Onyakeni omusha wesikole

Abafundi abaningi bebesendaweni ethile eholidini - kungakhathaliseki ukuthi lisezweni lethu elihle, emazweni angomakhelwane, noma mhlawumbe phesheya kwezilwandle. Masisebenzise leli thuba ngenkathi imingcele isivulekele ... Iluphi uphawu olwaluvame kakhulu ohambweni lwethu olufushane nolude? Lona umcibisholo obheke ekuphumeni komgwaqo, ukuqhubeka kwendlela yasentabeni, indawo yokungena emnyuziyamu, indawo yokungena ogwini, njalonjalo njalonjalo. Yini ejabulisa kangaka ngakho konke lokhu? Ngokwezibalo, hhayi kakhulu. Kodwa ake sicabange: lesi sibonakaliso sisobala kuwo wonke umuntu ... abamele impucuko lapho kwakudutshulwa khona umcibisholo. Yiqiniso, akunakwenzeka ukufakazela lokhu. Asiyazi enye impucuko. Nokho, i-pentagon evamile kanye nenguqulo yayo emise okwenkanyezi, i-pentagram, ithakazelisa ngokwezibalo.

Asidingi imfundo ukuze sithole lezi zibalo ziheha futhi ezithakazelisayo. Uma, Mfundi, uphuze i-cognac yezinkanyezi ezinhlanu ehhotela lezinkanyezi ezinhlanu e-Place des Stars e-Paris, mhlawumbe... wazalwa ngaphansi kwenkanyezi enenhlanhla. Uma othile esicela ukuba sidwebe inkanyezi, sizodweba amaphuzu amahlanu ngaphandle kokungabaza, futhi lapho u-interlocutor emangala: "Lokhu kuwuphawu lwe-USSR yangaphambili!", Singaphendula: Izitebele!

I-pentagram, noma inkanyezi enamaphuzu amahlanu, i-pentagon evamile, iphethwe yibo bonke abantu. Okungenani ingxenye yesine yamazwe, okuhlanganisa i-US kanye ne-USSR yangaphambili, ayifake ezifanekisweni zawo. Njengezingane, safunda ukudweba inkanyezi enamaphuzu amahlanu ngaphandle kokuphakamisa ipensela ekhasini. Lapho esekhulile, uba inkanyezi yethu eqondisayo, engaguquki, ekude, uphawu lwethemba nesiphetho, i-oracle. Asibheke eceleni.

Zisitshelani izinkanyezi?

Izazi-mlando ziyavuma ukuthi kuze kube yikhulu lesi-XNUMX BC, ifa lengqondo labantu baseYurophu lahlala emthunzini wamasiko aseBhabhiloni, eGibhithe naseFenike. Futhi ngokuzumayo ikhulu lesithupha liletha ukuvuselelwa kanye nokuthuthukiswa okusheshayo kwesiko nesayensi ukuthi ezinye izintatheli (isibonelo, uDaniken) zithi - kunzima ukusho ukuthi bona ngokwabo bakholelwa kulokhu - ukuthi lokhu bekungeke kwenzeke ngaphandle kokungenelela. yeziboshwa. kusuka emkhathini.

Uma kukhulunywa ngeGreece, leli cala linencazelo enengqondo: ngenxa yokufuduka kwabantu, izakhamuzi zasePeloponnesian zifunda kabanzi ngesiko lamazwe angomakhelwane (ngokwesibonelo, izincwadi zaseFenike zingena eGreece futhi zithuthukise izinhlamvu zamagama. ), futhi bona ngokwabo baqala ukwenza ikoloni yaseMedithera. Lezi yizimo ezikahle kakhulu zokuthuthukiswa kwesayensi: ukuzimela kuhlangene nokuxhumana nomhlaba. Ngaphandle kokuzimela, sizidela esiphethweni samariphabhulikhi kabhanana aseCentral America; ngaphandle koxhumana nabo, eNyakatho Korea.

Izinombolo Zibalulekile

Ikhulu lesi-XNUMX BC kwakuyikhulu leminyaka elikhethekile emlandweni wesintu. Ngaphandle kokwazi noma mhlawumbe bengezwa ngomunye nomunye, ongqondongqondo abathathu abakhulu bafundisa: Buddha, Confucius i I-Pythagoras. Izinkolo ezimbili zokuqala zakha izinkolo namafilosofi asekhona nanamuhla. Ingabe indima yesithathu yabo ilinganiselwe ekutholweni kwempahla eyodwa noma enye yonxantathu othile?

Ekuqaleni kwekhulu lesi-624 nelesi-546 (c. XNUMX - c. XNUMX BC) eMilethu e-Asia Minor yanamuhla kwakuhlala. Okufanayo. Eminye imithombo ithi wayengusosayensi, eminye ukuthi wayengumthengisi ocebile, kanti abanye bambiza ngosomabhizinisi (ngokusobala, ngonyaka owodwa wathenga yonke imishini kawoyela, wabe eseyiboleka ukuze akhokhe inzalo). Abanye, ngokwemfashini yamanje kanye nomfuziselo wokwenza isayensi, bambona, bona, njengomvikeli: ngokusobala, wamema amadoda ahlakaniphile, wawapha ukudla futhi wawaphatha, wayesethi: “Hhayi-ke, sebenzelani inkazimulo mina nayo yonke iSayensi.” Nokho, imithombo eminingi sína bathambekele ukugomela ukuthi Thales, inyama negazi, wayengekho nhlobo, futhi igama lakhe wakhonza nje samuntu imibono ethize. Njengoba kwakunjalo, kwaba njalo, futhi cishe ngeke sazi. Isazi-mlando sezibalo u-E. D. Smith sabhala ukuthi ukube abengekho amaThales, ngabe abekho oPythagoras, futhi akekho ofana noPythagoras, futhi ngaphandle kukaPythagoras bekungeke kube noPlato nanoma ubani ofana noPlato. Kungenzeka. Asishiye eceleni nokho ukuthi ngabe kwenzekani ukube.

UPythagoras (c. 572 - c. 497 BC) wafundisa e-Crotone eningizimu ye-Italy, futhi yilapho kwazalwa khona inhlangano yongqondongqondo eyaqanjwa ngenkosi: I-Pythagoreanism. Kwakuyinhlangano yokuziphatha-yenkolo kanye nenhlangano esekelwe, njengoba singayibiza namuhla, ngezimfihlo nezimfundiso eziyimfihlo, sicabangela ukutadisha isayensi njengenye yezindlela zokuhlanza umphefumulo. Phakathi nokuphila kwesizukulwane esisodwa noma ezimbili, i-Pythagoreanism yadlula ezigabeni ezivamile zokuthuthukiswa kwemibono: ukukhula kokuqala nokwanda, inhlekelele nokwehla. Imibono emihle ngempela ayiqedi izimpilo zabo lapho futhi bangafi unomphela. Imfundiso ekhaliphile kaPythagoras (waqamba igama azibiza ngalo: isazi sefilosofi, noma umngane wokuhlakanipha) nabafundi bakhe babusa zonke izikhathi zasendulo, base bebuyela eNkathini Yokuzalwa (ngaphansi kwegama lobuqaba), futhi empeleni singaphansi kwethonya lakhe. namuhla. Izimiso zePythagoreanism zigxile kakhulu emasikweni (okungenani eYurophu) kangangokuthi asiqapheli ukuthi singacabanga ngenye indlela. Simangele kakhulu kune-Monsieur Jourdain ka-Molière, owamangala lapho ezwa ukuthi ubekhuluma iphrozi impilo yakhe yonke.

Umqondo oyinhloko wePythagoreanism kwakuyinkolelo yokuthi umhlaba uhlelwe ngokuvumelana necebo eliqinile nokuvumelana, nokuthi ubizo lomuntu ukwazi lokhu kuvumelana. Futhi kuwukubonakaliswa kokuvumelana kwezwe okuhlanganisa imfundiso yePythagoreanism. AmaPythagoras ngokuqinisekile ayengama-mystic kanye nezibalo, nakuba kunamuhla kuphela lapho kulula ukuwahlukanisa ngokukhululekile. Bayihlahlele indlela. Baqala izifundo zabo zokuvumelana kwezwe, okokuqala befunda umculo, isayensi yezinkanyezi, izibalo, njll.

Nakuba isintu sanqotshwa umlingo "phakade", yisikole sasePythagorean kuphela esasiphakamisa saba ngumthetho osebenza ngokujwayelekile. "Izinombolo zibusa umhlaba" – lesi siqubulo besiyisici esihle kakhulu sesikole. Izinombolo zinomphefumulo. Ngayinye yayisho okuthile, ngayinye ifanekisela okuthile, ngayinye ibonisa ingxenyana yalokhu kuvumelana koMkhathi, okungukuthi. isikhala. Igama ngokwalo lisho "ukuhleleka, ukuhleleka" (abafundi bayazi ukuthi izimonyo zibushelelezi ubuso futhi zithuthukise ubuhle).

Imithombo ehlukene inikeza izincazelo ezahlukene amaPythagoras azinikeza inombolo ngayinye. Ngandlela thize, inombolo efanayo ingafanekisela imiqondo eminingana. Okubaluleke kakhulu kwaba eziyisithupha (inombolo ephelele) i ishumi - isamba sezinombolo ezilandelanayo 1 + 2 + 3 + 4, ezakhiwe ngezinye izinombolo, uphawu lwazo olusekhona nanamuhla.

Ngakho-ke, uPythagoras wafundisa ukuthi izinombolo ziyisiqalo nomthombo wakho konke, ukuthi - uma ucabanga - "zixube" komunye nomunye, futhi sibona kuphela imiphumela yalokho abakwenzayo. Idalwe, noma kunalokho yathuthukiswa uPythagoras, imfihlakalo yezinombolo ayinakho "ukuphrinta okuhle" namuhla, futhi ngisho nababhali ababalulekile babona lapha ingxube "yama-pathos kanye nobuwula" noma "isayensi, imfihlakalo nehaba elimsulwa." Kunzima ukuqonda ukuthi isazi-mlando esidumile u-Alexander Kravchuk wayengabhala kanjani ukuthi uPythagoras nabafundi bakhe bagcwalisa ifilosofi ngemibono, izinganekwane, izinkolelo-ze - njengokungathi akaqondi lutho. Ngoba kubukeka kanjena nje ngokombono wekhulu lethu lesi-XNUMX. AmaPythagoreans awazange ahlunge lutho, adala imibono yawo ngonembeza ophelele. Mhlawumbe emakhulwini ambalwa eminyaka othile uzobhala ukuthi yonke inkolelo-mbono yokuhlobana nayo yayingenangqondo, ikhohlisayo futhi iphoqelelwe. Futhi uphawu lwezinombolo, olwasihlukanisa nePythagoras ingxenye yesine yesigidi, lwangena ngokujulile emasikweni futhi lwaba yingxenye yalo, njengezinganekwane zamaGreki namaJalimane, ama-epic asendulo ama-knightly, izinganekwane zaseRussia mayelana neKost noma umbono kaJuliusz Slovak. uPapa wamaSlav.

Ukungabi nangqondo okuyimfihlakalo

Ku-geometry, abakwaPythagoras bamangala i-figurami-podobnymi. Futhi kwaba ekuhlaziyweni kwemfundiso yeThales, umthetho oyisisekelo wemithetho yokufana, lapho kwenzeka khona inhlekelele. Kwatholwa izigaba ezingenakuqhathaniswa, futhi yingakho izinombolo ezingenangqondo. Iziqephu ezingakwazi ukukalwa nganoma yisiphi isilinganiso esijwayelekile. Izinombolo ezingezona izilinganiso. Futhi yatholakala kwelinye lamafomu alula: isikwele.

Namuhla, esikoleni sesayensi, siyalidlula leli qiniso, cishe singaliboni. I-diagonal yesikwele ngu-√2? Kuhle, kungaba yimalini leyo? Sicindezela izinkinobho ezimbili kumshini wokubala: 1,4142 ... Hhayi-ke, sesiyazi kakade ukuthi iyini impande yesikwele sokubili. Yiphi? Ingabe ayinangqondo? Mhlawumbe kungenxa yokuthi sisebenzisa isibonakaliso esingavamile, kodwa ngemva kwakho konke Empeleni yi-1,4142. Phela isibali asiqambi amanga.

Uma umfundi ecabanga ukuthi nginehaba, khona-ke ... kahle kakhulu. Ngokusobala, izikole zasePoland azimbi kangako, ngokwesibonelo, eBritish, lapho yonke into ikhona ukungenakulinganiswa endaweni ethile phakathi kwezinganekwane.

NgesiPolish, igama elithi "ukungacabangi" alesabisi njengozakwabo kwezinye izilimi zaseYurophu. Izinombolo ezinengqondo zikhona ezinengqondo, ezilinganiselayo, ezinengqondo, i.e.

Cabanga ngesizathu sokuthi √2 inombolo engenangqondo, okungukuthi, akuyona ingxenyana ka-p/q, lapho u-p no-q beyizinombolo eziphelele. Ngokwesimanje, kubukeka kanje ... Ake sithi √2 = p / q nokuthi le ngxenyana ngeke isafushaniswa. Ikakhulukazi, kokubili u-p no-q kuyinqaba. Asikwele: 2q²=p². Inombolo p angeke ibe yinqaba, kusukela lapho p² kungaba futhi, futhi uhlangothi lwesobunxele lokulingana luyimpinda ka-2. Ngakho-ke, u-p ulinganayo, okungukuthi, p = 2r, yingakho p.²= 4r². Sehlisa i-equation 2q²= 4r². sithola d²= 2r² futhi siyabona ukuthi u-q kumele alingane, ebesicabanga ukuthi akunjalo. Kwamukelwe ukuphikisana ubufakazi buphela - ungathola le fomula ngezikhathi ezithile kuzo zonke izincwadi zezibalo. Lobu bufakazi besimo buyiqhinga eliyintandokazi lama-sophists.

Nokho, ngiyagcizelela ukuthi lokhu ukucabanga kwesimanje - abakwaPythagoras babengenazo izisetshenziswa ezithuthukisiwe ze-algebraic. Babefuna isilinganiso esivamile sohlangothi lwesikwele kanye ne-diagonal yaso, okwabaholela embonweni wokuthi kwakungeke kube khona isilinganiso esinjalo esivamile. Ukucatshangelwa kokuba khona kwayo kuholela ekuphikisaneni. Umhlabathi oqinile washelela ngaphansi kwezinyawo zami. Konke kufanele kukwazi ukuchazwa ngezinombolo, futhi i-diagonal yesikwele, lapho noma ubani angakwazi ukuyidweba ngenduku esihlabathini, ayinalo ubude (okungukuthi, kuyalinganiseka, ngoba azikho ezinye izinombolo). “Ukholo lwethu lwaluyize,” amaPythagorean ayesho. Okufanele ngikwenze?

Kwenziwa imizamo yokuzisindisa ngezindlela zamahlelo. Noma ubani onesibindi sokuthola ukuthi kukhona izinombolo ezingenangqondo uzobulawa, futhi, ngokusobala, inkosi ngokwayo - ngokuphambene nomyalo wobumnene - ufeza umusho wokuqala. Khona-ke yonke into iba ikhethini. Ngokusho kwenye inguqulo, amaPythagoreans abulawa (ngandlela-thile asindisiwe futhi ngenxa yabo wonke umqondo awuzange uyiswe ethuneni), ngokusho komunye, abafundi ngokwabo, belalela kakhulu, baxosha inkosi ekhulekelwayo futhi endaweni ethile uphetha ukuphila kwakhe ekudingisweni. . Ihlelo alisekho.

Sonke siyawazi amazwi kaWinston Churchill: "Akukaze emlandweni wokungqubuzana kwabantu kube nabantu abaningi kangaka abakweleta kakhulu abambalwa." Kwakumayelana nabashayeli bezindiza abavikela iNgilandi ezindizeni zaseJalimane ngo-1940. Uma sishintsha "izingxabano zabantu" ngokuthi "imicabango yomuntu", lesi sisho sisebenza kwabambalwa abakwaPythagoras abaphunyuka (kancane kakhulu) ku-pogrom ekupheleni kweminyaka yama-XNUMXs. Ngekhulu lesi-XNUMX BC.

Ngakho "umcabango wadlula ngaphandle kokulimala." Yini elandelayo? Inkathi yegolide iyeza. AmaGreki anqoba amaPheresiya (Marathon - 490 BC, Inkokhelo - 479). Intando yeningi iya iba namandla. Izikhungo ezintsha zomcabango wefilosofi nezikole ezintsha ziyavela. Abalandeli bePythagoreanism babhekene nenkinga yezinombolo ezingenangqondo. Abanye bathi: “Ngeke siyiqonde le mfihlakalo; singazindla ngakho kuphela futhi sibabaze i-Uncharted." Lezi zamuva zinengqondo kakhulu futhi aziyihloniphi i-Mystery: “Uma kukhona okungahambi kahle ngalezi zibalo, masiziyeke, ngemva kweminyaka engaba ngu-2500 yonke into iyokwaziwa. Mhlawumbe izinombolo azibuse umhlaba? Ake siqale ngejiyomethri. Akusezona izinombolo ezibalulekile, kodwa izilinganiso nezilinganiso zazo.

Abasekeli isiqondiso sokuqala baziwa izazi-mlando zezibalo njengoba ama-acousticsBahlala amakhulu ambalwa eminyaka futhi kunjalo. Laba bazibiza izibalo (kusuka ku-mathein yesiGreki = ukwazi, ukufunda). Asidingi ukuchaza kunoma ubani ukuthi le ndlela inqobile: isiphile iminyaka engamakhulu amabili nanhlanu futhi iyaphumelela.

Ukunqoba kwezazi zezibalo phezu kwe-auzmatics kwavezwa, ikakhulukazi, ekubukeni kophawu olusha lwamaPythagoreans: kusukela manje kuqhubeke kwakuyi-pentagram (pentás = emihlanu, uhlelo lolimi = incwadi, umbhalo) - i-pentagon evamile esesimweni se inkanyezi. Amagatsha awo anqamula ngokulingana ngokwedlulele: lonke lihlala libhekisela engxenyeni enkulu, kanti ingxenye enkulu ibhekisela engxenyeni encane. Wafona isilinganiso saphezulu, bese ikhishwa ngokwenkolo igolide. AmaGreki asendulo (kanye nezwe lonke le-Eurocentric ngemuva kwabo) ayekholelwa ukuthi lesi silinganiso sasijabulisa kakhulu iso lomuntu, futhi sasihlangana cishe yonke indawo.

(Cyprian Camille Norwid, "Promethidion")

Ngizoqeda ngesiqephu esisodwa, kulokhu kusukela enkondlweni ethi "Faust" (ehunyushwe nguVladislav August Kostelsky). Phela, i-pentagram nayo iyisithombe sezinzwa ezinhlanu kanye "nonyawo lomthakathi" oludumile. Enkondlweni kaGoethe, uDkt. Faust wayefuna ukuzivikela kudeveli ngokudweba lolu phawu embundwini wendlu yakhe. Wakwenza ngokunganaki, futhi nakhu okwenzeka:

Faust

M epistopheles

Faust

Futhi lokhu kumayelana ne-pentagon evamile ekuqaleni konyaka omusha wesikole.