCSI MaTe-
Mant'feC1G1M (t-ryMep011O-
nt'feCIG1M) CBOOcrsoM
HaUJerO MblwneHHR.
150
HYMeponorUR B anC/1aBuT8
lqaeTCJI K TOMY, KTO era
nocnan B TOM )Ke Ka'4e-
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nOCJ1aH «Ha CTapTe».
o MaTepManbHOCTM
MbienM nHweT E. nMca-
peBa (CHna MblcnH H
MblCJ1e06pa3b1, 1992), a
npMMepbf ee nocneA-
CTBH npHBoAMT c.r. 6y-
TOBCKMM (KaK 3aIqHTHTb-
c aT crha3a H HaKonMTb
6M03HeprHIO, 1991).
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naTbie Bbfpa>KeHMJI CBJlU4eHHblX nHcaHHM HMelOT 3aKOAMpOBaHHble
'4MCJ10Bble pe30HaHCbI M HaCblI14eHbI oKKynbTHbiM COAep>KaHHeM.
3 npeAblAYU4HX pa3AenOB AaHHoM KHMrH '4MTaTeJ1b nonY'4Hn He-
KOTopble TaMHble 3HaHMft no HYMeponorMM. nonp06yeM HX MC-
nonb30BaTb, '4T06b1 nonY'4MTb AononHMTenbHYIO, CKpbliylO aT «He-
nOCBJlU4eHHoro» en08eKa MH4>opMa MIO, 3aKOAHposaHHYlO
MYApe aMM ApeBHOCTM B KaKOM-nM60 CBJI U4eH HaM nHcaHMH, HanpM-
Mep B 6H6nHH. -B03bMeM AlUI npHMepa 6M6n8MCKoe Bblpa>KeHHe a
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+ (CBJlTOM AYx) - 3 + 9 +
... 7 - 19.
nonY\lHnH TO >Ke Hcno
KOAa -19, KOTopoe HMeeT
M CJ10BO «60r».
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HYMeponorHfI B ancpaBHTB
HYMepOnOrM'4eCKHe paC'4eTbi '4HCJ10BOM acrpOnOrMH nOKa3anH
HaJ1H'4He HYMepOnOrH'4eCKOM CBJl3H MK C nnaHeTaMH COnHe'4HOM CH-
CTeMbi. Ho MeeT nH TaKYIO >Ke CBJl3b C '4 CJ1aMH MX 3aKOHOMep-
HbiM paCnOnO>KeHHeM B KBaApaTe (a '4epe3 Hero C nnaHeTaMH-) 6M6-
neMcKoe Bblpa>KeHHe 4(OTe CblH, CBJlTOM AYx»? MO>KeT b, aHa
npHBOAHTCJI B CBJllqeHHOM n caH H CJ1 aMHO?
OKa3b1BaeTCJI, HeT. BocnpMHHMaeMaJl BHa'jine.KaK Ha60p CJ10B,
3Ta 4>pa3a MeeT CKpbll)'1O H crporo onpeAeneHHY.o MCJ10BYIO BH6-
paLtHIO. B AOKa3aTenbCTBO npOH3BeAeM BbI'4HeneHHJI. BHa'4ane
0603Ha'4MM Ka>K.qy1O 6YKBY 3THX CJ10B nOpJlAKOBblf14 HOMepOM aJ1-
4>aBMTa:
OT E Lt C blH (BflTO AYX
16 20 6 24 19 29 15 19 3 33" 20 1& 11 5 21 23
AnJl onpeAeneHHJI MeCT pacnOnO>KeHHJI 6YKB Bbfpa>KeHHJI B KBaA-
paTe ,QlOpepa npOBOAJIT 60nee CJ10>KHble HYMeponOrH'4eCKMe BbI-
'4MCJ1eHHJI. He 6YAeM yToMnJlTb HMH HTaTenJl. npMBeAeM KOHe'4-
tibiM pe3ynbTaT H Y>Ke nonHOCTblO COCTaBneHHblM MarH'4eCKHM
KBaAPaT (pHC. 9). nOCJ1e cyMM pOBaHHJI CABoeHHblX '4HCeJ1 KBaA-
paTa non MM MKA C '4McnaMH (pHC. 10).
CpaBH_ Te pe3ynbTaTbi CYMMM-
pOBaHMJI '4MCJ10BblX KOAOB MK.Q M
AaHHoro Bblpa>KeHHJI - OHH
oAHHaKoBbi (CM. pHt. 10 H 13).
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3b1BaeT Ha «3HepreTH'4eCKHM pe-
30HaHC» Me>KAY 6YKBaMM cnOB
npHBeAeHHoro Bblpa>KeHMJI H
'4HCJ1aM11 B MarH'4eCKOM KBaApa-
ECTb MH8HM8
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153
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5 11 20 16
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Puc. 10. npOBepKa 3aKoHoMepHoCTeM
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neMcKoM B..pa>KeHMM ero CyTb 3aKOAHpoBaHa CJ10BaMM (M nerKO nOA-
AaeTCJI npMBbI'4HOM HaJit AewM4>poBKe), a B MarH'4eCKOM KBaApaTe -
Bblpa>KeHMIO CMMBOnH'4eCKMX '4MCeJ1. OAHaKo «'4MCJ10BOM Jl3b1K» Mbi
nOKa nnoxo nOHHMaeM H He npMBblKnM 06U4aTbCJI Ha HeM C OKpy>Ka-
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TeMaTM'4eCKM npaBHnbHo nOCTpoeHHblM, cOAep>KaTb rapMOHMIO M
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nOBaJl at4MJI B 3TOM Bbfpa>KeHMM - npM3HaK '4MCJ1080M rapMO-
HMM, T(1 aHa AOn>KHa 6b1Tb ycrOM'4HBa. °HeCMOTpJl Ha pa3HblM Ha60p
6YKB M LtM4>p, nonpo6yeM KaK 6b1 B3BecHTb Ha «'4MenOBbiX Becax»
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154
HYMeponornR B anC/JaSHTe
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'4MCJ1a enO>KHM AO 06pa30BaHMJI OAHOrO '4MCJ1a. Bblpa>KeHMe MMeeT
'4eTHOe HCJ10 3HaKOB (16), n03ToMY era cepeAMHa COCTOHT M3 ABYX
'4MCen (OHM nOA'4epKHyYbI.):
OT E C blH CBRTO AYX
npoH3BOAHM '4HCJ10BOe KOAHpoBaHHe 6YKir.
16 20 6 24 19 29 15 33 20 16 11 5 21 23
, AenaeM Teoco4>M'4ecKoe CJ10>KeHHe '4MCJ10BOro KOAa Ka>KAOM 6YK-
Bbi M BbinOnHJleM apH4>MeTM'4ecKoe CJ10>KeHHe.
7+2+6+6-21 10+11+6-27 6+2+7+2-17 5+3+5-13
nonY'4eHHYIO cyMMY BHOBb CKJlaAblBaeM Teoco4>H'4 I(H:
21-2+1-3 27-2+7-9 17-1+7-8 13 +3-4
nOBTOpJleM apH4>MeTH'4eCKOe H Teoco4>H'4eCKOe CJ10>KeHMe AO
nony eHHJI 3neMeHTapHoro (OAMHO'4HOro) '4HCJ1a:
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3 HO C npHHJlTbiM B xpMCTMaHCTBe nOHIiTMeM a «TpHeAHHCTBe» M
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168
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171
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173
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PUC. 15. MarH'4eCKHM KBa,qpaT C BnHcaHHblM B Hero Ha3BaHHeM nnaHer (a)
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174
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4TO YAHBHTenbHO B npOBeAeHMM paC'4eTOB, KOTopble npMBenM K
non eHHIO crporo onpeAeneHHOM '4HCJ10BOM CHMBonMKM: 4>OPMY-
nbl ('4MCl1a 28)? OKa3b1BaeTCJI, CYAJI no HYMeponOrH'4eCKHM paC'4e-
TaM, He TonbKO H03S0Hue Ka>KAOM nnaHeTe 6PIno AaHO He tny'4aM-
HO - aHO 6b1no «3apaHee npeAonpeAeneKo». -Ho '4TO He MeHee
YAHBHTeJ1bHO: Ha COnHe'4HOM op6HTe OJ1R KOJKOOU e nJ10Hembr 6b1no
«yroTOBaHO» onpeAeneHHoe MeCTO OTHOCHTenbHO (onH a. Bce 3TO
cnMWKOM cornaCOBaHHO H ynopJlAO'4eHHO, '4T06b1 6b1Tb cnY"laM-
HOCTblO. Pe3ynbTaTbi HCCJ1eAOBaHHJI Bbl3BanH YAHBneHHe Aa>Ke y ca-
MOro aBTopa HYMeponOrH'4eCKMX npe06pa30BaHHM - AneKcaHApa
KHcel1J1 (1993).0 TOM, '4TO «CJ1Y4a HOCTb» 30KOHOMefJ/1l1, OH nHcan:
«HeMblCJ1HMOe nepenneTeHHe npownoro, MHCTHKM, nnaHeT H Jl3b1-
Ka - H Bce TOT >Ke pe3ynbTaT. KaKHM 06pa30M?» KMCeJ1b C'4HTaeT
'4TO, KpOMe KaK 3aKOHOMepHblMH '4HCJ10BblMH pMTMaMM, HMelOlqM-
MMCJI B crpyto'ype JlBneHH H 06'beKTOB npHpOAbI, 3TO. 06'bJlCHHTb
HeB03MO>KHO. BblJlBHTb H npOCJ1eAHTb pa3BMTHe «3HeprHH '4HCJ10-
BbiX crpyKlYP» B CyTH JlBneHHM H 06'beKTOB npHpOAbi MO>KHO C no-
MOU4blO HYMeponOrH'4eCKHX MeTOAOB HCCJ1eAOBaHHJI.
EneHa 6naBaTCKaJl nHweT:
«no onpeAeneHHIO nH4>aropa,
MOHaAa B03BpalqaeTCJI B 6e3-
MonBHe H TbMY, KaK TonbKO OHa
BblJlBMna TpHaAY '4HCeJ1, ne>KaU4HX
B OCHOBaHHH npOJlBneHMJI Bce-
neHHO » (Ta HaJl AOKTpHHa, T. !,
KH. 2, c. 155).
MarHl/eCKHU KBa,o.paT
B H8CTCHI&q88 Bp8MA
MO>KHO C'iIitTaTb. TO TpHa-
1¥1 "IHCeJ7 BbI Bl1eHa, -
3TO 'U1C110 147, KOHCTaHTa
$OPMYl1b1 3aKoHa E.c.IitH-
CTBS Bcel1eHHoH.
175
rn8B8 4
cnonb3Yft KOHCTaHiy H 4>opMyny 3aKoHa EAHHCTBa cyiijeCTBO-
BaHHJI H pa3BHTHJI AJlJI HccneAOBaHHSI KaKorO-TO JlBl1eHHSI HnH
06'beKTa, c nOMOiijblO Ka66aJ1HCTH'4eCKHX MeTOAOB paC'4eTa H MarH-
'4eCKOrO KBaApara MO>KHO HaXOAHTb HOBbie 3aKOHOMepHOCTM B HX
crpYKTYpe H pa3BHTHH. 3TO paCWHpJleT HaWH B03MO>KHOCTH B HX
n03HaHHH. TaK nonaraeT HYMeponOn1J1.
TaMHbl KBaApaTa AlOpepa
B «4HCJ10BYIO 3PY», T. e. KorAa 6b1nH H306pereHbI '4HCJ1a (ApeB-
HMMM WYMepaMH oKbno 6 TbiC. neT Ha3aA) MOiijHOe pa3BHTHe nony-
4HnH '4HCJ10BaJi CHMBonHKa H pa3nH'4Hble «MarH4eCKHe 4>HryPbl». B
ponH nOCJ1eAHHX 4aCTO BbicrynaJ1H KBaApaTbi C pa3HbfMH HX «4 C-
· nOA Ha M eBpone CKOIiI O( COOBO 3pbl» 06b1 HO no- ·
. H MaIOT BpeM BBeAeH COBpeMeHHoro apa6cKoro C C- .
· l1eH - 3TOro BpeMeH 6YAeM np ep)KIIIBaTbC Mbl. ·
. npo 30wno 3TO B 1120 r.. KOrAa MaTeMaT K Mel1apA 3 .
: DaTa Been COBpeMeHHYIO C CTeMY C Cl1eH , Ha3BaB ee :
· ..apa6cKO », XOT caM apa6b1 nepeH l1 ee Y ApeBH X H- ·
. eB. Apa6C1Ca .c CTeMa OKa3a11aCb CTOl1b YAOOHOO, TO .
· K 1600 r. B EBpone CTaJla cn0l1b30BaTbC nOBCIOAY. OHa ·
. COCTO l1a 1113 C1TOBbiX C MB0110B OT 0 AO 9. C nOMO 1O .
: KOTO MO)I(HO ooo3Ha Tb 11I000e C110. 3rOT 311eMeH- :
· TapHbI P A 6b1n aKT BHO Cn0l1b30BaH eBpone cK M HY- ·
. Mepol1o"aM <t> l1oco<J>aM .
176
nOBblMH HanOnHHTenJlMH», paCnOnO>KeH e KOTOpblX nOA4HHJlnOCb
crpOrOM MaTeMan1'4eCKOM 3aKOHOMepHOCTH. OKKYnbTHbie 4>Hnoco-
4>bI M HYMepOnOrH CTpeMHnHCb OTbiCKaTb aHaJ10rHIO '4HCJ10BblX CO-
OTBeTCTBHM «MarM4eCKHX $Mryp» JlBneHMJlM M f3eU4aM >KH3HM H, K
YAHBneHHIO HenOcBJlU4eHHblx, HO K c06CTBeHHOMY YAOB TPopeHMIO,
OHM HaXOAHnM HeKOTopble 3aKOHOMepHOCTM pa3nM'4HblX npo eCCOB
B >KH3HH, KOTopble TyT >Ke CBJl3b1BanHCb C «3HepreTH'4eCKHM C03BY-
HeM» MarH4eCK X 4> ryp H HX nOCTpOeHH&M. . .
npe e '4eM Mbi paCCMOTpHM OAHY H3 HaH60n H3BeCTHbiX Ma-
rH'4eCKHX 4> ryp - KBaApaT AlOpepa, onpeAenHMCJI C nOHJlTMeM
«'4HCnoBaJi 3pa», K KOTOPOMY HHorAa 6YAeM 06palqaTbCJI.
AeMCTBHJI C pa3HblMH CHMBona-
MH, HanOMHHalOU4He MaTeMaTH-
'4eCKHe npe06pa30BaHHJI, Y4eHble
ApeBHOCTH Ha'4aJ1H npHMeHJlTb C
He3anaMJlTHbiX BpeMeH, n03TOMY B
6YKBanbHOM c blcne nOHJlTHe
«'4HCJ10BaJl 3pa» cpaBHHMO C Bpe-
MeHeM ynOTpe6neH JI 4enOBeKOM
nepBblX CHMBonOB. B TaKOM nOHH-
MaHHH Ha4ano «'4HCJ10BOM 3pbl»
MO>KHO OTC'4 HTbI BaTb OT WYMepOB - OKono 6000 neT AO H. 3., C03AaB- ..
WHX CHMBonHKY C AeCJlTH HblMH (c OCHOBaHHeM 10) H weCTHAeCJI-
TH'4HbIMH (c OCHOBaHHeM 60) C'4HCJ1eHHJlMM. npHH Mnbl 060HX C4 C-
neHHM Hcnonb3YIOTCJI AO CHX nop, a nOCJ1eAHee - 60-TH4Hoe-
C4HCJ1eHHe npHMeHJlIOT B acrpOHOMHH H acrponorHM npH pac eTe ABH-
>KeHHJI.nnaHeT, M3MepeHHH ymoB BpeMeHM.
CYlqeCTBOBaBwaJl AO 3TOro pHMCKaJl CMMBonHKa '4MCen HynJl He
HMena, 6b1na rpOM03AKOM M HeYA06HOM B paC'4eTax. Hynb n03aHM-
MarU&.IeCKUU KBa,o.paT
MctOpM'I8CK8.?1 cnpaBK8
nOHsm1e Clt01'pfl..\aTel1bHoe
HCno. BnepBble Been He
MaTeMaTIilK. a manbJlHC-
1Gt t<yIlelt n&.13aHO B
1202 r: An 0603Ha eH&.1
&.1M CBOII1X y6b1TKOB.
177
rnasa 4
-
CTBOBanH y HHAH 1cKHX MaTeMaTHKoB,
KOTopble ynoTpe6nJlm 3TOT CHMBon
C VI B. AO H. 3. 3HaKH «nnlOc» (+) H
«MHHyc» (-) npeAJ10>KHn eWCKHM
MaTeMaTHK Jh-l BHAMaH B 1489 r. Ao
3TOro AeMCTBHJI CJ10>KeHMJI H BbI'4H-
TaHHJI 0603Ha'4anH Ha'4anbHblM na-
TMHCKHMH 6YKBaMH «p» (pLus) H «M»
(minus). 3HaK paBeHCTBa (-) BBen
HeMe KHM MaTeMaTHK r. KaHTop B
1550 r. AelO wYMepcKHx ",yAJ)e OB
o AeCJlTH'4HOM C'4HCJ1eHHH Hcnonb30-
BaJ1 wOTnaHAcKHM MaTeMaTHKA>+<oH Henep, KOTOpbl B 1614 r. H306-
pen, KaK OH HX Ha3Ban, ('4YAecHbie norapH4>MbI». 06 3TMX H APyrHx
oc06eHHOCTJlX pa3BHTHJI '4HCJ10BOM CHMBonHKH B «I.IHCJ10BYIO 3Py»
co06tqaeT C.r. 6epHaTOCJlH B KHHre «PeKoPAbI npHpOAbi H enOBe-
'4eCKOM AeJlTe!hHoCTH» (1994).
Y eBponeMcKMx HYMep0J10rOB 60nbwoM nonynJlpHoCTblO nonb3Y-
eTCJI KBaApaT Atopepa. MarH ecKHM KBaApaT AlOpepa (MKJ\ HnH MK)
06naAaeT HeO>KHAaHHblMH H He06bl'4HblMH MaTeMaTHl.leCKMMH H OK-
KYnbTHblMH CBoMcTBaMH. B ero CTPYK'TYpe ne>KHT npHHLlHn COOTBeT-
CTBHJI. npHH Hn ooTBeTCTBHJI - 3TO nOA'4HHeHHe 3aKoHY EAHH-
CTBa, B OCHOBe KOTopor .ne>KHT llYHHaJl 4>opMyna (28 - 4 x 7) H ee
KOHCTaHTa (147).
cnonb3Yjl npHHLlHn rooTBeTCTBHJI, B KBaApaT AlOpepa MO)f(HO BnH-
(arb J1I06b1e'1I a, KOTopble He Hapywar B HeM '4HCJ10BOM pe30HaHC.
(aM MK.Q Aa HHaeTCjI C HM)f(HerO npaBoro yma C '4HCJ1a 1. PaCCMOTpHM
'4HCJ10BYIO rapMoHHIO KBaApaTa AlOpepa-. KpoMe oAMHaKoBoM cyMMbl,
nOI1Y"faeMOM OT CJ10>KeHHJI '4HCen, pacnOnO>KeHHblX Ha Ka>KAOM npJl-
1ICyn. acero cYlQerolt
HYMepoJ10rM KMT8R M
EBponbi COCT8BJ1RJ1M
«MarM eCKMe" MCJ10-
Bble rpa<!> ecKMe
nOCTpoeHMR. Kl18CCM-
<!>MJ..U.1PYR ocCYTb Bcero
cyulero,. B MMpe. B
TOM MCJ1e M B eJ10Be.
Ke (M....KpoM....pe).
178
a
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5 10 11 8
9 6 7 12
4 15 14 1
34 34 34
34
34 34
Man1'1ecKHH KBap,par
6
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PUC. 16. 4MCJIOBOM (a) M rpacl>M'4eCKMM (6) KBaApar';tlOpepa
16 3
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179
rnass 4
MOi roptDOHTaIIM, BepTMKa11M MIIM AMaroHaJ1M, raK>Ke B KP'Jre, OXBaTbt-
UIOtqeM ymoBbte KneTKM KBa.qpaTa, 3Ta >Ke '4MCJ10BaJI cyMMa (34) no-
npM .",o60M paC'4J1eHeHMM KBaApaTa Ha '4eTb1pe paBHbIe '4aC-
till no '4eTWpe KIIer KH B Ka>t<AoA (pMc. 16 M 17).
CyMMa Mcen KIIeTOK. pacnOnO)l(eHHblX no nMHMJlM (nY'faM) mo-
6oro TaKOra KBaApara, AaeT '4McnO 34 (AM4>$epeH MaJ1"Hbie MC-
JIOIIWe pe30HaHcbI KBaApaT08 npeACTaBJ1eHbI- Ha pMC. 17). KpoMe
TOro, etnM M3 cepeAMHbI KBaAPaTa AlOpepa BbiAenMTb '4eTblpeXKne-
TO'UfWM KBaAJ>aT, TO cyMMa era 'fMCen BHOSb AaCT '4McnO 34.
B KBa.QpaTe AlOpepa HeT xaoca. LtM4>Pbl pacnonaralOTCJt He Tonb-
1(0 .. crporoi4 MaTeMaTM'4eCKOM nocneAoBaTeJ1bHOCTM, HO M B apo-
d CMMMeTpMH (pMC. 16, 6). KBaAPar. KaK 6b1 cMHTe3MpyeT M8TeMa-
TH'4eCKYIO 3aKOHOMePHOCTb,
reoMerpH'4ecKy1O ynoPJlAo-
'4eHHOCTb M «J1OrtNeCKYIO»
CB 3b 3neMeHTOB.
CYMMbI '4MCen BbI'UleHeH-
HbIX KBaApaToB (pMC. 17, a)
H «KBaApaTa B KBaApaTe»
(pHC. 17, 6), BK1IIO'W cyt4-
Mbi '4MCen no CTOpoHaM «Ha-
PY>+<Horo» KBaAPaTa (6),
COCTaBn IOT OAHY M TY >Ke
BeJtM'4MHY - 34 (06"bJlcHe-
HMA 8 TeKcre).
MO>+<HO C AOCTc1TO'4HblM
OCHOBaHHeM npeAnono-
>KMTb, '4TO TaKOM Ha60p
'4McnOBbiX Ka'4eCTB MarH-
..epa-M C8f'OAHtI
ManNecKw1 KB8JJP8T lJ.Jopepa
1BIA8T 11On.1'teCKoM
apeMeHM-. f1038OM-
IWtIII'1 cnpoceMBaTb CKB03b
oe6A» 'fMCI1OBbI8 xapaKTepMCn4-
ICM o6beKTOB M ABneHMH M OT.Q9-
IIA1b «3EJPH8 0t nneeen.: BbI,Ae-
I1ATb 8 'MCI108bIX.P8Q't8Tax npeA-
U8TOB M ABI19HMH aano)KeHHbIe B
1M)( KOCMOCOM "IMCI108bIe 381(0-
M 3HeprtmNeClCMe
, Tb
aptll'lecKOO CTMe 8
06Mra 3eMJtM,
180
'feCKOMY KBaAPaTy ,{\lOpepa AaH He CJ1y'faMHO. MKJ}. AonJtreH o6fta..
AaTb KaKMMM-TO He06b1KHOBeHHblMM, YHMKaJ1bHblMM B03MO)l(HOCTI-
MM. no MHeHMIO HYMeponoroB, YaK OHO M eCTb.
AcTponorH'4eCKaJlHYMepOnorH Mcaonb3yeT'4HcnOB pe3OHaHC
B MarM'feCKOM KBaApaTe (MK) OJ1Jf uCCAeOolfoHUJlIIBneHUU U 06w!K-
mOB npupoiJbl, nnaHeYapHblX CB"3eM '1eJToselio, ero KapMbI.
ZOo HYMep0110rM'4eCKHe KOAbi A11 TaKMX "'" 6epyT H3 MCA08WX
xapaKTepMCTMK 06DeKTOB MCCJ1eAOBaHMM. OrBeTbi flonY'4alOT B '81(-
11080M MIIM rpa4>H'4ecKoM CMMBOJaMKe, KOTOpaJl, HeCMOTp Ha MHO-
rOBeKoebie ytMJ1HJI HYMeponOfOB, AO CMX nop npHKpblBaeT CKMceeM
TaMHbI» AocrynHYIO HH4>oPMaLtMIO.
KoMY, KaK He caMoMY Y'4aCTHMKy C06biTMII, Ha OCHOBe CAeMHHWX
06U4MX npeACKa3aHMM t4 M3BecTHbIX TOnbKo'eMY <l>aKT MO)l(eT 6wn.
AaHa 3aMaH'4MBaIi B03MO)KHOCTb AOMblCJ1HTb peaI1bHb1e 1aITMJI. KD-
Aoe M3 TaKMX npeAcKa3aHMM MO)KHO APOOMTb AO 6eCKOHe'fHOCTM Ha
MHO>KecT80 YfO'4HeHMM, KOCBeHHO KltM CHanpIlMyK>. CBIlJaHHWX C ICOH-
KpeTHblM AeMCTByIOU4MM nMLtOM MJ1M npeAnonaraeMbiM BpeMeHeM CD-
6b1THJI. npeACKa3aHMe Aerane'4 Ae'4CTBMJt MJ1M KOHKpeTHO'4 mNHOC-
TM BPJlA JaM Lteneco06pa3Ho. KOH HO, MO)KHO COTKpbITb» 'fTO-TO
HO AClTb nOBOA AnJl tiOBOM T0'4KM 3peHMJI Ha c06b1TMe, 'IeJIOIIeKa
HnM OTHOweHMII C HHM, HO e J\ef"'fe
M oWM6MTb01. Ymy6neHMe B AeTaJ1M
CpaBHMMO, HjlBepttoe, C 6ecKOHe'4HO'4
TaMHOM MOMa MJ1M BceneHHO'4: '4eM
60nbWe Mbi ymy6nJreMCJt 8 MX CTpO-
eHMe, TeM 60nbwe OTKpblBaeM 3J\e-
MeHTapHbIX '&aCTM CBOitCTBa KOTo-
pblX el1&e He - M3lteAaHbI M nOTOMY
HenpeACKa3yeMbI.
Man"LleCKHH ICBa,NJIlT
AHOAMpoKa
1108 oObMHO BCer)UI
OCTaeTCA HeKOHICP8T-
HOM, oO eM, tf8AOCICB-
38HHOM, IC8K 6b1 OCT8B-
laAA MecTO A/1SI MNHO-
ro BC>06pa)KetiMA.
181
rnasa 4
nonY4HB npM rClAAHMH HYMe-
pOnOrM'4eCKM HnM" aCTponorM-
'4eCKHM «CMMBon» C06b/THJI 6y-
AYaqero - «npo3peHMe CBb/We»,
onbITHb/e HYMeponorM H acrpono-
rH roBOpJlT 0 HeM C oco60M OCTO-
po>KHOCTbIO MHOr03Ha'4HblMM CJ10-
BaMM, ocBeU4aIOT 06beKT ra.qaHHJI
C pa3HblX To eK 3peHMJI, B pa3HblX
. npoeKqMJI npMAaBaJl 06 eM-
HOCTb BocnpHRTHIO «86nM3M» (co-
BpeMeHHMKaMH) H «Ha paCCTOJl-
HMH» BpeMeHM (nOTOMKaMH).
HeAapoM 3HaMeHHTblM CBOM-
MM npeAcKa3aHHJlMM MMwenb
HOCTpaAaM 1503-1566) AOCTHr 3eHMTa enaBbi npeAcKa3aTenJl
TonbKO nOC1l .nepexoAa B CBOHX KaTpeHax ('4eTBepOCTMWMJlX) OT
KOHKpeTHbiX K 0606U(O,oil4UM 4>opMynMpoBKaM npeAcKa3aHHM. KaT-
peHbI C onMcaHHeM AeraneM '4aCTO JlBnJlnMCb AOCaAHOM KOHCTaTa-
LtMeM Hec6b1BWMXCJI, HO B03HOJICHbJX C06b1TMM, peaJ1bHOCTb KOTOpblX
OnMpaJ1aCb Ha CJ10>KHble '1UCJ10Sble paC'4eTbl no aCTponorMH. 3aTo
nocneAYIOU4Me ana,MaHaXM KaTpeHoB - «LteHTYPHM» (<<CTone-
TMJI») - nnoA er Ta H HeTpaAMqMoHHblx 3HaHH'M, YMHO>KeH-
HbiX Ha MHyYMqHIO, nO'4TM nORHOCmblO OTpa3MnM Bce COMble SO)l(Hbie
c06b1THJI nJ.1aHeTbi AO HaWMX AHeM. np030pnMBOCTb ero npeAcKa3a-
HMM nOpi3MTeJ1bHa.
HOCTpaAaMyc npeACKa3an CJ1eAYIOU4Me c06b1THJI B MCTOpMM: B
1597 r. Ha'4anH apenJlTb H3 KpeMHeBblx py>KeM; B 1642 r. oTKpblTa
ABCTpaJ1MJI; B 1769 r. B AHrnHH nOJlBMJ1aCb napoBaJl MaWMHS; B
Ha 38Mency
CrpeMneHHe <J>opMy.m1po- ,
88Th CBOO npe.o,cKa38HMR
TO'fHO M KOHKpeTHO oonee
np e Ha'4MH8 M
HyMeponoraM M 8Crpono-
raM. OnbITHbie npe,a.nO'fM-
T810T rOBOpm'b 0 6YAY-
uteM MHOCK838TenbHO,
H8MeK8MM,06o6uteHHO.C
oco6oH TutaTenbHOCTblO
nOA6MpaR caMY <t>opMY
BblCIC83b1BaHMR.
182
,1>776 r. CWA 06"b"SHnH 0 CBO-
eM He3aBMCMMOCTM; B 1778 r.
H306peTeH B03AYWHblM wap; B
1789 r. cBepwHnacb peBonlO-
I4HJI BO paHI4MM; 8 1795 r.
M306peTeHO 3neKTpH eCTBO; B
1812 r. Hanol1eoH 6b111 pa36MT
B POCCHH; B 1825 r. nocrpoeHa
nepBaa JK.e1Ie3HaJl Aopora 8 AH-
mMM; 81844 r. 6b1n H306peTeH
11!'JIerpacp, a B 1866 r. - AMHa-
NMT; B 1869 r. npopblT CY314KMM
KaHan; B 1873 r. nORBMnaCb
nepsaJl 3neKTpM'4eCKaJl lIaM-
nO'4Ka; B 1876 r. H306peTeH Te-
ne4>oH, a B 1895 r. - peHTre-
HOBCKHM annapaT. B 1903 r. B
COOTBeTCTBHM C npeAcKa3aHH-
JlMH KaTpeHoB AeMCTBHTenbHo
6b1n nocTpoeH nepBblM caMO-
neT; B 1912 r. Ha'4aJ1aCb BOMHa
Ha 6anKaHax; B 1914 r. npopblT naHaMcKMM KaHaJ1; B 1914 r. Ha'4a-
naCb nepBaJl MHpOBaJI BOMHa; B 1917 r. - peBonlOl4M B POCCHM.
Ha v1925 r. HM 6b111o npeAcKa3aHo po>K,QeHMeTeneBMAeHMJI; B 1927 r.
Ae CTBHTenbHo cOBepweH nepeneT Ha caMoneTe '4epe3 ATnaHTM ec-
KMH OKeaH; B 1927 r. 0CYU4eCTBneHbI CbeMKM nepBoro 3BYKoBoro
4>MnbMa; B 1929 r. - Ha'4anO BenMKoro 3KOHOMM'4eCKoro KpM3Mca;
B 1939 r. - Ha'4aJ10 BTOPOK MMpoBOM BOMHbI; B 1961 r. - nOJlB-
neHMe nepBoro '4eJ10BeKa B KocMoce, a B 1969 r. - a n He. 31"0 Te
Marltf ecKItff1 KBa,o.par
OCo6eHHOCTM
HYMeponorM ecKMx
nporH03OB
Bwt<Ho He TOl1bKO
H3 .npaaM11bHYK> IItH-
<t>oPMa 1O no MeTOAMKaM
HyMepoJiorw.ecKoro ra,Aa-
H R, HO B o6ltHx epTax
npeACK8aaTb B03MO>tCHYK>
seposmtOCTb cOObffi1SI, C
H M CSR3aHHOrD. O606U4eH-
HOCTb- KorO
npeJ.\CKa38Ha.tR CpaB-
HKTb C r1peAC1<838HMS\M
aCTpoJ1On.1 ecKoro ropocKO-
na: «He nplllH)')tCABlOlltHe, HO
npe.o.ynpe)l(,D,a 0 -
A}'U4eM co6b1rn », - roso-
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183
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npeACKa3aHHJI HocrpaAaMyca, KOTopble nOATBepAHnHCb BpeMeHeM.
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CTOHT npOBepHTb HaM H HaWMM nOTOMKaM, TaK KaK OHM OXBaTblBalOT
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iiMcnOBble M rpa<l>M"IeCKMe
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184
a
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186
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3HT Ha '4HCJ10BOM rapMoHHH KBaApaTa.
npH'4eM npM 3anonHeHMM KBaApaTa (pHC. 20, a) Mcnonb3yeM
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no JlMHMJlM «"MTKM» nocneAOBaTeJlbHOro pacnOJlO>KeHMJI
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187
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188
Marn&leCKHH KB8JWBT
no npMH"'Hny «06b1'4HOro» KBaApaTa, npHBeAeHHoro Ha pMC. 19, a.
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6MpaTb M3 pMC. 18, a, HO He no ero KneTKaM, a no CMMMetpM'4HblM C
HMM KneTkaM COCeAHero, nOKa3aHHOrO Ha pMC. 18, 6. T 06pa-
30M, MQ1Y 1 KneTKM Ha pMC. 18, a 6YAeT COOTBeTCTBOBaTb '4HCJ10
6 cMM"'eTpM Hoi4 KJleTKM Ha pHC. 18, 6; '4MCJ1Y 2 K/leTKM Ha pHC. 18,
a - 'iMenO 4 KJ1eTKM Ha pMC. 18. 6; '4MCJ1Y 3 10eTK¥ Ha pMC. 18, a -
'4MCJ1O 14 KI1eTKM Ha pHC. 18, 6 H T. A. :ffy nOCJ1eA08C1TenbHOCTb '4M-
cen 6yAeM BHOCMTb B KBaApaT Ha pHC. 20, a AO nonHoro ern 3anon-
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8 - CM. Ha pMC. 21.
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( MenOBaJl MaHAaJ1a - '-1M) MMeeT '4HCJ10&y1O M rp KYIO CMM-
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HI pHC. 18.0: 'fMenOBOe (0) .. rpa M'feCKoe (6) M306pa*eHMe
'fMcnOBOM MaHAaJlW
189
rnBBB 4
MeTpHIO, npH'4eM OHa cBoe06pa3Ha.
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pJlAOB KBaApaTa Ka>KAOM H3 nono-
BMH, npoC'4HTaHHble Teoco4>H'4ecKH,
paBHbI: cyMMa '4MCen BepXHHX pJlAOB
rio 36 MnH 9 (3 + 6), HH>KHHX - no
32 MnM 5 (3 + 2). He'4eTHbfM PJlA
KaK 6b1 3epKanbHo nOBTOpJleTCJI
'4HCJ1pM cyMMbI B Ka)f(.AoM nonOBH-
He. rpa4>H'4eCKOe H306pa>KeHHe
'4HCJ10BOM MaHAaJlbI Ha pHC. 20, S nOKa3b1BaeT 6nH3KYIO K CHMMeT-
pMM 4>HryPY C '4eTblpbMJI OCTpblMH yrnaMH C Ka>KAOM CTOpOHbI:
cBepxy, CHM3Y M C 60K08.
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tqMX» M «npoH3BoAHblX» '4HCJ10BblX MarH'4eCKHX KBaApaTOB cOAep-
>KHT CHMBOJ1 eCKMe 3aKoHoMepHoCTH CyTH BetqeM H 6blTHJI M MO-
>KeT 6b1Tb Mcnbnb30BaHa aK KapMH ecKMe nOACKa3KM AJ1J1 npHHJlTHJI
3HepreTH ecKH cornacoBaHHoro C 3aKoHoM EAHHcTBa peWeHHJI.
6YKBbI CJ108 (JlBneHHM, Bblpa>KeHMH, npeAMeToB, HMeH H T. A.) AJ1J1
nOn eHHJI npeACKa3aHHM KOAMPYIOT comaCHO npMBeAeHJiblM B CO-
oTBeTCTBYIOU4eM pa3Aene HYMeponOrH'4eCKHM KOAaM an4>aBHTa .H
BHOCJIT HX '4MCJ1OBbie KOAbi B MarH'4eCKHM KBaApaT. 3aTeM pHcylOT
rpa4>M'4eCKHM 06p!3 p;K:C'4MTaHHOro KBaApaTa H no ero CXOAHOCTM
C H3BeCTHOM '4"CJ10BOM HnH rpa4>H'4eCKOM MarHeM (rpa4>HKM MarM-
'4eCKOrO e.aApaTa AlOpepa M HX npOH3BOAHble COCTaBnJlIOT nHWb
'4aCTb H3J4Mx) CYASIT 0 KapMM'4ecKOM npeAHa3Ha'4eHHM C06b1THJI HnH
npHHHMaeMoro peweHHJI.
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MO>KeT OKa3aTbCJI CJ10>KHblM AnJl MHorHX '4HTaTeneM. n03TOMY Mbi
0cH0ew HyMeponOrMM
Lo1CCneAosaH R nOKa3b1-
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190
MarHl/eCKHU KB8,lJ.paT
.................................... ..
· nplo1 npoaeAeHlo1101 HYMepol1Ofli1 ecKoro ra.AaHlo1S1 no MarM e- ·
. CKOMY KBB,Apal)' MO>KHO BblAel1101Tb eTbipe OCHOBHblX 3Ta- .
: na. BHa ane CI10BO (TepMIo1H 10111101 Bblp8)l(eH e). Ha KOTopoe :
· ra.AaeTCSI, Ko PyeTcSI C\ltMBOl1aMIo1Io1 nOcneAHlo1e BtJQCSlT- ·
. CSI B KBB,ApaT. 3aTeM "Ha Io1HKalO KBB,Apa-ra HYMepoI10rM ec- .
· 1iI oOpa6aTbiBaeTCSI: np<WI3BOAIo1TCSI cno eHlo1e iii OMOHIiIM- ·
. Hoe ynpo eHlo1e lo1.Cel1 no BceM HanpSBl1eHIo1S1M ny e£t .
· CTpOIo1TCSI rpa4>lo1 ecKIo1 06pa3 MaHAal1b1. HaXoHe . npo- ·
· BO,Q\'1TCSI 3KcnepTHaSi o eHKa Ha CTeneHb TO>K,D,eCTBeH- ·
. HOCTIo1 np0lo13BeAeHHblX npe06pa30BaHIo1 Io1CI10BO 101 .
· rpa4>lo1 ecKo CIo1MMeTplo1io1. Pe3YJ1bTaTbi Io1CTonKOBaHIo1S1 ·
· BepOSITHOCTIo1 npeACKa3b1BaeMbiX C06 TIo1L:1 '80 MHOroM 38- ·
. BIo1CSlT OT CTeneHIo1 TaKO CIo1MMeTplo1lo1.
npeAnaraeM BHHMaHHIO 60nee npOCTOM '4MCJ10BOM KBaApaT, H3ApeB-
ne npHMeHSlBWH CJI AnJl OKt<ynbTHblX nporH030B pOAOHa'4aJ1bHHKa-
MH 4HCJ10BO MarHH - KHTaMCKHMH HYMeponoraMH. B AanbHeM-
weM OCTaHOBHMCJI Ha 3THX OTHOCHTenbHO npOCTblX KBaApaTax
nOAP06Hee H paCCKa>KeM 0 TOM, O ne>KHT B OCHOBe HX c03AaHHJI.
310 n03BonH"r '4HTaTenlO n we nOHHMaTb H HCTonKOBblBaTb HYMe-
pOnOrH'4eCKHe npe06pa30BaHHSI.
191
rnaBB 4
"IMcnoBaSi rapMOHMSI nnaHeT
MeTOAbi «'4HCnOBbIX pe30HaHcoB» HYMeponon1M n03BOnJllOT HC-
CJ1eAOBaTb B3aHMOCBJl3b MeJKAY acrponOrM'feCKMMH 06'beKTaMH, CTa-
BMTb HeO>KHAaHHble BonpocbI H OTBe'4aTb Ha HHX. OKa3b1BaeTCJI, eU4e
ApeBHHMH 6b1nH YCTaHoBneHbI 3aKOHOMepHble CBJl3H 3aBHCHMOCTH
>KH3ReAes n enbHOCTH '4eJ10BeKa OT 3Be3A nnaHeT. npH'4eM 06'bJlc-
HeHHe TaKHX BnHHHHM HepeAKo HCXOAMJlO He OT HCTOpHKOB HnH CJ1Y-
>KHTeneM 14epKBM, nOA'fepKHBaIOU4HX CBOIO CBJl3b C BceBblWHMM, a
OT HYMeponorOB H acrponoros.
TaK. Aonro HeBblJlCHeHHblM OCTaBanCJI Bonpoc: no eMY ApeB-
HHe HapoAbi co 3se3AoM CHpHyt COTHC (TaKoBo ee non Hoe Ha3Ba-
HHe) CBJl3b1BanH HMJI 60ra? Bo Bcex penMrHJlX BcerAa 6bln B 14eH-
Tpe BHMMaHHJI CHPHYC: IiH OAHa 3Be3Aa Hn C03Be3AHe HOe
ynoMHHalOTCJI B KopaHe, KpoMe CHpHyca (A. KHcenb). B ApeBHeM
ErMnTe 3Ta lBe3Aa C'4HTanaCb CBJlU4eHHOM H «6b1na 3HaKOM 60roB
K BocKpeweHHIO npMpoAbI, >KH3HH...» (B. HHKonaeB, B. XanaMnH-
eB. 3Be3A0'4eTbi ApeBHocTH, c. 75). E. 6naBaTCKa.A B «TaMHoM AOK-
TpHHe» nHweT: «3Be3AoM nca MMeHOBanCJI B ErMnTe CHPMYC. 3Ta
3Be3Aa 6b1na 3Be3AoM MepKYPHJI H
6YAAbl, Ha3b1BaeMOro BenHKMM HaCTaB-
HMKOM '4enOBe'4eCTBa» (T. 2, c. 469).
npH3HaBan 3a CHPHYCOM >KH3HeHHYIO -
cHny H 3HeprHIO H MMwenb HocTpaAa-
MYC, KOTopblft nHcan: «C06a'fbJl 3Be3-
Aa npHBeTCTByeT CBoero nocnaHHHKa»
(6lOnneTeHb «CYAb6a '4enOBe'4eCTBa».
1991. 12).
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BblC HTaH AHaMeTQ
CHPHYca A. t1HTe-
pecHO, O OH TO)t(e
COAepMQU o 28,
HO C HyJUIMH:
2 800 000 KM.
192
MarWleCKuiif KBap,par
· E. 6naBaTCKa Ha KOHKpeTHbiX npHMepax nOATBep>K,O.ana ·
. 06wHpHble n03HaHH JijJeBHHX 30A HX. B03BOAHBWHX nH- .
· paMHAY Xeonca, B L4HcnOBO MarHH, L4aCTb $OpMyn KOTO- ·
. po OHH HCnOnb30BanH B paC eTe nHpaMH,AbI. HanP.MMep, .
· BbiCOTa nHpaM .AbI TOL4HO COOTBeTcTByeT HCny KOHCTaH- ·
. Tbi - 147.
MO>KeT 6b1Tb, AIlJl TaKOM Ba>KHOH ponH 3Ta 3Be3Aa 6b1na Bbl6paHa
KaK CaMaJl JlpKaJl 3Be3Aa He60CBOAa? Alul 3TOro eCTb OCHOBaH H:
CHPHYC - 3Be3Aa l,5-3Be3AHOM BenH'4HHbI 60nbworo nca, n03TO-
MY TaK HpKO C"'JleT no cpaBHeHMIO C APyrHM.M 3Be3AaMM. CHpHyc -
ABO HaJl 3Be3Aa. Pa3nH'4a1OT 3Be3AY CHpHyc KOTOP ABoe 60nb-
we COnHLta H B 33 pa3a TJI>Kenee ero, M CMPMYC 6, KOTOpaJl B 100 pa3
MeHbwe ConHua, HO C TaKo >Ke MaccoM, KaK y Hero. 06e 3Be3AbI
06pautalOTcH BOK'pyr LteHrpa Macc, COBepWaJl nonHblM 060POT npH
MepHO 3a 50 neT.
BepOJlTHO, nOCJ1eAHIOIO TO Ky B 06'bJlCHeHMH ponH 3TOM 3Be3AbI
nOCTaBHn naBen MyxopTOB. B «TaMHe OAHOM aHOMaJ1bHOM 30HbI»
(<<M-CKHM rpeyronbHHK», c. 5).OH nHcan, '4TO HMH Hcyc XpMCTOC
COCTaBneHO H3 6YKB Ha3BaHHJI CHPHYC COTHC, nHWb OAHa 6YKBa
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3TMX 6YKB TaK>Ke 3anO>KeHa ApeBHHMH .antnTJlHaMH B KOHCTaHTy nH-
paMMAbl Xeonca - B HCJ10 5 132 000. CYIIIMa uH4>P 3TOro '4HCJ1a
(6e3 HyneM): 5 + 1 + 3 + 2... 11 cooTBeTCTByeT oAHHHaALtaTH 6YK-
BaM Ha3BaHHJI 3Be3AbI - CMpHyc COTHC.
B OCHOBe BOCTO'4HOM acrponorHH ne>KHT y eHHe 0 pHTMax 3Hep-
reTM'4eCKHX B03AeMCTBHM Ha 3eMnIO H Ha '4eJ10BeKa no nepHoAaM
193
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06pal1teHMJllOmrrepa M CatypHa (<<nna-
HeTbi CYAb6b1») BOKpyr ConH a. npe-
AycMoTpeHbI nH 3TM perynJlpHble
SMewaTenbCTBa KapMM'4eCKH, KorAa
c06b1THJI Ha 3eMne AOn>KHbI nepexo-
AHTb Ha HOBYIO ctyneHb pa3BHTMJI OT-
HoweHHM? OrBeT AaeT '4HCJ10BaJl aCT-
pOnOrHJI. npOM3seAeM HeKoTopble
paC'4eTbI:
a) nonHblM 060POT IOnHTepa BO-
Kpyr ConH a 11,863 roAa: 11 II: 2;
863 - 8 + 6 + 3 - 17 - 8. nonY'4eHbI M4>Pbf neBoM aCTH oKKynbT-
HOM 4>opMynbl - 28;
6) nonHblM 06opoT CarypHa 29,458 rOAa: 29 - 2 + 9.. 11- 2;
458 - 4 + 5 + 8 ...17 - 8. KaK BHAMM, HCJ1a 4>opMynbl 3aKoHa EAHH-
CTBa nOBTOp TCJI. .
ComaCHO tOKpOBeHHOMY nHcaHHIO, ApeBHMe BbiAenJlnH 12 3Ha-
KOB 30AMaKa M 7 npaBJlU(Mx nnaHeT (cenTHHepoB). KaKHe '4HCJ1a 3a-
nO>KeHbI B HX Ha3BaHHJI? HeT nH HCeII H3 YHMBepCaJ1bHOM 4>OPMY-
nbl EAHHcTBa pa3BHTHJI BceneHHoM? npOH3BeAeM oKKynbTHoe
CYMMHpoBaHMe no '4MCJ10BOM TpaHcKpMn HH, T. e. no Ha3BaHMJlM
3HaKOB. nonY HM CJ1eAYIOU4ee:
1) ConH e,.nYHa.I041MTep, MepKypMH, BeHepa, CarypH, Mapc "" 2;
2) K03epor, BOAon M, Pbl6b1, OseH, Tene 6nH3He bI, PaK. neB,
AeBa, BecbI, CKopnMoH, (TpeJ1e14 - 8.
Pe3Yl!braTbi aCTponOrH'4eCKHX Bbl'4HcneHHM TO HO COOTBeTCTBY-
lOT 4>opMyne: 28 (4 x 7);
3) B '4HCJ10BOM aCTponorHH Ka>KAoe '4HCJ10 HatypaJ1bHOrO pJlAa
OT 1 AO 9 cHMBonM3HpyeT He6ecHoe Teno:
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o PKTM HbIe BMe-
W8TenbCTBa IOnKTe-
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3eMn ee 06 TaTe-
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194
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1 - COnHLte, 4 - YpaH, 7 - HenryH,
2 - nYHa, 5 - MepKypHM, 8 - CarypH,
3 - tOnHTep, 6 - BeHepa, 9 - Mape.
B «cenTMHepbl» He BownH YpaH H HenryH, KOTopble e1oT '4MC-
nOBOM KOA 4 H 7. CnY4aMHO I1H :no? B npHBe.AeHHOM nep He HeT H
nnaHeTbl3eMnJl, KOTOpaJl, KaK H nnaHeTa BeHepa, MMeeT KOA 6 (noA-
p06Hee 06 3TOM l4H4>pe CM. pa3Aen «YHCJ1 3BepJl»). cnonb3YJI
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>KHAaHHble H nOY'fHTenbHble BbiBOAbi. PaCCMOTpHM CJ10BO «3eMnJl».
0603Ha'4HM ero KOA nOpJlAKOBblMH HOMepaMH 6YKB aJ14>aBHTa, a
l4H4>Pbl nepeBeAeM B CJ10Ba:
3 - 9 - AeBJlTb - 7
e-6-weCTb - 2
M - 14 - '4eTblpHaALtaTb - 5
n - 13 - TpHHaAl4aTb .. 9
JI .. 33 - TpHAl4aTb TpH - 5
cYMMa - 28
Y>Ke 3HaKOMoe C04eTaHHe LtH4>P. npOH3BeAeM cyfo1MHpoBaHHe
KOAOB HYMepoI10rH'4eCKo'1 AewH4>poBKH, Hcnonb3YSI CKB03HYIO HY-
MepaLtHIO LtH4>P: 3eMnJt - 9 + 6 + 14 + 13 + 33 - 75. cnonb3yeM
:310 MarH ecKoe 4!.1CJ10 cyMMapHoro KOAa CJ10Ba «3eMI1J1» B AaJ1b-
HeMwHx Ka66aJ1HCTH'4eCKHX BbI'4HCJ1eHHJlX H nonY'4MM nOY4HTeJ1b-
Hble pe3ynbTaTbi.
]\HaMeTp 3eMnH 12 740 KM. K 3TOM BenH'4HHe npH6aBHM H BbI'4-
TeM '4HCJ10 cyMMHposaHHoro KOAa Ka>KAOM 6YKBbI CJ10Ba «3eMnJl»
('4HCJ10 75):
12 740 - 75 - 12 665 - 20 - 2.
12 740 + 75 - 12815 - 8.
195
fnasa 4
BHOBb nOny'4eHO «KapMM'4ecKoe '4MCJ10» $>pMynbl 3aKoHa EAMH-
CTBa npMpoAbi - 28. Hey>KenM Ha3BaHMe HaweM nnaHeTbI «3eMJ1J1»
6b1J1o 3apaHee npeAonpeAeneHo '4epe3 4MCJ1OBYlO BM6pa4MIO C 3aJ10-
>KeHHblMM B acrpoHoMM'4ecKY1O xapaKJepMCTMKY MaHeTbi 4MenaMH?
Pe3ynbTaT O'4eBMAeH. HO MO>KHO nM 3TO Bce 06'bJ1cHMTb «OPToAoKcanb-
HblMM paCcy>KAeHMJlMM»?
MCJ1a 11 M 19 - cHMBonbl HY-
MepOnOrM'4eCKMX MCTOKOB, Ha'4ana
pJlAOB «'4eTa» H CHe'feTa», T. e. npo-
M3BOAHbfe Mcen 1 M 2: 11 - 1 + 1-
- 2 M 19-1 + 9 -10- i (cHMBon
MCTOKOB eCTb M B $>pMyne 3aKoHa
EAMHCTBa: 28 - 2 + 8 - 10 - 1 H 4 +
+ 7 -11- 2). A. KMcenb nMWeT, 'frO
3TMM '4HCJ1aM «B 04>MLtMaJ1bHOM HayKe M B HayKe OKKYJ1bTHOM OTBeAe-
Ha OAHa M3 CpblX 3Ha4MTeJ1bHblX poneM. OKKYJIbTHblMM HayKaMH OHM
BbiAenJlIOTCft'C:He3anaMftTHbiX BpeMeH KaK 'fMena, 06naAalOU4He HaM-
60nbweM MarH'4ecKoM CMOM» (4. IL c. 56). HanpHMep, AnJl COnHLta H
nYHbI '4MCJ10 11 onpeAenfteT KOnM'4ecTBO CyTOK. Ha KOTOpoe COnHe'4-
HbiM (rponM'4ecKMM) reA 60nbwe
nYHHoro roAa. A8eCCaJ10M nOA-
BOAHblM (paHee.BblCTynan nOA
nceBAoHMMOM A..TM MMpOB)
C'4MTaeT, '4TO '4MCJ10 11 B OKKYJ1b-
TM3Me cMMllonM3MpyeT «nepBwi4
BblXOA B. dfttpblTbiM KOCMOC», a
'4MCJ10 19 - 3TO HYMeponOnt'4ec-
KHM 06pa3 «AYX0BHoro nocnaH-
HMKa, n.popoKa, oc03HaHHoM MMC-
Ha 38M8TKy
B xapaKTePMcTHKe pa3-
1U1'iHbIX BneHH'" )KH3HM
'faCTO. BCTpe't8IOTC
Hcna 11 H 19.
TaAH'" HaYDt
'-fMCno 64 - 3TO KOI1M e-
CTBO OyKs, COCTaBJ1 IOl1tHX
Ha3BaHHe BCex 1230)Vlfa-
KBnbHblX C03S831.tHH (!),
KaK CHMBOI1 .D.HK. l1e)Ka-
l1.U-1X B OCHose Bcex acrpo-
J10rwtecKMX eHIII .
,j
196
M8mLiecK""w KB8J1.P8T
CHM», CHMB0J1H3MpyeT nOCSJlI14eHMe, OM MBbiM KaHaJ1 CBJl3M C Koc-
MOCOM (Ka66aJ1a '4HCen, c. 24).
«19 - :no '4HcnO neT 8 MeTOHoBoM [.4HKne ApeBHeKMTaMCKoro
nyHHO-COnHe'4HOrO KaneHAClpJl, cOCTojlU4ero H3 235 nyHHWX, MeCJILteB,
CJ1Y>KaU4Hx AllJI comacosaHMJI nepHoAoB 06pal14eHMJI nyftbi BOKpyr
3eMnM H 3eMJ1M BOKpyr (onHl4a», - nMweT K. 4epeBKo B >KYpHaJ1e
«HayKa M pe11MrMJI» (1991. 6). OH C"IHTaeT,.. Toa 19-'4J1eHHOM BHT-
Ke cOMpanH AHK oTpa>KeHbI 3aKOHbI 6HOHH4>OPM HH nYHHo-con-
He'4HOro roAa. 19 BMTK08 A80MHOM cnHpanH - TaKosa «A1IMHa» OA-
HOM MoneKynbl AHt(, COCTOjlI14eM M3 64 KOAOHOB.
4MTaTenb, HecOMHeHHO, 06paTHJ1 BHMMaHHe Ha TOT He06b1KHoBeH-
HbiM M nOTpAcalOl4MM 4>aKT, 'frO pycCKMM an4>aBMT, Kat< HHKaKOM APY-
rOM (3TO MO)l(HO nposepMTb, npoBeAJI TaKYio >Ke KOAM.poBKy 6YKB),
nepeAaer CJ10saMH «'4MCJ10Boe COAep>KaHHe» npeAMeTtft--M JlBJ1eHHM.
cc"lMcno 3SepR»
B HYMeponorMM ecTb '4HCJ10 C oc06b1M 3HepreTM'4ecKHM pe30HaH-
COM, MMelOU4ee MCKnIO'4MTenbHoe 3Ha'feHMe B MCTonKOBaHMM, - 3TO
'IHCJ10 6. 4Meno 6, KaK M '4MCJ10 28, OTHOCMTCJI K «cosepweHHblM» B
HalYpa11bHOM pJlAY '4MCen, T. e. pa8HblX cyMMe CBOMX npaBM11bHblx
AenMTeJ1eM: 6 - 1 + 2 + 3; 28 - 1 + 2 +
+ 4 + 7 + 14. C6nM)I(alOT nM '4Mcna 6 M
28 MX «coBepweHHble» Ka'4eCTsa?
OKa3b1SaeTCJI, Me>KAY "MMM MMeeTC
4<'fHCJ10BOM pe30HaHC». "IMCJ10 28 KaK
'4aCTb 4>OPMYJ1b1 3aKoHa EAHHCTBa He-
CKonbKO pa3 nOBTOpJleTCJI 8 crpyKTy-
197
MCIK) 8 BCerAB 6bu1o
CMM80l1OM 3ewM M
rapMOHMM nPMpo,Q,bI,
CMMBOl1OM UJeCl)1
*H3HeHHbIX CW1
rnssa 4
pe '4HCJ1a 6, npM'4eM B caMbiX Heo>KMAaHHblX BapHaHTax. HanpHMep,
eCJ1M CJ10BO «WeCTb» pa3nO>KHTb Ha KOAbf 6YKB, TO napHble cyMMbI
KpaMHHX (w + b, Hn 26 + 30) M BHyTpeHHMX (e + T, HnM 6 + 20) 6YKB
npM Teoco4>H'4eCKOM CJ10>KeHMM AaIOT '4MCJ10 56 H 26, KOTopble npM
O'4epeAHoM CJ10>KeHMH npeBpaU4alOTCJt B i4MCJ1a 2 H 8. npH'4eM CYM-
Ma KOAOB BCex 3THX 6YKB AaeT '4HCJ10 82, HnM «3epKaJ1bHoe» '4HCJ10
28 4>oPMynbl 3aKoHa EAMHCTBa. CpeAHJIJI 6YKBa CJ10Ba «WeCTb» -
6YKBa «c» - TO>Ke YHMKanbHa H MMeeT '4MCJ10BOM KOA 19 npH noc-
neAosaTenbHoM HYMepaltHM 6YKB aJ14>asMTa: 3TOT KOA JlBnJleTCJI
CMMBonOM CJ10Ba «OTelt» npM Teoco4>M'4ecKoM CJ10>KeHHH 'Otcen ero
6YKB H CJ10Ba «eAHHHlta» - MCTOKa scex HYMeponOrH'4eCKHX '4M-
cen (19-1+9-10-1).
OAHaKo, HecMoTpJt Ha 3aMe'4aTenbHble cBoMCTBa '4MCJ1a 6 (sblwe
nepe'4HCJ1eHa TOnbKO '4aCTb MX), KOTopble 06eCne'4MBaIOT eMY YHH-
KanbHble B03MO>KHOCTM AllJI HC'4MCJ1eHMJI XOpoWMX Ha'4HHaHMM, TpOM-
HOM pe30HaH 3Toro '4MCJ1a - 666 - Ha3b1BaIOT «'4HCJ10M 3BepSl».
BepOJlTHO, nepsbiM MCTO'4HMKOM nOJlBJIeHMJI 3TOro Ha3SaHMJI 6b1no
«OrKposeHHe» oaHHa 60roCJ1osa, B KOTOpOM 0 Tpex weCTepKax
HanMcaHO: «3Aecb MYAPOCTb... CO'4TH '4MenO 3BepJl, H60 3TO '4HCJ10
'4enOBe"!ecKoe» (rn. 13, CT. 18). K «'4MCJ1Y 3BepJl» HyMeponorH OT-
HOCSlTCJI no-pa3HoMY, HHorAa AHaMeTpanbHo npoTMBOnOnO>KHo.
HeKoTopble TOnKDBaTeJ1H CBJlU4eHHoro nHCaHMJI BOCnpHHJlnM 6YK-
BanbHO nepsylO n81l09'HY :noM 4>pa3b1 - C<'4MCJ10 3BepJl», 3a6b1B
npOaHaJ1M3MpOBaTb AononHHTenb-
Hoe onpeAeneHMe: «M60 3TO '4HC-
no '4enOSe'4eCKoe». npH Bcrpe'4e C
3TMM '4MCJ10M OHH CneWHJ1M npeA-
CKa3aTb B O)KMAaeMbiX MJ1M HaCTO-
JlWMX C06b1THJlX "!TO-TO Bpa>KAe6-
B OK TM3Me ""CI10
666 acTo' C""MBOI1""3H-
pyeT CWly )tG13HH "" ee
npOOy)I(,D,eH""e.
198
Hoe 4enOBeKY, «38epHt-toe», CaTa-
HHHCKoe.
nonp06yeM pa306paTbCJ1: cnpa-
BeA11HBO IIH 3TO? 4TO 60nbwe xa-
paKTepH3yeT 'iHCJ10 666 - «3Be-
pH HOe» HnM «4enOBe'4eCKoe»
3HepreTH'4eCKOe B03AeMCTBHe?
Anft 060CHOBaHHJI paCcy>KAeHHM
06paTHMcJI K ApeBHeM HCTOpHH, K
4>aKTaM, H3J10)t(eHHblM B CBJlU4eH-
HOM nHcaHMM.
B 'iMCJ10BOM acrponorMM '4HcnO
666 JlBnlfeTCft CMMBonOM CMnbl
3HepreTH'4eCKOM B3aMMOCBJl3H
nYHbI C 3eMJ1eM: '4HCJ10BOe OTHO-
weHHe KOAa CJ10Ba «JlYHa» K CJ10BY «3eMJ1J1», T. e. 'iMCell cyMM HX
KOAOB 50 K 70, AaeT BenH'4HHY 0,666 (c TO'4HOCTblO AO yPeTbero 3Ha-
Ka). B HYMeponorHM «Hynb» KaK KonH eCTBeHHaJl BenM HHa He Y"!H-
TbiBaeTCJI He3aBMCMMO OT Toro, rAe B HCJ10BOM Bblpa)f(eHHM OH HaxO-
AMTCJI, n03TOMY npHHMMalOT 3Ha'4HMblM nHWb yPH '4MCJ1a - 666.
ECJ1M HanHcaTb '4HCJ1a OT 1 AO 9 B CTon6HK CJ1eBa HanpaBo (KaK Mbi
npHBblKJ1H 4HTaTb H nHcaTb) no yPH LtM4>Pbl B PJlA «MarM'4eCKHM KBaA-
paTOM», CO'4eTaJl '4HCJ1a no 3HaMeHHToMY B oKKYnbTM3Me npMHLtMny
«rpOMLtbl», TO nonY"lMM «BeJ1HKoe 3HaMeHMe» KocMoca:
1 2 3 -6
4 5 6 -1+5-6
7 8 9 - 24 - 2 T 4 - 6
KaK BHAMM, B neBoM '4aCTH '4MCJ10BOro KBaApaTa cBepxy BHM3
pacnonaralOTCJI '4Hena KOHCTaHTbl (14?), a CYMMbI LtH4>P Ka)t(Aoro
M8rwlecKu&i KBBlW8T
.."IMcnO 't8nOBe'tecKoe"
BCTpe aeTcR B )K 3H
ropa3,IJ.o a e. eM Ka-
)KeTCR nOHa any.--J1anp -
Mep. HO aaKOAHpoBaHO
B np BbI"IHble AJ1R Hac
C Mat1I1b1.III.C"I ClleH R.
« cnOM 3depR" ero H -
KaK He HaaoBewb, TaK KaK
BbI ClleH RM 3aH -
MaeTCR TOllbl<O «rOMO
CamteHC", T. e. elloaeK.
...
199.
rnasa 4
ropH30HTanbHoro pJlAa 06pa3YIOT «'4HCJ10 3BepJl». 4Hcna 666 H
147 B3aHMOCBJl3aHbI «'4HCJ10BblM pe30HaHCOM». OHM BXOAJIT B '4HC-
nOBYIO crpYK1YPY MHOrHX nOHJlTHM H 06beKTOB, T. e. npH "IHCJ10-
BOM xapaKTepHCTHKe 06beKTOB HnH JlBJ1eHHM BXOAJlT B HMX KaK
COCTaBHaJl ,'4aCTb. nO MHeHHIO HYMepolforHM, '4HCJ1a 06eCne'4HBa-
lOT '4enOBeKY KOnH'4eCTBeHHblM (AHCKpeTHbIM) npoc eT '4aCTeM
enoro H n03HaHHe 4enoro no ero '4aCTJlM, Ba>KHOe AJ1J1 cy ecTBo-
BaHHJI '4enOBeKa KOnH'4eCTBeHHoe BOCnpHJlTHe M nOHHMaHHe 3a-
KOHOB npHpOAbl.
B KHHre «6bITHJI» (rn. 17, CT. 4, 15) npHBOAJITCJI AaHHble 0 nOJlB-
neHMH nepBblx nlOAeM H 06 HCTOKax enOBe"leCTBa: 60r HapeKaeT
ABpaMa ABpaaMoM, a ero >KeHY Capy - CappoH. OKKYJ1bTHOe COOT-
HoweHHe KOAOB 3THX CJ10B AaeT TO>Ke «"IHCJ10 3BepJl»: «ABpaaM»:
«Cappa» = 38 : 57'"" 0,666.
A. KHcenb 06paU4aeT BHHMaHHe Ha TO, '4TO B CBJlU4eHHOM HMeHH .
HCYC XPHCTQ.C peJ1HrHJI 3aKOAHpOBaJ1a Te >Ke TpH weCTepKH. OHH
nonY"IalOTCJI ripM CJ10>KeHHH KOAOB 6YKB ero HMeHH TpeMJI HYMepo-
nOrH'4eCKHMM cnoc06aMM": 1 - no cyMMe KOAOB nopJlAKOBbiX HO-
MepoB 6YKS; 2 - Hcnonb3YJI KOAbi nepesoAa 6YKBeHHoH 3anHCH
nOpJlAKOBblX HOMepos 6YKB (HanpHMep, 1 - «OAHH» = 16 + 5 + 10 +
+ 15 = 46 za 1); 3 - no MeToAY KOMnneMeHTapHoro nPe06pa30Ba-
HHJI C Y"leToM HC*>AHOH 3anHCH:
HCYG-{,rXp MC T OC
1 1 1 3 1 5 9 1 1 2 7 1 -6
1 1 3 1 1 7 1 1 9 6 1 -6
1 1 1-- 9 1 8 6 1 1" 5 7 1 -6
(noBa «3AeCb MYAPOCTb», BepOJlTHO, cne T nOHHMaTb B CBJl3H
C HCTopHeM '4enOBe'4eCTsa. «nOHJlTHJI CblH 60>KHM H CblH LJeiloBe-
ecKHH 6b1nH H3BeCTHbi H ynoTpe6nJlnHCb nOCBJlU4eHHbIMH 3a TblCJI-
200
'4M neT AO nOJlBneHHJI Hcyca XpHCTa» (A. KHcenb. KnaAe3b 6e3-
AHbI, '4. II, c. 17).
«3r0 Y'4eHHe 0 60>KeCTBeHHOM fnarone, - nHweT 3. WlOpe, - npo-
B03rnaweHO B HAHH KPHWHOH, B ErHnTe - >Kpe aMH o. H.pHca, B
fpe HH - 0P4>eeM H nH4>aropoM... 6bln0 H BeCTHO cpeAH npopo-
KOB nOA HMeHeM MHCTepHM (blHa 4enoBe4ecKoro H (blHa 60>Kbero.
60r KaK 6bl paCCeJlH H pa3Ap06neH BO MHO>K Be '4enOBeKOB... OH
CTpaAaeT. OH MU4eT ce6J1, OH 60peTCJI BHyrpH '4enOBeKa: OH - (blH
enoBe4ecKHM» (BenHKHe nOCBJll1teHHble. 11., 1991, c. 363, 388).
norM4ecKHM warolo1 B oKJ<ynbTHoM pacwH4>poBKe MYAPoro M3pe-
'4eHHJI oaHHa 60r0CJ10Ba JlBnJleTCJI HaAeneHHe '4HCJ1a 666 ponblO
cTHMyna AJ111 n06eAbi '4enOBe-
4eCKHX Ka4eCTB HaA 3BepH-
HblMH, H60 3TH Ka ecTBa nOA-
Aep>KaHbl AoneM CBJlTOCTH,
3anO>KeHHOM B 4enOBeKe,-
'4aCTH bl 60ra (no yTBep>KAe-
HHIO penHrHH) H KapMH'4eGKOH
3HeprHH Bblcwero Pa3YMa (no
npeACTaBneHHIO acrponorHM H
BOCTO'4HOM 4>Hnoco$HH).
TpH weCTepKH HMelOT CBJl3b
C AYXOBHOM. nCHxH4ecKoH 3HeprHeH, KOTOPYIO nonY4aer '4enOBeK
4epe3 Bepy. B nOATBep>KAeHHe CKa3aHHoro paccMoTpMM HCTOPH-
'4eCKHe cBeAeHHJI 0 BpeMeHH nOCJ1eAOBaTenbHoro B03HHKHOBeHHII
'4eTblpex BeAYU4Hx pem1rHH MHpa: HYAaH3Ma, 6YAAH3Ma, XpHCTL1aH-
CJBa H HCJ1aMa.
B HX OCHOBY COOTBeTCTBeHHO nernH Y'4eHHJI MOHcell, WaKbll-
MYHH, HHcyca H MyxaMMeAa.
Man1ttecKMu KBa;J,paT
BepolfTHo, ."'M ..,eno-
BeliecKoe- cl1eAyeT nOH&.1-
MaTb He l<aK caM 06beKT -
"Iel10Bel<, a I<al< eH&.1e &.111&.1
Bl1eH&.1e. 1<0TOpoe C03.O,aHO
KOCMOCOM «BO 611aro» paa-
B&.1WI "IenOBeKa, Kat< «60-
>KecTBeHHbllit rnaron...
201
rn8S8 4
BpeMJI C03AaHHSI HMH CBO-
HX eHMM:
MOHceH (ocHoBaTenb MYAeI-
M3Ma) -13 B. AO H. 3.
WaKbJl-MYHM (OCHOBaTenb
6YAAM3Ma) - 7 B_ AO H. 3.
1<1HCYC (OCHOBaTenb XpHC-
THaHCTBa) - 1 B. H. 3.
MyxaMMeA (OCHOBaTenb
MCJ1aMa) - 7 B. H. 3.
OnpeJ\enlltM '4McnO BeKOB,
OTAenJllOl14MX B03HHKHOBeHHe
OAHOM penHrHM OT APyrOM. nO-
J1 MM TpH wecrepKH: 13 - 7 -
6; 7 - 1 - 6 H 7 - 1 - 6 (CO-
maCHO A. KMcenlO, nOCJ1eAHHM
paC'4eT CJ1e,/:\YeT npoM3BeCTH OT
632 r. AO H. 3., KorAa pOAHnCJI
WaKbJl-MYHM, AO 1 rOAa H. 3.,
KorAa PoAHnCJl1<1HCYC H Ha'4a-
nOCb HOBoe BpeMJI neTOC'4HC-
neHHJI).
KapMH eCKoe 'fMCJ1Q. YKa3b1BaeT Ha TO, '4TO BpeMJI pO>K,O,eHMJt OC:
HOBaTeneM nepe'4MCJ1 HHblX peJ1HrHM H pa3BMTHe caMHX penHrMM
6b1nH He CJ!Y'4aMHbI, a 3anporpaMMMpOBaHHitl CHnaMH KocMoca. OK-
KynbTM3 : 9fO CBJl3b1BaeT C KOCMH'4eCKMM Pa3YMOM M O'4epeAHblM
3TanOM pa3BMTHJI '4enOBe'4eCTBa.
4MCJ10 666 YKa3b1BaeT Ha TO, '4TO 06'beKTbI M SlBneHMSI nonY'4alOT
M3 KOCMoca onpeAeneHHYIO A03Y 3HeprHH AJ1J1 CBoero «CYU4eCTBO-
'iMcno 666 He yrpo)l(SeT
npYl YlCTOI1KOBaHYlH B OK-
K}'l1bTH3Me " HCl1a 3BepRIO-
666 - C 6011bWHM OCHOBa-
HHeM MO)KHO nonaraTb, TO
C HHM CB 3aHa xopowa
nepcneKTHBa B )KH3HH '4eno-
BeKa. "4Y1CJ10 He yrpo)K8eT H
He nepeHOCHT Ha eI10BeK8
OTpHl¥i T e11bH'f1O KaPM eC-
K}'IO 3Hepn..tlO. a HanpoTHB.
CTpeMHTCR nO.DJJ,ep)l(aTb ero
)l(H3HeHHbI nOTeHlUiI811 H
BOCCTaHOBHTb ( epe3 O)l(H-
ABeMbie COObln1R) yrpa eH-
HYIO 6Hoo@!lwrHIO H eepy,
npeAocTasnRe T waHC AJ1R
pa3BHTHR Ha HOBOM ypoBHe,
C HOBbiM "HHTenl1eKTYaIlb-
HbiM Boopy*eHHeMIO.
202
BaHHJI H pa3BKT14R», '4TO CKa3b1BaeT-
CJI Ha 4>OpMHpoBaHMM HOBOrO nOBO-
pOTa B CYAb6e '4enOBeKa. CornaCHO
npOM3BeAeHHblM Ka66anMCTM'4eCKMM
'4MCJ10BblM npe06p 30BaHMRM, MO>KHO
nonaraTb, '4TO '4epe3 'fMenO 666 '4e-
nOBe'4eCTBO 06peno HOBYIO 4>OPMY
oTHoweHMM AnJl CBoero pa3BMTMJI
(ABpaaM H Cappa); nonY'4Mno «HH-
crpYMeHT CMMBonOB» AJlR n03HaHM"
MMpa (4Mena), MMR cBoero AYX08HO-
ro HaCTaBHMKa Lo1Mcyca M AYxOBHYIO
onopy B 60Pb6e C «MMPCKHMH np06neMaMM» '4epe KapMM'4eCKH
06yCJloBneHHYIO nOAAep)t(KY C nOMO blO peJ1MrMM.tt
... C '4HCJ10M 666 '4aU4e CBJl3aHO He Mpa'4HOe, a CBeTnoe M OnTMMH-
CTM'4eCKOe npeACKa3aHMe. no npeACTaBneHMIO BOCTO'4HOM cpMno-
C04>MH H Y'4eHMIO 0 npOTHBOnOnO>KHblX Ha'4anaX (MHb M JlH) :310
'4MCJ10BOe nOHJlTHe MO>KeT 3HaMeHOBaTb H He>KenaHHblM noeopeT
8 CYAb6e. HMeHYJlCb «KapMH'4eCKHM», HcnO 666 npeACKa3b1BaeT
TonbKO KOpMUl/eCKUe, 06b1'4HO HeOTBpaTHMble H3MeHeHMJI B CYAb-
6e '4enOBeKa. npH 3TOM He MCKJlIO'4aeTCJI H CJ1}1'4aMHOe pa3BMTMe
C06b1THM (nOCKonbKY CnY'4aM - To)t(e KapMM'4eCKaJl 3aKOHOMep-
HOCTb >KM3HM). He06xOAHMO nOMHMTb, '4TO npM nOJlBneHMM B pac-
'4eTax « Mcna 3BepJl»_ CBJl3b1BaTb C HMM TonbKO Bce nnoxoe He
eneAYeT.
nIOAM, HMelOU4Me B CBoeM «KOCMM'4eCKOM nacnopTe» (AaTe PO>K-
AeHHJI) nOBTOp AeBJlTOK, MornM B 1999 r. nepe)t(MTb 3HaMeHaTenb-
HbiM nOBopOT B >KM3HM, BepOJITHee Bcero CBJl3aHHblM C HeraTMBHbI-
MM.c06b1THJlMH.
203
Marlifl./eCKIlfH KBa.o.paT
ECIIM, ..pMn OK-
Ky" T..aMY, Mcny
666 B npeACK838-
TenbHOM 3H1NeHMM
60nee nPMcy e
3tjepreTM ecKoe
BMew8TenbCTBo c
ryM8HHOM 14enblO.
«M60 3TO Mcno e-
110Be'4ecKoe- .
rnasa 4
A eCTb nM nIOAH, AnJl KOTOpblX
He 38M8TXY B «KOCMM eCKOM» MMeHM '4HCJ10
BbI3bHIOOT onaceHMe .ne- 9 nOBTopJteTCfI MaKCHManbHO
peeepHYTBA L1J8CTepKa- - B03MO>KHoe '4MCJ10 pa3? OKa3b1-
'MC11O 9. 0Mrcu0T, 'fT0 He- BaerCJI, TaKoM '4enOBeK eCTb, HO
ralMBHOO ee 3Ha'feHMe KaK n08nHJleT Ha ero CYAb6y '4MC-
MO)I(eT ycMJ1MB8TbCs:I OT no 9, npeACTOMT yJHaTb B 6yAY-
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3Ha'4eHbI B KMTaMCKOM C03Be3AHM
W3Hb nOA BTopOCTeneHHblMM HO-
MepaMM 4, 7 H 5. «8 KMTaMC!(OM
aCTpOHOMM'4eCKOM TpaAM HM, -
nHweT K063eB, - C03Be3AMJI
· B CHCTeNe 28 «HeoocHbix CTBHL\H"'- C03Be3)U1A W3Hb H ·
. CHHb (<<QlpAL\e-) 3H8MeHytOT OCHOBHyK> npocTpaHCTBeH- .
· HO-BpeMeHHyK> OCb SOCTOK -aanB,A. TSK, B TpaKTaTe «rytib- ·
· HAH *Y8HH- (17 r. H. 3.) rOBop..TCSf 0 nOI1ApHO'" 3Be3P,e, ·
. CHHb H W3Hb KaK 0 TpeX «eel1"KMX Op..eHTHpax- He6a. IItH- .
· TepecHO, TO n0I10>KeHHe 3Be3,D, C038eaAHA OPHOH (W3Hb) ·
. HanOM..HSIO'Jo Ha epTBHHA K"TaAcKoro Heporl1"<I>a «5'-. .
: np"Me aTel1bHO H_l1e.o.YJOl!.'ee: B Ka ecTBe C..MB011OB BO- :
· CTOK8 aCTpol1orH npHHHMsl1H n0110>KeHHe C03Be3AHA ·
. C"Hb, a. aana,o,a -' UJ3Hb. 3TH C03BeaAHA OI:llI1H HMH Ha- .
· pe&fet:tbt TBeTCTBeHHO C"HHM APaKoHOM H 6e11b1M T..r- ·
· paM. C 12 3HaKOB KHTa"'cKoro 3o,AHaKa OHH 38HHMa- ·
. lOT 003"L\H" N2 3 H N2 5.
214
306pa)KanHCb-'B BMAe COeAHHeH-
HbiX nHHMJlMM KPY>KKOB, T. e. TO'4-
HO TaK >Ke, KaK HCna. CaM 3TOT
H306pa3MTenbHblM npHeM Ha-
rnJlAHO CBMAeTenbCTByeT 0 npo-
BOAHBWeMCJI KHTaMCKHMH Y'4e-
HblMH npJlMOM aHanorHH Me>KAY
aCTpOHOMM'4eCKHMH M MaTeMaTH-
eCKHMH CTpYKTypaM . 06U4HM
3HaMeHaTelleM AlU' HHX, KaK npaBH110, 6b1na HYMeponor JI» (K06-
3eB A.H. Y'4eHMe 0 CHMBonax M '4HCJ1aX, c. 243).
«KorAa 6bI HM Ha HHaJ1CJI roA, - nHweT KapaneTbJlH - Me>K-
AY OAMHHaALl.aTblO M ABeHaALl.aTblO aca).\M B HOBOfOAHIOIO. HO'4b
OpHOH 6YAeT TO'4HO Ha lOre» (06 HCTOKax M 6YKBeHHGM CMblCJ1e no-
'HJlTHJI «caHb y». MaTep. XIV Hay'4. KOH4>. M., 1983, 4. L c. 70).
K nonHoMY Ha60py He6ecHbix c03Be3AMM KHTaMcKoM CMCTeMbi
28 «CTaHLtMM» CJ1eAYeT A06aBHTb H 29-10 rnaBHYIO «He6ecHYIO CTaH-
LtHIO» - CeBepHblM KOBW (63M ,l\oy), MnM no eBponeMcKoM TpaHc-
KpMnLl.HM 60nbwylO MeABeAM!.tY. B ApeBHeM TpaKTaTe «WH Ll.3M» CKa-
3aHO: <<,nBaALl.aTb BoceMb c03Be3AHM Ha He6e HanpaBnJlIOT (>KM3Hb)
ABeHaAu.aTH 06nacTeM (nOAHe6ecHblx), a C03Be3AHe ,l\oy Aep>KMT
BnaCTb HaA HHMH, M TaK BeAeTCJI C ApeBHMX nop» (LtHT. no K063e-
BY A.H., c. 239). ECJ1M nepBOHa'4anbHOe BbiAeneHHe B HHAHH
27 «nYHHblX CTaHLl.MM», nO-BMAHMOMY, 6b1J1o CBJl3aHO C BenH'4MHOM
CHAepH'4eCKOrO MeCJlLl.a (27,3 CyTOK), TO B KMTae aHanOrM'4Hble
29 3neMeHTOB npMwnH B COOTBeTCTBMe C CMHOAM'4eCKHM MeCJlLl.eM
(29,5 cyTOK). Ha'4epTaHMJI 6enoro THrpa (3anaA) ':<MTaMcKMe acrpo-
norM C AaBHMX nop McnOnb30BaJ1H B HanMcaHMM OCHOBononaralO-
U4MX CHMBonOB KHTaMcKoM aCTponorHM, TaK >Ke KaK MepornH4>M ec-
Ka66ana KB8Apara ", KpecTa
MCTOpM'tecK8R
cnpS8K8
.QpeBH e K TaH Ha-
HanM OTCyer tta ana
ro,Qa.TOf",Q,a. Kor,Q,a co-
3Be3p.Me OPMOH HaxO-
.tU111 b Tot4HO H8 lOre.
215
rnaBa 5
Koe H306pa>KeHHe c03Be3AMM CHHe-
ro ApaKoHa (BOCTOK), KpacHoM nTM-
bI (lOr) M 4.epHoM 4epenax Hll
3MeJl (ceBep). HanoMMHaeM, 4TO Mbl
ycnOBHO Hcnonb3ye'" TepMMH «aCT-
ponorHSI» npMMeHHTenbHO K TeM
AaBHHM BpeMeHaM, XOTSI OTAeneHHe aCTponorHH OT acrpOHOMHH
TOrAa eU4e He npOH30wno. 3HaHHJI acrponorHH BXOAHnM B acrpOHO-
MHIO. n03TOMY aBTOp AonycKaeT B03MO>KHOCTb McnOllb30BaHMJI 60-
llee n03AHero TepMHHa «acrponOrHJI» AJ1J1 .o603Ha'4eHMJI 3HaHH'1
ApeBHHX acrpOHOMOB B H3Y'4eHHH He6ecHbix 06beKTOB: C OAHOM CTO-
pOHbI, TaK KaK 06beKTbI H3Y4eHHJI acrpOHOMOB M acrponorOB OAH-
HaKOBbi - He6ecHbie TeJla, MHorMe acrponOrM'4eCKHe TepMHHbI ac-
TpOHOMHM M acrpOllorHM C4>OpMHpOBaJ1HCb B ry nopy no eAHHOMY
Ha3BaHMIO; C APyroM CTOPOHbI, B AaHHoM KHMre aBTOp XO'4eT BblAe-
nMTb 1013 06UUIIX 3HaHM'1 no acrpOHOMMM acrponOn1'4ecKyIO '4aCTb M
CMHono.... C'tMT8IOT
TOTaJlbHaSl ..., MHoro-
ypOBHeBaSl T'JX»f<IHOCTb
W3Hb HeCOMHeHHa.
· (,B 30110TO BeK K""Ta CKO <t>...,110CO$...,H (V-III BB. AO H. 3.) ·
. pa3BHTHe 06w.en03HaBaTel1bHO MeToAol1orn..., W110 B ABYX .
· HanpaBl1eHHSlx. - n...,weT aBTopHTeTHbI oTe ecTBeHHbI ·
· CIi1H0110r A.&.-1 Ko03eB. - 1) HYMeponorwlecKoM, 6011ee ·
. .c.peBHeM... 2) npokmOrntieCKOM- (Y 4 eH...,e 0 C...,MBOnax H :
· HCl1ax. c. 339). Pa3B...,T...,e HYMepol1or...,H..., OKt<yl1bTH3Ma B ·
. uel10t.-! BCerAa 6b1110 CBSl3aHO C pa3B...,THeM 3HaH"" no aCT- .
: poHOM "" aCTponor...,...,. C n03HaH...,eM CTPYKTYP nocTpoe- :
· H...,Sl311eMeHTOB M""poBoro Pa3YMa - C03Be3A1'1 . Oco60e ·
. BH"'MaHHe .QpeBH",e MYAJ)elJ,bI YAel1S111..., C03Be3A...,1Q W3Hb. .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . -. . . . .
216
06paTHTb BHHMaHHe '4HTarenft Ha HeKOTOpble OC06eHHOCTH ApeB-
HHX HCTOKOB acrpOnOrMH, B TOM '4MCJ1e '4HCJ10BOM acrpOnOrHH.
HeCOMHeHHO TO, '4TO 3TOT acrpOHOMH'4eCKHM 06'beKT HMeJI CTary<:
YHHBepCaJ1bHOM HYMeponotH'4eCKOM crpYKlYpbl, Bblpa)i(alOiqe OC-
HOBY CXeMbi CTpoeHHft MHp03AaHHJI. PaCnOnO>KeHHe 3Be3A 'W3Hb -
OpHOHa - HAeaJ1bHO nOAXoAHT AnJl MOAeJlHpOBaHHJI ABOH'4HO-TpO-
H HOM H TpOH'4HO-nJlTepH'4HOH CHCTeM M H>C-flPOM3BOAHblX CHCTeM
4>HnOCO<!>CKHX paC'4neHeHHM 4enoro Ha «MarHL4eCKtte» '4aCTH. 3Be3-
Abi OpHOHa BownM B crpyKlYPY no wY H X3 Ty H, BMAHMO, nOACKa3a-
nH C03AaHHe 4>HJ10C04>CKOM CHCTeMbi «caHb Y» (<<TpOH'4HOe H nJlTe-
pH"iHoe»).
Bblwe Mbi npHBenH BapMaHTbI
pa3AeneHMJI 3Be3A W3Hb H 06b1'4-
HO 06beAHHJleMblx, CTOJlU4HX C HHM
pJlAOM C03Be3AHM U3H H cl>a no
KapAHHanbHblM HYMeponOrH'4eC-
KHM cxeMaM. HYMepa HJI 3Be3A
W3Hb B ApeBHeKHTaHCKHX TpaKTa-
Tax He CJ1Y'4aHHa (CM. pHC. 22, a).
PacnOnO)f{eHHe 3Be3A W3Hb 06pa-
3yeT "ieTKYIO TpOH'I OCTb. MO>KHO
BblAenHTb cneAYlOl14He TpoH'4Hble
6nOKH: ABa BepTHKanbHblx (4, 1, 6 H 5,3,7) H OAHH ropH30HTaJ1b-
HblM (1, 2, 3), OAHH BepTHKanbHblM 6noK AnJl cl>a (1, 2, 3) H OAHH
TpOHL4HbIH 6noK AnJl U3H (3, 1,2). KHTaMcKHe aCTponorH, KaK H HX
eBponeHcKHe KonnerM, ropH30HTanbHblM 6noK - nOJlc OpHoHa -
HHorAa 06'beAHHJlnH B OAHY 3Be3AY, TaKHM 06pa30M ynpol14aJl co-
3Be3AHe AO nJlTH 3Be3A (CM. pHC. 22,6 - 3Be3Abll, 2 H 3): nonY'4a-
naCb nJlTepH'4Haft MOAenb. 3Ty MOl1enb 4>Hnoco4>bl H HYMeponorH
Ka66ana KBa,o.paTa "., KpecTa
OCHOBbi HYM.E!ponOrM"
KpoMe WSHb; OCM0110-
nt ecKot1 npeAnOC l1-
KOt1 MHOntX OCHOBono-
naralOlUHX MaTpHUo HY-
MepOl1orHH SlBl1S1eTCSI
C03Be3AHe Mao, Hl1H no
eBponet1cKot1 TepMHHO-
l10rHH nl1eSlAbl.
217
rnasa 5
HaH60nee '4aCTO McnOnb30BaJ1H B CHCTeMe X3 TY H no wy AnJl n03Ha-
HHJI MHpa M npeAYraAblBaHMJI 6YAYU4ero.
PacnOnO>KeHO C03Be3AHe nneJlAbi (Mao) HeMHoro Bblwe 3KJ1Hnn1-
KM, Me)f(,qy C03Be3AMJlMM Tene M OBeH. Mao BHMMH 3Be3AO eTaMH
C HTaIIOCb mmt3Be3AHblM C03Be3AMeM, KaKHM era BHAeJlH 6onbwHH-
CTBO nlOAeM C HOpMaJ1bHblM 3peHHeM AO H306peTeHHJI OnTHKH. npH
60nee OapoM 3peHMH BblAeJlMM He MeHee ceMH 3Be3A (B A4>PMKe H Ha
ocrpoBax KYKa 3TO C03Be3AHe Ha3b18aIOT «Wecrb 3Be3A»). Ka)t(.qall H3
«He6ecHbIX craH HM» BKJ1IO aeT maBHoe C03Be3,qMe )TOM '4aCTM He6a.
«CTaH HM Mao», KpoMe OAHOHMeHHoro C03Be3AMJI, npMHClAJle>KHT M
C03Be3AMe TJlHb MHb - He6ecHaJl TeHb (MJ1H B eBponeMcKoM pa3Aene-
HMM He6a - '4aCTb OBHa), KOTOpoe TO>Ke COCTOHT M3 mmt 3Be3A. «CTaH-
4MH W3Hb» M «Mao», MMelOU4He Bbfpa>KeHHoe TpOM Ho-nJiTepH'4Hoe
pacnOJlO>KeHMe 3Be3A, BepoJITHO, lIBMJ1HCb np006pa3aMM pa3pa60TKM
KMTaMCKMMM Y'4eHbfMM 4>Hnoc<$cKoM KOH4en4HH «caHb y» - <<TpOM-
bI H nJITepH », nonaralOT A.M. KapaneTbJlHLt H AJ1. K063eB.
(MCTeMa 18 c03Be3AHM - «He6eCHbix CTaH MM» - 6b1na Ba>K-
HbiM 3neMeHTOM "PH pa3pa60TKe 4>MJ10C04>cKHX cxeM B HYMepono-
rH'4eCKOM MeTOAonorMM, Mcnonb3yeMoM AnJl WHpOKOM npaKTHKH.
eHMe 0 4<He6ecHbix CTaH HJlX» Hcnonb30BanOCb He TonbKO B aCT-
pOHOMHM M acrponorHH, HO M B APyrMx 06J1aCTJlX 3HaHMM, B '4aCTHO-
CTH B anXMMMM " ee nCHxo4>M3HonorM eCKoM nOApa3AeJle - MaK-
P06MoTMKe (MaKpo OT rpe'4eCKOrO «60nbwoM», a 6HoTMKa-
4<BonnOU4eHHe >KH3HM»; MaKp06MoTH a - «WHpOKMM B3rmtA Ha
>KH3Hb»). MaKp06MoTM1<a KaK y eHHe 0 npOAJ1eHHM >KH3H 6epeT
(Boe Ha'icWIo C ApeBHeM BOCTO'4HOM 4>Hnoco4>MM H 060CHOBbl8aeT
pa3YMHOCTb c06nlOAeHHJI onpeAeneHHoro 06pa3a >KM3HM, BKJ1IO'4aJl
nHTaHHe M cHCTeMY AYXOBHblX H 4JH3M'4eCKMX ynpa>KHeHMM (noA-
po6Hee CM. KHMry aBTOpa «MeAH MHcKaJl acrponorHJI»).
218
Ka66ana KSa,o.paTa H Kpecra
CxeMa X3 TY
L<13BecTHbiM HCCJ1eAOBaTenb KMTaMCKHX «MarM'4eCIU1X" tt>Mryp»
W. KaMMaH (neHCHnbBaHCKHM YHMBepCMTeT, CWA) ycraHbBMn, '4TO
B 3noxy WaH - XVI-XIV BB. AO H. 3., cy eCTBOBaJ1a npocrpaH-
CTBeHHO-'4MCJ10BaJl4>MnOco$CKaJl cxeMa «aJVIJa3WblM nJ1aH», Ha3BaH-
HaJl TaK H3-3a ee poM60BHAHOCTM (pHC. 27j.
ca»Hnoco4>bI ApeBHero BOCTO-
Ka C03AaJ1H MHOro cxeM nocrpo-
eHI>1H Ml>1pa, HO MO>KHO BblAeJ1'1TIt
HeCKonbKO HaM60nee npM3HaH-
HblX, BblAep>KaBWHX npOBepKY
BpeMeHeM M HaH60nee WMpOKO
ynOTpe6nJleMbiX B MarHH, B TOM
'4MCJ1e cxeMbi X3 ry H no wy. X3 ry
MMeeT «MarH'4ecKoe» KpecToo6-
pa3Hoe pacnOnO>KeHHe CMMBO-
nOB, aU4e :no '4MCJ10Bble 3neMeH-
Tbi HnH CHMBonbi nJlTM CTHXHM
(pMC. 28). KpeCTo06pa3Hoe pac-
nOnO>KeHMe 3neMeHTOB TO>Ke CMMBOnM'4HO. nepeBoA KHTaMcKMx
MepornM4>oB «X3 ry» 0603Ha aeT He KpeCT, a e.qHHeHMe ABYX OC-
HOBHblX «3neMeHTOB» >KM3HH: He6a H 3eMnM, TaK KaK HepornM4> «ry»
B AaHHOM KOCMOnOrM'4eCKOM nnaHe 0603Ha'4aeT nnaHery CarypH
(nnaHery CYAb6b1), a 4<X3» - 3eMnlO, nO'4BY.
C'4MTaIOT, '4TO cxeMa X3 ry BnepBble ynoMMHaeTCJI B ApeBHeKMTaM-
CK 4>MnOC*KHX TpaKTaTax VIII-IV BB. AO H. 3. (npoM3BeAeHHe
«XYHb 4>aHb»), a 60nee COBpeMeHHYIO pa3pa60TKy KpeCTo06pa3Horo
ECTb MH8HM8
KaMM8H C HT8J1 (1985),
TO «aJ1M83HbI nl1aH- no
CTpoeHHtO, OTqt'K8tO H
3H8HHR 8CipOI1orHH, Mor
HCn0I1b30B8TbCR I(HT8 -
I.t8MH A11R K8J1eHJ18pHbO<
paC'4eTOB, 8 T810Ke 6b1Tb
npoo6paaoM paapa60ToK
exeM X3 ry.
219
rnasa 5
pacnOnO>KeHMJI nJlTM 3neMeHTOB cxe-
Ma non}"4Hna B IV-III eB. AO H. 3.
(npoM3BeAeHMe «fyaHb-tpM»).
X3 Ty- 3TO n CTaBneHMe nocr-
poeHHJI MMpa B eOOTBeTCTBHM C ABO-
H'4H<rTpOM'4HOM H TpOM\fHG-nJn'epHt4ttOM
CHCTeMimM. npe>KAe '*!M aHa11H3HpoeaTh
cetlfYxaTy, Ba>KHO Yj1CHMTb ee B03HMK-
HOBeHMe H 3Ha'4eHMe BXOAJIU4MX B Hee
3neMeHTOB. PaCCMOTpHM CBJl3bee '4MC-
Puc.27. Cxe...a 4CaJlMa3HblM nOBbIX M 6yKBeHHblX (B KHTaMCKOM Hy-
nJ1aH» MeponorMM - MepornH$M'4eCKMx)
CMMBonOB.
MCJ1a npeHMYU4eCTeeHHo HcnOnb30BaJ1HCb B Ka eCTBe 4>Hnoco4r
CKOM CMMBOJ1HKM, a He AJ1J1 apH4>MeTH'4ecKMX npe06pa30eaHMM KaK
MHcrpYMeHT *bI'4HeneHHM. CTaJ1a pa3BMBaTbC.JI M reoMeTpH'4ecKaJI
CMMBonMKa. "B COBpeMe HOM nOHMMaHMM - 3apOAMnaCb HYMepo-
nOrMJI. C'4MTaIOT 1 '4TO Hap AY C 4>HJ1OCo$HeM H acrpoHOMMeM (B npo-
wnOM 3HaHMJI acrponorHH BXOAHJ1H B aCTpOHOMHIO, B CBft3M C 'feM 8
ApeBHMX pyKonMCJlX ynoMHHalOTOI TonbKO 3Be3A0'4eTbl), HYMepono-
rMJI B03HHKJ1a KaK 0AHa H3 nepBblX HayK - npHMepHO VI B. AO H. 3.
CxeMa X3 Ty AMT B cWHAaMeHT KMTaMcKOM HyMeponorMH, KOTO-
pyIO, no MHeHHIO K _a (1994), B CTpyKTypHOM OTHOweHMM MOJKHO
KJ1aCcM$1LtHpoBaTb no P1eA,Y1O HM TpeM OCHOBHblM TMnaM 06betcr0s:
· «cHf!'BOnbl» 4>Mryp: TpMrpaMMbI M reKcarpaMMbI;
· «'4 C HX npeMMYU4eCTBeHHblM Mcnonb30eaHMeM B cxeMax
HJ1M MX npoH3BoAHblX: X3 Ty M no wy;
· rnaBHble 4>Mnoco4>cKo-HYMeponOrM'4eCKHe 3Ha'4eHMJI «CHMBo-
nOB» H « Mcen» OCHOBaHbI Ha KOH en HH HHb-JlH H yeMH.
220
a
6
@£J
Ka668f1a KBap,para .., Kpecra
6
z
Puc. 28. CxeMa X3 ry C cHMBonaMM: '4MCen (a), H CBera (6),
CTMXMM (6) M nnaNer (z)
AaHHaJl K1Iaccml>HKa MJI Haooonee Bblpa3HTenbHa, TaK KaK nOA-
epKMBaeT oc06eHHoCTb tiYMeponorM'4eCKHX npe06pa30BaHMM. OHa
COpMeHTMpoBaHa Ha LteHTpaJ1bHbIe '4HCJ1a :.:.- 3 (He'4 Vloe, HJ1M «He-
6ecHoe») H 2 ('4eTHoe, HnM «3eMHoe») H nOKa3b1Baef Bce Ba>KHeM-
WMe BMAbi tf}'MeponorH'4eCKOM cHMBon...K.... K nOCJIeAHMM OTHOCJIT:
1) reoMeTPM ecKMe 4>oPMbI (<<cHMBonbl» 4>Mryp); 2) H4>Pbf {«'4MC-
na»); 3) nHCbMeHHble 3Hat(M - HepornM4>bI H MX 6YKBeHHble aHa-
norM.
II>Mnoco4>bI nlO6ylO BeU4b HnM
HBlteHMe Ha,QemInM CMMBonOM, KD-
TOpblM nOTOM KaK 3neMeHT BBO-
AMJlCJI B OKKynbTHyIO 4>oPMYny HJ1M
1eOpHIO. B OAHOM M3 AJ>eBHMX CPH-
nOC*KHX TpaKTaTOB «LPo '4>KyH»
(V-IV BB. AO H. 3.) CKa3aHO:
«PO>KAaIOTCJI BeutM, a 3aTeM B03-
HMKaIOT CMMBOJ1b1; BCJ1eA 3a CMM-
BOllaMM B03HMKalOT (4MCJ10Bble M
3HaKOBbie. - npUM. osm.) pa3-
1013 rny6MHbI BeKOB
<1>w1e>co<S>bI .QpeBHOCTM
3HepreTM t<yIO CBR3b
aeU4e ... RBJ1eH...... Bblpa-
)l(CUU1 CHMBOI1aMH H HC-
l1aMH. 3aTeM pa38HJ1OCb
<PHJ1oeo<1>cKoe HanpaBJ1e-
HHe. KOTopoe CTano HC-
OOJ1b30BaTb oonbUJe HC-
na. M HHbIe CHMBOI1b1
221
rnBBB 5
MHO>KeHMJI; BCJ1eA 3a pa3MHO>KeHHeM B03HHKalOT (reopHH) HCJ1a»
(u.MT. no KH.: K063eB A. .: Y4eHMe 0 cMMBonax H '4HCJ1ax, c. 83).
B ApeBHeKMTaMcKoM MaTeMaTH'4eCKOM KaHOHe «4>Koy 6H rOBO-
pHTCJI: 4<3aKOHbI '4HCeJI HCXOAJIT H3 Kpyrnoro... Kpyrnoe HCXOAMT M3
KBaApaTHoro, KBaApaTHoe - H3 npJlMoyronbHOrO».
npMnMCblBaJ1M '4HCJ1aM cBoMCTsa reoMeTpH'IeCKHX 4>Hryp M nH-
4>aropHMu.bl. cJ»Mrypbl, a TaK>Ke CBJl3aHHble C HHMH '4HCJ1a CHMBonH-
3HpOBaJ1H B ApeBHeM 4>Hnoco4>HM 3eMHble (KBaAPaTHble) M He6ec-
Hble (Kpyrnbfe) cBoMCTsa.
HeKoTopbfe 6b1TOBbie npeACTaBneHMJI 0 Ka'4eCTBaX reoMeTpH'4eC-
KHX 4>Mryp KaK HaCJ1eAHe ApeBHeMweM 4>Hnoco$HH coxpaHMnMcb
M nOHblHe. HanpHMep, reoMeTpM'4eCKHe cpaSHeHHJI nCMxonorH HC-
nonb3YlOT B CBOHX HCCJ1enOBaHMJlX l11IJI BblJlBneHHJI M OLteHKH BbI-
pa>KeHHOCTH HHTenneKTy-
anbHoro AHcKoM4>opTa H
cou.HanbHoM Ae3aAanTa-
LtHM 'IenOBeKa. B 6b1yY >Ke
AO CHX nop coxpaHHnHcb
HeKoTopble «HYMeponorH-
'4eCKMe» OLteHKH MYApeLta-
MH pe3ynbTaTos pa3nH'4-
HOM AeJlTenbHOCTH.
EAHHCTBO «HYMepono-
rH'4eCKOM apH4>MeTHKH» H
«HYMeponOrM'4eCKOM reo-
MeTpHH» B HYMeponOntH
npoJlSnJlnOCb'4epe3H306pa-
>KeHMe '4HCen B BHAe 4>Hryp.
EAHHHLte npHnHcblBanacb
nOCKOJ1 lCpyr CMMBOJ1M3M-
pyeT He6a, TO 'fe110BeKa, BbIe-
lea3blBaIOw.ero HepeanbHbfe
nnaHbI, no aHa11OfVli-1 xapaKTe-
PH3y1OT leaK tcBi-1TalOU.\ero B He-
6ecax. H npocRT occnycrnTbCSI
Ha 3eM111O- HJV'1 Ha3blBaIOT
tctcpyrl1b1M A , Ec11i-1 )ICe
3TOT 'fe110BeIC 6ecn bfe eH
HaB BaeT .QPyrHM Kpa&1He
nP"lM oH. tcnpH3eM11eH-
H<Wi- iJ>opMe. TO rOBopsrr 0 ero
tcKBa,D,p8THO rOl1OBe", YaK Kat(
KBaJ],paT - CHMB0I13eM11H.
222
Ka66ana KBa,LWara H KpeCra
ABOJlKaJl .npHpoA8 KaK 06U4eMY 3Jle-
Memy Ha'4aJ1bHOrO H HCJ1eHHJI '4eT-
HbiX H HE!YeTHbIX '4MCeJ1. B OKKynbT-
HOM nOHHMaHHH eAHHH4i) 06.na.qaer
YHHBepcanbHOM nOpO>KAalOU4eM
4>YHK HeM B ABOM'4HOM H TpOH'4HOM
MOAeJ1J1X 4>HJ10Co4>c K MX CHCTeM HY-
MeponorMH. 4Mcna 2 M 3 HaAeJ1MHCb
OC06bfMM cBoMCTBaMM KaK MCTOKM
eOOTBeTCTBeHHO '4eTHoro H HE!YeTHO-
ro pJlAOB HC HCJ1eHWI, eOOTHOCMMblX
e 3HepreTH ecKHM pa3AeneHHeM
MMpa Ha ABe KJ1aCeM4>HKa HoHHble
npHHCWle>KHOCTM: 3HepreTH'4ecKoMY
COTBOpeHHIO MnH BeAYU4eMY BnMJI-
HMIO 3eMJIH eOOTBeTCTBOBanH '4eTHbie '4HCJ1a; 3HepreTH'4ecKoMY 811MJI-
HMIO He6a (KocMoca) - He'4eTHbie MCJ1a.
no MHeHHIO KHTaMcKoro CMHonora nlO BeMxya (1981), Aa.tHoe
paCCY>KAeHHe oTpa>Kano 4<MarM'4eCKHM KpeCT» X3 ry, CMMBonM3Hpy-
IOU4HM 4>Hnoco4>CKyIO CBJl3b Kpyra H KBaApara e pacnOnO>KeHHblMM
B HeM nJlTblO 3neMeHTaMH: nJlTb '4HCJ10BblX CMMBonOB, nM60 nllTb
6YKBeHHblx CHMBonOB crpaH CBeTa, nM60 nJlTb CHMBonOB CTMXHM (eM.
pMC. 28). OH TaK>Ke oTpa>KaeT nJlTb «rnaBHblX no BnHJlHHIO Ha 3eM-
nlO nnaHeT M3 HCJ1a «cenTHHepoB», T. e. ceMb «rnaBHblX» nnaHeT
COnHe'4HOM CHCTeMbI, 3a HCKJ1IO'4eHHeM CBeTHn (ConH a M nYHbI).
HanpaBneHHe ABH>KeHHJI ConH a ycraHaBnMBaJ10 TaK>Ke CBJl3b
X3 ry co CTopoHaMH CBeTa. 36epxapAa nOAAep>KHBaeT OTe'4eCTBeH-
HblM'cMHonor A.H. K063eB (1994), KOTOpblM C'4HTaeT, '4TO npJlMOe H
06paTHoe nepe'4HCJ1eHHe 3neMeHTOB B cxeMe '<3 ry OTpa>KaeT Ha-
CMHOnOrM C'lMT8IOT
&.13BecTHbI aHrnHMcKH
CHHOnOf" B. 36eP PA
(1933) nHtan, 'l'!o noc-
ne,QQB8TeJ1bHOCTb pac-
nonO)l(eHH nRTH 3ne-
Mettit>e r. MX KOM6MHa-
UH B cxe X3 Ty
nOK83b1BaeT ac'TpOHO-
MM ecKH nyTb ABH)I(e-
HH ConH H l1YHbI,
oTP8*8 COn HbIe
H nyHHble l\MtCIIbI.
223
rnaBa 5
6J1IOAaeMOe C 3eMnM cyTO'4HOe ABH>KeHMe COnHI.4a (c BOCTOKa Ha
3anaA) H MeCJI'4HOe ABH>KeHHe nYHbI (c 3anaAa Ha BOCTOK). HapJlAY
C cyTO'4HblM ABH>KeHMeM ConH a C BOCTOKa Ha 3ana,q 4>oPMyna cno-
c06Ha Y'4MTblBaTb rOAM'4HOe ABH>KeHHe COnHI.4a no 3KJ1HnTHKe C 3a-
naAa Ha BOCTOK. 3Ty KOM6HHaLtMIO pa3HOHanpaBneHHblX ABH>KeJiHM
KMTaMCKHe HYMeponorH Bblpa>KanH HAeeM neHTarpaMMHOCTM (3Be3-
AbI), rpa4>M'4eCKH Bblpa>KaJl 4epe3 Hee «3HepreTH'4ecKYIO 4>oPMY-
ny» (TepMMH aBTopa) n03HaHMSI MMpa.
ECJ1H 3aMeHHTb '4HCJ1a B X3 TY COOTBeTCTBYlOlqHMM KHTaMCKHMH
MepornH4>aMH HnH HX aHanoraMH - 6YKBaMH, nonY4HM He '4TO HHoe,
KaK CTaHAapTHoe pacnpeAe.neHHe 3neMeHTOB no CTpaHaM CBeTa (CM.
pHC. 28). CornacHo TpaAH4MOHHblM 0603Ha4eHHJlM: B - ceBep (N),
o - lOr (5), A - BOCTOK (E), M - 3anaA (W), n - eHTp (C), B
KHTaMcKMx HYMeponorH4ecKHx TonorpaMMax lOr 3aHHMaJ1 BepXHlO1O
n03H4HIO, ceBep - HM>KHIOIO, 3anaA - npaBYIO, BOCTOK - neBYIO
(CM. pHC. 28,6 H 8). nOnO>KeHHe BOCTOKa H 3anaAa B TonorpaMMe
oTpa>Kano XOA M 3aXOA COnHI.4a, KaK ero BHAHT Ha6nlOAaTenb C
3eMnH. TaKoe >Ke 0603Ha'4eHHe CTOpOH 6blno npHHJlTO B aapono-
rM'4eCKOM ropOCKone, KOTOpblM H306pa>KaeTCSI KpyroM (CHMBon He-
6eCHOM C«PePbl) C TO'4KOM B ero I.4eHrpe - CMMBonOM 3eMnH M Ha-
XOA1IU4erOCJI Ha HeM '4enOBeKa - ropocKonHpyeMoro, CYAb6y
KOToporo onpeAenJleT COCTaBnJleMbiM ropOCKon.
npOpOJ.f@CTBO ccB3neTOB»
M : naAeHMM» - YA "I M HeYAa
npHBeAeM BapHaHT npOpO'4eCTBa «B3neTOB» (yAa'4) H «naAeHHM»
(HeYAa'4) B >KM3HM '4enOBeKa, cOCTaBneHHblM C Y4eToM 4HCJ1a, MeCJI-
224
Lia H rOAa p0>KJ\eHHJI no CYMMe
«HaTYpanbHblX» '4HCen 9-3Ha'4-
HOro HYMeponorw eCKoro pJlAa.
Vlcnonb3yeM ABa BapHaHTa: "IMC-
nOBOM KBaApaT <<Tj)OH4b1» - no
wy (3 x 3) H rpa4>H'4eCKMM npo-
C'4eT.
B nepsoM BapHaHTe nporH03
COCTaBnJlIOT no pe3ynbTaTaM
aHanH3a pHcyHKa, nonY'4eHHO-
ro OT coeAHHeHMJI nMHM MM
«3Ha HMblX» (TepMHH cneLiHa-
nHCTOB <<TO'4HbIX HayK», oc06eH-
HO MaTeMaTHKoB), T. e. MMelO-
U4HX npaKTH'4eCKOe 3Ha'4eHMe B
paC'4eTax, 4Hcen. AnJl 3Toro HC-.
nonb3yeM HYMeponOrH'4ecKYIO 06pa60TKY nocneAoBaTenbHoro
Ha60pa LtH4>P AaTbi p0>KJ\eHHJI. Bo"smopoM BapHaHTe nOCTpoHM
rpa4>MK H Bbl4HcnHM TO KH «3Ha'4HMblX» neT no 12-neTHeMY LtMK-
ny >KM3HH. 12-neTHHM LtHKn - 3TO 6HOnOrM'4eCKMM LiMKn npMpo-
AbI, 3aBHCJI MM OT aKTHBHOCTM 4>a3 M nepeMeU4eHMM nYHbI.
MycynbMaHe B 3HaK npH3HaHH 60nbworo 3Ha"leHM nYHbI M ee
3HepreTH'4eCKMX pMTMOB B Jt(H3HM &ienoeeKa, no TpaAHLiHH Ha CBOHX
roCYAapCTBeHHblX 4>narax H306pa>Ka1OT nonYMeCflLt. nYHa AllJI HHX
TaK>Ke CHMBon BpeMeHH, Be"lHOCTH.
AnJl npHMepa paC'4eTa nporH03a «B3neJ,OB» H «naAeHHM»
B03bMeM '4HCJ10 p0>KJ\eHHJI Hawero COBpeMeHHMKa, HanpHMep 30 aB-
rycra 1954 r. 3anMweM 3TM '4MCJ1a TaK:
4HCJ10 AHJI: 30.
Ka66ana KB8AP8Ta H KpecTa
MHTSpecHblii 4»aKT
BaaHMOCBR3b l1}'Hbi C 3eM-
l1eill ocyIJ..teCTB11S Ta-
KHM 06pa3OM: aa" fOA OHH
BMeC1'e CoeepWatOT OAiitH
o6opo pyr CoI1Hua. a
aa 3TO Slce JlyHa
12 pa3 npoxoAHT noc.ne.o.o-
BaTe11bHY1O CMeHy CBOH)(
ct>a3. 12-pa30 CMeHa
Q>a311}'HbllJP CHX nop HC-
nol1b3YST MHOf1.1MH Ha-
po,a,aMH KaK e,o.t;IHua &,13-
MepeHHR speMeHH rOAB.
225
rnasa 5
4MCJ10 MeCJI : 08.
rOA pO>KAeHMJI: 1954.
npoM3BeAeM TeOC04>M'4ec-
Koe CJ10>KeHHe 3TMX '4Mcen:
3+0+0+8+1+9+5+
+ 4 - 30 - 3.
Tenepb '4epTMM KBaApaT
no wy (pMC. 29) C HYMepaLtM-
eA KneTOK cBepxy BHM3 ..
eneBa HanpaBo. nepeHOCMM
'4MCJ1a PJ'Aa Ha 9-K1IeT0'4Hwf%
KBaApa1, CoeAMHJIJI MX npSl';'
MblMM nMHHJlMM nOCJ1eAOBa-
TenbHO TaK, KaK OHM pacno-
naralOTCJI B AaTe p0>KAeHHJI.
nocneAHee '4MCJ10 - «MarH-
'4eCKaJl CYMMa», onpeAenJle-
MaJl CJ10>KeHMeM Bcex '4HCeJ1
AO OAHoro '4HCJ1a (CM. Bbfwe).
B AaHHOM npHMepe - '4McnO 3,
KOTopoe cHMBonM3HpyeT
Ba>KHblM 0606U4alOU4MM 3Tan
>KM3HM. 3aTeM no ijilnetBneHMJlM nMHMM nOnY'4eHHOM v 4>Mrypbl cy-
AJlT 0 xapaKTepe O>KMAaeMOro npOrH03a. nOnY'4eHHblM B KBaApaTe
KJleTOK pHcyHOK cpaBHMealOT C «nporHOCTM'4eCKHMM KpMBblMM» M C
4>MrypaMI4, IOMcaHHblMM B KBaApaT no LVY HnM KpeCT X3 TY (0 HHX
CM. COOTBeTCT&yIOU4He pa3Aenbi AaHHoM KHMrM). '-IeM 6nH>Ke KPM-
Bble 4>Mrypbl raAaTenbHOro KBaApaTa «BpeMeHH pO>KAeHMJI H nyTM
>KH3HM» K cpaBHMBaeMoMY «craHAapry», TeM TO'4Hee MO)f(HO nepe-
Ha 80cT0Ke
12 ne'JHl,1" K11 »M3tWI CBR3bI-
B8IOT C perymlPHblMM B8*Hb1-
MM nepeMeHaMM BIM'4HOCTM
'fe11OBek8. UIo1K11 8bI,AeI1SIeT
"poMeJKyTICM speMeHM, 38 KO-
Topble OOR3aTeJ1bHO KaMH-
H811bHO M3Met1RIOTCft ero nose-
ASHMe, llCMXonontSI, COCTOSI-
HMe 3A0P08bA. npoMCXOAHT
nepeol4eHKa W1M yrC)LUieHM9
bO( , 8C-
TM'4HO (M nonHOCTblO)
Met1SI8TCSt MMJX>B033peHMe.
HeyAHBKTeJ1bHO, 'ITO see 3TO
01P8*8eTafHa B03MO)I(H()C1M
AC)C1'M)KeHMA- ycnex08 B, )l(M3HM.
CI1OCOOcTByeT MIlM MeWaeT
peanM38 M M8HOB, f103TOMy
CBS13aHO C OY M 'feJ1OBeKa.
226
BeCTM MCTOnKOBaHMe C CMCTeM
n_o WY MJlM X3 TY Ha npOrH03
>KM3HM eJ10BeKa.
4T06b1 nOKa3aTb '4MTat:enlO
npMH LtHn HYMepOnOrM'4eCKOrO
aHaJ1M3a no r aTenbHOM 4>Mry-
pe, KpaTKO npOaHaJ1H3MpyeM no-
JI eHHYIO Ha pMC. 29,6 4>Mrypy.
B (4eJ1OM '4eJ1OBeK, Ha KOTOpOro
ra,qatOT, AOCTHrHeT >KeJ1aeMoro YAOBJ1eTBOpeHMJI OT >KH3HM, YaK KaK
rpa$MKa MCeJ1 KBaApaTa HanOMHHaeT 3Be3AY, HanpaBJ1eHHyIO OCT-
pMeM BBepx. 3se3Aa OCTpMeM BBepx (<<OAHoporaJl» 3Be a) YKa3b1-
BaeT Ha TO, '4T0 AaHHoro '4eJ10BeKa B AaHHoM MHKapHa M oneKalOT
CMnbl He6a, OKa3b1Ba" eMY nOMOU4b B CBeTnblX nOMblCJi*x LtenM )1("3-
HM M 6naronpHJlTCTBYJl B BonnOU4eHMM 3aAYMaHHoro.
EcnM 6b1 4>Mrypa Hano-
MHHana «ABYPOrylO» 3Be3-
AY - 06paU4eHHYIO ABYMJI
OCTpMJlMM BBepx, CMMBonH-
3HpyIOutYIO HHb, MnM «>KeH-
CKYIO» CTMXMIO, TO MO>KHO
npeAnonO>KMTb, '4TO AnJl
AOCTM>KeHHJI LtenM nOTpe-
60BanOCb 6b1 MeHbwe CMn.
CTMXH"MHb eT60nee«MJI
KHM», HO HanonHeHHblM 3MO-
LtHJlMM (<<>KHBOTHOM CMJ10M,»)
nyTb >KH3HM. 4enOBeK pe>Ke
BCTpe an 6b1 nperpaAbI Ha
Ka66ana KBa,n,paTa '" K{>8CTa
He 38Mency
tcOAHOporast- 3Be3Aa CMM-
BOnM3MpyeT CTMXMIO H -
tcMY*CtcyIO- CW1Y CToM-
M8OC1J:» B npeo.QOJ1eHMM
TPYAHOCTeM He nyrM K AOC-
TM)KeH M.
a
6
1 4 7
2 5 8
3 6 9
Puc.29. KBaApar no wy (0)
M reoMeTpM'4eCKafi cpMrypa (6).
COCTaBJ1eHHafi no '4MCJ1090MY pfiAY
cspeMeHM p0*AeHMfI» "eJ10SeKa
227
rnaBa 5
>KH3HeHHOM nyrM, '4aU4e nonY'4an
6b1 OT >KM3HM YAOBonbCTBHJI (OHM
60nbweM '4aCTblO 6b1nH 6b1 «CO-
MHHTenbHblMH», «rpeXOBHblMH»),
HO B03HHKana 6b1 onaCHOCTb 6b1Tb
BOBne'4eHHblM B pHCKOBaHHoe H
nopHLtaeMOe 06tqeeTBOM npeA-
npHJlTMe. «AByporaJl» $Mrypa
npeAOCTeperaeT, 4TO B 3TOM eny-
'4ae paCCJ1a6nJlTbCJI Henb3J1: OAHa
M3 Ka3aJ10Cb 6b1 HeCJ10>KHblX npe-
rpaA BcerAa MO>KeT OKa3aTbCJI
«'4epTOBCKH KaBep3HOM», pOKOBOM.
TaK KaK C<AByporaJl» 3Be3Aa .-
CHMBon AbJlBOna.
IlHHHH '4HCen I(BaApaTa no wy He AalOT TO'4HOro paC'4eTa AflH-
TenbHOCTH >ttioHH, KaK 3TO n03BOnJleT CAenaTb rpa4>HK (CM. HH>Ke),
n03TOMY B paC'4eTaX CJTeAYeT HCXOAHTb H3 cpeAHeCTaTHCTM'4eCKO
BenH'4HHbI npOAOn>KHTenbHOCTH >KH3HH - OHa COCTaBnJleT OKono
65 neT. IlHHMH 4>Hrypbl nOKa3b1BaIOT Bee OCHOBHble H3nOMbi Ha
>KM3HeHHOM nyTH '4enOBeKa, a 06U4aJl AflMHa Bcex nMHHH COOTBeT-
CTByeT A1IHTenbJ\OCTH ero >KH3HH. AnJl onpeAeneHHft '4aCTK >KH3HeH-
Horo nyTH CJ1eAYE!l3HjtTb «LteHY» Ka>KAOM nMHHH >KM3HM. AnJl3TOro
w ..- w .
CpeAHHH B03paCT, KOTOpblH npeAnOnO>KMTenbHO Mbi OTHOCM,.. K A1IH-
TenbHOCTH >KM3HH AaHHOro '4enOBeKa, AenMM Ha 'tHCJ10 nMHHM 4>H-
rypbl KBaApara: 65 neT: 6 - 10,8 neT, o pyrnHM AO eJ10M BenH H-
Hbi - 1'1 neT. OAHa nHHHJI COOTBeTCTByeT l1-neTHeMY B03paCTHOMY
HHTepBany. COCTaBHM cxeMY B03paCTHbiX 3Ha'4eHHM Ka>KAOM nHHHH
4>Mrypbl: (pHC. 30): I - AO 11 neT; II - OT 12 AO 22 neT; III - OT
EcnM ..p OKieyl1b-
TM3MY, noaopoTbi B
peanbHoM >K...3H... 3aB"'-
CstT KaK OT caMorO e-
110BeKa, TaK ... OT 1110-
Ae , C KOTopbIM'" eMY
np"'XOAHTCR CTanK"'-
BaTbCst. KaPM... ecK...
nl1aH >IG13H... n03TOMY
"IaCTO OTI1WiaeTCst OT
peanbHoro $iKTa, HO
BO MHorOM MO>KeT C
H"'M ... COBna,o,aTb.
228
Ka66ana KBBAPBTa U KpeCTa
V (45-55 neT)
n (12 rOAa)
I (AO 11 neT)
VI (OT 56 neT)
IV (34-44 ro )
PUC. 30. B03paCTHbie COOTBeTCTBHJI /lHHHM cpMrypbl
23 AO 33 neT; IV - OT 34 AO 44 neT; V - aT 45 AO 55.Jter; VI - OT
56 neT AO KOH a >KM3HM (npeAnOnO>KHTenbHO - 6 mrr).
Tenepb BM3YaJ1bHO (Ha rna3) xapaKTepM3yeM Ka>KAYlOnHHHIO reo-
MeTpH'4eCKOM 4>Mrypbl (CM. pHC. 29,6) M 4>Hrypy B eJ10M. OKKYnbT-
HbiM aHaJ1M3 :nOM 4>Hrypbl AaeT nHWb 06U4Me npeACTaBneHMJI 0 npeA-
Ha3Ha'4eHHOM '4eJ10BeKY CYAb6e.
OTMeTMM Ba>KHoe 06crOJlTeJ1bCTBO: Bce oKKYnbTHbie paC'4eTbi (HY-
MepOnOrM'4eCKMe, acrponorH'4eCKMe MAP.) BblJlBnJlIOT KapltfUilecKyIO
nporpaMMY CYAb6b1 '4eJ10BeKa. 3TO nnaHMpyeMbiM AllJI Hero KOCMO-
COM npM HaCTOJlU4eM MHKapHaLtMM npMHLtMn >KM3HM, a He >KM3Hb,
KOTOpoM OH Ha caMOM AeJ1e >KHBeT.
no npeACTaBneHMIO ApeBHHX MYApeLtOB, Hawa KapMa BMeWMBaer-
CJI B Hawy >KH3Hb CTOJ1b '4aCTO, '4TO He Y'4MTblBaTb ee npocro Hepa3YM-
HO. npaKTMKa >KM3HM CBMAeTeJ1bCTByeT 0 TOM, '4TO ra,l:\aTeJ1bHbIe OK-
KynbTHbie npeACKa3aHMJI, K YAMBneHMIO,AOBonbHO '4aCTO caepWalOTCJI.
OAHaKO nOACKa3KM CHJ1 He6a H 3eMJIM Mbi nonY'4aeM, KaK nonaraeT
3TO Y'4eHMe, '4epe3 4>HJ10co4>cKMe 0606U4eHMJI M CMMBonMKy, KOTo-
229
rnaBB 5
pble CJ1eAYeT npaBHnbHo Ae-
WH4>POBaTb H HCTonKOBbiBaTb.
fS>Mrypa KBaJI.PCIT3 Ha pM(. 29,6
HanOMMHaeT 3Be3AY, HO MMe-
eT M CYU4eCTBeHHoe HCKa>Ke-
HMe ee c1>OPMbI, oc06eHHo B
npaBoM no PHCYHKY aCTH,
cOOTBeTCTBYlOtqeM nepBoM
nonOBMHe >KH3HM '4enoB i<a,
Ha 'KOToporo AenaeTCJI ntleX{-
CKa3aHMe.
lJenoBeK CTOnKHeTCJ1 C 3crt-
PYAHeHMJlMM B aAanTal4i(a.i 'K
3anpocaM 06U4eCTBa. Y Hero
nOJlBMTCJI HeKOTOpaJ1 HeYBe-
peHHOCTb B CBOHX AeMCTBMJlX
H nnaHax - «3aKOMnneKCO-
BaHHOCTb». CKa>KeM TaK, cyw. no 4>Hrype KBaApaTa no wy, OH 6YAeT
opMrMHanbHOM nH'4HOCTblO. OAHaKO ero HeAOCTaTKH He nOMewalOT
eMY B ,",enOM '6b1T» AOBonbHblM CBeeM CYAbOOi4. A06HTbCJI OCHOBHblX
l4fJ1eM B >KM3HM - Ha 31"0 YKa3b1BaIOT B qenOM npaBMnbHble COOTHO-
WeHMJI 4aCTeM 3 bI. npM'4eM maBHble M3MeHeHMJ1, npoMCXOAJIU4Me
B ero >KM3HM M Bern nM64HOCTM, 6yAYT KapMM'4eCKM 06ycnoBneHHblMH.
n03TOMY «nepeAenblB. caMoro ce6J1 MnM TeM 60nee TpaTHTb Ha .
3TO CMnbl.cOCTopoHbI (npMBneKaTb poACTBeHHHKOB MnH APY3eM) BPJlA
nM MMeeT ' blCJ1: ycnexM 6ypyr He3Ha'4MTenbHblMM HnM HeycrOM H-
BbiMM. 3roro '4enOBeKa J1Y'fwe BocnpMHMMaTI. TaKHM, KaKOB OH eCTb.
Cyw. no "IOCmU"IHONY HCKa>KeHMIO 4>Hrypbl 3Be3AbI, Bce OTpMLta-
TenbHble '4epTbi nH'4HOCTM M CBJ13aHHble C HMMH npo6neMbi B >KH3HM B
EcnM upM11I oaynllTM3MY,
MCKIDlCeHMe npaaoM 'laCTM
CHny3T8 38e3AbI yt(a3bIBaeT
H8 TO. I.fTO 'feI10geK)' 1CBpMM-
1G1 38nporpaMMHpoBaHbl
«HeOraHA8PTHbte lt OTK11OHe-
tMH B Il HOCTM no cpaBHe-
HMIO c npttHRTOit B o6t.!4ecrae
ttOPM<JM. HanPHM9P. OH He
BCerAa OY/JlSf A06p0A8Tenett
M .no-
CKOJJbICy MMeeTCR HStCOTopoe
MCKIDKeHW) (3Be3,D.a
&epUJMHOM BBepX - CHMBOI1
AoOpa '" CBeTllbIX noMblCJ1OB).
230
Ka66BJ1a KB8,DJJ8TB H KpecTB
OCHOBHOM npon,.RTCJI Y '4eJ10BeKa B IOHOWecKOM M MOnOAOM B03pac-
Te - AO CepeAHHbI >KH3HM. HaM60nbWMe MCKa>KeHM.R J1Y'4ei1 3Be bI
npMXOAJITCJI Ha nHHMM, CDeAMH.RIO Me '4MCJ1a 9 M 4 KBaAJ)aTa, 'lT0 co-
oTBeTCTByeT IV (34-44 rMa) M V (45-55 net) nMHMJlM.4>Mrypbl.
MO>KHO C YBepeHHOCTbIO CKa3aTb, '4TO 3TH MCKa>KeHM.R nKMMM 3Be3AbI,
T. e. CDeAMHeHMJI nOMaHOM KpMBOM '4MCeJI 9,,5 M 4 (BMeCTO TOro 'lT0-
6b1 wna npJlMaJI nMHMJI Me>KAY '4MCJ1aMM 9 4, npeAeJI.RIOU4aJl J1Y'4-
WYIO cMMMeTpHIO 3Be3AbI), npeAcKa3b1BalOt' enO)KHble np06neMbi B
)KM3HM, C KOTOpblMM CTOnKHeTCJI '4eJ10BeK B «B03pacre_ IV M OCo6eH-
HO V nMHHM. nMHMeM, ]aAaIOU4eM oWM6KM B )KM3HM 'H!1IoseKa, 6YAet
nOBopoT IV nMHMM (B03paCT 34-44 roAil). B 3TOf nepMoA OH ynyc-
TKT nY'fwMe CBOM B03MO>KHOCTM M COBepWMT OWM6KM, KOTOpble KpyrO
M3MeH.RT ero >KM3Hb. (NeHb TpyAHble BOn bI C&OeM )KM3HM npMAeT-
C.R peWaTb B Ha'4ane V nMHMH (45-46neT). B.qanb weM V nMHMJI
BbiBOAMT tyAb6y '4eJ10BeKa Ha 6narOnpMJfTHYIO n03Ml4MIO >KM3HM, Kor-
10 UMKTI
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231
Puc. 31. rpa4»MK JKM3HM
M onpeAeJleHMJI
KpMTM'feCKMX
( nOBopoTHblX)
neT nM'fHOCTM
rOAbi
72 84
rnaBa 5
Aa OH MO>KeT MaKCMManbHO pac-
KPbITb CBOH J1M4HOCTHbie Ka eCTBa.
CYAwa AaCT eMY eU4e OAHH «waHC»
B BHAe MaKCHMaJ1bHO YAa'4HO A/1J1
Hero cnO>KHBWHXCJI 06CTO$lTe11bCTB,
T06b1 A06HTbC1t B )f(H3HH HaMe'4eH-
HOM LtenM (npHMepHO B 48 neT - Ha
3TOT )f(e B03paCT YKa3b1BaeT H rpa-
4>HK pHC. 31).
no pacc MTaHHoMY KBaApaty no
wY MO>KHO nOnaraTb, '4TO '4eJ108eK
HMeeT «CpeAHHM ypoBeHb MHTen-
neKTa» .( «3 Be3A C He6a He XBaTa-
eT», HO B OCHOBHOM npaBMnbHO
pewaeT CBOH np06neMbI). OH HcnblTblBaeT YMepeHHYIO nlO60Bb K
6nH>KHeMY, He '4aCTO >KepTByeT nH'4HblMH HHTepecaMH H npH 06U4e-
HHH He 3a6bfjaeT 0 eBoeM BbirOAe. OH He nHweH CO'4YBCTBHJI H CO-
Y'4aCTHJI, HO npH 3TOM nW4HHT 0 nepBOO'4epeAHOCTH YAOBneTBope-
HHJI nH4HblX nOTpe6H00eM. HaJ1H'4He B '4HCJ10BOM pJlAe BpeMeHH
p0>KJ\eHHJI '4MCen 3 M 4 cBMAeTenbCTByeT 0 nOKpoBMTenbCTBe B ero
tyAb6e BblCWMX CHJ1 - CHn He6a, a '4MCJ10 5 YKa3b1Bae'r Ha 6naro-
npHJlTHbiM YPoBeHb-«nonO>KHTeJ1bHOM 3HeprMH» B 3HepreTM'4eeKHX
TeJ1aX ero opraHM3Ma. HTO YAep>KHBaeT ro Ha «npaBeAHoM nyTM».
3Ta "3HeprHJI npHAaeTJ1H'4HOCTH onpeAeneHHYIO HHH HaTHBHOCTb,
3HeprH HoCTb xapaKTepa. OH HMeeT 60nbwHe B03MO>KHOCTM B pe-
weHHH «nonO>KHTenbHbIX», «A06ponOpJlA0'4HblX» Aen, BCJ1eACTBHe
4ero B HMX eMY 6YAeT '4aCTO COnyTCTBOeaTb YAa'4a.
TO'4KH, KOTOpble Hcnonb3YIOT A/1J1 HCTonKOBaHHJI nporH03a, no-
ny alOT OT nepeCe4eHHJI ropH30HTaneM H BepTHKaJ1eM OT «KOHT-
f'pacj)MK
«nOBOpOTHbiX neT-
,D,nSl nocTpoeHHSI rpa-
4>HKa nporH03a «nOBO-
poTHbiX neT» )t('-13H'-1 HC-
nOllb3yeM rpa4>W4ecKoe
nOCTpoeH'-1e: no ropH-
30HTanH OTll0)t(IiIM paB-
Hble '-1HTepBaJ1b1 no
1211eT >K'-13HIiI, a no Bep-
THKaJ1'-1 - HytJleponorn-
ecKIiIH KOA OT 0 AO 9.
232
Ka66ana KBBApara ", KpeCra
ponbHbIX», H.RM «3Ha HMblX», '4HCen, T. e. MMelOU4Mx npaKTM'4ecKoe
3Ha'4eHHe B BbI'4HtneHMH (Ha pHcyHKe HX MeCToHaxO)f(AeHMe MO>KHO
onpeAenHTb no WTpHXOBbiM nMHHStM) (CM. pMC. 31). mMH '4HCJ1aMH
RBnJlIOTCJI ABa KpHTepHJI: '4MCJ1a uHouBuiJyanbHozo Kooa (oTMe'4aeMbie
no Bepn1KanM - OCM a6c Mtc) H '4MCJ1a cyMM 12-nemHuxqu B (OT-
M aeMbie no ropM30HTaJlM - oeM 0PAMHaT rpa4>MKa). nePec eHMe
nepneHAHKynJlpOB OT '4MCen ropM30HTaJ1H C nMHHJlMH, HAYU4HMH OT
Hcen BePTHKanH, H AaeT PJlA KOHTponbHblX Tot.eK;<:oeAHHeHHe KOTO-
pblX onpeAenJler rpa4>HK >KH3HM, HJ1M rpa4>HK tyAb6s.
OAHaKO AJ1J1 nocrpoeHMH rpa4>HKa Hy eponOrH'4eCKHM KOA on-
peAenHeTCJI He cnO>KeHHeM, KaK B nepBOM BapHaHTe, a nepeHHOJKe-
Hue,., '4MCen AaT pO)f(AeHHJI APyr Ha APyra:
('4MCJ10 OHR) x ('4HCJ10 HeCRqa) x (zoo-ROJKOeHUR).
Ka>KAoe HCJ10 M3 non eHHoro nOCJ1e nepeMHO>KeHMJI '4HCJ10-
Boro pe3ynbTaTa OTKnaAblBalOT no eepTHKanM rpa4>HRa B Ka'4eCTBe
HHAHBHAYanbHoro HYMeponOrM'4eCKOrO KOAa BpeMeHH pO>KAeHHSt
(HnH KapMUileCKOZO Kooa pOJKOeHUR). no npHBeAeHHOMY npMMepy
npOH3BeAeM paC'4eT: 30 x 08 x 1954 - 468 960. .QBe weCTepKH B
HYMeponorM ecKoM pJlAY KOAa rOBOpJlT 0 ABYX TO'4KaX paBHOBeCHJI
B «B03paCTHbix Becax» >KH3HM AaHHoro '4enOBeKa.
HAHBHAYaJ1bHblM KOA - 468960 - OTKnaAblBaeM no BepTH-
KaJ1H rpa4>MKa: Ka>KAoe '4HCJ10 Hcnonb3yeM nOCJ1eAOBaTenbHO TaK,
KaK OHO pacnOnO>KeHO B HHAHBMAYaJ1bHOM n1CJ10BOM KOAe, Hynb He
Y'4HTblBaeM. BepXHee, caMoe 60nbwoe, '4HCJ10 JlSnJleTCJI CHMBonM-
'4eCKOM «BePXYWKOM >KH3HH», KorAa CJ1eAyeT ycneTb MaKCHManbHO
peanH30BaTb ce6J1 H KorAa HaH60nee nonHO paCKpblBalOTCJI (eCJ1M
3TOMY COAeMCTByeT TaK>Ke M caM '4enOBeK) nH'4HOCTHbie B03MO>KHO-
CTH. Y AaHHoro '4enOBeKa MaKCHMaJ1bHblM nOAbeM ero B03MO>KHOC-
TeM OTMe'4aeTCJI B 48 neT. B nOCJ1eAYIOU4HM 12-neTHHM MHTepBan
233
rnasa 5
6YAeT MATM cnaA, KpMTM'4eC-
KHM MOMeHT B )l(M3HH Haay-
nMT B 60 neT: Ha Hero YKa-
3b1BaeT nOBTopeHMe '4MCJ1a B
KOAOBOM pJlAY ('4MCJ10 6). no
CJ1Y'4aMHOCTM 3TO «MarM'4ec-
Koe '4MCJ10» C nocneAYIOU4MM
HyneM, T. e. '4MenO 60 KOAa
COBnano C KpMTM'4eCKMM
MCJ10M B03pacTa enOBe-
Ka - 60 neT.
KpMBiULf"pa4>MKa MO>KeT
MMeTb pe3KMe OTKnOHeHMJI
OT nnaBHOM nHHMH. HanpM-
Mep, HeKOTopble. TO'4KM MO-
ryr «BblCKaKMBaTb» M3 KPM-
BOM OCHOBHoro rpa4>HKa
MnM Ha rpa4>MKe 6YAf!T AByrop6aJl (MnH C MenKMMM Kone6aHHJlMM -
«BonHaMM») KpMBaJl. npM npoeK4MM TaKMX MCKa>KeHMM Ha «J1MHMIO
>KM3HM» '4enOBeKa (ropM30HTaJ1b C 0603Ha'4eHMe.M '4Mena neT) no-
nY'4alOT MMeHHO Te roAbI, KorAa CJ1eJWeT O>KMAaTb «C60M» B >KM3HM,
KaKoM-To KpM3M(4. nOMKy B CYAb6e. 3T0 Bce KapMM ecKMe npeACKa-
3aHMJI, nOCblJ1aeMwe '4C110BeKy, a TO'4Hee, 3apaHee eMY 3anporpaM-
MMpoBaHHble tyAb60M.
CYASI no «KpMBOM >KA3HH», AaHHblM '4enOBeK «KapMM'4ecKH 3a-
nporpaMMMpoBaH» MaKCMManbHO peaJ1M30BaTb ce6J1 B B03paCTe
38-48 neT. OrBeAeHHblM eMY B03paCT >KH3HM, comaCHO ero Kap-
Me, COCTaBnJleT OKono 78 neT: onpeAenJlf!TCJI no npOAlleHMIO «KPM-
BOM >KM3HH» AO nepece'4eHMJI C rOJ)M30HTaJ1blO 4MKnOB neT >KM3HH.
Ecn. MH.H'"
"Ienoeet< MQ)K8T CBOMM noee-
A9HMeM C03H8T8nbHO M3M8-
HKTb CBOIO cy1JPfJy B n}"4wyK>
CTopoH)', M30eJKaTb T81OO(
-c6oeB» B JKM3HM W1M ycW1HTb
MX. HyMeponorM nonaratOT, 'fTO
3H8HM8 118T »13-
HM n0M0ra8T enoeeK)' ny'4W8
Tb ycwu.1S1 nM'fHO-
CTM MMeHHO B 3nt -1CpKTM'feC-
ICMe» AnSI HerO ro.D.bI, 'fT00bI
OCTBB8TbCSt X03S1MHOM CBOeM
cy , He coaepwKTb H8f1On-
paBMMYK> B )IG13HM OwMOK)'.
234
Ka66ana KBa.clPara iii KpeCra
Ho, KaK H3Bed"Ho, «CYAb6a npeAnona-
raeT, a '4enOBeK pacnonaraen. B ero
BnaCnt yt<OpOTMTb MnM npoA/lMTb CBoe
HaCTOJlU4ee npe6b1BaHMe Ha 3eMJIe.
CaMoy6MMLtbi M nonblTKM cyMLtHAa
Ocy>KAaJ1MCb BO Bce BpeMeHa B nOOOM
3ApaBoMblcnJlU4eM 06U4eCTBe. PenMrHJI
M roCYAapCTBO BeerAa aKTHBHO 60po-
&4eb co BeeMM eeKTaMM, KOTQPble CO-
1iept1Jci1IM YMblWJ1eHHbIe y6Mi1cTBa, npM-
HOCHnH '4enOBe'4eCKMe >KePTBbI. .npH
9'R>M pel1MrHJI YKa3b1BaeT Ha 4<MYKM CJAa»( a 6Ho epreTMKa - H
riOBYOPHoe peMHKapHltpoB8HMe Ha 60nee HH3KOM 3H reTM'4eCKOM
YPOBHe. YMblwneHHoe nMweHMe >KH3HM HapywaeT nnlkbl MHKapHa-
14MM (BonnoU4eHHe 3HepreTH eeKOro Tena AYWH B 4>M3M'4ecKoe Teno
opraHM3Ma C C03AaHMeM 4enOBeKa - nOAP06Hee CM. COOTBeTCTBY-
IOU4Me H3AaHMJI MnM e<CeMeMHYIO aCTponontlO» aBTopa). 3aTpYAHJI-
eTeJl «AeJlTeJ1bHOCTb Bblcwero KOeMM'4ecKoro Pa3YMa», C KOTOpblM
oKKynbTHbie liayKM (aCTponOrMJI, 6M03HepreTMK3, KOcM06MOnOrMJI
MAP.) CBJl3b1BaIOT pa3BMTMe '4enOBe'4eCTBa M npHxOA HOBbiX AYw Ha
3eMJIIO - MX MHKapHaLtMIO.
B TpYAHble MOMeHTbI B >KM3-
HM paCXO>KaJl 4>pa3a «YaK TJI-
>KeJ10, '4TO XOTb BeWaMCJI» MO-
>KeT ManOAY HOMY '4enOBeKy
BHYWMTb HexopOWMe aCC014M-
aLtHH. OAHoro 3TO MO>KeT nOA-
TonKHyrb, HanpMMep, K nbJlH-
CTBY, 3anolO, APyroro - K
PenH",_
M 0KKy1l1lTM3M Y'l8T
EcnM 'feJ1OBeK
YMblWl1eHHo....'«H8Kl1a-
,D,bIB8eT H8 ce6A
P.YJCH:. J1HWaeT ce6A
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CTporOl! HSK838HH8
era J1yuJH:
MHT8pecHW" ca._1CT
B TPYAHble MMHyTbI )KM3HM,
B nOJ1oce HeYA8 MblCJ1M
o caMoy6MMcTBe npHXQAAT
B r0J10BY n T14 OMY
}(OTS1 (5b1 OAMH pa3 B )KM3HiII.
235
rnSBB 5
CYUL(UOY (caMoy6MMCTBY). 06
3TOM co06lJ4aeT «nonynJlpHaJl ra-
3eTa» (MaM 1998 r.) B CTaTbe «Xo-
nOAH M MMr - rope'4b nycroTbi
(pa3roBop C nCMxoTepaneBToM 0
caMoy6MMLtax)>>. K CO>KaneHHIO,
CYHLtMA - He TaKoe Y>K peAKoe
IIBneHMe. KaK nMweT aBTOp 3TOM
CTaTbM AeHMc POra'4eB (KCTaTH,
COAep>KaHMe CTaTbH nOA'4epKM-
BaeT M Ha3BaHHe pa3Aena ra3e-
Tbi - «4epHaJl nonoca»): «B
peaHMMaLtMOHHOM OTAeneHMM
«CKnM4>a» (06MxoAHblM CJ1eHr MOCKBM'4eM, 0603Ha'4alOutMM HHcntTyr
CKOpoM nOMOU4M B MOCKBe. - npUH. osm.), Ha'4HHaH C weCTH-ceMH
'4aCOB Be'4eaa, - nOCTOHHHblM nOTOK. Ao mrTM '4aCOB yrpa. 6b1BaeT,
'frO Ha naH e CTOHT eCTb-ceMb «CKOpblX», He ycneBalOT npMHH-
MaTb. 4eTBepTb M3 nocrpa,qaBWMX - caMoy6MMLtbi. )fo Te, KTO nbl-
TaJ1MCb OTpaBMTbCJI. ECJ1M MX AOCTaBHT BOBpeM", Bpa'4aM YAaeTCH
cnacnt MX >KM3Hb. ..»
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npeACTaBnJlIOTC1t Ba>KHblMH. TalC, B nMTeparype no oKKYnbTM3MY M
penMrMM (a He TomKOW MeAMLtMHCKOM nMTepatype!) C'4MTaeTCJl60nb-
WOM oWM6KOM, «rpeXOM» He6pe>KHoe OTHoweHMe '4eJ10BeKa K CSDe-
HY 300fX)BblO M YMblwneHHoe COKpaU4eHMe «OTBeAeHHoro» nepMO-
Aa >KM3HM tyMLtMAbi HaM60nee '4aCTbI Y'HapKOMaHOB, y nCMXM'4ecKM
60nbHblx MJ1M HeypaBHOBeweHH X nIOAeM).
MHorMe penHrHM nponaraHAMpy1OT CBOM pa3pa60TaHHble MeTO-
Abi YKpenneHMJI 3AOPOBbJl M npOATIeHMJI >KM3HM aepYIOU4MX. npM-
3APa...," CMbICII
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CTBeHHOC1M nepe,t\ 6IM3m-
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ny'fWMe epeMeH8, YAeP*M-
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236
'4eM npOAOn>KMTeJ'IbHOCTb >KM3HM
4>opMynMpyeTCJI no-pa3HOMY:
MeAHLtHHa ee onp AeJ1J'eT KaK
«cpeAHeCTaTMCTM'4ecKMM Bo paCT
>KM3HH» '4enOBeKa, penMrMJI -
«CKOnbKO Ha POAY HanMcaHO», a
HYMeponorHJI H acrponOrHJI -
«KapMH'4eCKM 06ycnOBneHHOM».
CornaCHO 6M03HepreTHKe, HeMa-
nOBa>KHOe 3Ha'4eHMe B cOKpaU4e-
HMH cpoKa >KM3HH '4enOBeKa
MMeeT CTpeMneHMe 0eJ10mb 3110
OPYZUM nIOAJlM, OC06eHHO 6nH3KMM. «3HepreTM4eCKMM 6YMepaHr»
n0A110CTH 06J13aTenbHO B03BpaU4aeTCJI K nOCJ1aBWe ro. Hanpo-
THB, yOl1uHJlemcil >KM3Hb, KorAa '4enOBeK AenaeT iJo6po J1IOAJlM, Ae-
nHTCJI C HHMH CBeeM paAOCTblO, CO'4YBCTByeT MX 6eAe. AenaTb A06-
po nlOAJlM ttaCTOJlTenbttO nponOBeAYeT M penHrHJI.
COBpeMeHHaJl MeAHLtHHa nOATBep>KAaeT: KOH4>nHKTbI, CTpeCCbI,
3aBHCTb, HanpJl>KeHHOe O>KHAaHHe MnH npOAOn>KHTenbHoe '4YBCTBO
rpeBorH (HanpMMep, Bpa>KAe6Hble OTHOWeHMJI B ceMbe, Ha pa60Te)
nary6Ho BnHJlIOT Ha 3AopOBbe, a HapOAHaJf MeAMLtHHa npJlMO YKa-
3b1BaeT, '4TO «Bce 60ne3HH - OT HepBOB».
ComaCHO HeTpaAHLtHOHHOMY Y'4eHMIO, «TBOpHTb A06po» cne-
AYeT npH nlO60M YA06HOM cnY'4ae. B 3aBeAeHHoM HaWMMH npeA-
KaMH TpaAHLtHM 06U4eHMJI 3TO '4aCTO npOJlBnJfeTCJf. HanpMMep,
Y>Ke npH BCTpe'4e B npMBeTcTBMM (<<3ApaBcTByhe», «A06poe
YTPo») 3BY'4HT nO>KenaHMe 3AOPOBbJl, A06pblx Aen. 0 Bblpa>Ke-
HMH APY>KeCKHX '4yecTB cBMAeTenbcTBYIOT M APyrMe TpaAMLtMH
Hawero HapoAa, npM'4eM B cenbcKoM MeCTHOCTH OHH npOJlBnJl-
Ka66ana Ksap,paTa fit KpecTa
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'I8U4.8 BC8ro ....3....8.
T: npeHe6pe*eH e
MepaM np<><t> K
3a60neBaH . 3naynoT-
pe6netMe KYpeH eM.
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np BbI"IK nepeeAaTb.
HeAOCblnaTb, 3ac * -
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237
rnasa 5
IOTC" CMnbHee: HepeAKO B
cene 3AopOBaIOTC" Aa>Ke C He-
3HaKOMbiM BCTpe'4HblM '4eno-
BeKOM. C'4MTaeTC", '4TO Ao6po
norawaeT MenKHe npOC'4eTbi H
«rpeXM» B )t(H3HM. YBenH'4eHMe
npoAon)t(HTenbHocTH >KM3HM
06bJlCHJlIOT 3HepreTM'4eCKHM
nepeBonnoU4eHMeM opraHM3-
Ma, 3HepreTH'4eCKOM «B3aM-
MonoAnHTKoM AYW», YMHO>Ke-
HMeM «CMnbl A06pa». 3nble,
nOAJ1b1e nlOAM YKopa'4MBaIOT
ce6e )t(M3Hb «oTpM aTenbHoM 6M03HeprHeM» opraHM3Ma M 60-
ne3H"MM ('4TO nOATBep>KAaeT M MeAM MHa).
Aon" npaB bI B 3TOM eCTb: HaCblI14eHHa" C06b1THJlMM M A06pbl-
MM AenaMM 63Hb Ka>KeTC" '4enOBeKy P.nMHHee M nnOAOTBopHee.
CornacHo Y'feHMIO
npoAoroKKTenbHOCTb *M3-
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CR TIUOKe MCJ1OM J1IOAeM.
KOTopbIX OH oc aCTnMBWI;
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Mor B 6eAe, OKa3a1l no-
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Aena CnOCoOcTByeT -pac-
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ccHe6eCHbie CTBonbl»
M cc3eMHble BeTBM»
nOHJlTMJI «He6ej:H CTBonbf» M «3eMHbfe BeTBH» M3BeCTHbf B
4>HJ10C04>MM M HYMeponorMM KMTaJl C XIII B. AO H. 3., M BHa'4ane, AO
'4HCJ10BOrO 0603Ha'4eH 3neMeHTOB. MYApe bI n0J1b30BaJ1MCb na-
paMH MKntt CKHX 3HaKOB. AeCJlTb «H eCHbiX CTBonOB» CBJl3b1-
BalOT C AeC"TblO naJ1b aMH PYK, a 12 «3eMHblX BeTBeMJ> - C 10 nanb-
aMH H nnlOc ABe KMCTM. «BeTBM» M «CTBOnbl» 3HaMeHyiOT C060M
nepBblM BblXOA 3a npeAenbi onepaTMBHoM naMJlTM, 4>YHK MOHHPYIO-
238
U4eM B npeAenax CeMM 3neMeHTOB (noAP06Hee 0 3Ha'4eHMM CeMep-
KM B AeJlTenbHOCTM '4enOBeKa H B ern OnepaTMBHOM naMJlTM - C....
CJ1E!A,YIOU4MM pa3Aen). AenMTenM '4MCJ1a 10 «He6ecHblX CTBonOB» (2 M
5) M 12 «3eMHblX BeTBeM» (2, 3, 4 M 6) HaH60nee WMpOKO ,yICnOJ1b-
3YIOTCJI nlOAbMH KaK rpa.qaLtMM, rpynnbl AeJ1eHMJI npM-J'}i3pa60TKe
n03HaBaTenbHblX nporpaMM M B npMeMax 3aOOMMHaHMJI.
3Ha'4HMblM A11J1 HYMeponofHM JlBnJleTCJI TaK>Ke '4MCJ10 8 C y>Ke ne-
pe'4HCJ1eHHblMH Bblwe KpaTHblMH AenMTenJlfitM 2 M 4. o '4MCJ10
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B Hawy reHeTM'4ecKYIO naMJlTb, B Hawe
. KonneKTMBHoe 6ecc03HaTenbHoe. KaK
AOKa3b1SaIOT nCMxonorM, Ha onpeAe-
neHHOM 3Tane pa3BMTMSI AeTcKoM nCM-
XMKM OHO AaeT ce6J1 3HaTb KaK BoweA-
WMM B nnOTb nepBM'4HblM o6pa3: eCJ1M pe6eHoK pHcyeT, Aepeso B
ero pMcyHKax npe06naAaeT. 31'0 H eCTb MMpOBoe Ape80, Apeso
>KM3HH - MeCTO BCTpe'4M '4enOBeKa co BceneHHoM. Becb MMP, y>Ke
n03HaHHblM M eU4e He n03HaHHblM, ynopJlAO'4MBalOT M4>onOrM'4eC-
KMe KOHCTaHTbI ApeBa (pacU4enneHMe ero CTBona M BeTBeA 060-
3Ha'4a1OT "MenaMM. - npU/14. asm.). A80MKa, 06'bSlCHftIOT HaM 3T-
Horpa4>bI, BeAaeT 6MHapHblMH Onn03H(4MJlMM - CA80eHHblMM
npOntBOnOnO>KHOCTJlMM (pe'4b HAeT 06 OTpa>KeHHM 3aKOHa MHb-
JlH. - npUirf. asm.).
TpoMKa, npOMCXOASlU4aJl OT
'4neHeHHJI ApeBa no BepTMKaJ1M,
BonnOU4aeT a6cOnlOTHoe COBep-
weHCTSO M MC'4epnaHHOCTb. 01-
CIOAa xpMCTMaHCKaft TpOMLta, TpM
CblHa B CKa3Ke, TPM COCJIOBMJI
247
E MHeHMe
CxeM8 BeTBeM
«.Qpesa )ta43HM- -
C8Mb1M M M
MblH T0'4HblH MH-
CTPYMeHT cxeMbi
HMSt MMpa...
ero nOSHaHMSt, 3TO
CXeM8 CMM8OJ1M'feC-
KMX OCHOBHbIX Y'*t-
HMH, - C'MTSeT
.C. HsaHOB (1990).
Bc:noMonnenwtwe 'IMCII8
nStTepICM M wecTepKM Y
JJ.pesa HeT - 3TO MCn8
BcnOMOraTenbHble, T8K)lCe
K8K BOCeMb M AeBffTb.
rn8B8 5
MnH TpM cou,MaJ1bHble rpynnbl B nlO6oM 06u4eCT8e)'fPH nC*WT1CM BO
BCJlKOM Aene - OT CKa30'4HOro AeMCTBMJI AO cnopTHBHOM Hrpbl,
CHMBon Bcero. TO npeAnonaraeT B03HHKHOBeHHe. pa3BMTHe H 3a-
BepweHHe.
lJeTBepKa, npOHCXOAJIU4aJl OT '4neHeHHJI ApeBa no ropH30HTanH,
BocnpMHHMaeTCJI KaK 06pa3 BCJlKOM CTaTMCTH4eCKOM u,enOCTHOCTH.
(aMaJl yctoM'4HBaJl crpYK1Ypa, OHa npHTJlrHBaeT K ce6e Bce, '4TO Hy>K-
AaeTCJI B ycTOM4HBOCTH, - OT crpaH CBeTa AO CTOpOH AOMa.
CeMepKa HMeeT CaMOCTOJlTenbHOe 3 a'4eHMe, Aa eU4e KaKoe! Ce-
MepKa - 3TO cyMMa ABYX npeAblAY MX KOHCTaHT - TpOMKH H '4eT-
BepKH, T. e. ceMepKa HYMeponOrH'4eCKM COOTHOCHTCJI C AMHaMH ec-
KOM H CTaTH'4eCKOM KOHCTaHTaMM BceneHHoM. 3TO CHMBon eAMHCTBa
ABYX npOTHBOnOnO>KHOCTeM, He YMelOlqMX B CTonb CJ10>KHOM CHCTe-
Me, KaK MHP, CYlijeCTBOBaTb APyr 6e3 APyra.
60nbwe TOro! (eMepKa - 06lijaJl HAeJl BceM BceneHHOM B ee
nocrOJlHHOM B03po eHHH H OAHOBpeMeHHO HAeJl cOOTBeTCTBYIOU4ero
3TOM BceneitHoM MHcrpYMeHTa n03HaHHSI» (HayKa H penHntSi. 1990 r.
3).
Vl3BecTHbiM 3THorpa4>, 4>Hnoco4> H nHcaTenb nepBoM nonOBHHbI
XX B. MHp'4a 3nHaAe C'4HTan, '4TO Bce ceMepKH BeAyT CBOIO 4>Hno-
COc!>c;KyIO cHMBonHKY H3 MeconoTaMHH: ApeBHMe XaJ1AeH crpoHnH
6awHH - 3HKKypaTbi (aHaJ10rH cOBpeMeHHblx 6aweH-06cepBaTo-
pHM) - AnJl «C8ft3M < He6a C 3eMneM». Ka aSl TaKaJl 6awHJI CHM-
BonH3HpoBana KOCMOt:, a ceMb ee JlpycOB - ceMb He6ec, COOTBeT-
CTBYlOlqMX ceMH BMAAMbiM HeBooPY>KeHHblM rna30M He6ecHbfM
TenaM (c nTHHepaM): (onH!.tY, nYHe, MepKypHIO, BeHepe, Mapcy,
tOnMTeJ'Y, LaTypHY.
B 1956 r. MHMep, OAHH M3 aBTopoB cOBpeMeHHoM TeOpHH HH4>oP-
Mau,HH, mtcan B CTaTbe «MarH'4ecKoe '4HCJ10 ceMb nnlOc HJ1H MHHyC ABa»,
248
Ka66ana KSa,o.para u Kp eCra
npHY.eCWIM eMYJIIMpoBY'O,.3-
BeCTHOCTb: «nOBCIOAY MeHJI
npeCJ1 T OAHH 3HaK. B Te-
eHHe ceMH neT 3TO '4HCJ10
6YKBaJ1bHO CJ1e.qyeT 3a MHOM
no nJlTaM, JI HenpepblBHO
CTaJ1KHBalOCb C HHM B CBOHX
AeJlax... 3T0 '4HCJ10 npHHH-
MaeT MHO>KeCTBO 06nH'4MM,
MHOij\a OHO HeMHoro 6onbwe,
MHOl"Aa HeMHoro MeHbwe, HO
OHO HHKOij\a He H3MeHJleTCJI
HaCTonbKO, 06b1 ero HeJ1b3J1
6b1J10Y3HaTb.HaCTOM'4MBOCT
C KOTOpoM 3TO '4MCJ10 npecne-
AYeT MeHJI, He MO>KeT 6b1Tb
npoCTblM COBna.qeHHeM».
nOJlBHnaCb TeOpHJI HH4>opMa MM, B KOTOpO MHorHe YBHAeJ1M
YHHBepcanbHblM MeTOA aHam13a '4yTb nH He Bcex CTOpOH eJ10Be-
'4eCKOM AeJlTenbHOCTM M nCHXHKM, pe>KHMa BpeMeHHOM flepepa60T-
KH HH4>opMaLtHH.
KpaTKOBpeMeHHaJl H AonrOBpeMeHHaJl naMJlTb npeA'b BnJlIOT nCH-
XMKe pa3Hble ycnOBHJI. KpaTKospeMeHHaJl naMJlTb HHTepecyeTOI He
CMblCJ10M HH4>opMaLtHM, a '4MCTO sHeWHMMH, 4>H3M'4eCKHMH xapaK-
TepHCTMKaMH - TeM, '4TO cpa3Y 6pocaeTCJI B ma3a: 4>OpMOM, COOT-
HoweHMeM 4>Hrypbl H 4>oHa, ocseU4eHHOCTblO, BeTOM M T. A. KpaT-
KospeMeHHaJl naMJlTb aU4e Hcnonb3yeTcJI AnJl onepaTHBHOM
MH4>opMaLtHH H HenocpeACTseHHOM o eHKH CHTYaLtHH. HeAapOM ro-
BOpJlT, '4TO «BCTpe'4aIOT no OAe>KKe», - 3TO cpa3Y «3anaAaeT» B
MHTepecHwit 4»8KT
M"mnep OOHap}')lG1n. TO e-
nOBeK cnoco6eH c OAHoro
pa3a YAep)t(a.1BaTb B '1aMRTa.1 B
cpeAHeM 9 ABOa.1 HblX 'Mcen
(7 + 2), BoceMb AeCRTa.1 HblX
a.1cen (7 + . C Mb 6YKB an-
4>aBa.1Ta a.1 ns1Tb 0JViOCOO)KHblX
cnOB (7 - 2). Bce BepTellocb
BOKpyr CeMepKa.1. OKa3anocb.
TO OObeM HenOCPeACTBeH-
. HOH naMRTa.1 orpaHM eH He
KOIla.1 eCTBOM caMoH ....H4><>P-
MalUila.1, a KOn&4' ec «tcyc-
KOB» 3anOMa.1HaHa.1R.
249
rnasa 5
KpaTKOBpeMeHHYIO naMATb. nep-
Boe Bne'4aTneHMe, HH4>opMal4HIO
KpaTKoBpeMeHHoM naMJlTJ1 He TaK
nerKO 6b1BaeT BbiTeCHMTb MH Op-
aLtMeM AonrOBpeMeHHOM naMJI-
TM (HanpMMep, n03TOMYTaK Ba>K-
.HO nOArOTOBMTbCJI AllJI nepBOM
BCTpe'4M, '4T06b1 npoM3BeCTH nep-
Boe Bne'4arneHHe). CMblCJ10M MH-
TepecyeTCJI AonrOBpeMeHHalt na-
MJlTb; KOTOpoM Hwe>KMT Ol4eHMTb TO, '4TO AOCTMmo my6MH HaweM
nCMXMKM - «B AilHHblM MOMeHT HaXOAMTCJI nepeA HaWMM BHeWHMM
MJlM BHyrpeHHMM B30poM».
npMBeAeM ABa npMMepa M3BeCTHbiX nM HOCTeM, Koropble MomH
OAHOBpeMeHHO AeJ1aTb pa3Hble AeJ1a. PMMCKMM MMnepaTOp raM IOnMM
Lte3apb (102-44 rr. AO H. 3.) Mor OAHOBpeMeHHO enYWaTb AOK11aA
nOA'4MHeHHdfo, nMcaTb M OTAaBaTb npMKa3b1 APyrOMY nOA MHeHHO-
MY. MHOrAii OH MeHJln tROM Ha60p OAHOBpeMeHHO BblnOJ1HJ1eMbiX
AeJ1, 6naroAilPJl '4eMY np0(:11b1J1 B MCTOpMM «nCMX0J10rM'4ecKHM YHM-
KYMOM». B HaWM AHM M3BeCTHbiM MHeMOHMCTOM JlBJ1J1eTCJI IOpMM
rOpHblM. OH TO>Ke MO>KeT OAHOBpeMeHHO M C 60nbWMM ycneXOM, He
COBepWaJl OWM6QK M Ka'4eCTBeHHO, BbinOnHJlTb HeCKonbKO AeJ1. npM
3TOM OH 3arpY'f<aer pa60TOM nO'4TM Bce CMCTeMbi M opraHbI, npH'4a-
... v v -.II
CTHbie K AeRTeJ1bHOCTM: npaBOM pyKOM MO>KeT nMCaTb, a neBOM -
MrpaTb Ha pOJlne. ma3 MM C'4MTblBaTb 20-3Ha'4Hoe '4MCJ10 M 3anOMM-
HaTb ero,:rY6aMM wenTaTb CTMXM H T. A.
C. HsaHOB, aBTOp CTaTDM «MarM'4eCKaJl ceMepKa», BcnOMHHaeT,
'4TO 10. rOpHblM >KaJ10BaJ1CJI eMY Ha npeAeJ1 cBoeM B03MO>KHOCTM TpY-
AMTDCJI, orpaHM eHHblM CMarM'4eCKOM ceMepKOM». OH rOBOpMJI: «Ce-
YH"K8II W. n....HOCTM
Bcrpe alOTCst yHMK8J1b-
Hble M pa3HOCTopoHHMe
nIOAM. 06na.o.alOU4M8 803-
MOXHOCTblO OAHOBpe-
MeHHO AenaTb Macey Aen
683 CHM)KeHMst Ka'feCTB8
Ka)lC,AorO M3 HMX.
250
MepKa B BpaU4aeT MeH K cypOBOM AeMCTBMTenbHOCTM. enaTb
OAHOBpeMeHHO nJlTb Aen nerKO, CeMb - HeTpyAHO... 4MTaTb MWC-
nM TpeX MnH nJlTM '4enOBeK JI rOTOB XOTb i4enbiM Be'4ep, HO 8 MnM 9 -
YBonbTe! 3a '4ac ceMb nOTOB .coMAeT».
"IHCJ10 7 COOTHOCMMO C TaKMM H3BeCTHWM HYMepononNecKHM
'fMCJ10M, KaK 28 - '4aCTM nYHHOM 4>opMynbl HnH 4>opMynbl n03Ha-
HHJI MHpa. MO>KeT 6b1Tb, no:noMY '4MCJ10' 7 T 3aceno B Hawy na-
MJlTb H TaK TeCHO CBJl3aHO C HaweM nCMxMKoM, '4TO WiO COOTHOCHMO
C 'fMC110M 28?
B 'aHTM HOM MaTeMantire 6b1na ocooaJl BeTBb - reMaTpMJI (HY-
'MepononuI). 3MnHpM'4ecKM 6wnM ycTaHoBneHbI He06b1'fHbte CSoM-
ctBit" tteKOTopblx '4MCen, KOTopwe Ha3BaJ1M 4<TpeyI"OnbAblMH», a caMM
'fMCJ1a - COBepweHHblMH. OHM paCKnC!Abl8 MCb Ha-'fMCJ1a, Ha Ko-
TOpble caMH >Ke AenMnMCb 6e3 OCTaTKa:
6 - 1 + 2 + 3 - (6 : 6) + (6 : 2) + (6 : 3).
28 - 1 + 2 + 4 + 7 + 14 - (28 : 28) + (28 : 14) + (28 : 7) + (28 : 2).
496-1+2+4+8+ +31+
+ 62 + 124 + 248.. T. A.
Hit pHC. 32 npeACTaBneHa YHH-
BepCaJ1bHaJl mtpaMHAa AnJl noCT-
pOeHHJI nlO60ro «TpeyronbHoro»
'fHCJ1a. ECJ1H TalOKe COCTaBHTb nM-
paMHAY '4HCna 28, TO nonY HM
KOHCTpYKLtMIO, Ka>KAaJl ropM30H-
TaJ1b KOTOpoM AaCT cyMMY '4HCen,
paBHyIO nOpJlAKOBoi04y '4HCJ1Y pJlAa
OT eepwHHbI nMpaMMAbI: nepBblM
BepXHHM PJlA -1, a HM>Ke no npa-
BOMY CKnOHY nMpaMMAbi 6YAYT
Ka66anB KB8J1.PaTa H KpecTa
- -
I I I I I I I
,.,.,.,.,., .,
'__ __ __L__ __L__t
Puc. 32. YHMBepcaJ1bHaJi
nMpaMMAa AI'" l1Io60ro
«rpeyf'OJlbHoro» 'tMCJla
251
rn8B8 5
'4HCJ1a 2, 3, 4, 5, 6 M 7. ECJ1H CJ10>KHTb cyMMY '4HCen Ka>KAOrO pJlAa,
BK11IO'4aJl nOCJ1eAHMM - 7-M - pJlA, TO non HM '4HCJ10 28 (pHC. 33).
KaK BHAHM, Me>KAY 7 M 28 ecTb ropM30HTaJ1bHaJl H BepTMKaJ1bHaJl
CBJl3M.
(eMb cryneHeM nMpaMMAbi AaAyT '4MCJ10 28 no ropH30HTaJlH, eCJ1M
eCTb H APYrylO - nOCJ1eAOBaTenbHYIO - HYMepal,4MIO Ka>KAoro
KBaApaTa nMpaMMAbI: BTOpOM PJlA - 1 H 2; TpeTMM PJlA - 1, 2, 3;
'4eTBepTbiM - 1, 2, 3, 4 M T. A. (pMC. 34).
KaK BMAMM, '4MCJ10 28 3aJ10)f(eHO B CTpYK1)'PY nOCTpoeHMJI KaK
nHpalotMAbi Ha pMC. 33, TaK H nMpaMHAbi Ha pMC. 34.
«B OCHOBaHMM nMpaMMAbi cOBepweHHoro '4HCJ1a 28 ne)f(MT «1BO-
pJllqaJl» ceMepKa. ToF'AA Henb3J1 nM Ha3BaTb '4MCJ10 28 ee pa3BMTM-
eM, ee «rpeyrOJ1bHOM» $)pMOM - CBoe06pa3HblM xpaMOM TBOpe-
HMJI?» - cnpaWMBaeT peAaKI,4HJI >KypHana «HaYKa H penMrMjJ»
(1988. 12). BepOJlTHO MO>KHO, eCJ1M C'4MTaTb, '4TO Hcno 7KaK
PUC. 33. nMpaMMAa 'fMCJla 28
(I eapMaHT)
=1
=2
=3
=4
=5
=6
PUC. 34. nMpaMMAa 'fMcna 28
(II BapMaHT)
252
KpMTepHH «KyCKOB» OnepaTHB-
HOM naMJlTH ne>KHT B .oCHOBe
BOCnpHJlTMJI Hawefl nCMXMKOM
oKpy>KalOU4eM AeMCTBHTenbH C-
TH M JlBnJleTCJI TeMH «'4aCTJlMH»,
KOTopble CJ1eJWeT BbiAenJlTb H3
nlO6oM HOBOM HH4>op altMH AllJI
ee «nepeBapMBaHMJI», OTKnaA"'-
BaHHJI B xpaHMJlHI14e HaweM na-
MJlTM, B TaMHCTBeHHblM npOlteCC
3anOMMHaHHJI.
n1060nb1THO, cny aMHo nH
'4MenO 7 KaK «HYMeponOrH'4eC-
KaJl MaTpHlta» BXOAHT He Tonb-
KO B oKKynbTHYIO 4>opMyny n03HaHHJI MHpa (28 - 7 >< 4), H He C
3TMM nM HCJ10M CBJl3aHbI 3araAKH HaweM naMJlTH H npOlteCC no-
3HaHHJI? fOBOpHT nH 3TO 0 TOM, TO enOBeK H B CBeeM nCHXH'4eC-
KOM CYU4HOCTH COOTHOCHM C '4HCJ10BOM crpYKlYPOM nOCTpOeHHJI npH-
pOAbI, caM JlBnJlJlCb ee '4aCTblO? ni-1 3TO CBMAeTenbCTByeT 0 TOM,
'4TO, 06l1aAaJl «'4HCJ10BOM pe30HaHCHOCTblO» C npHpOAOM, '4enOBeH
nOl1Y'fM11 OT MMpOBOro Pa3YMa «HHcrpYMeHT» AllJI n03HaHHJI 3aKO-
HOB nOCTpOeHHJI MHpa H ce6J1 nH'4HO? BnonHe B03MO>KHO, '4TO KorAa
ApeBHHe MYApeltbl rOBopHnH: «4HCJ1a npaBJlT MMPOM», TO OHM AllJI
3TOro HMenH cepbe3HeMwHe OCHOBaHHJI.
Ka66ana Ksa,o,paTa H KpecTa
M3 rnytSMHW MKOB
<J>HnOC<><S>bI-nM$aropi.1 Ltbi
ApeBHe rpeLU1H -l"pey-
rOl1bHOCTb" COBep HHblX
Hcel1 BbiproKaTlH B r1ocT-
poeHHM ,,"paM , Bap-
WHHa K po£1 Ha HHa-
naCb C ..1Cl1a 1.. a KIDK.D.bI
HH)KHH pst,D. COCTORl1 H3
Ky(')HKOB C TO'iKOH. TO Ka
Ka oro. t<y6MKa nPMHMMa-
naCb 38 e,D,HHHL(y.
253
rnABA 6
rEOMETPMSI nSlTM CTMXMM
OKKYnbTHbie 'IMcn..,OBbie CBSl3M
CTMXMM
KMTaMCKHe MYApe bI no cpaBHe-
HHIO co CBOMMM eBponeMCKMMH Kon-
neraMM 3Ha'4eHHe Bblpa>KeHMJI «Y
CMH» nOHHManM WMpe. OHM BKnaAbI-
B nH B ero COAep>KaHMe He TonbKO
CTPYKTYPY MMpa - nJlTb OCHOBHblX
ero 3neMeHTOB, HO M nJlTb B3aMMO-
AeMCTBHM, nJlTb OCHOBHblX <J>yHKLtHM,
He 06J13aTenbt:f0 0AHHaKOBbiX AJ1J1
pa3HblX JlB11eHMM, HO 3aKOHOMepHblX
AllJI HMX. Ha 3TO 06pa aJ1 BHHMaHHe
M3BeCTHbiM KMTaMCKHR TeKCTonor 4)f(3H CIO-aHb (127-200). B era
MCTonKOBaHMM Mepom"4> «y» 03Ha'4aeT «nJlTb», a «CHH» - <<ynoT-
pe6neH «4>YHK HJI», «Mcnonb30B HHe». MHor..,e KMTaMcKMe
TpaKTaTbi nOA nJlTblO 3neMeHTaMH nOHHMalOT CHMBonbi nepBblx H
rnaBHblX neHOB nJlTM PJlAOB-Knc,CCOB, Ha KOTopble pa36HBalOTCJI
Bce npeAMeTbi H JlBneHHJI, B TOM MCJ1e HeBe eCTBeHHble: crpaHbI
YCMH
Y'feHMe 0() OCHOBHblX
nSlTM 3neMeHTax MH-
P03,D,8HHflt1 nSlTH
rnaBHbI>.< l"IpOSIB11eHHSlX
)IG13HH B KHTa CKO
$Hnoeo<l>HH H OK-
K}'nbTM3Me HOCHOO
Ha3BaHHe «Y CHH-.
254
CBeTa, BpeMeHa rOM LtMKnH'4ecKMe 3Ha-
KM H HCJ1a. B eBponeMcKoM CMHonorMM
nepBblM 6neCTJlU4e AOKa3aJ1, '4TO 5 3ne-
MeHTOB - KnaCcH4>MKaLtMOH aJl cxeMa
npOJlBJ1eHMM OCHOBHblX >KM3HeHHblX 3a-
KOHOB, 4>paHLtY3CKMM Y'feHblM M. fpaHe
(1934). OH >Ke YKa3b1BaJ1, '4TO cnop 0
TOM, JlBJ1J1IOTCJI nM 3J1eMeHTbl cy6craH M-
JlMH MJ1H CMJ1aMM, MMeeT C 4>MJ1OCo4>cKMX
n03HLt CXOJlaCTM'4eCKMM xapaaep, T. e.
JlBitJleTCJI n}UblM MYAPCTBOBiHMeM.
MO>KHO COCTaBMTb eneAYIOU4Y1O HY-
MepOnOrH'4ecKyIO cxeMY '4MenOBblX CO-
OTBeTCTBMM (Ta6n. 2).
KaK BHAHM, oKKynbTHbie cyMMbI '4MC-
nOBbiX pJlAOB Ka>KAOM CMCTeMbi HMelOT JlpKyIO TpOH'4HOCTb. CMCTeMY
no wy xapaKTepM3YIOT cyMMbI «He6eCHblX» '4MCen 7 H 3, cHCTeMY X3
Ty npeACTaBnJlIOT cyMMbI «3eMHblX» Mcen 4 H 6, a cyMMbI 4Mcen
Ka>KA6M CHCTeMbi 06pa3y1OT «yHMBepCaJ1bHoe» '4MCJ10 1 (MnM 10).
CMCTeMa no wY MMeeT C<BonHo06pa3HblM» HYMeponOrM'4eCKHM
pJlA, C pe3KHM nepenClAoM BenM'4MHbI '4MCJ10BOM CHMBonMKH, a X3
Ty - «J1HHeMHblM» MnM nOCTeneHHblM poCT '4MCJ10BOro pJlAa.
y cOBpeMeHHblx HCCJ1eAOBareneM $4J10Co4>MM MYApeLtOB ApeBHO-
CTM M 3aKoHoMepHocreM '4HCJ10BblX COOTHOweHMM B HYMeponorMM B
OTHoweHHM 06'bJlcHCHMJI 4>oPMyn M KaTerOpMM CJ10>KMnaCb CBOJI TO'4-
Ka 3peHMJI. Tal(, CMHonor AJ1. K063eB OTMe'4aeT, '4TO «pacnpeAene-
HHe '4MCen no napaM'" B no wY, H B X3 Ty... pa3YMeeTCJI, He CJ1Y'4aM-
HOCTb, a CBHAeTenbCTBO CTJ>YKTYPHOM CBJt3H «MarM'4eCKHX 4>Mryp» C
CMCTeMOM nJlTM 3neMeHTOB. C MareMantKD-I<OM6MHaropHOM T04KM 3pe-
255
reoMerpUR nRrn crnXUH
ECTIt MH8H...
YHcnOBbte 3Ha e-
HHR nRTH 3neMeH-
TOB (CTHXHH).. -
BpeMeHHbte .naH-
CK e HVMeponorH
C 3b68aIOT C CMM-
BOnH'4eCKHM HX
pacnp.e eneHMeM
4>Hnoco4K>M 6aHb
ry B APeBHeM TpaK-
TaTe ..IKITb 3ne-
MeHT08».
rnasa 6
HMJI 3TM ABa BHAa HHTepnpeTa4HH - no wy H X3 TY - aHaJ10rH'4HbI.
06naCTbIO onpeAeneHMJI B OAHOM cny'4ae JlBnJleTCJI nJlTH'4neHHblM
Ha60p 3neMeHToB, B APyroM - ABa ABOM'4HO-nJITepH'4HblX Ha60pa
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260
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CBJl3b aCTpOHoMHH H aCTponorHH C 4>YHK4HeM 3J1eMeHTOB B 4>OPMY-
nax 06HaPY>KHBaeTCJI npH JaMeHe '4HCJ10BOro KOAa 6YKB 4>oPMynbl CHM-
C'IMT8IOT, TO 4>OPMY-
nbl 2 on H 3 on B HYMe-
pol1orHH HMetOT 6011b-
WH'1 HH<!>opMaW<10HHblM
Bec B CHI1Y CBoe'1 L4HK-
nWleCKOH CTPYKTYPbI.
eM 4>OPMYI1b1 1 on H
4 on, HMetOlltHe nHHeH-
Hoe nOCTpoeHHe.
266
BOJ1H'4ecKHMH aHaJ10raMM nnaHer COJ1He'4HOM CMCTeMbi. npH ABOM'4Ho-
mrrepH'4HOM pa3AeneHMM '4Hten 311eMeHTapHoro PAAa - OT 1 AO 10 -
Ha ABe '4HCJ10Bble MaTpM bI no nJITb '4HCen B Ka>f<,AOM nJITM nnaHeraM,
HCKnIO'4aJ1 CBeTHJ1a, npMCBoeHbI CJ1eJW!OI14Me napHble 3Ha " '4MCeJ1:
1 M 6 - MepKypMM (cMMBon 3neMeHTa B),
2 H 7 - Mapc (cMMBon 3neMeHTa 0),
3 H 8 - fOnHTep (cMMBon 3neMeHTa A),
4 H 9 -:- BeHepa (cHMBon 3neMeHTa M),
5 H 10 - CarypH (cHMBon 3neMeHTa n).
KnaAe3eM TaMHbI JlBnJleTC" 4>oPMyna 4 on - MABOn, CMMBOnM'4-
HO Ha3BaHHaJl HYMeponoraMH «coBpeMeHHblU nOPJlooK». cJ»opKe C'fH-
Tan, '4TO 3Ta 4>opMyna Ae-
MOHcTpHpyeT «nonapHYIO
TpaHc4>opMa HIO 3neMeH-
TOB»: M H A B 0, a 3aTeM B
MOB n. 36epxapA BHAen B
ee CTpYKType ApeBHlO1O
«MHecTH ecKYIO Hrypy»,
a A>K. HHA3M - «TaHH-
CTBeHHblM 4>eHoMeH».
CTPYKTYPa 4 on AeMCTBM-
TenbHO 11I060nbITHa, n03ToMY
OCTaHOBMM Ha HeM BHHMaHHe
'4HTaTeJ1J1,npoaHanH3HpoBaB
CBJl3b 3TOM 4>oPMynhl C aCT-
ponOrMeM. Bo3bMeM ABa Ba-
pHaHTa nepeMeU4eHHJI 3Hep-
rMH no 3neMeHTaM 4>oPf"ynbl
4 on: B 06paTHoM HanpaBJIe-
reOMeTpHR nRTH crnxHH
TaAHbI H8YKM
Ha nee pacnpoclpaHeHHbI-
MVI a HYMepoJ10rVlVl VI $Ml1oco-
4>VIVI JJ,peaHVlx 6b1J1V1 eTbipe
..caMbiX OCH08HblX» nOPAAKa
nRTVI 3J1eMeHToa:
-+ -+ -+ -+
I on I 2 on. 3 on I 4 on - ace
OHVI w.1eIOT npRMOe (no
crpel1Ke - CMMBOJ1 .. -+ ») t<pyro-
aoe C'lKTbIB8tMe 3n8M8HT08
neHT8f"P8MMbI. XmpoyMHaR TeO-
pwI VI)( C03,Q,8HVIR tiS 0CH0Be reo-
P'*1 nR'J1,1 311eMeHTOB-cMM8OJ108
T8VIT a ce6e MHOro 38f"aAOLfHOI"O
VI nol1HOC'TbK> etJ.48 He VI3Y'EH8.
267
rnasa 6
HMH no AYJ"e Kpyra (40n) M no rry-
'4aM 3Be3AbI (n40n). CHMsonaMH
«on» 0603Ha'H!H «OCHOBHOM nopJl-
AOK» C'4MTblBaHMJI 3neMeHTOB no
Kpyry, a «n» - C'4MTb1BaHMe no ITy-
'4aM 3Be3J:\bl C Y'feTOM HanpaBJJeHMJI
CTpe110K nemarpaMMbI.
3aMeHMB 3neMeHTbl6YKs 4>op-
Myn COOTBeTCTBYlOutMMM CHMBO-
naMH nnaHeT no ABOH'4HO-nJlTe-
pM HOM '4MCnOBOM MaTpH
nonY'4MM nlO6onbiTHoe acrpono-
rM'4eCKOe COOTHOweHMe. nep-
BaR 4>opMyna COAep>KHT CJ1eAY-
1OU4Y1O HH4>oPMaLtMIO: nAMOB -
- CaTyPH, iOnMTep, Mapc, BeHepa,
MepKYPM T.e. AeMOHcrpHpyeT
nOpJlAOK nnaHeT, ynpaBnJllOutHx.
comaCHO BaBMnOHCKo-esponeM-
CKOM acrponorMM, 30AMaKanbHblMM C03Be3.qMJlMH. 3Ta acrponOrMJI
Y'4MTblBaJ1a 3HepreTH'4ecKHe CBJl3M nnaHeT no rema-rpaMMHOMY sa-
pHaH1)', KOTOpblM QcyuteCTBJ1J1eT «nepeCKaKMBaHMe» CBJl3M» He e-
pe3 OAMH, KaK npM JlTtM<OHe'4HOM 3Be3Ae, a '4epe3 ABa 3neMeHTa
(pHC. 38) - «3Be3oa MCJlOB'1I.
AaHHble pMaHTbI 4>6pMynbl oTpa>KalOT onpeAeJ1eHHble acrpo-
HOMM'4eC acrponorM'4eCKMe 3HaHMJI.3Be3A0'4eTOB KaK BOCTO-
Ka, TaK M 3anaAa.
ApeBHMe acrponorM nOKa3aJ1H, 410 MM 6b1J1M M3BecTHbi cHAepM-
'4ecKHe H CMHOAH'4ecKMe nepMoAbi 06pauteHMJI MepKypMJI, BeHepbl,
Ecn. MHeHMe
Basw1oHcKi'te aclpOHOM
c mani't, qrO nocneOOB8-
TenbHOCTb nnaHeT - Ca-
TypH, IOnmep. Mape, Be-
Heps i't MepKYPi" - ne-
pe.a,aeT W( noJ1O)KeHHe no
Mape nJ)M6I1H)1(etfMSI op6m
K Col1HL-'Y H COOTBeTCTBeH-
HO bUJeHMe nepHOAOB
06paU4E*it.1 BOKpyr HerO.
T8Koro )Ke MHeHt.1 n -
Aep)KHBal1i'tCb 38e3,0.0LfeTbi
f<Kras:I. B TpQKTa-
Tax 3Hepre1WfeCKoe B3m1-
MOA 0neMeHTOB
cI>OPMY n4 on.
268
Mapca H CHAepM'4eCKMe ne-
PMOAbi 06pa eHMJI fOnMTepa
H CarypHa.
A>t<. HMA3M KOHCTaTMpyeT
HanH He rny60KHX 3HaHMM no
aCTpOHOMHH y KMTaMCKMX MYA-
peL\OB, Mcnonb30BaBWMX MX Cp
AJ1J1 paC'4eTOB oKKynbTHbix
4>oPMYn. OH 06Hapy>KMn nepe-
'4MCJ1eHHble Bblwe nepMOAbi
06paU4eHMJI no seeM nJITM nna-
HeTaM B MX tpaKmiIX Ha-
'4 C I B. IV) H. 3. npM ]TOM
CU3bC nepHO,qaMM OOpauteHMJI
no bHblM nnaHeTaM B 3ne-
MeHTa)( $QpMY11 BCTpe'fE!Ha MM
M B 60nee paHHMX TeKCTax-
IV-n BB. AD H. 3.
KaK BHAHM, B 4(CMnOBblX» OTHOWeHMJtx 3J1eMeHTOB $)pMyn 3aKO-
AMpoBaHbI He TonbKO rapMOHMJt '4MCJ10BOrO paBHOBeCHJI, HO M 3aKO-
HOMepHOCTM 3HepreTM'feCKMX LtHKnOB He6ecHbiX Tell. nOCKonbJ<y CMnbl
KOCMoca BnHJlIOT Ha nOBeAeHMe nIOAeM, TO, KaK yTBep>KAaIOT KHTaMC-
KMe HYMeponOI14, 4>oPMynbl MOryr npor.H03HpoBaTb M 3aKOHOMepHble
OTHOWeHHJI Me>KAY HMMM. npH 3TOM esOOumCR eLije oOHO CUH80JlUKO:
nCMXOnOrM'4ecKMe M 3HepreTM'4ecKMe s03MO>KHOCTM Ka>KAoro '4e1Io-
BeKa C no3HLtHM aCTpOJ1OrMM CpaBHMBaIOT no xapaKTepy C onpeAe11eH-
HblMM xapaKTepHCTHKaMM He6ecHbiX Ten. ComaCHO 3TOMY npaBHJ1Y KaK
OAHOMY H3 Bapl4c1HTOB npaKTM'feCKoro BHe.qpeHMJI 4>oPMYJ1b1, AM 60-
nee 3CjxpeKTMBHOro Ae1IOBOro COTpyAHM'4eCTBa MO>KHO no COOTBeTCTBY-
reOMeTpUR nRTH CTHXUH
0Bc
2J. YT
nH»
TtC6
Puc. 38. renTarpaMMa
cMMBoir.. ecKoM C8Jt M AHeM
HeAenl4 c nnaHeTaMM,i CTMXMJtMM
cornaCHO 4>opMYllaM (no KPYry)
M (no lIy aM 3Be3AbI)
npOTMB acOBOM CTpellKM
269
rn8Ba 6
IOU4MM paC'4eTaM nOA6MpaTb '4J1e-
HOB «pa60'4eM rpynnbl».
nonaralOT, 'ITO onMcaHHblM Me-
TOA npoc'4era '4MCJ10BOM acrpono-
n4M n03BOnJleT 60nee TO'4HO Y'fM-
TblBaTb BeAY",He «nnaHeTapHble»
Ka'4eCTBa '4neHOB KonneKTMBa:
IOnMTepMaH MapcMaH MepKY-
pMaHLta MAP., CTpOMTb HX conOA-
'4MHeHHOCTb comaCHO 4>YHK(4MM
3J1eMeHTOB $>pMynbl. KaK BHAHM,
paC'4eTbi AOnOnHJlIOT 06w'4Hble pe-
KOMeHAa(4HH acrponorOB no nOA-
60py nIOAeMAllJlOnTHMaJ1bHOM.Ae-
JlTenbHOCTM no 3HaKaM 30AHaKa.
3TM >Ke paC'4eTb1 MO>KHO Mcnonb3o-
BaTh npM nOA60pe «OnTHMaJ1bHblX
aCTponOrH'4eCKHX nap», '4TO, no
MHeHMIO aCTponorOB, HepeAKO
MMeeT CYI14eCTBeHHoe npaKT" ec-
Koe 3Ha'4eHMe.
Ba>KHOCTb 3TOro yTBep eHMJI
TaKOBa, '4TO pa3'bJlCHHM ero nOA-
po6Hee. npH HenpaBHnbHOM nOHMMa'HHH CYU4HOCTM nporH03a HHor-
Aa COBepwalOT rpy6b1e 'OWM6KM! npeAYnpeAMM '4HTaTenJl, '4TO HY-
MepOnOnf'ltCKHe nporH03W B03AeMCTBM8 «3HeprHM nnvaHeT» HMelOT
TaKoe >Ke ycJ10BHoe 3HDlleHue, KaK H acrponOrM'4eCKMH nporH03 no
3HaKaM 30AHaKa. n03TOMY eU4e MYApeLtbi ApeBHOCTH rOBopMnH, 'ITO
«nporH03 npeAYnpe aeT, HO He 06J13b1Baen.
ECIIM aepMTIt OKKyn -
1'M3MY, HeOn8ronpHAT-
tiblH HYMeponorM ecKHH
nporH03 (ecnM npM-
3H8Tb, TO ero 3HepreTM-
ecKaR C}'U4HOCTb AeH-
CTBMTenbHO B03,O,eHCTBY-
eT) MO)l(eT npeACK838Tb
nMWb sepoRTHOCTb, 8 He
06R38T8JJbHOCTb ..aCTOTbi
cnY'tSeB HeAOCTaT HO-
ro B38MMOnOHHMSHMR,
H8npR)I(eHHOCTM B OTHO-
weHMRX, He06AYM8HHblX
AeHCTBHH. 06b1 HO TPYA-
HOCTI1 nO TbK) KOM-
neHCHp}'IOTal )l(en8HHeM
napTHepos COBMecTHO
npeoAoneeaTb TPYAHO-
cm, B38MMHblM yBIDKe-
HMeM H AosepHeM.
270
reoMeTpufl nflTU CTUXUU
B KaKof1-To Mepe TO BnHflHHe MO>KHO CpaBHHTb C B03AeMCTB eM
Ha napTHepa, C KOTOpblM npeACTOHT 06 eHMe, AO)t(AJ1HBOM noroAbI,
nnoxoro CaMO'4YBCTBHJI, 6one3H nM HOro «4>OHoBoro C06b1T fI»
HcnopTHBWMX eMY HacrpoeHHe BnHJlIOU4Hx }fa 06 eH c oHHM.
EcnH '4YBCTB M YBa>KeHHJI HeAOCTaT04HO, TO Ka>KAbI . napTHep
Ha'4HHaeT HCKaTb MOTHS.AnJl onpaBAaHHJI 'CBOHX AeMCTBMM, KOTO-
pble OH COBepWHT no paCTOp>KeHHIO OTHO H M, H 06J13aTenbHO
TaKOM MOTHB HaXOAHT. MOTHB MO>KHO HaMT nlO6pM. n03TOMY no-
HCK MOTMBa - 3TO CBHAeTenbCTBO «rpeU4HHKM B OTHOWeHHJlX», «OX.
na>KAeHHJI '4YBCTB». VlHorAa B nepHOA 4eCKOM ne'4aTH nOJlBnJlIOTCJI
3aMeTKH 0 «BpeAe aCTpOnorM'4eCKOrO nporH03a» B OTHOWeHHJlX
Me>KAY nIOAbMH. Hanp Mep, KaK nHweT AHHa CaMOHnOBa (MocKBa),
«3Be3Abl BMHOBaTbI» Bee pa3BOAe,.a T04H e, YBne4eHHe MY>Ka aCT-
ponorHeM (CM. «AMcJ»». 1998. N! 24, c. 4).
HaCTpOHTb Hac Ha npeAY6e>KAeHHe K napTHepy, C03AaTb HanpJl-
>KeHHbIM nCHXOnOrH'4eCKMM 4>OH B 06U4eH H C HHM MO>KeT J7106oe
HezomUBHoe npeACKa3aHHe: raAaHMe Ha KapTax, 3aMe'4aHHe POA-
HbiX. APY3eM HnM coceAa, '4TO OH (OHa) BaM «He napa» H T. A. Ba>KHO
TO, KOK Mbl BocnpHHHMaeM TaKHe npeACKa3aHHJI, HaCKonbKO BepHM
B CBO CHnbl H B03MO>KHOCTb ynpaBnJlTb B3aHMOOTHOWeHHJlMH. npH
pa3BHBWeMCJI COMHeHHH Ae CTBHTenbHO MO>KeT Ka3aTbCJI «4TO-TO
He TaK» B nOBeAeHHH napTHepa, CJ10BaX TOHe, B3rnJlAe.
n03TOMY «HacrpaHBaIOU4HM» Hac npOT B napTHepa «HHCTPY-
MeHT» MO>KeT 6b1Tb KaKHM yroAHO. HYMeponorHJI HnH aCTpOnOrHJI
T'fT HH npH eM.
B3a MHoe HenOHHMaHllle III KOH4>nHKTbI oryr B03H KHyTb H npH
«OnTHMaJ1bHOM» nporH03e.
He60nbWHX CCop 60JlTbCJI He £11eAYeT, TeM 60nee «HaY'4HO 060-
CHOBbiBaTb» HX npH'4HHY. He60nbwHe CCOpbl, no yTBep>KAeHHIO
271
rnasa 6
· C KTaeTCSI, TO npil1 611arOnpil1S1THOM HYMep0110rWfeCKOM ·
. nporH03e, KaK iI1 npil1 COOTBeTCTByJOl1.\eM aCTpononl ec- .
KOM, 111OAiI1 l1er'4e iI1 al1.\e HaXOAAT B3ail1MOnOHiI1MaHiI1e,
· pe*e CCOPSlTCSI. l1eNe AoOiI1BalOTCSI B3ail1MHOM CiI1MnaTiI1i11 ·
. iI1 ys8)KeHiI1S1. npil1 iI1H 3TOro HecKOl1bKO. Ecm He y'U1TblB8Tb
· "3HepreTiI1 ecKoe POACTBO AYW, iI1X comaC08aHHblM pe30- ·
. HaHC iI1 npil1TSlril1B8HiI1e-. TO Cl1eAyeT eCTb HeM8nOBIDtCHoe .
· nCiI1X0110ril1 ecKoe yOe)I(,AeHiI1e B TOM, 'frO Bce 38KOH iI1TCSI ·
XopoWO, l100ble TPYAHOCTiI1 6YAYT npeOAOl1eHbI, TaK KaK
. npeACKa3aHHblM nporn03 ..6naronpURTHblH-.
nCMxonorOB, BcerAa OOnJKHb/6b/mb B «HOpManbHOM ceMbe» - OHH
nOMoralOT napTHepaM nY'4we «opMeHTHpOBaTbCJI» B nnOXOM Ha-
CTpoeHHM A r APyra, a HHorAa Hy>KHbI AnJl «nepepacnpeAene-
HHJI» BeAYU4eM ponH OAHOro H3 HMX B KaKOM-TO cHrya HH. B3aMM-
HaJl Heycryn'4HBOCTb BbifiBnJleT rOTOBHOCTb I( KOH4>nHKl)' 060MX
Y'4aCTHMKOB, no:nOMY npH pa360pe npH'4HHbI '4aCTO HaKa3b1BaIOT
060MX - B CCope BHHOBaTbi 060 napTHepa.
Ka>KAaJl HYMeponorH'4eCKaJl 4>opMyna HMeeT CBoe MCTonKOBaHHe,
CBOM paCKJ1aA nniHeT, a B HX 06pa3e - M nlOAeM C «J1JIaHeTapHblMM»
Ka'4eCTBaMH 3neMeNTop;.$>pMynbl. nonaralOT, 4TO AflII HaH60nee 34>-
4>eKTMBHOM AeJlTeJ1bHQ0H KOnneKTHBa HeAOCTaTO'4HO nOA6MpaTb co-
CTaB era neHOB TOnbKO ho npo4>eccMoHanbHblM Ka'4eCTBaM. AnJl no-
BblweHM : PeaynbTaTMBHOCTM pa60TbI tiy>KHO eU4e Y'4HTblBaTb Ha60p
«nnaHeTapHblx» Ka'4eCTB nlOAeM B C04eTaHMH co 3Ha4eHHeM cylqHO-
CTM -caMOM 4>0PMYnbl: AflJI 1 on BeAYlqHM MOTMBOM AeMCTBHM 6YAeT
«c03MAaHHe» - rpynna nlOAeM C Ha60poM TaKHX Ka'4eCTB nnaHeT
272
60nee nOAXOAMT AllJI C03AaHHJI
MaTepHanbHblX eHHOCTeM.
cJ»opMyna 4 on C 4>YHKLtMeM
(<TpaHc4>opMa MH» M «COBpe-
MeHHoro nOpJlAKa» MO>KeT pe-
anM30BaTbCJI B npaKTMKe pa60-
Tbi KOnneKTHBa (npM nOA6ope
B Hero nlOAeM C onpeAeneHHbI-
MH nnaHeTapHblMH Ka'4eCTBa-
MH) C enblO 06pa3LtOBOrO co-
6nlOAeHHJI Bcex HHCTpyK HM H
nOpJlAKa B c4>epe ynpaBneH-
'4eCKOM M HCnOnHHTenbHOM Ae-
JlTenbHOCTH. C03AaHHe TaKoro
KOnneKTHBa, HanpHMep, MO>KeT
6bITb npeAnO THTenbHO AJ1J1 pa-
60Tbl B CMCTeMe McnonHHTenb-
HeM BJ1aCTH HnM KOHTpOnHpylO-
Iqero opraHa.
reOMeTpUR nRTU CTUXUH
AenOBbiM napTHepaM &o111
KOlllleKT&o1BY, CO HHOMY
no .aCTpoll0r&o1 eCKOMY
06pa3Y. 3HepreT Ko'1
opMy ,He06xo MO
Y &o1TblBaTb H ccHYMepOll0r&o1-
ecK&o1e nafU TapHble. Ka.
eCTBa BXOA &o1X B Hee
311eMeHTOB, C&o1MBOll&o13&o1Py-
IOUU1X ll&o1 HOCT&o111IOAe'1.
HYMepOll0r&o1 ecKoe KOM-
6&o1H&o1poBaH&o1e *enaeMbiX
n&o1 HOCTHbiX Ka'f8CTB nlO-
Ae'1 3aB&o1C&o1T OT KOHKpeT-
HO'1 C&o1TYal..l.&o1&o1, KOTOPYIO
npeACTO&o1T peW&o1Tb 1C01l-
lleKT&o1BY.
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CCT8MHbie nMCbMeH8»?
HYMeponOrH'4eCKOe '4TeHHe rpe6yeT onpeAeneHHblX HaBbiKOB M
nOHMMaHHJl4>YHK HM C'4HTblBaeMbiX 3neMeHTOB, OC06eHHO 3TO Ba>K-
HO B HYMeponOn4'4eCKMX rpaQJHKax .. cxeMax.
PacCMOTpHM npOLteCC C'4MTblBaHHJI 3neMeHTOB B neHTarpaMMe
KOTOpaJl KaK rpa4>M'4eCKaJl 4>opMyna nepeMelqeHMJI 3HeprHM WM
273
rn8S8 6
pOKO Hcnonb3yeTCJI cpeAH
«MarH'4eCKHX» 4>Hryp HYMe-
ponorHH. OHa OTHOCHTenbHO
npOCTa H 60nee AocrynHa AllJI
Ha'4HHalOU4HX HYMeponorOB
acrponoroB, '4eM renro- H reK-
carpaMMbI. C'4HTblBaHHe -
eT BbinOnHIITb no onpeAeneH-
HOMY npaBHny. 3MeHeHMe
HanpaBneHHJI C'4HT BaHHJI
npHBOAHT K H3MeHeHHIO OK-
KYnbTHoro CMblCJ1a 4>opMyn .
B 3neMeHTe MO>KeT 6b1Tb
CKpblTa CyTb BeU4H HnH JlBne-
HHJI. CHnOBbie OTHOWeHHJI
Me>K,qy 3neM TaMH 4>opMynbl 3aBHCJlT OT HaKOnneHHJI MnH OCJ1a
neHHJI 3HeprtfM B OAHOM H3 HH)(, TO H3MeHJleT paBHo.seCHe 3Hep-
rHH BO BceM 4>opMyne.
Vl3MeHeHHe CHnOBbiX nHHH BOCTO'4Hble MblCJ1HTenH OLteHHBaJ1H
Oc06b1MH Q>Hnoco4>cKMMM l<aTeropH$lMH. Mbi nepe HCJ1HM OCHOBHble,
HaH60nee ynOTpe6nJleMbie B HYMeponorHH M HYMeponorH eCKOM ac-
rponorHH nOHJlTMJI, nOA'4epKHYB OTAenbHble HX oc06eHHOCTH.
nOCJ1eAOBaTen o ISb KPYry C'4HTblBaeMbie 3neMeHTbI neHTarpaM-
M HMelOT OBOUC/HYIO C;BJl3b HHb-JlH nepeXOAa OT OAHoro 3neMeH-
-Ta K APyro y: HanpHMe , Ha pHC. 39, a 3neMeHT B HMeeTTaKYIO CBJl3b
C 3neMetfrCtMH M H A. ComaCHO CHMBonHKe MYApe40B ApeBHOCTH,
4>YHK4HOHanbHoe 3Ha'4eHHe 3neMeHTOB HYMeponOrH'4eCKMX 4>op-
Myn H reOMeTpH eCKHX 4>Hryp YAa'4HO OTpa>KfteT COOTHOWeHHe '4ne-
HOB B ceMbe: CTapWHX (pOAHTeneM C pe6eHKOM) H MnaAwero (pe-
Ha 3aM8TKY
BcerAa Cl1eAyeT nOMH Tb,
TO cOAep)KaH e Ka)t(,D.oro
311eMeHTa 4>OPMYl1b1 MHoro-
06pa3Ho, IiO rnaBHoe - OH
C MBon ecK OTpIDKaeT
3aKOHOMepHyK> AeRTel1b-
HOCTb.CTepeoTHn e110BeKa
(Hanp Mep. CKl10HHOCTb
pewaTb Bonpoc no onpeAe-
l1eHHO cxeMe). Ha HaR OT
BeAeH R Ael1a AO MaHepb&-
06weH R C 11IOJlbM .
274
PUC. 39. nopo>KAi! ( ) M npec>AOneBa (- - ) C8R3M 1I1eMeHTOB
neHTafl)aMMbI. B t<py>t<Ke - Ha'WIbHblA eaHMJI
6eHKa C pOAHTeneM). n03TOMY MC-
XOAHblM 3neMeHT MO>KeT HOCHTb
HMJt «OTeLt» (HnH «MaTb»), a 3aBM-
CHMblM OT Hero 3neMeHT - «CblH»
(MJ1M b»). Tal(, B Kpyre Ha pMC. 39,
a no '4aCOBOM CTpenKe 3neMeHT A
RBnJleTCJI «CblHOM» 3neMeHTa B, a
npeAWeCTBYIOU4HM 3neMeHTY B
3neMeHT M 6YAeT Y>Ke «OTLtOM»
3neMeHty B. npM ABM>KeHMM "PO-
THB '4aCOBOM crpenKH MJlM no ny-
'4aM 3Be3Abf COOTHoweHMe M3Me-
HReTCJI, M HCTOnKOBaHMe 4>YHKLtMM
3neMeHTOB 6YAeT APyrHM.
reoM8TpHfI nflTH CTHXHH
6
o
o
0cH08w IfYM8POIIOI'MM
B 0MHapH0M MO,QeJ1M OT-
HOWeHHM KKT'aM-
CKMe tiyMep0110rM Ha ponb
«po,a,HTeI1bCKoM
0IlpeAe11MM KaTef"OpMIO B
388MQ1MOC'TM OT caoero
M :JM60C
Y'f8TOM KOH<t>Yl'H8HCKoro
Y'feH 3J1eMeKT RH
(<<0T'eI.4.). llM60 c OM
AaOCCKoro nJ)M0PKTeT8
3neMeffT VlHb (tCM8Tb»).
275
rnasa 6
AnJl YKa3aHMJI HanpaBneHMJI ABM>KeHMJI 3HeprHM no nHHMAM MnM
AYraM reoMeTpM'4eCKOM $Mrypbl YA06HO Mcnonb308aTb 6YKBeHHytO
CBJl3b. 31"0 AaBHO 06HapY)KMnM MYApe14b1 Ape8HOCTM M BHe,qpMnM B
HYMeponorM'feCKHe 4>opMynbl. 6YKBaMM 0603Ha'4aIOT KOH bI OTpe3-
KOB nMHHM MJ1M JWrH, a no CMeHe npaBMJ1bHOM O'fepeAHOCTM 6yKB B
pJlAe onpe,qenJlIOT HanpaBneHMe ABM)t(eHMA 3HeprMM B $Mrype npo,;
TMB MJlM no '4aCOBOM crpenKe. CO eTaHMe pAAa TakMX 6yKB AaeT Y>Ke
HYMe"p0J10rM'fecKyIO PMYny reOMeTpM'fecKoM $Mrypbl. 6YKBbI B
«MarM'4ecKOM» 4>Mrype oc06b1e: OHM 0603Ha'faIOT nep&y1O 6YKBy
$4noco4>cKOM KaTerOpMM - CTMXMM. 6YK8a B 0603Ha'faeT «BoAY»,
A - «):\epeBO», 0 - «OrOHb», n - CCnO'fBy» M M - «MeTaJ1n». Ka>K-
AaJI 6yKBa - OHa )l(e «3neMeHT» 4>Mrypbl - CTOMT Ha crporo onpe-
AeJ1eHHOM MeCTe M He MO>KeT npoM3BonbHO J4eHATbCA J4ecrOM C APY-
rOM 6YK80M, Tak KaK 3TO HapywMT CnO)l(HOCTb M CTpOMHOCTb
reoMeTpM'4eCKMX M '4MenOBbiX CooTHoweHMM HYMeponorM'4eCKOM
4»oPMYJ1b1.
npM C'4K1ti1-.aHMM 3neMeHTOB 6yKe no Kpyry M no ac080M crpen-
Ke neHTarpaMMbI, nOKa3aHHoM Ha pMC. 39, a, C Ha'4aJ1bHblM 3neMeH-
TOM A nonY'fMM $oPMYny AonMB "nM 2 on, a npM TaKOM )Ke Ha-
npa8neHMM C'4MTblBaHHA 3J1eMeHTOB no KPYry neHTarpaMMbI
nOKa3aHHoM Ha pMC. 39,6, C 3amaBHblM 3neMeATOM B nOJ1Y'4HM <1>oP-
MYII'J BOMAn MnM 14 on comaCHO npMBeAeHHOM Bblwe CTapMHHOM
HYMepal4 MM 4K>PMYJ1.
C'4MT"'BaHMe no '4afOBOM crpenKe Ha3b1eaeTCJI npliNoti, a npo-
TMS - panlHOa MpKynJlLtMeM MJlM CBA3blO. npM OAHOHanpaBneH-
HOM npSMOM HpKynJlLtMH 3HeprMM CHapyJKM M BHyTPM Kpyra BHe-
WHAJI CBA3b Ha3b1BaeTCJI S30U/tfOnopo1KaaIOUfeU, a BHyrpeHHJlA-
BJOU/tfOnpeoOolleSOIOUfeu CBJl3blO Me>KAY A&yMJI 3neMeHTaMM neH-
TarpaMMbI. npH pa3HOHanpasneHHOM 3HeprerM'4eCKOM CBJl3M 3J1e-
276
reoMeTpwR nRTH CTWXHH
MeHTOB - npJlMOM BHewHeU " 06paTHOM BHympeHHeU - Ka'4ecTBO
CBJl3H M3MeHJleTCjI Ha npoT"BOnOnO>KHOe (CM. pMC. 39,6).
«npAMoe» pacnpeAeneHMe 3Hepr"M B 4>opMynax neHTarpaMMbI
2 on H 14 on (eM. pMC. 39,. a M 39,6) OLteHHBalOT nO- 3RoMY: 'B
2 on OHO MMeeT «nopo*l\alOutee», a B 14 on - «npeoA01feBalO ee»
Ka'4eCTBO. 6HHapHaA CBJl3b KaJKAoro 3neMeHta MMeeT co6creeHHoe
Ha3BaHMe: B 4>oPMyne 2 on (CM. pMe. 39, a) npE!.A&:TaBneHa «nop0)f(-
AalO JI» CBA3b «MaTepM» (HanpMMep, 3neMeHTa ft\) K «nopo>KAae-
MOMy» «CbI (3,neMetny B). «B3aMMonpeoAoneHMe» 3HeprMM Ae-
MOHCTpHpyeT 3Be3Aa CPOPMYJtw 14 on (eM. pMC. 39, a), rAe nOKa3aHO
OTHoweHMe «npeOAOneealOlqero» 3neMeHTa (HanpMMep M) K «npe-
OAOneBaeMOHy» (0).
Ha pMC. 39, a H 6 npeACTaB1leHbI neHrarpaMMbf ABYX. RCt3HblX 4>oP-
Myn C H3MeHeHHblM pacnonO>KeHMeM 3neMeHTOB. PacJ1I1e.qeneHMe B
HMX BHyrpeHHeM 3HeprMM MMeeT npoTMsonOnO>KHoe HanpaBneHMe,
M, COOTBeTCTBeHHO, eBJl3.b 31IeMeHTOB 4><>PMyn 6YAeT bTepHaTMBHa
no Ha3BaHMIO. ('fMTblBaHMe 3J1eMeHTOB BHeWHeM H BHyTpeHHeM neH-
rarpaMM (pMe. 39, a) O CT8J1fieTCJI 8 OAHOM - npJlMOM HanpaB-
neHMM, MJ1(t no 'laCOBOM crpenKe. C'4MThfBaHMe 3neMeHTOB nemarpaMM
(pMC. 39,6) npM BHeWHeM pacnpe HMM 3HeprHM nposoART B nPJI-
MOM, a BHyrpM nemarpaMMbI- B 06paTHOM HanpaBJM!HMM.
COBMeuteHHbIe MarM'leCKMe 4>Mrypbl - 31'0 o6beAMHeHMe B eAM-
HOM rpa MKe MK11M KoM, MJ1M 38e3OHOU (BHyrpeHHeM), H KpylO-
soU (Hapy*HOit) neHTarpaMM. Ka>twut"3 HMX COCTOMT 143 nJITM 3ne-
MeHTOB, CMMMeTpM HO pacnono>KeHHbIX OT ",eHTpa, '4TO COOTBeTCTByeT
npMHI.4Mny nocrpoeHMJI neHTarpaMMbI. MTblBaJi 3ry OCo6eHHOCTb
pacnOnO>KeHMJI fUITM 3J1eMeHTOB no KpyTy, Ka>KAbiM M3 KOTOpbIX Jl8-
J1JIeTCJI yrJIOM BHyTpeHHeM (38e3.QHOM) neHTarpaMMbI, MO>KHO ycnOB-
HO Ha3WBaTb ee 4<KpyrOBOM» neHTarpaMMOM.
277
rnBBa 6
KaK BMAMM, npM 4>MKCMpO-
BaHHOM pacnOnO>KeHMH 3J1e-
MeHTOB 3TH neHTarpaMMbI AalOT
AOCTaTO'4HOe '4HCJ10 BapHaHTOB
4>oPMyn AnJl npaKTH'4eCKOM Ae-
"TenbHOCTM: B npJlMOM M 06par-
HOM e'4MTblBaHHH 0T rnaBHoro
3neMeHTa, a TaK>Ke no KPYry H
nY'4aM 3Be3AbI. Aa>Ke B OAHOM neHTarpaMMe '4HCJ10 BapHaHTOB 3Ha-
MTenbHO, nOTOMY '1TO rnaBHblM 3neMeHTOM, C KOToporo Ha'lMHaeT-
CJI 4>oPMyna, MO>KeT 6b1Tb nlO60M M3 nJlTM ee 3neMeHTOB. npH M3Me-
HeHMM MeCTa OAHoro, a TeM 60nee HeCKonbKHX 3neMeHTOB M
nepepacnpeAeneHMM 3HeprMH B neHTarpaMMe '4HCJ10 BapMaHTOB
4>oPMyn eU4e 60nbwe B03paCTaeT.
npM cl>HKCMpOBaHHOM nOnO>KeHMH 3neMeHTOB neHTarpaMMbI Bee
OKKynbTHbie 4JQpMynbl, nonY'4aeMbie B nooblx.ee HanpaBneHHJlX no
KpyroBblf1 M .l4MK1IM'4eCKtt..M CBJl3J1M, Ha3b1BaIOT npOH3BOAHbl M M HnM
«poikmSeHHb/HU». npM M3MeHeHHM XOTJI 9b1 OAHOro 3neMeHTa no-
nY'4alOT Ha60p 4>opMyn C HOBblMM «ceMeMHblMM» OTHOWeHMJlMH.
Tal<, npH C'4MTb1BaHMH no ny'4aM 3Be3Ab1, npeAC'1'3B11eHHOM Ha pHc. 39, a, C
BeAYU4ero 3neMeHTa B B nepBoM neHTarpaJooo1e nonY'4MM 4>opMyny
BOMAn MnH 1 on,1 BO BTOpoM neHTarpaMMe npH C4MTblBaHHM no KPYry
C 3neMeHTa B nonyintM >Ke 4>oPMyny 1 on - BOMAn. ECJ1M B nep-
BOM CJ1Y'4ae 4>oPMyny l-Qn Mbi nonY'4a11H npH HTblBaHMM BHyTpeH-
Hero paCOS)eAeneHHJI 3HeprHM B neHTarpaMMe, TO Tenepb OKa3aJ10eb,
'4TO 3ma Jice1popHYl1a 3aKOAMpoBaHa TalO«e BO BHeWHMX CBJl3"X 3ne-
MeHTOB BTOpoM neHTarpaMMbI. C n03M(4MH HYMeponorHH 3TO YKa3b1-
BaeT Ha TO, '4TO 14e>KAY Mar 4ecKHMM 4>HrypaMH neHTarpaMM pMC. 39
MMeeTCJI 06pamHblu 3HepreTM'4eCKMM pe30HaHc.
2 8MA8 neHT8rp8MMW
B M8n1'48CKO,", 4>lItrype no-
J1Y'faeM K8K Obi ABS BM.D,8
neHTarpSMMbI: KJ)yrOBytO
(H8p}')KHYIO) lit 3Be3,AHylO
(BRyrpeHHIOIO) .
278
reOMe Tp UR nRTU cn,xuu
HYMeponorH ecKHe 4>OPMY-
nbl CHMBOnH'4eCKH nepeAalOT
peanbHOe nepepacnpeAeneHHe
3HeprHH Me>K.qy o raHaMH K CH-
CTeMaMH Hawero opraHH3Ma.
HanpHMep, nepepacnpeAeneHHe
3HeprHH no rpa4>H ecKoM cxe-
Me 4>opMynbl14 on H ee npm13-
BOAHblM 4>opMynaM (,QMOBn,
,QOnMB, BOM,Qn AP.) Y'4MTbI-
BalOT npH AHarHOCTHKe H ne'4eHHH 3a60neBaHMM, CBJl3aHHblX C Ha-
pyweHHeM 3HepreTHKM opraHH3Ma B MeAH4HHcKOA aCTp0J10rHH,
HapoAHoM MeAH4HHe KHTaJl, B HrnoTepami..... Tat<, np ...HrnoyKanbl-
BaHHH Hcnonb3yeTCJI npaBHno 3HepreTH ecKoM CBJl3H aTb-CblH»
Me>K.qy opraHaMH Mil «noAnHTKH» 60nbHoro H 0CJ1a6neHHoro opraHa
3AOPOBOM 6H03HeprHeM (noAP06Hee CM. «MeAH4HHCKaJl H HaTanb-
HaJl aCTpOnOrHJI»).
BOCTO'4Hble MYApeLtbi
C03AanH He TonbKO onpe-
AeneHHble B.apHaHTbI, HO
CTPYKTypHYIO 4enoCT-
HOCTb 3HepreTH'4eCKHX
4>opMyn, onpOBeprHYB
MHeHHe HeKOTopblX eBpo-
neMCKHX CHHonorOB, '4TO
TonbKO OAHH BHA CBJl3H
3neMeHTOB MHp03AaHHJI
JlBnJleTCJI nOAJU1HHblM H
OCHOBHblM.
HYMeponorM eCKMe
clK>PMynw OTpa)l(alOT
np HU1'tn pacnpeAel1E!H R
3Hepr..,.., B pa311"'4 CH-
cTeMClXs \.Be RBJ1eH..,-
RX, n03TOMY ..,cnOI1b3YIOT-
CR B He TOPblx co pe-
MeHHblX 06na TRx 3HaH iiI.
MCTopM ecKaA cnpaBKB
B APeBHOCT.., aCTponor .., HY-
Mep0 l1 0r.., B npeACKa3aTel1bHOiil
npaKT Ke Ha..,60l1ee aCTO "'C-
n0l1b30BaTI Teop"'lO B38:..,MHO-
ro npeOAOl1eH R nRT.., 311eMeH-
TOB. 06 3TOM n caI1 s:lH '-'ao B
KH..,re ..Y eH..,e 00 "'Hb-RH ..,
nRT.., 311eMeHTax B AOU...,HbCK..,iiI
nep..,oAIO (1956).
279
rn8B8 6
H.H. KOHPaA nMCaJ1: «e MAeeM 0 nepSOiJteMeHTax MaTepMaJ1b-
HOM npHpoAbi coeAHHHnaCb MAeJl HX Kpyro060poTa... Y KMTaMLteB
Kpyr006opOT Bblpa>KeH B KaTerOpMH 4<npeOAoneHMJI» - Ka)t(AbiM M3
nJlTM 3neMeHTOB nepeXOAHT APyr B APyra: BoAa npeOAoneBaeT
OroHb, OrOHb - AepeBo, AepeBo - MeTann, MeTaJ1n - 3eMnlO,
3eMnl! - BoA\'» (H36paHHble TpYAbi. CTOpHJI, c. 213). B KHTaMc-
KOM TpaHCKpHnl4MM rpe'4eCKHM 3neMeHT 3eMnJl 3aMeHeH nO'4BOM.
npM npJlMOM LtHpKYnJlLtHM 3HeprHM no l4MK/lH'4eCKOM CBJl3H 3neMeH-
TOB, oTpa)t(alOU4eM KaTeropHIO npeoAoneHHJI, nonY'4aeM OAHY H3 '4e-
Tblpex OCHOBHbfX 4>oPMyn - BOAMn, MnM 1 on (pHC. 40).
B Cnel4MaJ1bHOM nMTepa-rype HYMeponorH'4ecKMe $>pMynbl Bblpa-
>KalOT 60nee KOHKpeTHO. Hcnonb30BaHMe crpel10K npRMozo < -+) M
o6pamHozo < +-) ABH>KeHHJI
3HeprHH no Kpyry (O) HnM nH-
HMM qUKJ1UyeCKOU CBJl3M <*)
3neMeHTOB neHTarpaMMbI, KO-
He'4HO, ycJ10>KHJleT 3anHCb 4>op-
o Myn. OAHaKO npH 3TOM. nOBbI-
WaeTCJI TO'4HOCTb Bblpa>KeHHJI
crpYKTypbl 4>opMynbl, '4TO no-
3BOnJleT rpa4>H'4eCKH npaBHnb-
HO ee BocnpOH3BeCTM. CrpenKY
$>pMynbl 06b14HO pacnonaralOT
pJlAOM C 6YKBaMM MnH HaA 6YK-
BaMM, a CMMBon 4>Hrypbl (KPY-
ra WlH 3Be3AbI) - nepeA 6YK-
BaMH. BMeCTO reOMeTpH'4eCKOM
4>Mrypbl MO>KHO CTaBHTb OAHY
6YKBY: «0» - AnI! 0603Ha'4e-
M
B
PUC. 40. neHrarpaMMa C'tJoPMYJ1b1
. hi.QO (nO.J1Y'faM 3Be3,qbl)
C 3HepreTM'iecKoM CBfl3blO
no nmy «npeoAOl1eHMfI».
06'bflCHeHMfI B reKCTe
280
HMJ1 OKPY'KHOCTM; «3»...ntr«A» - AflJI 0603Ha4eHHJI «3Be3AbI», MnM
«neHTarpaMMbI». Bce mpu SHAa CMMBOnOB - reOMeTpH'4eCKaJl 4>M-
rypa,6YKsbI H CTpenKa - SMeCTe COCTaSnJlIOT «nOnHYIO» J1UHeU-
HYIO 4>opMyny.
npHBeAeM npHMepbl HCXOAJI M3 3HaKOMbiX y>Ke 3anMceM 4>op-
Myn. Ha pHC. 39,0 SHeWHee pacnpeAeneHHe 3HeprMM MO>KeT 6bfTb
3anMcaHO KaK oAonMB HnH «020n». BHY1lJpeIJHee, T. e. BHyTp
neHTarpaMMbI, pacnpeAeneHMe 3HeprMH Bblpa3HT , HanpMMep, Ta-
KOM 4>opMynoM: <tl BOMAn HnM n140n. npHBeAeHHaJl Ha pMC. 39,
6 reoMeTpH'4eCKaJl 4>Hrypa MO>KeT 6b1Tb 3anHcaHa AByMfI 4>OPMY-
naMH - OAHa OTpa3HT ee BHeWHee COAep>KaHMe, ApyraJl- BHyT-
peHHee. BHewHflJI 4>opMyna 4>Mrypbl - oBOMAn MnM n140n, M
BHyTpeHHJIJI 4>opMyna - <tlAOnMB HnM n2on. neHTafpaMMY pHC.
40 MO>KHO 3anMcaTb 4>opMynoM <tlBOAMn HnM nl00.;
TepMHH «rpa4>M'4eCKaJl 3anHCb 4>opMynbl», T. e. ee neHTarpaM-
MHoe Bblpa>KeHMe, '4aCTO ynpOutalOT AO Bblpa>KeHHJI «rpa4>MK 4>op-
Mynbl» TaKOM-TO (B OTnH'4He OT 3anHCH 3TOM >Ke 4>opMynbl 6YKseH-
HOM CMMBonMKOM). TepMMHbI «rpa4>HK 4>opMynbl» MJ1M «neHTarpaMMa
4>opMynbl» Mbi TO>Ke 6YAeM Hcnonb30BaTb B TeKCTe.
B 4>opMHpoBaHHM CBJl3H 3neMeHTOB 4>opMynbl Y'4MTblBanaCb
npe>KAe Bcero «CHMBOnH'4eCKaJl» (CUJ10S0R), a He «J10ZUlieCKOR»
CBJl3b 3neMeHTOB, HanpMMep no '4HCJ10BOMY COOTHoweHHIO HnH no-
PJlAKy y6b1BaHHJI M s03paCTaHHJI. Tat(, B OAHOM H3 KHTaMcKMx TpaK-
TaTOB II B. AO H. 3. HanMcaHO:
«nOpO>KAeHHe MaTepH CblHOM Ha-
3b1BaerCJI cnposeaJ1UBOCmblO, no-
pO>KAeHMe MaTepblO CblHa Ha3b1-
BaeTCJI noneIlUmeJ1bCmSOM...
npeOAoneHHe MaTepblO CblHa Ha-
reOMeTpMR nRTU CTUXHU
KMTaAcKMe Y'f8Hwe
OoI1bWOE! 3 ..,e nPH-
CBSl3H 311eME!HTOB
.., HX <l>VHKUHH B <I>oPMYnax
281
rn8B8 6
3b1BaeTCJI KOHmpOJ1eM, npeOAoneHHe CblHOM TepH Ha3b1BaeTCJI 06-
peMeHeHueM» ( HT. no A.VI. K063eBY, c. 307). AHrnHMcKHM CHHO-
nor Am. HHA3M (1959) nOHHMaeT 3TO KaK onHcaHHe Tex >Ke caMbiX
npOLteCCOB 4>opMyn 2 on H 3 on, HO B pa3Hblx acneKTax. «nopo>K,D,e-
HHe» MaTepH CblHOM B 4>Hnoco4>cKoM TepMHHonorHH onpeAenJleT-
CJI no CUJ10BOU (npM4MHHOM) CBJl3H. HanpHMep, f:l B 4>opMyne
«f:l20Ih> (ee orpa)f(aeT 6YKBeHHaJl 4>opMyna OnMB H 4>Hrypa Ha
pHC. 39,6) 3neMeHT A 6YAY'4H «CblHOM» 3neMeHTa B, '4epe3 nocpeA-
CTBO 3neMeHTOB 0, M H n caM «nopO>K,D,aeT» 3neMeHT B. B 6YKBeH-
HOM Ha3BaHMH 4>opMynbl 3neMeHTbI 0, M H Il CTOJIT B OAHOM pJlAY
(no ropH30HTanH), HO. B reOMeTpH'4eCKOM 4>Hrype HX COOTHoweHHe
BblrnJlAHT 06beMHblM, TaK KaK onpeAenJle:rCJI no ny aM 3Be3AbI. 4HC-
no 6YKB B 4>opMyne TO>Ke paBHO '4HCJ1Y nY4eM 3Be3AbI - 5.
npH npoBe,qeHMH pac-
'4eTOB no 4>oPMynaM Ka>K-
AOMY311eMeHlYnpMnHCbI-
BaIDTCS! onpeAeneHHble
Ba>KHble «Ka'4eCTBa» TOro
o6beKTa, JlBneHHJI HnH
BHAii AeJlTenbHOCTM, AnJl
KOTOpOro 0CYU4eCTBl1fteT-
CJI npeAcKa3aHHe. Ka'4e-
CTB8, Hy>KHble Ka>K,D,OMY
3neMeH1)' 4>opMynbl, on-
peAenJleT taM HYMepOnOr,
HCXOAJI H3 CBoero onblTa,
CBOMCTBa 3neMeHTa (ero
CTHXHH) H oc06eHHOCTH
06beKTa HnH JlBneHHJI,
EcnM BepMTIt OKKYnbTM3MY,
aneMeHT Mynbl. KaK '" eI10-
seK. MQ)KeT "'MeTh CWl.bHOO nono-
)KeH"'e. "'lWI BJ1aCTb. Ha.o, APyr"'M'"
aneMeHTaM'" (eC11'" paCCMaTp"'aa-
IOTCSI OTHOWeH"'R s 06 ecTse. TO
Ha.o,nIOAbM"'). HO np'" aTOM He
"'MeTb "'36b1TKa Ka TS "'11'" 3Ha-
HHH(Hanp"'Mep Ka cne an"'CT
nP<>4>ecc"'OHaIlbHOr KOl1neKT"'sa.
s KOTO rnaseHcTsyeT). np'" v
COsna,o.eH"'''' (,s11aCT"'. '" «3HaH"''''»
pol1b seAYll'erO aneMeHTa s <l>op-
Myne 3Ha "'Tel1bHO s03paCTaeT.
28Z
AnJl KOTOpOro npoBOAJIT paC'4eT.
HanpHMep, eCJ1H npeACKa3aHHe
KaCaeTCJI BMAa AeJlTenbHOCTM, TO
OAHMM H3 ero BeA,YutMX Ka'4eCTB
6yAeT «HHM HaTMBa», 4TO MO>KeT
COOTBeTCTBOBaTb 3neMeHiy 0
(<<OroHb»). 136b1TOK MnM HeAO-
CTaTOK 3TOro Ka'4eCTBa B 3neMeHTe 0 MO>KeT npMBeC!TH K pa3J1H'4HblM
pe3ynbTaTaM B 3aBHCHMOCTM OT BMAa AeJlTenbHOCTH MnH CMTyaLtMM,
'4TO onpeAenJleTC" Bbl60poM 4>oPMynbl.
npH M36b1TKe HnH He,AOCTaTKe Ka'4eCTBa BeAYU4ero 3neMeHTa B noc-
ne,AOBaTenbHOM CBJl3M ct>oPMYnbl BlAAenJiIOT QC06b1e COOTHOWeHHJl3J1e-
MeHTOB - «.HOCKOKUBOHUe» H «OCKop6/leHtJe». m COOTMOWeHMJI MJ1M
«KaTeropHH» B03HMKalOT Me>KAY 3J1eMeHTaMM 4>oPMynbt1,pH nOJlBJ1e-
HHH Me>KAY HHMH 3HepreTM'4ecKoM CBJl3M oco6oro Ka'4eCTBa.
Tal(, KarerOpHJI «ocKop6.neHMe» MMeeT, KOHe'4HO, 3Ha'4eHMe Tonb-
KO OC060M nepeAa'4M 3HeprMH B 4>oPMyne, a He oCKop6neHMJI OAHOro
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6YKBaMH'B OAHH pJlA, Me>KAY 3neMeHTaMH B03HMKalOT 3Hepren1'4eC-
KHe B3aHMOCBJl3H. Ka'4eCTBO CBJl3eM 3aBHCHT OT caMHX 3neMeHTOB,
HO 3TH COOTHOWeHMJI BnMJlIOT Ha MCTonKOBaHHe npOrH03a HYMepo-
nOrM'4eCKHX 4>opMyn. n03TOMY paCCMOTpMM CBJl3H 3neMeHTOB B
nHHeMHOM 4>opMyne nOApo6Hee. nOCKOnbKY C 3neMeHTOM (6YKBOM),
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coceACTBYIOT ABa APyrMx 3neMeHTa (6YKBbI), paCCMOTpMM B3aHMO-
OTHoweHMe HMeHHO 3TOM «rpOHLtbl».
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283
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TOpoe npHHJlTO 0603Ha'4aTb crpenKOM. B AaHHOM npHMepe ABH>Ke-
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a
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M He OCTaTKe Ka ecrB B 3neMeHTe.Q - OCHOBHOM 3neMeHTe
neHTarpaMMbI, pacnpeAenftlOU4eM B 4>HrypE! 3HeprMIO
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284
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npaBneHMe OCHOBHOM 3HeprMM B 4>oPMyne. npM u36b1mKe «Ka ecTB»
B BE!AYU4eM 3J1eMeHTe un ero «MaTb» (n) HaxOAMTCJI C HHM BO B3aH-
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«MaTepH». 3TO OTpa)t(aeT crpe11Ka cxeMbi Me>KAY 3neMeHTaMM.Q M n
(pMC. 41, a). B TO >t<e BpeMft «CblH» (M) BeAYU4ero 3neMeH'a un Bay-
naer C HMM BO B3aMMOCBJl3b no THny «HacKOKUBOHue»: 60nee CKnb-
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ern JHepreTM ecKMe CBJl3M «ocKop6neHHe» H «HaCKaKHBaHHe» ocy-
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«a6conlOmu3a ulO».
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A>t<. HHA3M 06'hftcHMn MX 3HepreTH'4eCKOe B3aMMOOTHoweHHe C
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xapaKTepHa) 60nee AocTynHO. OH Bblpa3Hn ee OTHoweHHeM
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n OTHOCMTenbHO «MaTepH» A.
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MeponorM npoBOAftT 60nee AeTaJ1bHYIO AononHHTenbHYIO pacwH4>-
pOSKY «Ka'4eCTB» 3neMeHTOB. Mbl He neperpy>KaeM HenpHBbI'4HOro
285
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npMeMbi M MCn0J1b3YJl npHMepbl npMBeAeHHoro Bblwe aHaJ1H3a HY-
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286
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M lJ,HKJ1H"IeCKOM CBJl3J1M 3neMeHTOB npeACTaBJ1eHbI MC. 42.
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287
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OT ycnOBHM pa60TbI. HTblBaJl, '4TO 3neMeHTbI neHTarpaMMbI CHMBO-
nM3HpylOT rnaBHble Ka eCTBa npeAMera Hl1H JlBl1eHMJI, BblAeJlJleM H3
Bcex B03MO>KHbIX npH'4HH nRTb OCHOBHblX, KOToJ1ble 4>oPMHPYIOT B3a-
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peanH3aLtMJI JanpoCOBnH'4HOCTH,TeXHH'4ecKoe06cnY>KHBaHHe {o6ec-
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288
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An aHaJ1H3a Sw6HpaeM 4>opMyny 1 on, KOTOpa S AeJrTeJlbHOC-
1M CHMBonM3MpyeT C03uiJOHU COBMecTHYIO pa601Y KOnneKTMSa, yc-
nex B TPYAe,.pe3ynbTaTHBHoCTb, T. e. HaM60nee COOTBeTCTsyeT LteJ1H
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2 on, 3 on M 4 on. cJJopMyna lon, MnM BOAMn, HMeeT «npRI!IY1O KpY-
rosYIO» CBJl3b 3neMeHTOB, Hapy>KHoe pacnpeAeJteHMe 3HeprMM (pMC
42, a). no npJlMbiM CBJl3J1 3neMeHT B KaK «"4Tb MMeeT «nopo)l(-
AalOU4YlO» CBJl3b C «CblHOM» 0 MnH no «4MKI1M ecKoi\np"MOM» CBJI-
3M - «npeoAoneaaiOU4YlO» CBJl3b C «CblHOM» A. ""HblMM CJ10BaMM,
B3aHMOOTHoweHM B KOnneKTMBe npJlMO CTHMynMpylOT «pa60'4Me»
HAeM (0) M YAOBneTBopeHHe OT peaJ1M3a4MH ce6J1 KaK nM'4HOCTM B
KOnneKTHBe un.
C ApyroM CTOpoHbI, B BbicrynaeT B ponH « Ha» 3neMe"Ta «MaTe.
PH» n no KpyroBO C8J13M M «MaTepM» M no 4MKnM'4ecK BJl3M. )fa
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weHMM (B) .oT TeXHH'4eCKoro o6ecne'4eHMJI (HanpHMep, ) MnM
OBMM pa60TbI B o<J>Hce (Me6enb, KOMnblOTepbl HAP.) - 3TO <J>yH-
K4MJI 3neMeHTa n. 3neMeHT M YKa3b1BaeT Ha ponb 3apa60THoM MaTlll
B rpY(1ne HnM MHOro MaTepHaJ1bHOro CTHMyna. Bce nJlTh 3neMeHTOB
B3aHMOCBJl3aHbI, HO ponb Ka)t(Aoro M3 HHX B C03AaHMM AeJ10BbOC B]a-
HMOOTHOWeHMM B rpynne pa3HaJl. 3Me+teHMe Ka'4ecTBa OAHOro 3.ne-
MeHTa Bne'4eT ]a c060M no 4en0'4Ke «OTJIroU4eHHe» Apyroro 3neMeH-
Ta. OAMH 3neMeHT MO>Ke'( OTpH eJ1bHO BnMJITb Ha APyroM 3neMeHT,
COCTOJlU4MM C HHM B npJlMOM MnM 06paTHoM, KpyroSOM MnM LtMKnM'4ec-
KOM !HepreTM'4ecKoM CBJl3M. Ho OH >Ke MO>KeT CM NMTb He6naronpM-
"THoe BnM"HMe npE!AblAYU4ero 31IeMeHTa - «MaTepM» Ha HaxoARU4MM-
CJI B «POACTBeHHblX OTHoweHM"X» ApyroM 3neMeHT - «CblHa».
B npMBeAeHHOM npHMepe paCCMOTpeHbI nMWb ABe CaJl3M 3ne-
MeHTOB: B30U/tfonopoHCOeHue M B3ou/tfonpeoiJOJ1eHue.
289
rnasa 6
Onpe.qeneHMe pa6o&4eM cpopMYn AlIA npoBeAeHMA MCc:ne,qOBaHMJI
M aHaJ1M3 B3aMMOC8J13M 3J1eMeHTOB B neHTarpaMMe 3aBMCJIT OT OnbiTa
HYMeponOra M acrponora. AHanM3 MO>KeT 6 Tb OTHOCMTeJ1bHO npo-
CTbIM M O'4eHb ymy6neHHblM. npM 60nee Ae bHOM aHanM3e 3aTpa-
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3neMeHTOB. B nOC11eAHeM cn B Mcc:ne,qOBaHMe BKJllO'4alOT APYrMe
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'4ecKOM 4>MtM>OM, KOTOpy1O Mbi Bbl6MpaeM MnM pMtyeM 6e3 BCJlKOM
3aAHt!M MblCJ1M, npocro18K? MO>KeT6bITb, caMa 4>Hrypa B03AeMCT&yeT
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BOT 'ITO nMwyT B. T. KOHApa-
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«06tijaA nCMxoTepanMA» (1993):
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Tan A MaTepManM30BaTb CBOM
npeACTaBneHHJI 0 MMpe B BMAe-
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AYIOU4eM, C03epLtaJi MX, OH Bbl3b1-
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290
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3J1eMeHTbI AllJI 0603Ha&feliltf1 &f p
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B03AeMCTBHe Ha nCMXM'4ecKoe COCTOJlHMe '4enOBeKa. TaJ(t3HrJaroo6-
pa3HaJl nHHMJI C OCTpblMH yrnaMH C03AaeT Bne'4arneHMe pe3KOro H3-
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KOM 6ecKOHe'4HOCTbIO H a6cOl1IOTHOM rapMOHHeM» (c. 169).
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291
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nCMXMaTpOB M nCMxoTepanesToB, 3aHMMaIOU4MXCJI rMnHOTepanMeM.
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6eTeHKO'B KHHre «TecTbI AllJI AenoBOro 'feI10BeKa H AllJI lICe><» (1995).
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CTpaXOM OKa3aTbCJI B 3aBMCHMOM nOnO>KeHHM.
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HyTb 60nbwMe TPYAHOCTH Ha nyT , '4T06b1 Bbi OTKa3aJ1MCb OT AOCTH-
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MeTOAY 06pe'4eHo Ha np0B¥.
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He MMeeT '4Y8CTBa IOMOpa M He nOHMMaeT WyTOK. Kapil CaraH B KHMre
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eM 3aAAJl3BM AnJi nepeBO,qa Ha KMTaMcKMM Jl30IK n0CJ10BMlW, KOTo-
past B nepeBoAe e iHJ11M14cKOro Ha pycCKMM 3By'4MT npMMepHO YaK: «C
ZR03 U3 cepiJqa SOH». 3BM. «nOAYMaB», cp.enana 6YKBaJ1b-
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298
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paM npeBOCXOAHna npeAblAYUWIO M CTOHna Beero 145 AonnapoB.
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4TO MO>KeT AenaTb 3BM e e 60nee MHHMaTlOpHblMM, HO, KaK nMWe1
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HeM nO'fTM TaKOM >Ke SeJ1M'4MHbI nMpaMMAa ere 6para Xecl»peHa. B
OAHOMM3nepBblXCO CKMx e6HMKOBnOAPeBHeMMCTOpMM
HMK npo4)eccepa P. BMnnepa, 1923 r. M3AaHMJI) coo6U4aJ1ocb, 'frO
301
rnaBa 7
HeAaneKO OT nHpaMMA HaxOAMTC" BblCe'4eHHblM H3 CKaJ1b1 rpoMaA-
HbiM C4>MHKC (TYnOBHU4e nbBa C eJ10Be'4eCKOM ronoBoM).
K BeJ1MKHM nMpaMMAaM B fM3e MO>KHO AoexaTb Ha TpaMBae M3
roPOAa. 31'0 nMpaMHAbi 4>apaoHoB IV AHHaCTHM: Xy$y (Xeonca no-
rpe'4ecKH), Xa4>pa (Xe4>peHa) M MeHKaypa (MHKepHHa), BbiCOTa MX
COOTBeTCTBeHHO 146,6; 143,5 M 62 M.
TpeTbJl BeJ1HKaJt nHpaMHAa
OCTaJ1aCb He3aKOH'4eHHOM H AO-
CTpaMBaJ1aCb y>Ke CblHOM MHKe-
pMHa WencecKa4>oM H He H3
KaMHJI, a M3 KKpnH'4a. nOCTpOi4-
KM AaTMPYIOTCJI: nHpaMHAa Xe-
onca - OKono 2525 r. AO H.3.,
Xe4>peHa - OKono 2500 r. AO
H.3., MMKepHHa - OKono 2475 r.
AO H.3. BOKpyr nHpaMHA pa3-
6pocaHbI OCTItkM KYnbTOBbix CTpOeHMM, nOMMHaJ1bHble xpaMbI, Mac-
ra6b1, OCTaTKM pa60'4MX nOCeJ1KoB. B oTAaJ1eHMH ne>KHT rMraHTcKMM
C4>HHKC, KOToporo OTHOCJlT K nOCTpOMKe BpeMeH Xe4>peHa. nHpaMM-
Aba KOma-TO 6b1J1H 06nMl,&oBaHba OTnonMpoBaHHblMM nnKTaMH H3Bec-
THJlKa. KOTopble BnocneACTBMM nO'4TM l,&enHKOM 6b1J1M rpy60 06OApa-
Hbf - B XIV 8. HMM, HanpMMep, YKpaCMnM MeApece cynraHa XacaHa.
OcraTKM 06nHt4oBK Ha aepWMHe nMpaMMAbi Xe(l>peHa.
HaCKonbKO OHM maAI5M, MO>KHO CYAHTb no TOMY, '4TO B 50-x rOAax
XX B. npM nonblTKe nOKopHTb BepWMHY nHpaMMAbi COpBaJ1CJI H pa3-
'6HnCJI Ha Tb M3BeCTHbiM CBOMMM BOCXO>KAeHHJlMH aJ1bnMHMCT
M3 BenMK06pHTaHMM.
npe.qnonO>KHTeJ1bHO, BepWHHHaJl '4aCTb nHpaMHAba nOBepx 06nM-
LtOBKH 6b1J1a nOKpblTa nHCTaMH n030no eHHOM MeAH. CoXpaHHBWaJlCJI
Ha 38M8TKJ
nMpaMH,A B Ernme MHOrO,
HO Ie YAec8M CBeT8 npM-
'ta.1CJ1RJ1l1tCb lU1Wb BeJ1MIG1e
nMpaMMAbI. BbICSI SI
Ha.D. nycTblHeM B rM3e (Te-
nepb - nPMropoA KaMpa).
302
HcnosaR aCTponOrHR. ..
nMpaMtfAa pHLtbI Y36TeH MMeeT cne,QbI 11030110Tb1 Ha Bepxy1Utte. Ha
Ka>tC.QOM rpal:fM Y aepWMHbI, BMAMMO, 6bU10 M M306pa>KeHMe rMraHTCKo-
ro mcua, nOA06Ho TOMY KaK B xpMCTHaHCKMX XpaMax M306pa>Ka11OCb
«BCeBMAJll14ee OKO» - B rpeyronbHMKe C paCXOARU4MMttCJi nY'faMM.
nOA06HblM 3HaK no ceM AeHb t<pacyeTCJI Hi epMKaHCKMX AOMapax.
rlepBoe 'fYAO nMpaMM,q: «HeBeAOMbiM Jf3hlK».). paco<a3all MCTOpMlO
apa6 MyrePAM B KHMT'e «ErMf1eD, nepeBeAeHHQf Ha1WaHqyJCKMM Jl3hlK B
XVII B. apa6MCTOM BaThe. 0 AJ>YI"MX noee.qan,.tlanpMMep, antrMa-
tyAH B.KHMre «npoMbiBatlbHM 3QI1O'1'3 M poccbInM HWX KaMHeM»:
«8naCTMTeJlb Ha3Ha'tMn K Mid<AQM nMpaMMA no OAHOMY crpaJKY:
1) crpa>KeM 8OCTO'fHOA nMpaMMAbi 6b1na criny,., Bblce'teHHaH M3
rpaHMTa, C oJ>Y')KMeM, HsnOMMHaIOtqMM KOQ . .Ha ntJy ee 6bU1 YKPblT
3MeM, rOTOBIitM HaKMttyTbCJI Iota BCJlKorO, KTO npM6nw.a"TCJI, 06BMTb
ero welO, 3aAYWMTb, a 3aTeM aepHyTbCJI B cawe npM U4e;
2) CTpa>K 3anCIAHoM nMpaMMAbi 6b1n M3 '4epHoro M 6eJ1oro OHMK-
ca. OH cMAen Ha TpOHe, BOOpy>KeHHblM Kon M MeTaI1 'MCKpbl M3
ma3. CToMno KOMY-HM6YAb nOJlBMTbCJI Y BXOA KaK Cpa3Y pa3AC1-
BaJ1CJ1 rnyxoM 3BYf(, M npMWenel4 YMMpaJ1; .
3) I4BeTHOM nMpaMMAe (MMKepMHa) OH onpeAenHn B crpa)l(M CTa-
tylO Ha nOCTaMeHTe, y KOTOpoM 6b1na TaKaJf CMJ1 'ITO OHa Mormr
C6MTb C Hor M YMepTBMTb nlO6oro '4enOBeKa».
(YAJI no onMcaHMIO aJ1b-MatyAM, no OKOH'faHMM C1pOMTenbCTBa
BltaqMTenb oTAan nMpaMMAbi B pacnOpJf)l(eHMe JKMBbiX AYXOB M no-
Be1Ien, '4T06b1 HM npMHocMHCb >KepTBbI:
«1) AYXa ceBepHoM nMpaMMAbI BMAenM B 06nM'4be 6e360POAoro
IOHOWM c AIIMHHblMM 3y6aMM M nO>KenTeBWeM KD)I(eM; .
2) AYX 3anaAHoM nMpaMMAbi - 06Ha)l(eHHaSi )l(eHI14MH KOTOpaSi
3aBlleKaeT nlOAeA M HaCbIJ1aeT Ha HMX 60ne3Hb. Ee MO)KHO y&MAeTb
poBHO B nonAeHb M npM 3aXOAe COJ1H ;
303
rnaaa 7
-'fy,AeCa nMpaMMA-
nMpaMH,D,bI M3JJ,a8H8 «HaCenMM-
.o,ecaMM. nOH8'fS11y 3TO 6b1J1M
'fY.neca MCTO nereH,QapHble:
«...3aTeM OHM no TeMHOMY KopM-
AOPY nOAOwnlil Ie /JPyrOMY ripoXO-
AY, as KOMM 3MMa '4eptiaSl RMa.
3 Hee THHyOO xonOAOM, 88Ot(-
pyr WHbIpRJ1M orpoMH ne1)"4Me
MblWM, nOXO>KMe H8 pHbIX op-
l1OB. OAHQrO 'fel1OBeKa nocnanM
tiS pa3B8AKY. OH "pIiIBR3al1K 00-
RCy ATlMHHblA KaH8T. 'fToObI B crry-
ae HeOOXQAMMOCn1 ero MOrnM
BblTa114HTb H8Bepx. Ho TonbKO OH
c,o.enan nbKO waroB Bne-
peA, Kale nPoXOA COMIEHY M
Cn1CHyn ern oObRTMeM CMepn1.
Pa3,A8J1CR Y*8CHbI tcpMK, Bblr-
HaBWM BCeX OCTanbHbIX nM-
paMH,D,bI. HelCOTopble OT CTp8X8
}'MepnM. Kor.o.a-QCT8atUMeCR B
)IG1BbD( H8'W1M O&ybTb crry-
-.MeweecR M pewaTb, HTO MM Te-
nepb , Mx nponaBWM
/JPyr tieQ)Qt,A8HHO nORBWlCR ne-
peA HMMM M asrOBOPlil/1 tiS HeBe-
AOMOM R3bIlee...-
304
3) AYX L4BeTHOM nMpa-
MHAbi - CTap.eL4, KOTOpblM
6POAMT BOKpyr Hee, pa3-
MaxHBaft orHeM B cOCYAe,
nOA06Ho KaAMnbHML4e M3
xpMCTMaHcKoro xpaMa, Ta-
KMM ero YBMAeJ1H».
nOA06Hble «OXOTHM-
'4bM paCCKa3b1» MHTepec-
Hbi TonbKO 3THorpa4>aM.
COBpeMeHHblM MCKaTeJ1J1M
4YAec Hy>KHO APyroe, Hfot
HY*HaMH pMaL4MJI.A6A
anb-nJlTM4> B CBoeM «no-
BeCTBOBaHMH 0 ErMnTe»
nMCaJ1: «nHpaMMAbi noCT-
poeHbI H3 orpoMHblx Ka -
HeM... KaMHH nOKpblTbi
ApeBHMMM nHCbMeHaMH,
KOTopble HblHe Y>Ke H.MK-
TO He MO>KeT npO'4eCTb. Be
BceM ErMnTe JI He Bcrpe-
TMn HMKoro, KTO 6b1 CKa-
3aJ1, TO YMeeT '4HTaTb 3TO
nMCbMO MnH 3HaeT TaKoro
'4eJ10BeKa. HaAnMceM Tyr
BenMKoe MHO>KeCTBO, M
ecnH 6111 y Koro-HM6YAb
B03HMKJ10 >KeJ1aHMe nepe-
nMCaTb TonbKO Te "3 tiHX, '4TO
BRAHbI Ha nOBepXHOCTM 3TMX
ABYX nMpaMHA (HaM60nb-
WMX. - npUM. asm.), OH ]a.
nonHMn 6b1 MMH CBblwe AeCJI.
TM TblCJI'4 crpaHMLt».
HWHe, OAHaKO, Ha BenH-
KMX nMpaMMAaX HeT HMKaKHX
TeKCTOB M M306pa>KeHHM, no-
CKonbKy KaMHH 06nMttOBKM,
no CBHAeTeJ1bCTBY OAHOfO M3
eBpOneMLteB, Hi'4anH CHM-
MaTb eU4e B 1335 r. AllJI crpo-
MTenbCTBa nY'4WMX 3AaHHM.
Bnpo'4eM; B03MO>KHO, MX HH-
KOrAa M He 6b1J10, nOCKonbKy C «HaAnHCJlMH» MornM 3neMeHTapHO
cnyTaTb '4MCTO reOnOrM'4eCKHe oc06eHHOCTM HeKOTopblX nopOA.
«BKnIO'4eHHJI KBap a npH6nM3HTenbHo napaJ1nenbHbI Apyr APY-
ry H, KpOMe TOro, HaAIIOMneHbI nOA yrnoM, - nHweT reonor H naJ1e-
OHTonor A.A. flKOBn B (>KM3Hb 3eMnM. M.; n.: rOCTexrH3, 1947). -
Ha nonepe'4HOM M3nOMe nerMaTHTOBOM nopoAbi. OHM HanOMMHalOT
BOCTO'4HbIe nM bMeHa, OTKyAa H 6epeT CBee Ha3BaHMe nMCbMeHHblM
rpaHMT, MnM e<eBpeMCKMM KaMeHb».
nOCKOJ1bKy nMWb 6nH>Ke K HaWMM AH"M aHrnH'4aHHH fpMBe AO-
Ka3a11, '4TO, BonpeKM yTBep>KAeHHJlM, nHpaMMAbi CTpOMnM He eBpeM,
a erMnT"He, 06CT0"TenbCTBa C «nMCbMeHHblM rpaHHTOM» MornM 6b1Tb
CYI14eCTBeHHblMM All" C03AaHMJI nereHAbi 0 «KnaAe3e 3HaHMM».
Bnpo'4eM B 06nMKe nMpaMMA BMAenM M «>KMTHMLtbI OCM4>a» (3eP-
HOCKIlaA), M rMraHTCKMe KIlap.oxpaHMTenbHM bI, M 06cepBaTopMM, M
4HcnOSBR 8CTPOnOrHR...
MHT8pecttwA cl»aKT
B KHMre B83M<t>-WaXa coo6-
b: «Ha nMpaMM,QaX .893-
Ae, rAe TOJ1bKO MMendQi}.49C-
TO: H8 noJ1Y... He noTOJ1K8X, He
cTeHax, - 6bu1M M3J1O)I(eHbI
HaYKM, M3B8t11-tbi.e ernnTR-
HaM, HapMCOB8H 3B83,Qp1,
HaOMC8HbI He TOJ1bKO He3B8-
HMR neKapcTB, HO M MX nOJ183-
Hwe M BpeAHbIe ceo4itcTBa.
CBeA8HMR.o T&nMCMaf:tax, MS-
TeM8TMKe, 8pXMTe ....
305
rnasa 7
«MeTKM npMWenbl4es», M HaArpo6HblM KaMeHb Kap;«.neTaIOU4eM 10-
penKOM», 3aKOnaHHOM my6oKO B nycrblHe, M T. n.
OAHaKo MAeJl noptyraJ1bLta He HOBa, MHeHMe 0 n_OTOne BblCKa3b1-
BaJ10Cb eU4e A06pylO TblCJI'4Y neT Ha3aA. Apa6cKMM aCTpOHOM aJ1b-
6anxM nMcan: «MYAPble MY>KM, nepeA nOTOnOM npeA Ka3b1BaBWMe
Kapy He6ec - BOAOM M11M OrHeM, SCJ1eACTBMe KOTOpoM ffyAeT ytfMI.,I-
TO>KeHO Bce >KMSoe, nOCTpoMnM B BepxHeM ErMrrre Ha BepwMHax rop
MHO>KeCTBO nMpaMMA H3 KaMHJli Aa6b1 HamM B HMX cnaceHMe OT rpo-
3J1U4eM KaTaCTpo4>bI».
EC11t MH8HMe
He YaK Aa8HO flayny r.,.,...
epMe ,Qbeca-l1ean (flopry-
ranMSt) npe,Ql10110)01J1, 'fTO
nMP8 CIJy)ICMI1M AIISt
cnaceHMR A8M e nepoo-
AbI HaBO,D,f18HM9. rMnGte38
6bu1a 6bt Xopot.U8. ecJ1M He
BCnOMMH8Tb, 'fTO nMpaMM-
AbI Kor,Aa- TO Obu1M o611M-
0B8HbI Be1U1KOflenHO OT-
WJ1M4>oBaHHblM&.1 MIIITSM&.1.
K TOM}' )ICe B lij)ei rM-
neTCIG1X MCTO'UiMK8X'..a'tM-
CTO O T nereH,D,bl
o 8ceMMptiOM OOTone,
nocK011bKY pa311MBb1 HW1a
B ErMrrre e)KerOAHbI.
cKaK nOJ1araeM MbI KYi46w-
WeBCKKM Y'4E!HblM BniAMMMpOM
BaHOBM'4eM ABMHCKKM, "Mpa-
MKAbI - "C CtBeHHwe rnyWM-
TenM 3eMneTpJ1CeHMM. Elije OAHa
Aep3KaJl TMnore3a», - 3aMen411 M
Haw OTe'reC1'BeHHblM MCCJ1e,qosa-
TeJ1b nMpaMMA C.6. npocKYPJ1KOB,
COTpyAHMK MHCTMtyTa np06neM
H HOCTM H AQ11roBe'fHOCTM Ma-
WMH AH 6CCP.
4TO )i(, nlO6MTenM TOKapHOro
Aena M BnpJlMb MOryr HaifrM OT-
AaJ1eHHoe CXOACTBO nMpaMMAbI
Xeonca C sM6poraCMTeneM, cra-
BJ1U4MMCJ1 Ha pe3el4 (Cla*eM,
BH6poraCMTenb A. . PbI*KOBa).
Bo BCJlKOM CJty'4ae, fpeHnaHAMJ1
H AHTapKTMAa, «npMAaBneHHbIe»
neAftHblMM WanKaMH, M BnpJlMb
306
JlBnJlIOTCJI paMOHaMH ManOCeM-
CMM'4HblMM. npaBAG, CKOpee M3-
]a xonoAa...
AOnOnHMTenbHble AaHHble 0
npeAnonaraeMbiX 4>H3M ecKHX
CBOMCTSax nMpaMHAbi '4MTaTenb
Mor n0'4epnHYTb H3 TeJ1eBH3MOH-
HOro aJlbMaHaxa «BoKpyr CBeTa»
(28.05.1989), me 6b1J1 BnepBble
nOKa3aH 4>MnbM «npOKnJlTMe
$lpaOHOB» (aBTOpbl- 3. THM,
A. neMc, repMaHMJI).
C03AaTenM 4»HnbMa KOCHY-
nMCb BbiCOKOM CMepTHOCTM MC-
cneAoBaTeneM erMneTCKHX nM-
paMMA «(MeCTb 4>apaoHoB») M
rp06HH bI nonbCKoro KOpOnJ1
Ka3MMHpa, y6eAMTenbHo 06'bJ1c-
HMB ee BAblxaHHeM cnop rpH6-
Ka-nneceHH Aspergillus flavu
npopaCTaBwero Ha MYMMJlX.
nOKa3aJ1M onbiTbi K. WneMxepa (BawMHrroH, CWA) C «MYMH4>H-
MPYIOU4HMMCJI» nOA nHpaMMAKaMH KyCO'4KaMH MJlCa a'TaK>Ke onbl-
Tbi np ccopa AMxMaMepa (MIOHxeH, repMaHHJI) C « aM03aT0'4KoM»
ne3BMM 6e30nacHbix 6pMTB.
nOCJ1e cl»tnbMa H.K. 60HAPOBCKHM nonyTHo ynOMJlHyn 0 npeA-
nonaraeMOM «cBJlTMnHI14e 60ra TOTa», BXOAbi B KOTOpoe 3aKpblTbi
B03MO>KHO, HMeHHO nMpaMM,QaMM, me, no onMCaHMJlM Waxepe3aAbI:
ecTb «CTeKnO, KOTOpoe rHeTCJI»,. «MeTann, KOTOpblM He p>KaBeeT»,
If'''CflOSBR BcrponOnfR .
06l14eHMe C AyxaMM
B IlOrIbI11CaX «KOHTaICTa- C
AYXaMM M CW18Wt n 101A
K H\ItM perynRpHO T-
CSt npeAC'tBBKTeSWI BCe903-
MO)t(HbD( c.;pcr_M -
IG1X Hafl . 0t*1 npo-
T,MO ,
Me,IJ}ffi1PYK>T (<<OTpeWaIOT-
CSt») Y rlO,D.H())ICMM .. H8 sap-
WMHaX 0MpaMHA;.1"IblT8K)T'CR
cn «BWaaTb
AYUJM-}(X)nWMX ,
Tenena «o6u4aJorcR-
C 6orOM TOTOM M
1tbt,QoM, yrBep)K,Q8JOT, 'frO
B6n n OK1 ynaB-
nMBalOT CMrHaIlbi KOCM -
IG1X U,HBW1M38L\,HM M T. A
307
rn8B8 7
«KpeMHeBbie KHMrM» M npo Me '4YAeca, no.q KOTOpWMM MO)l(HO nOA-
pa3YMeBaTb M «TeXHM ecKMe OiKpWTMR», M B03MO)KHbfe tneAbl «na-
neOBM3MTa» (MHonnaHeTRH) MJlM '4To-JlM60 nOA06Hoe.
fnyno raAaTb, ecTb nM CCBJlTMJlMU4e TOTa» Ha caMOM AeJ1e, OAHaKO
CJ1e YKa3aTb, '4TO aJ1b-MaCYAM (900-965) nepe'4MCJ1J1eT Bee Te
)Ke '4YAeca. npaBAa, 3aMeTMM nonyTHo, '4TO TepMMH crM6Koe CTeK-
no» MO)KeT 6b1Tb M OWMOO'4HblM nepeBOAOM, nOCKOJ1bKY erMnTRHe
Ha3b1BanM CTeKnO «paCTeKaIOU4HMCJI KaMHeM».
B OAHOM M3 3aMe aTeJ1bHblX 3aMeTOK *YJ)HaJ1MCT 3. Han6aHARH
paCCKa3WBan 06 OAHOM 6M3HecMeHe M3 H080M 3eJ1aHAMM, KOTOpillM
3a6pocMn Bce CBOM AeJ1a H npMexan B ErMneT. 6M3HecMeH no Ho-
'4aM 6pOAHJI BOKpyr nMpaMMAbf C npoTJUtyrWMM K HeM pyKaMM M]a-
TeM yreep>KAan' 'lT0 6eceijyeT C AYXOM caMoro Xeonca.
n.B. nepMHHOB B KHMre cYnbl6Ka C4>MHKca», B maBe «4eproa-
U4MHa BOKpyr nMpaMMA» OnMCaJ1 KoneHOHenpeKnOHeHHYIO TaJlny II
3KCTpaoaraKTHbfX OAe>KAaX: «B CTOpoHe OT OCHOBHOM' rpynnill «AT-
naHTOB» CTOMT CpeAHMX JleT )l(eHU4MHa C myOOKo 3anaBWMMM ma3a-
MM pe11MrM03HoA <J>aHa:n.'IKM. OAeTaR BO BnOJ1He COBpeMeHHble po-
30Bble 6plO'4KM M JlerKY1Q 6enyK> py6aWKY, 0Ha. KaK B TpaHee, CMOtpMT
Ha BepWMtty nMpaMMAbi Xeonca. m )t(eH MHa C MTaeT Ce6R 3eM-
HblM BOnJlOU4eHMeM ApeBHeerMneTcKoM 60rMHM CMAbI, cynpyrM
OCMpMca - 605MHM MOAOPOAMR Y AJ>eBHMX erMnTJlH. Yee Hor CTe-
HaeT M pblAaeT AJ1Yf >KeHIqHHa, TsePAO y6eJK.qeHHaJi B TOM, 'lT0
nna'f y Hor CMAbi npMHeCeT eM AYXOBHoe O'4MU4eHMe...»
Bnpo'4eM, HeTpyAHO' nOHRTb rpeneT OTAeJ1bHblX Bne'4aTJlMTeJ1bHblX
nlOp.eM,. 0006eHHO e xyAO)l(ecTBeHHiIIM TMnOM MblwneHMR, npM BMAe
MHOro neT 6oroTBOpMMOro M HeAOCTM)t(MMoro 'IYAA. nMcaTeJ1b AHA-
peA 6enblM, HanpHMep, yTBepJKAan, 'lT0 KOrAa OH nOAHRnCJI Ha nM-
paMMAY Xeonca, TO oAPyr nO'4YBCTBoBan, KaK M3 Hero CM30wna»
308
BBepx BOnHa, OXBaTMBW!R BeCb KOCMOC. dt 6b1J1 BO seeM pa3J1MT, It
6b1J1 Becb 3HaK 30AMaKa... '4Y8CTBOBaJ1 ce6J1 MJtKOTtilO nepcMKa, 06-
BonaKMBalOU4eM KOCT KY CBeem Tena.. .», - nMCaJ1 OH.
«OrOBCIOAY B30pbl MOM 6b1J1M npM&.ne'4eHbI, KaK MarHMf M, nMpa-
MMAaMH.. .», - OTMe'4aJ1 M pycCKMM nyre HHMK ABpaa }topeB.
B MHTepBblO ra3eTe «Time» (nOHAOH, 8enMK06pMTaHMJt) 4>M3MK
AMH-UJaMCKom YHMBepcMTeTa rOHeMA cKa3a/l Ha-.HaWM pe3YnbTa-
Tbi nOBnMJlna nM60 cy eCTBeHHaJI OWM6Ka, BKpaBwiJlcJt B reoMeT-
pMIO nMpaMMAbI, nM60 >Ke TaMHa, KOTOPYIO Mbi He B COCTOJlHMM ot7bJtC-
HMTb. Ha3b1BaMTe ee, KaK XOTMTe: OKKynbTM3M, npotU1BTMe 4>apaOHOB,
Bonwe6CTBo MnM MarMJt».
Bnpo'feM, K 1974 r. yp.a HM CbeMKa IICe)Ke npoM3Be.QeHa:
comaCHO eM, HeM3BeCTHbiX noMetqeHMM B nMpaMMAe Xeonta He 6b1J10.
8" M, Mcc.ne,qoBaHMJl80-x roAOB XX B. BHOBb AaJlM HeImTOpble Ha-
AeJC.qbl M nMU(Y AnJl nepecy-
AOB nlO6MTenJlM KnaAOB M
ceHcal4MM, nOCKonbKY 6b1J1H
06Hapy>t<eHbI HeKMe XOAbI,
3a6MTble neCKOM, KOTOpblM
Aa>f(e n0C'4MTaJ1M «paAKOaK-
TMBHblM».
«CMJlOBoe none nMpaMMA
onacHO!» Macna B oroHb OOA-
nMBaIIM cnyxM. 'fTO HeKOTOpbIM
lYPMCTaM (B CBoe BpeMJt-
etqe Hano1leOHY 6oHanapty)
AeJIC)/IOCb AYPHO B nMpaMHAe.
OAHa.Ko Aa)Ke 6e3 BCJlKMX
MHblX npM'4MH B nblnbHOM
4HCflOBaR acrponOrHR...
TaAHw HaYKM
8 1965-1968 n: 4>M3MK J1}'HC
Anb8apec (CWA) nOObfTaJ1CS1 C
I1()M()lUbIO annapaT)'pbl BbIHC-
HKTb INi'fJP8HHge CTpoettMe
Be.nMIG1X nMJ>8MM,O,. O.QHaKO
bHO ero *A8l18
HeYA8'fa, KOTopytO Koe-ICTO
OXOTHO CTaJ1 OObStCHRTb Ha11M-
'tM&M CW1bHOrO McirliKTHOrO
(MJ1M BOO6u4e HeM3BeCTHOrO
H8YKe nonSl, AKOObi Otepy)K8JO-
U49f"O nMpaM V Xeonca.
309
rnaSB 7
AYWHOM KOJ)MAOP€)cotb KOMY-
HM6yAb H3 MH/1J1MOHOB TYPHCTOB
M nOCeTKTe11eM HaBepHJlKa Aon-
>KHO CTaTb MOXO.
n03TOMY «noA03pMTenb-
HblM» <J>aKT rH6enH B nHpaMHAe
MCCJ1eAOBareJlJI reopra BaMCHe-
pa (1942) He AOn>KeH oc060
«paAOBaTb» nlO6KTeneM ceHca-
LtMM. CSJoTOrpa4>MJI, nOKa3aHHaJl
B 4>HnbMe «npoKJ1J1THe <J>apao-
HOB», HamMHO y6e>KAaer - Y
BaMCHepa 6b1nM Bce waHCbI
CKOH'4aTbCJ1 M paHee OT MH<J>ap-
KTa HnH OT anOMeKCH'4ecKoro
}'Aapa (KpoBQM311HJlHHJI B M03r). 06 310M rOBOpJIT H B03paCT, M 6b1'4bJl
weJl, TYro yraJl BOpoTHH'4KOM, M B3AYfb1e 114eK , H 6arpoBoe nHu.o
(nmeprOHMK), M 3AopoeeHHaJl KypKTe1lbHaJl rpy6Ka B 3Yf)ax - non-
HbiM «A>KeHT1IbMeHCKMM Ha60p,. KaPAHOnOrH'4ecKoM rpynnbl PHCKa.
OAHaKo Aeno MO>KeT 6b1Tb BOBce He B «CHnOBOM none» nHpaMHA,
XOTJI onpeAeneHHble 4>H3M'4eCKOe OC06eHHOCTM 3AeCb Bce >Ke eCTb:
nHpaMMAY MO>K"O npeACTaBHTb KaK 4-yronbHblM pynop, 4>OpMMPy-
10114HM CneLtM4>M ecKWP CTpYKTYPY MeXaHH'4eCKMX BM6pau.MM H 3neK-
TpOMarHMTHbiX BonH, H nOCTpOMTb 3AeCb AeCftTKM MaTeMaTH'4eCKMX
MOAeneM, KOTOpblX XBarMT Ha COTHM TOMOB.
Bce B TOM, '4TO XOAbl nHpaMMAbi He npeAHa3Ha'4anHCb AllJI
>KHBblX.
XHMM'4eCKYIO >Ke CTOPOHY Bonpoca, B '4aCTHOCTH COCTaB B03AYXa,
nOXO>Ke, HHKTO KOHKpeTHO He aHanM3HpOBaJ1. Me>KAY TeM AOCTa-
M3 6Monont'tecKMX «AOC-
Tonp Me aTenbHOCTeH., He
C Tast CJ1y'taHHblX ytCyCOB
3MeH,CKopn OHOB,n en,
OC, A,D,OBMTblX nayK08 np.,
KaK 3BeCTHO. eHble 06-
Hapy*W1 B n paMH,D,aX KaK
M H MYM ABa CMepTenbHO
onaCHbiX 4>aKTopa: nneceHb
Aspergillus flavus (Pwc fI
acneprnnnlOC) cneW14> -
eCK e B pycbl ne x
MbiweH.
310
TO'fHO Aa)Ke BefilitMc1.HS6onb-
WOM KOHLteHTpai4MM MbfWbJl-
KOBMCTblX I4nM PTYTHbfX CO-
eAMHeH M, npOnMTblX ,Ha
CTeHbf M non, .'4T06bf Ha COT-
HM M TbfCJt'4M neT 06eCne'fMTb
CMepToHocHoe BJ1MJlHMe, no-
CKonbKY HeOpraHM'4eCKMe
1IAbi npaKTM'4eCKM He pa3na-
r IOTCJ\,.XOTJI nerKO MoryT no-
nacrb B opraHM3M nOCeTMTe-
1111 C nbfnblO .. McnapeHMJlMM.
CBoe06pa3Horo Hacna B
QrOHb» nOAliMBaIOT nonMTM-
ecKMe HeA06po>KenaTeJ1M M
MMCTM'4eCKM HacrpoeHHbIe cy6"beKTbI, CTpeMJlIqMf!a «HarHaTb crpa-
xy» BOKpyr TaMHCTBeHMOCTM nMpaMMA.
Bnpo'4eM, JlI06MTeneM noo6U4aTbCJI C «AYXaMM» HeMaJ10. C i4eJ1blO
«nOCBJlTMTbCJI» M BblJlBMTb «MarM'feCKMe CMnbl» TYpMCT nonb 6p3H-
TOH (8eJtMK06pMTaHMJI) CKopoTall HO'tb B nMpaMMAe Xeonca. Hayr-
po COYpyAHMKM ErMneTCKOM CJty>K6bf ApeBHOCTeM M:J8neKJIM era B
nony6ecc03HaTeJ1bHON COCTOJlHMM, C nCMXM'4ecKMM paccrpOMCTBOM.
. no era cnOBaM, MbICJ1M era Ha'4anM nyraTbCJI, M Ott OOTePM C03Ha-
HMe OT Y*'tta. npMifMHOM :noro MO)KHO C'4MTaTb '4T0 ytOAHO, HO B npMH-
'4Mf1e OOAf)6HOe COCT09HMe He pa3 y>Ke onMCaHO y cneneonoroe, MOPft-
KOB, KOCMOHaBTOB, T. e. nIOAeM, OKaJaBWMXOI B ycnOBMJIX «ceHcopHOM
,qenPMBai4MM» (nonHOrO OAMHO'feCTBa) M BHe3anHO OC03HaBWMX ee.
Be BCJIKOM CJly'4ae M3BeCTHbie CBOMMM KHMraMM aBToM06MnbHble
nyrewecrBeHHMKM H. raH3eJ1Ka M M. 3MKMYHA B 5O-6o-x roAaXXX B.
'-IHcnoB8R 8CTponornR...
MKTep8CHwA .aKT
EcI1M B8PKfb pa3I1M HbfM
eo<:>6u4eHM M. B n Ha-
MepeH"' )(pyt14esa r'IOOeTwrb
EntneT M OfMOTpeTb nMpa-
MMAb'. BbfRCHMI1CSl3nM30A.
KOrAB B XOAOB
6bu1a OOH8PY*Sf'a I')'6l<a.
nponMTSHHaSt HeKMM pa3-
.D,paE_'" B8U.\8CT9OM.
M3-.38 ro 6wno TPYAHO
AbUOOTb. [y()Q 6btna OCTaB-
l1eHa RBHO cne .
311
rnBSB 7
6narononY'4HO nepeHO'4eBanM Ha BepW"He l1MpaMMA 'Xeonca M
OCTanHCb BnonHe AOBonbHbI. npaBAa, MX 6b1no ABoe.
BnpO'4eM, nOXO>Ke, eCJ1M cne HanbHO «He HacrpaMBaTbCJI» Ha
npeCJ10ByToe 4<CHnoBoe none», nHpaMHAa HH'4erO nnoxoro He CAe-
naeT. Ho H HM'4erO xopowero. KaK B 1991 r. co06U4Hna ra3era «He..
AenbHa npaBAa» (4eX0CJ10BaKHJI), OAMH 6pa3MnbcKHM TypMCT BbI-
HY>KAeH 6b1n npoBeCTH «HeCKonbKO >KyTKMX '4aCOB» B HeApax
3H.aMeHHToM nHpaMHAbi Xeonca (4<Tpy . 28.01.1991): 4<nOCJ1e oc-
MOTpa nOrpe6aJ1bHOM KaMepbl OH HeMHoro OTCTaJ1 OT rpynnbl, '4TO-
6b1 3aKYpHTb ('4TO, pa3YMeeTCJI,-3anpe eHo. - npUM. oem.). ryc-
TOM AbiM B y.3KOM npOXOAe M HeAoCTaroK KMCJ10pOAa npMBenH K TOMY,
'4TO TypHCT nOTepJln C03HaHHe. KorAa KYpHnbU4HK O'4HynCJI, KpyroM
CTOJina KpOMeWHaJ1 TbMa. OH HI OutYOb cran np06MpaTbcJ1 K BblXO-
AY, HO TOT OKa3anCJI Hamyxo 3aKpblTbiM. TonbKO nOCJ1e nonYH0'4M
KTO-TO Hi CTOpO>KeM ycnblWaJ1 HCTOWHble BonnH nepenyraHHoro Ty-
pHCTa M nOMor eMY Bbl6paTbCJI...» nCHXM'4eCKoro «c,qBMra» y 6eA-
HJlrH He 06"py>KMnOCb, XOTJI crpaxy OH HaTepnenCJI...
MCTOpM « McnOBOM
reOMeTpMM» nMpaMMAbl
COBpeMeHHble ojtcqpeAOBaTenH - J1. . 3a6pOAHHa (<<3araAKH
ApeBHero ErMnTa»), MeppM Xoyn (<<Pa3raAKa TaMH ApeBHero ErMn-
Ta») H- AP. - yTBep IOT, '4TO eU4e AO 3nOXH paC BeTa KYnbTyp
WYMepa BHero ErMnra CYU4eCTBOBana LtMBHnH3aLtMJI, Hay'4Hble
M TeXHOnOrM'4eCKMe AOCTH>KeHMJI KOTOpOM Aa>Ke HepeAKO npeooc-
XOAMnH COBpeMeHHblM ypOBeHb. noene Toro KaK npMpOAHble Ka-
TaKnM3MbI CTepnH C nM a 3eMnH crpaHY, rAe )l(Hn 3TOT HapOA, OT
312
BeJU1KOM qMIMfM438l&M" OCTa-
nMCb nMWb BOCnOMHHaHMSI, MH-
4>bI H nereHAbi.
Cno80«nMpaM npoMCXOAHT
OT rpe'4eCKoro cnoBa pyramis-
H '4T003Ha'4aeT HMBOnM'4ec-
Koe npeACTaBJ1eHMe EAHHOro 60-
)t(eCTBeHHoro nnaMeHM, )t(M3HH
Bcex C03AaHHA. CaMa cf>opMa nM-
paMMAbI, 06pa eHHaJl OCTpMeM
BBepx, CHMsonM3MpyeT ropJl
nnaMJI.
ApesHHe erMnTJlHe C'U4TaJ1i1 4>oPMY nMpaMMAbi MAeanbHblM CMM-
BonOM ceKpeTHoM AOKTpHHbI. nMpaMHAa SlBnJlnaCb aPfETMnOM CSJI-
lqeHHoM ropbl, HnH Bblco.'4aMwero MeCTa 60ra. nb npeACTaBneHMJlM
ApeBHHX, OHa HaXQAHTCJlliCnocepeAb» 3eMnH H OTHOCMTCJI K CKa-
30'4HOMY OnMMny.
nHpaMHAa 6b1na cosepweHHblM CMMB0J10M MMKpOKOCMa M MaK-
pOKOCMa, rp06HH4eM 60ra OCHpHca. OCHpMC npeACTaBnJleT MaHM-
4>eCTa4MIO conHe HOM 3HeprMM, M, eneAOBaTenbHO, ero AOM eCTb
3M6neMa BceneHHoM. n03TOMY «BceBMASlI14MM ma3» 60ra erMnTJlHe
nOMeU4aJ1H B rpeyronbHoe none nMpaMMAbi.
. Bo3MO>KHO, ApeBHeerHneTcKMe >Kpe4b1, nonY'4MBwMe 3HaHHSI OT
sbiweynoMJlHyTOM TeXHOnOrM'4eCKM pa3BMToA «AonoTonHoM» 4MBH-
nM3a4HM, TU4aTenbHO CKpblnM MX B CBOHX caMbiX TaMHblX pHlYaJ1aX
(n. . 3a6poAHHa). OAHaKo CMeHJlnHCb CTOneTMJI, a C HHMH AM Hac-
THH, npaBHBWMe ApeBHMM ErHnTOM. "faCTb 3TMX Mory1qeCTBeHHblX
3HaHHM nOCTeneHHO npeBparMnaCb B nosepbJl. TaK Ha3b1SaeMbie «OK-
KynbTHble» TaMHbI, AOWeAWHe AO Hac co BpeMeH wYMepcKoM, ApeB-
l/ucnosaR aCTponoruR...
H8 a8MeTJCy
HeKoTopble MccneAOS8Te-
nlo1 npeAJ1Qlt101T8IOT KOf!TC-
Koe 3H8'i9HIo1e cnots! nlo1pa-
MIo1A8- r::: «A8nIo1MOe H8
A8CS1Tb-. T. e. MQ)KH() TaIOKe
nonara-&. 'f1i> B COOSO «nM-
paMMP,8» AP91iHIo1MIo1 sno-
>lCeH 101 3TOT OKKYnbTHbI
'4Io1CnOBO KJ11O .
313
rnaB8 7
HeerMneTCKOM MJ1M BaBMJ10HCKOM qMBMJ1M)BQMit, Rlllfn01a Ke 'feM
MHblM, KaK Hay'fHblMM 3HaHMJlMM, KOTOpble HeKOrAa 6bU1M CneI4MaJ1b-
HO 06ne'4eHbI B $>PMY, AenalOlqyIO MX nOHJlTHblMM nMUlb nOCBJULI,eH-
HbiM nlOARM TOro BpeMeHM.
AMOAOP CMLtMnMMCKMA BIB. H. 3. nMcan: «ErMfTTJlHe 6bU1M npM-
W11b1MM nIOAbMM, KOTopble B AaJleKMe BpeMeHa nOCenlijnMCb Ha 6e-
perax HMJ1a, npMHeCJt C c060A LtMBMJ1M3aqMIO cseeM pDAHOM crpa-
HbI, MCi<yCCTBO nHCbMeHHOCTM M coaepweHHblM Jl3b1K. OHH npMwnM
0TTYAa, me 3axoAMT conH.14e, M 6bU1M caMblMM ApeBHMMM M3 nIOAeM».
HaCJ1eAMeM BonnOUleHMR 3HaHMM -M. MCKY«TS8 ApeBHero nepMO-
.Aa JlBnJlIOTCJt CcI>MHKcbI M nMpaMMJlbI. Ha rtpOT1UKeHMM croneTMM OHM
AaIOT 06MnbHylO nMU4Y AllJI AHCKyCCMM MeJKAY MCTOpMKiMM, Y'4eHW-
MM, MMCTMI(C)MM ... anXMMMKaMtt
KaMepbl BenMKOM nMpaMMAbi McnonbJosanMcb ApesHMMM AIIR
4CAYXoBHOro nocBRU4eHMR» M36paHHWX. BOT '4TO nMweT 06 3TOM
n.io1. 3a6poAMtta: «.. .OHM BxoAMnM KaK nIOAM, a BblXOAMJ1M KaK 6orM.
3TO 6b1J10 MenOM «BToporo pO>KAeHMJI». «JIOHOM» MMCTepMM. Bo
BpeMR MMCTepM HOBblM"ROCBRIijeHHblM - Heo4>MTaM - OTKpblBa-
nOCb 60>KecTBeHHoe MMR. CaMO 3TO 3HaHMe Aenano '4enOBeKa M ero
Tsopt.\a OCQ3HalO MMM AfIYT APyra... nOCBRI14eHMe B Bblcwee 3Ha-
HMe 6b1J1O 0TKpWT0 AaneKO He Ka)I(AOMY - Aa>Ke He Ka)f(AOMY erM-
neTCKOMY >KpeltY. npe)I(Ae 'teM MarM OKa3b1BaJ1MCb roTOBbi K BblC-
weMY nOCBR HM ...It.nDMxoAMnocb 8b1nOnHRTb MHO>KecT80 JaAa
H npoxOAMTh MHO>KecTBO MCnblTaHMM. Ka)I(Aoe MCnbITaHMe cny>KM-
no MepMJlOM ypoBHR MHtenneKTa, MOpanbHOM CTOMKOCTM H CMJlbI A.'{Xa
KaHAMAa tfMKOMY He pa3pewanOCb npoXOAMTb HcnblTaHMJI BTO-
pOM pa3:npM nocBR eHMM nepBoe MCnbITaHMe 6b1no HaCTonbKO TR-
>KeJ1b1M, 'fi0 He 06nClAaIOU4MM CMnbHblM AYXOM KaHAMAaT M r npoCTO
McnyraTbCJI M OTKa3aTbCR OT nOCBR eHMR. OAHaKO, eenM OH npo-
314
AOn>Kan C1IeA88afb npoqeccy no-
CBJlI14eHHJI, eMY OTKpblBaJ1M nep-
Bble CHMBOnbi TaMHOrO 3HaHHJI.
ECJ1M >Ke OH He npOXOAHn noc-
ne.f\YIOU4HX MCnblTaHHM, TO He Mor
H36e>KaTb HeH3MeHHoro H >Kec-
TOKoro 3aKOHa CMepTH cpeAM
MarOB. B 3TOM CJ1y ae OH 60nb-
we HHKorAa He BHAen COnHe'4HO-
ro CBeTa. (KCTaTH, MAGOS -
Mar - CJ10BO, WHpOKO Mcnonb-
30BaBWeeCJI paHee M pacnpoCT-
paHeHHoe CeM'4aC, - 3TO CJ10BO rpe'4ecKoe H JlSnJleTCJI 06b1KHO-
BeHHblM npOM3BOAHblM nOHJlTHM MOG, MEGH, MAGtiJiKoTopble Ha
neX11eBM M 3eHA - ABYX Jl3b1KaX ,QpeBHero BOCTOKa - 0603Ha a-
lOT «>Kpe4», «MYAPblM», «eenMKonenHblM».)>>.
rpe eCKHe 4>Hnoco4>bI- cJ»anec, nHcI>arop, nnaTOH M EBAOKC-
6b1nH caMblMM 3HaMeHMTblMH H3 Tex '4Y>KeCTpaHLteB, KOTopble yc-
neWHO npownH MHOrO HCJ1eHHble HcnblTaHHJI «nOCBJlU4eHMJI».
nH4>arop 6b1n nOCBJlU4eH CBOHM MaCTepOM, npopoKOM COHXMCOM.
cnonb3YJI nonY'4eHHble 3HaHHJI, nH4>arop nOCJ1e CBOHX CTpaHCTBHM
OCHOBaJ1 B KpoTOHe (to>KHaJl TaJ1MJI) wKony, KOTOPYIO '4aCTO Ha3b1-
BalOT YHHBepCHTeTOM. B 3TOM WKone H3Y'4eHHIO reOMeTpHH, MY3b1-
KH H aCTpOHOMHH npHAaBaJ10Cb 6onbwoe 3Ha'4eHMe. nH4>arop OT-
Kpbln, '4TO MY3b1Ka MMeeT TepaneBTH'4eCKOe SnHJlHMe, a npHJlTHDe
BOCnpHJlTHe nOA HHJleTCSI MaTeMaTM'4eCKMM pac eTaM (CM. CO-
OTBeTCTBYIO(14HM pa3Aen KHHnt). OH TaK>Ke 3KcnepMMeHTHpOBaJ1 C
LtBeTOM H «.ne'4e6HblM» pHTMOM ronoca. CBOMX 60nbHblx OH ne'4Mn,
AeKnaMHPYJI MM CTHXH M3 « nHaAbI» H «OAHcceM» fOMepa.
4HcnOB8R 8crponOnfR...
MCTopM'tecKali cnpaaKa
ComaCHO repoAOTy, KOTO-
pblH 06 ancst y en1 eTC-
K....X OB, n....Cb HHaR
IIICTOP"' erlllnTRH H8 IIIHa-
l1aCb 3a 11 340 l1eT 1JP
3n0>G1,fA K<'t9PYK>)KHfI
caM repoAot: ....11.... n TIII
3a 14 TblCst eneTIIIM AO
Hawero BpeMeHIII.
315
rnaBS 7
ErMnTJlHe BenMJ<YIO nMpaMM-
AY aCCO MMpoBaJlM C repMecoM,
6oroM MYAPOCTM M nMCbMa. Co-
OTHeceHMe repMeca C nMpaMM-
AOM n03BonReT nOllaraTb, '4TO
nMpaMMAa JlBnJleTCR «nepBblM
XpaMoM MMcTepM", nepBoM
CTJ>YKTYPOM, KOTOpaJl JlBIIJleTa
xpaHMnMU4eM MCTMH,lIeJKaU4MX B
OCHOBe HCKycCTB M HayK».
nMpaMHAa MMeeT CJ1o)t(Hoe
CTpOeHMe (pMC. 47). He Bce ee
XOAbi M3Y'feHbt COBpeMeHHHKa-
MM. ComaCHO cxeMe, nMpaMMAa
pa3AMAeTCJI Ha HaKnOHHbte XOAbt, B nepece'4eHMM KOTOpbtX (npM-
MepHO B I,4etppe nMpaMMAbt) HaXOAMTCJI ycblnaJ1bHHLta 4>apaOHa.
HiUKe no ypo 1O pacno raeTCJI ycblnaJIbHHqa )f(eHbt 4>apaoHa. 60-
KOBbte.. aepntt(aJlbHble XOAbl nnoxo M3Y'feHbt M onaCHbi AllJI npo-
xO*AeHMJII.'
BepoRTHO, KaJKAblM yYHHenb (npoxoA) MMeeT CBOIO enb. KpoMe
roro, HeceT onpeAeneHHoe CMbtenoBoe 3Ha'4eHMe M HaKnOH Ka)t(AO-
ro M3 HMX. Bce m Bpnp,ocbl npeACToMT MCCJ1eAQBaTenJlM BblJlCHMTb
II 6YAYU4t!M. nMpa U4e coxpaHAer MHoro 3ara,qOK M HaCbtU4eHa
'4MtneBbtMM CMMBona.ut KocMoca...
nOlla IOT, '41'0 eCJ1M 6b1 OCb MccneAOBaTb OCHOBaHMe nMpa-
MMAJII, TO. o.swapy>KMnM 6bt 3aOC1pRIO CJI I( HM3Y KOHCTpYK MIO,
JIIBIIRIOU(YIOCJI 3epKaJlbHblM OTpa)f(eHMeM HCJA3eMHOM '4aCTM. Hawe-
MY B30py OTKpbtnCJI 6b1 OKTa3AP - OAHO M3 CMMMerpM'4HblX reo-
MeTpM'4ecKMx Ten, onMCaHHbtX nM4>aropoM (pMC. 4& CTp. 341).
MMCTepMM !'leT
6o)l(ecTBeHHble 3HeprMM OT
woe tMCXOAAT Ha septUM-
HY n . KOTOpaR
ynoAQ6nReTCR nepesepHY-
TOMy AeP8BY. c KPO
BHM3y M KopHeM ooepxy. 3
3Tom nepeBepHyTOfO Ae-
peoa MYAPOCTb T80puB
pacnpocTpaHReTCR OHMa
no HaKI10HHblM CT HaM M
p&CTeKaeTCR no MMPY.
316
'-IHcnoBBR aCTpononfR...
Puc. 47. (e'feHMe BenMKoM nMpaMMAW B fie3€!
c nQA]eMHblMM XOACIMM (ErMneT):
A - ycblnaJlbHM 4>apaoHa; 8 - BeHTMJUU4MOHHwe KaHanbl;
( - nepeAHee nOMelijeHMe ycblnanbHM4w; 0 - maBHaJI
ranepefl; E - nOAHMMalOU4MAcR npoxoA; F - rOpM30HTaJ1bHblM
npoxo.R, B M lCycblnanbHM4e >KeHbI $ipaoHa; G -
ycblnaJ1bHM >KeHbI 4>apaoHa; H - onycKalOlijMMCJI npoxOA;
I - sepTMKalIbHblM npoxOA; J - He60JIbWoe nOMelijeHMe
no nMHMM BeprMKaJlbHOro npoxoACI; K - nQA3eMHoe nOMelijeHMe
ECJ1M 3TO COOTBeTCTByeT AeMCTBMTeJ1bHOCTM, TO B nOA3eMHOM 'ta-
CTM nMpaMMAbi apxeonoroB M Y'4eHblX eU4e O>KMAaeT MHoro ClOpnpM-
308. OHM MOryr nOJlY'fMTb OTBeTbi Ha MHOrMe BOnpoc....
KcraTM, no 4>MJIOCo4>cKMM npeACTaBneHM"M, OKTa3AP CMMBOJlM-
3MpyeT MOAeJ1b COTBOpeHMJI MMpa: Ka)I(AOM CBoeM rpaHblO OH Ae-
317
rn8B8 7
EcTit MHeHMe
B TaKOM KOl1OC-
canbHOM apXMTeK-
typHOM TBOpeHMM,
KaK nMpaMM,D,a,
COOp}l}KeHMe KU-
Aoro xo,a,a BHYTPM
Hee CTOW1O 00l1b-
WMX el1oB ecIG1X
)KepTB.
MOHCTpMpyeT Ma1eMaTM tKYIO v MOAenb
Hepa3pblBHoM cornaCOBaHHOM CBJl3H
BOCbMH ero OCHOBHblX «nepB03neMeH-
TOB» (CM. COOTBeTCTBYIOU4HM pa3Aen
KHMrH). YAMBHTenbHblM COBnaAeHHeM
JlBnJleTCJI H TO, '4TO B Ka>KAOM CTopOHe
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318
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TMHe» M «npaBMJ1aM yxoAa M3
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KOMCTBe C nMpaM AOM, KOTOpa" Bne'4amAeT He TOJ1l t<O pa3MepaMM
3TOM MCKyCCTBeHHO C03AaHHOM ropbl, HO M OC03HaHMeM TOro, '4TO
COCTaBnJlIOU4Me ee KaMeHHble rnbl6b1 nepeMeU4aJ1MCb erMnTJlHaMM
npaKTM'4ecKM BPY'4HY1O. npM'feM MHoroTOHHble TecaHbIe KaMHM MM
IfY)KHO 6b1J10 He TonbKO nepeMe aTb no nececy RycTblHM BAonb oc-
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K TOMY >Ke nopa3MTenbHO M TO, '4TO OWM YMeJ1M nOArOHRTb Apyr K
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TO'4HOCTblO. K ApeBHMM 3OA'4MM HeBonbHO npoHMKaewbC1I60nbwMM
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CTpOMTenbHblM MaCTepcTBOM.
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COOPY>KeHMM, KaK nonaralOT, B Ka>KAYK> BOnJ10TMn HeKHM MMCTM-
'4ecKMM pyx. 3Ta TaMHCTBeHHaR CMna 06eperaeT nMpaM AbI AO Ha-
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319
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B COOTBeTCTBMM C pacnpeAeneHMeM 3HepreTH'4eCKOrO nOnJ' 3eMnH)
H C OnpeAeneHHOM opHeHTa HeM no CTopOHaM CBeTa.
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>KeT caM o eHHTb, HMelOT nH 3TH '4HCJ10Bble eTpbl nHpaMMAbi
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,3yeT BpeAHYIO 3HepreT11t<y KOMHaTbI (KBaPrM})bI, o4>Mca)<,.ecnM B HeM
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321
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TMe 100 TblC. eJ10BeK. ApeBHHe erMnTJlHe He OCTaBHnM CBeAeHHM 0
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MeHHHKH TonbKO CTpOJlT AOraAKM, KaK, MTblBaJl B03MO>KHOCTM ApeB-
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TeopMJI 8b1CKa3b1BaeTCJI B >KYpHane «Ha rpaHM HeB03MO>KHOro» B ClG-
The «KaK CTpOMnMCb erHneTCKMe nMpaMMAbf» (1999. 10).
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322
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npOTHBHOM CJ1Y'4ae KaMeHHble 6nOKH Bp'e3anMCb 6w pblXJ1b1M
neCOK, H Tal1-'HTb HX 6b1no 6b1 HeB03MO>KHO. AepeBJlJrnbiM HaCTHn
nepeA Ka>K,qOM nOACbmKOM neCKa CHMManCJI, a 3aTeM CHOBa YK-
naAblBanCJI. nHBHeBbie AO>KJ\M, KOTopble 3a BpeMJI CTpOMTeJ1bCTBa
m paMHAbi enY'4aJ1MCb HeOAHOKpaTHO, pa3MblBaJlH nec aHYIO Ha-
Cblnb, H ee npMXOAHnOCb BOCCTaHaenHBaTb.
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AeHb Bblwe '4eJ10B eCKHX B03MO>KHOCTeM (n03TOMY HeKOTopble aBTD-
pbl H BblCKa3b1BaIOT rHnOTe3b1 0 nOMOU4H HHOnnaHerJlH). Aa>Ke npocro
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MaJ10 TPYAa M BpeMeHH.
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323
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tfj AJ>eBHMX erHnTJlH MO>KHO B3J1Tb 3a
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npaKTM'4ecKMMM 3HaHMJlMM no pa3HblM HayKaM. TaM. OHM He TOllbKO '
BnaAenM MCKycCTBOM CTpOMTenbCTBa, HO XopOWO 3HaJ1M MaTeMaTM-
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324
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pa>KeHMJI MHOnnaHeTJIH B CKa4>aHAPiX M J1eTJlLqMe pllKeTbi AO CM)(
nop BCTpe'4aIOTCJI Ha HaCKaJ1bHblX pMcyHKaX ApeBHMX. BoT npM Ta-
KON paCK11(tAe c06b1TMM MOryr 6b1Ttt Bf10nHe 06ocHoBaHbI nlO6b1e
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? KoMy M KaK nepe.qm HaUl! pa3yMHOe HaCJIeACTBO? A teaK
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325
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npeAnOnO>KKreJ1bHO HaceneHHoro pa3YMHblMH CYU4ecrBaMH, B KOCMOC
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330
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. SenM'4MHbI MOp03a CHapy>KM, HO eCJ1M COCYA CBOAOM BC'!'RIXHyTb, TO
Ha rna3aX BOAa B 6yTbIJ1Ke npeBpaI14aeTCJI B neA M MO)Ke11>a30pBaTb
COCYA. npOA,YKTbI nOA TaKMM KYnonoM Aonro OCTaIOTOI CBe>KMMM H
He nopTJlTCJI. - 3TO, B03MO>ttHO, CBJl3aHO C nOAaBneHMeM aKTMBHO-
crM MMKp060B 3HeprMeM KOHyca.
ApxeonoraM M Y'feHblM npeACTOMT elite pa3"bJlCHMTb t4HOrMe He-
nOHJfTHbie HayKe MaTepMaJ1MCTM'4ecKOM TO'fKM 3peHHJI JlBJ1eHHJI, CBJI-
3aHHble C erHneTCKHMM nHpaMMAaMM, H, B03MO>KHO, OTKpblTb HO-
Bbie, 3aKOAMpOBaHHble B HHX CMMBonbi ApeBHMX MYApe40B, KOTopble
ycKonb3HyI1M OT BH..MaHMJI npe>KHMX 3KCneAMLtMM, noceU4aBWMX YCbl-
nanbHHLtbi apaOHOB.
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I.{HcnoB8R 8crpononfR...
349
rnABA 8
TAMHblE CMnbl KPMTEPMEB
Bonwe6Hbie pa3AeneHMH
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HHM BOCTOKa ne)t(aT 4MCJ1a 2,3 M 5. 3TM MCJ1a He CJ1Y'4aMHbI. B MHO-
rOTOMHblX H3AaHHJlX cne HanHCTOB no HeTpaAHLtHOHHblM 3HaHHSlM
pa3HblX crpaH EBponbi H BOCTOKa npHBOAJITCJI Hay Ho-4>Hnoco4>c-
KHe H HCT '4eCKMe 060CHOBaHMJI He06xOAHMOCTM BBeAeHHJI 3THX
'4HCeJI B HYMeponOrH'4eCKHe H 4>H-
noco4>cKHe cxeMbi MOAeneM ",Hpa
H AeJlTenbHOCTH" '4enOBeKa. Ho B
HaCTOJlU4eM H3AaHHH, paCCMaTpH-
BalOlqeM TonbKO OCHOBbi HYMepo-
norHH H '4H.cnOBOM aCTponorHH,
npHBeAeM nHWb HeCKonbKO pa3'bSfC-
HeHMM HCTOpM'4eCKOM npeAnOCbln-
KH Mcnonb30BaHHJI HX B HYMepo-
norHM.
npH H3Y'4eHHH OKpY>KalOlqerO
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paU4aTb BHHMaHMe Ha OCHOBHble
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Halil60nee III,3BecTHblMIiI
iii "YHIiIBepCallbHblMIiI» no
nplilMeHeHlil10 B HYMepo-
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Ha3b1B{ Mble ABOH"#HO-
rpO "#HBR iii rpoWlHO-
f7RTepH"#HBR CIilCTeMbi
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350
CBOMCTBa JlBneHMM M 06'beKTOB
COCTaBnJlIO HX cy Hocrb HX 6b1-
THJI. TaK B03HHKnO pa3AeneHMe
HG c/UCJ1G (CMMBOnH3MPYIO Me
CBOMCTBa, Ka4eCTBa) l.(enOZO (JlB-
neHHJI, 06'beKTa). HCJ10Bbfe MJ1H
HHble pa3AeneHMJI npM06penH
l/JUJ10col/JcKoe MCTOnKOBaHMe
n03TOMY HYMeponorMJI TeCHO
CBJl3aHa C 4>H1IOC04>cKMM eHH-
eM (npe>K,qe Bcero 4>Hnoco4>oB
BOCTOKa). AeJ1eHMJI 4enoro Ha
4aCTM B BMAe MCJ10BblX M 6YKBeHHblX CMM'B0J10B M3 tMJIOC04>MM
nepeKO'4eBaJ1H.B HYMeponorHIO, B KOTOpOM non MnM Heloe pa3BM-
n..e KaK B '4MCJ10BOM, TaK M B rpa4>H'4eCKOM Bblpa>KeHMM (reOMeTpH-
4eCKHe 4>Hrypbl). HcnoBbie pa3AeJ1eHHJI H npOH3BOAHble OT HMX
HYMeponorM CTanM Mcnonb30BaTb A11J1 COCTaBneHHJI Ta6nH4 H rpa-
4>HKOB «nporH030B».
TeopeTH'4eCKOe M npaKTH'4eCKOe Mcnonb30BaHHe ABOM4HO-TpO-
H'4HOM M TpOM'4HO-nJlTepM HOM CHCTeM B HYMepQnorMM paCCMOTpMM
n03AHee. BHa'4aJ1e yT04HMM OC06eHHOCTH Hcnonb30BaHHJI B CMCTe-
Max CMMBonOB H '4Mcen.
B 4>Hnoco4>cKHX H HYMeponorM'4eCKHX cxeMax H 4>oPMynax '4MC-
na 06b14HO He Hecyr KonM eCTBeHHOM HH4>opMa4 . OHH Mcnonb-
3YIOTCJI KaK CUltfSOJ1uC/ecKue 4>Hnoco4>cKHe eAMHM4b1 '4aCTH MnM 4e-
noro. npM'4eM B 3TOM 3Ha'4eHMM '4MCJ1a OTpa>KalO T nepeMeHHble
cBoMCTBa 4eJ10rO, M3MeHJlIOtqHeCJI B 3aBMC MOCTM OT BpeMeHH H CO-
6b1TMM >KM3HM, B KOTOpblX OHH Y4aCTBYIOT, TOf'Aa KaK caMM '4MCJ1a
06b14HO C<HC'4MCJ1J1IOT» nocmoRHHbJe cBoMCTBa.
TaUHb/e CMnb/ KpMTepMeB
CMMBonw M "Mens
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uteCTBeHHO MCnO/1b3ys1.
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IJfJ npt.1MeH eT HX no -npsl-
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351
rnaBa 8
TaK. '4TO >Ke npeACTaBnJlIOT C060M tiyMeponOrH'4eCKMe M 4>Mno-
co4>cKHe cxeMbi (HnM cHCTeMbI)?
T;JoUC/HOR CHCTeMa pa3JIH'4aeT B 06DeKTaX H JlBneHHJlX HHble Ka'4e-
CTBa, KOTopble B HHX TO>Ke nOCTOJlHHO npHcyTCTBYIOT, HO B pa3HblX
COOTHOWeHHJlx, TO onpeAenJleT MePY}"4aCTHJI B >KH3HH 3THX 06DeK-
TOB M JlBJleHMM. TpOM4HYK> CHCTeMY OTpa>KaIOT 4>Hnoco4>cKHe KaTero-
pHM UHb, RH H nepeXOAHoe COCTOJlHHe - 03H .(6e3 A3H CHCTeMa HHb-
JlH nepeXOAHT B ABOH'4HYIO). x.3HepreTH'4eCKOe COOTHow HMe
CHMBonH3HpyeT BOCTO'4HaJl MOHaAa: cnnereHHble B Kpyre, nepenHBa-
IO MeCJI Apyr B APyra ABe KannM 3HeprMM, a B Ka>KAo.M «ronOBKe».
KannH HMeeTCJI TO'4Ka - 3apo>K,qaIOIqMMCJI A3H. nOA KaTerOpHert MHb
nOHHMalOT MJlrKHe, nOABH>KHble, CJ1a6ble, He)f(Hble, ycryn'4HBble H npM-
cnoca6nHBalOU4HeCJI Ka'4eCTBa JlBneHH" HJlH 06DeKTa, a nOA KaTero-
pHeM JlH - Bce MX npOTHBOnOnO>KHOctM. AJH KOJ1H'4eCTBeHHO ypaB-
. . . . . . . . . . . . . . . . . . . . . . . . . . ... . . . . . . . . . .
· ,llsOH'lI'IfJfI CMCTeMa Bbl,Aen eT Bcerp,a npMCYTCTB e B ·
. 06b8KTaxM B1IeH anbTepHaTHBHble, npoTIilBOnoOO*Hble. .
· Ka ecTBa. KOH<t>YU.M nepBblM BbI,D.BMHyn M <t>Mnoco<t>clGt ·
· OOOCHOBaJ1 «,D.Be CTOPOHbI-, ,D.Ba O,D.HOBpeMeHHO npMcyr- .
: CTBYJOUU1X npoTMBDpe'fM B nlOOoM eneHMM M11M 06b8KTe. :
· TaK. OH BbWJ,enW11J1!8 CTOpoHbI CMMMerpMM Tena y OOb8K- ·
. TOB, Be et1t .. Tf\Pa 'feIlOBeKa. IJ1!8 nporMBOnOnO>ICHbIe CTo- .
· pOHbI BeUU1 (nepe,D,HlOtO M 3a.D,H1OfO), ,D.Ba npoTIilBOnOCTaB- ·
· neHH no eeprlncanM MMpa - 3eMnM M HeOa M T. ,D.. An .
. Ii1X Ta OH BBe11 ,D,BOWfHYfO CMCTSMY CMMBOnWieCKoro MC- .
· MCneHHR. C KTaK>T, .'4TO OKOH'iaTenbHoe npM3HaHHe 3ToM ·
. <t>W10c0<t>cK<WI CMCTeMbI cnO)KWI()Cb B V-III BB. AO H. 3.
.................. ........ ............
352
HOBeWHBaeT aJ1b1'epHaTHBHble Ka-
'4eCTBa B nepexOAHblM nepHOA. BbI-
AenJlnaCb rnaBHClft 4>Mnoco4>cKaJl
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3BeHO, A3H.
4Mcna 2 H 3 B 4>Hnoco<l>cKoM
nOHHMaHMH ApeBHHx pa3AenJllOT
l4enoe Ha 3neMeHTapHble '4aCTH,
06ner'4aJl n03HaHHe ero CyTH H 3a-
KOHoMepHoCTeM. COBpeMeHHbfe oKKynbTH e Y'4eHMJI npM3HalOT 3Ha-
'4eHMe 06eHx cxeM 4>Mnoco<l>cKoro pa3AeneHHJI KaK «MHcrpYMeH-
Ta» n03HaHHJI MHpa. COBMecTHoe Hcnonb30BaHMe a- n03HaHHH
3aKoHoMepHoCTeM l4enoro C nOMOU4blO cxeM ABOH'4HOAMM TpOH'4HO-
ro H MCJ1eHMJI Tenepb Ka>KeTCJI O'4eBMAHblM. Ho TaK 6b1no He Bce-
rAa. He cpa3Y 3TH 4>HnOC.KMe cxeMbi OUCKpemHOZO (pa3Aene-
HHJI l4enoro Ha '4aCTM) non MnH 06U4ee npM3HaHHe 4>Hnoco4>oB
ApeBHOCTH. Aa>Ke B OAHOM crpaHe -KMTae, «poAHHe.4>Hnoco4>HH
H oKKynbTH3Ma» (no Bblpa>KeHHIO AJ1. K063eBa) - MHorMe CTOJ1e-
THJI wna 60pb6a 3a 4>Hnoco4>cKHe MAeH M «HHCTpYMeHTbI» (T. e.
MeToAbI, cxeMbI) B n03HaHHH. npH3Hasanacb opHeHTal4MJI TonbKO
Ha ABOH'4HOCTb MnH TpOM'4HOCTb HC'4HCJ1eHMJI Ltenore, T. e. «3eMHoe»
KOH y uaHcmBo('4eTHOeHC'4HcneHHe)npoTHBonOCTaBnftnOcb«He-
6ecHoMY» oaocu3MY (He'4eTHoMY HC'4MCJ1eHHIO). KOH4>Yl4HaHCTBO
3apoAHnocb B VI-V BB. AO H. 3., a AaOCH3M - B IV-III BB. AO H. 3.
B ApeBHeKHTaMCKMX TpaKTaTax ynoMHHanOCb, '4TO OT KOH4>Yl4HJI
«tieJ1b3J1 6b1no yCJlblwaTb paCcy>KAeHHM 0 He6ecHoM nyTH», a OAHO-
ro M3 C03AaTeneM AaOCH3Ma - 4>KyaH-l43b1 - ynpeKaJ1M B OAHO-
60KOM npHcrpaCTHH K «He6eCHblM» np06neMaM.
TaHHble CUflbl KPHTepHes
ComacHO Y'teHMIO
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BeU.l.eM M R811eH -
CTByIO B MX -
KOM pa3BMn1M, 06ecne-
Maatdt cak> MX e-
CTBOBaHMe, 6bffi.1e.
353
rnasa 8
nmepM'4HaJI CMCTeMa 6b1J1a
peAHblM HYMeponOrH.'4ec-
KHM warOM cyMMMpoBaHMJI
4>Mnoco4>cKoro onbiTa no-
3HaHHJI MHpa: coeAMHeHHe
Y>Ke H3BeCTHbiX '4MenOBbiX
OCHOB (2 + 3 - 5) Aano CJ1e-
AYIOU4YIO 3neMeHTapHYlO
eA"HMLty «norM'4eCKoro»
pa3AeJ1eHMJI MHpa Ha 4>Hno-
C04>cKYIO cxeMY ero n03Ha-
tU4J1 (A. . J<o63es).
3TM 4>Mnoco4>cKHe cxe-
Mbi n03HaHHJI ynoMMHalOTcSI
B ApesHeM TpaKTaTe «Lt30
'4>KyaHH» (510 r. AO H. 3.):
«Or pO>K.O,eHMJI BeU4aM M JlB-
neHMJlM npMCYU4H ABQM'4-
HOCTb, TpOM'4HOCTb M nJlTe-
pH'4HOCTb, Y'4aCTBYIOT B HX KapMH'4eCKOM pa3BHTHM, o6ecne'4HBaIOT
caMO MX CYU4eCTBOBaHMe. 6b1TMe». M Aanee: «...'4enOBeK ABOH'4eH B
06naAaHMM neBoM M npaBOM nonOBMHaMM Tena; He60 TpOM'4HO B
06naAaHMH TpeMJI QpMtJfTMpaMH - ConH eM, nYHOM H C03Be3AHJI-
MM; 3eMnJl nJlTepM'4Ha B o6naA HMM nJlTblO 3neMeHTaMH» (LtMT. no:
Ko63eB A. . eHMe 0 CMMsonax M '4MCJ1ax, c. 93).
nOHJlTMe.-.o nJlTM 3neMeHTax M nJlTepH'4HOH CMCTeMe npH06pe-
TaeT OC06b1M pe30HaHC B rpe'4eCKOM M KHTaMcKoM 4>Mnoco4>MJlX,
TaK KaK BXOAHT B COCTaB «4>YHAaMeHTaJ1bHblX HYMeporpaMM»-
TpMrpaMMbI, reKcarpaMMbI, B cxeMbi no wy, X3 ry, HHb-JlH, Y CHH H
ntITWA aneM8HT
HeKOTOpble 4>W10c04>bI rpe-
lUIIM BbI,D,e11SUlM nATbiM ane-
MeHT, Ka'fecTBeHHO OTnM alO-
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(.Map01HanbHbtM 3neMeHT.):
nnaToH (427-347 n: JJ.O H. 3.)
ynoMMHaeT 0 HeM B TPaKTaTax
. TMMeM. M .nocne3aKOHMe.,
ToTenb (384-322 n: JJ.O
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4>Mnoco<I>bI. M 60nee npM3HaH-
HOM B EBpone OCTanaCb eTbI-
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TBOpeHMA MMpa».
354
TSHHble CHnbl KpHTepHeS
APyrHe nOcrpOeHHJI, Hcnonb3yeMbie B HYMep0J10rHH. HanOMHMM
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nJlTb 3neMeHTOB MHp03AaHHJI (nJlTb CTHXHM): BoA,Y, OrOHb, Aepe-
BO, MeTaJ1n, nO'4BY. fpe'4ecKHe 4>Hnoco4>bI roBopMn l4eTblpex
3neMeHTax: BOAe, B03A,YXe, OrHe, 3eMne.
3 '4eTbipeX 4>Hnoco4>cKMX 3neMeHTOB MMp03AaHHJI OAHH rpe-
eCKMM 3neMetiT - B03A,YX - OTCyTCTByeT .tOtTaMCKOM neHTaHa-
Ae, a ABYX KHTaMCKMX 3neMeHTOB - AepeBa M MeTanna - HeT B
rpe'4eCKOM TeTpaAe. HerO>KAeCTBeHHbI nOHJlTHJI rpe'4ecKoM «3eM-
nH» H KHTaMCKOM «nO'4BbI» (A. ; K063eB). TaKMe pa3J1M'4MJI B BOC-
npHJlTMM nocrpoeHM MMpa BOCT04HblMH M eBponeMCKHMM 4>Mno-
co4>aMM CBJl3b1BC!I01' C OCOOeHHOCTJlMM «reHeTH'feCKoro pa3BMTMJI»
HX Hay'4HOrO B033peHHJI. TaK. ApHCTOTeJ1b'S «MeTa4>tQHKe» nMCaJ1,
'4TO rpe'4eCKJ1M '4eTblpeX4neHHblM Ha60p CcI>OPMHpOB' CJI B TpaKTa-
TaX 3MneAOKJIa nOCJ1e TOro, KaK TOT MI1H MHOM BeA,YU4HM 4>Mnoco4>
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B03Ayx, fepaKJIHT - OrOHb, KceHo4>aH - 3eMnlO. KHTaMCKMM >Ke
nJlTH'4neHHblM Ha60p JlBMnCJI pe3ynbTaToM He CMHTe3a, KaK y rpe-
'4eCKHX 4>Hnoco4>oB, a aHaJ1H3a COCTaBnJllOutHX MHp03AaHMe 3ne-
MeHTOB, T. e. pe3ynbTaToM BblAel1eHHJI H3 60nee 06WMpHOro nepe'4-
HJI OCHOBHblX KaTeropMM. npH'4eM HH OAHH M3 KHTaMCKMX 3neMeHTOB
HH AO, HH nOCJ1e ero c4>opMHpOBaHHJI He C'4HTaJ1CJI eAHHbfM 06U4e-
MHpOBbiM cy6crpaToM. «,l\a 3TOro M He Morno 6b1Tb, - nMweT K06-
3eB, - nOCKonbKy, C OAHOM CTOpOHbI, COCTaBnJlIOU4Me ero 3neMeH-
Tbi cyTb TaKOBbie He B cy6cTaHLI,HOHHOM, a B 4>YHKLtHOHanbHOM
CMblCJ1e (HX ponb 3aBHCHT OT 4>Hnoco4>cKHX OnepaLl,HM C KaTerOpM-
JlMH. - npUM. osm.), C APyroM CTOpoHbI, B Ka'4eCTBe eAMHoro 06-
uteMHpOBoro cy6cTpaTa KMTaMCKHe MblCI1HTenH paCCMaTpMBanH
355
rn8B8 8
nHeSMY - qu, aHaJ10r TOro Bo KoropwM Kat< pa3 OTCyTCTByeT
B HX Ha60pe» (Y eHMe 0 CMMBOJ1aX M '4MCJJaX. c. 288).
npH HeKoTopoM 3T M0J10r ecKoM cxoACTBe KMTaMCKoro M rpe-
'4eCKOro repMMHa «3neMeHT» MMeeTCJI ern cS»u1oc Koe OU1M'4Me
OT HHAMMCKOro aHaJ10ra «6xyra» (OT marona «6b1Tb»). fpe'4eCKoe
nOHJlTHe «3neMeHT» MMeeT HeKoTopyao 6nM3OCTb K MHAMMCKOMY
nOliJlTMIO «6xyra», MaTepHaJ1M3YX)lije'1Y pe3yJ1bTaThf KaKOM-nM60 Ae-
JlTeJ1bHOCTM '4enoBeKa HnH npMpoAbi. Y fpe'4eCKMX MwcnMreneM 3ne-
MeHT «BOAa» CBJl3aH C BOAOM KaK C cy6cTaH14MeM. C TO'4KM 3peHM
KHTaMcKMx 4>Hnoco4>oB, 3neMeHT «BoAa» CB 3aH C BOAOM nMWb
4>YHK4HOHaJ1bHO M MMeeT pe30HaHc C TalOtMM nOHIITMAMM, KaK BeC-
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f pel.lecKMe M KMTaMCKMe Ha3BaHMJI 311eMeHT08, cocraBRH MM-
po3AaHHe. a TOI.fHee npoJlB11eHMe )f(M3HM, He OOHMMaTb y.JK0,
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CKMe KaTefO()MH. B OT11MtfMe OT KMTa fJ)e'M!CKMe 4Mmoc nOA
3neMeHTaMH NMP03AilHHJI 6anee n0APi!3YMeBanM MaTepMaI1bHl1Ie co-
CTaBnJlIOU4Me cyTM BeU4eM. 3TM pa3I1tNM$! Koro BOCnpMRTMA
MHpa Orpa>KaJ1MCb Ha HYMepoJ1OllNeC1<MX MCTOnKOBaHMRX.
o TOM, '4T0 nHTb 311eMeHTOB 4Mmoco$cKoii CMCTeMbi M3Mefi\fMBbi B
CBoeM COAep>K.IHMM H oTpa>KaIOT HaM60nee atnyaJ1bHbIe CMIOMMHyT-
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nepo (1950). OH nMCaJ1: «nJtTb 3JJeMeHTOB 6wnM B3J1'1D1 143 OOwMpHO-
ro Ha60pa 'iMCJ10BbIX lO1accM4>MKa4MM BCeX BeU4E!M... K KOTopbIM 6bU1
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'4neHHble rpynnbl, KOTopble... 6b1J1M HaM60nee MHOro'4MCJ1eHttlll, M
npeBpaTMJ1M MX nH60 B caMH nRTb 3neMetfT08, COOTBeTCT&yIOU4MX on.
peAeJ1eHHblM OBHJlM (LtBeTa 06pa30BaltM fbnb 3neMeHTOB 3peHMJI.
356
3BYKM - nJlTb 3neMeHTOB
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sa 06ytecTBa - cyn nRTh
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cyTb rbn'b 3neMeHTOB C KOCMO-
OOrM'feCKOM KH :JpettMJI».
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CTM, B Csa f1McattMftx. Tat(. B «EBaHrenMM OT cJ)HJ1Hnna» npHBO-
AJITOt 'fe1'Wpe o4JcKMX CMMBona cyn1 >KM3HH: «Xo-
3JlMCTBO MMpa - M3 'IerWpeX BMAOB. B xpaHHJ1M HX COAep>Kar. BoAY,
3eMJMO, Bo3AYX M Cser. M xtmMcreo 6ora. nOA06HO 3TOMY, M3 eTblpex:
M3 8epw, H bI, nlO6eM M 3HaHM". Hawa 3eMnJl - :no Bepa...
80Aa - 3TO ItCJt'OpOM (Mal) mrraeMCJI, Bo3AYX - 3m nK>60Bb,
6narQAaPJI (KOYOpoM) Mal paaeM. a CBeT - (3m) 3HaHMe».
MTaK. nOA 311eMeKJaMM tj)MJtOC*KMX cxeM M HYMeponorM 4 ecKHx
4>0pMy11 CJ1e.qyer nOHMMa'Tb RBJ1eHMJI, }UlOBMJI MJlM MaTepHaJ1bHble
o6DetcrbI, KOTOpYe RBMIOTCJI maBHWMK. OCHOBHblMM «y'faCTIiHKaMM»
npoJlBJIeHMI1 )b3HM. 3neMeHT «3eMnJt» He 06J13aTenbHO AOn>KeH 6b1Tb
3eMlM!i B 6yuanbHOM CMWCJIe - 3TO MO>KeT 6bITb CMMBon HaAe>r<,qbl,
onopw, 4>YHAilMeHTa SKora-TO AYa. 3neMeHT «B03A,yX» He 06J13a-
TenwtO 0603Ha'taeT taM B03AYX - :no MO>KeT 6b1Tb CHMBon m06BH,
B3aMMOOTHO&UeHKM MaCAY napntepaMM, KOTOpwe M3MeH4MBbI, KaK
TaUHble ClI1flbl K{)MTepll1eB
y eepot tfYM8POI1OOI-
't8Ct(M8 CXeMbl a npeA-
CKa3b1BanH MaTepHaJ1bHJ,je
K3AAeHeHMR B )KI43HU< '\e.nose-
Ka, a KHTat4cKHe H}'Mepol1OrH
,QenanH 8KlJeHT IiCi AestTel1b-
HOCTH e.ndseia, BbI.D,eJ1RI1H
CMJ1bI, cnoco6cT8 e Ma-
T H3a H pe3ynbTara
ero AeRTenbHOCTlif, a He caM
ICOHe4Hbli:4 pe3ynbTaT.
357
rnasa 8
S03AYX- tiO TO>Ke 06ecne4H-
BalOT HM ycnOBMJI COCYU4e-
CTBOBaHMJI,cotpyAHM 4 ecTBa,
M T. A. 3Ha'4eHHe 3neMeHTa
>KM3HM Y Ka)t(Aoro '4eJ10BeKa
CBoe, M 3TO Y'4MTblBaIOT B HY-
MeponorH'4eCKHX 4>oPMynax.
CamacHo «Bonwe6HOMy»
pa3AeneHMIO Ltenoro Ha '4a-
CTM M fCMarM4ecKHM» cxeMaM
ABOM'4HO-TpOM'4HO-nJlTepM'4-
HOM' B3aMMOCBJl3M 3neMeH-
rOB, MO>KHO npOH3BOAMTb
Ka66anMCTM eCKHe paC'4e-
TbI, npeACKa3b1BalOU4He KOHe'4HbfM pe3ynbTaT B3aMMOAeMCTBHJI BbI-
AeneHHblX «3n MeHTOB». nOCKOnbKY 3neMeHTbI HYMeponOrH'4eCKHX
cI>oPMyn CHMslJtH3MPYlOT nM'4HOCTH nlOAeM M MX AeMCTBHJI, TO, 3Ha-
'4MT, B03MO>KHO «no '4HCJ10BblM pMTMaM >KM3HH» npeACKa3b1BaTb 6y-
AYU4ee.
0Icxy...TM3M ..... C8I"OAtfR
B OM rpaKTaTe
..{Mtib-Lt3bI.. nsm, 3neMeHTOB
CMMBOnK3&o1PYlOT «nSlTb nocro-
RHClB": ryMaHHOCTb, cnpaBeA-
I1MBOCTb. 611aronpMCToMHOCTb,
paayMHOCTb .... 6narOHa,Ae)l(-
HOCTb. B 3M....H oM ip8-
,D,HLI,H.... HM COOTBeTCTByIOT rpe-
'«»1e aHa11Of1iI: sepa, Ha,Ae)l(,Q,a,
11I06oeb.... 3HaHHe ('*'1bIpe 311e-
MeKTa 0CH0BbI ).
HYMeponOrMileCKMe ycnoBHOcTM
Ka)t(AaJl HYMeponOrM'4ecKaJl4>opMyna MMeeT «He6ecHDe» (no Kpyry
neHTarpaMMbI) H <<3eHHCJe» (no ny'4aM 3Be3AbI) C4MTblBaHMe 3neMeH-
TOB M coo11liraBytOU4ee rpa4>M'4ecKoe Bblpa>KeHHe: 4>MrypOM «KPY-
roBOM» (n THyronbHOM) M 4C3Be3AHOM» neHTarpaMMbI. nOA'4epKHeM,
'4TO TepMMHbI ycnOBHbI. nOCJ1eAHH TepMHH npI4eMJ1e'" AllJI BblAeJ1e-
HMJI OCo6eHHOCTM HanpaBneHHJI C'4HTblBaHHJI (no nY'4aM 3Be3AbI), TaK
358
KaK B reoMeTpM'feCKOM CMblCJ1e Tep-
MMH «neHTarpaMMa» y>Ke BKnIO'4a-
ernOHJlTMenRTMKOHe'4HOM3Be3AbI:
«neHTa» - nJlTb yrnoB, MMMeT-
pH'4HO OTCTOJlU4MX Apyr OT Apyra M
06pa3YIOU(Hx pa3HoyronbHYlO 4»M-
rypy, KOTOPYIO MO>KHO BnMCaTb B
Kpyr. nO:nOMY npH MCnOnb30BaHHM TepMMHa «neI\TarpaMMa» CJ10BO
«3Be3AHaJl» MnM «3Be3Ail» B Hyto1eponOrH'4eCKMX TeKCTax '4aCTO ynyc-
KaeTCJI. MbI, OAHaKO, 6yAeM ero perynJlpHO HcnOnb30BaTb, '4T06b1 pa3-
nM'faTb ABa BapHaHTa C'4HTb1BaHMJI neHTarpaMMbI.
. TepMHH 4<KpyroBCUI» neHTarpaMMa COOTHeceH C rpa4>M'4eCKMM
BW MeM K.a>KAOO> yma nocpe.qcTBOfo4 nodIe,qoeaTenbHOR) (pMC. 49, a)"
a B 4<3Be3AHoM» neHTarpaMMe - «npocKaKHBaIOU4e"*(nponYCKaIO-
aqero) Ka>K,qblM 6nH>Ka WHM yron coeAMHeHMJI. B pe3ynbTaTe y nep-
BOM 4>Mrypbl cepeAMHa n a y BTOpOM nepe'4epKHyTa nMHMJ1MM, HO
TaK, '4TO CBOHMH nepece'4eHMJlMH OHM >Ke 06pa3Y1OT B cepeAHHe nep-
BYIO 4>Mrypy, nepeBepHYTYIO M B MMHManope (pMC. 49, 6).
3Be3AHaJI neHTarpaMMa cBeeM
cepeAMHOM Kaf:( 6b1 nOATBep>K,qa-
er «poACTBeHHoCTb» c KpyroBOM
neHTarpaMMOM (3aWTpMXoBaH-
HaJl '4aCTb 4>Hrypbl Ha pHC. 49,
6). cJ»Hlioco4>CKoe 3Ha eHMe
4»Hrypbl ycMnMBaeTCJI npMcoe-
AMHeHMeM K Ka>K,qOM ee CTOpO-
He TpeyronbHHKa - CHMBona
TpOM'fHOCTH(MHb-JlH- H)B
nJlTepM'4HOM 4>Mrype 3Be3AbI.
TaifHbl8 CHnbl KpHrepH8S
H8 38U8ncy
KpyrOBytO- neHTarpaM-
My H83b1Ba1OT eU4e «He-
OecH -, a «3 -
_ - «3eMHOH-.
a
6
O@
Puc. 49. CxeMbi 4CKpyroBoM» (a)
M «3Be3AHoM» (6) neHTa-
rpaMM, BnMcaHHblX B Kpyr
(Kpyr - CMMBon He6a,
He6ecHoM C pbl)
359
rnasa 8
KpyroBaJl neHTarpaMM! npM6nM>Ka-
eTCJI no 4>opMe K KPYry, H n03TOMY
C'4HTaIOT, 4TO OHa MMeeT npeHMYU4e-
CTBeHHO «He6eCHble» Ka'4eCTBa.
3Be3Aa pe3KO OTnH'4aeTCJI no 4>opMe
OT I<pyra M nHweHa ero Ka'4etTB-
eM npHnHcblBalOT «3eMHble» CBOM-
CTBa. «3Be3Aa, paCnanO>KeHHaJl Bep-
XYWKOM BBepx, - CMMBon JlH, BHyT-
pH Hee 0603Ha'4eHa neHTarpaMMa
BepxywKoM BHM3 - 310 MHb, n0310-
MY 3Be3Aa HMeeT nnOAOTBopHoe, HnH
60raToe B oKKynbTHoM MCTo.nKOBa-
HHM, coeAMHeHMe «MY>KCKoro» .. «>KeHCKoro» Ha aJ1, B3aHMOnOpO)f(-
AaIOIqHX pa3BHTMe.
AnJl Hac., >KHTeneM 3eMnH, «3eMHaJl» neHTarpaMMa - 60nee
CJ10>KHaft reo..eTpMLleCKaJl 4>Hrypa, 4eM «He6eCHaft» (KpyroBaJl), H
no HH4>opMaLtHOHHOM nepeAa'4e OHa 60nee LteHHa H 60raTa, eM
«He6eCHaft». nonaralOT, '4TO «He6eCHaJl» neHTarpaMMa nepeAaeT
HaH60nee Ba>KHble, rnaBHble MOMeHTbI CyTM, KOTopble yrO'4HJler, Ae-
TaJ1H3Hpyer «3eMHaJl» neHTarpaMMa.
B npHBeAeHH Aanee nepe'4He 4>opMyn (CM. pa3Aen «11HHeM-
Hble 4>opMynbl MarM..H» m. 9) HeT CHMBonOB no yTO'4HeHHIO Bblpa-
>KeHHJI «OCHOBHOM 4>opMynbl»: «He6ecHaJl» OHa MJU1 «3eMHaJl». npH
ee HanHcaH - «on» '- '4aU4e Bcero MMelOT B BHAY «He6ecHblM»
BapHaHT eTpH4eCKOM 4>Hrypbl, a PJlA 6YKBeHHblX CHMB0J10B B
nHHeMHot1 4>opMyne COCTaBnJlIOT npH C4HTblBaHHH 3neMeHTOB no
KPYry (TaKoro HanHCaHHJI, HanpMMep, 06b1 HO npHAep>KHBaeTCJI
A. . K063eB).
0cH0ew tfYM8POIIOI"MM
«3Be3,D,Ha . .., e«pyro-
aa . neHTarpaMMbI B
HyMeponor..,.., C "'Ta-
IOTC KapMi-1 ecIG1M'"
<pi-1rypaM..,. co,o,ep)l(a-
LU..,M.., KOA HaweM
3eMHOM KapMbI, - ee
i-1 nbiTalOTC MaKC"'-
ManbHO nOl1HO pac-
Wi-1<PpoBaTb OKKyl1bT..,-
360
TaUHble cunbl KpUTepUeB
OAHaKO «6eCCMMB0J1M'4ecKOe», o6U4ee 0603Ha'4eHHe OCHOBHOM
4>opMynbl TepMHHOnOrH'4eCKH 06beAHHJleT BCe ee 4>OpMbI HYMepO-
nOr:M'4eCKoro Bblpa>KeHMJI. AnJl 4>opMynbl 2 on 3TO COCTaBHT CMMBO-
nM'4eCKHM PJlA: 0200, 020n, *20n, *200, a TaK>Ke MX npoH3BoA-
Hble. nOA'4epKHeM, '4TO s 4>opMyne 2 on CHMBon crpenKw'":Yka3b18aeT
He TonbKO pa3Hble HanpaBneHMJI 3HeprMM f1Q nHHHJlM ee reoMeTpH-
'4eCKOM 4>Hrypbl, HO M pa3Hble Hal.jana npH «IJ.PJlM_OM H «06paTHOM»
C'4MTblSaHHM 3neMeHTOB (pHC. 50). npH'4eMo3Ta .bc06eHHoCTb BXO-
AMT H B 06paTHbiM npo ecc: HanMcaHHe reoMeTpM'4eCKOM 4>Hrypbl
no nMHeMHoM 3anHCH 4>opMynbl. .
OCTaHOBHMCJI Ha 3TOM npHMe'4aTenbHOCTH nOAP06Hee.
npM rpa4>H'IecKoM M nMHeMHoM 3anHCH npoH3BoAHOM OT OCHOB-
HOM $>pMynbl - «on» - Y'4HTblBaIOT HYMeponOrH'4eCKYIO ycnoB-
HOCTb. npOTHBOnOnO>KHble '4aCTM neHTarpaMMbI HMeKit MHb-JlHCKoe
pa3AeneHHe 4>Hrypbl KaK no sepTHKanH, nposeAeHHoM '4epe3 ee Bep-
XHHM 3neMeHT (neBaJl OT '4HTaTenJl CToPOHa 4>Hrypbl COAep>KMT 3ne-
MeHTbI to cBoMCTBaMH JlH, npaBaSi - HHb), TaK H no ropM30HTaJ1M
(BepXHJlR aCTb 4>Hrypbl- JlH, HH>KHJlJI- HHb) (CM. pHC. 50). nPH
TaKOM pa3AeneHHH 3J1eMeH-
Tbi sepxHero neBoro yrna H
HH)f(HerO npaBoro yrna -
«rnaBHaJl AHarOHaJ1b neH-
TarpaMMbI» - YCMneHbI
«ABOMHblM pe30HaHcoM»: M
npM BepTMKaJ1bHOM, H npM
ropH30HTanbHoM pa3Aene-
HMH 3neMeHT A JlBnJleTCJI
JlHCKMM, a M - MHbCKHM.
HHblMH CBOMCTBaMH 06na-
a 6
H 0 Hb 0 H
n "Hb
8 I M 8 M
PUC. 50. Q)opMyna 2 on c «npRMblM» -
AOnMB (a) M «o6paTHblM» -
BMnOA (6) C'IMTblBaHMeM
ee 3neMeHTOB
361
rnasa 8
a
6
AalOT pacnOnO>KeH-
Hble no AMarOHaJ1M 01
HMX 3neMeHTbI B H n,
KOTopble npH BepTM-
KanbHOM pa3AeneHMH
MMelOT MHb-JlHCKOe
napHOAMarOHanbHoe
CO'4eTaHHe (COOTBeT-
CTBeHHO 3neMeHTbI n
M B), a npM nonepe'f-
HOM pa3AeneHMM 4>H-
rypbl npM06peTalOT
IIH-MHbCKoe 3BY'faHMe,
T. e. MMelOT «npoTMBO-
nono HblMn03Hepr
TMKe pe30HaHC». Hy-
MeponorH nonaralOT,
'4TO He H3MeHJlIOU4He
CBOH MHb-JlHCKMe CBOM-
CTBa M OTnH'4aIOU4HeCJI
C80HM nocrollHCTBOM
31IeMeHTbI neHTarpaM-
Mbi (A H M Ha pMC. O) elOT vH 60nbWHe 3HepreTH'4eCKHe B03MO -
HOCTM, nOABH)KHOCTb H B03AeHCTBHe no cpaBHeHHIO C OCTanbHblMM
ee 3neMeHTaMH. neBblM"'8epXHMM JlH'CKHM yron neHTarpaMMbI C'4HTa-
eTCJI «ZI10tIlJj.ll'f»: Ha pMC. 50 ero 3aHMMae:r 3neMeHT A.
n03Toky B tpa4>M'4eCKOM cI>oPMyne rnaBHblM 3neMeHT rpa4>M'4eC-
KOM 4>oPMynbl «on» 06b1'4HO pacnonaralOT Ha neBoM CTopoHe neH-
TarpaMMbI (pHC. 50, a; 51, a; 52, a). ECJ1M HanpaBneHMe OT 3Toro
M
f<8(=:t
B n
M
.n O
n
6(; = JJ.MonB1' 6;; = BnOMjI,J,
B
z
M M
Atr o
B;'n B'n
6(; =1' OBMfIl]. 6;)0 =,J, JJ.nMBO
PUC. 51. KpyroBwe (a, 6)".. 3Be3AHwe (B z)
neHTarpaMMW cJ>oPMYJ1W 6 on
c «npJlMwM» (a, B) M «06pantWM» (6, z)
C MTWBaHMeM 3J1eMeHTOB
362
3neMeHTa MAeT no aCOBOM crpenKe, TO 6epyT B Ha'4aJ10 nMHeMHOM
4>opMynbl 3neMeHT BepXHero neBoro yrna neHTarpaMMbI, MMelOU4e-
ro CBJl3b C «3HeprHeM He6a»: 3neMeHT AHa pHC. 50, a; 51, a; 52, a.
ECJ1H 3HeprHJI B 4>oPMyne M,qeT npoTHB '4aCOBOM CTpem ":1t, 9 C'4MTbI-
BaHHe Ha'4HHaIOT C «3eMHoro» 3neMeHTa HH>KHero neBoreyrna neH-
TarpaMMbI, 6nH>Ke pacnOnO>KeHHOrO K 3eM'ne: 3neMeHT B Ha pMC.
50, 6; 51, 6; 3neMeHT 0 Ha pHC 52, 6. T aKHM a6PaJOM, B TepMMHono-
rHH c06nlOAaeTcJI 4>H-
J10C04>CKHi4 npMHLtMn a 6
MHb-JlH no BepTHKanH M M
H ropH30HTamt, KaK B t pB
Kpecre X3 ry. A B
B cHny H306pa>KeH-
Horo Ha pMC. 51 nOJ1y'4a- 0 n 0." n
eM CJ1eAYIOU4He BapHaH- _
Tbi «KpyroBblX» 4>opMyn 7 on = 11MB not 700= OnBMl1.J.
neHTarpaMMbI C CHMBO- 8
nHKOM «on»: 60" -
AMOnB H 60n - BnOMA.
EcnH Ha reoMeTpM-
'4eCKOM 4>Hrype OCHOB-
Hoi/4>opMynbl npoBoAAT
C'4MTblBaHHe 3neMeHTOB
ee npOUJBOoHoi/ 4>op
Mynbl, rOBOpJlT, '4TO nep-
BaJl 4>opMyna JlBnJleTCJI
HYMeponorH'4eCKOM MaT-
pMLtei4 BTOpOi4. nepeA
HYMeponorH'4ecKHM BbI-
TaHHbIe CHnbl KpHTepHeB
z
M M
A1;r B
0;' n to' n
7 on = t BOMIll1 700 z.J. I1n OB
Puc.52. KpyroBble (a, 6) M 3Be3AHble (8, z)
neHTarpaMM.bI cl>OPMYJ1b1 7 on
c «np MblM» (a, s) M «06paTHblM» (6, z)
C MTblBaHMeM 3J1eMeHTOB
363
rnasa B
pa>KeHHeM MarpM(4b1 CTaBJIT 6YKBY «M»
HanpMMep, M60n- nOMAB 03Ha aeT,
'ITO 60n RBnJleTCJI MaTpMtteM J-onBAM.
OHM MMelOT oOUHOKOsoe pacnOnO>KeHMe
3neMeHTOB neHTarpaMMbI, HO pa3Hoe Ha-
'4aJ10 C'lumbISOHUJI
4aCTO MCnOnb3YlOT cOKpaaqeHHblM
BapMaHT HanMcaHMJI $opMynbl. COKpa-
U4alOT HanMcaHMe CMMBona Kpyra H
crpenKM npJlMOrO HanpaBneHHJI. Ha-
npaBneHMe C'fMTblBattMJI 3neMeHTOB
<t>opMynbl YKa3bfBalOT crpe11KOM: no '4aCOBOK crpe11Ke - «npJlMoe»
(CMMBonbf «t» MnM « ») .. "POTMS aCOBOM CTpeJ1KM - «06par-
Hoe» C'4MTb1BaHMe (CMMBonbi «-1..» MnM «+-»). npM HanHcaHHH $>p-
MYnbl «on» M ee npoM3BOAHOM CHMBonbi KpyrOBOM neHTarpaMMbI
(<<0») He CTifJlT nepeA «MMeHeM» 4>oPMynbl, a crpe11Ky ( ) «npJl-
MOro» KT'Y9aHMJI He CTaBJIT HCij\ «MMeHeM» 4>oPMynbl - «on». Ho
eCJ1M $>pMyna HnM ee iTpoM380,1\HaJl MMeeT «06paTHoe» C'4HTblBa-
HMe MIIM «3se3,qHYIO» neHTarpaMMY, TO HX CMMBonbi nHWyT 06J13a-
TenbHO: CMMBon 4>Mrypbl CTaBJlT
nepeA 4>opMynoM, a crpent<y Ha-
npaBneHMJI C'4HTblBaHHJI 06b1'4HO
nMwyT nocne MJ1M HaA «HMeHeM»
4>oPMynbl 6On. HanpMMep, <t>OPMY-
na 60n MnM t6 on MTaeTCJI KaK
KpyroBaR C npJlMbiM (C'fHTblSaHM-
eM) ABM)KeHMeM 3HeprHM no ee
3neMeHTaM. rpa$M'4ecKHe CMMBo-
nbl 4>Mrypw neHTarpaMM '4aCTO
Ha 38MeTKy
HanpaaneHHe M-
TblBaH.m, H8 MHaSf
C rnaBHOfO 300-
MeHTa, CMMBOnM-
3MpyeT HanpaB11e-
HMe A8'QCeHMSf
3HeprMM no 300-
MeHTaM cSx>PMYnbl.
nPM Hanpa8l1ett....
C\fl4TblBaHM AetrrarpaM-
Mbi M I1MHeMHOM 3af\MCM
4>oPMY11bI Y'fMTblBalOT
HaXO Me ane 08
Ha 6e'AH-MHbCKOM Mm1
COOTBeTCTBeHHO OOBO-
npaooM CTopoHe.
364
nepeAalOT 6yKBCMtM: co- - :no «0» (<<K'pyD), a «*» - «3» (<<JBe3-
IJP.»). B 3roM cny'4ae «38e3Atf()e» Bblpa>KeHMe 4>opMyllbi 6 on C Ha'4a11b-
HbiM C'4MTb1BaHMeM C 3I1eMeHTa 1\ npoTMB l.&aCoaoM CTpe11KM 6yAer MMefb
B : M3600-1\. 6yKBa M 8 Ha'W1e 4>opMYllbi yRa3b1BaeT, 'fTP & AiUfHOM
MCnOnHeHMM rpa$M'4eCKaSl4>opMyna JtB.IUIeTCJI Ma1pM bl6 Of\
T. e. sapuaHI'1JOH ee 8b1pa>KeHMJI (a 3Ha'4MT, M ClJyHKqMM, 3Ha'4eHMJI).
KaK YKa3b18anOCb, AllJl6 on Ha pMC. 51, a K"MM no MeCTOf1011O-
)KeHMIO &iAYr 3J1eMeHTbll\ M B, a MHbCKMMM -:'.0 M n. KaK BMAMM, JtHC-
!<aft CTopoHa ()yKsanbHO nepeAaeT HanpaBl1eHMe MTbIBaHMJI: BsepX M
npJlMO OT ma8HOro 3JleMetfTa «on» - 31'0 cnp1lMoe» HanpaBl1eHMe" a
8HH3 - «06paTHOe», Tal{ KaI.S 000 M,QeT npoTM8 '4acOBOM CTpe11KM. Ha
MHbCKOM CTOpotte - ece Ha060por. Hanpa8J1eHMe MTbIBaHMJI Beepx
MJlH npJlMO OT MetmI Ha3blBaeTCJI «o6pantblM», a BKM3 or HerO no
nMHMftM neHTarpaMMbI MI1M ny'4aM 3&e3Abl- «nPJIMbI.QiI 3fa oco6eH-
HOCTb C'4KTbfBaHMJI l.(acaeTCJI ronbKo reoMeTpM'teCKoM 3anMCM OCHOB-
HOM 4>opMynbl (MaTpMI4bI) K npoM3BO,qHbIX or Hee 4>opMyJl, KOma reo-
MeTpM'4eCKyIO 3anMCb nOClleAHMX npoel4MpytOT Ha 4>Mrypy «on».
(Ka3aHHoe OOftCHMM Ha npMMepax pM(. 51 M 52, eepHyBWMCb K aHanM-
3y 4>opMyTI 600 M 7 oft B 60n 3neMeKTb1 MMetOT «nPfttcylO» IQ¥"OBYIO
CBR3b M BKb,QlOE (Ix. 51,a
a 70n- AMBnO (pMC. 52, a).
npM «o6paTHoM» KpyroeoM CBSI-
3M 3TH 4>opMynbl MMetOT C'OO'bI-
BaHHe Ha'4al1bHOfO 3J1eMeHTa t
HM>KHerO neeoro (no pMC. 51, 6 M
52, 6) yrna neHTarpaMMbI-
BnOM.Q M OnBMn - M COOTBeT-
C11IyIO 3amtCb'fepe3 CMMBO-
J1MKy «on»: 600 M 70n .
TSHHbIe CHJJbI KpHTepHes
31'0 H8AO 3H1ITIt
AnSI -3Be3AHOM» cSx>PMYJ1b1
Mbi AOJ1*HbI B3RTb 3neMeH1
npeBOro BepXHef'"O (-He6ec-
Haro») yma neHT8J"p8MMbI, a
AnSI MYnbl - HWlCHerO
(<<3eMHOrO») yrna MHbCKoM
CTOpottbl neHTarpaMMbI.
365
rnSB8 8
CornaCHO npMBeAeHHOMY 3600 HHb-JlHCKOMY npaBHny C'4HTblBa-
HMJI neHTarpaMMbI 4>oPMYnbl «on» C y eToM HanpaBneHHJI CTpenKH
no KPYry M nY'4aM 3Be3AbI ee 4>MryPbl, nepeBoA «on» B rpa4>H'4eC-
t<y1O 3anMcb, Ka3aJ10Cb 6b1, He COCTaBnJleT TpYAa.
AnJl 4>OpMynbl 360n-l- nonY MM Bblpa>KeHHe OBMnA (pMC. 51,8),
a AnJl 37 onJ. - BOMnA (CM. pMC. 52,8) - 3TM 4>opMynbl cOBpe-
MeHHble CMHonorM M HYMeponorM AeMCTBMTenbHO HaxOAJIT B ApeB-
HMX PYKonHCJlx.
npoAOn>KMB 3Ty TeHAeHLtMlO, AnJl Cl>opMyn 36 on M 37 on nony-
'4MM BapMaHTbI «npJlMoro» M «06paTHOro» C'4MTbfBaHMJI HX 3neMeH-
TOB: AnJl 36 on - 4>OpMy,nW 3nAOBM M 3nMBOA, a AnJl 37 on-
3nABOM M 3nMOBA (pHC. 51,8 M 52,8). KaKaJl H3 HMX HCTMHHaJl?
OAHaKO HH OAHa H3 npHBeAeHHblx Ha PMCYHKax ct>oPMyn H nony-
eHHaJl «J1MHeMHO» He HaM,qeHa B TpaKTaTaX ApeBHHX HYMeponorOB
KaK aHaJ10r $>pMyn 6 on M 7 on.
cJ»Mnoco4>bI,BocroKa, MCnOlllt3YA Y'4eHMe HHb-JlH, Ha «3aKOHHOM
OCHoBaHMM». rMHaJ1bHO ycrpaHHnH ABoMCTBeHHoCTb C'4HTblBaHHJI
$opMyn C HH>KHero npasoro yma 3Be3AbI HHbCKOM CTOpOHbI.
OHM McnOnb30BaJ1H HHb-ftHCKMe CBOMCTBa, KOTOpble BonnoU4eHbI
«Be3Ae M BO BceM», B TOM MCJ1e B Ka>KAOM 3neMeHTe 4>opMynbl: pa3
CTOpOHbI {neBaJl-npaBaJl} H '4aCTH (BepX-HH3) 4>Hrypbl CHMBonH-
3HPYlOT 3anO>KetiHylO KOCMOCOM COOTBeTCTBYIOU4Y1O npOTHBono-
nO>KHYIO CYU4HOCTb.Be MnM JlBneHMJI, TO COOTHeceHHblM co CBO-
eM npoTHBOnOnO>KHOM CTOpOHOM 3neMeHTTO>Ke AOn>KeH npOJlBnJlTb
aJ1bTepHaTHBHble HHb-Jl'Ht:KHe Ka'4eCTBa, H3MeHJlTb HX Ha 06paTHbie.
no 3AbI- «maBHOM AHaroHaJ1H nemarpaMMbI» - C HHbC-
KOM CTOpoHbI MYApeltbi B Ha'4aJ1e C'4MTbIBaHHJI nepexOAMJ1H Ha BepXHHM
neBbiM yron JlHCKOM CTOpoHbl, T. e. C «3eMHOro» Ha «He6ecHblM» 31IeMeHT
4>oPMynbl. Bbl60p 3TOro 3neMeHTa H HanpaBJ1eHHJI C'4HTb1BaHHJI OT Hero
366
n03BOJUIJ1M CoxpaHMTb B CMIIe maBeHCTBO JlHCKOM CTOpoHbI M JlHCKOro
311eMeHTa neHTarpaMMbI: MAYU4CU1 dT Hero BHH3 CBJl3b, KaK M npe>f(Ae, MMeeT
«06parHoM». KaK pa3 3Ta 4>oPMY11MpoBKa HY>KHa AM HanMcaHMJI
3Be3AHOM neHTarpaMMbI C «06parHoM» CBJl3b1O ee 3.neMeH111@ .6Ha IJj)(!f
TOJIbKO OAHH BbIOOp «06parHoro» C'4MTb1BaHMJI - no 3Se3p.bl BHM3:
trAnMBOJ. AM 360n (pMC. 51,z) H trAnMOB AJ1J1 3700 (pMC. 5 z).
m 4>opM}OTbi HbIe M HaXOAJIT B ApeBHMX nMP'X HyMeponoroB.
TaKHM 06pa30M, 6b1nH 06pa30BaHbI HOBbie 4>opMynbl co CMeWM-
BaHMeM 3neJ4eHTOB CTopoH eJnuYPbl, HO C coxpaHeHMeM BeAYU4ero
MHb-JlHCKOrO Ka'4eCTBa Ka>KAOro Hcnonb3yeMoro 3neMeHTa.
6naroAaPJl nepexo,qy Ha CTOpoHy JlH M Hcnonb30BaHMIO ee anbTep-
HaTHBHOro no OTHOUleHMIO K CTopoHe MHb CBOMCTBa OiJoUtlHocmh 'ITe-
HMft nK>60M 3Be3AHoM neHTarpaMMbI C «06paTHoM» CBJI nonHOCTbIO
UCKRlOtioemCR. Y'4HTblBaJl npoTHBonOnO>KHble HHb-)1Ha8te Ka'4ecTBa
3J1eMeHTOB npoTMBonOnO>KHblX CTOpoH 3Be3Abl, M3 JlHCKOM CTOpoHbI no-
J1Y'4alOT HHbCKYK> 4>oPMYny {; «npJlMoi1» CBJl3blO ee 3neMeHTOB.
npH'4eM HanpaBnE!HMJI C'4HTblBaHMM, npM KOTOpblX 06pa3YIOTcJI
OnpeAeJ1eHHble6yKBeHHbleCO'feTaHHJI,COmaCHOAJ)eBHHM pyKOnMCJlM,cXr
naAalOT OCo6oM cMMBonH-
KOM.
TaK, KMTaMcKMe 4>Mno-
COcl>bI nMwyT 0 CJ1eAYIOU4Hx
MCTonKOBaHMJlX CBJl3eM
3neMeHTOB cl>OPMYI1b1 6 on
(TpaKTaTbi «MO-t,t3b1» M
«XyaMltaHb-Lt3b1» ):
1) CO'4eTaHHe BnO CMM-
BOJIM3HpyeT «comaWeHMe»;
2) OM - 4<nnaBneHMe»,
TaifHble CHflbl KpHTepHes
Ka'lecTBO CBR3M
HYMeponorn noAJ.)06Ho aHastllt-
3 PytOT reoMerp ecK e 11 -
He Hble $OPMYnbl, CTOI1KOBbi.
BaR He TOl1bKO npoH3BCJ,,4HYKJ
OCHOBY HanpasneHHfI AB )Ke-
H R 3Hepr B $OPMYl1e B u.e-
110M; HO KBl.lecTSO CBA3 Me)K-
AY OTAenbHblM 3neMeHTaM .
361
rnBBB 8
a
6 «CMSlr eHHe», «pacCJ1a6-
neHHe»; 3) MA - «KOHT-
JJ. ponHpoBaHMe»; OAHaKO
crt:J M 31M >Ke CO'4eTaHHJI MO>KHO
1 HCTOnKOBbiBaTb H C APyroM
'. «3HepreTH'4eCKOM oKpac-
n 0 KOM»: 1) BnO - «rapMo-
BnOM,[l,... IiH3a HJI»; 2) OM - «npe-
z 06pa30BaHHe»; 3) MA -
«ynopJlAO'4eHHe» (Aen,
M C06b1TMM,OTHoweHMM).
A 0 «npoe OHHo-MaTpH'4-
" HOe» H «caMOCTOJlTeJ1bHDe»
" " «(He3aBMCKMOe») HanHcaHHSI
B "n 4>opMyn J1Y'4we AeMOHCTpH-
py10T xapaKTepHCTMKH 3ne-
".3l{nMBOJ, MeHTOB H BbIJIB11J1IOT CBSl3H,
KOTopble CKpblTbi npH rpa-
Puc. 53. (BJl3b 311eMeHTOB 4JOPMYI1b1 6 on 4>H4eCKoMBblpa>KeHHM4>op-
npM «CaMOCTOJlTeJ1bHOM» Mynbl. AnJl 4>opMynbl 6 on
(<<He3aBHcMMoM») HanMcaHMH: a - nanO>KeHHe3neMeHTOB H HX
6<m 6.- 60q B - tl60Jq, «caMOCTOJITenbHaJl» CBJl3b
L-ti 6on q nOKa3aHbI Ha pHC. 53 (cp.
C pHC. 51).
AJlJ1 '4HTaTenJl AO npJ106peTeHHJI HM HaBbiKOB HYMeponOrH'4eC-
KHX pac't&t()B 6YAYT cnQ>KH AeTanH aHanH3a B3aHMOCBJl3H
3neMeHToB 4>opMyn, no:noMY Mbi HX nOAP06HO He H3naraeM. npeA-
naraeM AO YCBoeHHJI AaHHoro B KHHre MaTepMana OrpaHM'4HBaTb-
CJI 06U{eii OLteHKOM CBJl3eM 3neMeHTOB nepsblx nRmu 4>opMyn
o
B n
l{MonBt
B
n
B
M JJ.
,-<'
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368
TaUHble ClI1flbl Kpll1Tepll1eB
npMBeAeHHOrO CnMCKa (CM. pa3Aen «nHHeMHble 4>opMynbl Ma-
rHH» B rn. 9). cJ»YHKLtHeM CBOHX 3neMeHTOB 3TH 4>opMynbl CHM-
BOnH'4eCKM OTpa>KalOT CYTb HaH60nee '4aCTO BCTpe'4alO(J4HXCJI B
>KH3HH CHtyaIJ,HM. 0 KOTOpblX Y>Ke 6b1no CKa3aHO 8 npeAblAY-
(J4HX pa3AenaX.
neHTarpaMMa B pOnM TanMCMaHa
(3aI1\MTbl)
B npeACTasneHHM HYMeponoroB M acrponorOB '4HCJ1a M reOMeT-
pH'4eCKMe 4>Hrypbl 06naAalOT onpeAeneHHOM 3HepreTMKOM M MOryr
OKa3b1BaTb IJ,eneHanpaBneHHoe BnHJlHHe npM MaHHny.nJtIJ,HH C HHMH.
B03AeMCTBHe npOHCXOAMT OC06b1M cnoc060M «nepeHi:a 3HeprHH»
'4MCen H 4>Hryp. 3TH MaHHnynJlIJ,MH Ha3b1BaIOT MarH4eCKHMH, CBJI-
U4eHHblMH, KonAOBCKMMH, oKKynbTHbiMM. namoc (1991), 6eAaw
(1995), Kp3r (1991) H APyrHe C HTaIOT, '4TO npH COBMe(J4eHHM OK-
KynbTHOM 3Be3AbI C KpyroM ropocKona Bonwe6HaJl CMna 06pa3ye-
MOM reOMeTpH'4eCKOM 4>Hrypbl MHorOKpaTHO B03paCTaeT.
J,hBeCTeH ranHCMaH WapnJl cJ»yPbe, COCTOJl(J4MM H3 neHTar:paMMbI
(38e30b/), snHcaHHOM B KPYZ ZopOCKona. CaM no ce6e, Ka3aJ10Cb 6b1,
OH HH'4ero oc06eHHoro He npeACTaBnJleT. TaK KaK JlBnJleTCJI BapH-
aHTOM Y>Ke onHcaHHOM Bblwe
reOMeTpH'4eCKoti 4>Mrypbl B '4HC-
nOBOM acrponorHH. Ho eCJ1H HC-
nonHHTb 3yY 4>Hrypy OC06b1M 06-
pa30M, TO, no YTBep>KAeHHIO
MaroB, OHa npH06peTaeT «BOn-
we6HYlO cHny». Lh06pa>KeHMe
no cnoBaM Maroa
rpa<l> K neHTarpaMMbI
aCTO CnOI1b3yK>T Kat<
T8J1MCMaH A11S1 3a TbI OT
BCS1K X HanaCTe .
369
rnaS8 8
HaHOCJlT Ha KYCO'4eK nepraMeHTa, BbiAenaHHoro M3 KO>KM HePO>K-
AeHHoro JlrHeHKa: 3TOT CMMBon «CBJlTOM HeBMHHOCTM» A06b1BaIOT
M3 yrpo6b1 OBe'4KH. Pa3Mep nepraMeHTa AOn>KeH 6b1Tb He MeHee
nJlTM caHTHMeTpOB, HO M He 60nee 9 CM, T. e. KOHeYHOZO '4MC!1a 3J1e-
MeHTapHoro pJlAa, Mcnonb3yeMoro B HYMeponOrH'4eCKMX ynpoU4e-
HMttX.
Ha npHMepe M3rOTOBneHMJt
3TOro aMyneTa nOKa)KeM '4HTa-
TeJ110 OC06eHHOCTM CBJl3aHHO-
ro C HMM oKKynbTHoro AeMCTBa.
ABTOp TpeXToMHMKa «TaMHaJt
Mar"JI B.M. 6eAaw C'4MTaeT,
'4TO MarM'feCKHe onepal4HH '"'0-
ryr HMeTb ycnex TonbKO npM yc-
nOBMM Bbl60pa 6J10Z0npURmHD-
zo AnJl 310M l4enH MOMeHTa,
KorAa CBeTHna - COnHl4e MnM
nYHa, a n we OHM 06a - CBO-
HM nOnO>KetiMeM COAeMCTBYIOT MarMM. K Bbl60py Hy>KHoro BpeMe-
HM «COTBOpeHHIt TaHHCTBa» npeA'bJlBnJlIOT CTpOrMe rpe60saHMJI,
KOTopble HeYKOCHHTenbHO c06nlOAalOT. AnJl 3Toro 'He06xOAHMO,
'4T06b1 nYHa HaXQAMnaCb B OAHOM M3 6narOnpHltTHbiX AOMOB M He
6b1na BO Bpa)KAe6tU>M iCneKTe, T. e. 3HepreTH eCKOM CBlt3M, C Ca-
TYpHOM HnH MapcoM M He «C)KMranaCb» COnHl4eM. nnaHeTa C'4HTa-
eTCJI «cropesweM», eCJ1k ee npOeKLtMJI Ha 3eMnlO npH6nH>KaeTCJI K
TaKOM >Ke njioeKLtHH COnHl4a 6nM>Ke '4eM Ha 4°, KorAa 06e nnaHeTbi
OAHoBpeMeHHo HaXOAJI'tCJI B none 3peHMJI Ha6nlOAaTenJl. B 3TOM
CJ1Y'4ae nnaHeTa «He pa60Taen, C'4MTaeT X3T MOHCTep. 3HeprMJI
COnHl4a «3a6MBaeT» ee.
HYMepoIlOnl'l8CKa.
8CTpOIIOnlW MTa.T
An p,06pblx Mar ecKlilX
Ae CTB J1YHa AOn>KHa
ObITb OTAeOOHa OT Koneca
<J>oPTYHbI ObITb npMObI-
BatOllteH (paCTYli'e ). 8
A11 3/lbiX - HeH8 C
H M Obl blB8tOU4e .
370
npM AHeBHOM KOnAOBCTBe npeAnO'4HTaIOT BHAeTb nYHY BOCXO-
AJluteM M HaXOAJIuteMaI B OAHOM M3 AHeBHblX 3HaKOB 30AHaKa. HO'4-
Hoe KOnAOBCTBO, HanpMMep M3roTOBneHMe aMyneTa MnM neHTaK11J1,
6YAeT 34>4>eKTHBHee, eCJ1H ."36paTb BpeMJI, kOrAa HO e- 30AMa-
KanbHble 3HaKH 6yA'fT BOCXOAJIU4MMM.
KOCMM'4eCKHe 3HeprHM 3aTpYAHJlIOT HnM ' Ka>KaIOT KOnAOBCTBO
npM CJ1eAYIOU4HX cMTYaLtHRx: 1) KorAa l1YH Ha oAHTcJI B npoMe-
>KyTKe OT 18 0 BecoB AO 3 0 CKopnHoHa HnM's nOQ1eAHeM rpaAYCe
nlO60ro 30AHaKanbHoro 3HaKa, nOToMY '4TO «nOCJ1eAHHM TepeMoM
Ka>KAOrO 3HaKa ynpaBnJlIOT 3n06Hble nnaHeTbI», - C HfaeT nanlOc;
2) KOrAa nYHa HaXOAMTCJI B lIt VL IX HnH XII AOMax; 3) KorAa Ko-
neeo CS»OPTYHbI HaXOAMTCJI B BOCXO>KAeHHH.
AnJl MarM'4eCKoro AeMCTBa peKoMeHAY'fTCJI McnOnb3OBaTb BpeMJI,
KOTOpoe «ynpa8nJleTaI» HnM A06poM nnaHeToM cenTMHe,a, HnH «nna-
HeToM p0>KAeHMJI» raAaTenJl, M11H Toro, Ha Koro raAalOT. (enTHHep -
7 rnaSHbiX nnaHeT COnHe'4HOM CHCTeMbI, KOTOpble MornM Ha6nlOAaTb
MYApeLtbi ApeBHOCTH 3aAonrO AO M306peTeHHJI TeneCKona. 31'0 Te
nnaHeTbI, KOTopble,BHAHbI Ha HO'4HOM He6e HeBoopy>KeHHblM rna30M.
«nnaHeTa pO>KAeHMJI)J) - 3TO fa, KOTOpaJl (BMeCTe co 3HaKOM JoAHa-
Ka) nepBaJl BCTpeTHna Bawe po>KAeHHe, T. e. OKa3anaCb BOCXOAJIuteM
Ha ropH30HTe B MOMeHT PO>KAeHHJI.
npMBeAeM peKoMeHAaLtMH
'4MCJ10BOM acrponorHM no Bbl60-
PY HaH60nee YAa'4Horo 8peMeHH
MJI MarH'4eCKOrO AeMCTBa. AnJl
3aroBopoB nlO6BH nY'4we Bcero
nOAXOAMT '4ac npaBneHHJI ConH-
Lta M11H B.eHepbl, MJI Bbl3b1BaHMM
AYXOB - '4ac MepKypMJI HnM
TaHHble CHnbl KpHTepHeB
Ao6poMY KOIlAOBCTBY
6naronp SnCTBYK>T A06-
pble nnaHeTbi oco6eHHo
HaXO)t(AeH e IOn Tepa
BeHepbl B BOCXO)t(AeH
n Ha CepeAHHe He6a.
371
rnasa 8
11yHbI. AnJl 3aroBOpoB HeHaBMCTM - ..ac Ca1YPHi MnM Mapca, AllJI
cocraBJleHMII neHTaMeM M aNyneToB - '4ac MepKYP AIU' 6onb-
WMX MarM'4ecKMX t4epeMoHM - BpeMfllOnMTepa MnM 8eHepbl. Kpo-
Me TOro, He06xOAMMO MT1II8aTb no 803MO.HOCTM «AeHb MX BnCiAe-
HMII.. B TOT AeHb, KOTOpblM MaHera cynpaBJtflen, 3HepreTMKa ee
B03P,eMcr8MII, KaK C""TenOT acrponor"* n 8I1"eTa. CMJ1bHee.
MMe}1 b nMWb 03HaKDMMTb "MTareM C MexaHM3MOM McU14 feO(MX
AeMcrBMM, aBrop ynya<aer MHorMe AeTaI1M. a TcUOKe He nl*BOAMT ra6-
nM BpeMeHM ynpasneHMJI lWI(AoM nnaHeroM CBOMM 'W:OM tyrol<,
AHeM H M M roAOM. AeTaJ1M
Ma.......ecKMX"AeikTBMA ..MTaTeI1b
MO)l(eT yJKaTb 143 Cnel\MaJ1bHblX
pyKOBQACTB no MafMM. HanpMMep
M3 KHMfM AOHanbAi Kp3ra «Co-
BpeMeHHaJt MarMII. OAMHHaAAiITh
ypoKOB 8b1Cwero MarM..ecKoro
(1994).
Ta6nMt4bI npa8l1eHM" nnaHeT
..aCTO npMBoARTCfI B KHMrax no
aCTponorMM. npMBeAeHbI OHM
M B KHMfe aBTopa «60ltbWOM
acrponOrM'4eCKMM npaKTMKyM»
(1994). TaM *e MO)I(HO no epn-
Hyrb AOCTaT0'4Hble AllJI npaKTM-
f(M CIJeAeHMII 06 acrponorM'fec.-
KMX AOMaX.
«Bee BMAeJ1M, - nMWeT na-
moc B KHMre «"IepHafl M wall
MarM". (KH. L c. 12), - KaK BO
Ecnt ..........
ComacHo aBTOpMTeTHOMy
38SBI1etMO f1ar1IOC8.
WapJ1b <1>ypbe COCTaBW1
ny csoero T8I1MCM8-
He. o Kale pa3pa-
6oTal'l PK-
t<yJ1b1M3M9 -mopHIO 'l6Tb1-
pax ,l.tBIQCSHHH- 3Hep04M.
ero nocne coeep-
3TOrO -oncpbl B
McU')61- pe3K .
AHre11-xpattKTenb r1eMoran
eMy 8 C8MbI8 He8OO()pa3M-
MbI8 MOMetfTbt
)t(M3HW 'Mcne roro K8K <S>y-
pbe caM M3r0TOBW1 lit Ha,o,en
Ha ceoM Ta11 H.
372
BpeMe..a pa3AOpoB W. 6pocaJ1CA B CepeAMHY pa3DJ1peHHOM
TOnOW C HaMepeHMeM B03AriCTBOBaTb Ha HeC'4aCTHwx. BOJ1HyeMbI>C
nOnMTM'4eCKMMM CrpaCTJIMM. MHoro pa3, MCnOnRJU' :310 6J1aropoA-
HOe AMO, CMeJtWM CS»ypbe BWAeP*MBaJ1 OroHb C ABYX poH, He-
CKonbKO pa3 OH nOABepranOt BblcrpenaM, nyn" HMKorAa Aa*e
CJ1erKa He KaCaJtacb ero KO>KM, OHa HMKorAA He .,3MeHMa Aa*e no-
nmKeHMJI CKnaAOK ern QAe)l(,qW».
60nee nOAPOOHO 0 TaJlMC.....He $ypbe MO)t(HO n MTaTb B KHMre
namoca. AnJi YAoeneTBopetfM" nOOonWTCTBa '4I4TaTeneM npMBeAeM
flMWb HeCKOJIbKO 3aM HMi 00 era M3rOT08neHMIO. Bee comacyeT-
CjI C Y>Ke OpMBe,QeHHoM HaMN paHee MH4>oPMat4MeM 06 M3roT08ne-
HMM MarM'feClCorO MHBeHTapJl: AOn>KHW 6b1Tb c06nlOAeHw MeCTO,
BpeM onpe.QeneHHbIe 3HaHMJ\ Cnet4l4aJtbHblM MarepMaA..Hy>KHO Bna-
AeTb TaMHCTBOM caMoro np0t4ecca.
Oc8"U4eHHe TanMCMaHa
COBepWaIOT no OOR3aTeJtb-
HOMMafM4eO(oi
cnonb3YJ1 Cnet4ManbHwe
*AbI. f'aA1HMA no neKTar-
paMMe " CMarM'«KMM MHCT-
pyMetffi)pMib - '4awy, BOlt-
we6tfbIe naIIO'fKy M wnary.
(OBepweHCTBO BlJaAeHMft
«MarMQecKMM MHCTpyMeHTa-
pMeM» M ceoMMM ABK)KeH....
JlMM npM nepeAiNe 6M03ttep-
fKM AeMOHCTpMposanM MarM M Bonwe6HMKM Ha Me*AYHapoAHOM
KOHKypCe Mar08" BOnwe6HMK08 B 1995 r. Hx HeMbKnMMbIe MCTBMjI
Te.ne3pMTe11M MornM BMAfTb 8 aBf)(:TOBCkoM ne LteHTpal1bHOro
TaHHble Cl:fJ1b1 KPHT8pu8B
ComacHO Y't8KMIO
He MarM'fecKoro H-
BeHTapR COBepUJaJOT C TOM
8CTpaI1OfWteClG\X noKa3aTeneM
ecaMaJ . Hanp Mep 3H8KOB
3o,(u4atca. .neMcTBO oOcraBI1SUOT
MarW4eC1CoM uepeMOHMeM B
3aBMCMMOCTH OT ynp8B11RI()U.te-
ro 3HaKOM uAyxa- ero «'fMHa».
313
rn8S8 8
TeJ1eBHAeHM" B TOM >Ke mAY. MarH nOKa3b1Ba11M CBOM Ba3MO>KHOCTH no
MC'4e3HOBeHMIO '4enOBeKa, AeMOHCTpMpoBa11M neBHTa MIO (CB060AHoe
napeHHe HaA c eHOM), nepeMeU4eHMe npeAMeTOB M T. A.
He TaK AaBHo no TeneBMAeHMIO nOKa3aJ1M B03MO>KHOCTH aMepH-
KaHCKoro Mara A3BMAa Konnep<J>MJ1bAa. 3pMTenH MornH BOO'4HIO YBH-
AeTb ero '4YAeca.
«HMKOr,qa Mar He ADn>KeH npMMeHJlTb OPYAMM, He OKHraTb 6narooo-
HMM, He ynOTpe6nJn'b BO HIIM OroHb HeOCBJlI14eHHblMH, - npe.qynpe>K-
IJPf!T nanlOC. - OcBJlI14eHHe ecTb poA «MarHeTM3MpoBaHH"» npeAMeTOB
nocpeACTBoM cnosa H JKecmos (BbI,qeI1eHO asr.). Ynorpe6J1eHHe KpOnu-
17D npM KaTDnM'4ecKMX 06pAAaX TeCHO CBJl3aHO C :3ToM aCTblO npaKTM-
......... ..... .... ... .................
.
· np&o1BeAeMA11 np&o1Mepanepe eHb« &o1HOn()tf&o1T8H&o1H..no ·
. nanlOCY
· 3HSKH 3o.,tp'fSKS Kst56ans (lJ.yxH)
DBeH (Ma1ST) MaTlx&o1A&o1enb
: Tene (anpenb) ACMOAeJ1b
· 6n&o13H (MaH) AM6p&o1eJ1b
. PaK (&o1lOHb) MlOp&o1eJ1b
· J1eB (&o1lOnb) Bepxenb
· .neBa (aBrycTJ XaMaTlbeJ1b
. Becbl (ceHT 6pp) 3yp&o1enb
· CKOpn&o10H (OKT 6pb) 6a6p&o1eJ1b
. CTpene (Ho 6pb)"I. AeHax&o1eJ1b
· K03epo{(AeKa6pb) XaHaeJ1b
· BOAoheH ( HBapb) 6apX&o1enb
. Pbl6b1 (4)eBpal1b) 6apX&o1enb
374
LlHHbI SHrenbCKHe ·
Cepa<t>&o1MbI
XepYB&o1MbI
npecTonbi
rOCnOACTBa
BJ1aCT&o1
C&o1nbl
Ha aTla
ApxaHreJ1b1
AHrenbi
HeB&o1HHOCT&o1
MY"IeH&o1K&o1
CnOBeAtu'K&o1
'4ecKoit MarM" M HanOMHHaeT
yn01pe6neHHe OUHOHUJUpoBOH-
HOil SCAb! Bonwe6HMKaMM «TbI-
CJI'4H M OAHOM HO'4M»... PaHee
CKa3aHHoe 0 >Kecre nOKa3bfBa-
er, KaKoe Ba>KHoe 3Ha HHe OH
MMeer. >Kecr 3aBHCHT OT (ABM-
>KeHMJI)... M Te/la, OpraHOB
Bblpa>KeHMJI (6M03HeprMM.-
npuH. OBm.)>KMBOrO
(KH. 1, C. 99).
npM OCBJlU4eHHM TanMCMa-
Ha Y'fHTblBaIOTTaK>Ke 3HeprO-
pe30HaH cooTBeTCTBYIOU4eM
nnaHeTbi.
AHrenbi nnaHeT BblCWMe M HM3w e MOryr 6b1Tb C OAMHaKOBblMM
HMeHaMH.
C Y'4eTOM M3J10>KeHHoro Ha nOAroTosneHHblM, KaK YKa3aHO Bblwe.
OK nepraMeHTa HaHOCJIT ABa Kpyra: OAHH y KpaJl, APYroM '4yTb HM>Ke
BHyTpH nepBoro, '4T06b1 Me>KAY HHMM 6bU1 npoMe>KyrOK AJ1J1 COCTaB-
neHHJI ropocKona (TO'4Hee, KOCMorpaMMbI); Hapy>KHblM Kpyr - KpaC-
HbiM (Mcnonb3YIOT '4epHHna), BHyTpeHHMM - cepe6pJlHblM (KpaCKa).
Cepe6pJlHblMH ABOMHblMH nonOCKaMM WiCK AeJ1I1T Ha 12 CeKTopoB H
B Ka>KAOM ceKTope, Ha'4HHaJl oTOBHa M no nopJlAKy, HO npomuB '4aCO-
80M crpenKM pMcylOT 3HaKM 30AHaKa. B i4eHTpe Kpyra '4epTJlT 3Be3AY,
Me>KP,y nY'4aMM KOTOpOM nOMeU4aIOT aCTpOnorM'4ecKMe CHMBonbi cen-
TMHepoB: ceHU «OCHOBHblx»°He6eCHbix Tell ConHe HOM cMCTeMbI, BH-
AHMblX HeBoopy>KeHHblM ma30M npM HopManbHOM 3peHHM. B eHrpe
3Be3AbI pHcylOT ConH e KpaCHblMM '4epHMnaMH Ha 30nOTOM 4>oHe.
TaHHbl8 CHflbl KpHT8pH8S
MHTepecHwA cl»8KT
CospeMeHHblMH &103Hepre-
TMIC8MH H epa..aMH-ro -
TaMH HCflOnb3yeTCR -
pyKTYpHpqeaH . BO,D,bI (T0'-4-
Hee - }nepe.a.
BBe,D,eH B flee J1e'fe6HoH
3HePf1'WI. .lJ,11R 31brO, HanPH-
Mep, otWI nPHMeHRIOT MQU.4-
Hble 3H8Pf'"en1'feCKHe noTOIG1.
HanPHMep CBeTa, A11R CHsm1R
C BO,O,bI oo 3HepreTM-
OOH .
375
rnasa 8
.............................. .. II.....
. .
· nepe .-tc1U1M nl1aHeTbI, .l!YXOB nl1aHeT .-t COOTBeTCTByK> .-tX ·
. .-tM BHrenoB, BblnOI1H IO .-tX BblCWHe .-t HH3WHe <t>YHKLU1H .
· HOCHTenbCTBa 3HeprnH He6a (no namocy):
· He6ecHbie AHrenbi AHrenbi
. Tel1a nl1aHeT nnaHeT
BblCWHe HH3WHe
MHxael1b MHxaenb
Pa<t>ael1b Pa<t>ael1b
ra6PHe11b ra6p.-tenb
XaHHel1b AHael1b
CaMael1b
lI.8,D.KHel1b
3aq>KHel1b
. ConHLte
: MePKYPH
· J1YHa
. BeHepa
· Mapc
· tOn.-tTep
. CaTypH
3aKX.-tel1b
KaCCHel1b
,QYXH
nl1aHeT
Ox
O<PHe11b
<1>HI1
Xal1.-tel1b
<1>811er
6eTOp
ApaTI?OH
"..................................... .
B npoMe>Ky1UX Me>KAY nY'4aMH 3Be3AbI no naTblHH nHWyT Ha3BaHHJI
ceMM nnaHeTapHblX MeTaJU10B. AnJl COnHLta Ha3BaHHe MeTanna nH-
WyT B CepeAMHe 3Be3AbI. HH>Ke 3HaKa 30AHaKa nOMe alOT MY3b1Kanb-
Hble HOTbI, KOTOpble COOTBeTCTBYIOT MeTaJ111aM. 1306pa>KeHHe Ka>K-
AOro acrponorH ecKoro CMMBona nJ1aHeTbi AOn>KHO 6b1Tb Ha'4epTaHO
B HOI/Hoe BpeMJI.B I/ac zocnoacm8a :nOM nnaHeTbI.
«npHroTOBHB TajUtfi96pa30M neHTaK11b, - nMwer nanlOc (C. 112),-
6epyr Kpyr11yK> cepe6pj!HYK> nnaCTHHKy (cepe6po AO/I>KHO 6bITb caMoe
Mcroe. KaKoe TOIIbKO MO>Ioto AQCTaTb),AO bHO WHpoKylO, 4T06b1 MO>KHO
6bUto Ha HaK11eHTb 4>Mrypy, He crH6aJl. ee, KOTOpylO npHKI1eHBaIOT]a
KpaJI t<neeM, npHroTOBJ1eHHblM H3 OMeJ1b1, TOM CTOpoHOM, Ha KOTOpoi:1 Ha-
XOAMTCJI H306pa>KeHMe. 3aTeM TaI1MCMaH OCBJlU4i3IOT, JaWHBaIOT B MaUD-
&4eK M3 3eIIeHOrO amaca M HOCJIT Ha WeJ1KOBOM WttypKe».
376
TaUHble CHflbl KpHTepHes
no' t4eHMIO nanIOC , B He6ecax HaXOAHTCJI «O'feHb 60nbwaJl
3HepreTH'4eCKaJl CHna, KOTOPYIO nnaHeTbi H 3Be3AbI M3nMBalOT Ha
MeTannbl, >KMBOTHblX, TpaBbI, AepeBbJl». OCBJlU4eHHble OKKynbTHbie
npeAMeTbl, MarH'f CKHe TaJ1M.CMaHbI, aMyneTbI, neHTaKJ1M , neKa-
lOT K ce6e H K HX HOCHTenlO AononHMTeJlbHYIO KOCMH'4ecKYIO 3Hep-
rHIO. TeM caMbiM '4aCT 'fHO KOppeKTMpyeTCJl1<'ipMM'4eCKaft 3HeprMJI
'feJIOBeKa, H3MeHJleTCJI era CYAb6a - nonara T "!arH. Ha 3TOM OC-
HOBaHa 3aU4HTa 3HeprHeM KOCMoca CBoero 3H Ka, 'nl1aHeTbI, MMeHM,
KaMHJI OT «3HepreTH'4eCKOM HH4>eK4HM» H 3arOBO B.
rpaHM bl .snacTM MarM"IeCKOM
cl>Mrypbl
4HTaTeJlb, BepOJlTHO, 06paTHJ1 BHHMaHHe Ha TO, '4TO BHeWHue (He-
6eCHble) CBJl3H rpa4>M ecKoM 4>opMynbl 60nee npOCTbI, c03MAaTeJlb-
Hbi M 6naronpHflTHbi M 60nee «CTHMynHpYIOT» npOJlBneHHe >KM3HM,
'4eM BHympeHHue CBJl3H no nY'iaM 3Be3AbI, nepeAalOU4Me conpoTMB-
neHHe M 60pb6y. OHM TO>Ke - 3aKpH >KH3 H KaK B HYMeponOrH'4eC-
KOM, TaK H B MaTepHaJ1HCTH'4eCKOM nOHHMaHMH pa3BMTHJI H COBep-
WeHCTBOBaHHJI MexaHH3MoB 06ecne'4eHMJI >KH3HH - Bce pa3BHBaeTCJI
H COBepweHCTByeTC1t 'fepe3 60pb6y. MarH ecKaJl4>Hrypa - CMMBon
He TonbKO 60pb6b1 npoTMBOnOnO>KHOCTeM H npOJlBneHHJI.3QKOHQ
UHb-RH, HO H pa3AeJleHMJI Bpa>KAe6HbI.X, npOTHBOCTOJIU4HxAPyr Apyry
CHn: He6ecHbix (KPYZ) H 3eMHblX (3Be30a) (pHC. 54).
npH MarH'4eCKHX AeMCTBHJlx 3neMeHTbI HYMeponOrM'4eCKHX 4>H-
ryp - Kpyr W1H 3Be3Aa - MOryr Mcnonb30BaTbCft H OTAeJlbHO APyr
OT APyra. nOnO>KeHHe 3Be3AbI TO>Ke CHMBOnH'4HO. HanpaBneHHaJl
OAHHM CBOMM nY'i0M BBepx, 3Be3Aa nepeAaeT «He6ecHbie cBoMCTBa»,
377
rnasa 8
npMBJleKaeY1fY'MUMe HI A66pble
AnJl 'fenOBeKa He6ecHbie ..
3eMHble CHnbl, nOAAep>KMBalO-
U4Me ero >KH3HeAeJlTenbHOCTb.
ITonO>KeHHe 3Be3AbI ABYMJI ny-
'4aMM BBepx, KaK '4eTHoe '4HC-
no, npMHaAne>KMT 3eMne. npH-
'4eM nY'4M «AByporoM 3Be3AbI»
nepeAalOT ee XYAWHe CHnbl.
nOnO>KeHMe 3Be3AbI OAHMM
nY OM BBepx - CMMBon CMn
He6a, nOMO CBblwe, BnMJlHMft
BceBbiwHero. sypofCUl» 3Be3-
Aa - CMMBon CHJI 311a, BnMftHMJI
AbJlBona. KHJl3ft TbMbI, c06na3-
HOB M npoTMBOAeMCTBMM no BbI-
nonHeHHIO '4enOBeKOM CBoero
npeAHa3Ha'4eHMft Ha 3eMne:
CBeTnOM enM HHKapHaLtHM.
«):tByporaJI 3Be3Aa» - CHMBOn
pornB '4epra M ronOBbi K0311a.
Kpyr - CM"Bon pa3AeneHHJI xopowero M nnoxoro BnHJlHMJI,
rpaHM a Me>KAY-AO OM H 3nOM, npM'4eM B K 66anHCTH'4eCKOM
nOHMMaHMM 06naAa1OU4M MarM'4eCKOM CMnOM 3HaK, npM3b1Ba-
IOU4MM CMnbl He6a M A06pa Ha nOMOU4b enOBeKY. Kpyr M3AaB-
Ha Mcnoa...3YlOT KonAYHbI M MarH An" OTAeneHMJI CHn A06pa OT
3na 30HbI BnMftHHJI BceBbiWHero OT AbJlBOna. Kpyr - :no 3a-
U4M;a OT 6eAbi M B03MO>KHOCTb nonY'4eHHJI nOAAep>KKM 3HeprMH
KOCMoc.a.
OCHOaW ttyMeponorM"
B HYM8JX)J1OI'"HH 3Ha1.feHHe
MalWteCKOO $.1rypb1 - KpYIO
C BI1MC8HHOM B HerO nsmtKO-
He'fHOM 38e3AOO - MHOrO-
4>YH . 3ro He
TOm o EW1HCTBO He6a (tcpyr)
3eMnH (3Be3A8), COOTBeT-
CTBeHHO Q1MB011
H86ecHyto c<I>ePY H nsrTD rnas-
HbIX 3eMHbIX MaTepHKOB, HO
H CXeMa nepe.a,a H.Q1MB011H-
'fSCKOO C8s:I3IiI 38K0Ha 1lOC1J>O-
etMSI MIo1I)a, 't8I1OBe-
I<a. 3ro He TOnbKO CXeM8 OT-
bHOrO
H O.3eMnHH
He6a, HO H CHMB011 rpatMu,bI,
HX B1'Ia,IJ,etMR.
378
H.B: foron!. (1809-1852) HcnOnb30BaJ1 CHMBon Kpyra AllJI 3a-
I14MTbI cBoero repoJl OT CMn 3J1a B paccKa3e «BHM». BOT KaK OH 3TO
onHCblBaeT (C06p. CO'4. B ceMM TOMax. T. 2, c. 165-205).
AO'4b COTHMKa 6b1na AbMOM H
BaMnHpoM - 06 3TOM 3HaJ'IH MHO-
rHe OAHOCeJrb'4aHe. YMepna OHa
HeO>KMAaHH " lIepeA CMepTblO
HaKa3ana oi4.v: «.. .nownM, Tary,
ceM >Ke ac B KHeBCKyIO ceMMHa-
pHIO H npHBeAH 6ypcaKa XOMY 6pyTa. nycrb TpH HO'4M MOnMTCJI no
rpeWHOM AYWe MoeM...»
BbinonHJIJI nO>KenaHHe AO'4epH, COTHHK npHrnaCMn XOMY K '4Te-
HMIO MonMTB Ine'4eHMe Tpex HO'4eM B LtepKBM;TAe ne>KaJ1a YMepWaJl.
XOMa OT OAHOCeJ1b'4aH COTHHKa y3HaeT, '4TO ero AQ'4b 6 BeAbMOM,
Hi KOHe'4HO, n06aHBaeTCJI. Ho ero npHBneKalOT 60nbWMe AeHbrH.
KOTopble o6eU4aeT eMY COTHHK 3a a 6
3TH TpH HO'4H. @ W
3anepTbiM B ijepKBM OAHH Ha
OAHH C rpynoM, KOTOpblM ne>KHT B'
rp06y,oH B nepBYIO HO'4b caM ce6J1
ycnoKaHBaeT (C. 194-195):
«4ero 60JlTbCJI? - AYMan OH Me>K-
AYTeM caM npo ce6J1. - 8eAb OHa
He BCTaHel H3 cBoero rpo6a, no-
TOMY '4TO n060HTCJI 60>Kbero CJ10-
Ba. nycrb ne>KMT! Aa H '4TO JI 3a
Ka3a1(, Koma 6b1 ycrpawHnCJI?.»
«.. .OAHaKo >Ke, nepenHCTblBaJl
Kij>KAY1O crpaHHLtY (MonHTBeHHH-
no npeA8HMIO
BOI1 YM&>1palO ero e-
J10BeKa - 3aKOH.
TaRHble CHnbl KpHTepHeB
PUC. 54. nOnO)l(eHMe 3Be3AbI nY'4oM
BBepx - CMMBon
npMBne'leHMft «csernblX»
CMJI M «He6ecHO »
nOAAep)l(KM 'IeJIOBeKa (a);
«AByporaJi 3Be3AC1» -
CMMBOJI BJlMJlHMJI epTa.
,qbftBona. KHft3J1 TbMbI (6)
379
,nasa 8
Ka. - npUM. oem.), OH nOCMarpMBan MCKoca Ha rpo6, M HeBoilbHoe
'4YBCTBO, Ka3anOCb, wenTano eMY: «BOT, BOT BCTaHeT! BoT OOAHM-
MeTCJI, BOT BblrnJlHeT M3 rp06a!»
«Ho TMWMHa 6b111a MepTSaJl. r po6 CTo"n HenOABM)KHO. CBe'4M nH11M
l,tenbiM nOTOK CBeTa. (TpaWHa OCBeU4eHHaJl l,tepl(OBb HO'fblO, (Mep-
TBblM TenOM M 003 AYWM nIOAeM!
B03BblCJI ronoc, OH Ha an neTb Ha pa3Hble rollOCa. )t(enaJl 3arny-
WHTb OCTaTKM 6oJl3HM. Ho Ka>KAY1O MMHyTy 06paaqan rna3a CBOH Ha
rp06, KaK 6YATO 6bl 3aAaBaJI HeBOnbHbtM Bonpoc: «4TO, ecnM nOA-
HHMeTCJI, eCJ1H BCTaHeT OHa?»
«.. .OHa nOAHJlna ronOBY.
OH AHKO B3mllHyn M npoTep ma3a. Ho OHa TO'#f() y*e He ne1t04T, a
CHAMY B CDOeM rp06y. OH OTBen ma3a CBOH H onJlTb C y>KaCOM OOparMJI
Ha rpo6. OHa BCTaJ1a... MAeT no l,tepKBM C 3aKpbITWMM rna3aMH, 6&-
npeCTaHHO pacnpa8J1J1" pyKM, KaK 6bI >KenaJl nOMMCI'Th KOnF-HM6yAb».
«OHa MAEt\ npJlMO K He MY . B CTpaxe oyepmUJ1 OH OKOJIO ce61f KPYZ
(BbiAeneHO liT.). C ycHnMeM Ha aJ1 '4HTaTb MonMTBy M npoM3HOCMTb
3aKJIHHaHMJI, KOTOpbfM Hay'4Hn ero OAMH MOHax...»
«.. .OHa CTaJ1a nO'fTM Ha caMOM epTe; HO BMAHO 6b1no, TO He
HMena CMJ1 nepeMTH ee, H BCII nOCMHena, KaK '4enoBef(. y>Ke HecKOnbKo
AHeM YMePWMH... (OHa) pacnpoCTepna PYKH, OXBaTblBaJ1a MMM Ka)t(-
AbiM CTonn Myron, CTapaJlCb nOMMaTb XOMY. HaKoHeLt, OCTaFtOBM-
naCb, norpo3MB nanlt M, M nerna B rp06.
<2>Hnoco$ Bce elite He Mor npMMTM B ce6" M CO crpaXOM nomJl-
AbiBan Ha TecHoe >KMnMllte BeAbMbI. fp06 BAPyr COpBanCJI CO CBO-
ero Mecf co CBMCTOM Ha aJ1 neTaTb no BceM ltepKBM, KpeCTR BO
Bcex Ha'npaBneHMJlX B03AYX. cJ»Hnoco4> BHAen ero nO'4TM HaA ro-
nOBoM, HO BMeCTe C TeM BHAen, TO OH He Mor 3altenMTb Kpyra. MM
O'4ep'4eHHoro.. .»
380
M B nOClle.AHIOIO HO'4b He-
'4MC1"U CMAa. npMHMMaSWaJl
pa3Hwe crpaWHwe 06pa3bl, He
Morna npeo.qaneTb tta'fepTaH
HbiM XoMOM CBJfU,feHHblU KpyZ,
B KOTOpOM OH HaXONUICSI. Ho
OH He 0CTaJ10t B JKMBWX: OH He
nocnywan01 ceoero BHyTpeH-
HerO ronoca, KOropwM wenHY1l
eMY: cHe mJlAM». He BbiTep-
nen OH .. I'MHyJI - M YMep OT
CT))iIXa. ..
cMarM'leCKyIO 3Be3A.Y», UK BMAMM Ha pMC. 49, MO>KHO pa3Ae-
IItITb Ha '4aCTM: BHYfPM Hee pa3nM'4aIOT neHTarpa..MY, a' KpaJlM -
rpeyronbHMKM-ny'fM, npMneralOU4Me K CTopoHaM neHTarpaMMbI. B Ma-
rM" AOf1}': eT01 Mcnonb30BaHMe He BceM 3se3AbI, a 'faCTM ee-
OAHoro -rpeyronbHMKa, HanpasneHHoro BepWHHOM B CTOPOHY
CaepweHM1I A06poro Aena MnM K enOBeKY, 3aKa3aBweMY 3TO Kon-
AOBCTBO. OAHOBpeMeHHO TpeyronbHMK OTrpaHM'fMBaeT OT 311b1X AY-
XOB M CMn, nOMoraeT MeAMTaI4MH. rperopM MaKAOHanbA B KHHre
CnOKoMHMK M3 HaMpOOM» (MMHC : 6en4>aKc, 1994, c. 299, 302) TaK
OnMCblaaeT BCTpe'fy repaJl KHMrH C K011A.YHbeM: «Kap 3aCTbln nepeA
KOllAYHbeM; ero KpenKMe, MycKynHCTble PYKM SMcenM, KaK nneTH.
OHa CMAeM Ha 3eMJle Y BXOAa B AOM co CTeHaMM M3 nepeBMTblX
npyrbeB, oo..a3aHHblX mMHOM, BblTJlHYB nepeA C060M 60cble HorM,
YKpbfl"hle AO KoneH '4epHOM I06KOM. fonosy 3HaxapKM YKpawana Ty-
pet4KaSl 4»ecKa... (rapYWKa-KOnAYHbJl MenOM HapMcosana BOKpyr
C mpeyZOJlbHUH.. 4aCTb nMHMM npowna He no 3eMJ1e, a no TeM-
HOM TpJlnKe, '4TO neJKaJ1a c60KY. TeM)t(e Men OM 3a6enHna ce6e BHC-
TaUHble CUflbl KpUTepues
EcnM II8J)MTIt OIOCYn TM3MY,
3Be , HSnpaBJ1eHH8R 0.0.-
HIltM KOHl4C)M BBepx, IItCn J1b-
3yeTCR ATlR M8rM'4ec p.e -
CTBIitH lit nm 3arOBopoB.
«3HepreTM ecKO MH$eK-
1It. VI H T. B epHo£1
MarMlit KOl1,D,ytibi nOJ1b3Y1OT
"',D,ByporylO 3Be3AY. ATlR YCIIt-
J1eHMR cBoero BJ1I1tRHIltR.
381
rnasa 8
HS38BMCMMO OT AsA-
CTBM. 6eno ....n.... ep-
HoM Mar......... np.... Bbinon-
HeH........ 3a.D.YMaHHoro
Mar AOIDKeH onpeAe-
I1....Tb n0I10>KeH....e nnaHeT
B ....30paHHblM A11R one-
pa .... AeHb. Ha ""HaR
c J1}'Hbi - BI18.Qb1 ""Ubi
MarOB to'! BOl1weOH....-
KOB - 0603H8 aIOT Mec-
TOHaxO)I(,AeHIo1e
nnaHeTbi. BK11lO'iaR npe-
6b1BaIOU4Io1e He TOl1bKO
Ha.A rop....3OHTOM. HO
. .... nOA ropM3oHTOM.
Men Ha BMCKax KonAYHbH CHM-
BonH3MpoBaJ1 CHer BepwHHbI ropbl.
Ee M03r '4epe3 MeAHTaLtHIO Hacrpa-
MBaJ1C1I Ha «3HepreTH'4eCKHM pe30-
HaHC» C AYwaMM f1PeJp0B.
Vl3 naJ1bLteB PYK MO>KHO C110-
>KMTb «MarH'4eCKMM" Tpeyronb-
HHK», pa6nonO>KeHHblM Bepxyw-
KO BBepx, H Hcnonb30BaTb ero
AllJI npMBne'4eHMJI A06pblx CHn B
TaJ1MCMaH (pMC. 55). 06 3TOM nH-
382
KH. 3aTJlHyna HeMenoA '4HYIO
necHb-MonMTBY HnH 3aKJ1HHaHHe».
MarH'4ecKoe AeMCTBo npoMcxoAH-
no B KeHMH, ropa KOTOpoM CTonb
BbiCOKa, '4TO, HecMoTpJl Ha a4>PM-
KaHcKyIO >Kapy, Ha BepwMHe ee ne:
>Kan CHert 3Ta ropa BepwHHoM
«ynMpa11aCb» B He60.
«A 3a'4eM OHa HaMa3ana MenOM
BKCKH?» - cnpocHna 6ap6apa.
A>t<eMMc nOCMorpen Ha Hee TaK,
CJ10BHO OHa cnpOCHna, BcerAa nH
ConHLte BCTaeT Ha BOCTOKe: «4TO-
6b1 06utaTbCJI co CBOHMH npeAKa-
MH '4epe3 60rOB Ha BepwHHe ropbl
KeHHJI».
6
PUC. 55. «TpeyroJlbHMK
npoJ1BJleHHJ1» J1YHbI
weT KpM B «CoBpel4eHHOM MarMH» (1991). AnJl npHBne'4eHMJI B Ta-
nHCMaH «>KeHCKOro 60>KeCTBeHHoro acneKTa focnoAa», KOTOpbtM
cHMBonH3Mpyer HHb J1YHbI, OH peKoMeHAYeT B nYHHYIO HO'4b 3aKnIO-
'4MTb B TaKoM rpeyronbHHK M3,naJ1bLteB Kpyr nO"HoM nYHbt M pyKaMM
KaK 6b1 «npMBeCTH» ee B TaJ1HCMaH. npH CMeU4eHHM piK);r nYHbI
Ka66aJ1a cOBetyeT COCpeAOTO'4MTbCJI H npeAct8BMTb ce6e, '4TO nYHa
HaxOAHTC1t B 3TOM «>KHBOM rpeyronbHMKe np BJ}eHMJI». AeMCTBo
Ha3b1BaeTCJI «3aXBaT nYHbI» H OTHOCMTC1t k OM MiirHM.
Ka66aJ1a npHnHcblBaer KCUf(AOM nnaHeTe oc06b1e 6YKBbI M 3Ha-
KH, '4MCJ1a, TanMCMaHbI, aHrenOB M AeMoHoB. CBeAeHHJI 06 3TOM nOA-
po6HO H3J10>KeHbI B CO'fMHeHMJlX no MarMH: rpHMynax, «KnIO'4MKax»
(Bonwe6Hblx KHMrax), npoH3BeAeHMJlX ArpHnnbl, neTp8 A6aHa, KHp-
xepa, 3nH4>aca neBH, nanlOCa, nona XeM30Ha.
KaK YKa3b1BaJ1OCb, «CBJlU4eHHo-
AeMCTBMe» Mar COBepwaeT B 6na-
rOnpHJlTHbie AnJl Hero AeHb M Bpe-
MJI. npHCTynaJl K H3rOT0BJ1eHHIO
aMynera, Mar BHa'4ane COCTaBmt-
eT ropoCKon, BblACHJlJI, B 6naro-
npHJlTHOM nH AnJl ero AeMCTBa no-
nO>KeHMH HaXOAJlTCJI nnaHeTbt
CenTHHepa. AnJl 3TOro OH Ha 6y-
Mare O'4ep'4HBaer Kpyr, pa3AenJl-
eT ern Ha 12 paBHblx CeKTOpOB, H Ka)t(AbiM ceKTop pa3AenJIeT eU4e Ha
30 0 , '4T06bf Bcero B Kpyre nonY'4Hnocb, 360 0 . no CeKTopaM pa3HOCMT
3HaKH 3oAHaKa. 3areM, Hcnonb3y1t 3<l>eMepHAbi nnaHer (Ta6nM bt no-
nO>KeHMJI nnaHeT Ha He60cBOAe) H 3Be3AHble KapTbI, nOMe'4aeT MecTO
HaxO)t(AeHHJI Ka)t(AOM H3 CeMH «rnaBHblX» nnaHeT COnHe'4HOM CHCTe-
Mbi - cenTMHepbl, KOTopble BMl1HbI HO'4blO HeBoopy>KeHHblM rna30M
TaHHble CHnbl KpHTepH8B
no cnoaaM Maroa
3H8H A 8CTPOHOM 'fec-
ICOM xapaKTepMCT 1CM 000-
HeTb! He.o.OCT8TO'fHO ,D.TIA
Mara - eMY HY*HO 3HaTb
T8101Ce K8t56an Cnt ectcylO
aCTb 8crponor .
383
fnasa 8
npM HOpMaJ1bHOM 3peHMH. 06 3TMX AeMCTBMJtx nMweT namoc B CBoeM
KHMre «4epHaJl H 6enaJl MarHft,.: «AnJl OCBJlU4eHHH npeAMeTa 06b1'4-
HO AOCTaTO'4HO Y'4ecTb COOTHOWeHMe nYHbI H nnaHeT, H TaKoe OCBJI-
lijeHMe MO>KeT 6blTb npoBeAeHO B nK>6b1e cyTKM... ECJ1M OCBJluteHHe
npoM3BOAHTCJI CO maCHO AHJlM HeAenM (KOma '4eTBepTb nYHbI ynpaB-
nJleT «C80MM» AHeM), 3TO BnHJlHMe HeMHOrO npOAOn>KMTeJ1bHee. ECJ1M
}l(e n0J10>KeHMe nYHbI B 6narOnpMJlTHbIX 3HaKax 30AHaKa MnHBalO-
lijMX ee 3HeprMIO. - npUM. oem.), TOrna BnHHHHe npOAOJT>KaeTCJI rOA
It 60nee. CaMoe )f(e AeMCTBeHHoe OCBJluteHHe cOBepwaeTcJt B TOT
MOMeHT, KOrAa Y'4HTblBaIOT COOTHOWeHMe COnHLta (B ytMJIMBalOU4Mx
ern 3HeprMIO 3.HaKax 30AMaKa, HanpHMep BO nbBe. - npUM. oem.), -
3TO BJ1HJlHHe npeAnO'4THTenbHO npH OCBJlweHMH MarH'4eCKOM naJ10 -
KM M wnarH» (KH. I, c. 98).
Aanee paccKameM '4HTaTenlO 0 MerOAMKe pa60Tbi Mara, Bonwe6-
HMKa, KonAYHa, .HCn0J1b3YlOlijero B CBOMX «cBJluteHHoAeMCTBHJlx»
aCTpOnOrH'4eCKHe H HYMeponorM ecKHe npHeMbi.
npMeMbl cCCBSnl,eHHOAeMCTBMSI
B MarMM
(ne MaJ1MCTbI.no MarHM - nanlOC, Kp3r, KapAeK HAP. - npe-
AYnpe>KAalOT >Ke.n IO x 3aHMMaTbCJI MarHeM, '4TO 3TO HenpOCToe
Aeno, rpe6YIOU4ee 06WHpHblX 3HaHHM no pa3J1H'4HblM AHC HnnHHaM,
B TOM 4MCJ1e no acrpohorHM, HYMep0J10rHM, MeTaJ1nOBeAeHHIO, ro-
TOBHoCTwrIilnonHJlTb PJlA rpe60BaHHM B. nOBeAeHMM H cnoc06HOC-
TM orpaFtH'4HTb CBOM npHBbI'4HblM pacnOpJlAOK. Heo6xOAHMbI M
«CKJ10HHOCTb K MarMH», H HHTepec K 3aHJlTHJlM elO, H TepneHHe, H
CMJ1a BonM, H HaCTOM'4HBOCTb B AOCTH>KeHHM enH. OCBoeHMe nHWb
384
'4aCTH 3HaHHM HnM AeMCTBHM MarMM, KaK OHM OTMe'4aIOT, He npMHO-
CHT ycnexa, HanpHMep B C03AaHMH Bonwe6HOM naJ10 KH.
B KHHre « epHaJl M 6enaJl MarMJI» ponb MarH'4eCKOM nanO'4KM
nanlOc 04eHHBaeT TaK: «AnJl TOro '4To6b1 HanpaBHTb npOJl neHMe
cBoeM BonH, Mar HMeeT nano Ky, OKOBaHHYIO >Kene30M: a CJ1Y-
>KHT Allfi cocpeAOTO eHHJl60nbworo KonH eeua 4>nIOHAa (3Hepre-
TH'4eCKOM CHnbl. - npUM. oem.), BblXOM ero H3 Mara H HanpaB-
neHHoro HM Ha on peAeneHHYIO TO'4Ky. 3TO a bHaJt CHna, HO caMa
no ce6e OHa He HMeeT HHKaKoro TaMHCTBeHHoro cBdMCTBa, H nlOAM,
npeAnonaralOU4 M e, TO AOCTaTO IiO OBnaAeTb MarM eCKOM naJ10 -
KOM, '4T06bl npOH3BOAHTb JlBneHHJI, ynoA06nJlIOTcJI '4enOBeKy, AY-
MaIOU4eMY, TO AOCTaTO'4HO MMeTb 4>neMT}', '4T06b1 YMeTb Ha HeM Mr-
paTb» (c. 84).
B 3aBHCHMOCTH OT 4enH na-
no'4Ky H3rOTaBnMBalOT H3 pa3HO-
ro AepeBa. MaTepMan AOn>KeH
COOTBeTCTBOBaTb nnaHeTe - yn-
paBMTenbHH4e Aena, Ha KOTopoe
pacnpOCTpaHJleTCJI MarHJI. Io1c-
nonb3yIOT TatOKe «nnaHeTapHblM»
MeTann. Ha nanO KY HaHOCJlT
cne4H4>M eCKYIO rpaBHpOBKY.
Bce 3TO M3rOTaBnHBalOT B AeHb M
BpeMJI ynpaBneHHJI TOM nnaHeTbI,
3HeprMIO KOTOpOM npHBneKalOT
AllJI B03AeMCTBHJI. KaK BHAHM,
Mano 3HaTb 06 3HepreTH'4eCKOM B03AeMCTBHH 4>Mrypbl. CneAYeT eU4e'
3HaTb, '4eM MO>KHO ycHJ1HTb ee B03AeMCTBMe H KaK 3TOT ycHnHTenb
MarH'4eCKOrO B03AeMCTBHJI H3rOTOBHTb. .
TaHHble CHflbl KpHTepHeB
Bonwe6H8R
nMeNK8 nlO6BM
.D.n &.1HTMMHblX AeI1 8011-
WOOtrylO n811 KY &.13roTaB-
11&.183IOT &.13 6ya&.1HbI B AeHb
&.1 ac BeHepbI. OTBepcTM
Ha ee KOHu.ax 38J1&.183IOT
BOCKOM &.1 06&.183IOT KOH
TOHKOO 118TyHblO &.1n&.1
Me,D.bIO. Otcypt.1BaIOT cne-
UJ.1811bHO CMeCbIO.
385
rnaBa 8
TaK. nnaHeTapHblMM l4eTaJ1naMH, ytMnMBalOLijtiMM B03AeMCTBMe
MarH'4ecKoM 4>Mrypbl B AeHb AeMCTBHJI nnaHeTbI, JlBnJlIOTCJI: AllJI Con-
H - 30nOTO, AllJI BeHeplll - MeAb, AnJl nYHIll - cepe6po, AnJl
Mapca - M<ene30, AIIft MepKYPMSI - PTYTb, AnSI K)nM!epa - onOBO
(cnnaB 30nOTa M cepe6pa), AnJl CarypHa - CBHHeLt.
Ha OAHOM CTopOHe TaJ1HCMaHa M306pa>Ka1OT nnaHery-ynpaBM-
TenbHMqy, Ha APyroM - ee rpa4>H'4eCKHM CHMBon.
Ha pMC. 56 M 57 npMBe,qt!HbI eapMaHTbI «MarH'4ecKHx TaJlMCMaHOB»
AllJI XOPOWMX H nnOXMXAeJ1. CMMBonoM csembIX nOMbicnoB 6b1J1a «n03a
pacnnaCTaHHoro, oTKpbIToro H 6e33a HOro» '4enOBeKa. CMMB0J10M
KHJl3J1 TbMbI - ronoea K03J1a.< Ha TaJlMOtaH AllJI AOOPblX AeJ1 HaHOCM-
nMCb MMeHa nepB03a4MHareneM poAiJ '4enose Koro - A,qaMa H EBb!,
Ha TaJlHCMaH AllJI 3J1bIX Aen - HMJI MOU4HOM CHJ1b1 (CaMaenb) nHJ1MT
. ( epHoM nyHbI). ECTb KOJIAOBCKMe
aTpH6yTbI pa3HOM reoMeTpM'4ecKoM
4>oPMbI, KOTopble HOCJIT nocrOftH-
HO KaK 06b1'4Hble yKpaweHHJI, Ha-
npMMep KOnbLtO (pMC. 58) HJ1M nOA-
BecKY, CTHMynHpYJl onpeAeJ1eHHbIe
3HepreTH'4ecKHe CHnbol y HX HOCM-
TenJl. OCBJlU4eHHblM MarHeM aTpH.6yr
KonAYH MO>KeT nOAapHTb HM'4ero He
nOA03peBalOU4eMY '4enOBeKY. C
BHyTpeHHeM CTOpoHbI TaKoro YK-
paWeHHJI HnM Ha ero Hapy>KHOM
cTopoHe ('4aU4e BOKpyr KaMHJI
nepCT JI) rpaBMpYIOT CHMBonbi
KonAoBcKoro MMeHM HJ1M 3aK1lHHa-
HHJI. MeTaJ1II, H3 KOTOporo M3roTaB-
PUC. 56. MarM"ecKMij
TaJ'IMCMaH.pJ1R XOPOWMX AeJl.
(OCTa8Ji Me TaJ'IMCMaHa
npMnMCblBalOT 3HaMeHMTOMY
Mary ApeBHOCTM ArpMnne
386
nMBaeTCJI KOJ1bLtO MnM nOABecKa,
MO>KeT 6b1Tb nOOblM, KaKOM Bbi
nO>Kenaere, nHweT non XeM30H B
CBoeM KHMre «OCHOBbi KonAOB-
CTBa. npaKTM'4eCKOe PYKOBOA-
CTBO AnJl BeAbM H KonAYHOB». Ho
AllJI cTHMynJlLtHH MarH'4eCKMX
CBOMCTB cBcero KonAoBcKoro xa-
paKTepa OH peKOMeHAYeT BeAb-
MaM H KonAYHaM HOCHTb YKpawe-
HMJI H3 onpeAeneHHoro MeTa1111a
B 3aBHCMMOCTH OT 3Ha'lMMOCTM
CHlYaI.tHH: 30noTO - npMAaeT
AononHHTenbHYIO 3HeprHIO H
TaifHble CHnbl KJ)HTepHes
PUC. 57. MarM'jeCKM" TdnMCMaH
ATIJI 3nblX Aen (<<HaCblnaHHJI
nop'jH», HarOBO R T. A.)
8
(]
z
Puc. 58. K011AOBCKHe atpH6yrbI: nepcreHb M «3aKOJJAOBaHHoe»
KOJ1 O (a), cOAep>t<atqHe MarM'jecKHe O1MBO.nbl: «nOAnHCb .Qb$IBOJIa» (6);
CHMBO.n nnaHeTbi CaTYPH, nl1aHeTbi CYAb6b1 (8), KOTOpaJl JlBI111eTal TalOKe
npoBOAHHKOM He'jMCTOM CHllbI; He HMelOU4HM aapo.nOfM'jeCKoro aHaJlOra
CHMBOI1 tPHrypbl CMepTH (CKe.neTa C KocoR) (z); tPHrypa Z 1I8J111eTOI
CHMB0l10M 13 apKaHoB Mar"H
387
cnoco6cr8yer exy Aena; cepe6-
po - MnMBaeT MKTyMLtMIO M Maf)4-
'IeCKMe CnOC06HOCTM; MeAb MnH
6poH3a - 6naronpMJlTCTBylOT }CAe-
xy B nK>6BM; ncnyHh, 6poH3a - pa3-
BMBal>T npoRBneHMe nCMxtNeCKMX
cnoco6HocreM; 0J10s0 - CTMMYnM-
pyer 3KcnaHCMBHOCTb M BeJ1MKOAY-
WMe;)KeneJO - npMAaeTxpa6pocTb
M npoRBJUIeT arpecCMBHbIe MHCTWH-
1C11II; CBMHelt - cnoco6cr8yer cra-
6MJ1M3al4MM MtfAMBMAYaJlWfYX 'fepT
xapaKTepa. .
nonaraeM, none3HO AononHMTb 3HaHMR 'fMTaTenR 0 3Ha'feHMM
3HepronepeH ca KpaTKMMM CBeAeHMJlMM M3 6M03HepreTMKM M He-
YpaAMLtHOHHOM MeAM MHbI.
HOf"Aa '4aIOTCJI nIOAM, KOTopble 6M03HeprMeM CBoero Te1Ia
MnH BCJ1eACT8Me annepnt'teCKOM peaKLtMM HecOBMecTMMbI C AJ)aro-
eHHblM MeranJlOM MJ1M KaMHeM
(noAP06Hee CM.: MeAH MHCKaJI
M HaTaJ1bHaJi aCTpOJlOrMJI).
KpOMe TOro, 'TYree Konb O Ha
naJ1b e, cornac.t'o HeTpaAH M-
OHHOM MeAM HHe,- '4 3MepHO
pa3Apa>KaeT 6MOnOrM'feCKM aK-
THBHble T KOJKM (6AT). 310
MO>KeT COAeMCTBOBaTb Mapywe-
HMIO 4>YHKLtMM H pa3BMTHIO 60-
ne3HM B opraHe, C KOTOpblM 6AT
rnaBa 8
OCHOaW ttyMeponO....M
«CBslU.teHHoAe"cTBHRIO
C .MarH ecKHMMIO 4>H-
rypaMH M nOBTopsno-
U.tHMM HX 4>OPMY npeA-
MeTaMM, TO)Ke HecywM-
MM onpeAeneHHbdit
3HepreTH ecKM" 3a
PSVJ.. CBR3aHbI C H8-
npaBneHHo" ne -
eH 3HeprHM.
MHTepecHwA cl»aKT
MHOrMe )KeHU4MHbI H M'f1I..-
\jMHbA HOCSIT T L\MOHHb16
lij)arQLteHHOCTM H3 30n0Ta
W1M cepe6pa. He nQAoope-
B , '4TO, C TO'tKM 3peHWI
(5H03ttepreTMKM, OHM CTM-
MynMPYIOT OnpeAeneHHbIe
Q1J1bA nH'*fOCTM.
388
TaifHble cunbl KPUTepUeB
CBJ13aHa no 3HepreTM ecKMM «KMTaMCKMM MepMAHaHaM». TaK, TY-
roe KOJ1bLtO Ha MM3MHl4e MO>KeT Bbl3b1BaTb HapyweHMe 4>YHKLtMM
CepAl4a M TOHKOro KMW HMKa, Ha 6e3b1MJlHHOM naJ1b e - 3HAOK-
pMHHW< opraHOB M, B '4aCTHOCTM, cnoc06CTBOBaTb MaCTonaT M. no-
CTO"HHoe ()tCMMaHMe cpeAHero nanb a 0c.na6nfleT MMf4YHMTeT M
clJyHKl4MIO COCYAMCTOM CMCTeMbi (BeH H apT pMM). Konb O Ha YKa-
3aTeJtbHOM nanbl4e cnoco6cTByeT HapyweH YHK HM HepBHOM
CMCTeM M TonCTOro KMwe HMt<a. HcxoAJI M3 M3J10 eHHOro, enonHe
peaI1bHO, '4TO YXYAUM!HMe CaMO'4YBCTBHJI M nofiBneHMe )l(aJ106 MOryr
6WTb BW3BaHW nOCTO"HHblM C>KMMaHMeM TYrMM Konb OM naJ1b a.
npM'teM neKapCTBO B AaHHOM CJ1Y'4ae 6YAeT nOMoraTb speMeHHO,
TaK KaK OHO He HReT caMY npM HHY. n03TOMY He peKOMeHAY-
eTa. HOCMTb TYrMe Kon a. Aa>Ke 06b1'4Hoe 1(Onb O none3HO HHorAa
CHMMaTb C naJ1b AaBaJt B03MO>KHOCTb 3Hepren1'4et aKTHBHblM
T KaM «OTAOXHYfb» OT nocro"HHoro TpeHMR M AaBJ1eHMJI.
Bo3MO>KHOCTb 3HepronepeHoca npeAMeTOM MJ1H )l(HAKOCTblO, 4atqe
BOA<*. CBoeM MJ1M CHaBeAeHHoM» APYrMM '4eJ10BeKOM 3HeprHM H3Be-
CTHa AaBHO. Oco6eHHO 310 KacaeTa. M3AenHM py'4HOM pa60Tbl, BKnIO-
4aJt npoM3BeAeHM" MCKyCCTBa: nonOTHa, eKaHKd, MaCKH, CTa1)'3TKH
M T. A- H3AeJ1MSI PY'UfOM pa60Tbl 3apSl>KaIOTCJI OT MCnOnHHTe11J1 3Hep-
fMeii C'4aCTbJI MJ1M H CTbR. KOTopwe conyTCTBYIOT aBTOpy BO Bpe.
MA TBOf)'feCTBa. OrCIQAa «MH4>MLtMpoBaHMe» 6b1BaeT A06poM H 3nOM
3HeprMeM. A06py1O 3Hepnuo, HanpMMep KapTMH xyAO>KHMKOB, MO>K-
HO MCn011b30BaTb WlR J1e'teHMJI 6one3HeM HnM KOppeKTMpOBKM Ha-
crpoeH T. e. Mcnonla308aTb He TonbKO KaK XYAO>KeCTBeHHYIO, KTe-
TM'feCKYIO HOCTb. HO M KaK 3HepreTM'4eCtcyIO. KapTMHbI MJlH MaCKH
Het'4aCTMM, 3J1OObi - He WlA ceMeMHblX Konneic MM.
H.n. nynM'4eB B CBoeM KHMre «3neKTponYHKTypHaJl AMarHoCTM-
Ka, roMeOnaTMJI M 4»eHOMeH AaJ1bHOAeMCTBHJI» (M., 1990, c. 44) pe-
389
rn8B8 8
KOMeHAYeT C ne e6HoM enblO AenaTb «OTBOA 3HeprHH» OT KapTH-
Hbi (KoHe'4HO, 6e3 nOBpe>KAeHMJI ee, C nOBepXHOCTM xonCTa). MO)l(-
HO npoeLtHpOBaTb CJ1aMA 3TOM KapTMHbI Ha 3KpaH H3 anIOMHHMJI, a
3neKTpOAbI, MAYU4He OT 3KpaHa, Ha 10-15 MHHyT npMKJ1aAblBaTb K
6MOnOrH'4eCKH aKTHBHblM TO'4KaM Tena 60nbHoro (cooTBeTCTBYIO-
U4MM TO'4KaM aKynYHKTYPbl). $IK06b1 y>Ke nOCJ1e HeCKonbKHX ceaH-
COB 60nbHble MOryr OTMe'4aTb ynY'WeHMe He MeHbwee, '4eM OT 06b1'4-
HbiX MeTOAOB ne'4eHHJI, a MHorAa M npeBocxOASlU4ee HX.
Tal(, nynH'4eB OnMCblBaeT CHJlTMe ynopHoM H cHnbHeMweM Kay3aJ1-
rH'4eCKOM 60nM nOCJ1e aMnyTaLtHH neBOM PYKH. ne'4eHHe npOBOAM-
nOCb C nOMOU4blO KapTHHbI 60TIH'4ennH «BecHa» C JlpKMMH H paAOCT-
HblMM KpaCKaMM B03pO>KAeHMJI >KMBoro. nOCJ1e 7 nepBblx ceaHCOB
60nb y 60nbHoro YMeHbWHJ1aCb Ha 8O'Yo, a nOCJ1e nOBTOpHbfX 7 ceaH-
COB - MC'4e3J1a. Ao 3Toro HHKaKoe ne eHMe He AaBaJ10 nOnO>KMTenb-
HOro pe3ynbTaTa, BKJ1IO'4aJl caMoe MOU4Hoe, Kal(, HanpHMep, HapKoTH-
KOTepanHJI, CHMnaT3KTOMHJI H
Aa>Ke TpenaHa HJI '4epena (one-
pa MJI Ha ronoBHoM M03re B 30He
"pOeK HH 60nH). nynM'4eB OT-
Me'4aer, '4TO B03AeMCTBHe 3Hep-
rHH KapTHH nHKacco 06b1'4HO
none3HO npH HapyweHHJlx eH-
TpanbHoM HepBHo. CHCTeMbI,
3HeprMM KapTHH MaTMcca - np
60ne3HJlx no eK H T. A.
K Mra H.n. nynM'4eBa HanH-
caHa AnJi Bpa'4eM H AnJl TeX. KTO
HHTepecyeTCJlHeTPaAH HoHHOM
MeAHLtHHoM.Cepbe3HOCTbH3Aa-
EcnM aepJl'rb OKKYn. TM3-
MY, ir1CnOllb3}'S1 aHa11or 1O
nO.AJU1 eHir1R nOBepxHoc-
Tir1 npeAMeTa K TellY. MO>K-
HO C ir1TaTb. '4TO. Ha.o.eBaR
KOllbU,O, KYll0t+ir1llir16pac-
lleT c acaMir1, oti ir1nir1
py6awKY ..c Y>Koro _cnlle-
a., Mbi To>Ke HenocPeA-
CTBeH'::Io'flo.AJU1IO aeM ce6R
K BOCnpir1RTir11O 3Heprir1ir1,
KOTOPYIO cOAep>Kir1T Be b.
390
HHJI nOATBep>t<,qaeTCJI TalOKe TeM, '4TO aBrop CCblnaeTCJI Ha H3nO>Ke-
HHe B KHMre onbiTa MHoroneTHeM pa60TbI Ha Ka4>eApe pe4>neKtOTe-
panMM UeHrpanbHoro HHCTMTyTa YCOBepweHCTBOBaHMJI Bpa'4eM
(MocKBa). TaK '4TO, HecMOTp" Ha CBOIO He06b1'4aMHOCTb, AOCTOBep-
HOCTb MH4>opMaLtHM He Bbl3b1BaeT COMHeHMM.
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KOPOH9; - TOPYIO KopOl1esa
nep o eclQl1 Ha,a.esaeT no
CI1 alO TOp>KeCTS.
398
TaUHble cunbl KpUTepUeB
HaJl CMepTb npKH&4a AAb6epTa, My>Ka BMKTOpMM, KOTOpOrO OHa O'4eHb
nI06MJ1a. OAHaKO yraCJ1a nM Ha 3TOM 3HeprMft 3nOrO M npeKpaCHOrO
KaMHJI?
B 1937 r. nepeA KopoHa4HeM Koponb feopr VI npMKa3all nepe-
CTaBHTb Ma3 B 6pMTaHCKylO HMnepaTopcKyIO KOpOHy.:)fcyOPMKM
nOCJ1e 3Toro KOHCTaTMpOBaJ1H o epeAHoe ..eC'4aCTbe: npM >KM3HM
KOpOnft, B 1948 r., 6pMTaHcKaJl HMnepMJI 6.b1na nMKBMAMpoBaHa,
MoryU4eCTBo aHrnMMcKoro KOpOnJi "aJ10.
KaKHe O'4epeAHble HenpHJlTHOCTH MO)f(HO YBJl3aTb C pOKOBbiM
BO]J\eMCTBHeM «npoKJ1J1Toro aJ1Ma3a»? Bce nM 6naronOnY'4HO B ce-
Mbe caMoM KoponeBbI? 3 COO6uteHMM ne'4aTM M TeneBHAeHMJI Mbi
3HaeM 0 pOKOBbiX pa3HOrnaCMJlX Me>KAY npMHLteM Y3J1bCKMM M npMH-
4eccoM AHaHoM, 0 TparM'4eCKOM CYAb6e npM+t4 CCbI AMaHbf. MO>KeT
6b1Tb, npOKJ1J1THe 6YAAbI npoAOn>KaeTcJI?
B03bMeM APyroM npHMep - TO>Ke 3HaMeHMTblM aJ1Ma3 « BeTHoM
MHAYC» YHHKaJ1bHOro can4>HpoBoro 4BeTii M Beca (112 KapaT). OH
6b1Jl BCTaBneH «TpeTbMM ma30M» B CTaTYIO 6YAAbI, HaxOAJIU4YIOCJI B
OAHOM H3 HHAHMCKHX xpaMoB. ComacHo nOBepblO, noxMU4eHHe K M-
HJI HaBneKaJ10 Ha BHHOBHoro npoKJ1J1TMe. B KOHLte XVIII B. aBaHTIO-
pHCT H3 cJ»paH4HH )l{aH-KnoA TaBepHbe npeHe6per nOBepbeM, no-
XHTHn aJ1Ma3 H npMBe3 ero Ha POAHHY, nOAaPMB CblHy Ha CBaAb6y.
npOKJ1J1THe Ha'4aJ10 AeMCTBOBaTb...
4epe3 HeCKonbKO He,qeJ1b nacne nOJ1y'4eHMJI nOAilPKa no HeOObJlC-
HMMOM npH'4HHe CblHa TaBePHbe Ha OXOTe pa30pBana ero Co6crBeHHaJI
cOOaKa. nOTpJlCeHHblM OTeLt BCnOMHHn n(>eAYnpe>KAeHMe 0 npoKJ1J1-
ntH M nocneWHn H36aBHTbCJI OT anMa3a. 4epe3 npMABopHOto IOBenH-
pa 3a orpoMHble AeHbrM OH npoAan anMa3 KOponlO nlOAOBMKy XIV. no
npHKa3Y KoponJl aJ1Ma3Y npHAanH 4>oPMY cepA CAenaB ero nO'mt
BABOe MeHbwe. OAHaKO CHna npoKJ1J1TbJl OT 3TOro He YMeHbWMnaCb:
399
rnaBa 8
«3HeproMH4>eK HJI» He 3aBHCHT OT
06DeMa npeAMera.
nlOAOBHK XIV HaAeJ1 :nOT KaMeHb
Bcero OAMH pa3, nocne '4ero BCKope"
3a60nen HeH3J1e HMOM TorAa 60ne3-
HblO - ocnOM - M YMep. CBena
CYAb6a C'4eTbi H C TaBepHbe: BO.BpeMJI
nyrewecTBHJI no POCCMH OH 6b1n y6HT npH HeBblJlCHeHHblX 06CTOJI-
TeJlbCTBax.
MMa3 CTaJ1a HOCHTb MaAaM AI06apPH, OAHa H3 nK>60BHHLt nIOAO-
BMKa'IN. Ee TO>Ke HaCTHraeT HeC aCTbe: BO BpeMJI peBonlO HH OHa
6b1na rMnbOTMHHpOBaHa. TaKOM >Ke HaCHnbCTBeHHOM CMepTH nOABep-
rnHCb ABa CJ1eAYIOU4Mx X03JIHHa aJ1Ma3a: Koponb J1IOAOBMK XVI H KO-
pOl1eBa MapMJI-AHTyaHerra, non HBWaJl «aJ1Ma3 HeC'4aCTHM» B Ka-
'4eCTBe nOAapKa. KHJlrMHJI, 6nH>KaMWaJf nOAPyra KoponeBbI, '4acro
HaAeBaBWaJl npoKnJlTbiM aJlMa3 H 3aBHAOBaBWaJl ero X03J1MKe, 6b1J1a
paCTep3aHa tePHblO npH pa3rpOMe BepcaJIbCKOrO ABop a. B 6ype
peBonlOLtHH anMa3 HC e3ieT HeM3BeCTHO KYAa Ha Aec1lTKH neT.
B 1930 r. OK nOJlBnJleTCJI B AH.mHH.. MMa3 nOKYnaeT nOPA Xoyn,
HMeHeM KOTOpOro CTanH Ha3b1BaTb 3TOT al1Ma3 BnOCJ1eACTBMH -
«anMa3 Xoyn». HTepecHoe COBnaAeHHe: aJ1Ma3 «KOXHHOP» TO>Ke
ABa>KAbf t4eHJln CBoe HCTOpH'4ecKoe Ha3BaHHe M ABa>KAbi «XYAeny;
, C MOMeHTa nOJ\ ne JI B CeMbe Xoyna npoKnJlToro anMa3a ero
6nH3KHx Ha HHaIOT nJfeCJ1eAOBaTb HeYAa'4H. CeMbJl Ha rpaHH pa30-
peHMJI. BHYK Xoyna BblHY>KAeH npoAaTb lIaCTb AparOLteHHOCTeM,
BKnIO'4aJl a3, Type KOMYTOproB4Y AP rOLteHHOCTJlMM Xa6H6-6elO.
Yepe3 MeCJlLt nOCJ1e npH06peTeHHJI aJ1Ma3a Xa6H6-6eM nOTep-
nen Kopa6neKpyweHHe H yToHyn. l!enoliKa HeC'4aCTHM npOAOn>KH-
naCb... tOBeJlHp, KYnHBwHM aJ1Ma3 y pOACTBeHHHKoB Xoyna, pa30-
ComaCHO OKJCynbT-
HOMy Y'f8HMIO
npoK11RTHe - 3TO
"3HepreTH ecKaSl
HH$eK'-'HSI» .
400
TaUHble cunbl KpJ.1TepUeB
pHnCJlIo1 6b1n BblHY>f(AeH nepenpOAaTb aJ1Ma3. BTOpO IOBeIlMp, CTaB
X03J1HHOM «anMa3a HeC'4aCTMM», norH6 npH orpa6neHHH.
nOCJ1e BTOpoM MHpoBOM BOMHbI «aJ1Ma3 Xoyn» KYnHn aMepHKaHC-
KHM ra3eTHbiM MarH&t 3ABapA MaK-nHH. BepeHM CMepTeM J1poAon-
>KHnaCb. BCKOpe nOCJ1e nOKYnKH anMa3a YMepna MaTb M'U.l1HHa, 3a-
TeM ero lQ-neTHIo1M CblH, nOCJ1e Hero OT CJ1 MHOM nepeA03MpOBKM
CHo opHoro norM6na ero A b. MaK-nHH cow C 'jMa, 3aKOH HB CBOH
AHH B CYMaclUeAweM AOMe. Ero >KeHa 3BeJ1HH: tny4aMHO y3HaBWaJl 0
BHceBweM HaA anMa30M npOKnJlTHeM, 6b1CTpO npo a ero MHJ1J1Hap-
Aepy fappH YHHCTOHY (He ynycrHB npH 3TOM AJ1J1 ce6J1 MaTepHnbHOM
BbiroAbI). Ho 0 TaMHe npoKJ1J1Toro anMa3a - HaBl1e'4eHHH Het'4aCTMM
Ha nH'4HOCTb ero BJ1aAeJ1b - y3HaeT YHHCTOH. OnaCaJlCb 6eAbI, OH
nOAapHn anMa3 CMHTCOHOBCKOMY MHcnfTYTY, COBepWMB 6naroe AeJ10:
nonO>KHn Ha'4aJ10 ero KonneK HM AparoLteHHblX KaM YHHCTOH He
nO>KaJ1eI1 3aTpa4eHHblX Ha nOKynKY aJ1Ma3a CpeACTB (rpoMa,o.Hble no
TeM BpeMeHaM AeHbrH - 24 MW1I1HOHa AonnapoB) - >KH3Hb Aopo>Ke.
B MCTOpMH H3BeCTHbi (np0KnJlTble» COKpOBHuta TyTaHxaMOHa,
nOCJ1eAHerO erHneTCKoro 4>apaoHa XVIII AHHaCTHH. B Te ApeBHHe
BpeMeHa B Erlo1nTe HcnOBeAOBaJ10Cb "'Horo60>K e, HO npeAweCTBeH-
HHK TyTaHXaMoHa cbapaoH 3xHaToH cseeM BnaCTblO BBeII n0KJ10He-
HHe OAHOMY 60ry -. ATOHY, 3a '4TO 6b1n npOKnJlT >KpeLtaMH. npo-
KnJITHe nepewl10 Ha 3J1Tfl 3xHaToHa: TyTaHXaMOH YMep B 18 neT npM
TaHHCTBeHHblX 06CTOJlTenbCTBax. HHTepeCHO, '4TO '4MCJ10 9 B era
>KH3HH 6b1no KpHTH'4ecKHM (0 «KpHTH'4eCKHX» B >KM3HM eJ10BeKa
'4MCJ1aX - CM. COOTBeTCTBYlOutHM pa3AeJ1 AaHHOM KHHrM): TyTaHxa-
MOH 6b1n erHneTCKHM 4>apaoHoM 18-M AHHacTHH (1 + 8 - 9) B
1350 rr. AO H. 3. (1 + 3 + 5 + 0 - 9).
fp06HHLtY TyTaHXaMOHa He YAaJ10Cb 06Hapy>KMTb, XOTJI ee ynop-
HO HCKaJ1M KaK Hay4Hble 3KcneAM MH, TaK M «OXOTHHKH 3a COKPOBM-
401
rnaBa 8
U4i1MH». B.1922 r. 143BeCTHbiM ap-
xeonor M erHnTonor rOBapA Kap-
rep, opraHH30BaB 3KCneAHl4HIO Ha
cpeACTBa nOPAa KapHapBoHa, 06-
HapY>KHn HeTpOHyTylO rp06HMLtY
TyTaHxaMoHa - 3TO Bbl3BaI10 MH-
poBYIO CeHCaLtHIO. MHOro YHHKaI1b
HbiX AparOLteHHOCTeM OTKpblnOCb
MI4PY. 6eCl4eHHOM, HanpHMep, JlB-
nJleTCJI 3HaMeHHTaJl 30nOTaJl Mac-
Ka IOHoro 4>apaoHa - HeKOTOpble
'4HTaTenH, BepOJlTHO, BHAenM 3TO
COKpOBH e, KorAa KaHpcKHM MY-
3eM BbiCTaBnJln CBOM 3KcnOHaTbi B
CCCP. fonorpa4>H'4eCKHe CHHMKH
'4aCTM 3KcnOHaTOB MO>KHO 6b1no
nOTOM BHAeTb Ha BbiCTaBKe XY-
A0>KeCTBeHHblX npOM3BeAeHHM B
MHHcKe.
npoKnJITl4e nOAeMCTB0BaJ10 He3aMeAJIMTeJ1bHO. nOPA 6biJ1 YKYweH
MOCKMTOM H 3a60neJ1 nMxOpaAKOM, npoTHB KOTOpOM OKa3aI1MCb 6ec-
CMJ1bHbI Bce cOB MeHHble neKapCTaa. CMepTb nOPAa KapHapBoHa,
KaK HM crpaHHo, COQpoEU?>KAanaCb pa3rynoM CTHXHM npHpoAbi. Ap-
xeonor LtepeH B KHMre 6H6neMCKMe xonMbI» onHCblBaeT 310 TaK:
«>KH3Hb nOPAa KapHapBOMa 06opBaJ1acb B caMOM POCKOWHOM roCTM-
HHLte KaH !,. 6ypHYIO rpo30BYIO H0'4b, K KHe peAKO CJ1Y"1aIOTCJI B
ErMnTe. Or YAapa MonHMM' noraCJ10 3neKTpM'4eCTBO. C>KHraeMbiM nM-
XOpclAKOM KapHapBOH, HanyraHHblM crpaWHblM YAapoM rpoMa, Hanpac-
HO 3Ban B TeMHOTe CHAeJ1KY, OT crpaxa y6e>KaBWYIO B nOABaJ1.. .».
n0'l8TH08 npallO nep-
BbiM BOHTII'I B rpo6HIo1UoY
TyraHXSMOHa OblJ10 npe-
AOCT8BJ1eHO nopAY Ksp-
HSPBOHY. OH C PaAOCTbIO
nplo1HSln nP8AflO)KeHlo1e.
OpraHIo138TOpbI 1013 aTelo1-
CTIo1 ecKIItX y6e)K,D,eHIo1H
He nplo1,D,8Tllo1 Aon>ICHoro
3H8'fBH101S1 Ha,o,nlo1clo1 HS
6amce HB,D. BXOAOM B
rpo6Hlo1u.y: «6e3JKBnO-
CTHBR CMepTb,D,8 nocTHr-
HeT HBPYWHswero no-
KOH era SenH'Iecrsa H
nOCRf"HYBw'lfO HB npH-
H8A/1eJKaUlf'Je eMy».
402
TaHHble CURbi KpHTepUeB
ATeHCTbI, BepmlTHO, ynbl6HyTC , a nIOAH, BepJlI14He B '4YAeca H B
«He3eMHble CMnbl», npH3aAYMaIOTCJI... BOT eU4e nMU4a AllJI pa3MblW-
neHMM, AononHHBwaJl BblwecKa3aHHoe OAHOBpeMeHHo npoMcweA-
WHM CTpaHHblM 4>aKTOM, KOTOpblM, KaK H BCJI LtenO'4Ka 4(Q1Y'laMHOC-
TeM», He nOAAaeTCJI norM eCKOMY 06'bJlCHeHHIO. KorAa ITOPA YMep B
ErMnTe, ero nlO6MMaJl c06aKa, HaxOAJICb 3a n.CJI'4M MHnb OT X03J1M-
Ha B AHrnHH, O'f\laJlHHO 3aBbfna H TO>Ke ynaJ14 ",epTBOM.
K 1929 r. YMepnH 11 '4eJ10BeK, TaK HnH HHa e CB HHblX C COKpO-
BMU4aMH 4>apaOHa. CpeAM HMX TpH poACTBeHHHKa nOPAa. neAM Kap-
HapBOH, KaK 6b1 aHaJ10rH'4HO C MY>KeM (:no MO>KHO Ha3BaTb KapMOM),
TO>Ke nOCTHrna TaKaS! >Ke CMepTb: OHa YMepna ot YK}'Ca MOCKHTa! K
1935 r. 6e3BpeMeHHaJl cMepTb nOCTHrna B 06U4eM CJ10>KHOCTH 22 '4e-
nOBeKa, npUl/ocmHblx K COKpoBMU4aM TyTaHStclMOHa. CnMILIKOM A/lMH-
HaJl H perynJlpHaJl no BpeMeHH HcnOnHeHHJI Lteno'4 eC'4aCTHM H
CMepTeM! CTpaHHaJl 3aKOHOMepHOCTb, He npaBAa nM?
npOeKL\MM CXeM MarMM
KaK nOKa3ana >KH3Hb, KpaTHbie AeJ1HTenM «He6eCHbiX CTBonOB»
H «3eMHblX BeTBeM», oc06eHHO nepBble HX napbl - '4MCJ1a 2, 3 H 5,
JlBJ11InHCb H JlBn IOTCJI nOCTO HHbIMH cnyTHMKaMM AeJlTeJlbHOCTM
'4eJ10BeKa. OCHoBaHHble Ha HHX ABOH'4Hble M TpoM'4Hble MOAeJ1M nemH
B OCHOBY u,enoro pJlAa 4>eHoMeHoB, KOTopble pacnpocrpaHeHbI B
npaKTHKe. 3T0 '4neHeHHJI 64-M reKcarpaMMbl KBaApaTa 8 x 8 - CMM-
Bona ABOH'4HOH MOAenH H 81-TeTparpaMMbl KBaApaTa 9 x 9 (MMelO-
U4ero 324 '4epTbI) - cHMBona.TpOH Hoi1 MOAenH, CHCTeMbi no wY H
X3 ry H T. A. 3TH CHCTeMbi AownH AO crpaH EBponbi H HepeAKO CO-
xpaHHnHCb AO HaWHX AHei1. HanpMMep, B HHTenneKryanbHblx
403
rnasa 8
cnopTMBH X Mrpax npM3HaHMeM no.nb3Y1)TCJI 64-KJleTO'fHbIe wax-
MaTbi M waWKM. Ha BocroKe Bcrpe'taIOTCJI M 60nee cnO)l(H e 324-
KIIeTO'fHwe waWKM, i1po06pa3 'fepr 81-A TeTparpaMMW.
npMBeAeM npMMepw oKKYnbTHwx cxeM, cn qMpoBaHHbIX Ha
caMY >KM3Hb.
AnJi 3.neMeHTapHWX c eTHbiX
npoqt!AYP O'feBMAeH OCHOBono.na-
ralOutMM xapaKTep '4MCen 2, 3 ..
5 (pa3yMeeTCJI, BMecre (: «yHMBeP-
canbHWM» 'IMcnOM 1). npaKTMlCa
cBM,qeTeJlbCTByeT, '4T0 MOHeT MMeH-
HO TaKOra AOCTOMHCTBa AQC1CI1'O'4HO
AM npoBeAeHMJI nlOObIX pa3MeHHbIX
onepaqlllM, '4T0 M Mcno.nb30BanOCb
ApeBHMMM npaBMTe.nJlMM npM '4e-
KaHKe ,qeHer. HYMepo.norM'4eclCoe
3Ha'4eHMe '4MCen 2, 3 M 5 npM3Ha-
BaJ1.. M B ApeBHeM BaBMnoHe, r,qe Ha OCHOBe MX crpOMnaCb B -
'4MCJ1MTenbHaJl npaKTMKa.
M3BeCTHO, TO 64- .neHHblM KOMMeKT reKcarpaMM COCTOMT M3
384 '4epr MnM OTpe3KOB, M MMeHHO B TaKOM COOTHOweHMM 1/384 'Ia-
CTM HaxoAMnMCb.6a30Bble AllJI 3nOXM )I(oy Mepw 'BeCa - tpMHb
(KMTaMCKMM cWm, ilCr\S"b3yeMblM M nOHblHe) M 'I>ICY (oKano 0,6 r).
Een.. npMHJlTb Ka)l(AYlO '4epTY reKcarpaMMbI - a MX 384 - ]a eAM-
HMLW aeca B 1 '4JKy, 10' ace 64 eAMHMq reKcarpaMMbI 6YAYT «Be-
CMTb» poliMo 1 tpMHb.
AHanOrM'4HblM MeiponOrM'IeCICMM 3Ta110HOM JlBII_era CMCTeMa
M3 81-M TerparpaMMbI, 06pa30BaHHOA M31620 '4epT, T. e. mm4KpaT-
HO YBenM'4eHH X MaTpM'4HblX '4epT: 384 x 5. Ee TpOM'4tfY1O CMCTeMY
CI>Mn w C'tMT8nM,
TO cxeMbI no wy ... X3
TY COAep)K8T yti...aep-
C8nbHyK> CTPYKTYP')I
I103HaHMA.. opraH....38-
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OKKynbTHbie cxeMbI
'faCTO npoeuMpoaan...
Ha C8M')1 )KM3Hb.
.
404
McnOnb3osan Y'"!HWM flH CIOH.
npeAl10>KMB '4MCJ1O&yIO MaTpM-
LtY 06'beMa MMnepaTOPY BaH
MaHY (9 r. H. 3.), BBeAeHWYIO
nocneAHMM B >KM3Hb 06u4ecTI,a
KaK 3TanOH MepHoro cocyAa xy.
06'beM cOtyAa onpeAenReTCR
'fMcnOM 1620 06'beMHbIX e.qM-
HMq. 310 Meno npM pa1l10JKe-
HMM Ha MHO)l(MTenM AaeT BWpa)l(eHHYIO TpOM'4HOCTb, YaK KaK OHO
OCHOBaHO Ha nM4>aropoBoM TpOMKe: 1620 - (3 x 3) x (3 x 4) x (3 )(
x 5). TaKMM 06pa30 'fMCJ10 16206b1J10 Bblpa3MreneM BaJt(HoM B
Toproene KMTaR Me1pOnorMqecKoM eAMHMijbl 06'beM
B 3l1Oxy >Koy (XI-III BB. AO H. 3.) McnonbsyeMblh Toprosne B
Ka ecT8e 3Ta110Ha MepHblM cocyp. Y COOTBeTCTBOBa11 eMK , paB-
HoM 64 6a30B M e.qMHM4ilM - W3HaM. ECJ1M C'4MTa 'ITO Ka)I(AaJl
reKcarpaMMa MMeeT 06'beM 1 W3H, TO Becb HX 64-'UleHHblM KOMn-
neKT 6yAeT MMeTb 06'beM, paBHbfM 14Jy.
B KMTaMcKoM KyJ1blYpe M B )l(M3HM 06U4ecTBa oKKynbTHbie cxe-
MW M MarM'4ecKMe KBaAJ)aTbi McnOnb30BanMCb KaK MOAenM CTpyK-
lYPMpoBaHM M cI>opMbf M3-
nmKeHMR npOM3BeAeHMM
caMOro WMpoKoro cOAep-
Jt(aHMR: c1JMJ10C04>CKMx,
n03TM ecKM MaTeMaTM-
ecKMX. reorpacl>M'4eCKMX
MAP. B TpaAM14MOHHOM KM-
TaMCKOM KyJ1blYpe YaKMM
06pa30M CMOAenMpoBaH
TaHHb/e CHnb/ IqJHTeJ]HeB
MCTOPM'f8CItMI cnpa_a
B HeKOTOpbO< C'TpBHax Boc-
TOKa OKKY"bTHbie Bentr4MHbI
MCel1 MX n
MHorO geKOB MCnOnb30B8-
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HIi'IR Beciir M .QnMHbI.
M3 my6MHW 1181(08
Bl\pesHeM KMTae I1pM KOHCT-
PYKL\MM H8}"tHbO< MHCTPYMeHTOO
M B CTPyuype 3aKOttQABTe11bHbIX
TetCCTOB McnOllb308a11li'1 MeTPO-
I10rWfeCIGte scneKTbl, 8K111O'48-
lOU4Me pS3,Ael1eHMR Ha 2. 3 M 5.
405
rnasa 8
3HaMeHHThlM 4>HJ10C04>cKMM rpaKTaT
«XYHb 4>aHb», HnM «BenM'4aMWMM
06pa3el4». Ero Ha3BaHHe rOBopHT
caMO ]a ce6J1. OH COCTOHT M3 rpex
'4aCTeM, Ka>KAaJl M3 KOTOpbIX MMeeT
9 pa3AenoB C H3nO>KeHHeM Bcex Ha-
Y'fHblX n03HaHHM BpeMeH xaHbCKHX
Y'feHblx (npHMepHo 50 r. AO H. 3. -
200 r. H. 3.).
,[\peBHMM TpaKTaT « >KOY H»
HMeeneKCTOBYIO MaTpMLtY, COCTaB-
neHHYIO M3 64 aCTeM. B 3TOM rpaK-
TaTe co06l14anocb, '4TO 384 '4epTbi
64-'4neHtiOM reKcarpaMMbI 8 KaneH-
AapHOM H acrpOHOMH ecKOM acneK-
Tax CMMBonH3HpYIOT KOnH'4eCTBO
AHeM BMCOKOCHoro KHTaMcKoro
roAa. }rOT rOA HMen 6 MeCJll4eB no
29 AHeM H 7 MeCJlLteB no 30 AHeM.
'ineHeHHIO reKcarpaMMbI TaK>Ke COOTBeTCTBOBaJ10 AeneHHe pa3Ae-
nOB TeKCTa «4>Koy M»: 729 OCHOBHblX M 2 AononHHTenbHble CTp04>bI
TeKCTa «KaHoHa lIenHKoM TaMHbI» (pa3Aen «4>Koy H») MOAenHpo-
BaJ1M KOnH'4eCTBO Q0¥Y10K (AHeM M HO'4eM) B roAY, COCTOJuqeM
COOTBeTCTBeHHO M3 364,5: 365,5 CyTOK.
B HYMeponOrHI4 Mi1fa 2 H 3 ne>KaT B OCHOBe H3MepeHHM Bcero
CYU4ero, HaWpMMep BpeMeHH. npH'4eM 3T.M HCJ1a He BcerAa «ne>KaT
Ha nOBepXHOCTH», a CKpblTbf B rny6HHe. Tat<. '4HCJ10 360, CHMBonM-
3HpYIOI14ee CTe6nH TblCJI'4enHCTHHKa, B ApeBHOCTH 6b1no MepMnoM
BpeMeHH rOAa. 4HCJ10 TblCJI'4enHCTHHKa COCTaB1lJleT cyMMY 216 «He-
ECTIt MHetlM8
Co3AaTe11b K&ifTalilcKOIiI
IilCTOpl>1'fecKOIiI HaYK&II
CblMa UslHb B CBoeM
3HaMeHKTOM TpSKTaTe
« cTOpl>1 eCK&IIe 3an&llC-
K&IIIt (11-1 BB. AO H. 3.)
nio1C811: «AnR Tex. !<TO
I>1CKYCeH B HeOecHbIX
nOAc eTax,cneAyeT
npoHl>1KHyTb (B CI>1MBO-
I1&11KY) I>1Cel1 «TP&>1» &>1
«nRTb lt I - &II .o,anee nOA-
epKI>1BaJ1: - npaBR-
UU11i1 rOCYASpcTBOM
A011)tceH B O LteHI>1Tb
I>1Cl1a 3 1>1 5».
406
TSHHble CHnbl KpHTepHeS
6ecHblx» H 144 4C3eMHb1X» '4MCen. 3a 3TMMH '4HCJ1aMM CTOMT B3aMMO-
CBJl3b '4MCen 3 («He6ecHoro», HnM He'4eTHOro) H 2 («3eMHoro HnM
'4eTHoro), TaK KaK 216: 144 AaeT cootHoweHMe 3 2. B BOCTO'4HOM
MaTeMaTH'4eCKOM npaKTMKe CTe6nM TblCJI'4enHCTHMKa MCb npo-
06pa30M Ha60pa C'4eTHbfX naJ10'4eK-'4eTOK - CHMBon Bp"eMeHM rOAa,
Te'4eHMJI AHeM. nepe6MpaHMe nanO'4eK-'4etoK B YA06HOM n03e, C
norpy>KeHMeM B c06CTBeHHoe C03HaHHe BoenplfHHMaJ10Cb KaK CO-
eAHHeHMe C BpeMeHeM: naJ1bLtbi «J1MCTanH» AHM. «BpeMJI ne'4HT
paHbI», - rOBopMnH ApeBHMe; Mcnonb3YJI nepe6MpaHMe '4eTOK AnJl
ycnoKoeHMJI H KOHLteHTpaLtHM BHHMaHMJI.
C03AaTenb KMTaMCKoM MCTOpM'4eCKOM liayKM CblMa Hb OTMe'4aJ1
Ba>KHOe Y'4aCTMe 3THX '4MCen B HYMeponOrM'4eCKOM MaTpHLte pacno-
nO>KeHHJI 3se3A MHorMX cp3Be3AHM H KaK KpHTepMM «""BopOTa Bpe-
MeHM» 3Be3AHblx opHeHTHpOB He6a OTHOCMTeJlbHO MnH. nOCJ1e-
AHee HM BbiAeneHo B M3MeHeHHe «He6ecHoro BpeMeHH», KOTOpoe
HMeno cneAYIOU4Me HHTepecHble KpMTepHM: 3a 30 neT (npHMepHO
nOn>KM3HH, eCJ1H ee cpeAHlO1O npOAOn>KMTenbHOCTb C'4MTaTb 65-
70 neT, '4TO B CBOIO O'4epeAb JlSnJleTa BpeMeHeM nOBOpOTa OAHoro
3HaKa 30AMaKa Ha OAMH rpaAYC c4>epbl MnM BpeMeHeM npe4eCCMM
3HaKa no He6ecHoM c4>epe. - npUM. asm.) cosepWaeTCJI OAHO
«He6onbwoe M3MeHeHHe He6eCHoro BpeMeHM»; 3a 100 net (npM-
MeHHTenbHO K '4enOBeKy - 3TO >KH3Hb crapeMWHHbI I4nH nonTopbl
MX npOAOn>KHTenbHoCTH >KM3HH) - «cpeAHee He6ecHoe M3MeHe-
HHe»; 3a 500 neT (>KH3Hb HeCKonbKHX nOKoneHHM) - «60nbwoe
M3MeHeHHe». TpH 60nbwHx M3MeHeHMft BpeMeHH He6a AaIOT 3no-
xy - 1500 neT. KaK BMAMM, 3TH OTpe3KM «He6ecHoro BpeMeHM»
KpaTHbi '4HenaM 3 H 5.
npaBMTe11M BOCToKa nOMHHnH 3anOBeAH BHAHeMwHx eHblx CBo-
ero BpeMeHH, co CCblnKOM Ha He6ecHbie 3aKOHbI 060cHoBaBwHx oco-
407
rnBSB 8
6ylO eHHOCTb CHCTeMbi «caHb
y» - «1peX M nJlTH» B ynpaBne-
HMM roCYAapCTBOM M CO HaJ1bHOM
ero MCTBe. KHTaMCKHM MCTO-
pHK cJ»aHb 83Hb11aHb B <<J\peBHe
MCTOpMM KMTaJl» (M., 1958) nM-
CaJ1, TO npH WaHCKOM AHHaCTHH
HMeJlHCb Bcero TpM BblCWHX nrry-
na M nJlTb BHAOB BnaCTH.
B reorpa4>H'4eCKHX H3b1CKa-
HMJlX 3Be3A0'4eTbI 06HapY>KHnM,
'4TO 9-K/leT0'4HblM KBaApaT no wy KaK Henb3J1 peanbHee OTpa>KaeT
M3MepMTenbHble BeJlH HHbI H npoc eT nnoU4aAM He TonbKO roCYAap-
CTBa KHTaM, HO M BceM nOAHe6ecHoM - Bcero 3eMHoro wapa. Cpe-
AH KHTaMCKHX MblCJ1HTeJleM 06lqenpHHJlTbiM 6b1no HYMeponOrM'4eC-
Koe pa3AeJI He nO.AHe6eCt::IOM Ha 906naCTeM. M3H lPbI (IV B. AO.
H. 3.) pa3pa50TaJ1 cxeMY HYMeponOrM'4eCKOM KOH enLtHH «KonOAe3-
HbiX 3eMenb», B OCHOBe KOTOpOM ne>KaJ1 06pa3 aCTKa 3eMnM (nonJl)
B BMAe AeBJlTHK/leTO'4HOrO KBaApaTa co CTOpOHOM B 1 nH. OH >Ke
yTO'4HMn pa3Mepbl TeppHTopHH KHTaMcKHx roCYAapCTB (4)KyH ro),
3aHHMaeMoH HMH B TO BpeMJI. no ero AaHHblM, OHa COCTOJlna H3
9 KBaApaToB, CTQPOHa Ka)t(AOrO H3 KOTOpblX paBHa 1000 nH. np
MCTOpH'4eCKOM npoeepke C Hcnonb30BaHMeM cOBpeMeHHblx pac'4e-
TOB OKa3aJ10Cb, '4TO 3TO COOTBeTCTBOBaJ10 HCTHHe.
eHblM 4>Koy jlHb (Iv-ill B. AO H. 3.) Ha OCHOBe KBaApaTa no my
pa3pa60 .cBolO reorpa4>MKo-HYMep011OrM'4eCKyIO cxeMY, comaCHO
KOTOPO 4>KyH ro 3aHHManM 1/9 OAHOro H3 AeBJlTH MHpoBblX MaTepH-
KOB, HnH COOTBeTCTBeHHO 1/81 BceM nOAHe6ecHOM. no ero paC'4eTaM,
nnOlqaAb BceM nOAHe6ecHoM npeACTaBJ1J1eT KBaAPaT co CTOpoHOM B
MCTOpM'I8CKSIi cnpSBKS
npaKT eCKOe BHeAJ)e-
H e KaTeroplil1il occaHb y. B
>K1iI3Hb 06l!.1.ecTBa BOCXO-
A T no Kpa"'Heft Mepa K
cepeAIiIHell cR eneTIiIR
AO H. 3., T. e. cOlil3Meplil-
MO c Ha aJ10M AOtcyMeH-
TaJ1bHQft CTOplillil KIiITaR.
408
27000 nH, '4T0, K YAMBne-
HHIO eOBpeMeHHblx reorpa-
4>OB, OKa3anOCb AOBonbHO
T0'4HOM BenH'4HHOM.
ECJ1H yQ""eCTb ABa HeTO-
pH'4eCKMX BapHaHTa AJ1M-
Hbi nH KaK eAHHHLtbi nH-
HeMHoro H3MepeHHJI, TO
nonY'4HM ClIeAYIOU4Me CO-
OTHOWeHHJI: '4>KOytKoe nH
paBHo 477)34 M, a UHHbC-
Koe nH - 497,7 M.
enonb3YJI HaY HYIO
HHQ>opMaltHIO A. . K063e-
Ba B KHHre «Y'4eHMe 0 CHM-
Bonax H '4HCJ1ax» (c. 344)"
4>YHAaMeHTanbHo npopa-
60TaBwero TeKCTbI MHorHX
KHTa cKHx TpaKTaTOB III-II BB. AO H. 3., COCTaBHM Ta6nHLtY ApeB-
HeKHTa CKHX AaHHblX 0 pa3Mepax 3eMnM, epaSHHB MX C COBpeMeH-
HblMH AaHHblMM (Ta6n. 5):
«C npHHJlTHeM '4>KoycKoro nH pa3HHlta B ycpeAHeHHblx BenH4H-
Hax Me>KAY peaJ1bHOCTblO H HYMeponorH'4eCKOM cxeMoM OKa3aJ1aCb
HH'4TO>KHO MaJ10M, pasHoM npHMepHo 16 KM, T. e. 1,25% H3MepJle-
MO npOTJI>KeHHOCTH ('4TO C n03HLtHM HaY"lHOM CraTMCTI4KH MO>KHO
OlteHHTb KaK BbfCOKyIO CTeneHb AOCToBepHoCTM oKKynbTHOfo pac-
'4eTa. - npUM. osm.). BecbMa TpYAHO C'4HTaTt;» :310 CJ1Y"1aMHblM co-
BnaAeHHeM, - nHweT K063eB. - CKOpee Beero TyT HMena MeCTO
no rOHKa HYMeponOrH'4eCKHX paC'4eTOB nOA 3apaHee M3BeCTHbie
TaHHble.cunbi KpuTepueB
OKtcyllbTM3M
.'tepa M cerC)AH1l
nopa3KTel1bHb1M OKa3a11CS1.0K-
KYl1bTHbI paCl.feT, OCH<iBawHbI
Ha nOI1b30eaHIltIlt OCHOBono-
l1aralOl1I.e ATl KIltTa CKOO H}lMe-
pol10rlltllt 9-KneT04HO MaTpllt1..4bl
110 wy lit ccKPyrl1b1X- lItcel1 Bpo.a,e
1000 1111t. B Te .a.peBHHe BpeMeHa
3TOT pac eT n03BOI1I1tI1 npocl.flil-
TaTb pa3Mepbl 3eM1\IIt KaK wapa.
cnl1locH}'Toro no BepTlltKal1I1t (B
nOl1locax), TO COO TByeT
cOBpeMeHHoMY npe.a.cTaBl1e-
HIltIO, npllt' eM BblCl.flltTaTb c nopa-
3KTenbHO TO'iHOCTbIO
409
rn8B8 8
Ta6J1ULfCl5
Pe3y.nIbTaTW cOllpeMeHHlllx M ApellHeKMTaiicKMx paC'IeTOB
pa3Mepo8 3eMHoro wapa
AMaMeTp 3eMnM COBpe- PaC'4eTbi KHTaMCKHX
no BepTHKaJ1M MeH- MYApe OB
ct (1) Hble III-II BB. AO 11. 3.,
!III;
Q. M ropH30HTaJ1M paC'4e- nepec'4MTaHHbfe Ha KM
0
c
0 (2) TbI,KM
c >,$ .l:I $
Q. o c::: :J:: c:::
cu :IE >$ $ >$
2:
0 0 ::ro
:J: o o
c u c u
tOr-ceBep 12 713,5 12 423,8 12 940,2
oK-3anaA 12 756.3 13 379.5 13 935.6
Cpe.qHJIJI ..
BenM'4HHa 12 742,0 12 901,7 13 437,9
peaJ1bHble BenM MHbf (? - nOMemKa aem.). HCTO'4HMK me, H3 KO-
TOpOro non}"4eHbI 3TM BenH'4HHbI, OCTaeTCJI CKpblTblM» (c. 144).
TO'4HOCTb oKtcynl4Hblx BbI'4HCJ1eHHM OKa3anaCb HeO>KHAaHHOM
Aa>Ke AnJl npo4>eccH,OHaJ1a TaKoro YPOBHJI HCCJ1eAOBaHHM KMTaMc-
KHX TpaAHLtMM, KaK A:H. K063eB. OH, KaK BHAMM, OTKa3aJ1CJI npH-
3HaTb 1rM-pe3ynbTaT KaK AeMoHcrpa4MIO cOBepweHCTBa «MaTeMa-
TH'4eCKOrO MHcrpYMeHTapHJI» ApeBHMX HYMeponoroB, HeMblCJ1HMblM
. 06pa30M oTpa3HBwHx peaJ1bHOCTb >KM3HH, paCWHPMBWHX B03MO>K-
HOCTH n03HaHMJI. BnpaBe nH Mbi B TaKoM 4>opMe COMHeBaTbCJI B HX
410
BbI'fMCJ1eHHJlX (<<secbMa rpYAHO C'4MTaTb 3TO CJ1Y'4aMHblM COBnaAe-
HMeM», «CKOpee BCerO TyT HMena MeCTO nOAroHKa») M rpe60BaTb OT
ApeBHMX HYMeponorOB 06'bJtcHeHHM, He cyMeB c6epe'4b MHorHe MX
LteHHeMwHe PYKonHcH, rAe, B03MO>KHO, M 6b1nH OTBett( HaWH
BOnpOCb/? BeAb e Te CTapb/e BpeMeHa (AO H. 3.) H KpyroCBeTHbiX
nyTeWeCTBHM-TO He 6b1no! HeKoMY 6b1no XOD 6b1 npH6nM3MTenbHo
H3MepMTb BenH'4MHY MaTepHKOB 3eMnH, a cnWH H 3eMnM - Bepx
TeXHH'4eCKoro AOCTH)f(eHMJI '4eJ10BeKa, - etrecT¥HHO, He CYU4e-
CTBOBaJ1H: Henb3J1 6b1no 06'bJlTb 3eMnIO HH no BepTMKaJ1H, HM no ro-
pH30HTaJ1H. He Morno 6b1Tb AaHHblX (3TaJ10Ha) AnI! «nOArOHKH».
Ha 3TOM oCHoBaHHH MO>KHO
npHcoeAHHHTbCJI t< MfieHHIO
K063eBa, KOTOpblM nHweT:
«...He cneAyeT ynycKaTb H3
BHAY, '4TO B HYMeponOrH'4eCKMX
Ae6pJlx MOryr CKpblBaTbCJI no-
pa3HTeJlbHbie Hay'4Hble AaHHble,
npoHcxo eHHeKoTopblXTpyA-
HO 06'bJlCHHTb» (K063eB A.VI.
Y4eHHe 0 CHMBonax H '4HCJ1ax.
c. 343).
He YMeJl 06'bJlcHHTb nopa3H-
TenbHO TO'4Hble paC'4eTbi Hn
cpopMynHpoBKY 3aKOHOB >KH3-
HH ApeBHMx MYApeLtOB C MaTepHanHCTM'4eCKMX n03H HM, HeKOTO-
pblP. aBTopbl npHBneKalOT K 06'bJlCHeHHIO BMewaTenbCTBO CHn CBbI-
we, rOBOpJlT 0 nepeAa'4e MH4>opMa MH M03ry '4enOBeKa OT Bblcwero
Pa3YMa HnH Ha3b1BaIOT pe3ynbTaToM nOCeU4eHHJI 3eMnH MHonnaHe-
TJlHaMH. TaKHe 06'bJlCHeHHJI COMHHTenbHbI. Henb3J1 HCKnIO'4HTb OT-
TaUHble CHnbl KpHTepHes
-OKKYllbTHW" KII 't..
reHHH eJ10B eoJP8' MC-
nonb3ys1 <PW\OC IO. aCT-
poHOMHIO H HYMepoJ10rH-
'feCKHe npHeMbI, CYMeJ1H
npaBHJ1bHO c<PopMYJ1Hpo-
BaTb H COCT8BHTb «yttHBep-
canbHbI OKKYJ1bTHbI Kl11O'f»
n03H8HHR, 'fT06b1 A080J1bHO
TO'fHO p8CC HTaTb 3eMHytO
nOBepXHOCTb.
411
rnasa 8
pa>KeHMe peaJ1bHblX 3aKOHOB >KH3HM '4epe3 YHMsepcanbHytO CMCTe-
MY CHMBOn08 4>MJ10C04>cKI1X cpopMyn. BonHo06pa3HoMY npot4eccy
CYU4eCTBOBaHMJI nOA'4MHeHO Bee cyutecTBYIOU4ee He! 3eMne - >KM-
Boe M He>KMBOe, 06naAaJl pa3HbiM BpeMeHeM CYU4eCT80BaHMII. $op-
Myny, oTpa>KalOl14YlO 3TOT 3aKOH npMpoAbI, MO.>KHO OTHeCTM K oKKynb-
THOM H, ecnM He MTbl8aTb '4MCJ10ByIO CHMBonMKy ee 3neMeHT08.
TO>Ke MO>KHO He nOHMMaTb, KaK MO>KeT OHa OtpCUKaTb KaKMe-TO 3a-
KOHbI >KM3HM. nOA06Hble Bonpocbl '4aCTO aApecy T cI>opMynaM HY-
MeponorOB.
BepOJlTHO, ypOBeHb HHTenneK-
Ta HaWMX npeAKOB B HeKOTopbfX
06naCTJlx HayKM 6b1J1 no KpaMHeM
Mepe He HM>Ke Hawero. B nOATBep-
>KAeHMe MO>KHO npMBeCTM et1\e
OAMH nOpa3MTeJlbHbfM npMMep re-
HHaJ1bHOCTH HblX lij)e8HOCTM.
ECJ1M Mbi H3MepJleM C80M BblCO-
KMM ypOBeHb 3HaHMM 4>M3MKM H
4>H1IOC04>MH aTOMapHOM TeopMeM
nocrpoeHMJI MMpa, TO OKa3b18aeTCJI, 4TO TaKaJl TeopMII, KaK HM CTpaH-
HO (MJlM YAMBMTeJ1bHO!), y>Ke 6bU1a H3BecTHa MbICI1MTeJ1J1M Ape8HOC-
TM, HO ee pa3BHT1&e nowno He B COBpeMeHHOM HanpaB11eHHM: C03,qa-
HMe aTOMHOM 6oM6bI II1H aTOMHOM CTaHLtHH. «PJlA HCCJ1eAOBaTeneM
KHP, - nMwer K063e , - 06Hapy>KHBaIOT nOHJlTMe aTOMa B TpeX
TepMMHax peBHeKMTaHCKOM 4>Hnoco4>HM: «A.Y3Hb» - «Ha'4aJ10, oc-
HOBaHHe»:- o M» - «Manoe eAMHoe»...; «CliO, TIIHb CJI MO»-
«Mance, 'KOTOpoe He MO>KeT 6b1Tb pa3AeJ1eHO» (C. 348). nOCJ1eAHee
Bblpa>KeHMe KMTaMcKMM CMHonor flHb HCnOnbJOBaJ1 AnJl cpaSHe-
HMJI C eBponeMcKHM nOHJlTMeM arOMa.
CornacHO Y'f8HM1O
lllOOOi4 3aKOHO i4
npo MO)I(HO 38f1M-
C8Tb B BM,AB 4><>PMYl1b1:
Ha ano (po)l(,D.eHMe)
pa3BHTMe {bo3PeeaHMe)
M aaaepweHMe (CMep:rb).
412
"IaCTb TOro, 'fTO He nOAAaeTCJI no-
fM'4eCKOMY, OC03HaHHOMY 06'bJlCHe-
HMIO. MO)t(HO OTHecT14 K 3neMeHl)' nOA-
C03HaHMR - MHTYMLtMM. . BepOJITHO,
BeK TeXHM3attMM M McnOnb30BaHMJI BbI-
COKOTO HWX npM60poB ocna6Mn y CO-
BpeMeHHMKOB pa3BMTMe MHl)'MttMM, '4TO
Orop'4MTeJUtHO, TaK KaK nCMxonOnt OT-
HOCRT ee K OAHOM M3 cpyHKttMM HaweM
nCMXMKM. B TBOP'feCKOM AeRTenbHOC-
TM ApeBHMe Hwe KaK pa3 60nbwe, '4eM MX COBpeMeHHble Kon-
nerM, C "TaJ1MCb C MHl)'MttMeM, pa3pa6aTbiBaR CBOM cpMnoco4>cKMe
" OKKynbTHwe cxeMbi. HeKOTopble M3 HM 'AO CMX nop nOpa)f(alOT
Hac my6MHOM MYApocT M, KaK Mbi HepeAKO y6e)l(,i.ieMCR, RBnR-
IOTCR 06pa3ttOM H HOM npo30pnMBOCTM.
TaHHb/e cunb/ KpuTepues
06 MlfTYMI4MM
B HaCTORlltee Bpe-
Y'feHbIe n 3Ha-
lOT, '0"0 MH R
O)l(eT «Cpa6aTbI-
88Th. H8 OCHOBe
t01KOFIneH 0c03-
H8HHOf"O OOblT8.
rnABA 9
CbOPMynbl HYMEPOnOrMM
nMHeMHbie cl>opMynbl MarMM
AaM)I(eHMe 3H8prMM no «Ma-
r eCKHM- 3J1eMeHTaM MO}K-
HO a06JM:3 Tb cc06beMHO-,
Ha epTH8 'reoMeTp., eCkYtO
<S> ryPY. a NO}KHO TO}Ke ca-
Moe nOkaaaTb «J1 He HO».
6YkBaM.., (B Kmae lit nOH 1It
eporn <S>aM ). Han caHHbI-
Milt B PR.O.. o oaHa:1 B Ha aJ10
c TblBaH 3tleMeHTOB.
HanpaBJ1eH e YJ:1)bI nOBO-
pOTOB J1&.1H i1 B reOMeTp -
C4ecKo rype, - TaklltM
06paaOM Han caTb «<S>OPMY-
J1Y nepeMeuteH 3Hepr »
npHHI,tHnHanbHoe Bblpa-
>KeHHe ABH>KeHHJI 3HeprHH
no nJlT 3neMeHTaM nocpeA-
creoM rpa4>HKa HnH nHHeM-
HOM 4>opMynbl - OAHO H TO
>Ke. Ho nepsoe 60nee HamJlA-
HO nOKa3b1SaeT ABH>KeHHe
3HeprHH, a eTopoe pal,tHO-
HaJ1bHee - C>KaTO H 3KOHO-
MH'4HO nepeAaeT Ha 6YMare 1Y
>Ke HH4>opMaI,tHIO. nocne-
AHee, OAHaKO, pacc HTaHo Ha
60nee rJOArOTosneHHoro IiY-
Meponora, nerKO nepeeoAJI-
U4ero 4>opMyny B rpa4>HK HnH
MblCJ1eHHO npeACTaBnJlIOU4e-
414
ro ero nepeA c060M npH '4TeHHM
C MBonOB 4><>PMynbf, TOrAa KaK
rpa4>HK ABM>KeHMJI 3HeprHM no-
HJlTeH nK>6oMY Ha'4HHaIOU4eMY.
nocrapaeMCJI e 31I0ynoTpi!6-
nJrTb M TeM. H ApyrMM, Hcnonb3j'JI
B TeKCTe '4aU4e rpa4>H'4eCKOe
H306pa>KeHHe 3Hepren4 eCKHX
4>opMyn. Ho TaK>Ke 6YAeM MC-
nOnb30BaTb HX 6YKBeHHoe, nH-
CbopMynbl HYMeponorHH
OcHOBW ttyMeponorMM
B tiyMepononut cnol1b3Y-
lOT AB8 sap HTa HTblsa-
H R 3HepreTM..ecK 4>Op-
MYI1b1 C reoMeTP KOrO
ee BbI H R - C tcpeCTa
X3 TY eM C APyrw<
<I> rYP, c' eH'TarpaM!-4b1.
... ...... ........ ... ........ ...... ....
.
YeTBep HOCTb CXOAHoiit MaTp pecnOnO)KeH R- 3ne-
. MeHTOB B KpecTe X3 TY COOTHOC Ma C eTblpbMR OAB-
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)KeH e eTbipex 311eMeHTOB Ha KOHu.ax KpeCT8 X3 TY ·
C MB0I1 3 PyeT X KapA HB11bHYJO <l>YHKU. IO: 3 MHee ·
l1eTHee COI1Hu.ecTORH e, OCeHHee BeceHHee paBHOAeH-
CTB e, a TalOKe eTblpe He,o.ellbHble <l>a3b1 J1ytibl. npM CO- ·
Bna,o.eH 3Ha'4eH R 311eMeHTa C C MB0I1 3 PyeMbiM M .
. c06b1TMeM np po,o.bI npoRBlleH e ern B )K 3H B aepo- .-
. RTHOCT CBepWeH R nporH03 pyeMoro co6b1T R yaenWUt- .
BaeTCR. nepeBeP.eH e 311eMeHT8 C ero MecTOnOnO)KeHMR :
B KpeCTe X3 TY B neHTarpaMMY He ..,3MeHReT OCHOBHyto C..,M-
BOll KY, HO C HYMep0I10r 'feCK X n03 lI.Miit Ha,o.el1AeT ero
6ol1bweiit «CTeneHblO CB06o,Abf» cBR3eiit C APyr M 311e-
MeHTaM <l>OPMYI1b1 no Kpyry l1 aM 3Be3,lJ.bl, 8 3Ha'4HT
OOl1bW M «Marn'4ecK M B11&.1RH eM" OyP3)KeHMeM )KM3H . .
..................................... .
415
rnasa 9
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neHTarpaMMY B oKKynbTH3Me nonY'4alOT H3 npe06pa30BaHHOM
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neHTarpaMM pH TaKOM npe06pa30BaHHH 4>Hrypbl Kpecra yrnoBaJl
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npMBeAeHHble npe pa30BaHHJI KpeCTa X3 lY c nepeMeuteHHeM
era 3neMeHTOB '4aCTO HCnonb3YlOT npH 4>oPMHpoBaHMH «MarM ec-
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cMlYaLtHM H .npoBeAeHHJt oKKynbTHbix nporH030B.
nepeMeuteHMe 3neMeHTa C yrna CBJl3H 90° HMeeT H acrponorH-
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