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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 nJl.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 H8flbI noeecTM, -1OHocTD» - B 1856 r. (= 2). 11 
Bse,lteHHe no BocnOMMHaHMJlM crapwero CblHa TonCToro - (epreJl nbBO- BMa, 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 BCTpeIOTCR '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 (ToHee - ;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 &.1BMAyaneH, 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 cnMM 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 ropM1I MarepM: - weHbKa, OOAOJlW1 AD nOnyHM». 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 4CJ10BaJl 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 TpaAa4MM, 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 npKTHKe, H BpeMeHa 3aCTOJl, naAeHMJI K HMM MHTepeca co CTOpOHbI HCCJ1eAOBa- TeneM M 06CT8a. OAHaKO npHMe'4aTenbHO TO, '4TO O'4epeAHOe CHM- >KeHHe aKTBHOQM 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 aCTpOnOreM 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 - APeBHMWee 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"). CecKorO BOCnpil1sm1 if! Mif!poeo33peHif! if! bHbD( MeTOAOB HCcne- AoaaHif!. OTl1i11'f8. OT npif!BHbD(,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 BOCTOHOM 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 Haany I TblCJleneTHJt AO H. 3. ApeBHe- HHAHMCKaJl H ApeBHerpeecKaJl$HJI0co4>HM nOJlBMnMCb n03AHee - npHMepHO K 1500 r. AO H. 3. B CBoe BpeMJI TepMHHonorMeCKaJl OLteHKa H AaTa npH3HaBanMCb MapKCHCTaMH - 06 3TOM 4>aKTe nMCaJ1 B.. neHHH (KoHCneKT KHHrH frenJl «neKu,HM no HCTOpHH 4>Hnoco4>HH», T. 29). B KHTae «Hay'4- HbiM MHcrpYMeHToM» MnM n03HaBaTenbHoM MOAenblO (opraHoHoM) 6b1na HYMeponorMJI, onpeAenJleMaJt KaK «4>opMaJ1M30BaHHaJt Teo- peTH'4eCKaJl CHCTeMa, 3neMeHTaMH KOTOpOft JlSnJlnHCtI '4MCJ10Bble KOMnneKCbf M reoMeTpHecKHe crpYKTyPbl. OHM 6b1nM CBJt3aHbI Me>K- AY C060M rnaSHbiM 06pa30M He no 3aKOHaM MaTeMaTHKH, a CHMBO- nM'4ecKH, aCCOLtHaTMBHO, MHeMoHMecKH», - OTMe'4aeT M3BeCTHbiM CHHonor A.. K063eB B KHHre «YeHHe a CMMBOl1aX M HCJ1aX B KH- TaMcKoM KnaCcHecKOM 4>Hnoco4>HM (1994). OAHH H3 BeAYU4Mx Y'4eHbIX 3anaAHoM CHHonorHH A>K. HHA3M (KeM6pMA>KCKMM YHHBepcMTeT) nposen <J>yHA(iMeHTaJ1bHble MCCJ1e- AOBaHMJI ( Mcnonb30saHMeM 60rareMwero cnekTpa 4>aKTOs: aT 3KO- nOnt'4eCKHX AO nHHrBHCTHeCKHX. OH nepBblM AOKa3an 3anaAHoMY MHPY, '4TO Hay'lHble TpaAMLtHH KHTaJl «BO MHorOM COAeMCTSOBaJ1M Hay'4Ho-TeXHM'4eCKoMY nporpeccy Ha 3anaAe». CMHOnorM - eHble, &o13alO&o1e KYl1bTYPY; <!>&01- l1OCO<!>HIO, Sl3b1K HAP. KHTaSl. 16 
A3b1 HYMepOnOrnu B HayHOM H nOBceAHeBHOM >KH3HH 06U4eCTBO 4aCTO Hcnonb3yeT CTepeOntnbl MblWneHMJI. npH gTOM He nOOU4pJleTCJI MblwneHHe APY- r'HMM KaTerOpHJlMM, KOTopble BblXOAJIT «3a paMKH A03BoneHHoro». Ho HMeHHO nOCJ1eAHHe, KaK H3BeCTHO H3 HCTOpHH, OTpa>KaIOTCJI Ha n03HaBaTenbHblX cnoc06HOCTJlX enOBeKa H Ha pa3BHTM" HOBOro HanpaBneHHJI B HaYKe (B.B. HBaHoB, 1994). AHrnMMcKHe CMHonorM A. rp3M M A>t<. HHA3f04 06paU4aIOT BHHMa- HMe Ha AOBonbHO n03AHee npHHJlTHe eBponeMcKoM HayKOM TepMHHa «3aKOH» - B nOCJ1era- . . l1..neeBCKYIO 3noxy (c KOHLta xvn B.), AO 3TOro HcnOnb30BaJ1HCb TaKHe TepMMHbI, KaK «npo- nOp14HJI», «n pM H 14M m, «paLtHO» H «pa14HO- HanbHOCTb»:KHTaM14b1 HaXOAMnHCb B 60nee 6narOnpHJlTHOM CH1Ya- 14HM, YaK KaK paHbwe eB- poneMLteB BBeJ1H B 4>HJ1OC<$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. HeoKoHaHCTBO «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. npHn «111>1- CHTanCA 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», ynoMMalOU4MM- 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 MYApeOB AOBonbHO THO 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 MYApebI 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. 4HCJ10Be 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 coeTaHIilA (IIICl1oBbie CIIIMBOl1b1l1111111 «,D,IiICKpeTHbie 3HeprOpIilTMbI»), BepoATHO,.onpep,el1A- lOT CTPYKTYPY Bcero cytJ4ero, nOCKOl1bI<Y OHIII B onpeAel1eHHbIX cO'teTaHIilAX pery- l1ApHO nOBTopAIOTCA B OKpy*alOeM Hac Mlilpe B ABl1eHIIIAX III Beuta>(. 19 
rnasa 1 VlAeH )f(aK06a 6b1nH pa3BTbI 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 ye- HMJI a cHMMeTpHH '4HCen. Era HAeM nOAAep>KanH naypeaTbi H06e- neBCKOM npeMHM no 4>H3MKe 11H H flH B CBOHX pa60Tax a BnJlHMH Jl3b1KOBbiX CHMBonOB CHMMeTpHH Ha 4>opMpoBaHHe HaHbIX 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>KalOero 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 nonMJ10 B $13MKe Bce06U4ee npH3Ha- HHe eHMe rpMHa H WBapLta a TeopHH CsePXcrpYH H cyneprpaBHTa- i4HH. XapaKTepM3yJ1 OCo6eHHOCT pa3HblX 4>H3H'4eCKMX JlBneHHM, 3TH TeopMH nOTH 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 B3rnOB 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'4eCKM 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 4CJ10- 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 nOHMaHHe 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>lit30110rnKiIte MexaH3MbI, nOllywapYISl ro- 110BHOro M03-ra OObl'iHO YH- KlU'10HlitpyK)T C nonepeMeHHo cMeHSleMoH aKTlitBHOCTbfO. 3TO H8AO 3H8n. KlitTaHCKaSl KYllbTypa OCHOBaHa He Ha aJ1aBTHOM (l1eBonOllY- wapHOM), a tia litepornlit'feC- KOM (npaBonollywapHOM) nplitH- u,litne MblWneHlitSl, CTaeT aBTO- pTeTHblH COBeTCKlitH ClitHOll0r, 3aHMalOUl.litHCSI TeopliteH ClitM- 80110B, A.. KOO3eB. B nOAXOAe K MCllY OHa conOCTaBMMa C «anaBMTHOH kyllbTypoH rpe- Koro Tna". 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. Kit M3BeCTHO, BocnpMHMMaTb peaJ1bHOCTb npeAMera MO>KHO npH pa3HOM era OCBeI14eHMH, npM'4eM 60nbwee '4HCJ10 MCTOHMKOB 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- lOro MHpa. npHeM 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 HanpaneHMM 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-nOrHeCKOMY (neBononywap- HOMY) MblwneHHIO eeponeMCKMe Y'4eHble Ol4eHHnM ceOH np06neMbi nocpeACTBOM 3M0l4HOHal1bHo-06pa3Horo (npaBononywapHoro) MblWneHHJI, TO pe3ynbTaTbi npeB30wnH O>KMAaHMJI HaCTonbKO, 'fTO HeKOTope 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  MJoe 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*8ef'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 CMMBonMeCKHX 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- raAOHoro c4>HHKca 6YAer OCTaBaTbCJI AllJI Hac BClI Kynbtypa KHTaJI, nOCKonbKy 4>Hnoco4>HJI B HeM Hrpana ponb 60nee 3HaHTenbHYIO, '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 npMHnbl KM- Tast HaM60nee 6J1M3KM K M,D,eanb- HOH HaYKe 6y.o.Y11\ero (BCeMMp- HOH.YHMBepcanbHOH.3eHM- 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 Ilp04TaTb «Me>KAY CTpOK» nepeAaBaeMbie ApeBHHMH MYApeLtaMH MblCJ1H. K TaKMM KHHraM MYAPOCTH OTHOCJlT H 6H6nHIO. «KaHOH» B nepeBOAe C rpeecKoro 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», «MareM»: '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 oeHb npocrOM npM'4HHe, - nM- - WeT A. KHcenb, - 3TH KHHrH COAep>KanH TaM- Hble 3HaHHJI.  HMeHHO K 3THM TaMHblM KHHraM «AnOKpM4»MecKMe" KHMrM BeTX 3aBeT 66n COCTOT 3 39 KaHOHeCKHX  11 HeKaHO- HJ.14ecKJ.1X, «anOKpJ.14>J.1ecKHxlO, KHr, He BKJ1eHHblX 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 MHOrOHCJ1eHHbIX MHOfOBe- KOBbiX nepem1CblBaHMH 6116- I1HH I1IOAbMH, He scefA8 00118- A81OMH AOCT8TO'fHblMH 3H8HHMH 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 TaHble 3HaHs.1S1 LfeJ1oaee- 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.1HblX 6M6nIo1OTeteaX. 27 
rnasa 1 TOpbfX c06b1TMM 3eMHOM >KH3HM. npeM 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 cmbHoe 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 KOHe KOHOB 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 WOTnaH - 8 1727. 80 <!>paHW1111 - 8 1745.8 rep- MaHHH - 8 1775 r: 29 
rnBBB 1 «BOMCTMHY eCTb He'4TO 06eCKYPa>KMBalOee B TOM MCTOpH'4eC- KOM TpaeKTOpMM, KOTOPYIO, npoH3MB BpeMeHa H npocrpaHCTBa, onH- CaJ1a MarMJI, B03BpaTMBWMCb B KOHLte KOHL40B Ha KpyrM CBO$l»,- nMweT EpeMeM napHOB B «TpoHe nlOL4H4>epa». 4HTaTenb, BepSlU4MM B 3HepronepeHOCbI, T.. e. B B03MO>KHOCTb nepeAa'4H '4aCTM 3HeprHH aT OAHoro 4>M3Heckoro Tena (BK/lIO'4aH Teno '4enOBeKa) MnH JlBneHHJI APyroMY Teny HnM JlBneHHIO, a TaK>Ke npM3HalOU4MM 3aBMCHMOCTb nOBeAeHMJI '4enOBeKa aT CHJ1 npMpOAbi H B03AeMCTBHJI KOCMM'4eCKOrO Pa3YMa, HaMAeT B :nOM KHHre AO- nonHMTenbHble TOMY nOATBep>KAeHHJI. 4HTaTenb, KOTOpblM C COM He- HHeM OTHOCMTCJI K MMCTHKe H MarHH, nonY'4HT nlO60nblTHYlO «nMU4Y» A/1J1 pa3MblwneHMM, He BCerA'! 06'bJlCHMMYIO C MaTepMaJ1HCTH'4eCKMX n03H4HM. C OAHOM CTOpOHbI, nonaraeM, \'4TO :310 ero pa3BJ1e'4eT, C APyroM - 3aCTaBMT 3aAYMaTbCJI HaA crpaHHoM pHTMH'4HOCTblO (MnH Aa>Ke 3aKoHoMepHoCTblO) npOMCXOAHHX B era >KM3HH 4<CJ1Y'4aMHO- CTeM» M «ClOpnpH30B». nOHRTMe 0 pM-ryanaX B npOJlBneHHH 3araA0'4HblX JlBneHHM H npH «CBepweHHH Ta- HHCTB» He Bce .MO>KHO 06'bJlCHHTb c n03ML4MH OPTOAOKcanbHOM HaYKH. EcnH npeAnOJlO>KHTb, '4TO HenOHJlTHbie C MaTepHanMCTH- '4eCKOM TOKM 3peHHJI JlBneHHJI cYU4ecTBYIOT, TO npH H3Y'4eHHH MeTOAMK '4McnOBOM actponorMH '4HTaTenlO none3HO nonY'4HTb 06- ee npeACTaBneHHe a ponH pHryanoB, a TaK>Ke n03HaKOMHTbCSI C nOHJl1HeM 6enoC1 H '4epHOM MarMH. eHHe 6enoM, A06poM, MarHH nonY'4Hno HaH60nbwee pacnpocr- paHeHHe H npOAOn>KaeT Bbl3b1BaTb HHTepec. ABTOp He CTpeMHTCJI 06y- 30 
ifMTb 'ifUtcninJl TaMHblM ...erona....- 6enoM MnH TeM 60nee '4epHOM MarMH. Era Ltenb - AaTb 06U4He npeACTaBneHMJI a B03MO>KHOC- TJlX Ka66anbl '4MCen, paCCKa3aTb a HeKoTop"'" OCo6eHHOCTJtX OK- KynbTHbix 3HaHMM, 3aMHTepeco- BaTh H Bbl3BaTb Y '4KTaTenJt >KenaHMe y>Ke 4eneHanpaBJleHHO, no cne- 4ManbHblM PYKoBoACTBaM, yrny6nJlTb H pa38MBaTb n03HaHMJt B COOTBeTCTBMH co C80MM MHTepecOM. npO$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 ne '" 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, npopMb (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 HeaCTbe. 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 (ynpoeHHoM, Ha4aI1bHoM) · . ypooHe. YAOBl1eTBOpRlOlJ.¥iR HeCl1O)KHblM n"'HblM 3anpo- - : : caM. npoe .., AOCTYf1Hee KIDKAOMY (HanpMMep, BbILII4CJ1e- : · H..,e nOBopoToB B cBoeill cYAbOO c nOMOblO 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, noAac YH..,KaI1bHblM..,. · . cnoc06OcTRM'" (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 KOHa K Ha- '4a.AY.. COBepWalOTCJI TalOKe 60nee CnO>KHble pMTyanbi C Hcnonb30- BaHHeM CAenaHHblX c06CTBeHHbfMH PYKaMH Mara arpH6yTOB, peLtenroB. (Ma01ecKHM KpHCTan.A. MarHJI rJ1a3aMH yeHblx 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 nCII1XOJlOrll1ecKII1. 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,AeHR '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» $>pMynbl M ee KOH- CTaHTbl. - '4MCJ1a 2, 8, 1, 4 M 7 nOBTOpJlIOTCJI B pa3HblX CO'4eTaHHJOC B '4MCJ1e pO>KAeHMJI MMeeTCJI «ABOMHOM pe30HaHc» '4MCen 4>op- Mynbl: 28; B MecJlLte pO>KAeHMJI oTpa>KeH eAHHH4HblM «'4HC/lOBOO pe30HaHC» (B nOpJlAKOBOM 'fMCJ1e'MeCJll.ta): 8-M no c'4ety; OTMe'4aeTCft «rpOAHOM pe30HaHc» '4HCen KottPaHTbI a n.epSbIX '4HCJ1aX rOAa pO>KAeHMJI: 174 (BonnmqeHMe BceM «CYMto1h1» 4>oPMY- nbl KOHCTaHTbI). no MHeHMIO HYMeponoroB, 3TO HecnpoCTa. «We4>CTBo» HaA co- 6b1THJlMH B >KM3HM feTe KaK 6YAYU4eM MCTOpH'4eCKO nH'4HOCTM era CYAb6a (KOTopylO OTO>KAeCTBnJlIOT C BnHJlHHeM KocMoca HnM Bblc- wero Pa3YMa) 83J1na BCKOpe nOCJ1e ero p0>KAeHHJI. npoJlBHnOCb 3TO ynpaBneHMe '4epe3 3aKoHoMepHble CO'4eTaHHJI '4HCen. n03TOMY B >KM3HM feTe 4HCJ1a 4>opMynbl 3aKOHa EAHHCTBa HnH KOHCTaHTbI '4ac- TO OOBTOpftnMCb B f)Hble AI1J1 Hero (CYAb6oHoCHble) AHM. KaK M3BeCTHO, «'4enOBeKy HH'4TO '4enOBe'4ecKoe He '4y>KA0». OK- KynbTHCTbI KaK .tCTMHHble xpaHMTenM TaMHblX 3HaHHM npOBOAMnM T1I4arenbHblM 01'601> «nOCBJlt4eHHblX», HCKnlO'4aJl «HH3KHX H HeAOCTOM- HblX» (no ou.eHKe H3 OKKYnbTHOM nMTepatypbl). OAHaKO HawnHCb H- TenJl, KOTOpble npeAnO'4J1M HCnonb30BaTb HX B AOCTH>KeHHH nH'4HbI><, KOPblCTHbiX LteneM. OHM McnOnb30BaJ1M MeTOAbi MarHH AllJI npHHYAH- TenbHoro B03AeMCTBHJI Ha APyrHx nlOAei1 H ynpaBneHHJI HMH. 4aU4e Bcero Ltenb HX B03AeMCTBMJI 6b1J1a B YAOBneTBopeHHH HM3KHX CKpbl- BaeMbiX >KenaHHM H nopOKOB. 3TOMY H<e Hcnon30BaHHIO cpeACTB 34 
A3b1 H}'MeponOrHH MarMM «HeAOCTOMHble Y'4MTen"» 06Y'4anH CBOMX Y'4eHHKOB. n03TOMY B HeKOTopblX wKonax TaMHble Y'4eHMJI CaTaHbI (HnM '4epHaJi MarMJI) 3aHMH '4ecro Y'4eHMJI BceBbiWHero (HnH 6enaJl MarHJI). C'IHTaeTOI, '41'0, BC1YrtaJI B nooosylO 6nH3OCT'I,. MyHNM  eHU4HHa OOABepralOTCSl B11HJ1HMIO «He'fMCTbIX CMn», H pa38MTHe AiiI1bHeMWHX OTHO- weHHM Me>t<AY HHMM nepexOAKT B pyKM Ab$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- nMblX 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 npeAHa3HaaBwYlOcJI 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'lHCneHbI K 803- AeCTBHIO 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>MnoCOHJI. 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 BerAa 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 npoeHllle. Ha 38M8TJCy r1l1(),AOM TPYAOB L4epKOBHbtX MblC- nlllTene CTano OAHO OTKpbITllle: OK83b19aeTCR.3HaIIITenbHoe OOnbWIt1HCTBO npMcnY'KHIIIKOB Ca- TaHbI... COCTaBl1Rnlll JKeHU.U1HbI. 36 
A3b1 HYMeponOrHH MO>KHO OnMCaTb CJ10>KHble AeCTBHJI 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 TpaoBe- 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, 06yalOTcJI HeCKonbKO neT, YMeTb «3HepreTHeCKH 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 paBoeHHe» 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, BOCTOHYIO <l>Hnoco<l>HIO H, kOHeHO, 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 BeeCTBO no- 6b1BaJ10 y Hero B PYKax (HanpHMep, eAa, Boa MnH KaKoe-TO HHoe BeeCTBO), aHa Bbl3b1BaeT COBepweHHO HHoe B03AeMCTBMe, eM TO, KOTOpoe CJ1eAOBaJ10 6b1 O>KHAaTb, OCHOBblBaJlCb H H3BeCTHbiX Ha- YKe era 4>M3M'4eCKHX CBOMCTBax M npMBbIHblX KaeCTBax. · B OKKYJ1bT"'3Me "'MeeT 3HaeH"'e '" TatCO <!>aKT: Y"I"'TblBaS1. · . TO aCTb TpaHc<!>opM"'pOBaHHO opraH"'3MO 3Hepr"'''' . : Mar nepe,o,aeT HaMeHHO eJ1"', OH AOJ1)KeH cosepwaTb : · 3TO C Ha"'MeHbW"'M'" norpeWHOCTRM"'. n03TOMY OH C8M · . AOJ1)KeH "'MeTh 3AOpoByK> '" «"'CTYK>. O3Hepr"'lO, T. e. He . · Clp8A8Tb T)KeJ1b1M 3800J1eBaH"'eM, "'Hae 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 CneHaJ1HCTOB 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>HHpoBaHHe» 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>eKHIO» (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 3HepreTHCKHe AeM- CTBa - naJ1Ka-o AB.YX KOHLtax. 3MoHoHanbHo 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 nOAII1HeHIite CBoe Bone .QPyroro enoae- Ka "111 COBepWeHIite 3na 061i1A- II1KaM. Ee pa npe.o.ynpe)K- A8eM, TO TaKoe YBneeHlI1e R8nReTC.fI3a6nY>KAeHlI1eM.3a KOTOpoe paHO II1nll1 n03AHO npli1AEnCR pacnnaII1B8TbCR. npll1eM 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. naHbIblK 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 AerpaAaHIO nH'4HOCTM. XpMCTHaHCTBo HMeHyeT HX c06HpaTenbHblM HMeHeM «CblH norM6enH», HCJ1aM >Ke rOBop1T 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 ceraHMe 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 CJ1aH 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 - HcIkLtMOHHblM 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 B03PAHBWCb AYXOBHO. 3T0 «'4epHble MarM», HOCMTenH oc06b1x BnHRKMM H cno- C06HOCTeM. OHM COBepwalOT '4YAeca, TaKMe, KaK «6MonOKa14MJI», «J1eBTa14HJI», HO Mcnonb3YlOT x B LteJ1J1X yc1<OpeHHJI npMxoAa AH- THxpMcTa. WHpOKO M3BeCTHO H APyroe onpeAeneHHe CaTaHbI KaK «06e3b1lHbI 60ra». B npoTMBoBecCYU4HM ceMH «6narHM» (CBJlTbiM. - npUM. aem.) MernM Ha 3eMne MMeerCJI ceMb «6aweH CaTaHbI». nonaralOT, '4TO aT HMX HCXOART AbJlBOnbCKe B03AeMCTBHJI '4ep- HaM MarHM Ha MHp. 3TH «6awHH CaTaHbI» pacn0J10>KeHbI B ct>opMe AYrM, orH6alOU4eM EBpony Ha He- KOropoM paCCTOJlHHH. OAHa Ha- XOAMTeJl B paMOHe HHrepHH, a KOTOpoM Y>Ke BO BpeMeHa ApeB- HHX erHnTJlH roBOpHnH, 'frO 0TTYAa npHxOART caMbie crpaWHble KOJ1AY- 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 aeMHK 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 "u.eHTpbl» Y"teHMI CaTa- libl - x KoopHaTbi YMblwneHHO HKTO reorpa- <S>'feCK He cornacoBbI- 8811, HO 'fTO YBTenbHO, Ha KapTe X pacnonO)Ke- t-Ie t-IanOMHaeT nOAKOBY. 43 
rnaSB , TaHe (ecTb CBeAeHMJI, 'fTO B HeM 6b1J1 nOCBJIH 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 '4epe3 BMAeo4>MJ1bMbI M HeKOTOpble HanpaSJ1eHMft poK-MY3b1KM. He- 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 oBJ1aAeTb caTaHMCTCKMMM PMTYaJlaMM. 3a pacnpOCTpaHeHMeM «'4epHblX 3HaHMM:» CTOJIT HeKOTopble TaM- Hble opraHM3al4HH EBponbi. OC06eHHO 3TO KaCaeTCJI H3BeCTHoro «'4epHoro ra» AnCTepa 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 TOM '4MC11e M a TOM, O CTOKT 3a pacnpocrpaHeHMeM caraHM3Ma, roeopJIT a npM6.nM>KeHMH pewa- lOU4eM CXBaTKM Me>KAY CMJlaMH CIeTa M CMJlaMM TbMbI». C 31M'" 3aMe'iaHMeM A. naHbI'4b1K Henb3St He ComaCMTbCJI. BepoJlTHO, oeo- 6eHHO C>C'TpaJI60pb6a npoH30M- MHTepecHw" (j)aKT Ta£1HOe ecTBO AnMCTe- pa KpoyI1M 0Ka3aI1o 3HaM- TeJ1bHoe BI1MRHMe Ha pstA H3eecbO( 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 onopbl. K CO>KaneHM!<>, Te, KTO nonan nOA SnMJlHMe '4epHOM MantH H npe>KAe 8cero ee HaM- 60ne arpeCCMBHoro Y'4e- HHII - CanaHU3/1fO, He CKOpo CMOryr CTaTb Ha nyTb MCTMH- HbiM. Y TaKHX MonOAbIX nlOAeM MMeeTCJI JlBHblA CABHr, npomutJlIOM- CJI B atm1MOpanDHbDC H aHTH06LqeCTBeHHblx HOBKaX. Tal<, OAMH H3 caraHMCTOB Ha Aonpoce C na4>ocoM 3aJlBMn CJ1e.q0- BaTenlO: «MHe npHJlTHO OC03HaBaTb, '4TO JI He TaK KaK BC- 06b1'4HaJl cepaJl Macca. MbI, caraHMCThI, - 3TO BC OhanbHble - '4epBH, KOTOpblX HaAO TonTaTb]l). MHorHe H3 HMX y>Ke nOMaTM1IMCb 3a CBoe He3HaHMe 3aKOHOB 06- aqecrsa, B KOTOpoM OHM npo>KHBaIOT, M nOCTpaAaJ1M 3a perynJlpHoe Ha- pyweHHe 3aKOH08 MOpanM, 'frO npoJlBMOOCb B A$pMaqHM nM&4HOCTH, 060cTpeHMM CMMnTO- MOB nCMXM'4eCKOM na- TonorMH Y nOBblweHHO BHywaeMbiX HJlM OOnb- HbIX nIOAeM. OAHM H3 HMX Y>f(e COBepw..nM yronoBHble npecryn- HMJI H OrobiBaIOT Ha- Ka3aHHe no 3aKOHY, ApyrMe ne'4aTCJI Y nCM- XHaTpOB H nCMxono- eomaCHO Y't8HMIO Y caTaHMcTOB ecTb ymep*Ae- liMe, 'frO 3a Bee COAeStHHOe paHO MJ1M f103,AHO yeT pacnnsrn, npaB,D,a, «Pf'AOBbiM caT8HMCTaM- 3TO .npRMO He MCTOJ1KOBbisaeT. Ms- rn:yt5M"" MKOB no Y'feHMIO .QpeBHMX My,QpeUoOS, Ieap- Ma (<<TO H8 POAY HanMcaHOlO) Y Ka)I(- Aoro CBOR, HO 3a COBepWeHMe npo- CTynKOB OOsI3aTeJ1bHO (5YAeT OTBe- Tb TOT, KTO MX COBepwMJ1, 11&.1(50 (ecJ1M ero )IC&.13Hb OICCi)t(eT CI1MW- KOM KOpoTKoM) pacnnaTs:tTCR 38 3TM «nOABMrn- ero nOTOMKM. 45 
rnaea 1 roB. 06U4ecTBO 60peTCJI ]a COHanbHYJO H MeAMHCKyIO nOnHOLteH- HOCTb. ]a npeBpaHMe caTaHMCTOB B paBHonpaBHblX rpa>KAaH. K CO>Ka11eHMIO, HanpJl>KeHHe 60pb6b1 «CBeTa H TbMbI» He YMeHb- WaeTCJI. B Bbl60pe npaBMnbHoro wara B >KM3HM, B M3Y'4eHHH «TaM- HbiX 3HaHMM» CJ1eAYeT 6b1Tb oc06eHHO OCTOpO>KHblM. cc3anpeTHaR TeMa», MnM CeKC B pMTyanax MarMM AnJl ytMneHHJI 3Hepre- TMKM M ycnexa CBepWeHHJI HeKOTopblX MarH'4eCKHX AeMCTBMM HeOOXOAHMbI He- CKonbKO '4enOBeK (Y'4aCT- HHKM MnH XOTJI 6b1 nOMOU4- HMK Mara), HanpMMep npM Bbl3b1BaHHH AYXOB HeKO- TOpblMM npHeMaMH Ka66a- nbl, B TOM '4MCJ1e HYMepoJ10rM'4ecKHMH H acrponOrM'4eCKHMH MeTOAa- MM (c Hcnonb30BaHMeM «MarM'4eCKMX» '4HCen H reOMerpM'4eCKMX 4>Mryp). MarHJI C'4MTaeT, '4TO> HepreTH'4eCKHe BnHJlHHJ1 MarHH npOJlBnJl- IOTCJI CHnbHee, eCJ1M TaMHCTBa BbinOnHJlTb npM onpeAeneHHblX no- nO>KeHMJI)( cseTMn M nnaHeT. n03TOMY Mar nepeA AeMCTBOM npOH3- BOAMT pac\i!TbI HX nOnO>KeHHJI Ha He60CBoe. KpoMe Taro, npM Bbl3b1BaHHH AYXOB pa3HblMM MeTOAaMM Ka66a- nbl, camaCHo KYnbTy, HHorAa Teny Mara CJ1eT npHAaBaTb onpeAe- neHHoe nOnO>KeHHe. B H3MeHeHMM nOnO>KeHHJI Tena B npocrpaH- 0IcKym.TM3M II't8p8 M C8f"0AH. HeKoTopble MarecJG1e Ae- CTBa. CKTaIOT cpo4>eccVloHa- nbl oKtcynbTVl3Ma AOH8J1bA Kpar; A. AasHA-Heanb, MaH11V1 n. XOM VI, 0e3ycnewHbI; KorAS Mar cosepwaef VlX OAHH. 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 MaTpMbI», &,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&ltt14». 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 HaM60weM 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 '4eJ10SeK 6b1n ceKcyaJ1bHO '4YB- CTBMTenbHblM M nOBblweHHO B036YAMMblM, 3MOI\HOHaJ1bHblM. npM 310M «CMOTpJlU4HM» AOn>KeH B OCHOBHOM YMeTb KomponHpo- BaTb CBoe nOBeAeHHe H KaK MO>KHO pe>Ke 6b1Tb HeynpaenJl- eMbiM B COCTOJlHMH TpaHca. A3b1 HyMeponOrHU 3To H8AO 3Ma,... ..CMOTpR'1» eftcTByeT K8K nOCpe.D,HiIIK Me)I<AY PiII- TYaJ1i11CTOM-M8rOM ill Bbl3b1- 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 npHMeT, no KOTOpblM AnJl AeMOHcrpaLtHM cBoero HC- KyCCTBa Mar MO>KeT BblAe- nHTb H3 cBoero OKpy>KeHHJI 6YAYutero KaHAHTa B no- MOU4HHKM. HanpMMep, ern BHMMaHMe AOn)KHbl npMsneb COLtManbHO aKTMBHble eHbI 06U4eCTBa, TaK KaK AOKa3aHO, TO HepeAKo ceKcy- anbHaJl 3HeprHJI B '4enOBeKe CO'4eTaeTCJI C AenoBo aKTMBHOCTbIO M HHHLtHaTHBHOCTblO. OAHaKo AnJl MarHeCKOM AeJlTenbHOCTM 3TMX no- nO>KKTenbHblX Ka'4eCTB Mana: nOMOutHHKy CJ1eAYeT 06naAaTa; eute H pa3BMTO MHTyMHeM. XYAwee, '410 MO>KeT npOH30HTH B pe3ynbTaTe MarH'4eCKoro AeM- CTBa, CMTaeTi<p3r, 3TO TO, '4TO «CMOTpJlutHM» nOMOutHHK HMero He YBMAMT. Ho 3TO MO>KeT cnMTbCJl He 06J13aTenbHO nOTOMY, '4TO Mar HeYAa'4HO npOBen ceaHC Bbl3b1BaHMJI AYXa, a B CHnY Taro, '4TO no- MOU4HMK «He 06naAaeT aAeKBaTHo pacKpblTbiM nCHXHeCKHM 3pe- HMeM» - Me>KAY HMM M MarOM He YCTaHOBMI1CJI 3Hepren14eCKMM pe30HaHC acrpal1bHblX Ten. ECJ1M Mar He M<»KeY,PO CBOHM Ha6nlOAeHHJlM BbiAenHTb Koro-nM60 M3 OKpy>KatOutHX Ha ponb «cMoTpJlU4ero», TO Mary peKOMeHAYeTCJI onpOCMTb npMCyTCTBYlOutHX Ha npeAMeT TJlrH K MarHM. B KaeCTBe MHHHMJtl,HOrO rpe60BaHHJI OH 06pautaeT BHHMaHHe Ha cnoc06- HOCTb '4enOBeKa '4aCTO BHAeTb BeutHe CHbI, YBne'4eHHOCTb era «He- TPaAHHOHHblM" 3HaHHJlMH» MnH B KpaMHeM CJ1Y4ae npHcyTCTBMe y Hero 60nbworo >KenaHHJt acTBoBaTb B npeACTOJlU4eM 3KcnepHMeH- So BpeMR 8rM'IecKOro AeA- CTa8 peKoMeHAyeTcSI pe3KO nOBblCHTb 3MOlU'IOHaJ1bHOO H8- 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 3MOH- oHanbHoro HanpJl>KeHHJI Ten Mara M «CMOTpJllqero» npH- MeHJlIOT pa3Hble MeTOAbi. nO'4TM BCe OHH AnJl perynJl- MM ypOBHJI C03HaHHJI HC- nOnb3YIOT acrpaJ1bHble CBOMCTBa opraHM3Ma - '4YBCTBa, 3MOHM. 310 MO>KeT 6b1Tb 'fYBCTBO HaMBblcwero 6na>KeHCTBa, opra3Ma MnM CMnbHOM 60J1H. Vl3BeCTHo, '4TO HeKOTopble nlOAH HCnbITblBa10f MKCHMan.bHoe HaCJ1aeHHe H YAOBonbCTBHe TonbKO npM CHJ1bHOM 'MOMOHaJ1b- HaM B036Y>KAeHHH, crpecce. TaKoe COCTOJlHHe MO>KeT B03HHKaTb aT npH'4HHeHHJI ce6e HecTepnHMoM 60nM (Ma30xHcTbI) HnM npM Ha- 6nIOAeHHH 3a npOJlBneHMeM 3MOMOHaJ1bHOM 6YPH Y napTHepa (Ha- npMMep, npM ceKcyaJ1bHOM 6nH30CTH). OnpeAeneHHoe 3MOHOHaJ1bHOe B036y>K,qeHHe Mara Hero nOMOIq- HMKa, KOTOpblM OHH B 60nbWMHCTBe CJ1ae8 C03HaTenbHO ynpaBnJl- lOT, JlBJ1J1eTCJI eOTheM1ieMbiM ycnOBHeM CBepWeHMJI MarMH. AOCTHl.lb 3MOHOHanbHoro 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, Kora 06b1I.1HO HerpYA- HO A06HTbCJI HY>KHoro ypOBHJI B036Y>KAeHMJI (oc06eHHO npM YMblX AeMCTBMJlX napTHepa npOTMBOnOnO>KHOrO nona). n03TOMY ceKcyanb- H.oe B03eHMe KaK OAMH H3 BapMaHTOB «3MOMOHanbHoro HaKa- A3b1 HYMeponOrHH no enOBaM Maroa 6oJ1b COCTaBneT 8CTb AYX08- HOO npaKT'-1IC'-1, WHpoKO H- nOJ1b3yeMoH B WaMaHCIC)( KYJ1bTax.EcTbxp'-1cT'-1aHclC'-1e ceKTbI, B p'-1TY8f1ax KOTOpbIX npMMeHIOT caM06HeB8H'-1e. 49 
rnasa 1 na» AllJI M3Bne'4eHMJI M3 opraHM3Ma He06xOAM- MOM AflJI MarH'4eCKOrO AeMCTBa 6M03HeprMM Hcnonb3yeTCJI B HeKO- TOpblX pM1)'aJ1ax MantM. CeKcyaJ1bHblM B03- 6y)tij\eHMeM te6Jt HnH napTHepa /!tar AOBOAMT AO «6na>KeHHOm TpaH- ca», 3MOMOHanbHOM HeynpaBnJleMOCTM, 'Op- ra3Ma. He06xOAHMY AJlJI MCTonKOBaHMJI MHcI>op...aMIO Mar rionY'4aeT Ha rpaHM C03Ha- renbHoro M 6eCC03HaTenbHoro BOCnpMJlTHJI peanbHOCTH. HanOM- HHM '4MTaTUIO, '4To.cYU4eCTBOBaHHe B .KOCMoce H4>opMaHOH- Hare non";.8 KOTOpOM XpaHJlTCJI 3HepreTM'4eCKHe MaTpHbI a npownOM HaCTOJlU4eM M 6YAYU4eM nnaHeTbi 3eMnJl H a Ka)tij\OM ee >KHBOM cYU4eCTBe, npM3HaeTCJI cOBpeMeHHoM HaYKoM (CM. pa3Aen KHMrM «n03BonHTenbHo nM 3HaTb CBoe 6YAYU4ee)l). B 3TOM COcrt>JlHHM nO-MHoMY npoHcxoAMTBocnpMJl1MepeanbHo- CTM, M3MeHSfeTat OeHKa C03HaHM- eM oKPy>.KcuoU4ero. Y nlOAeM C no- BbiweHNoit '4}'BCTBMTenbHOCTblO aT nepeB036Y>KAeHHJI B03HHKaeT He- KOTOpaJl HeycrOM'4HBOCTb C03Ha- HHJI, He06b1'4HOCTb 4>H3H'4eCKHX Ecn. MH8HM8 n().(18l"8lOT, 'fT() B COCTOAHMM C03H8- TeI1bHOfO iii 6ecc03HaTenbH0ro soc- nplilSfTMSt peanbHOCTM 3Hepfe114LfeC-  rena 'fe11OeeI(8 HaM60nee aKTHB- HO scrynaJOTB pe3OH8HC C  KOCMOCa, TCHiee - C ern- 11oJ1eM.C- HOrO noIm B 3TO BpetAR I'IpCMCXO,O,MT C'fIiITbIBaHlile HY*HOM M8tIY 3H8JX"8iM- I.feCKOO IiIH4>oPMa'-'IiIM. 50 3ro HBAO 3H.n., S SOCnpIilSlT\ltM peanbHO- CT\It OOJ1bWee 3HaeH\lte nOny'iaeT noAKOpKa (YB- CTBa, 3MOLt\lt\lt), eM KOpa rOl1OBHOro Moora (OC03- HaHHOCTb,paCCYA\ltTenb- HOCTb, J10r\ltKa \It T. A.). 
(Tena,opraHM3Ma) M 3Hep- reTM'feCKHXou.weHHM (Ha- WHX 3HepreTH'4ecKMx Tell). nocne B03Bpara C03HaHHJI B peaJ1bHOCTb Mar OCHOB- Hoe BHMMaHHe 06paU4aeT Ha aHanH3 3anOMHMBWMXCJI 3HepreTM'4ecKHx BOCnpMJI- THM (npeMMYU4etTBeHHO ac- TpanItHblx). AcrpanltHbiM 06MeH '4y&- creaMM Me>KAY My>K'4MHOM M >KeHMHOM (Aa>Ke 6e3 ceK- cyaJ1bHOM CBJl3H) npoxoAMT Slp'4e M '4YBCTBHTenbHee, 'leM Me>KAY Ma- rOM M era nOMOHMKOM OAHoro nona. n03TOMY Bce MarM CTpeMJlTCJI K TOMY, '4T06b1 Y HHX 6b1J1M noMOHMKaMH nHI,4a APYroro nona. nOCKonb- K'J Man4 4aU4e foty>K'4MHbI, TO nOMoU4HMKM Y HMX - >KeHHHbI. 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 om1T 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'" nP8AflOKTa- eTCR ecTecTBeHH8A nOOOBaR CBA3b MeY pa3HOnOnblM&>1 n8pTHepaM&>1 51 
rnasa 1 CTexHMKa nCKa3aHH", 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 Toa Ltenb nOMo",HMKOB MeHJI- eTCJ1. OHM AOn)KHbI nonbnaTbCJI pc136YAHTb pM1YaJ1MCTa, HO nocPeA- CT80M ceKcyaJ1bHO CTHMynJlMM. 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 MeAMMHe 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 n03MHJI, - nMweT A. Kp3r AaJ1bWe,- HO OHa All" CHnbHblX nIOAeM: B TaHTpe aHa Ha3b1BaeTCJI n030M «Bopo- 52 
Ha». nocne 06HOM ceKCy- aI1bHOM CTMMynJlHH MY>K- '4MHa, BCTaBaJl, nOAHMMaeT )KeHMHy, craBMT ee BBePx HoraMM. B 3TO,.. nonO)Ke- HMM OHM 3aHHMalOTCJI 060- IOAHblM opanbHblM ceK- COM. 06b1'4HO >KeHHHa onneraer HeraMM welO MnH ronOBY My>K'4MHbI - 3TO 3aBMCMT aT AIIMHbI ee Hor. MMHa >l<e Aep>KMT >KeH- U4MHy ](I TalIMIO. EcnH MHHa 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 >KeHI14HbI. - npulf. Dsm.). A06aBMM, '4TO «ceKcyaJ1bHblM pMTyan» MarHH B nOCJ1eAHeM IIC- nonHeHMH n03b1 He6e30naceH KaK AllJI >KeHHHbI H3-3a nepeRaAa KpOBJIHOrO AaBneHHJI, oc06eHHo B CTOPOHY era YBenH'4eHMJI (no3a npoBoMpyeT 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,nIr1HCKoe 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.Q8HO 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 HaCbIeHbI 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 onblealOT no.o. TepMHOM «ByrpeHH(CeKcyanbHa) an)(J.1M-. npM'teM I-tHCTPYMeH- Tap'" aI1XMMMKOB - wa  6ynaea-necTMK AI1 paCTpaH npenapaTOB M noJ1Y'fSH 3Hep- reTWfeCKoo CMeC - B «CeKcy- anbHO an)G1M- MeeT onpe- AeJ1eHtfYK) CMBOnMt<y. . 54 
r. C_be>. -:- rpaKTyeTQJ..B MAH"HCKOM 3HMKJ10neAHH 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 peaKM- eM H HanpaBneHHoCTblO Ha BOCCTaHosneHHe HOpMaJ1bHYHKi.4HM opraHH3Ma. no cpaBHeHHIO C APyrHMH BHAM 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 nCHxHecKOM, HHTenneKTyaJ1bHOM AeJJTeJ1b- HOCTbIO, 3MOHOHaJ1bHyiO 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 BcnecTBHe 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- WeHJI, nonY'4MTb era pa3peweHe. 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 '4enOBeeCKOM >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 M31OHKOM» (eU4e rOBOpJlT - «Kl1y6HtJ'4KOM»), ceKcyaJ1bHblM apecc no MeTO- AHKe Bbl3b1BaHHJI 6nHH<e He K '4enOBKOMY, a K >KHBOTHO- MY Hcnonb30BaHHIO CBOHX B03MO>KHOM. Ho Aa>Ke >KH- BOTHbie He AOBOAJIT ce6 AO B M8rM" ceKcyanWlblM TPBHC - OH ...,3 MeTOAOB Bocnp...,stT...,st ...,3MeHeHHblM C03HaH...,eM cna6b1x KOCM""- 46CK...,X 3Hepr...,'" (MeHTaT1b- HbIX. aCTp8J1bHbIX ..., /JPY- niX), KOTopble B HOpMaT1b- HOM COCTOstH...,..., 06b1HbI'" 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, 003TY AaHHblM MeTOA Bbl3b1BaHMJI TpaHCa B MarHM Mcnonb3YlOT O'4eHb peAKO. ACTponorMeCKMe M reorp8c1»MecKMe ccCBSll1.\eHHble» 3H8KM 3HaK Pbl6b1 (pHC. 1, a) Bowen B cHny H CTan Mcnonb30BaTbCJt B oKKynbTH3Me, KorAa (onHe 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 ConHe nepeMAeT B APY- rOM 30AHaKanbHblM 3HaK- a OAHMM 3 CaMbQi C8steH- HbiX  np3HaHHblX B OK-' KYl1bT3Me 3HaKOB, ecJ1 He caMbiM 3HaMeHHTblM H3 HHX, stBl1steTCst 3HaK Pbl6b1. C\o1MBO.n KOTOporo H300pa- >KaeTCst OAHM pocePKOM. 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 BeHOM >KM3HM; peHHKapHa- MM (O'4epeAHoro- TeJteCHoro BonnOeHMJI 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 CneanMCTbI no OM03Hepre- TMKe H 3KCTp8ceHCbI CKTaIOT. TO H8110>KeHMe Ha CeOsf.q>ecT8 pa3rnIDKHBaeT .o.e<l>eKTbI H8weH aypbl. nocne 3TOro 3HepreTH- ecKHe o6oKI1 CTaHoBsrrc YCTOH'4HBeH K «3HapreTH'feC- KOH HH<l>eKH.. 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 KOHMH (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°. KOHW 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 OTI1MM8 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- . MeponorMecKoM Ka66aJ1b1: pMcoBaTb MnM CMTblBaTb 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 Al1.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- TOHO MHoro. 3Ha'4HTenbHoe KOnM'4eCTBO HX 6b1no n03aMM- CTBOBaHO M3 O'4epTaHHM oc- HOBHblX cone3AttM Ha He6e, HanpMMep COBe3.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 MeAHHHe eCTb AOCTOBepHble M «ManoMH4>op- MaTMBHble» nOKa3aTenH HccneAOBaHHJI AnJl YCTaHOBneHMJI AMarHo_3a. KaK anbTepHaTHBHblM npHMep BcnOMHHM M3BeCTHoe yTBep>KAeHHe, '4TO «OTpMaTenbHblM pe3ynbTaT - 3TO TO>Ke no- ne3HblM pe3ynbTar». A3b1 HyMenOrHH Ha 3aMenty TSCHOe CO'feTaH..,e C..,Mson..,- IG1 a.tCen C rpa<l>..,KoM 3Be3,A Bel1W1O  aClpOnont.., ee <t>W1OC BeTBb - 1ItC- nOByiO (HeponOnt'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 oTpHaTenbHwx '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 - aeCKHe» '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 npHaA11e>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 OCHOBaHe. np "paBHnb- HaM BHeApeHHH B npaKTHKY OHH MOryr AaTb '4enOBeKY LteH- HYIO HH4>opMaMIO. 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 H306peTeHn1 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 npaBMb- Hble AeMCTBHJI? ECTb nH Y>Ke cerOAHJt KaKHe-nH60 H3BeCTHbie HaYKe AOCTOBepHble CBeAeHHJI, '4T06b1 «nHTaTb HaAe>KAbI»? OKa3b1BaeTCJI, HaKonHnOCb MHoro KaK mopemu4ecKux pa3pa60TOK, TaK M t/JOK- mOB, nOATBep>KAeHHblX 3KcnepHMeHTanbHO. OHH CTonb OCHOBaTenb- HbI, '4TO yeHble 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 GKnannTCTBa8 OCTaeTCR y enOBel(8 CTOJ1b BenHK8, TO tf8 npoTR)I(e- H CBoe... TOp OH c03A811 MHoro B8pH8HTOB Ca0e06paeHbIX .M8WH 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 YMHpaT»,- 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 rpelr1. A3b1 H}'MeponOrHH OKKYnlltTM3M ....pa M C8r0AH- B TOM, o Mblcnb MaTe- f)HBnbHa. CXOASIT MHe- HIr1R BCex Y'leHbIX, K8K npeATaB_Ir1Tene «OpTO- AOKC8J1bHb1X-, T8K Ir1 «He- OPTOAQKcaflbHbIX», OK- KYJ1bTHbiX H8YK. CJ>Ir1I1OCO- <l>bI, OCo6eHHO BocTOKa Oonee TecHO CBR38H C OJ1bllil3MOM, nOJ1a- ralOT. 'fTO M8R J1IOAbMir1 MblCnlr1TeJ1bH8R 3HeprMR He Ir1CT, 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 CecTBOB8HMe B U4ecTByeT HeKall npeAonpeAe- KOCMoce HeKoero 3Hep- neHHOCTb, npeAYrOTOBaHHOCTb reTWfecKoro OOil8Ka. Ero TeeHHJI )fU13HM Ha 3eMlJe (c He- npoMCXO)I(.QeHe CBR3b1- KOTOpblMH' ee Kone6aHHJlMH). BaIOT c Bbl,D.eneHeM 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'4HTaTCJI, '4TO '4enOBe'feCtCMM OOlite- '4eJJOBeK 8 He60nbWOM AHana30- CTBOM  peanH3osaHHO He BapMaHTOB C80eM CYAb6b1 MO- B npocYp8HCTBe B <l><>PMe >KeT COBepWaTb «nOAnpaBKH B MpoBoM 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 nOKoneHR MY, nOKa3aTb CBoe COBepweH- 6YAeT C03A(iHO «'4YAO CTBO M CTOMKOCTb B npeoAone- enoeeecKoM Mblcn....., HHM >KH3HeHHblX npenJlTCTBHM, T. e. M8wHaepeMeH. '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 cyeCTByeT, 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>. «AcJ» MH4>OpMHpyeT: B03MO>KHOCTH cOBpeMeHHoM HayKH TaKO- BbI, '410 OHa «BnnOTHYIO nOAowna K TOMY, '4To6bf HHTbCJI C'4HTbI- BaTb 3T'j MH4>opMaMIO (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 614ee... 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 YHTblBaJl MaCCOBoe npOH3BOACTBO TaKMX MaWHH B 6YAYU4eM, BeeCTM B HHX orpaHHHTenb 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)K8wee 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 nOb30M 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 OOblHO 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 HHcpopMaLtJI a '4enOBeKe M era TaMHblX nOMblCJ1aX 6YAeT 3a- paHee npeAonpeAenJlTb nOCJ1eACTBHJI 06U4eHHJI C HMM, aBTOp YCMaT- pHBaeT B 3TOM 3Ha'4HTenbHble >KHTeMCKe CJ10>KHOCTM. n03TOMY Aa>Ke KpaTKOBpeMeHHblM nporH63 a CBepweHKK C06b1TKM 6YAeT i4MeTb pOKOBbie nOCJ1eACTBMJI. BblCKa3b1BaeTCJI MHeHMe, '4TO n.paao Ha Bna- AeHHe MaWHOM BpeMeH Aa>Ke C KOpOTKMM nporH030M (AO He- CKonbKHX AHeM) AOn>KHO 6b1Tb pa3peweHO orpaHHeHHOMY '4MCJ1Y nL\. CKopee Beero 3TO A011>KHbI 6b1Tb PYKOAJIHe 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 KOHI<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 KapMHecKH 06poBlleHHblM 3aKOHo- MepHOCTJlM - C11Y'4aMHOCTJlM. Pa3pa60TaHHble B HaCTOJlee 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 H3YaTb 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 HKTO He (5b1BaeT ca- tiblM: Bee CJ1Y'iaHOC- TK - 38KOHOMepHbI. 
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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 '4MO 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 MblWbI, a aKonneHMe 31Oro CBOM- CTBa B CBOIO O'4epeAb Bbl3b1BaeT M3MeHeHHe crpYKTYPblfl'b1WbI, pa3- BHTMe B HeM AononHMTenbHblx MblWe'4HblX BonOKOHnpOMCXOAHT 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 MeAHMHe 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 H3eHMe! TonbKo HY>KHO 3HaTb, KorAa, npM KaKHX 60ne3- HJtX, B KitKOM A03e  B KaKoM nOCJ1eAOaTenbHoCTH 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 anbTepHaTB- HbiX np3HaKoB  CBOCTB.. KaK n0J10)l(&llTeJ1bHbIX (xeJ1aH- HblX), TaK  OTP"1TeJ1bHbIX (He)KeRaHHblx). III BceM 3TM npoTMBOpeRMcBocTaeHeH npoecc pa3BTR. 3TOT npo- ecc 06b1HO HepasHoMepeH. B I(8)K,D,OM 06beKTe W1 RBJ1e- HMH npoHCxoART 6opb6a, .KOH- K}'peHUMR COCTaBJ1RIOX ero pa3HOHanpaBJ1eHHblX KaecTB. 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 BeHOM, npeACTOJlno YM.epeTb B 3aneaTaHHOM peTopTe. O'4e- BMAHO, npaKTMKa A06b1BaHHJt JlAOB, B '4eM oceHHO 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 oepKH MarHH H oKKynbTH3Ma, 1991, c. 120). MaTepHanCTH'4eCKOe yTBep>KAeHMe, '4TO Bce pa3BHBaeTCft '4e- pe3 npoTHBOpeMJI 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 3HaHJI, OTAeJ1HTb HCTHHHoe aT HaAYMaHHoro, HCKa>KeHHO AOHeceHHoro K HaM epe3 75 
rnasa 1 C88A8HM.noonbTM3MY MO>KHO socnplllHIiIMaTb no- pa3HOMy. nonaraeM, 'ITO 3Ta IIIH<t>oPMa He cpa3Y 1113- MeHlIIT nplilBbIHYIO TKY 3peHIIIR miTel1R: OJ],HaICO KpecKM OLteHeHHbIe CBe- AeHMR no HyMepo110rMIIIIII IIIC110BO aCTpOl1on1l11, B03- MO>KHO.n03B0l1RTliITaTel1lO 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). B CTaTbe co06tijaeTcJI, '4TO 60nee nonOBMHbI npeACKa- 3aHHM HOCTpaAaMyca ycnenM Y>Ke HcnonHMTbCR B T04HOM COOTBeTCTBHM C HanMcaH- HbiM. PeBOnlOLtMM B POCCMH H 80 CbpaHl4MM, ABe MMposbie BOMHbI, pa3BaJI CCCP, BOMHa B A4>raHHCTaHe H MHoroe APyroe 6b1no npeAcKa3aHO C THOCTblO AO HeCKonbKHX MeCJlLteB 3a MHOro BeKOB AfJ Taro, KaK Bce 3TH c06b1- THJI npOH30wnH. TO'4HOCTb npeACKa3aHMM HocrpaAaM npeBblCH- na 90 OJo. OAHaKo caMbiM neanbHblM OTKpblTHeM CTaJ10 TO, '4T0 Y>Ke B HeAaneKOM 6YAYU4eM nepeA '4enOBe'4eCTBOM B,:raHeT np3pa HO- BOH MHpOBOH BOMHbI, HI1H, rOBopR cnoBaMM HOCTpaAaMyca, «Tpe- THM nOTon '4enOBe'4ec- KOM KpOBH». npeACKa3aHMR era Mpa'4HbI. Bo Bce Bpe- MeHa B BOMHax Mcnonb- 30BanHCb caMbie HO- Be£1wMe AOCTM>KeHMJ\ TeXHHKM M HayKM. ECTe- CTBeHHO, '4T0 B 6opb6e 3a Bbl>KHBaHHe MHO- rHe crpaHbI Hcnonb3YlOT An- nI0603H8T8JlbHWX B CBOX nOCl1aHRX nOTOM- !<aM 3HaMeHTbllit n3a- Tel1b MmueJ1b Hocrpa.naMYC CnOI1b30BaJ1 lie TOl1bKO aCT- pol1e i>acenli no nl1aHeTBM  3HaKaM 3o,QMaKa, HO  "CI108ble KO,D,bl. Corn8cHo Y'leHMao npeAcKa3aHe - ee He pok, He 6e3b1CXOAH8A cyAbt)a. ACTpol10rMA  H}'Mepol10rMA BCerA8 nOAepK- B8I1, TO npeACKa3aHA - 3TO I1Wb BepoATHbie YC11OBA, coeTa- H KOTOpblX MO>KeT c4>OPMPO- BaTb npeACK83aHHble C06blTI1A. HO enOBeK BcerA8 MO>KeT pa3YMHO BMewaTbCA B XOA COOblTA BpeMe- H  3MeHiofTb J1 06J1em-b no- cneACTBA co6b1TIit. 77 
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fnasa 2 TOHM'feCKOM 6one3HM) M npM 3HJ\OKPHHHblX HapyweHHJlX (npeHMY- 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- Hee, '4eM 3AopOBbie. Oc06eHHo onaCHblMH C'4HTaIOTCJI «ABoMHble» H «1'pOMHble» KpHTH'feCKHe AHM, Kama OHM JlBnJlIOTCJI caMOM my60KOM OTpHLtaTeJ1bHOM 4>a30M AnJl HeCKonbKHX 6HOPHTMOB. fpa4>HK 6MOpHTMOB O'4eHb nOMoraer U4aAHTIt ce6J1 B nepHOA «KPM- TH'4eCKHX» nepenaAOB, 3apaHee rOTOBHTbCJI K HMM (HanpMMep, OT- nO>KMTb Hecpo'4Hble Aena HnH npHHJlTb. neKapCTBO). MaKCHManbHO HarpY>KaTb ce6" B «3Be3AHble», 3HepreTH'4eCKH Ha- CblLqeHHble 6H03HepreTHKOM AHH, H AO- 6HBaTbCJI HaH60nbweM 34>4>eKTHBHOCTH B AeJlTenbHOCTM. Ho KaK COCTaBMTb CBOM rpa4>HK? AnJl nOCTpOeHHJI rpa4>HKa pHcyeM OCH a6CLtHCC H OPAHHaT. BepTHKanbHYIO OCb Bbi6HpaeM AnJl 0603Ha'4eHHJI BenH- '4MHbI K0J1e6aHHJI 6HOpHTMOB, a ropH30HTanbHYlO - An" 0603Ha- '4eHMJI BpeMeHH -M on"eaeM Ha HeM AHH. fOpM30HTanbHaJl OCb AOn>KHa COAep>KaTb '40 AHeM Ha'4HHaJl aT paceTHoro nepHOAa M AO KOH14a rOAa: TaK. eCJ1H paceT Ha'4MHaIOT C 1 MaJl, TO HMeHHO C :noro AHJJ H no 31 AeKa6p.JI COCTaBnJlIOT rpa4>HK (06b1HO He06- XOAHMYIO AnMHY nHCTKOB AOKneHBaIOT).. ):\eHb Ha'4ana paC'4eTOB . AOn>KeH 6b1Tb B Ha'4ane ropH30HTanM, Ha nepeCe'4eHHH a6CLtHCC H °PAHHaT. He 38MeTKY BblLtMCJWIB rpa<l>Mk 6MOpMTMOB, MO>K- HO 60nee rwa- BMnbHO nJ18HMpo- BaTb CBOIO AeSl- Tel1bHOCTb. 96 
Tenepb C Y'4eTOM '4MCJ1a poeHMJI onpeAeAAeM TO'4KY -AeHb Ha- '4aJ1a BblX0Aa rpex CHHycOHA COOTBeTCTBytoU4MX KaOMY 6MOpKTMY. C'4MTaIOT, '£TO B MOMeHT poeHHJI 3anycKalOTCJI OAHOBpeMeHHO cpa3Y Bce nepe'4MCJ1eHHble 6HOpKTMbI. nO:nOMY HaLlano MX «3anyc»'Ha cxe- Me 6YAeT M3 OAHOM TO"IKH, HO AaJ1bWe B rpa$tKe CMHycOHAbt-Bte 6onb- we 6'JAyT OlXOAKTb" Apyr aT Apyr TaK KaK Y i<a>K,qOM H3 HMX pa3HaJI AnMHa nonHoro Kone6aHHJI' (nepHOAa). Aan rpa$MKe BepxywKa HnH ttH>KHHM cnaA HecKonbKHX CHHycOMA MOryT COBQaAaTb MJ1M npM- 6nM>KaTbCJI Apyr K APYry. npH 3TOM B03HMKaeT nM60 npHnMB COOTBeT- CTBYJOI14eM CHHycOHAbi 3HeprHH (npH COBnaAe!fMH aepxyweK CHHycO- HA HaA rop30HTanblO), nM60 pe3KHM cnaA 6H03HeprMM (npH COBneHMH KpMBbiX nOA ropH30HTaJ1blO). Kone6aHHe CHHYCOHAbi 6HOPHTMOB 06J13aTenbHO WtCC'4MTblBa- lOT C Y'4eTOM AHJI pOeHHJI. CTpOJlT rpa4>MK Kone6aHMf'!6MopHTMOB Ha AeHb pO>KAeHHJI, a aT Hero npOAneBalOT CHHYCQMAbi BnepeA (AnSI Y'4eTa HarpY3KH Ha 6YAYU4ee BpeMJI) HnM Ha3aA (eCJ1M '4enOBeKa MHTepecyeT npH'4HHa era HeYAa'4 B npownOM - HHorAa aHa 06bJlC- HlleTCJI cnaAoM B 3TOT AeHJ) 06ecneLlHBalOU4Mx ycnex 6H03HeprHM 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 BHCOKOCHbtM'rOA 3TOT fo\eCJI paBeH 29 AHJlM). PaC'4eTbi npOBOAJlT no 4>opMyne, n03BOnJllOU4eM onpeAenKTb '4HCnO npO>KMTblX AtieM (A): 97 4>opMyna «HOIiHOa cf>eH» M388CTHO, 'fTO... fOAOB<WI plltTM npllt- HstT paBHblM speMe- Hilt 06paeHIltSJ 36M- nllt BOKpyr COJ1H - 365,25 CyrOK. 
rnBSB 2 A - (rTeK - rpo*A) x-365 + NBHe, 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, rAe 4 - '4HenO neT, '4epe3 KOTOpble HacrynaeT BMCOKOCHbiM 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, 3MOMOHaJ1bHblX 164 376 : 28 - 587 M B OCTaTKe 0 AHeM, HHTenneKTyaJ1HblX 16 436 : 33 - 498 M B OCTaTKe 2 AHJI. Tenepb HaM nCTO"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 
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" . . na -HO'lHoH ". » "I ",en a M MY3b1Ka nyHHOM HO'IM MYApet4W ApeSHOCTM AOnJKHW 6wnM nPMAYMan. KaKoM-TO 4»MnO- C04»CKMM KplilTepMi - HeKMM «CMMBOJ1MifeclUf" :nanOH», KOTO- pwii MO)l(f40 6WIIO 6t.I MCnOJ1b3G- 'Ba11t KaK eNIHM&CY M3MepeHIiIJI pcu- HWX CTpyIOyp npM paCeHMRX iii COT80peHMM acero cy. KMM 3TaJfOHOM» Mbi Ha3WBaeM ycnOBHO iii TOnbKO noTO- My, '4TO OH ..toonb3oaana MMeHHO 113TOM ]Ha'4eH_XOTJI cl»tnoco- cI>..M leaK HayKM B n! ApeBHIIIe BpeMeHa  He 6WRO.-c3ranOH» He MMe1I 'tMCJ1080ro BWpa1KeH". OH 6 Ka'feCReHH_a He KOJ1M44e- cneHHWM, TaK Kat( '4MCAa 6W11M M306pereHW ropa3AO nOHee. Co- BpeMeHHcU CMCTeMa MCneHQ 6wBa 8ae.qeHi ropa3Ao no]JKe AAe- MPAOM M3 6ara (1120) M pacnpoapaHMnacb noeceMeCTHo noA Ha3BaHMeM capa6CKoib '4MtnOao" CMCTeMbi (6epHaTOOlH c.r. Pe- KOPAW npMpo.qbI M 'feIt08e'4ecKoM bHOCTM). MYApe'4w C'4MTanM, 'fTO cxeMa noapoettMII BteJIeHHOii Aon*Ha COAePTb rapMoHMIO KaK HiM- 6Mee }UOM'tMBWM BapMaHT npM- cnoc06neHM. K CYU4ecTBoBaHMIO, 6wnuo. OHM nOliaranM: Bce, '4TO COWHO pyKaMM 'feJ1OBeKa M Ha- AeJM!1jO rapMOHMeM MM KpaCOTOM (HanpMMep, MyJbIKa), 6yAeT yae- KOBe'4eHO, ecnM He BpeMeHeM , TO AoC5po 1II1qNMX)T8 B IC8'teCT1I8 CMMBOJ1M"teC- lCorO . cS*J 0 3T811OH8- npMHAT8 -ntp- MOHMA-, KOTOpaSI B C8OeO 0'tepeAb MMeeT COCT88- HbI8  - «,Q06po-, «1Cp8CO"y- M T. A. Mcl"'" .. CaMyIo paHttlOlO-'CMcTe- MY MCnete4R   wyM8PbI OKOOO 6 Tb«:. lleT,,_38A- 101 
rnasa 2 naMJlTbIO nlOAeM. npHcyrCTBHe B JlBneHHM HJ1H 06beKTe 06ero C BceneHHOM npH3HaKa - rapMOHMM - paCCMaTpMBaJlOCb KaK $Hno- C04>cKHM BapMaHT 06U4eM MOAenH nOCTpOeHHJI. TaK 6b1nH C03AaHbI pa3Hble MOAenM nOCTpOeHMJI MHpa, OCHOBaHHble Ha MY3b1KaJ1bHOM CMMBonHKe (c MCnOnb30BaHHeM HOT M MY3b1KaJlbHblX OKraB). KpaCOTa H rapMOHHII nOHHManHCb KaK 3aKOHOMepHble CO'4e- TaHMJI '4aCTeM JlBneHHM H BeU4eM, nOpJlAOK KOTOpblX MO>KHO ne- peAaBaTb 'fMCnOBOM CHMBOnHKOM. rapMOHMJI BOCnpMHMManaCb KaK COCTaBHaJl '4aCTb MHp03AaHHJI, npMAalOU4aJl era CTpYK'rype 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, npMcyaJl nppOAe '4enOBeKa. AnJl HYMepanora n0Y'4HTeneH 3Tan $>pMMpoBaHHJI npeACTaBne- HHJI ApeBHMX.9 KpHTepHJlX H CHMBonax H ynOTpe6nHHJI HX B pac- cy>KAeHHIIX. aco6eHHO HHTepeceH :nan Mcnonb30BaHMII MMM Ka'4e- CTBeHHbfX CMMBonOB. nep1sble npeACTaBneHMJI a rapMOHHM MYApebI 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 AYW1{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)ebI, ecTb npo- JlBneHHe BonH Bblcwero Pa3YMa, Be'4HOrO A06pa. no npeAaHHIO, 60ry fepMecy, OCHOBaTenlO HC- KycCTB, rpe'4eCKHe 4>Hno- C04>bI npHnHCblBanH KOH- .CTP1poBaHHe-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»MMM M3HIU1 n. Xonn (1992) OTHOC- rel1bHO ynorpe()11eH CMB01lO8 B CPW10c0cp nweT: «B MTe' PMRX l1pa 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 rapMOH1O HOp- M811bHOH My.3bIIG1, KOTopaR, CA- H8KO, nTCSI B AHCrSPMOHIO. 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 paceHHII: «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 BpeMeHctCMTaJ1H, '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 MY3b1KanHO-'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. CTMH B cBoeM KHMre «npeBpaTHoCTH Hay'4HblX HAeM»), OTKpblTHIO nAWeCTBOBaJ1a 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, oeHHBaJl 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 R8J1HR H npeAMeTbl. B noHCKaX B HHX TatG1X )ICe CO'feTaHHH aCTeM OH C Y8J1eHHeM OOHapY*\iI1T. "ITO. 3T..,...ceTaHHR 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. .......... ............... ............. · n4>arop npOCT8J1 MaTeMaTeCKYIO MOAenb CBoero . HaMeHTOrO Tea7p8K7JfCa, KOTOpblH CTaJ1 Y rpeKoB Bep- . : XOBHblM CMBonOM yHBepcanbHblx .Cn  npOL\eccoB  · · COAep)k8J1 TeQJ)M1O MaTeMaTMeCKoro npnO)l(eHR K RB- . neHRM nppo.ilb' 'f8CTOT MY3bUC  L\BeTa. MOAenb npeA- · CTaBnRl1a co60H cMBonecKYIO npaMH,IJ,Y, 06pa30BaH- . HytO 3 :rO'4eK M nej:JBblx eTblpex '4ce.A 3neMeHT8pHoro · ti}'Me'feCKOrO pR,D,a - 1, 2, 3  4. 3m 'fcna B pa3- · HbiX CO'feTaHRX A8BaJ1 rapMOHM OKT8BbI, AHaneH,D.e  . AHaTeccapoH. 106 
«AnJl nM4>aropa My3b1Ka 6btna npOM3BOAHOM aT 60>KeCTBeHHOM HayKH MaTeManIKM,  ee rapMOHM >KeCTKO KOHTponMpOBaJ1HCb Ma- TeMaTMeCKHMM nponOPLtHIIMH, - nHweT Xonn. - nHd>aropHMI4b1 yTBep>KAaJ1H, '4TO MaTeMaTMKa AeMOH- CTpMpyeTT0'4HblM MeTOA, KOTOpblM 60r ycraHOBn 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 '4C- 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 YB MY3b1KY leaK T04HyIO YKY, nH<I>- rop npMMeHHn H8- AeHHbIe MM 38KOHbI raPM<>HMecKHX OTHO- weHH KO BeeM <l>e- HOMeHaM "PMPOAbi. 107 
rnasa 2 Puc. 6. nPM",clW cxeMa Ccl>ePbI MeJKAY He60M M 3eMJ1eM. npeACTaBJIeH MOHOXOPAOM KaK ABoMHU OKTaaa. nOKa3b1BaIO- -.aa A8e KpaMHOCTM eCTIOBaHMJI raptllOHMM. (OIlHe. BwcCNaiauee He60 .. 3eMIt MMelOT oAMHaICoBbiM TOH, pa1J1M"ao- IIMiCJI.RMWIt no BblCOTe ("3 KHMrM ..nYAAi «3eMHU M}l3b1Ka») 108 
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rn8e8 2 M3 rny6MHbI 88KOB B APeBHOCTH ct>MI10e0<S> yr- Bep)l(,D,8J1H. 'ITO KiiI el1o- BeK HMeeT CBoiil MY3K8J1bHiiI KJ1, npHeM, ecnH OH 3a- 3BHT B nonHytO C'I11y, TO 3,Q,OpOBbe "Iel10BeKa OYAeT nOBpeeHO(*H3HbnOA- TBeP>KAaeT cnpaaeA11HBOCTb yrseP*AeHHR .QpeBHKX, TO B&>10palU1R 6011bWoiiI CMn MOJKeT AeiilcTB&>1TenbHO no- BpeAJ.1Tb 3,Q,OpoBbe: MOIJ..tHiiI 3ByK MO)lCeT pa3PYWHTb OpraH CJ1yxa, 8 O'feHb RpKaR BCnw- I<a CBeTa  ocnenKTb). a KOTOpOH OH HH'4erO He 3HaeT, nOTOMY '4TO 14eH1pbl tiyBCTBMTenbHOro BOCnpMJI- TMJI He pa3BHTblI\AOCTaTO'l- HaM CTeneHH» (c. Z95}. Y'4eHblMM ApeBHoCTH pa3pa60TaHbI MCJ10Bble'Co- OTHoweH J<oTopble B CO- oTBeTcrBHH C HaWHM BOC- npHATMeM KnaCcM4>H14HpyIOT 3aKoHoMepHble 4aCTOTHbie 4am'!roM BH6H eocnpH- HHMaeTCJI HaMH KaK 3BYK, a aCTb - KaK LtBeT HnM CBeT. XanJ1 yt<a3b1BaJ1: «TO, '4T0 Ha3b1- BaeT CBeTOM, Ha AeJ1e Jl811I1- eTCJI ypoBHeM BH6pa14HM, B03- AeMCTBYkJU4MX Ha OnTM'feCKHe 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 &>1Cl1eHHe (.tBeTa, KOTOpble Mbi He Mo*eM BeTb; TaK *e, Kal< &>1 3BYl<H, KOTope 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 ccreMa OCHOBaHa Ha :laKa- He OKTaBbI, ycTaHaBnHBalOeM paMKH BOCnpHJlTHJI. Haw CJ1yx MMeeT60nee WMpoKMM AMana30H 'faCTOTHbiX BocnpHJtTMM, 4eM 3pe- HHe. TaK, yxo MO>KeT perHcTpM- pOBaTb aT AeBJlTM AO OAHH- HaAaTM 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>opMaMH - AO 80o 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- nlOCTpaHeM 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 nl1HeT8p- 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 aCTprHH :- 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). 3MB 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 MopTa CWlbHoe nOnO>KeHHe ]a- HMMaI1 Map<: - 31MM 06eHJlIOT 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- HIO KOMnooopoB. 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 
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rnasa 2 JlocneAHMM 3HaKaM 3oAMaKa, B acTHOCTM Pbl6aM. AocraeTCJI OcraB- WMb HaOOp MeHee MHMU,MaBHWX 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 KaecTB OTMe'falOT: «XOPOWMMM 124 
MCHlm!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(, OTMeHO 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 CJ1lOiqMe 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 nOMM 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 «acrponorHec- 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- BMeeHMM 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. /IyHbIMI 4HCJ10BaJl aCTpOnOrHJI onMpaeTCJI Ha Y'4H BOCTO'4HOM M- noco4>MH M oKKynbTM3Ma. no MX npeACTaBneHMtp, B crpYKTYpe, 06eCne'4HBaIOU4eM cyeCTBOBaHMe 06'beKTOB M JlBneHMM npMpo- Abr M OKPY>KaIOU4erO MMpa, MMeeTC" 3HepreTM'4eCKOe '4aCTOTHO- BonHOBoe «Ha'4aJ10» M «nepBopOAHaJl (KapMMeCKast) 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 JlBneHIO npMcyU4e «CBoe» 3HepreTH'4eCKOe a'4aJ1O, BepOJlT- Hee Bcero, 3aBHCJlU4ee OT KOM6HHaLl.HM ero COCTaBnstlOMx, a He 127 
rnasa 2 KaK 06pa30BaHHe HOBoro 3HepreTH'4ecKoro Ha'4ana, HHa\fe 6b1 HX 6b1no HeCMeTHoe KOnM'4eCTBO (BPJlA nH nppoAa H BblCWMM Pa- 3YM CTonb paCTO'4HTenbHbI); 3) 3HepreTM'4eCKOe Ha'4anO HMeeT npaBMnbHYIO H nOCTOJlHHYIO nynbCaLtIO, 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 oepeAb, 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,Tee BCI1YX). HO B OTnHHe OT <S>3KH HYMeponorHSI Ha- Ael1S1eT 3HepreH  MblC- l1eHHoe nporosapHIlaHHe to CMB0I10B (c:el1. 6YKB- BeAb MC11b CHTaeTCSI MaTepahbHoH, polO- eH 3HeprHIO MHkpol1en- TOHHblX nepeMeU-\eHH). 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 "pOrH03HpOBTb C06b1THJI 6YAYU4erO no rllOSt9neHMIO 3HeprHH B «HeMaTepHanbHblX» JlBneHHJlX >KM3HM (HaflpHMep, 8 MCTOpM'4eCKHX C06b1THS!X) H KapMMeCKoA 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 BapHHToB 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 SlBneHH  06beKTOB 3eMHOH nppo- 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 3HepreTHeCKMX 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- paMH JlBJleHHM MJlM 06'beKTOB). 4aCTOTt1b1e BM6paHH 'U1cen 4>op- MYJ1b1 M ee KOHCTaHTbI MMelOT CBOIO 3aKOHOMepHYlO oepeAHOCTb H CO'4eTaHHJI, nTOMY. Tpe6YIOT nOJlCHeHMJI, HCXOM H3 CJ1eAYIOU4HX oKKynbTHbix rtpe06pa30BaHHM: a) 28 - 4 x 7 - 3TO cpopMyna 3aKOHa EAHHCTBa. npe06pa3YJl neBYIO '4aCTb 4>opMynbl, Mbi nonyaeM HCJ10 1 (2 + 8 -10), a B CO- eAHHeHMM C npaBoM '4aCTblO 4>opMynbl nonyaeM 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 YABOHHbI 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. BpoJlTHo, OTAa- Ba" AOn>KHOe 3Ha'4eHMIO 4>opMynbl 3aKoHa EAMHCTBa, Bce >Ke He CJ1eAyeT ee nepeoeHMBaTb 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 «MarHeCKMMM» 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 tMTaTb, '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, nOn3aerO 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 MCTHMKOM CBepweHMJI c.CJJy- 'taMHblX» C06WTld4 B08ce He enY'faMHO. 06paTMMCJJ K 4>aK- raM. TaK, CAaJIHCKaJl a36YKa KM pMnna M Me4>oAMJI 6wla C03a 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 HYMeM 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 Hyueponon1ecK-n03M- ....." 3MT TO JlCe caMoe) OTpucaT 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 MCTopeM pwv,? CM. ConoB 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  cpaMHnSI A8H HaM He C11Y'f8MHO, OH CBOIltM 3Hepren1ecta1M plltTMOM OT- pWICBIOT Hawe COOTBeTCTBlite TOM ponllt B )l(1It3HIIt, KOTopaSi OTBeAeH3 HaM lEapMoM. 3Hep- reTIItecKIltM plltTM IItMeHIlt aano- )l(eH B HawMX .o.enax. 134 
CPopMyna tcHO&lHOU cpeU» «ApM4>MeTHKa, CMpe'4b HaYKa HMCJ1HTenbHaJl» - 8. 3HaMT, 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. npeAHa3HaeHHe. 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 nonyaeT 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 paceTa 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 CMB0110M CTPYKTYPbt «TOHKoro nnaH81t ABne- HHH  OObeKTOB KaK BMAHM, OTKpblTHe 3TMX '4MCen KaK MaTeMaTH'4eCKOrO HH- cTpYMeHTa B n03HaHHH MMpa 6b1no BO MHorOM npeAonpeAeneHo. x BenHMHbI 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.QBHfI 4>I1oco4> KaHJ BOCKJ1: «KaK 3TO B03MO)I(H0, 'fTOObI Me>K.D.Y CTOI1b pa3J1bI M CyllteCTBOBa1Ia TatcaR com8CO- I;!aHHOCTb... npmOM comaco- BaHHOCTb CTOI1b 60I1bWafl. CTOI1b .o.aJIeKO .o.Yl1-'8f1  8 ",:0 )tee BpeMfI CTOI1b TH8R". 
rnABA 3 HYMEPOnOrM B AnABMTE KOAbi ancl»aBMTa MeAMHHCKHMM HccneAOBaHHMH 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'4MJI. ECJ1H CTHMynMpoBaKMe nCHXM'4eCKHX npoeCCOB B AaHHOM eny- ae He npeACTaBnJleTCJI peaJ1bHblM, nOCKonbKY peb pe6eHOK eU4e He nOHHMaeT; TO, KaK r10naralOT CneHaJ1MCTbI 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 06paHH8R K HaM 3HeprlitR 6yKB  CJ10B OKB3b1aaeT CTMYJ1pU4ee B03,D,eMcT8Me Ha pa3BTMe nCXK. 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 06eHHe 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....Bae co CB<»1M HOBO- po*AeHHbfM, pe6eHOK paHbWe H8""HaeT rOBop....Tb ....  ....HTenReKTy.anbHopa3B....saeT- CR. eM Y MVep..... KOTOpaR MOI1a 06ceT 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 3HepreTMecKyIO 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 BenMMHa KOAa He npeBblwaeT '4HCJ1a 3) BHa'4aJ1e npoM3- BOWtT '4MCnoBYIO WM4>POBKY Ka>KAOrO 3HaeHMJI 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- 30BaHe 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::: 15nATTb= 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 = TPTb OAHH = 3. 10 = 32 = TpTb 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>Hec- KH, H TaK AO nonY'4eHHJI KOAa C Be- nM'4HHOM '4HCJ1a He 60nee «rpH». npMMep nonyeHHJI 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 HYMeponorMecKHe 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 c901n1- Ka ... paLU1QHaJ1bHOe Ae- neH no Kon...tfeCTBeH- HOMY j'I ka'4eCTBeHHOMy 3Hae..HiM OTpaOOTblBa- n...Cb CTOnen1M"'. "3Heprope30HaHc»6YKB C "IMCnaMM VlcCJ1eAOBaHHJlMH MHorMX HYMeponoroB AOKa3aHbI MaTeMaTHec- KaJl crpOMHOCTb crpYKTYPbl aJ14>aBMTa, era '4HCJ10BaJl rapMOHHJI H cHMMeTpHJI. PacnOnO>KeHHe 6YKB B pycCKOM an4>aBHTe nOAHHJleT- 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 CJ1yaMHoM, '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 KOHCTaHTy1j,1cno 147) j,1 Ha "J1eBYIO nonoBMHY- <l><>PMYJ1b1 38KOH8 H- CTB8 np"'POAbi (j,1CJ10 28). 144 
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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 OCHOBatlfpycCKO- MY aJ14>aBHTy M Mcnonb3YIOU4eMY ero PyccK9J13b1HOMY 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 oeHKe 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 nMropMMqeB, 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- 'tMCJleHlUt OOt.NHblM MaTet.m'M'feCKMM M OAHMM "3 ffYMepoJlOfM'feC- KMX moco6oa. McnOnb3yeM All" 31orO KaKoe-l1MOO '4MCJtO, HanpMMep 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 I(O- J'J11ftIJ- H)iMepoIlOf"MM, 1-. _' HeCeT B ce6e ..ryIO MftCI>op- ....,m 0 BCex 'MCJ18X». 148 
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rnSB8 3 xonorM H nCMXMaTpbl. OHH npo- CJlT HcnblTyeMoro HanMCaTb nepBble npMweAWMe Ha YM cnOBa MnM pHCOBaTb cxeMbl (npocTo '4epTHTb) «B cB060A- HaM noneTe MblcnH». nOTa,.. aHanH3HpYlOT nonY'4eHHble pe- 3ynbTaTbI, AenaJl Ha 310M OCHO- BaHHM -3aKnIO'4eHMe a COCTOJl- HMM nCMXMKM '4enOBeKa. 3MrMYHA cJ»peMA (1856-1939) npMAaBan 60nbwoe AMarHOC-' TH'4eCKOe 3Ha'4eHMe «c8060A- HbiM aCCOt4MaLtMJlM» MblcnH. A TonKOBaTenM CHOB Mcnonb3YlOT BMAeHMJI KapTMH, HaAnMceM, cn08 H nMHMM cHoBMAeHHM AnJl nporH03a 6}IAYU4erO '4enOBeKa, KOTopoe TO>Ke 3aBHCHT aT CO- CTOJlHMJI erohCMXMKH._ CnOBO HMeeT CKPbllYlO MOULb, 3HeprMIO '4aCTOTHO-BonHOBOM BH6- pat4MH, KOTOpaJl, no 3aKOHaM 4>M3MKH, MO>KeT C «'4eM-TO pOACTBeH- HblM» BCTynaTb 8 pe30HaHC. MarHJI C'4HTaeT, '4TO pe30HaHCHaJl CBJl3b 06b1'4HO 6b1BaeT C TeM, '4TO 3anO>KeHO B CMblCJ1 CJ10Ba. «HMKOfAa He n03BOnftnOCb Y'4HKy M3naraTb KaKMe-nH60 MCTOpH'4eCKHe, penH- rM03Hble MnH peantJHbfIl C06b1THJI 8 TO'4HblX CJ10Bax... M3 onaCeHMJI, '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- OKKYnTM3M .'tepa M C8r0AHtl A. I<Mcenb nonaraeT, 'lTO pycclG1'1 81$8BHT a.1MeeT crporO CKoop,tJ.HHHfJ0B8H- 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- CTBe, B KOTOpOM OH 6b1n 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). CornaCHO &to3Hepr8TMK8 Hel1b3 AyM8Tb 0 On3Kx IWI APyrx 111O,D.SIX n110XO, pyraTb MX '1-1111-1 onacaTbC Toro, o H co- BepwaT He6nroBMAHbI nocTy- nOK, a TalOKe )l(enaTb I-1M Hec- aCTbR MeHHO 3110  MO)l(eT C HMI-1 npoI-130TI-1: M"CI1 BCTyna- lOT B «pe30HaHCH}'IO CB3b. C TeM. o eM Bbi AYMaeTe,  «npl-1B11eKa- lOT. ero K pean3alU't B )l(1-13HI-1. Ha 3TOM OCBaHbI Man.NeCKl-1e npotU1TI-1  HarOBOPbI · Mp C03.D,aH «no oopa3Y  nOAOOIO. comaCHO 3aKOHY · . HCTBa 1-1 ynpaB11eTC M. n03TOMYI-1TaeTC, TO pe- . · 30H8HC 'icel1 1-1 cnOB CBSf3b1B86r «AYWY. (3HepreTecKoe · . Te110) '4e110BeKa, OObeKT 111-1 BneHe npl-1 MX «3eMHOM 06- . · eHI-1. AI1 HOBoro BI-1TK8 B3aMHOrO KapMI-1'feCKOrO pa3- · . BIr1m. 151 
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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 '4CJ1aMH  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 ncaHH CJ1aMHO? 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 cyMMpOBaHHJI CABoeHHblX '4HCeJ1 KBaA- paTa nonMM 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). . MO>KHO nonaraTb, '4TO 3TO YKa- 3b1BaeT Ha «3HepreTH'4eCKHM pe- 30HaHC» Me>KAY 6YKBaMM cnOB npHBeAeHHoro Bblpa>KeHMJI H '4HCJ1aM11 B MarH'4eCKOM KBaApa- ECTb MH8HM8 «enoseecK»3K nOHTeH nWb mOARM, a Ha C(cnOBOM 3b1Ke» 06u.,aeTc Bee, 'iTO «CO- 3P.8HO no,o. JlYHO" we Hes (A. Kcenb, 1994).. 153 
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rnasa 3 HOCT1t M npeeMCTBeHHOCTb nOKOneHtU4 OT O'rqa K (wtty, JlBllJlJlCb 1UIk>- '4014 K TeICIY nMcaHMJI B paCKpbITMM 3aKOHOB >KM3HM" TaK M cxeJ4a MarM'teCKoro KBwarct aHaBJIM8aeT CBJl3b '4eAOBeKa C KOCMO- CO C BWC1UMM Pa3YMoM M MO)KeT 6b1Tb «KnIO'fOM» K paCKpblTMk> ero (YAb6w. YaK yrsep)t(AaeT HYMeponorMJI. 4»pa3a cOre Cw CBJlToA AYx» He tny'4aMHa, MHa'4e OHa He 6b1J1a 6111 YaK MaTeMaTM'feCKM TO'tHO caM006pa30BaHa, KaK 8ecb ancJ>aBMT, MaTeMaTM'leCKMM «KnIO'40M» K KOTOpoMY aHa JlBnJleTOl. TaK C'4MTa- eT A. KMCeJlIt (1994). MO)Ktf() cornacMTbC?I C TeM, "ITO TaKoM PJlA '4MC- nOBbIX notITopo& )t '4MCI10BOM cMMMeTpMM AOCTaTO'4HO 3aKOHOMe- peH, T06w 6b1Tt. B 06pa30BaHHoM cl>pa3e M3 '4eTbipeX enDS CJ1Y'4aMHOCT1tIO. nlt'lH8R KOI1AOBCKaR CMMBOnMK8 AnJi B nUIlHOZO Bonwe6Horo CMMBona M MMeHM JitO)KH() Bocnon cneLtManltHo 06Y'falOtijMM :noM npoeAYpe pyKD- BOACTBOM no MarMM, HanpMMep KHM aHrnMMcKoro cneqManMCTa no MarMM M Bonwe6crBY nOAa XeM30Ha «OCHOB KonAoB- CTBa» (1991). 13ero peKOMeH- AaqMM Hac MHTepecyeT J1lfWb ttyMeponorM'IecKMIi aCneKT Ma- rM'feCKoro AeMcrBa, M TO 8 06- UlttX '4eprax, TO.nbKO AM 03Ha- KOMJ1eHMJI C HMM '4MTaTenJi {3Ha'4eHMe OCTaJ1bHblX conyr- CTBYIOU4MX «C8RU4eHHOAeM- ConuaIo ... 11".1 tlfJoMy J'MIHIUO "fenoBeK. 3atU1 6eJ1cM4. cepoA MI1 'lepH0i4 M8fM8It ,APmKeH MMaTh C8OIO  KOMOSC«YJO CMM8OIIMKy. B TOM '61CJ1e Hyueponont'feCKy. 156 
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rnasa 4 ECJ1H C'4HTaTb OT COnHLta, TO OCHOBHble nnaHeTbi COnHe'4HOM CHCTeMbl pacnonaralOTCJI B CJ1e- AYlOiqeM nOpJlAKe: MepKypHM, BeHepa, 3eMnJl, Mapc, IOnHTep, CatypH, YpaH, HentyH, nnyTOH (nnHeTbI, HMelOU4He 3Ha'4H- TenbHO MeHbWYIO, '4eM nepe'4HCJ1eHHble, BenH'4HHY, Y'4MTblBaTb He 6YAeM). BnHweM B MtQ:\ 6YKBbf Ha3BaHMM nnaHeT, CTOJlI1\HX OT Con.:'" HLta B '4HCJ10BOM nOpJlAKe 1,4, 7, - :no 6yA'fT COOTBeTCTBeHHO nna- HeTbi MepKYPHM, Mapc H YpaH (pHC. 15, a). Cpa3Y 06paU4aeT Ha ce6J1 BHHMaHHe TO, '4TO, HeCMOTpJl Ha, Ka3a- nOCb 6b1, CJ1Y'4aMHblM Ha60p 6YKB Tpex Ha3BaHH nnaHeT, OHM non- HOCTblO C<BnMCaJ1MCb» B MK. CTpaHHOCTH Ha'4aJ1HCb! 3aMeHMM Ka>KAY1O 6YKBY nOpJlAKOBbiM '4HCJ10M, KOTopoe OHa HMe- eT B aJ14>aBH (pHC. 15,6). nOnY\4eHHble B KOHe'4HOM pe3ynbTaTe OCHOBWHYMepOnOrMM B pacnOlJO)l(8HHH nl1aHeT BOlCpyr Col1Hua MeeTCSI 3aKOHOMepHoe HYMepono- r\IIecKoe COOTHoweHe. a 6 M e p K Y p H M M a p C Y P a H 14 6 18 12 21 18 10 11 14 1 18 19 21 18 1 15 } - 110 - 2 } - 107 - 8 PUC. 15. MarH'4eCKHM KBa,qpaT C BnHcaHHblM B Hero Ha3BaHHeM nnaHer (a) .. HYMep0I10rM'4eCKHM KOAOM nnaHeT (6) 174 
'4HCJ1a 4>opMynbl 3aKOHa EAHHCTBa BCeJ1eHHOM n03BOnJllOT npeAno- nO>KHTb CYlqeCTBOBaHHe 3HepreTH'4eCKoro 4('4HCJ10BOro pe30HaHca» Me>KAY nnaHeTaMH COnHe'4HOM CHCTeMbi. 4TO YAHBHTenbHO B npOBeAeHMM paC'4eTOB, KOTopble npMBenM K noneHHIO 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 (onHa. 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 «CJ1Y4aHOCTb» 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» (TaHaJl AOKTpHHa, T. !, KH. 2, c. 155). MarHl/eCKHU KBa,o.paT B H8CTCHI&q88 Bp8MA MO>KHO C'iIitTaTb. TO TpHa- 1¥1 "IHCeJ7 BbIBl1eHa, - 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 «4C- · nOA HaM eBponeCKOIiI O(COOBO 3pbl» 06b1HO no- · . HMaIOT BpeM BBeAeH COBpeMeHHoro apa6cKoro CC- . · l1eH - 3TOro BpeMeH 6YAeM npep)KIIIBaTbC  Mbl. · . npo30wno 3TO B 1120 r.. KOrAa MaTeMaTK Mel1apA 3 . : DaTa Been COBpeMeHHYIO CCTeMY CCl1eH, Ha3BaB ee : · ..apa6cKO», XOT caM apa6b1 nepeHl1 ee Y ApeBHX H- · . eB. Apa6C1Ca.cCTeMa OKa3a11aCb CTOl1b YAOOHOO, TO . · K 1600 r. B EBpone CTaJla cn0l1b30BaTbC nOBCIOAY. OHa · . COCTOl1a 1113 C1TOBbiX CMB0110B OT 0 AO 9. C nOMO1O . : KOTO MO)I(HO ooo3HaTb 11I000e C110. 3rOT 311eMeH- : · TapHbI PA 6b1n aKTBHO Cn0l1b30BaH eBponecKM HY- · . Mepol1o"aM  <t>l1oco<J>aM. 176 
nOBblMH HanOnHHTenJlMH», paCnOnO>KeHe 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 YAOBTPopeHMIO, OHM HaXOAHnM HeKOTopble 3aKOHOMepHOCTM pa3nM'4HblX npoeCCOB B >KH3HH, KOTopble TyT >Ke CBJl3b1BanHCb C «3HepreTH'4eCKHM C03BY- HeM» MarH4eCKX 4>ryp H HX nOCTpOeHH&M. . . npee '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 cblcne nOHJlTHe «'4HCJ10BaJl 3pa» cpaBHHMO C Bpe- MeHeM ynOTpe6neHJI 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 AeCJlTHHblMH (c OCHOBaHHeM 10) H weCTHAeCJI- TH'4HbIMH (c OCHOBaHHeM 60) C'4HCJ1eHHJlMM. npHHMnbl 060HX C4C- neHHM Hcnonb3YIOTCJI AO CHX nop, a nOCJ1eAHee - 60-TH4Hoe- C4HCJ1eHHe npHMeHJlIOT B acrpOHOMHH H acrponorHM npH paceTe 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 0603HaeH&.1 &.1M CBOII1X y6b1TKOB. 177 
rnasa 4 - CTBOBanH y HHAH1cKHX 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 HeMeKHM MaTeMaTHK r. KaHTop B 1550 r. AelO wYMepcKHx ",yAJ)eOB 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. MarHecKHM 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. npHHHn 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'1Ia, KOTopble He Hapywar B HeM '4HCJ10BOM pe30HaHC. (aM MK.Q AaHHaeTCjI 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 «MarMeCKMe" 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 16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1 34 34 34 34 34 34 Man1'1ecKHH KBap,par 6 -34 -34 -34 -34 PUC. 16. 4MCJIOBOM (a) M rpacl>M'4eCKMM (6) KBaApar';tlOpepa 16 3 5 10 9 6 4 15 a 2 13 :>- 11 8 3 7 12 >- 14 1 6 -34 34 16 3 2 13 5 U 8  >: 9 6 7 12 4 15 14 1 .. 34 4- 34 -34 Puc. 17. ,qHcI>cpepeHManbHble '4HCJIOBble pe30HaHcbI KBaApaTa ,qlOpepa 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 KIIerKH 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>$epeHMaJ1"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» CB3b 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), COCTaBnIOT 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'4eCKaJlHYMepOnorHMcaonb3yeT'4HcnOBpe3OHaHC 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. KOHHO, 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, oOeM, 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 ToeK 3peHMJI, B pa3HblX . npoeKqMJI npMAaBaJl 06eM- HOCTb BocnpHRTHIO «86nM3M» (co- BpeMeHHMKaMH) H «Ha paCCTOJl- HMH» BpeMeHM (nOTOMKaMH). HeAapoM 3HaMeHHTblM CBOM- MM npeAcKa3aHHJlMM MMwenb HOCTpaAaM1503-1566) 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 erTa 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 npe Ha'4MH8M 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 3neKTpHeCTBO; 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. AeCTBHTenbHo cOBepweH nepeneT Ha caMoneTe '4epe3 ATnaHTMec- 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 nHe. 31"0 Te MarltfecKItff1 KBa,o.par OCo6eHHOCTM HYMeponorMecKMx nporH03OB Bwt<Ho He TOl1bKO  H3.npaaM11bHYK> IItH- <t>oPMa1O no MeTOAMKaM HyMepoJiorw.ecKoro ra,Aa- HR, HO  B o6ltHx epTax npeACK8aaTb B03MO>tCHYK> seposmtOCTb cOObffi1SI, C HM CSR3aHHOrD. O606U4eH- HOCTb-KorO npeJ.\CKa38Ha.tR  CpaB- HKTb C r1peAC1<838HMS\M aCTpoJ1On.1ecKoro ropocKO- na: «He nplllH)')tCABlOlltHe, HO npe.o.ynpe)l(,D,a 0 - A}'U4eM co6b1rn», - roso- pwI ,QpeBHio1e. 183 
Tnasa 4 npeACKa3aHHJI HocrpaAaMyca, KOTopble nOATBepAHnHCb BpeMeHeM. OCTanbHble npeAcKa3aHM1I BenMKoro acrponora H Bpa'4a eU4e npeA- CTOHT npOBepHTb HaM H HaWMM nOTOMKaM, TaK KaK OHM OXBaTblBalOT CJ1eAYIOU4ee CToneTHe. iiMcnOBble M rpa<l>M"IeCKMe pe30HaHCbl MarM"IeCKOrO KB8ApaTa PaCCMOTpHM oc06eHHOCTH MKJ\ nOAP06Hee. MeIOTCft eTblpe BapHaHTa '4HCJ10BOrO COCTaBneHMJI MKA Y KO- TOpblX cyMMa Mcen no ropH30HTa.nJlM, BepTHKaJ1J1M H AHarOHanJlM COCTaBnJleT OAHY H Ty >Ke BenH'4HHY - 34 (pHC. 18). npHBeAeHHble MKJ\ HMelOT oAHHaKoBbiM pa3Mep KBaApara (4 x x 4 - 16) M APyrHe 06U4He '4HCJ10Bble KaeCTBa, nepeHC/leHHble HaMM paHee.: B MKA Bonnow.eHa neBaJl 4aCTb 4>opMynbl 3aKoHa EAHHCTBa (2'8' - 4 x 7):.2 + 8 - 10... 1 (Hynb B oKKynbTM3Me He Y'4H- TbiBaeTCJI) - 3TO CHMBon enoro, HeAenHMoro KBaApaTa; 2 x 8- - 16 - 3TO '4HC/lO K/leTOK B MKA. 'IMcn8 M8rMecKoro KBSAP8Ta AtopeR8 ,,",MeIOT cBoeo6paaHbt t.t,,",CJ10BOH peaOHaHC C TeM,,", C06blT,,",RM,,", ""' OObeKraM,,",. Ha KOTOpbte ocyw,eCTBJ1RIOT ra,aaH,,",e C ero ,,",cn0J1b30BaH,,",eM. KaK BHAHO M3 pMC. 18, rpact>M- '4eCKOe M306pa>KeHHe '4HCen MarH- '4ecKHX KBaAparOB (MK) YKa3b1Baer Ha reoMeTpH'4ecKYIO 3aKoHoMep- HOCTb, YaK KaK rpa4>HK HMeeT JlB- HYIO CHMMeTpHIO nMHM. npH'4eM «rpa4>H'4eCKaft 3epKanbHOCTb» HanpaBJ1eHMft OCHOBHblX /lMHHM KaK 6b1 nepeBepHyTa: He TonbKO cneBa HanpaBo, HO H ceepxy 184 
a 16 3 2 13 5 10 11 8 9 6 7 12 4 15 14 1 34 34 34 -34 34 34 34 6 1 14 4 15 8 11 5 10 13 2 16 3 12 9 7 6 MarW.lecKMii1 KBaApaT 34 -34 -34 =34 PUC. 18, a, 6. ltMC110BaJi (CJ1eBa) H rpa4>M'IeCKaJl (cnpaBa) 3aKOHOMepHOCTb MKA 185 
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MarHl/eCKuif KBap,paT BHH3. fpa4>H'4eCKaJl 3epKanbHOCTb paCnOnO>KeHMJI '4MCeJ1 B Mt{.q ycrOM'4MBa H npOJlBnJleTCJI npH, Ka3anOCb 6b1, COBepWeHHO HeMblC- nMMblX KOM6HHaltMJlX '4MCen. npMBeAeM npHMep. npOH3BeAeM npOM380nbHoe, Ka3aJ10Cb 6b1, HenOrH'4JU>.el1pe06- pa30BaHHe '4MCen, nepeMewaB MX B KBaApaTax (KaK nyriuoT H ne- peMeWHBalOT KapTbi MnH KOCTM AOMMHO, '4To6b1 MCKnHTb noene- AOBaTenbHblM MX Ha60p). AnJl 3Toro B ...,..et.KM «06b1'4HOro» '4eTblpeXKneTO'4HOrO KBaApaTa C nOCJ1eAOBaTenbHOMJiYMepaLtMeM ro- pM30HTaJ1bHblX pJlAOB (pMC. 19) BHeceM '4MCJ1a MKA, npeABapHTenb- HO «CnyTaB» MX nOCJ1eAOBaTenbHOCTb. nOCMOTpMM, KaK 3TO oTpa- 3HT Ha '4HCJ10BOM rapMoHHH KBaApaTa. npH'4eM npM 3anonHeHMM KBaApaTa (pHC. 20, a) Mcnonb3yeM TonbKO nOCJ1eAOBaTenbHoCTb 3anOnHeHMJI itneToK no Q>pH30HTaJ1H o 1 2 3 4. 5 6 7 8 9 10 11 12 13 14 15 16 6 ., PUC. 19. «06b1"HblM» "McnOBOM KBaApaT c nocneAoBaTenbHblM "McnOBbiM 3anOJlHeHMeM (0). E.ro rpacpM'4ecKoe M306paJKeHMe (6) no JlMHMJlM «"MTKM» nocneAOBaTeJlbHOro pacnOJlO>KeHMJI l4Mcpp KBaApaTa 187 
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Marn&leCKHH KB8JWBT no npMH"'Hny «06b1'4HOro» KBaApaTa, npHBeAeHHoro Ha pMC. 19, a. (aMY>Ke nOClleAOBaTenbHOCTb '4HCeJ1 (1,2,3,4 H T. A.) 6YAeM BbI- 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"'eTpMHoi4 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- HeHMA (pHC. 20,6). 3anonHeHHe KBaApara '4epe3 '4Mcna Ha pMC. 18. 8 - CM. Ha pMC. 21. KaK BHAHM H3 pHC. 20,6 H 21, O. noneHHblM MenoBoM KBaApar (MenOBaJl MaHAaJ1a - '-1M) MMeeT '4HCJ10&y1O M rpKYIO CMM- o 4 6 12 14 8 2 16 10 11 13 3 5 15 9 7 1 6 -9 -9 -5 -5 Puc. 21. nOCJleAOSaTenbHoe 3anonHeHMe C06W'fHOfO» KBaApaTa "MenaM" 143 pMC. 18, B 'fepe3 'tMena cMMMeTpM'fHWX lUIeTOK HI pHC. 18.0: 'fMenOBOe (0) .. rpaM'feCKoe (6) M306pa*eHMe 'fMcnOBOM MaHAaJlW 189 
rnBBB 4 MeTpHIO, npH'4eM OHa cBoe06pa3Ha. CYMMbI '4MCen '4eTHbiX H He'4eTHbiX 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. HYMeponorH nonaralOT, '4TO rpa4>M'4eCKaJ! cMMMeTpHJI «HaCToJ!- tqMX» M «npoH3BoAHblX» '4HCJ10BblX MarH'4eCKHX KBaApaTOB cOAep- >KHT CHMBOJ1eCKMe 3aKoHoMepHoCTH CyTH BetqeM H 6blTHJI M MO- >KeT 6b1Tb Mcnbnb30BaHa aK KapMHecKMe nOACKa3KM AJ1J1 npHHJlTHJI 3HepreTHecKH cornacoBaHHoro C 3aKoHoM EAHHcTBa peWeHHJI. 6YKBbI CJ108 (JlBneHHM, Bblpa>KeHMH, npeAMeToB, HMeH H T. A.) AJ1J1 nOneHHJI 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. OAHaKO Hcnonb30BaHMe 16-KBaApaTHoro MK AnJl npOC'4eTOB MO>KeT OKa3aTbCJI CJ10>KHblM AnJl MHorHX '4HTaTeneM. n03TOMY Mbi 0cH0ew HyMeponOrMM Lo1CCneAosaHR nOKa3b1- 8a1OT, TO CMeWeH&r1e ""cen 8 Man1ecKIItX KBa.QpaTax coxpaHReT onpeAeJ1eHHyK> C""M- MeTp""lO np"" ""X rpa<l>""- ecKOM ""306pIDKeH"""". 190 
MarHl/eCKHU KB8,lJ.paT .................................... .. · nplo1 npoaeAeHlo1101 HYMepol1Ofli1ecKoro ra.AaHlo1S1 no MarMe- · . CKOMY KBB,Apal)' MO>KHO BblAel1101Tb eTbipe OCHOBHblX 3Ta- . : na. BHaane CI10BO (TepMIo1H 10111101 Bblp8)l(eHe). Ha KOTopoe : · ra.AaeTCSI, KoPyeTcSI C\ltMBOl1aMIo1Io1 nOcneAHlo1e BtJQCSlT- · . CSI B KBB,ApaT. 3aTeM "HaIo1HKalO KBB,Apa-ra HYMepoI10rMec- . · 1iI oOpa6aTbiBaeTCSI: np<WI3BOAIo1TCSI cnoeHlo1e iii OMOHIiIM- · . Hoe ynpoeHlo1e lo1.Cel1 no BceM HanpSBl1eHIo1S1M nye£t . · CTpOIo1TCSI rpa4>lo1ecKIo1 06pa3 MaHAal1b1. HaXoHe. npo- · · BO,Q\'1TCSI 3KcnepTHaSi oeHKa Ha CTeneHb TO>K,D,eCTBeH- · . HOCTIo1 np0lo13BeAeHHblX npe06pa30BaHIo1 Io1CI10BO 101 . · rpa4>lo1ecKo CIo1MMeTplo1io1. Pe3YJ1bTaTbi Io1CTonKOBaHIo1S1 · · BepOSITHOCTIo1 npeACKa3b1BaeMbiX C06TIo1L:1 '80 MHOroM 38- · . BIo1CSlT OT CTeneHIo1 TaKO CIo1MMeTplo1lo1. npeAnaraeM BHHMaHHIO 60nee npOCTOM '4MCJ10BOM KBaApaT, H3ApeB- ne npHMeHSlBWHCJI 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 nwe 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: noeMY 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). MHTepecHwi 4»aKT BblCHTaH 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 30AHX. B03BOAHBWHX nH- . · paMHAY Xeonca, B L4HcnOBO MarHH, L4aCTb $OpMyn KOTO- · . po OHH HCnOnb30BanH B paCeTe 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 OCHOBaHH: CHPHYC - 3Be3Aa l,5-3Be3AHOM BenH'4HHbI 60nbworo nca, n03TO- MY TaK HpKO C"'JleT no cpaBHeHMIO C APyrHM.M 3Be3AaMM. CHpHyc - ABOHaJl 3Be3Aa. Pa3nH'4a1OT 3Be3AY CHpHyc  KOTOPABoe 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 TOKy 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 '4MTaeTCJI no-pyccKM KaK <<X». OH C'4HTaeT, \4TO HH4>OPMaUHJI KOAa 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 yeHHe 0 pHTMax 3Hep- reTM'4eCKHX B03AeMCTBHM Ha 3eMnIO H Ha '4eJ10BeKa no nepHoAaM 193 
rn8B8 4 06pal1teHMJllOmrrepa M CatypHa (<<nna- HeTbi CYAb6b1») BOKpyr ConHa. 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 ConHa 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 nOBTOpTCJI. . 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 TpaHcKpMnHH, T. e. no Ha3BaHMJlM 3HaKOB. nonYHM CJ1eAYIOU4ee: 1) ConHe,.nYHa.I041MTep, MepKypMH, BeHepa, CarypH, Mapc "" 2; 2) K03epor, BOAonM, Pbl6b1, OseH, Tene 6nH3HebI, PaK. neB, AeBa, BecbI, CKopnMoH, (TpeJ1e14 - 8. Pe3Yl!braTbi aCTponOrH'4eCKHX Bbl'4HcneHHM TOHO COOTBeTCTBY- lOT 4>opMyne: 28 (4 x 7); 3) B '4HCJ10BOM aCTponorHH Ka>KAoe '4HCJ10 HatypaJ1bHOrO pJlAa OT 1 AO 9 cHMBonM3HpyeT He6ecHoe Teno: *"3HIt 3eMJIM npeAonpeAeneH8 Cne.c.yeT no118r8Tb. o PKTMHbIe BMe- W8TenbCTBa IOnKTe- p8  CaTYPH8 B >lGt3Hb 3eMn  ee 06TaTe- neill KapMecK npe- .o.onpe.o.eneHbI. 194 
Manf&leCKJlfH KBB,DJJaT 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 nepHe HeT H nnaHeTbl3eMnJl, KOTOpaJl, KaK H nnaHeTa BeHepa, MMeeT KOA 6 (noA- p06Hee 06 3TOM l4H4>pe CM. pa3Aen «YHCJ1 3BepJl»). cnonb3YJI OKKynbTHble BbI'4HCJ1eHHJI no HaweM nnaHeTe, MO>KHO nonY'4MTb Heo- >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 MarHecKoe 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..TMMMpOB) 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 KOI1Me- CTBO OyKs, COCTaBJ1IOl1tHX 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, OMMBbiM 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>OPMHH 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 OKTM3Me ""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 KonHeCTBeHHaJl BenMHHa 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" BCTpeaeTcR B )K3H ropa3,IJ.o ae. eM Ka- )KeTCR nOHaany.--J1anp- Mep. HO aaKOAHpoBaHO B npBbI"IHble AJ1R Hac CMat1I1b1.III.C"IClleHR. «cnOM 3depR" ero H- KaK He HaaoBewb, TaK KaK BbIClleHRM 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) npoceT '4aCTeM enoro H n03HaHHe 4enoro no ero '4aCTJlM, Ba>KHOe AJ1J1 cyecTBo- 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, cneT 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 - >KpeaMH o.H.pHca, B fpeHH - 0P4>eeM H nH4>aropoM... 6bln0 HBeCTHO cpeAH npopo- KOB nOA HMeHeM MHCTepHM (blHa 4enoBe4ecKoro H (blHa 60>Kbero. 60r KaK 6bl paCCeJlH H pa3Ap06neH BO MHO>KBe '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 KaecTBa nOA- Aep>KaHbl AoneM CBJlTOCTH, 3anO>KeHHOM B 4enOBeKe,- '4aCTHbl 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- J1MM 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). KapMHeCKoe 'fMCJ1Q. YKa3b1BaeT Ha TO, '4TO BpeMJI pO>K,O,eHMJt OC: HOBaTeneM nepe'4MCJ1HHblX 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 CB3aHa xopowa nepcneKTHBa B )KH3HH '4eno- BeKa. "4Y1CJ10 He yrpo)K8eT H He nepeHOCHT Ha eI10BeK8 OTpHl¥i T e11bH'f1O KaPMeC- K}'IO 3Hepn..tlO. a HanpoTHB. CTpeMHTCR nO.DJJ,ep)l(aTb ero )l(H3HeHHbI nOTeHlUiI811 H BOCCTaHOBHTb (epe3 O)l(H- ABeMbie COObln1R) yrpaeH- 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 npe06p30BaHMRM, 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 nOMOblO 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 nPMcye 3tjepreTMecKoe BMew8TenbCTBo c ryM8HHOM 14enblO. «M60 3TO Mcno e- 110Be'4ecKoe- . 
rnasa 4 A eCTb nM nIOAH, AnJl KOTOpblX He 38M8TXY B «KOCMMeCKOM» 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- TJX)eICJJ8'TMOr noBTopeHHR U4eM, nocKonbKY :310T '4enOBeK 'fToc6lH1CaeTee c C\{- eU4e oeHb Man. TaK, ra3eTa 110M 38epH-. HanPMMeP. B «TPYA" (21.09.1999) co06U4Mna, ,AaTeJ>O*,t\BHMH wtM B yKa- 4TO B ropoAe 6enoMT (wTaTBHc- 3aHMM epeMetM BC'T'P&IM. KOHCMH) Y HMKonaca CTHBeHa Y3Ana B 9 '4aCOB 9 MMHyT yrpa 9 ceHTJl6pJl (T. e. B 9-14 Mecln) 1999 r. pOAHncJ1 pe6:HOK. HOBO- po>KAeHHblM BecMn npM pO>KAeHMH 9 4>YHTOB H 9 YHLtHH (npMMepHo 45 Kr). MeA.....HCKMM nepcoHan 6b1n nopa>KeH 3HaMeHHeM «AeBJlT- , KM» B >KM3}iM HOBOPO>K- AeHHoro. BnHJlHMe '4MCJ1a 9 Ha CYAb6y MamOTKM eU4e, BepOJlTHO, TonbKO Ha'4MHaeTC: eAHHCTBeH- Hoe cB060AHoe MeCTO AnA MaTepH H HOBOPO>K- AeHHoro OKa3anOCb Tonb- KO B naJ1aTe tiOMep 2115 CYMMa 3THX '4HCen TO>Ke palHa 9. KaK nMweT ra3e- Ta, «Bce HMelOHe OTHO- weHMe K HOBOpO>KAeHHO- o .........M aaTM8HMA r1eper1aA 3HeprMM llytibl M ConH- ua eo ep8MS1 aaTMetMA AeHcTBY- eT Ha Bee. 'fTQ,ecTb H8 3eMne (K3MettAA TE!'4etiMe p>AbI. npMl1M- BbI M O111MBbI, coeepw8A nOAbeM KopbI, cnoco6cTeysi C5ypS1M, 3eM- neS1M M T. A.), HO 60nee .S1p1CO H8 aaTMeHMe pearMpytOT pacTMTeIlbHblH MMP, JKMBOTHbie M oco6eHHo 'f8J1OBeIC. 204 
MY 3aAalOT ce6e BOnpoc: KeM >Ke CTaHeT AllJI 'IenOBe'leCT8a 310T MaJ1W, poeHMe KOTOporo COnpOBO)t{AaeT KaKO-TO &4M4>poBO WM4>p?» 3HaMeHMe nM 310 MnM TOnbKO YAMBMTenhHoe CQBnaAeHMe, nOKa>KeT 6YAYU4ee. nonaranM, '4TO yrpo3a CBepWeHMJI '4pe3B'4aMHbIX CMTya(4MM B >KM3HM nlOAe.. pa3HX crpaH ytMnMBaJ1aCb TM, 'ITO 1999 r. MMen ABOHoe 3aTMeHMe - COJlHfNHoe M nyHHO€,  RO MHeHMIO acrpo- noroB, npoBO(4HpyeT onaCHe nOBOpOTbi cyAb6b1 M yxyAweHMe ]AD- POBbJl. 3aTMeHMe B03AecrByeT Ha nlOAeM Bcex CTpaH, no TeppMTOpMM KOTOpblX nO>KHTCfl ero TeHb. OAHaKO 60J1ee JlpKO pearMpyIOT Ha 3Hep- rHIO 3aTMeHHM HeKOTOpe nIOAH: y HMX HapaCTaeT AMCKOM4>opr ca- MO'4YBCTBMJI, 06ocTpJlIOTCJI XpOHM'4eCKMe '60ne3HM, .11()BWaeTCJI pa3Apa>KMTenbHOCTb, CKnOHHOCTb K pMcKoBaHHIllM npMtnIO'4eHMJlM. KorAa >Ke 3HeprMJI 3aTMeHMM AOn>KHa «nOMOraTb» npoJlBJ1eHMIO onaCHX npeAcKa3aHMM rOAa «Tpex AeBJlTOK»? nYHHoe 3aTMe- HMe npoM30uDto 28 MlOn" 1999 r. (c MaKcHMYMOM AllJI CpeAHeM no- noc CHf Ha 14 '4aCOB 34 MM- HyT), COJ1He'4Hoe - 11 aBrycra 1999 r. (c nMKOM 3aTMeHMJI B 14 '4aCOB 04 MMHyTbI). CBJl3aH- Hble C 3aTMeHMJlMM MarHHTHbie 6YPM 06b1'4HO Bbl3BaIOT B opra- HM3Me '4enOBeKa (B CepAe'4HO- COCYAMCTOM cMcreMe, HepBHo- nCMxM4ecKoM c4>epe M T. A.) Bblpa>KeHHble M3MeHeHMJI, He- peAKO KPH3b1. MafH'IecKHH KB8,OJJCfT MtfT'8P8CHwA .8ItT Me,D,HKM KOHCTaTMpyK>T, TO caMHX MarHMTHhIX OYPb y*e AOCTaTO'tHO. T06b1 npeAyJ1pe*A8Tb TSt)KenO 60nbHbIX H ncHXH- ecKH HeypaBHOBeW9H- HbIX, arpeccHSHbIX nlO,Q,eM o npo4>H11aJmNeCKOM npHeMe neKapcTB H OCTO- po>ICHOCTH S AeMcTBMS1x. 205 
rn8S8 4 Co CBoeM CTOpOHbI acrpo- norM H HYMeponorM TO>Ke npe- AYnpe>KAalOT 06 onaCHOCTH. 3BecTHO, 'frO KanenbKH AO>K- AJI, Ha KOTopble He 06paU4alO1 BHHMaHHJI. (KaK H Ha 01P.enb- Hble npeA,Ynpe>KAeHHII), MOryr cnHBaTbCJI BMeCTe, 06'heAH- HJlTb CBOIO cHny H npeBpa- U4aTbOt B rpo3HblM nOTOI<, CMe- TalOutHM Bce 'Ha nyTM... TaK M OTAenbHble «KanenbKH»-npe- AYnpe>KAeHHJI MOryr eCJ1M He 6narOnpHJlTCTBOBaTb npOJlB- neHHIO OAHOM KpynHoM 6eAbI, TO no KpaMHeM Mepe AaTb Lte- nO'4I<)' 0utYTHMblX HenpHJlTHO- CTeM B >KH3HH... npaBbi nH npeACKa3aTenH? flBnJlJlCb O'4eBMALteM nepe- XOAHoro BeKa, '4HTaTenb y6e- AHnCJI B 3TOM nH4HO, nOCKonb- KY CMor O[teHMTb He TonbKO BepOJlTHo.<;tb npeAcKa3a.HHOrO 1999 r., HO Hero nOCJ1eACTBHJI AllJI rOCYAapa:8,8.aLtHH, ceMbM, a TaK>Ke CYb60HOCHbie H3MeHeHHJI B nH'4HOM JKH3HH. E MH8HM8 npe,o.OCTepe)l(eHe B OTHO- weH 1999 r. MeeTCst  B npopoecKx KaTpeHax Hoc- rpa.QaMYca. OH C'MTan. TO B 3TOT rOA cne.o.yeT npostBJ1stTb 6AKTenbHOCTb  He Aonyc- KaTb KOHnKTOB KaK Ha ro- cy,AapcTBeHHOM ypoBHe. TaK  Ha nHOM. CeMeMHoM. nOCKOnbK}' 3TOT rOA MO)l(eT OKa3aTbCst B n11aHe Hac- TH£1 Cy.D,b6OHOCHbiM Anst He- KOTOpblX H£1  ceMe£1. HOCyPaAatgc pet<OMeH,Q.OBaJI CKJ1IO11t"CK. B pa3J1IfNHbIX ero npostB11eHstX. 6biTh OCTO- po)I(HbfM ... npe.o.ynpe.D.Vl- TeJ1bHblM.... aute AYMaTb 0 nocne.o.CTBstX COBepwae- MblXAen. 206 
rnABA 5 KA55A11A KBAAPATA M KPECTA KOCMM'feCKMM npoo6pa3 HYMeponorMM CTpYK1YPHO-'4HCJ10BbI napaMerpbl C03Be3AMJI OptiOH n03BOnJl- lOT KBaJ1H4>HLtHpOBaTb era KaK HYMeponOrM'4ecKyIO (MCTeMY, 06na- AalOU4Y1O rpOH'40-nJlTepH4HblMM CBOMmaMM. B C03Be3AMe OpM- OH, comaCHO ApeBHMM  COBpeMeHHblM aCTpOHOMM'4eCKMM HCTOHMKaM, BXOWlT AO 10 OCHOBHblX 3Be3A (BHAMMblX HeBoopy- >KeHHblM rna30M npH pa3HoM OCTpoTe 3peHMJI), 0 '4eM, HanpHMep, cBMAeTenbCTByeT acrpOHOMH'4eCKMM TOM 60nbWOM KHTaMcKOM 3HMKnO- neAHH. B HeM, nOMHMO COBpeMeHHblX cxeM M Ta6nHit BocnpOH3BeAeHbI 4>oTorpacpHH 3Be3AHblX KapT VIII, XI H XIII BB. (60nbwaJl KMTaMCKaJl 3H- LtHKnOneAHJI.AcTpoHOMMJI.neKHH-- WaHxaM, 1960, c. 567,575). CrpyKTYP- Hoe H306pa>KeHHe W3Hb (OpMOHa) npeACTaBneHO Ha pMC. 22, a, rAe apa6cKHMH LtH4>paMH 0603Ha'4eHbI 207 0cHc-.I ttyM8pOI1OntM KOCMII1ecKII1M np006- pa30M HYMeponorll1111 no COCTaBneHHIO «Ma- rll1ecKII1X <S>lI1ryp. CII1- TalOT C03Be3All1e OPIl1- OH. B KII1TaMcKolit TpaHCKpll1nLWIIl1 060- 3HaaeMoe KaK W3Hb. 
rnaBa 5 1 3 A 2 6 4a. >r Y54 a. Y5 4 >( 5 1 3 H 1.2.3 6 1 137 1 - 3 6 7 2 6 137 3 o B PUC. 22. OCHOBHble 3Be3AbI C03Be3AMst OpMOH (0) M OKKYJlbTHOe ynpOLqeHMe HX pacnOJlO>KeHMfl C pa3AeJlbHOH (6) M 06'beAHHeHHOH (s) cepeAMHOH HOMepa 3Be3A B KHTaMCKOM HOMeHKnaTYpe, a rpe'4eCKHMH 6YKBa- MM - HX n03ltHM B KayeCTBe COCTaBnJlIOU4HX OpHoHa (K063eB A.. eHHe 0 cHonax H '4HCJ1ax. C. 237). B 60nbwoM KHTaMcKopycCKOM CJ10Bape (M., 1983-1984) B OT- HoweHHH OpHoHa AonYU4eHa oWH6Ka: C03Be3AHe cJ»a OTHeceHO K '4aCTH c03Be3AHM CKOpmtOH H 3MeeHOCeLt (M., 1983-1984, T. 4, c. 213; T. 2, C. 998). Or OpMOHa 3TH C03Be3AHJI HaXOMTCJI Ha 3Ha- '4HTenbHOM pacqoJlHHH - Ha paCCTOJlHHH nJlTH 3HaKOB 30AHaKa (6nM3Heltbl, Pal<, J\eB, l.1eBa, BecbI). KCTaTH, B OTHoweHHH C03Be3- AMJI 3MeeHOCeLt. B nOCJ1eAHee BpeM' 0 HeM 6b1no co06U4eHH"e B no- nynJlpHblx ra3eTax KaK 0 HOBOM C03Be3AMH, JlK06b1 He H3BeCTHOM paHee. O'UeM, KaR BHAHM, y)f(e nHCaJ1a pTe'4eCTBeHHaJl neaTb no- '4TH AeCftTb neT Ha3aA, a H3 60nee CTapblX acrponorH4eCKMX H3Aa- HHM H3BeCTHO, '4TO 0 3MeeHOClte (HnH, KaK ero HenpaBMnbHO HHor- Aa Ha3b1BaIOT, - 3MeeAep>Klte) 3HaJ1H eU4e ApeBHMe acrponorH. TaK 208 
Ka66ana KB8ApaTa ", KpeCTa '4TO OTKpblTHJI HOBOro C03Be3AMJI», KOTOpOe, KaK 06eU4anH KOp- pecnOHAeHTbI HeKOTopblX ra3eT (HanpHMep, «BeepHero MHHCKa», neTO 1995 r.), «nepeBepHeT» npeACTaBneHHJI aCTpOnorOB, He CO- CTOJlnOCb. HaXOWll14HMCJI IJOA C03Be3AHeM CKopnMOHa 3MeeHOCel4 KaCaeTCJI 30AHaKanbH6ro nOJlca TonbKO OAHOM CBoe-(H>KHeM) 3Be3AOM, n03ToMY OH K 30AHaKanbHOMY C03Be3A1O He npM'IHCJ1eH. Ho BnHJlHHe 3MeeHOCl4a Ha CYAb6y '4enOBeKa acrponorH Y'lHTblBa- lOT B paC'4eTaX KapMHeCKOM acrponorHM. PacnOnO>KeHHe OpHOHa H 3MeeHOCLta Ha 3Be3AHOM He6e OTHO- CHTenbHO 3HaKOB 30AHaKa, KOTopble pa3MeU4eHbI BAonb 3KJ1HnTHKH (OHa 0603HaeHa KpyroM, cMeI14eHHblM OT l4eHTpa), MO>KHO paCCMOT- peTb Ha pHC. 23. PacnOnO>KeHHe 3Be3A OpHoHa JlBHnOCb rpaHl4eM OAHOro H3 28 ceK- TOpOB (<<cTaHl4HM»), Ha KOTopble KHTaMcKHe aCTponorH pa3AenJlnH He60cBoA. CeKTop OpHoHa nOTH KaCanCJI nHHMH 3KnHnTHKH CHH3Y Me)f(J\y 30AHaKallbHblMH C03Be3AHJI- MH TeneLt H 6nH3HeLtbl. OrHocHTenb- HO HeAaBHO C'4HTaJ10Cb, '4TO 0603Ha- eHHe 28 He6ecHbix «cTaHl4MM» KMTaMcKHMH aCTponoraMH Hcno'nb30BaHO C nt-II BB. AO H. 3. Ho B 1978 r. apxeonoraMM B npOBHHl4HH Xy63M 06HapY>KeH napel4 VB. AO H. 3. C H306pa>KeHHeM AaHHOM acrponOrH'4eCKOM CHCTeMbI, '4TO 3Ha'4HTenbHO «YA/1HHHno» npeACTaBneHHe 0 «B03paCTe» acrponorHH KHTaJl. no 60nee paH- HHM apxeonOr'4eCKMM CTOHHKaM, TaKoe >Ke pa3AeneHMe He60c- BOAa Ha 28 CeKTOpOB - (<nyHHblX CTaHLtMM» - npHMeHJlnH ApeB- HHe acrponorH HAMH. KMTai4CKMe aCTpOno- I'M B Te A3BHe BpeMe- Ha nepeHWI Ael1eHe tte6ecHOIit C$epbl Ha 28 "cTaHIIt.. y IIt- CKMX aCTponoroB. 209 
rnBBB 5 PUC. 23. J1en.ee He60. nOcepeAHHe IIHHHH 3KBaTopa BHAHO C03Be3AHe . 3MeeHoce. WTPHXOBO nHHMeM 0603Ha'leHbI 3K.nMnTMKa H paCnOIlO>KeHHble Ha HeM acrpoHOMH'IecKHe C03Be3AHSI, "MeHyeMbie B acrpollor.... 3HaKaM.. 30AMaKa 210 
HanOMHMM, '4TO '4HenO 28 B HYMeponorMM C'4HTaeTCJI «'4Y- AecHblM», a B MaTeMaTMKe- «coBepweHHblM» (0 cOBepUJeH- HbiX 'fHCJ1aX CM. COOTBeTCTBYIO- U4MM pa3Aen). fpaHHbI nM CO- 3Be3AMM l-faTOnKHynH ApeBHMX aCTponorOB HAHH H KHTaJl Ha «COBepweHHoe» '4MCJ10BOe pa3- AeneHHe He6a Ha CeKTOpbl MnH ApeBHHe MYApeLtbi YMblwneHHO npo- H3BenH TaKoe pa3AeJ1eHHe «He6eCHble CTaHLtHM», 3HaJl 06 OC06eH- HOCTJlX 3TOro «MarH'4eCKoro» '4HCJ1a, - BOI1POC ocraeTCJI OTKpblTblM: ApeBHHe PYKonHCH no aCTpOHOMMH He 06'bJlCHJUOT M'4MHbI YKa- 3aHHoro '4HCJ10BOrO AeJleHMJI 3Be3AHoro He6a. . YHCJ10 28 '4aCTO BMeWHBaeTCJI B Hawy >KH3Hb, M60 «'4MCJ1a 310M 4>opMynbl Be3Ae H BO BceM», - rOBopMnH ApeBHHe. YeTHoe C MaTeMaTHeCKHX n03HMM, '4HCJ10 28 C HYMeponorM- '4eCKOM TO'4KH 3peHHJI JlBnJleTCJI 4CHe6ecHbIM», HMelOlqHM He'4eTHYIO cylqHOCTb, TaK KaK npH oKKYnbTHoM ynpOlqeHHH (CJ10>KeHHH) AaeT He'4eTHoe 3neMeHTapHoe '4HCJ10: 2 + 8 - 10 - 1. «He6ecHoe» '4HCJ10 (<<3eMHblMH», KaK ynoMHHaJ10Cb, C'4HTaJ1HCb '4eTHbie 3neMeHTapHble '4MCJ1a) onpAeJ1J1eT KpyTble nOBopoTbi B >KH3HH MHorHX nIOAeM. B HaweM H3nO>KeHHH '4MTaTeJlb MO>KeT y6e- AHTbCJI B 3TOM Ha npHMepe TaKHX BeJlHKHX nlOAeM OTe'4eCTBeHHo HCTOpHM, KaK neTp I M neB TOJ1CTOM (CM. KpaTKHM HCTOpH'4eCKHM 0630p B Ha'4aJ1e KHHnt).  KOHe'4HO, '4HTaTeJ1b MO>KeT «npHMepMTb» 3TO '4HCJ10 K npOJlBneHMIO Ba>KHblX C06b1THM c06CTBeHHoM >KM3HH. CHnY3T pacnOnO>KeHHJI 3Be3A OpHoHa «BnHCblBaeTCJI» B pa3pa- 60TaHHbie oKKYnbTHCTaMH «MarM'4eCKHe» $HryPbl. BapHaHTbI TaKHX Ka66ana KBa,ttpara H Kf)8CTB Com8CHO Y'l8HMIO L.fcno 28 o(Sl1a,o.aeT y- AecHb'M CBOHCT88MH. OHO COCTaSl1S1eT eTb OKKyl1bTHOH <S>OPMYI1b' 3a- KOHa EAHHCTBa nOCTpoe- HS1 Miltpa (2 = 4 x 7). 211 
rnBBa 5 a 6 B:paToB npMBeAeHbI Ha pMC. 24 YnpoU4eHHaJI nJlTM'4neHHaJi MO- . Aenb OpMOHa M3BecTHa M3 acrpo- HOMM'4eCKMX TpaKTaTOB APeBHero KMTaJl, HO M 60nee enO)l(HaJi MO- Puc. 24. PacnpeAeJleHMe 38e3A Aenb 3Toro C03Be3AMJI BBOAMnaCb OpMOHa B 4CKaHOHM'4eC- B «MarM'4eCKHe» 4>Hrypbf AllJI CO- KON» KBaApaTe npM CTaBJJeHMJI npeACKa3aHMM. 06 3TOM C06W'4HOM» (0) >Ke nMweT CblMa UJlHb - rnaB- M cnJlTepM'fHoN» (6) HbiM 3HaTOK M nepeBOA'4MK ApeB- ynpoaqeH.... Hero TpaKTaTa «WM loPM» (K06- 3eB A.H. Y'4eHMe 0 CMM80nax M '4MCJ1CV<, c. 241-242). CblMa L\JtHb YaK onMCblBaeT C03BeJAMe OpM- OH (W3Hb), nonaraJl, '4TO ero 3Be3AbI C,BJl3aHbI C 3eMHOM JKM3HblO: «C03Be3AMeJlbHb (<<3aCJ1yrM») eny>KHT CHMBonOM 6enoro TMrpa. TpM 3se3AbI eto ne>KaT n npJlMOM M npeACTaBnJlIOT KaK 6w 6anaHc o  o 6 B z mill. Puc. 25. BapMaHTw pacnOJlO>KeHMJI 3Be3A OpMoHa B OCH08HtaIX (o M 6) M npoM38QAHblX (B H z) HyMepoJlOrM'feCKMX KBaAparax. Kea.qpaTbi a M 6 cooTBeTCTBYIOT TpOM'4HO-nJiTepMLfHOM cHcreMe 212 
C03Be3AMJI. HH>Ke HAYT TpM 3Be3AbI OCTpHeM (eeepx), Ha3b1BaIOTCJI OHH cJ»a (<<Kapa») H CBJl3aHbI C Ka3HJlMM M 3aBepWeHMeM (CKpblBae- MblX, npeaynHblX) AeJ1. 4eTb1pe 3Be3AbI BHe (6anaHCa) npeACTaBIIJl- lOT neBoe M npasoe nnE!'lH M 60Ka C03Be3AMJI. TpM 3Be¥ItJI hOMeU4a- IOfCJI B ymy C03Be3AMJI M Ha3b1BaIOTCJI 3M (<<,MoPAa»). OHM Q6pa3YK>T ronoBy 6eJ1oro THrpa M BeAalOT AenaMM 06ecriel.feHMJI BOMCK» (BOMH- CTBeHHOCTbIO, HaKonneHHeM CMn arpeccHM.  fJpU/tf. asm.). feOt4eTpM'4ecKMe 4>Hrypbl, nOKa3b1BaIOU4He nMHMJlMH HanpaBlle- HHJI C'4MTh1BaHMR cHnY3Ta OpMOHa no I.fMCJJaM «MarH'4ecKMn KBaApa- TOB, M306pa>KeHbI Ha pHC. 26. npM COBnaAeHHH nMHMM C CMJ1Y3TOM OpHoHa «He60 6naronpMJlTCTBOBaJ10» peweHHIO Bonpoca MnM AE!11a. npM MCKa>KeHMM «HOp- MaJ1bHblX» nMHHM cHnyna C03Be3AMJI MeCTO MCKa>Ke- HMJI nOACKa3b1BanO Ha- H60nee YJt3BMMoe MeCTO CpblBa JKenaeMbiX pe3ynbTa- TOB. Tal(. MCKa>KeHMe «XBo- CTa» C03Be3AHJI OpHoHa. cooTBeTcTBYIOU4ero 3Be3- AaM Ci)a, MO>KeT YKa3b1BaTb PUC. 26. reoMerpM'fecKMe $Mrypbl IIMHMM Ha OnaCHblM crOBOp, CKpbl- C'fMTblBaHMR 311eMeHTOB OpMoHa Tble CMnbl npOTMBOAeMCT- npM pacnollQ)KeHMM  CMJlY3Ta eMJt. B KaHOHMl.fecKOM (0), B A80M'fHO- 06palJ4aeT Ha ce6,. BHM- nflTepM'fHOM (6) M B npoM3BOAHOM MaHMe nocneAoBaTenb- (s) KBaApare. J1MHMM 4>MryptI' a HOCTb HYMepa(4MM 38e3A C()()T&.:I\.11JjI01' 003MqMM pMC. 22,,0; W3Hb - OT cepeAM HbI IIMHMM cl»4ryp 6.. B - COOT8eT- (noJlca OpMoHa) BBepx, CTBeHHO (>Mc. 25.6 M z. Ka66ana KBBAPaTa H KpecTa $ a 6 S 213 
fnaBS 5 nocn8Ao.aTenwt r8A8HMR npH ra,o,aHHH HYMepo- nOrM'48CKMe l4H<t>Pbl HaMMeH088HHM rn8BHblX ,Ae"CTBytOU4Hx I1H1.\ BHO- CHI1H B «MsrH'4ecKHM- KBa,ApaT  CTpOWIH rpa- <l>HK. no KOTOpoMY on- peAel1AI1MHsnpaaneHHe I1HHHM CHTbIBaHH"'. 3aTeM - BH"M3. 3Ta Hy...epaMJI COOTBeTCTByeT C'4HTblBaHMIO KM- TaMCKMX '4MCJ10BblX AMarpaMM H He COOTBeTCTByeT JlpKOCTM acrpOHO- MM'4eCKHX 06'beKTOB. TaK, maBHble no "PKOCTM 3Be3AbI OpMoHa - aJ1b4>a (6eTenbreM3e), 6eTa (PH- rem.) M raMMa (6ennaTpMKc) 060- 3Ha'4eHbI B KMTaMCKOM C03Be3AHM W3Hb nOA BTopOCTeneHHblMM HO- MepaMM 4, 7 H 5. «8 KMTaMC!(OM aCTpOHOMM'4eCKOM TpaAMHM, - 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 HaepTBHHA K"TaAcKoro Heporl1"<I>a «5'-. . : np"MeaTel1bHO H_l1e.o.YJOl!.'ee: B KaecTBe C..MB011OB BO- : · CTOK8 aCTpol1orH npHHHMsl1H n0110>KeHHe C03Be3AHA · . C"Hb, a. aana,o,a -' UJ3Hb. 3TH C03BeaAHA OI:llI1H HMH Ha- . · pe&fet:tbtTBeTCTBeHHO 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 HYMeponorJI» (K06- 3eB A.H. Y'4eHMe 0 CHMBonax M '4HCJ1aX, c. 243). «KorAa 6bI HM HaHHaJ1CJI 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>Mec- Ka66ana KB8Apara ", KpecTa MCTOpM'tecK8R cnpS8K8 .QpeBHe KTaH Ha- HanM OTCyer ttaana ro,Qa.TOf",Q,a. Kor,Q,a co- 3Be3p.Me OPMOH HaxO- .tU111b 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""TaCKO <t>...,110CO$...,H (V-III BB. AO H. 3.) · . pa3BHTHe 06w.en03HaBaTel1bHO MeToAol1orn..., W110 B ABYX . · HanpaBl1eHHSlx. - n...,weT aBTopHTeTHbI oTeecTBeHHbI · · 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- HHOM 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. HYMepaHJI 3Be3A W3Hb B ApeBHeKHTaHCKHX TpaKTa- Tax He CJ1Y'4aHHa (CM. pHC. 22, a). PacnOnO)f{eHHe 3Be3A W3Hb 06pa- 3yeT "ieTKYIO TpOH'IOCTb. 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- ntecKot1 npeAnOCl1- 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 3Be3AOeTaMH CHTaIIOCb 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 craHHM» BKJ1IOaeT maBHoe C03Be3,qMe )TOM '4aCTM He6a. «CTaHHM 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 TpOMHo-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 CTaHMM» - 6b1na Ba>K- HbiM 3neMeHTOM "PH pa3pa60TKe 4>MJ10C04>cKHX cxeM B HYMepono- rH'4eCKOM MeTOAonorMM, Mcnonb3yeMoM AnJl WHpOKOM npaKTHKH. eHMe 0 4<He6ecHbix CTaHHJlX» Hcnonb30BanOCb He TonbKO B aCT- pOHOMHM M acrponorHH, HO M B APyrMx 06J1aCTJlX 3HaHMM, B '4aCTHO- CTH B anXMMMM " ee nCHxo4>M3HonorMeCKoM nOApa3AeJle - MaK- P06MoTMKe (MaKpo  OT rpe'4eCKOrO «60nbwoM», a 6HoTMKa- 4<BonnOU4eHHe >KH3HM»; MaKp06MoTHa - «WHpOKMM B3rmtA Ha >KH3Hb»). MaKp06MoTM1<a KaK yeHHe 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 «MeAHMHcKaJl 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., cyeCTBOBaJ1a npocrpaH- CTBeHHO-'4MCJ10BaJl4>MnOco$CKaJl cxeMa «aJVIJa3WblM nJ1aH», Ha3BaH- HaJl TaK H3-3a ee poM60BHAHOCTM (pHC. 27j. ca»Hnoco4>bI ApeBHero BOCTO- Ka C03AaJ1H MHOro cxeM nocrpo- eHI>1H Ml>1pa, HO MO>KHO BblAeJ1'1TIt HeCKonbKO HaM60nee npM3HaH- HblX, BblAep>KaBWHX npOBepKY BpeMeHeM M HaH60nee WMpOKO ynOTpe6nJleMbiX B MarHH, B TOM '4MCJ1e cxeMbi X3 ry H no wy. X3 ry MMeeT «MarH'4ecKoe» KpecToo6- pa3Hoe pacnOnO>KeHHe CMMBO- nOB, aU4e :no '4MCJ10Bble 3neMeH- Tbi HnH CHMBonbi nJlTM CTHXHM (pMC. 28). KpeCTo06pa3Hoe pac- nOnO>KeHMe 3neMeHTOB TO>Ke CMMBOnM'4HO. nepeBoA KHTaMcKMx MepornM4>oB «X3 ry» 0603HaaeT He KpeCT, a e.qHHeHMe ABYX OC- HOBHblX «3neMeHTOB» >KM3HH: He6a H 3eMnM, TaK KaK HepornM4> «ry» B AaHHOM KOCMOnOrM'4eCKOM nnaHe 0603Ha'4aeT nnaHery CarypH (nnaHery CYAb6b1), a 4<X3» - 3eMnlO, nO'4BY. C'4MTaIOT, '4TO cxeMa X3 ry BnepBble ynoMMHaeTCJI B ApeBHeKMTaM- CK 4>MnOC*KHX TpaKTaTax VIII-IV BB. AO H. 3. (npoM3BeAeHHe «XYHb 4>aHb»), a 60nee COBpeMeHHYIO pa3pa60TKy KpeCTo06pa3Horo ECTb MH8HM8 KaMM8H CHT8J1 (1985), TO «aJ1M83HbI nl1aH- no CTpoeHHtO, OTqt'K8tOH 3H8HHR 8CipOI1orHH, Mor HCn0I1b30B8TbCR I(HT8- I.t8MH A11R K8J1eHJ18pHbO< paC'4eTOB, 8 T810Ke 6b1Tb npoo6paaoM paapa60ToK exeM X3 ry. 219 
rnasa 5 pacnOnO>KeHMJI nJlTM 3neMeHTOB cxe- Ma non}"4Hna B IV-III eB. AO H. 3. (npoM3BeAeHMe «fyaHb-tpM»). X3 Ty- 3TO nCTaBneHMe nocr- poeHHJI MMpa B eOOTBeTCTBHM C ABO- H'4H<rTpOM'4HOM H TpOM\fHG-nJn'epHt4ttOM CHCTeMimM. npe>KAe '*!M aHa11H3HpoeaTh cetlfYxaTy, Ba>KHO Yj1CHMTb ee B03HMK- HOBeHMe H 3Ha'4eHMe BXOAJIU4MX B Hee 3neMeHTOB. PaCCMOTpHM CBJl3bee '4MC- Puc.27. Cxe...a 4CaJlMa3HblM nOBbIX M 6yKBeHHblX (B KHTaMCKOM Hy- nJ1aH» MeponorMM - MepornH$M'4eCKMx) CMMBonOB. MCJ1a npeHMYU4eCTeeHHo HcnOnb30BaJ1HCb B KaeCTBe 4>Hnoco4r CKOM CMMBOJ1HKM, a He AJ1J1 apH4>MeTH'4ecKMX npe06pa30eaHMM KaK MHcrpYMeHT *bI'4HeneHHM. CTaJ1a pa3BMBaTbC.JI M reoMeTpH'4ecKaJI CMMBonMKa. "B COBpeMeHOM nOHMMaHMM - 3apOAMnaCb HYMepo- nOrMJI. C'4MTaIOT 1 '4TO HapAY 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,Y1OHM 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 KOHenHH 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>HKaMJI Haooonee Bblpa3HTenbHa, TaK KaK nOA- epKMBaeT oc06eHHoCTb tiYMeponorM'4eCKHX npe06pa30BaHMM. OHa COpMeHTMpoBaHa Ha LteHTpaJ1bHbIe '4HCJ1a :.:.- 3 (He'4Vloe, HJ1M «He- 6ecHoe») H 2 ('4eTHoe, HnM «3eMHoe») H nOKa3b1Baef Bce Ba>KHeM- WMe BMAbi tf}'MeponorH'4eCKOM cHMBon...K.... K nOCJIeAHMM OTHOCJIT: 1) reoMeTPMecKMe 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 3HepreTMt<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 6ecnbfe eH HaBBaeT .QPyrHM  Kpa&1He nP"lMoH. 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 HHCJ1eHHJI '4eT- HbiX H HE!YeTHbIX '4MCeJ1. B OKKynbT- HOM nOHHMaHHH eAHHH4i) 06.na.qaer YHHBepcanbHOM nOpO>KAalOU4eM 4>YHKHeM 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 HCHCJ1eHWI, eOOTHOCMMblX e 3HepreTHecKHM pa3AeneHHeM MMpa Ha ABe KJ1aCeM4>HKaHoHHble 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 (ConHa M nYHbI). HanpaBneHHe ABH>KeHHJI ConHa 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. 36ePPA (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- MMecKH nyTb ABH)I(e- HH ConH H l1YHbI, oTP8*8 COnHbIe 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 ConHa 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 HYMeponorweCKoro 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 nMHMMM «3HaHMblX» (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 TOKH «3Ha'4HMblX» neT no 12-neTHeMY LtMK- ny >KM3HH. 12-neTHHM LtHKn - 3TO 6HOnOrM'4eCKMM LiMKn npMpo- AbI, 3aBHCJIMM 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 o6opopyr 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 12ne'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 peanM38M M8HOB, f103TOMy CBS13aHO C OYM '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 raTenbHOM 4>Mry- pe, KpaTKO npOaHaJ1H3MpyeM no- JIeHHYIO 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» 3Bea) YKa3b1- BaeT Ha TO, '4T0 AaHHoro '4eJ10BeKa B AaHHoM MHKapHaM 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"MHbeT60nee«MJI KHM», HO HanonHeHHblM 3MO- LtHJlMM (<<>KHBOTHOM CMJ10M,») nyTb >KH3HM. 4enOBeK pe>Ke BCTpean 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, opyrnHM AO eJ10M BenHH- 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 KOHa >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 '4enoBi<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 3bI. 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 HeycrOMH- 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 IlHOCTM 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 3BebI npMXOAJITCJI Ha nHHMM, CDeAMH.RIOMe '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 BOnbI C&OeM )KM3HM npMAeT- C.R peWaTb B Ha'4ane V nMHMH (45-46neT). B.qanbweM V nMHMJI BbiBOAMT tyAb6y '4eJ10BeKa Ha 6narOnpMJfTHYIO n03Ml4MIO >KM3HM, Kor- 10 UMKTI 9 8 7 6 5 4 3 I 2 " , 1 I I o 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 KaeCTBa. 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 paccMTaHHoMY 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 HHHHaTHBHOCTb, 3HeprHHoCTb 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- nyalOT 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 «3HaHMblX», '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 a6cMtc) H '4MCJ1a cyMM 12-nemHuxquB (OT- MaeMbie no ropM30HTaJlM - oeM 0PAMHaT rpa4>MKa). nePeceHMe 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 HyeponOrH'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 noneHHoro 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 HYMeponorMecKoM 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 KapMMecKMe 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 6HoepreTMKa - H riOBYOPHoe peMHKapHltpoB8HMe Ha 60nee HH3KOM 3HreTM'4eCKOM YPOBHe. YMblwneHHoe nMweHMe >KH3HM HapywaeT nnlkbl MHKapHa- 14MM (BonnoU4eHHe 3HepreTHeeKOro 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 ManOAYHOMY '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 "3MM, 9TO B119'teT CTporOl! HSK838HH8 era J1yuJH: MHT8pecHW" ca._1CT B TPYAHble MMHyTbI )KM3HM, B nOJ1oce HeYA8 MblCJ1M o caMoy6MMcTBe npHXQAAT B r0J10BY nT14 OMY }(OTS1 (5b1 OAMH pa3 B )KM3HiII. 235 
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'4eM npOAOn>KMTeJ'IbHOCTb >KM3HM 4>opMynMpyeTCJI no-pa3HOMY: MeAHLtHHa ee onpAeJ1J'eT KaK «cpeAHeCTaTMCTM'4ecKMM BopaCT >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 nOCJ1aBWero. 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 COIq)8U4.8HM8 )l(M3HM 'I8U4.8 BC8ro ....3....8. T: npeHe6pe*eHe MepaM np<><t>K 3a60neBaH. 3naynoT- pe6netMe KYpeHeM. anKorQI!Je BpeAHbte npBbI"IK nepeeAaTb. HeAOCblnaTb, 3ac*- BaTbCR 3a nonHb  T. A: 237 
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eHHOHY AMaMeTpY (n03TOMY «He6ec- Hble»''4MCJ1a He'4eTHbie - M «rnaBHblM» CM HMX JlBnJleTCJI '4HCJ10 , C KOTO- poro Ha'4MHaeTCJI He'4eTHbiM PJlA. - npUH. osm.), a nepMMeTp KBaApaTa, BnMcaHHoro B Kpyr, paBeH Y'4eTBepeH- HOM CTOpOHe, T. e. KpaTHbiM iJSYH (22). C TO'4KM 3peHMft CnMpHHa, KOTOpy1O OH BblCKa3b1BaeT B CBoeM pa60Te «nocrpo- eHMe ApeBHeKMTaMcKMx TeKCTOB» (1976), paccMoTpeHHaJl cxeMa opMrH- HanbHO CBJl3aHa C nJrTbIO M3BecTHblMH B . 4>MJ10C04>MM 3neMeHTaMM. OAHO M3MepeHHe Ha nnOCKO- CTH 3aAaeTCJI ABYMJI 3neMeH- TaMM, APyroe - TpeMJI. OH nonaraeT, 'lT0 3Ta cxeMa ftB- nJleT C060M YHHBepcanbHYIO «oKKynbTHYIO MeTOAonore- M'j'Ii, COOTHOCHMYIO co BceMH B03MO>KHblMH c4>epaMH 6b1- THJI M MblwneHHJI. «3ra 06'beKTMBHaJl MaTe- MaT M4 ecKaJl3aKOHOMepHoCTb }/Aa'4HO BnHCblBaeTCJI B CHCTe- MY OCHOBHblX CHMBOnOB KH- TaMCKOM HYMeponorHH,- nHweT K063eB. - (HMBon 3eMJIH - KBaApaT - 3HaMe- rnasa 5 OKKJI1TM3M lI'Iepa M cerQAHtl «MantecKtJfl. cl>wypa J<Ba,A- paTa, BnlltCaHHoro B tcpyr, Y HYMeponoros, aCTponOrOB M cl>Wloeo<l>OB npownoro BpeMe- HM RBnR11aCb Ba)l(HbiM CMMBO- 110M eAMHCTBa 3eM11M M He6a WlM npocrpaHeTBa M BpeMe- HM. OHa WMpokO-MCnonb30Ba- nacb AP8BHMMM Ha npe.o,MeTaX KYnbTa  Obrra; Ha MOHeTax, 3e CXeMax reKcar- paMM, Ha pHbIX cocy1JljX M PKT)'a11bHbIX npeJ),MeTax. Kpyr M 08.Ql)aT MbIC11MT811b "b{y Q1 C'MTaTI, '(f() Q1M8O- 110M He6a RB11A8TCR t<pyr, a QNB()!1OM 3eMnM -ICBaJJP8T noTOMy, '(f() Me'1l.JJ.Y HMMM ecTb «MaTeMa- TMKO-HyMepO.I1Or}1- 'teCKaR CBSI3b». 242 
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rnaBa 5 KorAa raJ1MneO raJ1MneM (1564-1642) Ha6J11op,aJl 3a IOnMTepoM '4epe3 co6CTBeH- HOPY'4HO cAenaHHblM TeneCKon, oTKpbln '4e- Tblpe ero nnaHeTbI-cnYTHHKa, TO HeKTO cJ)paH'4eCKO CyJ3H HamtCaJ1 faJ1MnelO nHCb- MO, B KOTOpOM onpOTeCTOBan norMHOCTb ero OTKpblTHJI. CyJ3M 060CHOBn cBOM npo- TeCT TaKHM OpHrHHaJlbHblM 06pa30M: «B ro- nOBe MMeeTCJI ceMb OTBepCTM: ABe H03A- pH, ABa yxa, ABa rna3a M pOT, nOA06Ho TOMY KiK 8 He6ecax (MMeIOTCJI. - npUM. oem.) ABe 6narOnpHJlTHbie 3Be3AbI, ABe He6naro- npHJlTHble, ABa CBeTHna H eAHHCTBeHHblM MepKypHM, HeonpeAeneHHblM H 6e3pa3nM'4HblM (CY33H HMen B BHAY TaK Ha3b1BaeMbie nnaHeTbI-CenTMHepbl, T. e. ceMb «OCHOBHblX» nna- HeT, BHAMMblX Ha He6e HO'4blO HeBoopy>KeHHblM rna30M npH HOp- MaJ1bHOM 3pet.h,. '4enOBeKa. - npUM. oem.). OTCIOAa H H3 MHorHX APyrHx aHanOrH'4HblX JlBJleHHM npMpOAbI, TaKHx. KaK ceMb MeTan- nOB M TOMY nOA06Hoe, KOTopble 6b1no 6b1 yTOMHTenbHO nepe'4HC- nJlTb, Mbl3aK11IO'4aeM, 'fTO 'fHCJ10 (cnyTHHKOB. - npUM. oem.) C He- 06XOAHMOCTblO AOn>KHO paBHJlTbCJI ceMH». CyJ3M C'4MTaJ1 He06xOAHMblM HCKaTb OCTaJ1bHble 3 nnaHeTbI-cnyT- HMKa IOnMTepa, no.oaraJl, '4TO HHa'4e CMCTeMa HX CBJl3H 6YAe T Heyc- TOM'4HBOM, He 6YAeT oTBe'4aTb «3aKOHY npHpOAbi - ceMH KpMTepM- JIM BeeM». faJ1Mneit:ffe CMor c nOMoU4blO cBoero TeneCKona OTKpblTb 60nee 'feTblpex'tnyrHMKoB IOnttrepa (OHM BHAHb. B XOPOWHM 6MH0K11b). B HaWH AHM 6b1nM OTKpbITbl HOBbie cnyTHMKM IOnMTepa - Bcere 16 (.A. KnHMMWHH, 1991). Ecn. MH8HM8 '-f 7 He npo- cree. a, no MHe- HHIO 3HePf'"OAH-' arnocrOB H 600- 3HeprernKOB, HMeeT «3Hepro- pe3OH8HC- c 6oo11<nNeCK oco6eHHOCTbK> HaUJeM nCMXHKYI. 244 
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rnasa 5 6ecOB M3roHJleT HHcyt H3 6b1B- weM npocTHTyrKM, «naAweM >KeHI14MHbI» MapHH MarAaJ1MHbI. "IMcnO 7 C'4MTanOCb «CBIt- I14eHHblM» 14 HaHOCHJ10Cb Ha yT- Bapb, BoeHHoe CHapJl>KeHMe, HaCTeHHble YKpaWeHHJI, npH- '4eM 3TO AenaJ1M HapoAbI, pa3- fofye. no npoHCXO>KAeHHIO M Jt<H- &yIqMe AaneKo APyr OT ',qpyta,. Ao CMX nop rOBOpItT: «ceMb:He 6eC», «ceMb 60roB»; «ceMb 'f- Aec (BeTa» M T. A. Ha 8oC1'o '4MCJ10 7 MTaeCJI C'4acrnHBblM, ero CTapalOTCJI BHOCHTb B HO- Mep MHorMX 6b1TOBbiX M npo- MblwneHHblX npeAMeTOB, H3Ae- nMM H MaWMH. Tal(" '4MenO 7 ]a AOnOJ1HMTeJtbHYIO nnalY CTaBJlT Ha HOMepa MaWHH: '4eM 60nbuie Ha HOMepe ceMepol(" ItK06b1 06eperalOU4Hx BO,AMTeJtJl. TeM 60nbwe nnaTa ]a «C'4acmM&yIO» e3AY Ha MaWMHe. 4Heno 7 4>H1I\)Co4>aMM ApeBHoCTH 6b1no M36paHo KpMTepMeM KonHeCTBeHHoro tt3M1peHMJI l4eJ1oro. ApeBHMe 4>HJ10C04>bI c03Aa- nH MMpoBoe AepeBo, COCToJl'U4ee M3 ceMM '4aCTeM - ceMM ero BeT- BeM. KaK.1Q11bKO 3TO AepeBO He Ha3b1BaJ1M: «J\peBO >KM3HM», «J\pe- BO nnOAO})()AMIt», «ApeBo l4eHTpa MMpa», «ApeBO n03HaHMJI» M T. A. CMMBono,", «ApeBa >KM3HM» HaAeJteHbI He60 M 3eMnJl, ee 06MTa- TelIM B 3HepreTH'4eCKOM Kpyro06opoTe npMpoAbf. Tal(" MOnHHJI npH pa3pJlAe HMeeT BHA pa3BeTBneHHoro AepeBa, 06paeHHoro «orHeH- Mcna . 6M6I1MM no.a.CHTaHO, 'fT0 CBblwe 30 pa3 BClpe'4aeTCfI ceMep- Ka B OAHOM TonbKO 0rKp0- BeHHH VloeHHa 6or0C110Ba (AnOKal1HnClltCe), a BO seeM 6&.16nHH - oonee 160 pa3, KaK HH CW'tO ,Qpyro8 'iHCno. He 8TOpOM MeCTe - "lpOM- Ka (60nee 140 pa3), TQ>Ke HCno CBftU&eHHOe M oipa- >Kaee, Kate Y*\3 yt<a3b1Ba- OOCb. 3a1cOH TpHe,r:J,HHcma COTBopeHHfI MHpa. Ha Ype- TheM MecTe - AecflTKa, A&nee - Jipyrne MCna. 246 
Ka66ana KB a.o.pa Ta H Kpec Ta HOM KpOHOM» 8HM3, 3eMnJl ynaBnMBaeT nOCJIaHHYIO eM C He6ec 3HeprMIO Aepe- BbJlMM, KyqaMM H TpaBaMH, 06paU4eH- HblMH KpOHOM BBepx. KposeHocHbie co- CYAbi Hawero Tena B opraHax BeTBftTCJI, nOA06Ho AepeBY, OTAasaJl nMTaHMe TKa- HftM, M T. n. TaK B npMpoAe C06nIOAaeT- CJI 3aKOH 06paTHoCTM MHb-JlH. C. BaHoB nMweT: «Aepeso Bowno 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 3a'4eHMe, Aa eU4e KaKoe! Ce- MepKa - 3TO cyMMa ABYX npeAblAYMX KOHCTaHT - TpOMKH H '4eT- BepKH, T. e. ceMepKa HYMeponOrH'4eCKM COOTHOCHTCJI C AMHaMHec- 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 B03poeHHH 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». KaaSl TaKaJl 6awHJI CHM- BonH3HpoBana KOCMOt:, a ceMb ee JlpycOB - ceMb He6ec, COOTBeT- CTBYlOlqMX ceMH BMAAMbiM HeBooPY>KeHHblM rna30M He6ecHbfM TenaM (cnTHHepaM): (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 npeCJ1T 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>opMaMM, 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'bBnJlIOT 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 oeHKH 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.1HblX 'Mcen (7 + 2), BoceMb AeCRTa.1HblX a.1cen (7 + . CMb 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 orpaHMeH He KOIla.1eCTBOM 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 MHOp- 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 nMHOCTeM, 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 nOAMHeHHO- 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. ma3MM 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, orpaHMeHHblM CMarM'4eCKOM ceMepKOM». OH rOBOpMJI: «Ce- YH"K8IIW. n....HOCTM BcrpealOTCst 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 BBpaU4aeT 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 'aHTMHOM 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!Abl8MCb 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 nonYHM 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 nonHM '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» $)pMOM - CBoe06pa3HblM xpaMOM TBOpe- HMJI?» - cnpaWMBaeT peAaKI,4HJI >KypHana «HaYKa H penMrMjJ» (1988.  12). BepOJlTHO MO>KHO, eCJ1M C'4MTaTb, '4TO Hcno 7KaK PUC. 33. nMpaMMAa 'fMCJla 28 (I eapMaHT) =1 =2 =3 =4 =5 =6 PUC. 34. nMpaMMAa 'fMcna 28 (II BapMaHT) 252 
KpMTepHH «KyCKOB» OnepaTHB- HOM naMJlTH ne>KHT B .oCHOBe BOCnpHJlTMJI Hawefl nCMXMKOM oKpy>KalOU4eM AeMCTBHTenbHC- TH M JlBnJleTCJI TeMH «'4aCTJlMH», KOTopble CJ1eJWeT BbiAenJlTb H3 nlO6oM HOBOM HH4>opaltMH AllJI ee «nepeBapMBaHMJI», OTKnaA"'- BaHHJI B xpaHMJlHI14e HaweM na- MJlTM, B TaMHCTBeHHblM npOlteCC 3anOMMHaHHJI. n1060nb1THO, cnyaMHo nH '4MenO 7 KaK «HYMeponOrH'4eC- KaJl MaTpHlta» BXOAHT He Tonb- KO B oKKynbTHYIO 4>opMyny n03HaHHJI MHpa (28 - 7 >< 4), H He C 3TMM nM HCJ10M CBJl3aHbI 3araAKH HaweM naMJlTH H npOlteCC no- 3HaHHJI? fOBOpHT nH 3TO 0 TOM, TO enOBeK H B CBeeM nCHXH'4eC- KOM CYU4HOCTH COOTHOCHM C '4HCJ10BOM crpYKlYPOM nOCTpOeHHJI npH- pOAbI, caM JlBnJlJlCb ee '4aCTblO? ni-1 3TO CBMAeTenbCTByeT 0 TOM, '4TO, 06l1aAaJl «'4HCJ10BOM pe30HaHCHOCTblO» C npHpOAOM, '4enOBeH nOl1Y'fM11 OT MMpOBOro Pa3YMa «HHcrpYMeHT» AllJI n03HaHHJI 3aKO- HOB nOCTpOeHHJI MHpa H ce6J1 nH'4HO? BnonHe B03MO>KHO, '4TO KorAa ApeBHHe MYApeltbl rOBopHnH: «4HCJ1a npaBJlT MMPOM», TO OHM AllJI 3TOro HMenH cepbe3HeMwHe OCHOBaHHJI. Ka66ana Ksa,o,paTa H KpecTa M3 rnytSMHW MKOB <J>HnOC<><S>bI-nM$aropi.1Ltbi ApeBHe rpeLU1H -l"pey- rOl1bHOCTb" COBepHHblX Hcel1 BbiproKaTlH B r1ocT- poeHHM ,,"paM, Bap- WHHa Kpo£1 HaHHa- naCb C ..1Cl1a 1.. a KIDK.D.bI HH)KHH pst,D. COCTORl1 H3 Ky(')HKOB C TO'iKOH. TOKa Kaoro. t<y6MKa nPMHMMa- naCb 38 e,D,HHHL(y. 253 
rnABA 6 rEOMETPMSI nSlTM CTMXMM OKKYnbTHbie 'IMcn..,OBbie CBSl3M CTMXMM KMTaMCKHe MYApebI no cpaBHe- HHIO co CBOMMM eBponeMCKMMH Kon- neraMM 3Ha'4eHHe Bblpa>KeHMJI «Y CMH» nOHHManM WMpe. OHM BKnaAbI- BnH 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 06paaJ1 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>YHKHJI», «Mcnonb30BHHe». 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 HeBeeCTBeHHble: crpaHbI YCMH Y'feHMe 0() OCHOBHblX nSlTM 3neMeHTax MH- P03,D,8HHflt1 nSlTH rnaBHbI>.< l"IpOSIB11eHHSlX )IG13HH B KHTaCKO $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>MKaLtMOHaJl cxeMa npOJlBJ1eHMM OCHOBHblX >KM3HeHHblX 3a- KOHOB, 4>paHLtY3CKMM Y'feHblM M. fpaHe (1934). OH >Ke YKa3b1BaJ1, '4TO cnop 0 TOM, JlBJ1J1IOTCJI nM 3J1eMeHTbl cy6craHM- 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 3Hae- HHR nRTH 3neMeH- TOB (CTHXHH)..- BpeMeHHbte .naH- CKe HVMeponorH C3b68aIOT C CMM- BOnH'4eCKHM HX pacnp.eeneHMeM 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 Hcen: 5 nap 4<He6eCHblX» (He'4eTHblx) M 4<3eMHblX» ('4eTHblx) AflJI no wy; 5 nap 4<nOpO>KAaIOU4HX» (nOpJlAKOBbiX '4HCen AO nJlTH. - npUM. To6nuL4o 2 OKtcynbTHbie 'IMcnollble COOTBeTCTBMII CTHXMH 0 c:; HYMeponorH .0 CD  "' "' % 8. CD '4eCKaJl CMcTe- COAep>KaHHe c:[ 0  7 0 0 cv cv 0 Ma co c:t  r:= CYMMa B 0 A M n no Het)o, JlH, MY>KCKOe, HeeTHoe, nHeBMa (4H), 3HeprMJI 1 7 3 9 5 - 25 - 7 wy 3eMnJl,.MHb, >KeHCKOe; '4eTHOe, ,K.OHCMCTeH4HJI (H ), MaTepHanbHOCTb 6 2 8 4 10 - 30 - 3 X3 nOpO>f<,QeHHe 1 2 3 4 5 - 15 .. 6 ry cJ»OpMHpoBaHHe 6 7 8 9 10 -40-4 256 
osm.) M «4>oPMMPYIOU4HX» ('4HCen OT 6 AO 10. - npUH. osm.) - AnJl X3 rp (Y4eHMe 0 CHMBonax H '4MC- nax, c. 294-295). A.. K063eB (1994) nHweT, '4TO C ApeBHOCTH H BnnOTb AO XVIII B., T. e. AO 3HaKOMCTBa C eBpOneMC- KOM MaTeMaTHKOM, KHTaMCKHe Y"Ie- Hble BbiBOAHlTH '4eTbipe OCHOBHblX MaTeMaTH'4eCKMX AeMCTBMJI (CJ10- >KeHHe, BbIHTaHMe, YMHO>KeHHe H AeneHHe) H3 LteHTpanbHblX HYMe- pOnOrH'4eCKHX 4>Mryp: «MarM'4eC- KOro» KpeCTa X3 TY H «MarHecKoro» KBaApaTa no wy. f1atorMe TpaK- TaTbi ApeBHOCTH nOCBJlI14eHbI Mcnonb30BaHHIO 3TMX «yHMBepcanbHblX MarM'4eCKMX 4>Mryp» l(aK HHcrpYMeHTa "aTeMaTM\leCKMX'MaHHnynJl- HM. TaK. BonpocaM '4HCJ10BblX npe06pa30BaHHM cxeM X3 TY H no wy nOCBJlI14eH TPYA H3BeCTHoro MaTeMaTHKa H acrpoHoMa 6YAAHMCKOro MOHaxa cHHa «C'4eTHbiM KaHOH YHTenJl CYHJI» (III-IV BB.), a BbI- AalOU4HMcfI KMTaMcKHM MaTeMaTMK MHb L,plOwao (1202-1261) pa3- pa60TaJ1 06HM MeTOA peweHHJI 'MaTeMaTMeCKHX 3aAa (ypaBHe- HMe nepBoM CTeneHM) HCXOAJI H3 aHaJ1H3a KOM6HHaTopHblxycnOBHM raAaTeJ1bHblX npoLteAYP 3THX «MarH'4eCKHX» cxeM. MnepaTopbl cJ>yH H 1010 c03AanH 6naronpMJlTHbie ycnOBHJI AnJl TBOp'4eCTBa KHTaMcKMM MaTeMan1KaM, pa3pa60TaBwHM PflA C'4eT- HO-H3MepHTeJ1bHblX npMeMoB. TaKHM 06pa30M, B crpYKType CHCTeM no wY M X3 TY AeMCTBHTe11bHO 3aJ10>KeH eKMi4 «Bonwe6HblM KJlIO'4», KOTOpblM npH YMeJ10M Hcnonb30BaHHM MO>KeT nOMoraTb OTKpblBaTb H pewaTb HeKoTopble 3aKoHoMepHoCTM >KM3HH. reOMeTpHfI nfiTH CTHXHU CMltOnorM C'tMTa101 CxeMbi X3 Ty &>1 no wy SlB- J1SUOTCSI reHeTJ;NecKOO H cTPyJ(TypHOU nep- 800 rBHbIX H}lMeno- rwfeClOOc 1C00000YK"'. - rpHrpaI[tM If reKcarpaMM. Lttx MaTeMaTI1WeCICHe CTpYKtypbl r1Q3BOJ1W1&>1 pa3paOoTaTb pa3J1HbIe nf)MeMbi BbNIItC11etMH. 257 
rnaea 6 reOMeTpH"4eCKOMY 06pa3Y Ma- rH"4eCKHX cpHryp npHcya apH4>- Mentt4ecKaJl HnOCTaCb H Hao60poT. HYMeponOrH'4eCKHe TepMHHbI «He- 6eCHoe» H «3eMHoe» B reOMe'TpH- eCKOM nnaHe HHTepnpeTHpOBa- nCb KaK Kpyrnoe H KBaAparHoe, B apH4>MeTH'4eCKOtot - KaK He'4eT- Hoe H '4eTHoe, B 4>Hnoco4>cKOM - KaK 'TpOHt4HOe H ABOMt4Hoe. B BOCTO'4HblX HYMeponorHec- K  4>Hnoco4>cKMX cxeMax «reOMeTpM'4eCKMe» nOCTpoeHHfi (c cnonb30BaHHeM CHMBonOB 6YKB) He OTAenJlnHCb ot «apH4>- MeTM'4eCKHX» nOCTpOeHHM (c Hcnonb30BaHHeM '4HCen). HanpHMe 3Ta TpaH".1JeaJ1H30BaHa B TpaKTaTax KMTaMCKoro MaTeMaTHKa B3H 60JlHa (II B.) npH onMaHHH cxeMbi «caHb y» - 6YKBanbHO <<1pOH- bI M nJlTepMb1». 60Jlt4 '4HCJ10Bble 3Ha'4eHJI 3neMeHTOB B TpO'4HO- nJlTepHt4HOM crpyKType KBaApara pacnonaran acrpOHOMH'4eCKH: no CHnY3Ty C03Be3AHJI OPHOH, T. e. 6YKBOM «x». npH 3TOM BO Bcex rpex CTon6ax Bepl11KaJlbHaJl npo- eKMfi Hcel1 AaeT paBHble cyMMbI - 5 (pHC. 35, a, apen- Ka YKa3b1BaeT HanpaBl1eHHe cHTblBaHHJI).CpaBHMTe:pac- npeAeJleHHe t4HCeJI B KBaApa- Te no wy HaAeJlJleT era ell4e 60nee YHHBepcaJlbHblM HYMe- H8 38M8Ttcy C03A8HHe OCHOBHblX ceTHO-H3MepHTel1bHblX npHeMOB B MaTeMaTHKe H aCTpoHOMHH npHnHCblsa- lOT HMnepaTopaM <J>yH H 1010 (II B. AO H. 3. - I B. H. 3.), KOTopble BBe11H B peweHHe npaKTHeCKHx 38Aa HYMepOl1orHec- KHe TpHrpaMMbI, reKca- rpaMMbI, npoH3BOAHble cxeM X3 TY H 110 wy. MCTOpM't8CK8. CLlllp8BK8 ACTpol1orHecKHe r9pocKonbi .o.peBH' H306p8)KaIlHcb CHM- B0110M 11H - K88APaT8, BnHcaHHoro B Kpyr - B Koc- MH"4ecKYIO cHcTeMY. 258 
reoMe Tp HR nRTH CTHXHH 6 ... 4 9 2 -15 3 5 7 -15 8 1 6 -15 15 15 15 15 15 a 02 B1 n5 A3 M4 5 5 5 .Puc. 35. "fMcnoBwe COOTHOWeHMA cxeM X3 ry (a) - c pa3MeuteHMeM 311eMeHTOB no CHnY3ry OpMOM M no wy (6) ponorMecKMM cOBepWeHCTBOM, TaK KaK AaeT oAMHaKoByIO BeJ1M"tM- HY cyMMbI - '4HCJ10 15 - BO BCex HanpasneHMJlX «CMTbl8aHHJI»: B BepTHKanbHOM, ropM30HTanbHOM H AHaroHanbHoM (pMc. 35, 6). 3Ty >Ke CTpOMHOCTb '4HCJ10BOM M HepornM4>M'4eCKOM (B eBponeM- CKOM TpaHcKpHnLtMM - 6yKBeHHoM) CBJl3M nJlTH 3neMeHTOB X3 TY nOA'4epKHBaJ1 OCHOBOnOnO>KHMK HeoKoH4>YLtMaHCTBa 4>Koy A,yHbM (1017-1073) B eBoeM 3HaMeHHTOM TpaKTaTe 0 TeopMM «caHb y» «3bJlCHeHHe nnaHa BenHKoro npeAena». nOCMOTpHM Ha BepTMKaJ1bHo-ropM30HTanbHoe pacnOnO>KeHMe '4MCnOBbiX 3neMeHTOB B KpecTe X3 TY B nonOBMHHOM (AO '4MCJ1a 5 BK11IO'4HTeJ1bHO - pHC. 36, a) MnM B nonHOM Ha60pe '4HCen 3J1e- MeHTapHor MCJ10BOro pJlAa (AO 10 - pMC. 36, 6). 31'0 OCHOBono- naralOU4Me '4HCJ1a B HYMepoJ10rMeCKMX npe06pa30BaHMJlx. OAHaKo BMAHO, '4TO MX OOHopRoHoe pacnOnO>KeHHe He HaAenJleT 4<MarM'4ec- KMM KpeCT» AOCTaTO'4HblM MaTeMaTHeCKHM COBepweHCTBOM. 259 
rnasa 6 a 6 2 7 2 3 5 4 8 5 4 3 10 9 1 1 6 PUC. 36. 4MCII09b1e COOTHOWeHMf! eepTMKallbHO-ropMJOHTaJ1bHOrO Kpecra X3 Ty npM n0J10BMHHOM (a) M nOJ1HOM (6) PJIAe 3J1eMeHTapHblX '4MCen HanOMHMM, '4TO HYMeponOntJl AonycKaeT MaTeMaTM'4eCKHe npe- 06pa30BaHHR C '4HCJ10BblMM CMMBonaMM, HO nonY'4eHHYIO cyMMY 06b1'4HO ynpO(14aeT (CJ10>KeHHeM) AO 3neMeHTapHOrO, OAHOro '4MC- na. «OAMHaHblM» KpeCT X3 TY He MMeeT '4MenOBOM CHMMeTpMM. 3aTO nr*.COBHeuceHUU C KOppenMpylOM 'IMCJ10BOM CMCTeMOM «He6ecHbix CTB0J10B» )S TY npeBpalqaeTCA 8 CTonpoeHTHWM «Ma- rH'4ecKHM KpecT»! B HeM cyMMbI Bcex OAHOMepHblX BepTHKaJ'IbHblX M - ropH30HTaJ'lbHblX 6-'UleHHblX '4HCJ108b1X PRAOB OAMHaKOBO paBHbI 34 (pMC. 37), KaK M B '4HCJ10BOM KBaAJ)aTe AlOpepa (pHC. 16). Bnepsble 3TOT «MarM'4ecKjlM KpeCT» B OTe'leCTBeHHOM flMTepatype onMcaH A.M. K063eBbiM. KaK B_HAHI4, oBoiiHOii «MarMecKMM KpeCT» X3 TY 11Y"Iwe nepeAaeT '4MenoBYIO CMMBonHt<y CBJl3M «He6ecHoro» ('4HCJ10 3) H «3eMHoro» ('4MCJ10 4). «MarHCjeCKHe» KpecT X3 TY H KEJaApaT .fIO wy, nocrpoeHHbIe c eTOM crporofo MaTeMaTM'4ecKOro paBHOBeCMR CBOMX 311eMeHTOB, KOAMpyIO- I14ero KOCMM'4ecKoe COOTBeTCTBMe 3Be3p, B C038e3AMM OpMOH. no MHe- HHIO HYMeponoroB, MOryr BblJlBnJlTb pe30HaHC 3HeprMH He6ec B B- 260 
reoMe Tp l1R nRTI1 CTHXI1M neHHJlX 3eMJ1H H B )f{M3- HH '4enOBeKa». 4eM TO'4Hee  C MeHbWMMM MCKa>KeHMJlMH '4HCna KOAa, CHMBOnH'4eCKM OTpa>KalOl14He TO HnH MHoe JlBneHHe >KM3HM, YKI1C!AblBaIOTCJI B CTpyK- Typy X3 Ty HJ1M no wy, TeM TecHee no CBoeMY npOHCXO>KAeHMIO OHM CBJl3aHbI C KOCMOCOM M BepoJlTHee HX B03HMI(- HOBeHHe B HaCTOHU&eM HHKapHaMM '4eJ10BeKa KaK npeAHa3Ha'*!HHoe eMY HCnblTaHMe C8bftOe. Or nM'4HOCTM '4eJtO- BeKa 3aBHCMT, npa- EcnM aepMTlt OKKYnb- TM3My, TecHaA CBA3b C KOCMOCOM OeHBaeT- CA KaK KapM"'ecKOe ",cnblTaH",e, T. e. HeH3- (je)l(Hoe 8 *"'3H'" 'feno- BeKa, 38paHee eMY npeonpeeneHHoe. 7 3 2 4 8 3 5 5 4 9 1 2 10 6 7 8 1 6 9 10 PUC. 37. «BOMHOM» 'fMCnOBOM KpeCT X3 TY C CMCTeMOM 4CHe6eCHbiX CT80110B», KOTOpaJl AenaeT ero «co8epweHHblM BMnbHO nH OH npeOAoneeT B03HHK- wee nepeA HMM npennCTBHe B >KM3HH, CYMeeT nM "cn0J1b30BaTb CMTyaHIO A/lJI CBoero COBepweH- CTBOBaHfi, pa3BMTMSI B ce6e A06- pa, npMHeceT nH nonb3Y ce6e H nIOAJlM. no MHeHMIO HYMeponorOB M aCTponorOB, OAHOBpeMeHHO C HMM M ApyrHe nlOAM npoXOAJIT Kap- 261 
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reoMeTpufl nflTU CTUXUU B KaKof1-To Mepe TO BnHflHHe MO>KHO CpaBHHTb C B03AeMCTBeM Ha napTHepa, C KOTOpblM npeACTOHT 06eHMe, AO)t(AJ1HBOM noroAbI, nnoxoro CaMO'4YBCTBHJI, 6one3H nM HOro «4>OHoBoro C06b1TfI» HcnopTHBWMX eMY HacrpoeHHe  BnHJlIOU4Hx }fa 06eHc 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 OTHOHM, 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 nepHOA4eCKOM ne'4aTH nOJlBnJlIOTCJI 3aMeTKH 0 «BpeAe aCTpOnorM'4eCKOrO nporH03a» B OTHOWeHHJlX Me>KAY nIOAbMH. HanpMep, KaK nHweT AHHa CaMOHnOBa (MocKBa), «3Be3Abl BMHOBaTbI» Bee pa3BOAe,.a T04He, 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 06U4eHH 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 AeCTBHTenbHO MO>KeT Ka3aTbCJI «4TO-TO He TaK» B nOBeAeHHH napTHepa, CJ10BaX  TOHe, B3rnJlAe. n03TOMY «HacrpaHBaIOU4HM» Hac npOTB napTHepa «HHCTPY- MeHT» MO>KeT 6b1Tb KaKHM yroAHO. HYMeponorHJI HnH aCTpOnOrHJI T'fT HH npH eM. B3aMHoe HenOHHMaHllle III KOH4>nHKTbI oryr B03HKHyTb H npH «OnTHMaJ1bHOM» nporH03e. He60nbWHX CCop 60JlTbCJI He £11eAYeT, TeM 60nee «HaY'4HO 060- CHOBbiBaTb» HX npH'4HHY. He60nbwHe CCOpbl, no yTBep>KAeHHIO 271 
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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 
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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 - «npeoA01feBalOee» Ka'4eCTBO. 6HHapHaA CBJl3b KaJKAoro 3neMeHta MMeeT co6creeHHoe Ha3BaHMe: B 4>oPMyne 2 on (CM. pMe. 39, a) npE!.A&:TaBneHa «nop0)f(- AalOJI» 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) OCT8J1fieTCJI 8 OAHOM - npJlMOM HanpaB- neHMM, MJ1(t no 'laCOBOM crpenKe. C'4MThfBaHMe 3neMeHTOB nemarpaMM (pMC. 39,6) npM BHeWHeM pacnpeHMM 3HeprHM nposoART B nPJI- MOM, a BHyrpM nemarpaMMbI- B 06paTHOM HanpaBJM!HMM. COBMeuteHHbIe MarM'leCKMe 4>Mrypbl - 31'0 o6beAMHeHMe B eAM- HOM rpaMKe MK11MKoM, MJ1M 38e3OHOU (BHyrpeHHeM), H KpylO- soU (Hapy*HOit) neHTarpaMM. Ka>twut"3 HMX COCTOMT 143 nJITM 3ne- MeHTOB, CMMMeTpMHO 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 Mar4ecKHMM 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 HYMeponorHecKHe 4>OPMY- nbl CHMBOnH'4eCKH nepeAalOT peanbHOe nepepacnpeAeneHHe 3HeprHH Me>K.qy oraHaMH K CH- CTeMaMH Hawero opraHH3Ma. HanpHMep, nepepacnpeAeneHHe 3HeprHH no rpa4>HecKoM 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 3HepreTHecKoM 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. HYMeponorMeCKMe clK>PMynw OTpa)l(alOT npHU1'tn pacnpeAel1E!HR 3Hepr..,.., B pa311"'4 CH- cTeMClXs \.Be  RBJ1eH..,- RX, n03TOMY ..,cnOI1b3YIOT- CR B HeTOPblx cope- MeHHblX 06naTRx 3HaHiiI. MCTopMecKaA cnpaBKB B APeBHOCT.., aCTponor .., HY- Mep0 l1 0r.., B npeACKa3aTel1bHOiil npaKTKe Ha..,60l1ee aCTO "'C- n0l1b30BaTI Teop"'lO B38:..,MHO- ro npeOAOl1eHR nRT.., 311eMeH- TOB. 06 3TOM ncaI1 s:lH '-'ao B KH..,re ..YeH..,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 nyaM 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 06ecTse. TO Ha.o,nIOAbM"'). HO np'" aTOM He "'MeTb "'36b1TKa KaTS "'11'" 3Ha- HHH(Hanp"'MepKacnean"'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 
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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 6Tb OTHOCMTeJ1bHO npo- CTbIM M O'4eHb ymy6neHHblM. npM 60nee AebHOM aHanM3e 3aTpa- rMBalOT pa3HbIe acneKTbl «OTHoweHMM» He TOJ1bKO OCH08HOro 3ne- MeHTa, HO M CBA3aHHblX C IiMM no 4>YHKI.tMM BTopOCTeneHH)( 3neMeHTOB. B nOC11eAHeM cn B Mcc:ne,qOBaHMe BKJllO'4alOT APYrMe neHTarpaMM (OHM npMBOARTD' B ra6nMl.te AaJ1ee B COOTBeTCTByK>- U4eM pa3Aene), B KOTOpblX maBHM Y'faCTHMKOM 6yAer KOJKiJblU M3 MCCJ1eAYeMbiX BroopocmeneHHbIX 3J1eMetfl'OB.pa6o&.eM cpopMynbt-. Cl)MrypW  MHAMK8TOpbl COCTORHMR nCMXMKM HMeeTCJI nM B3aMMOCBA3b Hawero HacrpoeHMJI C TOM reoMeTpM- '4ecKOM 4>MtM>OM, KOTOpy1O Mbi Bbl6MpaeM MnM pMtyeM 6e3 BCJlKOM 3aAHt!M MblCJ1M, npocro18K? MO>KeT6bITb, caMa 4>Hrypa B03AeMCT&yeT Ha Hawy ftCMXMKY, perynMpyA ee cWHKI.tMIO 8 3a8MCMMOCTM OT cBoeM «reOMeTpM»? OKa3BaeTCA, H TO M Apyroe AeMcTBMTenbHo MMeeT MetTO - yTBepT HYMepoliorM M nCMX0J10rM. BOT 'ITO nMwyT B. T. KOHApa- WeHKO M A.H. AOHCKoM B KHMre «06tijaA nCMxoTepanMA» (1993): «Y>Ke nepB06b1THbiM '4enOBeK n- TanA MaTepManM30BaTb CBOM npeACTaBneHHJI 0 MMpe B BMAe- HaCKanbHWX pMcyHKOB. B nOCJ1e- AYIOU4eM, C03epLtaJi MX, OH Bbl3b1- M3 rny&tHw DKGe Ha B03,Q.ei1cT8Me- M reoTPMecKoM <l>Mrypbl Ha n 't6I1OBeK 06- paTI1J1 BHMMaHMe e B rnv6oKoM APeBHOCTM. 290 
reoMeTpHR nRTH CTHXHH ODDQ* PUC. 43. reOMerpM&fecKMe ctnUYPbI, 06J1(IAaIOIqMe pa3J1M&fHoI't"MnOM MnJl1030pHOro B03AeMCTBMJI M MCnOJlb3yeMbie KaK OCHOBHble 3J1eMeHTbI AllJI 0603Ha&feliltf1 &fp Ban y ce6J1 (tAeKBaTHbie 3MOLtMOHanbHble nepe>KMSaHHJI. CHa'4aJ1a 3TO 6b1nM H306pa>KeHHJI peaJ1bHblX 06pa30B (nIOAeM, 3BepeM, Aepe- BheB), a nOTOM - MX CMMBOl1bf. B 3TOM OTHoweHMM Bepxa COBep- weHCTBa AOCTMrna erHnerCKaJl CMMBonMKa. 13BeCTHO, 'frO R306pa- >KeHHJI pa3Hoo6pa3HoM 4>oPMbI M" LtBeTa 6ka3b1BalO! .,pa3nM'4HOe B03AeMCTBHe Ha nCMXM'4ecKoe COCTOJlHMe '4enOBeKa. TaJ(t3HrJaroo6- pa3HaJl nHHMJI C OCTpblMH yrnaMH C03AaeT Bne'4arneHMe pe3KOro H3- MeHeHMJI, HaKOnneHHJI H pa3pJlAa 3HeprMH, Bbl3b1Baery '4enoeeKa '4y&- CTBO Han pJl>KeH HOCTM, TpeBorM. 3aKpyrneHHble nMHMH MO>KHO Ha3BaTb nerKHMH, nOMaHble - TBepAblMH. cJ»Mrypbl C PaAHaJ1bHO paCXOAJIU4M- MHCJI npJlMblMM C03AalOT HJ1J1103MIO M311Y'4eHHJI, Kpyr - C KOCMH'4eC- KOM 6ecKOHe'4HOCTbIO H a6cOl1IOTHOM rapMOHHeM» (c. 169). cJ>MryPbl, KOTopble H306pa>KeHbI Ha pHC. 43, C'lMTaIOTCJI CBJlI14eH- HblMM nO'4TH BO Bcex penHI11J1X. OHM npMBeAeHbf B O'tepeAHOCTM no npHHLtHny B03paCTaHMJI HnnlO- 3HM. 3TH reoMerpH'4ecKHe 4>Hrypbl JlBnJlIOTCJI OCHOBHblMH 3neMeHTa- MH AnJl C03epHHJI C L4enblO BBe- AeHHJI ce6J1 B oc060e nCMXM'4eC- Koe COCTOJlHHe - MeOumoLlUlo, KaK nHwyr KOHApaweHKo M .QOH- 3To H8.QO 3Ha,... S-06pa3HaH KJ»1BaH Ha- 3b1BaeT nHe rpalU'f  4>oPMpyeT '4Y8C T BO rapMOH, ycr1OICoeHH. 291 
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'4HCnaMM M MX «06'beMHblM patnpeAeneHHeM», Hanptt- Mep paCKnaAKa B nMpaMMAY «rpeyronbHblX» '4Mcen. OKa3b1BaeTCJI, BocnpH"- TMe M3MeHieTc" B 3aBMCM- MOCTM OT 3anonHeHM" BHY- TpeHHero 06'beMa 4>Mryp pa3nM'4HblMM BKnIO'4eHM"MM: '4epTO'4KBMM, TKaMM, 3Mna- raMM. 3TM n03HaHM" 6b1nM Y'4TeHbI HYMeponoraMM 8 OLteHKe AenOBbiX B03MO>KHO- CTeM '4enOBeKa. nporH03 CTpOMnat Ha OCHOBe pe3ynb- TaTOB TeCTMpoBaHM" OCo6eH- HOCTeM BOCnpMJlTMJI reOMeTpM'4ecKMX CPOPM. CocrOJlHMe nCMXMKM 0HMBaJ10Cb c nOMOU4blO «MarM'4eCKMX cl>Mryp» M COOTBeTCT&yIO- U4MX HM «rpa4>MKoB nporH03a ero». Tal<. ecnM M306pa3MTb '4ep- HiIIM Kpy>KOK, BnHcaHHblM B KBaA- paT CMMMeTpM'4HO (pMC. 45, a) M HecHMMeTpM'4HO (pMC. 45,6), TO npM KOHl4eHTpal4MH Ha 3TKX 4>M- rypax BHMMaHMJI MO>KHO nony- '4MTb pa3Hble nCMXOnOrM'4ecKMe COCTOJlHMJI. PUC. 45. «YpaBHOBeWeHHa",. (0) C nOMOuiblO HYMeponOrM'4eC- M «Heypa8HOBeweHHCUJ» (6) KMX npe06pa30BaHMM CMMMeT- Mrypbl reoMBrpHflI1RTH CTHXHH Ma my&IHW ..0.  Bel1MKonenHblMM I1CMXOnoraMM M B118.D.8S' - I1OB.WM K. 4»WYP, ,QpeBHMe , K0He'4- HO, He MOI'71M"He 06paTl4Tb SHMM8HM8 Ha oco&HHOCTM BOCnpMSm1R '4eoM nacxMKoM CMMM81J>'4'fHb1X (c6anaHcMpoBaHHbIX, yp&BHO- aeweHH).M HeCHMMe- HbO( (HeC6anaHcMHbIX, )4»Mryp. a 6 [;] 293 
rnasa 6 pH'4HblX H HecMMMeTpM'4HbtX 4>H- ryp B CTapMHY O(4eHHBaJ1M B03- MO>KHOCTM nCHXHKM. nOnY'4eHHble HHblecpaBHMBanHC«3TaJ10HOM HOpMbI» - pe3YnbTaTaMM MCCJ1e- AOBaHMJI nCHXH4eCKH 3AOPOBbiX nIOAeM. Y'4MTblBanocb, '4TO BOC- npHJlTMe H3MeH'4HBO no BpeMe- HH M 3aBMCHT OT MHorHX CJ1arae- MbiX nCMXH'4eCKOM AeJlTenbHOCTH (HacrpoeHHJI, BHHMaHMJI H T.A.). n03TOMY c nOMOlqblO reOMerpH- '4eCKHX 4>Mryp HYMeponorM H nCH- xonorM no pe3ynbTaTaI'I TeCTMpOBaHHJI C 60nbweM YBepeHHOCTblO c:rpOJrT nporH03b1 Ha 6nM>KaMWee BpeMJI (HeAenlO, MeCJI(4), a He Ha OTneHHoe 6yAYlqee '4enOBeKa (Ha roAbI). Ho H 06YAYU4eM HcnblTy- eMoro MO>KHU:cKa38Tb HeMano MHTepeCHoro, OnHpaJlCb Ha BblHBneH- Hble OCo6eHHOCTH erp nt+1XHKH. Tal(, npH Bblpa>KeHHOM pa3HHu,e pe- 3ynbTaToB MCCJ1eAOBaHHJI no cpaBHeHHIO C AaHHblMH «3TanOHa» MO>KHO AOCTaTO'4HO YBepeHHo nporH03HpOBaTb nH60 OCo6eHHblM yc- nex B MHTenneK1YaJ1bHOM AeJlTenbHOCTM-(npM npeBblweHHH AaHHblX HOpMbI), nM60 HAa'4M (npH nnOXHX nOKa3aTenJlx). Ha, Ka3al1OCb 6, noM TecTHpoBaHMH - Bbl60pe «noHpaBHB- werOCSl» cMJ1y3Ta 4>Hrypbl - nOCTpoeHbI Ba>KHbIe nCHXOnOrH'4ecKHe TeCTbI, WMpoKO MCnOnb3yeMbfe nCMxonoraMH AllJI O(4eHKH AenOBbiX B03- MO>KHocreil'feJIoBeKa. npHMepTaKoro MCqteAOBaHHJI OnHtan AJ1.11te- 6eTeHKO'B KHHre «TecTbI AllJI AenoBOro 'feI10BeKa H AllJI lICe><» (1995). Ha pHC. 46 AaHbI '4eTbipe rpynnbl CHMBonOB (Bcero MX 16 BHAOB), ycnOBHO Ha3BaHHblX: I - «ABH>KeHHe», 11- «cnoKoMCTBMe», III - Cl»Mrypa co c6anaHcMpo- B8HHWM I48HTPOM (ypas- HOBeUJeHHBR <l>wypa) 6y- AeT CKI10HSITb K 'fYBCTBY YCnoKoeH"-'A, YM"1POTBOf)e- H, a <I>"-'rypa c HeC6a- naHCll'lpoeaHHbIM u,eHTJX>M (HeypaSHOBeweHHaR <1>"-'. rypa) - K 'fYBCTBY - KOM4>oPta ..-, llQt)G1ecKorO HanpsvKetI"-'A. 294 
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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 npMU4e; 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*HaMHpMaL4MJI.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 KBapa npH6nM3HTenbHo napaJ1nenbHbI Apyr APY- ry H, KpOMe TOro, HaAIIOMneHbI nOA yrnoM, - nHweT reonor H naJ1e- OHTonor A.A. flKOBnB (>KM3Hb 3eMnM. M.; n.: rOCTexrH3, 1947). - Ha nonepe'4HOM M3nOMe nerMaTHTOBOM nopoAbi. OHM HanOMMHalOT BOCTO'4HbIe nMbMeHa, 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.oxpaHMTenbHMbI, 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 npeAKa3b1BaBWMe 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 cnaceHMRA8M 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)eirM- neTCIG1X MCTO'UiMK8X'..a'tM- CTO OT 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 - "CCtBeHHwe rnyWM- TenM 3eMneTpJ1CeHMM. Elije OAHa Aep3KaJl TMnore3a», - 3aMen411 M Haw OTe'reC1'BeHHblM MCCJ1e,qosa- TeJ1b nMpaMMA C.6. npocKYPJ1KOB, COTpyAHMK MHCTMtyTa np06neM HHOCTM 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>H3MecKHX 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 rp06HHbI 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 npccopa 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 n101A 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 nOK1 ynaB- nMBalOT CMrHaIlbi KOCM- IG1X U,HBW1M38L\,HM M T. A 307 
rn8B8 7 «KpeMHeBbie KHMrM» M npoMe '4YAeca, no.q KOTOpWMM MO)l(HO nOA- pa3YMeBaTb M «TeXHMecKMe 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 3aMeaTeJ1bHblX 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(eHMHa CMTaeT 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 KOCTKY CBeem Tena.. .», - nMCaJ1 OH. «OrOBCIOAY B30pbl MOM 6b1J1M npM&.ne'4eHbI, KaK MarHMfM, nMpa- MMAaMH.. .», - OTMe'4aJ1 M pycCKMM nyreHHMK ABpaa }topeB. B MHTepBblO ra3eTe «Time» (nOHAOH, 8enMK06pMTaHMJt) 4>M3MK AMH-UJaMCKom YHMBepcMTeTa rOHeMA cKa3a/lHa-.HaWM pe3YnbTa- Tbi nOBnMJlna nM60 cyeCTBeHHaJI 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.aHM 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 nMpaMV 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>MecKWP 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- TonpMeaTenbHOCTeH., He CTast CJ1y'taHHblX ytCyCOB 3MeH,CKopnOHOB,nen, OC, A,D,OBMTblX nayK08  np., KaK 3BeCTHO. eHble 06- Hapy*W1 B npaMH,D,aX KaK MHMYM ABa CMepTenbHO onaCHbiX 4>aKTopa: nneceHb Aspergillus flavus (PwcfI acneprnnnlOC)  cneW14>- eCKe Bpycbl nex MbiweH. 310 
TO'fHO Aa)Ke BefilitMc1.HS6onb- WOM KOHLteHTpai4MM MbfWbJl- KOBMCTblX I4nM PTYTHbfX CO- eAMHeHM, 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- rIOTCJ\,.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 pa3I1MHbfM eo<:>6u4eHMM. 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 cneHanbHO «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,-3anpeeHo. - 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. - yTBepIOT, '4TO eU4e AO 3nOXH paCBeTa 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 nMa 3eMnH crpaHY, rAe )l(Hn 3TOT HapOA, OT 312 
BeJU1KOM qMIMfM438l&M" OCTa- nMCb nMWb BOCnOMHHaHMSI, MH- 4>bI H nereHAbi. Cno80«nMpaMnpoMCXOAHT OT rpe'4eCKoro cnoBa pyramis- H'4T003Ha'4aeTHMBOnM'4ec- Koe npeACTaBJ1eHMe EAHHOro 60- )t(eCTBeHHoro nnaMeHM, )t(M3HH Bcex C03AaHHA. CaMa cf>opMa nM- paMMAbI, 06paeHHaJl 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 conHeHOM 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 OCQ3HalOMMM 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 nOCBRHM...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 KaHAMAatfMKOMY He pa3pewanOCb npoXOAMTb HcnblTaHMJI BTO- pOM pa3:npM nocBReHMM nepBoe MCnbITaHMe 6b1no HaCTonbKO TR- >KeJ1b1M, 'fi0 He 06nClAaIOU4MM CMnbHblM AYXOM KaHAMAaT Mr npoCTO McnyraTbCJI M OTKa3aTbCR OT nOCBReHMR. 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 CJ1yae 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 - 0603Haa- lOT «>Kpe4», «MYAPblM», «eenMKonenHblM».)>>. rpeeCKHe 4>Hnoco4>bI- cJ»anec, nHcI>arop, nnaTOH M EBAOKC- 6b1nH caMblMM 3HaMeHMTblMH H3 Tex '4Y>KeCTpaHLteB, KOTopble yc- neWHO npownH MHOrOHCJ1eHHble 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 nOAHHJleTCSI MaTeMaTM'4eCKMM paceTaM (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 06ancst y en1eTC- K....X OB, n....CbHHaR IIICTOP"' erlllnTRH H8IIIHa- l1aCb 3a 11 340 l1eT 1JP 3n0>G1,fA K<'t9PYK>)KHfI caM repoAot: ....11.... nTIII 3a 14 TblCsteneTIIIM AO Hawero BpeMeHIII. 315 
rnaBS 7 ErMnTJlHe BenMJ<YIO nMpaMM- AY aCCOMMpoBaJlM 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 ypo1O pacnoraeTCJI 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. nMpaU4e coxpaHAer MHoro 3ara,qOK M HaCbtU4eHa '4MtneBbtMM CMMBona.ut KocMoca... nOllaIOT, '41'0 eCJ1M 6b1 OCb MccneAOBaTb OCHOBaHMe nMpa- MMAJII, TO. o.swapy>KMnM 6bt 3aOC1pRIOCJI I( HM3Y KOHCTpYKMIO, 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 CTHaM 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, BM 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 el1oBecIG1X )KepTB. MOHCTpMpyeT Ma1eMaTMtKYIO v MOAenb Hepa3pblBHoM cornaCOBaHHOM CBJl3H BOCbMH ero OCHOBHblX «nepB03neMeH- TOB» (CM. COOTBeTCTBYIOU4HM pa3Aen KHMrH). YAMBHTenbHblM COBnaAeHHeM JlBnJleTCJI H TO, '4TO B Ka>KAOM CTopOHe OKTa3Apa 3ane'4arneH nonepe'4HblM Cpe3 erMneTCKOM nHpaMHAbI, TaK KaK OKTa3AP COCTOHT '13 8 npaBHnbHblx rpeyronbHM- KOB - CMMBonOB COnHe'4HOM 3HeprHM erHneTcKoro 60ra OCHpHca. KSK erMnTRHe CTpOMnM CBOIO 3H8MeHMTYIO nMpaMMAY J1peBHMe erMnTJlHe MenM 60nbwoM onbiT CTpoHTenbCTBa 4>YH- AaMeHTanbHblX COOpy>KeHHM. OHM nOCTpOHnM HeCKonbKO rpoMaA- HbiX nHpaMMA - Y5=blnanb- HHLt 4>apaOHoB. Ka>KAbiM 4>apaOH nHpaMMAY AnJl c06- CTBeHHoro norpe6.eHMJI c:rPO- HJ1 eU4e npH >KH3Htt, nfiAro- TaBnMBaJl CBOM «nepe9A B MMp MHOM_. 0 nepeXOAe H3 >KM3HM ((&-'f4HP MHOM» y ApeBHHX 6b1nM pa3pa60Ta- Hbi Y'4eHHJI M 4>Hnoco4>cKMe HanpaBneHHJI, HanMcaHbI 3arpo6HWM MMp JJ.o Hawero BpeMeHM Aowna 3H8MeHMTaR «KHMra MepTBbIX», - B KOTO onMC8HbI OCo6eH- HOCTM ';aarpOOHOf'O MMpa..  ero OOMTaTenefi. TaK TO npM- )I(J.13HeH,Hoe npMrOTOBJ1eHMe I< CMepn1 M ClpOMTel1bCTBO YCbl- nanbHM He 6bU1M A11R en1nTRH eM-TO HeOObI..HblM. 318 
TpaKTaTW; MYApeqbf 06yHanM «MC- TMHe» M «npaBMJ1aM yxoAa M3 >KM3HM» CBOMX Y'feHMKOB. OAHaKO Ha.roOJ1bWee BHMMa- HMe noroMKoB npMBneKna caMaR 60J1bWaJl ycblnanbHH - nMpa- MMAa Xeonca. nOCTpoMTit TatcylO nMpaMMAY Aa>Ke cospeMeHHblM MRBDOpy.*eHHblMcaMOM MO.U4HOM TexHMKOM, npeACTaaMeT- CJI B ycnOBMRX npwHM O'4eHh.TJ- >KenOM no BbinonHeHMIO 'feM. TeM nOHJlTHee noypRceHHe M MC- KpeHHYAM8JIeHMe .HautMX COBpeMeHHltKOB npM neploM >Ke 3Ha- KOMCTBe C nMpaMAOM, KOTOpa" Bne'4amAeT He TOJ1lt<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 nepeMeaTb no nececy RycTblHM BAonb oc- HOBaHM" nMpaMMAbI, HO M nOAHMMaTb Ha BblCOT}' nTM'Ibero nonera. K TOMY >Ke nopa3MTenbHO M TO, '4TO OWM YMeJ1M nOArOHRTb Apyr K APyry rpoMaAHble mbl6bf M 06nMOB0'4Hbfe nJ1MTbI C oeHb BbiCOKOM TO'4HOCTblO. K ApeBHMM 3OA'4MM HeBonbHO npoHMKaewbC1I60nbwMM YBa>KeHMeM 3a MX KOnOCCaJ1bHblM TpyA M Bblpa>KaeWb MCKpeHHee YAMBneHMe no TOM}' nOBOAY, '4TO enmTJIHe BnaAenM TaKMM BbiCOKMM CTpOMTenbHblM MaCTepcTBOM. TaMHa nMpaMMA COCTOMT M B TOM, '4TO ApeBHMe erMnTJlHe npM MX COOPY>KeHMM, KaK nonaralOT, B Ka>KAYK> BOnJ10TMn HeKHM MMCTM- '4ecKMM pyx. 3Ta TaMHCTBeHHaR CMna 06eperaeT nMpaMAbI AO Ha- 4HcnOS8f1 8CrponorHlf... .YaAHw nMpaMMA- CyAb6bt noceTKTeneM nMpaYM.O,boI, KaK n- 110, CKl18,D,b1Ba11ne- 'fa11bHQ. O MHOrMe tlC- CJ1eAOBaTeJ1M, OOMCblBa- M.O,boI, HapeIC8K>T *.. 00K8 He06bRCHMMbIe CTEJ'fe- HMR 06cTOSfTenbCTB «T8MHaMM m1P8M.. 319 
rnBSB 7 WMX AHeM OT npOHMKHOBeHHJI B HHX Koro 6.., TO JIM 6..,no, KTO Hapy- waer nOKoM yconwero u,apJl. Ha'4HHaJI OT BceB03MO>KHblX «Hen pO- weHblX» noceTMTeneM - «OXOTHMKOB 3a u,eHHOCT"MM», pa3nH'4HblX rpa6HTeneM M MapOAepoB - M 3aKaH'fMBaJI npOHMKHOBeHMeM B nM- paMHAbi apxeonoroB M MCTOpMKOB All" Hay'4Horo M3Y'4eHMJI MCTa- pHH H t<ynb-rypbl npeAKOB. no MeTOAHKe coopy>KeHM$I Ka>KAaJl H3 nMpaMMA npaCTa M BpOAe 6b1 He npeACTaBnJleT C060M HH'4ero oco6eHHoro -- 3TO coopy>Ke. HMe H3 npaBMnbHo 06TecaHHblx npJlMoyronbHbIX 01..,6. BHyTpM nH- paMHAa MMeeT 1-2 He60nbwMX 3aJ1a M HeCKonbKO Y3KMX npoxo- AOB. Ha nepBblM B3rn$lA, Tat<y1O nHpaMMAY COOf)YAMT nJ060M pe6eHOK M3 Mrpywe'4HblX Ky6MKOB. B03MO)KHO, «MarM'4eCKaJl» CMna nMpaMM- Abi 3aKnIO'4aeTCJI B TO'4HOM copa3MepHoCTM reoMeTpM'4ecKKX BenM- '4MH, KOTopble ApeBHMe erMnTJlHe «n03aMMCTBosanH y He6a» (KaK TyT He BcnOMHMTb 0 «'4MCJ10BOM acrponorMM»!), - B CTpOroM COOT- BeTCTBMM J<a)t(AOM rpaHM nMpaMHAbI, ee BbiCOTbi M OCHOBaHM$I yr.naN BXOAa conHoM M KOCMM'4eCKOM 3HeprMM Ha ee BepxywKe M nno- U4aAM «KOHLteHTpaLtHM.'HeprMM» Ha OCHOBaHMH nMpaMHAbi. nHpaMMAa C «30nOTbiM Ce'4eHMeM» HaKannMBaeT B ce6e «Ion. we6HYlO COJ1He'4HYIO 3HeprMIO» M Ha'4MHaeT 06J1aAaTb AeMcTBM- TenbHO He06JlCHHMblMM cOBpMeHHoM HayKOM '4y- AOAeMcTBeHHW4M CBOM- CTBaMM (c,... cooTBeTCTBY. IOU4MM pa3AeJ1 KHMrH). An" peanM3au.MH CBOMX «Bon- we6Hblx Ka'4eCTB» nMpa. MMAa AOn>KHa CTO"Tb Ha onpeAeneHHOM MetTe (CO- &M08H8pr8TMKa yraeP*A88T OT reOMeTpVleVlX BenVlVlH nVlp8MVlAbI 3aBVlo.1T ee 3Hep- reTVI'feCKaA CylitHOCTb. 3Ta . Cyl1ttiOCTb MO)l(eT OblTb- AeH. CTBVlTenbHO ytiVlK8J1bHOM VI nop83V1TenbHOM. . 320 
BpeMeHHHKH Y'4MTblBaIOT ee paCnOnO>KeHMe B reOnaTOreHHOM 30He, B COOTBeTCTBMM C pacnpeAeneHMeM 3HepreTH'4eCKOrO nOnJ' 3eMnH) H C OnpeAeneHHOM opHeHTaHeM no CTopOHaM CBeTa. He HMeJI B03MO>KHOCTH paCKpblTb '4HTaTeJ11O «oc06b1e JPOMTeJ1b- Hble ceKpeTbI» nHpaMHAbl (BCJ1eACTBHe He3HaHHJI TaKoBbIX); npMBe- AeM nHWb HH4>oPMalO, H3seCTHYlO cOBpeMeHHHKaM. 4MTaTenb MO- >KeT caM oeHHTb, HMelOT nH 3TH '4HCJ10Bble eTpbl nHpaMMAbi Het<y1O «MarH'4eCt<y1O HarpY31<Y» HnH B HHX Her «HMfP oco6eHHoro». 3aMeTHM TonbKO, '4TO eCTb COBpeMeHHble 4>MpMbI, KOTopble co crporMM Y'feTOM pa3MepoB nHpaMMAbi Xeonca BblnKaIOT ee YMeHbweHHyIO Ko- moo pa3MepoM '4yrb 60nbwe naAOHM. OHM yrBep>KAaIOT, '4TO 3Ta KOnHJI nMpaMMAbl Xeonca 06naAaeT «3HeprerH'4ecKoM MarMeN» M HeMrpanH- ,3yeT BpeAHYIO 3HepreT11t<y KOMHaTbI (KBaPrM})bI, o4>Mca)<,.ecnM B HeM HaxOAMTCJI. 3roTOBHTeJ1M peKOMeHAYJOT KonHIO nMpaM opHeHT11- poBaTb onpeAeneHHblM 06pa30M: ronorpa4>H'4ecKMM Kpy>KOK Ha OAHOM M3 CTOpOH nHpaMHAbI AOn>KeH 6bITb 06paU4eH K ceBepy. TaK, KaKOBbi >Ke peaJ1bHble pa3Mepbl 3HaMeHMTOM H TaMHCTseH- HOM nHpaMHAbI? BbiCOTa nHpaMMAbi Xeonca 146 MeTpos. OHa HMe- eT '4eTbipe cryneH'4aTbie rpaHH, A11MHa Ka>K.Q.OM B OCHOBaHHH pasHa 231 M. Yron HaKl10Ha Ka>K- AOM rpaHM CTporo OAHHa- KOB M COCTaBnJteT 52 rpa- AYca. Ha cTpoMTenbcTBo nMpaMMAbi nowno OKono 2,3 MMnnHOHa KaMeHHblX 6J10KOB co cpeAHHM BeCOM 2,5 T. nMpaMHAbi He MMenH OKOH M 06nHOBbiBanHCb nonMpOBaHHblMM nnHTaMH. '-IHcnOB8R acrponorHR... no  .BCDIM AOqtoBnaI nMP8M Xeonca eMMa Ha CO/1H. OTJ)CVlCaSt CBeT seeM... CBOMMH CTopoHaMM. OAHaKO B 60nee  BpeMeHa o611H- HbIe MMTbI C nHpaMH,AbI pacraH A11st MCnO/1b3OBaHHA B ,Qpyn.1X COC>py)KetMAX. 321 
rnasa 7 nHpaMMAa OOCTp<>eHa 4,5 TbtC. neT Ha3aA. no C&e.qeHMRM rpe'4ec- KOro MCTopHKa fepoAOTa, >KHBwero Ha 2 TbiC. neT n03>Ke, CTpOMTenb- Hble pa60TbI MMnHcb 20 neT, M B HMX nOCTOJlHHO npHHMManM. ac- TMe 100 TblC. eJ10BeK. ApeBHHe erMnTJlHe He OCTaBHnM CBeAeHHM 0 npMMeHJleMbiX MMH MeTOAaX crpOHTeJ1bCTBa. n03TOMY HaWM COBpe- MeHHHKH TonbKO CTpOJlT AOraAKM, KaK, MTblBaJl B03MO>KHOCTM ApeB- HMX enmTJlH, MO>KHO 6b1J1o COOpYAHTb roponoA06Hoe PYKOTBOpHoe '4YAO. 60nbWMHC'TBO CXOAJITCJI Ha MHeHMM, '4TO 6b1nM Mcnonb30BaHbI 3aKOHbI pblarOB, pa3J1M'4HblX wapHMp08 M KonOBopoTOB. TaKaii >Ke TeopMJI 8b1CKa3b1BaeTCJI B >KYpHane «Ha rpaHM HeB03MO>KHOro» B ClG- The «KaK CTpOMnMCb erHneTCKMe nMpaMMAbf» (1999.  10). 4eJ10Be'4ecTBO HapoM HCnblTblBaeT '4YBCTBO rQPAoCTM ]a CTJ>PM- TeJ1bHble AOCTM>KeHMJI ApeBHHX erMnTJlH, npoJlBneHHble MMH nOTpJlca- IOU4He B03MO>KHOCTM '4eJ10BeKa M OTHOCMT nMpaMHAY K OAHOMY M3 CeMM '4'jAeC CBera. nMpaMHAbi CTOJIT B nycTbIHe, BOKpyr necOK. MHOroTOH- Hble 6noKH HY>KHO 6b1no BblCe'4b M3 6nM>KaMWeM ropbl M AOCTaBMTb K MeCTy crpoMTeJ1bCTBa. Y>Ke caMa 3Ta «AOCTaBKa» cOnpJl>KeHa C He- MblCJ1MMblMH 4>H3H'4eCKMMM YCH- nMJlMH TblCJI'4 nIOAeM. Aanee, H3 AoCTaBneHHblx «Ky6MKOB» Hy>KHO 6b1no COOpYAMTb nMpaMMAY. no HaM60nee pacnpOCTpaHeHHO BepcMM, KaMeHHbfe 6nOKH nOAHH- ManMCb BBepx BonOKOM no Ha- KnOHHbfM HaCblnJlM (naHAYCaM), KOTOpbl6 no Mepe HapaU4HBaHHJI nMpaMMAbi nOACblnanMCb Ha HY>K- OKecyl1ltTM3M .-tepa .. cerOAHA Ecn rOBopTb 0 c03Aa- H npaMAbI. TO. KO- HeHO. B Hee B11O)KeHa 3Hepr MHorMX TblC nAe.aC03A8HH ....M.... ..06naKO 3Hepn-wl-  MO)KTb TO OCHO- BO. Ha KOTOPO npoB nATC «MareCKe CBOHCTBa- npaM"'Abi. 322 
l/ucnoBaR aCTpOnOrUR... HYIO BblC01Y. TaJO(e HaCblnH MomM B03BOAHTb co Bcex '4eTbfpex CTO- poH npaMHAbi HnH TonbKO C OAHOM ee CTOpOHbI. 6H03HepreTKa TaK>Ke yTBep>KAaeT, '4TO npeAMeT rpYAa M3nY"fa- eT Het<y1O 3HepreTMect<y1O cHny, BnO>KeHt:lY.o B HerO cteJ1J1MH. 3ra 3HepreTM'4ecKaJl CHJ1a npOJlBnJleT ce6J1 f1PM 06l1-'eHMM; KOHTaKTe C opYAMeM rpYAa. ., 06beM 3arpa'4eHHOrO pY"fHoro TpYAa np.,.oeonMcyeM - OH KOnOCCaJ1eH! Aa>Ke eCJ1H npeAnOnO>KHTb, '4TO HaCbN'Ib B03BOAHJ1aCb - TonbKO C OAHOM CTOpOHbI nHpaMHAbI, TO 06'beM neCKa COCTasnJln npHMepHo 10 MMnnHOHOB Ky6oMeTpOB. Aa>Ke eCJ1H 3TOT OObeM M3- MepTb 5-TOHHblMH caMocsanaMH, TO HX nOTpe6yeTcJI ABe TbfCJIqM! Aopora no HaCblmt YKpennJlnaCb AepeBftHl:fblM Hacn1J10M, YaK KaK B 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 mpaMHAbi enY'4aJ1MCb HeOAHOKpaTHO, pa3MblBaJlH necaHYIO Ha- Cblnb, H ee npMXOAHnOCb BOCCTaHaenHBaTb. MeAMKH M 4>M3H0J10rM nOAC'4HTaJlH, 4TO ACI>Ke Al1J1 TOJ1nbl OT60PHbIX CHnaeM no,qbeM TJI>KeJ1bIX 6J10KOB BbiCOKO eBepx no HeCKOJ1bt<y pa3 B AeHb Bblwe '4eJ10BeCKHX B03MO>KHOCTeM (n03TOMY HeKOTopble aBTD- pbl H BblCKa3b1BaIOT rHnOTe3b1 0 nOMOU4H HHOnnaHerJlH). Aa>Ke npocro HaJlerKe,6e3 rpy3a '4eJ10Bet<y HecKOJ1bKO pa3 B AeHb nOAHJITbaI Ha 106- MerpoBYJO BbiCOTY - 3TO M3HYPHTeJ1bHblM 4>H3HecKHM TpyA. nOCJ1e 3aBepWeHHJI CTpoHTenbCTBa nHpaMMAbi «OTCnY>KHBWHM CBoe» neCOK HaAo 6b1no t<yAa-To y6paTb, '4TO Tpe60BaJ10 TaK>Ke He- MaJ10 TPYAa M BpeMeHH. KaK Bce npoMcxoAMno B AeCTBHTeJ1bHOCTM npH CTpoHTeJ1bCTBe nHpaMHA H KaKHM 6b1n cnoc06 nOADeMa KaMeHHblX 6noKoB? Kat<y1O 323 
rnSBa 7 B03MO>KHyK) CTpOHTenl>HyIO MeTop,M- tfj AJ>eBHMX erHnTJlH MO>KHO B3J1Tb 3a OCHOBY, 'fT06b1 HaWM AOraAKM 6b1J1M KaK MO>KHO 60nee peaJ1bHblMM? npH nlO6b1x npeAnOnO>KeHMJlX eCTb onaCHOCTb HeAOOLteHKM 3HaHMM M B03MO>KHOCTeM BeJ1MKOro ApeS He- ro HapoAa. Henb3ft He Y'lHTblBaTb, '4TO ApeBHMe erMnTJlHe 06naAaJ1M rny60KMMH TeopeTM'4eCKMMM j,i npaKTM'4ecKMMM 3HaHMJlMM no pa3HblM HayKaM. TaM. OHM He TOllbKO ' BnaAenM MCKycCTBOM CTpOMTenbCTBa, HO XopOWO 3HaJ1M MaTeMaTM- Ky M acrpOHOMMIO, npeKpaCHO BJ1aAenM MCKyCCTBOM H3roToBneHMJI 6poH30BblX H 30nOTbiX npeAMeTOB, 3HaJ1M MexaHMI<Y. B03MO>KHO, OHM 3HanM 60nee pal4HOHanbHbfe cnoc06b1 nOA'beMa TJI>KeCTeM Ha 60nb- WytO BbiCOTy. BepoftTHO,pa3YMHO o6oMTH BHMMaHMeM M APyrMe TeopMM CO- 3AaHM" erMneTCKMX nMpaMMA. B 60nbwMHCTBe enY'faeB OHM OCHO- BaHbI Ha OTpMHMH caM B03MO>KHOCTH C03AaHMJI HCKyCCTBeH HbiX rop - nMpaMHA C Y'leTOM CJ1a6b1X TeXHH'4ecKMX B03MO>KHOCTeM TOM ApeBHeM 3nOXH. AeMCTBMTenbHO, BJ10>KeHHblM ApeBHMMM erMn- TJlHaMH rpYA HaCTonbKO orpoMeH M HepeaJ1eH (XOT" caM <J>aKT pe- aJ1bHOCTM CTOMT nepeA ma3aMM B BMAe BeU4eCTBeHHoro AOKa3aTenb- CTsa - caMHX nMpa.), HaCTonbKO rpYAHO OC03HaBaeM, TO HaxOAJITCJt MCCJ1eAOBaTe!lM, OTBepralOU4Me nMpaMMAbi KaK nnOA TpYAa '4enOBeKa. QHM C'4HTaIOT, O nOMOU4I> erHnTJlHaM 6b1J1a AaHa «CBbI- we». OAHflHt3 BapMaHTOB TaKOM nOMOU4M Ha3b1BaIOT Y'laCTMe MHO- nnaHeTJlH. B «AOKa3aTenbCTBO» npMBOAJIT HepeaJ1bHOCTb 0CYU4eCTB- "eHM" ApeBHHMM enmT"HaMM Ha'4aJ1a crpOMTenl>CTBa - AOCTaSKY MHorOTOHHblX mbl6 OT 6nM1KaMWMX rop no nycTbltte K Meay CTpOH- ECTIt MtteHMe HeKOTopble COSpeMeH- Hble Y'fE!HbIe nonaralOT. TO er""mSUfe MCnonb- 3QBaJ1"" He KaMeHHbIe 600K"". a 6eTOH. 324 
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rnaBa 7 YpOBeHb HaKonneHHhlX '4enOBe'4e- CTBOM 3HaHHM, AOCTH>KeHHM  OWH- 60K Ka>KAoM 3nOXH BcerAa none3eH nOTOMKaM. n03ToMYTaK Ba>KHO 06ec- ne'4HTb npeeMCTBeHHOCTb nepeAa'4 3HaHHt1 Me>KAY nOKOneHHJlMH nIOAeM, Me>KAY pa3HblMH 3noxaMH. 3n1 3Ha- HHJ1 nOKa3h1SaIOT ypoBeHb pa3BMTHJ1 06uteCTsa. KpoMe Toro, 3cTa4>eTa 3HaHHM nOAXBaTbiBaerCJI H pa3BHBa- eTCfI Ka>KAbiM HOBblM nOKOJ1eHHeM, nOAHMMaeTCJI Ha HOBYIO BbiCOTy, C KOTOpOM 60nee peaJ1bHO OeHH- BaeT Hawe npownoe H 6YAYU4ee. OAHaKO 3aL4eM nOTOMKaM nepeA(ikaTb roRbKO '4aCTb 3HaHH (OrpaHH- '4eHHbIX cnoco6oM r1epeAa'4H, HanpHMep pa3MepoM MeTaMM'4ecKOM AOCKM HnH eMK.HH4>oPMaHoHHoro Alo1cKa), ecJ1H Mbi caMH AO>KHSeM AO BHYK0B, a MQJItC'eT 6bITb H AO npaBHYKoB (c Y"IeTo nOCTOJlHHO YA11HHJlIO- uteMCJI CpeAHeM_ npoAomKkTenbHOCTH >KH3HH), H nH'4HO CMO>KeM nepe- ACITb HM CBOH 3HaHMJI? Aa H B HanHcaHHbIX '4eJ10Be'4ecTBOM KHHrax (60J1b- WHHCTBO KOTOpblX 0611\E!CTB.OM COXpaHJleTCJI) AOCTaTO'4HO nOAP06Ho H31IO>KeHbI AOCTM>KeHMJI HaweM 3nOXH. 3a'4eM Bbl6HpaTb cnoc06b1 nepe- Aa'4M TaKMe, '4To6bI Ha HMX He nOAeMCTBOBano BpeMJI, 'lT06b1 nOCJ1aHHe 6b1J1o M'4HBO K&  H3BeCTHbiM cnoco6aM ero pa3pyweHHJI? Ha 31M BonpOCbI MQ,ryT 6b1Tb pa3Hble BapHaHTbI OTBeTOB. HanpH- Mep, nOTY '4TO '4enOBeeCTBO onaCaeTCJI HeO>KMAaHHhlX KaTaKJ1M3- MOB,. «KP CBeTa», HaWeCTBMJI «HHOJ1naHeTJlH» M eU4e KaKHX-TO HeBepOJlTHbiX H lienpeAcKa3yeMbix 6eA. TaKHe peaJ1bHble yrp03b1 '4eJ10Be'4eCTBY Y>Ke 6b1nM KaK CO CTOpOHbI KOCMoca, TaK H Ha caMOM nn-aHeTe. HanpMMep, «npoMaxHYnaCb» KOMera fanneJl (nOCJ1eACTBHII KOI:.'eKC nOBeAeHMR . Ecmil HHonl1aHeTS1He AeCTBHTel1bHO cy- LLLeCTByJOT H HMelOT CBO KOAeKC nOBeAe- HHS1. TO 3TO nOHS1THO, TaK KaK HTO nOA06- Hoe CYLLLeCTByeT H y KOCMOHaBTOB 3eMI1H. 330 
"'",cnoBaR aCTpOnOr",R... B3pblBa OT TaKOrO CTOnKHOBeHMJI TpyAHO ce6e npeACTaBMTb!), yr- po3a MHpOBOM JlAepHOM BOMH (0 nOCJ1eACTBMJlX MO>KHO CYAHTb no KHMraM H 4>HnbMaM 4>aHTaCToB, nOKa3b1BaIOU4x, '4TO MaJ10 KTO H '4TO Ha 3eMne yLteJ1eeT) M TOMY rtoA06Hble crpaCTM. Mpa'4Hble MblCJ1M HaBOAJIT Ha TO, '4TO neAa'4a nOTOMKaM «BM- 3HTHOM KapTO'4KH HHTeJ1neKTa 3nOXH» - '4aCrH HaWHX 3HaHMM - MOJKeT OKa3aTbCJI HenMW.HHH. ECJ1H '4enOBe'4ectao  CMO>KeT BbI>KHTb, TO n Hawe nocnaHHe AOCTaHeTCJI «pa3YMHblM eCTBaM», KOTO- pble npHJ1eTJI'f Ha 3eMJ11O MJ1M nOJlBJlTCJI Ha HeM BHOBb, - nOCKonbKY npMpOAa TaK nlO6MT nOBTOpJITb CBOM Kpyro06opoT >KM3HH (BcnOM- HMM HC'4e3HOBeHMe ATnaHTMAbi H HOBoe B03pO>KAeHMe JKM3HH)... OKa3b1BaeTCJI, onaceHMe B03MOJKHblX rpareAMM B tyAb6e 'fe110Be'4e- CTBa 6bi110 He TonbKO B Hawy 3noxy, - 310 nOpa>KaeT M '4MBaeT. B MCTOpHM '4enOBe'4eCTBa He Mbi OAHH HaCTonbKO npe,rwcJ4bTpMTe1IbHbI H OCTOpoJKHbI (<<3AOPOBblM» necCHMM3M BCerna ycneWHO npoTMBOCTO- M «6e30mJlAHOMy» onTMMM3MY) H AOCTOMHO OLteHMJlM Ba>KHOCTb ne- peAa'4M 3HaHHM nOTOMKaM.  ApeBHMe nlOAH B AaneKMe MCTOpM'4eCKMe BpeMeHa AenanH nOA06Hoe, Me'4TanH 0 B3aHMonOHMMaHMM C nOTOMKa- MM. npHeM cnoc06 H 4>oPMY nepeAa'4M 3HaHMM OOTOMKaM OHM M36M- panH pa3Hble. O 6bi11M He TOJ1bKO MeTa11J1M'4ecKaJl AOCKa, nanMpyc HlIM HacKanbHblM pHcyHOK C nerKO on03HasaeMblMM CMMBonaMM 4>oPMyn MIIM pe3YnbTaTOB paC'4eTa, HO M Momo 6biTb KaKoe-TO coopy>KeHHe MIIM npeAMeT, CTOpoHbI KOToporo COOTBeTCTByIOT M3BecTHM '4HcnOBbiM 3Ha- '4eHHJlM, T. e. HH4>oPMHpylOT 06 ypoBHe 3HaHMM cBoeM 3nOXM. OAHy M3 TaKMX nepeAa «HHOM MH4>oPMaLtMM» Ai111eKHx npeAKoB Y'4eHble 06- Hapy>KH/lH B TaMHe enmeTCKMX nMpaMMA. COnHe'4HaJt CHCTeMa CBOMMH pa3MepaAM nOAaBnJteT 06beM 3eM- nM, a KOCMOC - pa3Mepbl COnHe'4HOM CMCTeMbi. B03MO>KHO n0310- MY erMnTJlHe, Hay'4HblM ypOBeHb 3HaHHM KOTOpblX B TO BpeMJI Ha- 331 
rnasa 7 MHoro npeBbfWaJI 06DeM 3HaHMJI Ha- POAOB ApyrMX CTpaH, OCTaSMnM CBO': MM nOTOMKaM MMeHHO acrpoHoMM- '4ecKMe '4McnoBbie «lnO>KeHMJI. B nMpaMMAbi. npMeM nOKa3anM 8 MenOBbiX AaHHblX 60nlitwylO TO'4- HOCTb pac-.eTOB, BnonHe COM3MepM- MbIX C COBpeMeHHblM ypOBHeM. Ha paBHMHe 6nM3 r M3W, HeAaJIe- KO OT KaMpa, B03BblWalOTCJI TpM nM- paMMAbI, cnerKa pi3JIMalOl14MeCJI no pa3Mepy. Kpyn+teMWalt M3 TpeX nMpaMMA paCnOllOJKeHa Ha ceaepe, HanpoTMB AeJ1ltTbI HMJ1a, M CMM- 8O.RM3Mpyer CMy npMpoAb!. BTOpaJI HaXOAMTCIt Ha paCCTOJlHMM no- nera crpenw OT nepaoM 14 CMMBOJlM3MpyeT ABM>KeHMe. 1peTbJl paC- nonoJKeHa Ha paCCTORHMM 6pocKa KaMHeM OT BTOpoi 14 JlBnJleTOJ CMMBMOM H". 80Kpfr nOCJIeAHeM - BenMKOM nMpaMMAbi - pacnonaral)tClt 1»M paMMAW MeHltlllero pa3Mepa, a OrpOMHIlle pa3BanMHW QMtteiI HeriOAaneKY yg3WBaIOT, '(f() PJlAOM CTOJina M. Ce.AbMaJI nMpaMMAiI. He coxpaHMBlllaJlCJI AO HaJUMX AHeM. B nocneAHee BpeNR MCCJleAOBareRM ony6nMKoBanM AaHHble 0 pe3ynbTaTax TO'fHiltX 06MepoB BenMKoi nMpaMMA'" (HanpMMep, n.M. 3a6PDAM"" 1999). MareMaTM'feCKaR TO'4tiOCTb nOC1'pOitKM CBM- AeTeJ1T 0 eo&er;weHcrae n03HaHMM enmTJlH 14 AOCTM>KeHMM MMM 60nw»0r0 MCKYCa B cIJybHOM CTpOMTE!11bCT8e. Ta yron MeJKAY KU(AOM 143 rpaHei 14 nnOCKOCTbIO OCHOBaKMJt OAMH .. TOT)lCe ;':'1  1 MMR)'T! 14 ceKJHA. OTHoweHMe nepMMe1pa OCHOBaHM.I K IlweoTe COCTiIBJ1AeT 3,14159, T. e. paBHO '4MCJJy p. «'iMCJM>BaH acrpanorMR» nMpaMMAb' 3T'MM He orpaHM'4MBaeTCJI. Oc- HOBHOM eAMHMI.&E!M M3MepeHMR, KOTOpyIO MCnonb3OlanM npM CQ3Aa- B"...T".1OIIo\8tI MaC- CMIIHOCTIt nMINIMMA onTBOpAeT - HOCTb M tte3blOne- MOCTb, no,AaBmteT CBO- eM ropor1OA06HocTblO, HeCOM3MepMMoM C 4>MrypoM 'teJ10BeK8. 332 
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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 - ConHeM, nYHOM H C03Be3AHJI- MM; 3eMnJl nJlTepM'4Ha B o6naAHMM 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 OTnMalO- U4HM OT eTbipex 3neMeHTOB (.Map01HanbHbtM 3neMeHT.): nnaToH (427-347 n: JJ.O H. 3.) ynoMMHaeT 0 HeM B TPaKTaTax . TMMeM. M .nocne3aKOHMe., ToTenb (384-322 n: JJ.O H.3.) - B TpaKT8Te.0 He6e.. O,AHaKO MX B3rnAJJ.bl He noJJ.- JJ.ep)l(anM APY018 rpeMe 4>Mnoco<I>bI. M 60nee npM3HaH- HOM B EBpone OCTanaCb eTbI- pex3neaA CMCTeM8 .co- TBOpeHMA MMpa». 354 
TSHHble CHnbl KpHTepHeS APyrHe nOcrpOeHHJI, Hcnonb3yeMbie B HYMep0J10rHH. HanOMHMM A11J1 cpaBHeHMJI. KMTiMCKMe 4>Mnoco4>bI npH3HaBanM eneA,YlOutMe 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> ApeBHOCTH npH3HaJ1 Ka)t(AbiM M3 ero KOMnOHeHTOB B Ka'4eCTBe eAM- Horo 06uteMHpOBoro cy6CTpaTa: cJ»anec - BoA,Y, AHaKCMMeH- 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» (YeHMe 0 CMMBOJ1aX M '4MCJJaX. c. 288). npH HeKoTopoM 3TM0J10recKoM cxoACTBe KMTaMCKoro M rpe- '4eCKOro repMMHa «3neMeHT» MMeeTCJI ern cS»u1ocKoe 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» CB3aH C BOAOM nMWb 4>YHK4HOHaJ1bHO M MMeeT pe30HaHc C TalOtMM nOHIITMAMM, KaK BeC- Ha (BecHoM TaeT CHer, npeBpalqaACb B BOAY), BK (MHOfMe peKM Hecyr CBOM BOAbi C BOCTOKa C Y'feTOM BpatijeHM$I 3eMnM) M T. A- f pel.lecKMe M KMTaMCKMe Ha3BaHMJI 311eMeHT08, cocraBRH MM- po3AaHHe. a TOI.fHee npoJlB11eHMe )f(M3HM, He  OOHMMaTb y.JK0, TonbKO 6yKbHO. 3ro, KaK H '4MCJIa, TOJKe CMMBOJItNeCKMe  CKMe KaTefO()MH. B OT11MtfMe OT KMTa fJ)e'M!CKMe 4Mmoc nOA 3neMeHTaMH NMP03AilHHJI 6anee n0APi!3YMeBanM MaTepMaI1bHl1Ie co- CTaBnJlIOU4Me cyTM BeU4eM. 3TM pa3I1tNM$! 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- Hble norpe6HOCTM H<IQHH, roBOpMT M paHqy3CKMM CMHOnor A. Mac- nepo (1950). OH nMCaJ1: «nJtTb 3JJeMeHTOB 6wnM B3J1'1D1 143 OOwMpHO- ro Ha60pa 'iMCJ10BbIX lO1accM4>MKa4MM BCeX BeU4E!M... K KOTopbIM 6bU1 OCo6eHHO..CKnOHeH KMTaMCKHM cIJonbKllOp... OHM CU3a1lM see nJmt- '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  MT. A.).nM60 B MX pa3- I1M'fHbIe CBOMcT8a. nRTb,Q06- po -OCHOBa MOJHl11" M nJITb OrHOweHMM ..- OCtiO- sa 06ytecTBa - cyn nRTh 3neMeHTOB, paCCMaTPHBae- MbIX C TO'4KM 3peHMJI 3TMKM, TaK)I(e KaJ( mob opaH... cyTb rbn'b 3neMeHTOB C KOCMO- OOrM'feCKOM KH :JpettMJI».  3peHMA  Ha CMCTeMY CTpOeHHSI MMpa M . w nyTM ero n03HaHMJI HatWIa mpa>KeHMe " B eBponeMCKMX ""'Mrax MyAJX>- 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, HbI, 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, cnoco6cT8e Ma- TH3aH 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 Ka66anMCTMeCKHe paC'4e- TbI, npeACKa3b1BalOU4He KOHe'4HbfM pe3ynbTaT B3aMMOAeMCTBHJI BbI- AeneHHblX «3nMeHTOB». 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 BOM rpaKTaTe ..{Mtib-Lt3bI.. nsm, 3neMeHTOB CMMBOnK3&o1PYlOT «nSlTb nocro- RHClB": ryMaHHOCTb, cnpaBeA- I1MBOCTb. 611aronpMCToMHOCTb, paayMHOCTb .... 6narOHa,Ae)l(- HOCTb. B 3M....HoM 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» (nTHyronbHOM) M 4C3Be3AHOM» neHTarpaMMbI. nOA'4epKHeM, '4TO TepMMHbI ycnOBHbI. nOCJ1eAHH TepMHH npI4eMJ1e'" AllJI BblAeJ1e- HMJI OCo6eHHOCTM HanpaBneHHJI C'4HTblBaHHJI (no nY'4aM 3Be3AbI), TaK 358 
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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- 3PytOT reoMerpecKe  11- HeHble $OPMYnbl, CTOI1KOBbi. BaR He TOl1bKO npoH3BCJ,,4HYKJ OCHOBY  HanpasneHHfI AB)Ke- HR 3Hepr B $OPMYl1e B u.e- 110M; HO  KBl.lecTSO CBA3 Me)K- AY OTAenbHblM 3neMeHTaM. 361 
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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 CHTaIOT, '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 3aTbI OT BCS1KX 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 nwe 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. 3HepreTHeCKOM 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 MarecKlilX AeCTB J1YHa AOn>KHa ObITb OTAeOOHa OT Koneca <J>oPTYHbI  ObITb npMObI- BatOllteH (paCTYli'e). 8 A11 3/lbiX - HeH8 C HM  OblblB8tOU4e. 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 HOe- 30AMa- KanbHble 3HaKH 6yA'fT BOCXOAJIU4MMM. KOCMM'4eCKHe 3HeprHM 3aTpYAHJlIOT HnM 'Ka>KaIOT KOnAOBCTBO npM CJ1eAYIOU4HX cMTYaLtHRx: 1) KorAa l1YHHaoAHTcJI 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», - CHfaeT 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 6naronpSnCTBYK>T A06- pble nnaHeTbi  oco6eHHo HaXO)t(AeHe IOnTepa  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"* n8I1"eTa. CMJ1bHee. MMe}1 b nMWb 03HaKDMMTb "MTareM C MexaHM3MOM McU14feO(MX AeMcrBMM, aBrop ynya<aer MHorMe AeTaI1M. a TcUOKe He nl*BOAMT ra6- nM BpeMeHM ynpasneHMJI lWI(AoM nnaHeroM CBOMM 'W:OM tyrol<, AHeM HM 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 noepn- 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 Ta11H. 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 nMTaTb B KHMre namoca. AnJi YAoeneTBopetfM" nOOonWTCTBa '4I4TaTeneM npMBeAeM flMWb HeCKOJIbKO 3aMHMi 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. HanpMep 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 neBHTaMIO (CB060AHoe napeHHe HaA ceHOM), 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&o1BeAeMA11np&o1MepanepeeHb«&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 (ceHT6pp) 3yp&o1enb · CKOpn&o10H (OKT6pb) 6a6p&o1eJ1b . CTpene (Ho6pb)"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 HaaTla 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 3HaHHe 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 HM3we 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 ConHeHOM cMCTeMbI, BH- AHMblX HeBoopy>KeHHblM ma30M npM HopManbHOM 3peHHM. B eHrpe 3Be3AbI pHcylOT ConHe 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, BblnOI1HIO.-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 nOMealOT MY3b1Kanb- Hble HOTbI, KOTOpble COOTBeTCTBYIOT MeTaJ111aM. 1306pa>KeHHe Ka>K- AOro acrponorHecKoro 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),AObHO 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'fCKHe 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 - nonaraT "!arH. Ha 3TOM OC- HOBaHa 3aU4HTa 3HeprHeM KOCMoca CBoero 3HKa, 'nl1aHeTbI, MMeHM, KaMHJI OT «3HepreTH'4eCKOM HH4>eK4HM» H 3arOBOB. rpaHMbl .snacTM MarM"IeCKOM cl>Mrypbl 4HTaTeJlb, BepOJlTHO, 06paTHJ1 BHHMaHHe Ha TO, '4TO BHeWHue (He- 6eCHble) CBJl3H rpa4>MecKoM 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 >KH3H 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. MarHecKaJl4>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 nYOM 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, rpaHMa Me>KAY-AOOM H 3nOM, npM'4eM B K66anHCTH'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 TOmo EW1HCTBO He6a (tcpyr)  3eMnH (3Be3A8), COOTBeT- CTBeHHO Q1MB011 H86ecHyto c<I>ePY H nsrTD rnas- HbIX 3eMHbIX MaTepHKOB, HO H CXeMa nepe.a,aH.Q1MB011H- 'fSCKOO C8s:I3IiI 38K0Ha 1lOC1J>O- etMSI MIo1I)a,  't8I1OBe- I<a. 3ro He TOnbKO CXeM8 OT- bHOrO HO.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&>1palOero 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 Haan 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 HaaJ1 '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 nanltM, 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 Mecfco CBMCTOM HaaJ1 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 OIOCYnTM3MY, 3Be, HSnpaBJ1eHH8R 0.0.- HIltM KOHl4C)M BBepx, IItCnJ1b- 3yeTCR ATlR M8rM'4ecp.e- CTBIitH lit nm 3arOBopoB. «3HepreTMecKO MH$eK- 1It. VI HT. 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 - 0603H8aIOT 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 npBJ}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 (Ta6nMbt 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 3H8HA 8CTPOHOM'fec- ICOM xapaKTepMCT1CM 000- HeTb! He.o.OCT8TO'fHO ,D.TIA Mara - eMY HY*HO 3HaTb T8101Ce K8t56anCntectcylO 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 HYMeponorMecKHe npHeMbi. npMeMbl cCCBSnl,eHHOAeMCTBMSI B MarMM (neMaJ1MCTbI.no MarHM - nanlOC, Kp3r, KapAeK HAP. - npe- AYnpe>KAalOT >Ke.nIOx 3aHMMaTbCJI MarHeM, '4TO 3TO HenpOCToe Aeno, rpe6YIOU4ee 06WHpHblX 3HaHHM no pa3J1H'4HblM AHCHnnHHaM, 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 naJ10KH. B KHHre «epHaJl M 6enaJl MarMJI» ponb MarH'4eCKOM nanO'4KM nanlOc 04eHHBaeT TaK: «AnJl TOro '4To6b1 HanpaBHTb npOJlneHMe cBoeM BonH, Mar HMeeT nanoKy, OKOBaHHYIO >Kene30M:a CJ1Y- >KHT Allfi cocpeAOTOeHHJl60nbworo KonHeeua 4>nIOHAa (3Hepre- TH'4eCKOM CHnbl. - npUM. oem.), BblXOMero H3 Mara H HanpaB- neHHoro HM Ha on peAeneHHYIO TO'4Ky. 3TO abHaJt CHna, HO caMa no ce6e OHa He HMeeT HHKaKoro TaMHCTBeHHoro cBdMCTBa, H nlOAM, npeAnonaralOU4 M e, TO AOCTaTOIiO OBnaAeTb MarMeCKOM 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 nanOKY HaHOCJlT cne4H4>MeCKYIO 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 n811KY &.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 6e33aHOro» '4enOBeKa. CMMB0J10M KHJl3J1 TbMbI - ronoea K03J1a.< Ha TaJlMOtaH AllJI AOOPblX AeJ1 HaHOCM- nMCb MMeHa nepB03a4MHareneM poAiJ '4enoseKoro - 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 nepCTJI) rpaBMpYIOT CHMBonbi KonAoBcKoro MMeHM HJ1M 3aK1lHHa- HHJI. MeTaJ1II, H3 KOTOporo M3roTaB- PUC. 56. MarM"ecKMij TaJ'IMCMaH.pJ1R XOPOWMX AeJl. (OCTa8JiMe 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», HarOBOR T. A.) 8 (] z  Puc. 58. K011AOBCKHe atpH6yrbI: nepcreHb M «3aKOJJAOBaHHoe» KOJ1O (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 3HepronepeHca KpaTKMMM CBeAeHMJlMM M3 6M03HepreTMKM M He- YpaAMLtHOHHOM MeAMMHbI. HOf"Aa '4aIOTCJI nIOAM, KOTopble 6M03HeprMeM CBoero Te1Ia MnH BCJ1eACT8Me annepnt'teCKOM peaKLtMM HecOBMecTMMbI C AJ)aro- eHHblM MeranJlOM MJ1M KaMHeM (noAP06Hee CM.: MeAHMHCKaJI M HaTaJ1bHaJi aCTpOJlOrMJI). KpOMe TOro, 'TYree KonbO Ha naJ1be, cornac.t'o HeTpaAHM- OHHOM MeAMHHe,- '43MepHO 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 .MarHecKHMMIO 4>H- rypaMH M nOBTopsno- U.tHMM HX 4>OPMY npeA- MeTaMM, TO)Ke HecywM- MM onpeAeneHHbdit 3HepreTHecKM" 3a PSVJ.. CBR3aHbI C H8- npaBneHHo" ne- eH 3HeprHM. MHTepecHwA cl»aKT MHOrMe )KeHU4MHbI H M'f1I..- \jMHbA HOCSIT TL\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 3HepreTMecKMM «KMTaMCKMM MepMAHaHaM». TaK, TY- roe KOJ1bLtO Ha MM3MHl4e MO>KeT Bbl3b1BaTb HapyweHMe 4>YHKLtMM CepAl4a M TOHKOro KMWHMKa, Ha 6e3b1MJlHHOM naJ1be - 3HAOK- pMHHW< opraHOB M, B '4aCTHOCTM, cnoc06CTBOBaTb MaCTonaTM. no- CTO"HHoe ()tCMMaHMe cpeAHero nanba 0c.na6nfleT MMf4YHMTeT M clJyHKl4MIO COCYAMCTOM CMCTeMbi (BeH H apTpMM). KonbO Ha YKa- 3aTeJtbHOM nanbl4e cnoco6cTByeT HapyweH YHKHM HepBHOM CMCTeM M TonCTOro KMweHMt<a. HcxoAJI M3 M3J10eHHOro, enonHe peaI1bHO, '4TO YXYAUM!HMe CaMO'4YBCTBHJI M nofiBneHMe )l(aJ106 MOryr 6WTb BW3BaHW nOCTO"HHblM C>KMMaHMeM TYrMM KonbOM naJ1ba. npM'teM neKapCTBO B AaHHOM CJ1Y'4ae 6YAeT nOMoraTb speMeHHO, TaK KaK OHO He HReT caMY npMHHY. n03TOMY He peKOMeHAY- eTa. HOCMTb TYrMe Kona. Aa>Ke 06b1'4Hoe 1(OnbO none3HO HHorAa CHMMaTb C naJ1b AaBaJt B03MO>KHOCTb 3Hepren1'4et aKTHBHblM TKaM «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 HCTbR. 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 KonneicMM. 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 nee6HoM 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 neeHMe He AaBaJ10 nOnO>KMTenb- HOro pe3ynbTaTa, BKJ1IO'4aJl caMoe MOU4Hoe, Kal(, HanpHMep, HapKoTH- KOTepanHJI, CHMnaT3KTOMHJI H Aa>Ke TpenaHaHJI '4epena (one- paMJI Ha ronoBHoM M03re B 30He "pOeKHH 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 noeK H T. A. KMra H.n. nynM'4eBa HanH- caHa AnJi Bpa'4eM H AnJl TeX. KTO HHTepecyeTCJlHeTPaAHHoHHOM MeAHLtHHoM.Cepbe3HOCTbH3Aa- EcnM aepJl'rb OKKYn.TM3- MY, ir1CnOllb3}'S1 aHa11or1O nO.AJU1eHir1R nOBepxHoc- Tir1 npeAMeTa K TellY. MO>K- HO Cir1TaTb. '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.AJU1IOaeM ce6R K BOCnpir1RTir11O 3Heprir1ir1, KOTOPYIO cOAep>Kir1T Beb. 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. OAeBaJI '4Y>KY1O BeU4b, Mbi nomOU4aeM ee HeprMIO. ECJ1M :na 3Hep- rMJI OTpMTenbHa, TO B nY'4weM CJ1Y'4ae B03N!M,,",MJI OHa YXYAwaeT HaM HacrpoeHMe (TaK Ha3b1BaeMbie 4CHeMOrMBMp01'aHHble ero Kone- 6aHM"»), a B XYAweM - Bbl3b1BaeT pa3J1M'4Hble HeyAa'4M B >KH3HH, BnnOTb AO O'4eHb cepbe3HblX. YKpaWeHMe C'4MTaeTCJI 3HepreTM'4ecKM 60nee none3HWM, ecnM OHO KYnneHO He B Mara3MHe, a nOAapeHO OT AYWM, CO CBemblMM 'fYB- CTBaMM H C paAOCTblO MnM AOCTaJlOCb no HaCJ1eACTBy. npH 3TOM Ba)t(- HO, '4T06b1 C HMM 6b1J1M CBJl3aHbI xopowMe C06b1TMft.j>KM3HM AapJl- U4ero, HOCHBwero AO 3TOro MOMeHTa TaKoe YKpaweHHe. Ho ecnM Y Hero 6b1nH '4aCTble HeC'4aCTbJl, TO YKpaweHMe MO>KeT 6b1Tb «3Hepre- TM'4eCKH oTJlrOU4eHo», H Ltenb HeC'4aCTHM, comaCHO Ka66aJ1e, MO>KeT nepeMTM Ha HOBoro HOCMTenJl YKpaWeHHJI - TaKMe CJ1Y'4aM HCTO- pHJI '4enOBe'4eCTBa 3HaeT (CM. CJ1eAYIOU4MM pa3Aen «3HeprMJI npo- KnJlTHM H "3HepreTH'4eCKaJl MH$eKLtHJI"»). B 3aK/lIO'4eHMe BepHeMCft K CHMBonaM neHTarpaMMbI, Ha- HOCHMOM Ha MarM'4eCKMe aT- pH6yTbI H Hcnonb]yeMOM npH raAaHHH. BnMJleT nH nonO>Ke- HHe H306pa>KeHHJI 4CMarH'4eC- KOM» 4>Hrypbl Ha npOBeAeHMe npeACKa3aHMM no nJITH ee 3J1e- MeHTaM? ):\a, BnHJleT, C'4MTaIOT TaaHble cunbl KpuTepueB Corll8CHO Y'leHMIO HOBbie. 1It3rOT0B11eHHble npo- MblwneHHblM cnOCOOoM nep- CTeHb, KOnb140 He cOAep)t(aT "3HepreTHecKoH HH$elC- 14HH-, nOCblnaeMOH OAHHM enOBeKOM APyrOMY. 391 
rnasa 8 IiYMeponOrMJI M .HCJ10BaJl aCT- pOnOrHJI. npoBeAeHHe C'4HTbI- BaHHJI 4>opMynbl no «A06pOM 3Be3Ae», pacnOnO>KeHHOM OA- HHM nY"fOM BBepx (KaK Ha pHC. 54, a), npHBneKaeT A06pble CHnbl 3HeprHH KocMoca H 3eM- nlo1 AI1J1 KapMH'4eCKOrO peweHHJI Aen no BblJlBneHHblM B «neHTar- paMMe cpopMynbl» np06neMaM >KH3HH. npoBeAeHHe C'4HTblBa- IiHJI 3neMeHTOB B HeA06poM no- nO>KeHHH 3Be3AbI - no «ABY- . poroM 3Be3Ae», oc06eHHo B CO'4eTaHHH C AeMCTBHeM '4epHOM MarHH, npHBneKaeT 3HeprHIO 3JlblX nnaHeT, ycHnHBaeT npOJlBneHMe B >K1013HH BblJlBneHHblX no neHTar- paMMe HeAct1aTKOB. 3TO cOAeMCTByeT HeYAa'4e HnM MeHbweMY yc- nexy Aena, Ra KOTopoe np0lo13BOAMTCJI raAaHHe. OKKynbTH3r.t npH3HaeT Y 4 eHHe Bcex penHrHM no '4aCTH MX yT- Bep>KAeHHM, '4TO C03AaTenb COTBopMn He TonbKO CMnbl 1J.06pa, BonnOTHB HX B 60>KeCTBeHHblM 06pa3 - Y xpHCTHaH B VlHcyca XpHcTa, HO M c03Aan AI1J1 ypaBHoBeWHBaHHJI ero Clo1nbl no 3aKOHY npHpoAbi HHbJfti H MeHee MOU4Horo HOCHTenJl npOTHBOnOnO>K- HOM 3HeprM., - KHJI:bI TbMbI, MnH IJ.bJlBOna. 06a 3T.,x paBHblX no CH.Re BnaCTenHHa, comaCHO penHrHH, 60plOTCH 3a OBnaAeHHe AY- WOM enKa (<<6eCCMepTHaJl AYwa»  n03HHH 3HepreTHKH - :310 3HepreTH'4eCKaJl CYU4HOCTb Tena, 6e3 KOTOpOM «nonHoeHHblM» '4enOBeK He 6YAeT, a 6YAeT '4epCTBbIM, 6e3AYWHblM, nHweHHblM-CO- YBCTBHJI H cocrpaAaHHJI). EcnM BepMTb 0KKYnItTM3- tilt Mar MO)l(eT 38UU1TI1Tb ce6R OT 3HeprOHana.o.eH'-1R .3HepreT'-1eCM Konna- KOMJO &iln&il c<3860poMIO. «38- BecOJO, a MO)l(eT caM ne- peABTb CBOIO 3J1ytO 3Hep- r&iltO 4epea APyroro enOBeKa, )t(&ilBOTHOro W1&i1 npeAMeT, '-1cnonb3yst MeTO- AbI paaHbOC Mar&iliil: 6eno, cepoii1 &iln&il epHoii1. 392 
. TauHble cunbl K{JUrepUeB Bc 60nbwee 'fMCJ10 MarOB npH3Ha1OT, '4TO pe3ynbTaTbi MHKapHa- LtHH (HOBbiX MaTepHaJ1bHblX BonnoU4eHHM AYWH) BceneHCKHM Pa- 3YM OLteHHBaeT no A06pblM AenaM '4enOBeKa. n03TOMY He YAHBH- TenbHO TO epHblX aroB .. 1(0nAYHOB CTaHOBHT BCeJ4eHbwe. 3HeprMSI npOKl1I1TMM M cc3HepreTM&feCKaSi MHeKL\MSI» KaK co06U4aJ10Cb Bblwe, reOMeTpH'4eCKaJl 4>opMa npeAMeTa- Kpyra, KBaApaTa, TpeyronbHHKa, OBaJ1a, 3Be3AbI - MMeeT onpeAe- neHHYIO CHMBonHKy H 3HeproHacblU4eHHOCTb. TaK.AOka3aHa, HO nOKa Hay'4HO He 06'bftCHeHa, B03MO>KHOCTb u.ene'HanpaBntJ..HbIX 3Hepre TH'4eCKHX npe06pa30BaHHM B Be(J4eCTBe, nOMet14eHH BHyTpb HnH nOA OCHOBaHMe nMpaMM- Abl. HaM60J1bWeM 3Hepre- TH'4eCKOM B03MO>KHOCTblO 06naAaeT nHpaMHAa. ce'4e- HMe OTOPO paBHO onpe- AeneHHOM '4HCJ10BOM BenH- '4MHe - TaK Ha3b1BaeMOMY «30nOTOMY ceeHHIO» (0 TaMHax reOMeTpH'4eCKHX 4>Hryp C «30J10TblM ce'4e- HMeM» He pa3 nHCaJ1H Ha- Y'4HO-nonynJlpHble >KypHa- nbl «HaYKa H JtU13Hb» H «TeXHHKa - MOnOAe1KH»). Tena, HMelOU4He >KIo1BYIO H TaAHbI H8yt(M CospeMeHHbIe crpomeJ1&o1 nHpa- MH,D. - HaWH COOTHH- IG1 - OOpaTWlH BHHMaHHe Ha TO. 'frO BbKX>Ta nHpaM101AbI «.D,I1R A06- pbIX n» He AOl'DlCHa npeBblUJ8Tb 40 M. npllt nJ)H6nH)t(eHHH K 3TOMy npeAeJ1y BOKpyr IlHpaMH,QbIl11O,QH . HaYIilHaTlIiI Tb KaKoe-TO 3HepreTWteCKoe HanpmKetMe, HanoAo6He IiIR tc3HePf"e- ecKOro crycn<a» y I1Ii1HIiIIiI BbI- COKOBOl1b1'HC>H 3neKTpOr1epe.o,aYIiI 393 
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rnaBa 8 «3HeproMH4>eKHJI» He 3aBHCHT OT 06DeMa npeAMera. nlOAOBHK XIV HaAeJ1 :nOT KaMeHb Bcero OAMH pa3, nocne '4ero BCKope" 3a60nen HeH3J1eHMOM 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 HeCaCTbe: BO BpeMJI peBonlOHH OHa 6b1na rMnbOTMHHpOBaHa. TaKOM >Ke HaCHnbCTBeHHOM CMepTH nOABep- rnHCb ABa CJ1eAYIOU4Mx X03JIHHa aJ1Ma3a: Koponb J1IOAOBMK XVI H KO- pOl1eBa MapMJI-AHTyaHerra, nonHBWaJl «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 ABopa. B 6ype peBonlOLtHH anMa3 HCe3ieT 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\neJI B CeMbe Xoyna npoKnJlToro anMa3a ero 6nH3KHx HaHHaIOT nJfeCJ1eAOBaTb HeYAa'4H. CeMbJl Ha rpaHH pa30- peHMJI. BHYK Xoyna BblHY>KAeH npoAaTb lIaCTb AparOLteHHOCTeM, BKnIO'4aJl a3, TypeKOMYTOproB4Y APrOLteHHOCTJlMM 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 "3HepreTHecKaSl HH$eK'-'HSI» . 400 
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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 COKpOBHe, 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 cOBMeHHble 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, KKHe 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- CTIo1ecKIItX 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 norMeCKOMY 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 HHae CBHHblX 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'4eC'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 JlBnIOTCJI nOCTOHHbIMH 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.TpOHHoi1 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 cnopTMBHX Mrpax npM3HaHMeM no.nb3Y1)TCJI 64-KJleTO'fHbIe wax- MaTbi M waWKM. Ha BocroKe Bcrpe'taIOTCJI M 60nee cnO)l(He 324- KIIeTO'fHwe waWKM, i1po06pa3 'fepr 81-A TeTparpaMMW. npMBeAeM npMMepw oKKYnbTHwx cxeM, cnqMpoBaHHbIX Ha caMY >KM3Hb. AnJi 3.neMeHTapHWX ceTHbiX 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'4eHHX MaTpM'4HblX '4epT: 384 x 5. Ee TpOM'4tfY1O CMCTeMY CI>Mnw C'tMT8nM, TO cxeMbI no wy ... X3 TY COAep)K8T yti...aep- C8nbHyK> CTPYKTYP')I I103HaHMA.. opraH....38- LU4M JKM3H.... f103TOMY 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 KaecT8e 3Ta110Ha MepHblM cocyp. Y COOTBeTCTBOBa11 eMK, paB- HoM 64 6a30BM 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, n03TMecKM 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- I1MCb KaK eAMH M3Mepe- 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 acrpOHOMHecKOM 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>1eCK&IIe 3an&llC- K&IIIt (11-1 BB. AO H. 3.) nio1C811: «AnR Tex. !<TO I>1CKYCeH B HeOecHbIX nOAceTax,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 BO 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 COHaJ1bHOM 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 BeJlHHHbI H npoceT nnoU4aAM He TonbKO roCYAap- CTBa KHTaM, HO M BceM nOAHe6ecHoM - Bcero 3eMHoro wapa. Cpe- AH KHTaMCKHX MblCJ1HTeJleM 06lqenpHHJlTbiM 6b1no HYMeponOrM'4eC- Koe pa3AeJIHe nO.AHe6eCt::IOM Ha 906naCTeM. M3H lPbI (IV B. AO. H. 3.) pa3pa50TaJ1 cxeMY HYMeponOrM'4eCKOM KOHenLtHH «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 npaKTeCKOe BHeAJ)e- He KaTeroplil1il occaHb y. B >K1iI3Hb 06l!.1.ecTBa BOCXO- AT no Kpa"'Heft Mepa K cepeAIiIHellcReneTIiIR AO H. 3., T. e. cOlil3Meplil- MO c HaaJ10M 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 HaYHYIO HHQ>opMaltHIO A.. K063e- Ba B KHHre «Y'4eHMe 0 CHM- Bonax H '4HCJ1ax» (c. 344)" 4>YHAaMeHTanbHo npopa- 60TaBwero TeKCTbI MHorHX KHTacKHx TpaKTaTOB III-II BB. AO H. 3., COCTaBHM Ta6nHLtY ApeB- HeKHTaCKHX 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 norOHKa 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 KIltTaCKOO H}lMe- pol10rlltllt 9-KneT04HO MaTpllt1..4bl 110 wy lit ccKPyrl1b1X- lItcel1 Bpo.a,e 1000 1111t. B Te .a.peBHHe BpeMeHa 3TOT paceT n03BOI1I1tI1 npocl.flil- TaTb pa3Mepbl 3eM1\IIt KaK wapa. cnl1locH}'Toro no BepTlltKal1I1t (B nOl1locax), TO COOTByeT 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- MYApeOB 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 BenMMHbf (? - 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 cnWHH 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, npoHcxoeHHeKoTopblXTpyA- 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 n03HHM, HeKOTO- pblP. aBTopbl npHBneKalOT K 06'bJlCHeHHIO BMewaTenbCTBO CHn CBbI- we, rOBOpJlT 0 nepeAa'4e MH4>opMaMH 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 eJ10BeoJP8' MC- nonb3ys1 <PW\OCIO. aCT- poHOMHIO H HYMepoJ10rH- 'feCKHe npHeMbI, CYMeJ1H npaBHJ1bHO c<PopMYJ1Hpo- BaTb H COCT8BHTb «yttHBep- canbHbI OKKYJ1bTHbI Kl11O'f» n03H8HHR, 'fT06b1 A080J1bHO TO'fHO p8CCHTaTb 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 aApecyT 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 3aKOHOi4 npo MO)I(HO 38f1M- C8Tb B BM,AB 4><>PMYl1b1: Haano (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- COKOTOHWX 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 HHOM npo30pnMBOCTM. TaHHb/e cunb/ KpuTepues 06 MlfTYMI4MM B HaCTORlltee Bpe-  Y'feHbIe n3Ha- lOT, '0"0 MHR 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- reCKHM- 3J1eMeHTaM MO}K- HO a06JM:3Tb cc06beMHO-, HaepTH8 'reoMeTp.,eCkYtO <S>ryPY. a NO}KHO TO}Ke ca- Moe nOkaaaTb «J1HeHO». 6YkBaM.., (B Kmae lit nOH1It eporn<S>aM). HancaHHbI- Milt B PR.O.. ooaHa:1B HaaJ10 cTblBaH 3tleMeHTOB. HanpaBJ1eHe  YJ:1)bI nOBO- pOTOB J1&.1Hi1 B reOMeTp- C4ecKorype, - TaklltM 06paaOM HancaTb «<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, paccHTaHo Ha 60nee rJOArOTosneHHoro IiY- Meponora, nerKO nepeeoAJI- U4ero 4>opMyny B rpa4>HK HnH MblCJ1eHHO npeACTaBnJlIOU4e- 414 
ro ero nepeA c060M npH '4TeHHM CMBonOB 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 3Hepren4eCKHX 4>opMyn. Ho TaK>Ke 6YAeM MC- nOnb30BaTb HX 6YKBeHHoe, nH- CbopMynbl HYMeponorHH OcHOBW ttyMeponorMM B tiyMepononut cnol1b3Y- lOT AB8 sapHTa HTblsa- HR 3HepreTM..ecK4>Op- MYI1b1 C reoMeTPKOrO ee BbIHR - C tcpeCTa X3 TY  eM C APyrw< <I>rYP, c' eH'TarpaM!-4b1. ... ...... ........ ... ........ ...... .... . YeTBepHOCTb CXOAHoiit MaTp pecnOnO)KeHR- 3ne- . MeHTOB B KpecTe X3 TY COOTHOCMa C eTblpbMR OAB- M rOAMHoro B03,IJ.eiitcT8R COI1H Ha 3eMnlO. Pacnono- )KeHe eTbipex 311eMeHTOB Ha KOHu.ax KpeCT8 X3 TY · CMB0I13PyeT X KapAHB11bHYJO <l>YHKU.IO: 3MHee  · l1eTHee COI1Hu.ecTORHe, OCeHHee  BeceHHee paBHOAeH- CTBe, a TalOKe eTblpe He,o.ellbHble <l>a3b1 J1ytibl. npM CO- · Bna,o.eH 3Ha'4eHR 311eMeHTa C CMB0I13PyeMbiM M . . c06b1TMeM nppo,o.bI npoRBlleHe ern B )K3H  B aepo- .- . RTHOCT CBepWeHR nporH03pyeMoro co6b1TR yaenWUt- . BaeTCR. nepeBeP.eHe 311eMeHT8 C ero MecTOnOnO)KeHMR : B KpeCTe X3 TY B neHTarpaMMY He ..,3MeHReT OCHOBHyto C..,M- BOllKY, HO C HYMep0I10r'feCKX n03lI.Miit Ha,o.el1AeT ero 6ol1bweiit «CTeneHblO CB06o,Abf» cBR3eiit C APyrM 311e- MeHTaM <l>OPMYI1b1 no Kpyry  l1aM 3Be3,lJ.bl, 8 3Ha'4HT  OOl1bWM «Marn'4ecKM B11&.1RHeM"  OyP3)KeHMeM )KM3H. . ..................................... . 415 
rnasa 9 0 6 B 0 /i/ /0 .0. n M .0. IU/M .11 __:]u A B "" : %90- \ \ / L72" B B-M PUC. 59. CxeMa nepeMeaqeH..fI 3J1eMeHTOB Kpecra X3 Ty (a) npM cpOpMMpoBaH.... neHTarpaMMbI (6, 8) HeMHoe Bblpa>KeHHe, T06b1 Ha'4MHalOutHM HYMeponor H acrpononpe- HHpoBanc" B '4TeHHH 4>opMyn. neHTarpaMMY B oKKynbTH3Me nonY'4alOT H3 npe06pa30BaHHOM 4>Hrypbl KpeCTa C BblHeceHHeM H3 ee LteHTpa 3neMeHTa Ha op6HlY neHTarpaMMpH TaKOM npe06pa30BaHHH 4>Hrypbl Kpecra yrnoBaJl CBJl3b era 3neMeHTOB H3.90° (MMeHyeMaJl B acrponorHH Yemsepm- Hoil MJlH ICsoopamHoil CBJl3blO) nepexoAHT B ymoBYIO CBJl3b 3neMeH- TOB AYrH 72° (HMeHyeMYIO B acrponorHH ICSUHmU/1e/tf) - pHC. 59. - npH Ha'4aJ1bHOM 3neMeHTe C'4HTblBaHHJI neHTarpaMMbI A no '4a- COBOM CTpenKe no KPYry (M. pHC. 59, s) rpa4>H4ecKoe Bblpa>KeHHe 3HeprHH "'O>KHO JanHcijJb n..-HeMHo Bblpa>KeHMeM AOnMB. npMBeAeHHble npepa30BaHHJI KpeCTa X3 lY c nepeMeuteHHeM era 3neMeHTOB '4aCTO HCnonb3YlOT npH 4>oPMHpoBaHMH «MarMec- KMX» neHpaMM H «MarH'4eCKHX» KBaApaToB no wy AllJI aHaJ1H3a ...... cMlYaLtHM H .npoBeAeHHJt oKKynbTHbix nporH030B. nepeMeuteHMe 3neMeHTa C yrna CBJl3H 90° HMeeT H acrponorH- '4ecKoe 3BY'4aHHe. KBaApar, HJ1H ICsoopamypa (90°), HMeeT AHcKpeT- 416 
HOCTb M nepMOAHHOCTb npoJlBJ1e- HHJI MnM B03AeMCT.BHJI, '4TO comacy- eTCH C nepHOAH'4HOCTblO BpeMeH rOAa. OAHaKo KBaApatypa TaBHT eJ10BeKa B COCTOJlHHe nOCTOJlHHOM HanpJl>KeHHOCTM, 60Pb6b1, caMoyY- Bep>+<.o.eHHJI. B acrponorHM KBa.Qpa- TYPY OTHOCHT K OAHOMY M3 caMbiX Ba>KHblx, 3Ha'4HMblX aCneKTOB (3Hep- reTH'4ecKoM CBJl3H) nnaHeT. A KBHHTHnb JlBnJleTCJI nepBblM H maBHblM H3 TBOp'4eCKHX aCneKTOB. AcneKT B 72° Ha3b1BaIOT eU4e ypOHU'IecKUM M3-3a HepeAKHx clOpnpH30B, HeO>KHAaHHblx npoJlBneHHM. ECJ1H B ropocKone '4eJ10BeKa HMeeTCJI «iJeHOK» - acneKT nJlTM OCHOBHblX nnaHeT ropocKona 6nH30K K 72°, TO, no MHe1O n.n. fno- 6bt, Y Hero YAa'4HO CKnaAblBaeTCJI.CYAb6a (KoH4>HrypaHH acneK- TOB, c. 330). KHTaMcKMe 4>Hnoco4>bI nOCJ1eAOBaTeJ1bHOCTb 3aKoHoMepHblx 3Hep- reTH'4eCKHX B3aHMooTHoweHHM Me>KA,Y 3J1eMeHTaMH nJlTH CTHXMM 0603Ha'4anH 6YKBeH- HOM O'4epeAHoCTblO MX pacnOnO>KeHHJI B Kpec- Te X3 TY HJ1H B 3HepreTH- '4ec.KHx 4>opMynax, HC- nonb3YJl nepe'4HCJ1eHMH 3J1eMeHTOB no MX 3amaB- HbiM 6YKBaM: B - BOAa, 0- OroHb, A - .o.epe- BO, M - MeTaJ1n, n - nO'4Ba. npM OKKYnbTHbiX ctJopMynbl HYMeponOnfU Ha 38MeTtcy neHTarpaMMa co CTO- poHaMIII.IIIMelOU,tIilMIll yroJ1 72°. B aCJ1Orllllll H83b1BaeTCSI ccseilKoM» III OTHOCHTCR K KapMIIIec- t<OH rypa1iI1II B. 36epX8PA (1933), canbHO IIICCl1e,D,OBaBWIIIH OKono 30 AQCTyn- HbIX eMY .o.peBHeKIiITaHcKIiIX TeKCTOB xaHbCKIiIX III AOxaHbCKHX neplilOAOB (AO III B. H. 3.). BblRBIiIJ116 3aKOHO- MepHblX nOPRAKOB 5 3neMeHTOB. a A.&i1. K063eB (1994) AOnOJ1HIIIJ1Ii1X eU,te BOCbMblO OCHOBHblMIll nop- KaMIll 1113 D,peBHeHWIIIX pYKonlllce 417 
rn8S8 9 paC'4eTax 3TM 4>oPMynbl BHOCHnMCb B CHCTeMY X3 Ty nH60 B 9-KneT0'4- HbiM «MarM'4ecKMM» KBaApaT no wy A11J1 onpeAeJ1eHMJI HanpaBJ1eHHJI M nepepacnpeAeJ1eHHJI 3HeprHH «He6a» (nHeBMbI- «"'H») M «3eMM» (KOHCHCTeHLtHM- «'4>KH»). Ha OCHOBaHMH KOM6MHaLtMM 3neMeHTOB AenaJ1MCb MarH'4ecKHe HCTOnKOBaHMJI. C'4MTa11ocb, 410 MarepManbHble M HeMarepManbHbfe JlBneHHfI "MeIOT B >KH3HM 06U4He 3aKOHOMepHOCTH 3HepreTM'4ecKOM CB"3M, KOTOpble oTpa>KalOT OKKynbTHbie 4>oPMYnbl, a 3HaS! B03MO>KHOCTH BXOARU4HX B 4>oPMyny 3neMeHTOB CTMXMM, MO>KHO nMOTpeTb pe3YnbTaT MX BJaMMoAeMCTBMfI, npeACKa3aTb 6yAYutee. Boo6U4e rOBopJl, pa3JfM'4HblX nOCJ1eAOBaTeJ1bHblX CO'4eTaHMM n"TM 3neMeHTOB MO>KeT'6b1Tb ropa3Ao 60nbwe. OAHaKO BOCTO'4Hble 4>M- nococpbl M COBpeMeHHble HYMeponorM MX '4MenO OrpaHM'4HBaIOT pe- aJ1bHO B03MO>KHblM B3aHMOOTHoweHHeM 3neMeHTOB B 3HepreTtNeC- KMX 4>opMynax, KOTopble nepeAalOT H3BeCTHbie B HaCTOJlU4ee apeM" 3aKOHOMepHOCTH npMpOAbi H KOCMoca. 3 Bcex nepe'4HCJ1eHHblX nopfiAKOB Cb HblHe JlBnJlIOTCJI HaM60nee ynorpe6nJleMblMH, a M3 HHX nepBbITblpe - «rnaBHblMH». B AaJ1bHeMWeM HX CTaHAaPT- HbiM Ha60p B opMynax"6YAeM 0603Ha'4aTb CHMBonOM «on» - «oc- · nepeeHb HYMeponon1ecl(io1X <PoPMyn no Mepe y6b1BaHio1R · . aCTOTbi io1X WCnOnb3OBBHio1R: : 1. BOAMn i AMOBn. 13. BMO,lJ,n. · 2. ,lJ,OnMB. 8. OMn. 14. BOM,lJ,fl. 3. n,lJ,tv10B. 9. BoI'1.D.M. 15. nMO,lJ,B. 4. MJ.;t8()fl. 10. MB,lJ,On. 16. nM,lJ,OB. · 5. M,lJ,flOB 11. f1.D.OMB. 17. nOMB.Q. 6. ,lJ,MnOB. 12. OB,lJ,Mn. 18. B,lJ,nOM. 418 19. MnO,lJ,B. 20. BMjJ1/0,lJ, · 21. ,lJ,MOnB. 22. ,lJ,MBnO. 23. BM,lJ,flO. 24. ,lJ,BOMn. 
4>opMynbl HYMepOnOrHH HOBHOM nOpJlAOK» 3neMeHTOB: lon, 2 on, 3 on, 4 on, 5 on, 6 on M 7 on (HYMepaL1.HJI cooTseTCTByeT O'4epeAHOCTH opMyn B CTon64ax nepe'4HJI). KaKoe 3Ha'4eHMe HMeeT KOM6HHaL1.HJI 3neMeHTOB 4>oI1;KaK OHa HCTonKOBblBaeTCJI? npMBeAeM 3TM AaHHble no HaM60nee ynorpe6- J1J1eMblM B npaKTHKe HYMeponora nepBblM ceMM 4>opMynaM: 1 on - BO.QMn: CepMJI cMMBonH3Mpye1l:'f10IV'AOK c03HAaHMJI, oTpa>KaeT O'4epeAHoCTb c03AaHMJI >KM3He06ecne4MaalO1.qMX 3neMeH- TOB (no A. cJ»opKe) HnM CTpeMneHMe K «KocMOrOHM'4eCKoMY nopJlA- KY MMpa» (no J\>K. HHA3MY); 2 on - .QOnMB: nOpJlAOK B3aHMHoro nOpO>KAeHHJI, BocnpoM3- BOACTBa 3J1eMeHTOB, «nepenHBaHMe» 3HeprHH H3 oAHoro 3neMeHTa B APyroM; 3 on - n.QMOB: nOKa3b1BaeT nOpJlAOK B3aHMHcm> pa3pywe- HMJI 3neMeHTOB (no A. cJ>opKe) MnH B3aHMHoro npeoAoneHMJI (no .Q>K. HHA3MY); 4 on - M.QBOn: CepMJI cHMBonH3HpyeT rpaHc4>opMaL1.HIO, nepe- BonnOU4eHHe 3neMeHTOB (no A. cJ>opKe) MnH «coBpeMeHHoro no- pJlAKa» (no .Q>K. HHA3MY). C'4HTblBaHHe 3neMeHTOB 4>opMynbl o KpyrOBOM neHTarpaMMe nOCJ1eAOBaTenbHO H npM nepecKaKMBaHHH '4epe3 3neMeHT H3MeHJI- eT CMblCJ1 HCTonKOSaHHJI. 3TO HamftAHO BHAHO no «poACTseHHblM» 4>opMynaM 2 on H 3 on. npH nOCJ1eAOBaTenbHoM C4HTblBaHHH 3ne- MeHTOB nonY'4aeM nHHeMHYIO 4>op'Myny .QOnMB (pHC. 60, a), KOTO- paJl TpaKJyeTCJI KaK «B3aHMHoe nopo>KAeHHe», a «nepecKaKHBaHHe» '4epe3 OAMH 3neMeHT AaeT 4>opMyny - n.QMOB (pHC. 60, 6) HnM «B3aHMHoe npeoAoneHHe». Cl»opMynbl 2 on M 3 on C4HTalOTCfI HaH- 60nee ynOTpe6HTenbHblMM H3 oCTanbHblx 7 «rnaBHblX 4>opMyn», HO OHH HeHHAHBHAYanbHbI, HeCaMOCTOJlTenbHbI HnH HeopHrHHanbHbI 419 
rnaBa 9 no «pO>KAeHHIO», TaK KaK B3aMMo06paTMMbI: OAHY MO>KHO nonY"fMTb H3 APyroM. OpHrHHanbHo C03A(1HMe CTpyKTyPbI 4>opMynbf 5 on. MaTpMLW 5 on BbI'4HCJ1Hn A.. K063eB (1994), HCnOnb30BaB «HYMeponOfM'4ecKyIO TexHonOrMlO» cocraBJ1eHHJI AJ>E!BHMMH HYMepoJ10raMH OCTanbHblX MaT- pM'4HblX 4>oPMyn, HaMAeHHblx no KKTaMCKHM MCTO'4HHKaM M npMBeAeH- HbiX B neHe Bblwe: MaTpH'4HaJI 4>opMyna H306pa>Kanacb KpyrOBOM neHTarpaMMoM c npJlMbiM (no '4aCOBOM CTpe1IKe) C'4MTb1BaHMeM 31Ie- MeHTOB, T. e. on. eTCJI BepKTb, 410 4>oPMYna 50n WlH MJ.\nOB e 6YAeT «HaMAeHa» CMHonoraMM B epeAHOM pyKonHcM AJJeBHMX MYA- peLtOB, YaK KaK no CerOAHJlWHHM AeHb apxeonorH'4ecKMe paCKOnKM B KHYae npenOAHOCJIT HCTopH4ecKHe ClOpnpM3b1. OAHaKO B PMe era- pHHHblX pyKOBOACTB KKTaMCKMX 4>WlOC<$oB Y>f(e HaMAeHbI npoM3BOA- Hble $opMynbl OT 500: 50n, 350n M 50n (B. 36ePxaPA 1933). nepBble nJlTb nOCJreAoBaTeJ1bHOCTeM KOM6MHaLtHM 3neMeHTOB 4>opMyn nepe 4H JI - OT 1 on AO 5 on - oTpa>KalOT ABM>KeHMe maB- Horo KOCMMeCKoro 06beK- Ta - COnHLta, a pa3Hoo6pa3- Hble nOpJlAKM nJliM 3neMeHTOB B nMHeMHoM MnH neHTarpaM- MHOM 4>opMyne MMelOT CMC- TeMHblM xapaKTep M 0603Ha- '4alOT COnHe'4Hbfe H nYHHble LtHKJ1b1, COOTHOCHMble co CTO- pOHaMM CBeTa. ComaCHO 3TOM Mee, npJlMOe M 06paTHoe CMTbfBaHHe 3neMeHTOB no KPYry neHYarpaMMbf COOTBeT- CTByeT Onn03HLtHH COnHLte - 6 o rm  M B M S 0 a Pur:. 60. «PO)l(J\eH"f:' $)pMYJ10 :- ,QOnMB (0) cl><>PMYJ1111 30" - n.QMOB (6) npM «nepeCKaKMBaHMM» C'IMTIllSaHMJI ee 3J1eMeHTOB 420 
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