No ka makahiki kula hou
ʻO ka hapa nui o ka poʻe heluhelu ma kahi hoʻomaha - inā ma ko mākou ʻāina nani, ma nā ʻāina pili, a i ʻole ma waho paha. E hoʻohana kākou i kēia ʻoiai e hāmama ana nā palena no kākou ... He aha ka hōʻailona pinepine i kā mākou huakaʻi pōkole a lōʻihi? He pua keia e kuhikuhi ana i ka puka o ke alanui, ka hoomau ana o ke ala mauna, ka puka o ka hale hoikeike, ka puka i kahakai, a pela aku. He aha ka mea hoihoi i kēia mau mea? Ma ka makemakika, ʻaʻole nui loa. Akā, e noʻonoʻo kākou: ʻike ʻia kēia hōʻailona i nā mea āpau ... nā ʻelele o kahi moʻomeheu kahi i pana ʻia ai ka pana pana. ʻOiaʻiʻo, hikiʻole ke hōʻoia i kēia. ʻAʻole mākou ʻike i kekahi civilization ʻē aʻe. Eia naʻe, ʻoi aku ka hoihoi o ka pentagon maʻamau a me kona ʻano hoku, ka pentagram.
ʻAʻole pono mākou i kahi hoʻonaʻauao e ʻike i kēia mau helu he mea hoihoi a hoihoi. Inā, e ka mea heluhelu, ua inu ʻoe i ka cognac hōkū ʻelima i loko o kahi hōkele hōkū ʻelima ma Place des Stars ma Paris, a laila paha… ua hānau ʻia ʻoe ma lalo o kahi hōkū laki. Ke noi mai kekahi iā mākou e kahakiʻi i kahi hōkū, e huki mākou i kahi ʻelima mau kikoʻī me ka kānalua ʻole, a i ka wā e kahaha ai ka interlocutor: "He hōʻailona kēia o ka USSR mua!", Hiki iā mākou ke pane: Stables!".
ʻO ka pentagram, a i ʻole ka hōkū ʻelima, he pentagon maʻamau, ua haku ʻia e nā kānaka āpau. Ma kahi o ka hapahā o nā ʻāina, me ka US a me ka USSR mua, ua hoʻokomo iā ia i kā lākou mau hōʻailona. Ma ke ʻano he kamaliʻi, ua aʻo mākou e kaha kiʻi i ka hōkū ʻelima me ka ʻole e hāpai i ka penikala mai ka ʻaoʻao. I ka wā makua, lilo ʻo ia i hōkū alakaʻi no mākou, ʻaʻole loli, mamao, kahi hōʻailona o ka manaʻolana a me ka hopena, kahi ʻōlelo. E nana kakou ma ka aoao.
He aha nā hōkū e haʻi mai nei iā mākou?
Ua ʻae ka poʻe mōʻaukala a hiki i ke kenekulia XNUMX BC, ua mau ka hoʻoilina naʻauao o nā kānaka o ʻEulopa i ka malu o nā moʻomeheu o Babulona, ʻAigupita a me Phoenicia. A hiki koke mai ke ono o ke kenekulia e lawe mai i ka renaissance a me ka ulu wikiwiki o ka moʻomeheu a me ka ʻepekema i ʻōlelo ʻia e kekahi poʻe nūpepa (no ka laʻana, ʻo Daniken) - paʻakikī ke ʻōlelo inā manaʻoʻiʻo lākou i kēia - ʻaʻole hiki ke hana me ka ʻole o ka hana. o na pio. mai ka lewa mai.
I ka hiki ʻana mai i Helene, he wehewehe kūpono ka hihia: ma muli o ka neʻe ʻana o nā kānaka, aʻo hou ka poʻe noho o ka Peloponnesian Peninsula e pili ana i ka moʻomeheu o nā ʻāina e pili ana (no ka laʻana, komo nā leka Phoenician i Helene a hoʻomaikaʻi i ka alphabet) , a hoʻomaka lākou e noho i ke kai Mediterranean. He mau kūlana maikaʻi loa kēia no ka hoʻomohala ʻana i ka ʻepekema: ke kūʻokoʻa i hui pū ʻia me nā pilina me ka honua. Me ke kūʻokoʻa ʻole, hoʻopaʻi mākou iā mākou iho i ka hopena o nā repubalika maiʻa o ʻAmelika Hui Pū ʻIa, me ka ʻole o nā pilina - i North Korea.
Heluhelu
ʻO ke kenekulia XNUMX BC he kenekulia kūikawā i ka moʻolelo o ke kanaka. Me ka ʻike ʻole a lohe ʻole paha kekahi i kekahi, ua aʻo nā mea manaʻo nui ʻekolu: Buddha, Confucius i Pythagoras. ʻO nā mea mua ʻelua i hana i nā hoʻomana a me nā ʻepekema e ola mau nei i kēia lā. Ua kaupalena ʻia ke kuleana o ka hapakolu o lākou i ka loaʻa ʻana o kekahi waiwai a i ʻole kekahi waiwai o kekahi huinakolu?
I ka hoʻomaka ʻana o ke kenekulia 624 a me 546 (c. XNUMX - c. XNUMX BC) i Miletus i kēia manawa ʻo Asia Minor i noho ai. ʻO ia. Wahi a kekahi mau kumu, he kanaka ʻepekema ʻo ia, ʻo kekahi ʻē aʻe he mea kālepa waiwai, a ʻo nā mea ʻē aʻe i kapa iā ia he ʻoihana (ʻoiai, i ka makahiki hoʻokahi ua kūʻai ʻo ia i nā mīkini ʻaila a pau a hōʻaiʻē iā lākou no ka uku usurious). ʻO kekahi poʻe, e like me ke ʻano a me ke ʻano o ka ʻepekema i kēia manawa, ʻike ʻo ia i kahi kahu: ua kono ʻo ia i ka poʻe naʻauao, hānai iā lākou a mālama iā lākou, a laila ʻōlelo ʻo ia: "E hana ʻoe no ka nani oʻu. a me ka ʻepekema a pau. Eia nō naʻe, nui nā kumu koʻikoʻi e ʻōlelo nei ʻaʻole i ola ʻo Thales, ka ʻiʻo a me ke koko, a ʻo kona inoa wale nō ka mea i hoʻohālikelike ʻia i nā manaʻo kikoʻī. Pehea, pēlā, a ʻaʻole paha mākou e ʻike. Ua kākau ka mea kākau moʻolelo makemakika ʻo E. D. Smith, inā ʻaʻohe Thales, ʻaʻohe Pythagoras a i ʻole kekahi e like me Pythagoras, a inā ʻaʻole ʻo Pythagoras ʻaʻohe Plato a i ʻole kekahi e like me Plato. ʻOi aku paha. E waiho nae kakou i ka mea i hanaia ina.
Ua aʻo ʻo Pythagoras (c. 572 - c. 497 BC) ma Crotone ma ka ʻaoʻao hema o Italia, a ma laila i hānau ʻia ai ka ʻoihana naʻauao i kapa ʻia ma muli o ka haku. Pythagoreanism. He neʻe hoʻomana a me ka hui i hoʻokumu ʻia, e like me kā mākou e kapa ai i kēia lā, ma nā mea huna a me nā aʻo huna, me ka noʻonoʻo ʻana i ka ʻepekema ʻo ia kekahi o nā mea e hoʻomaʻemaʻe ai i ka ʻuhane. I ka wā o ke ola o hoʻokahi a ʻelua paha hanauna, hele ʻo Pythagoreanism i nā pae maʻamau o ka hoʻomohala ʻana i nā manaʻo: ka ulu mua a me ka hoʻonui, ka pilikia a me ka emi ʻana. ʻAʻole hoʻopau nā manaʻo nui i ko lākou ola ma laila a ʻaʻole make mau loa. ʻO ke aʻo naʻauao o Pythagoras (ua haku ʻo ia i kahi huaʻōlelo āna i kapa ai iā ia iho: philosopher, a i ʻole hoa o ka naʻauao) a ua lanakila kāna mau haumāna i ka wā kahiko, a laila hoʻi i ka Renaissance (ma lalo o ka inoa o ka pantheism), a aia mākou ma lalo o kāna mana. i kēia lā. Ua paʻa loa nā loina o Pythagoreanism i ka moʻomeheu (ma ka liʻiliʻi loa ma ʻEulopa) ʻaʻole hiki iā mākou ke ʻike hiki iā mākou ke noʻonoʻo ʻē aʻe. Pīhoihoi mākou ma mua o Molière's Monsieur Jourdain, ka mea i kāhāhā i ka ʻike ʻana ua kamaʻilio ʻo ia i ka prose i kona ola a pau.
ʻO ka manaʻo nui o Pythagoreanism ka manaʻoʻiʻo ua hoʻonohonoho ʻia ka honua e like me kahi hoʻolālā koʻikoʻi a me ka lokahi, a ʻo ka ʻoihana o ke kanaka ke ʻike i kēia lokahi. A ʻo ka noʻonoʻo ʻana i ka lokahi o ka honua ka mea e aʻo ai i ka Pythagoreanism. ʻO ka poʻe Pythagoreans he poʻe mystics a me ka makemakika, ʻoiai i kēia lā wale nō ka maʻalahi o ka hoʻokaʻawale ʻana iā lākou. Ua hoʻokaʻawale lākou i ke ala. Ua hoʻomaka lākou i kā lākou aʻo ʻana i ka lokahi o ka honua, aʻo mua i ke mele, astronomy, arithmetic, etc.
ʻOiai ua hāʻule ke kanaka i ke kilokilo "mau loa", ʻo ke kula Pythagorean wale nō i hoʻokiʻekiʻe iā ia i ke kānāwai kūpono. "Numbers rule the world" – ʻo kēia ʻōlelo ʻōlelo ka ʻano maikaʻi loa o ke kula. He ʻuhane ko nā helu. ʻO kēlā me kēia mea he mea, kēlā me kēia mea hōʻailona i kekahi mea, kēlā me kēia mea i hōʻike i kahi ʻāpana o kēia lokahi o ka Universe, i.e. hakahaka. ʻO ka huaʻōlelo ponoʻī ʻo ia ka "kauoha, kauoha" (ʻike ka poʻe heluhelu i ka hoʻomaʻamaʻa ʻana i ka maka a hoʻonui i ka nani).
Hāʻawi nā kumu like ʻole i nā manaʻo like ʻole a ka Pythagoreans i hāʻawi i kēlā me kēia helu. ʻO kekahi ala a i ʻole, hiki i ka helu like ke hōʻailona i kekahi mau manaʻo. ʻO nā mea nui loa ʻeono (helu kūpono) i he umi - ka huina o nā helu ʻokoʻa 1+2+3+4, i haku ʻia me nā helu ʻē aʻe, ka hōʻailona o ia mea i ola a hiki i kēia lā.
No laila, ua aʻo ʻo Pythagoras ʻo nā helu ka hoʻomaka a me ke kumu o nā mea āpau, ʻo ia - inā ʻoe e hana - "hui" lākou me kekahi, a ʻike wale mākou i nā hopena o kā lākou hana. Hoʻokumu ʻia, a i ʻole i hoʻomohala ʻia e Pythagoras, ʻaʻohe "paʻi maikaʻi" ka mysticism o nā helu i kēia lā a ʻike pū nā mea kākau koʻikoʻi i kahi hui ʻana o "pathos a me absurdity" a i ʻole "science, mysticism and clean exaggeration." He mea paʻakikī ke hoʻomaopopo pehea e hiki ai i ka mea kākau moʻolelo kaulana ʻo Alexander Kravchuk ke kākau iā Pythagoras a me kāna mau haumāna i hoʻopiha i ke akeakamai me nā hihiʻo, nā moʻolelo, nā superstitions - me he mea lā ʻaʻole ʻo ia i maopopo i kekahi mea. No ka mea, ʻo kēia wale nō ke ʻano mai ka manaʻo o kā mākou kenekulia XNUMX. ʻAʻole hoʻopaʻapaʻa nā Pythagoreans i kekahi mea; ua hana lākou i kā lākou mau manaʻo me ka manaʻo maikaʻi loa. Malia paha i loko o kekahi mau kenekulia e kākau kekahi i ka manaʻo holoʻokoʻa o ka relativity he mea lapuwale, hoʻopunipuni a paʻakikī. A ʻo ka hōʻailona helu, ka mea i hoʻokaʻawale iā mākou mai Pythagoras i ka hapaha miliona mau makahiki, ua komo hohonu i loko o ka moʻomeheu a lilo i ʻāpana o ia mea, e like me nā moʻolelo Helene a me Kelemania, nā moʻolelo naita kahiko, nā moʻolelo Lūkini e pili ana iā Kosc a i ʻole ʻo Juliusz Słowacki i ka hihiʻo o ka Pope Slavic.
Pohihihi noʻonoʻo
Ma ka geometry, kāhāhā ka poʻe Pythagoreans figurami-podobnыmi. A ma ka nānā ʻana o ka Thales theorem, ke kānāwai kumu o nā lula o ka like, ua hiki mai kahi pōʻino. Ua ʻike ʻia nā ʻāpana like ʻole, a no laila nā helu irrational. Nā ʻāpana ʻaʻole hiki ke ana ʻia e kekahi ana maʻamau. Nā helu i like ʻole. A ua loaʻa iā ia ma kekahi o nā ʻano maʻalahi loa: kahi huinaha.
I kēia lā, i ka ʻepekema kula, kāʻei mākou i kēia ʻoiaʻiʻo, ʻaneʻane ʻaʻole ʻike. He √2 ka diagonal o ka huinaha? Nui, pehea ka nui o ia mea? Kaomi mākou i ʻelua pihi ma ka helu helu: 1,4142 ... ʻAe, ua ʻike mua mākou i ke kumu huinahā o ʻelua. ʻO ka mea hea? He noonoo ole anei? Malia paha no ka hoʻohana ʻana i kahi hōʻailona ʻē, akā ma hope o nā mea a pau i kaʻoiaʻiʻo ʻo ia ka 1,4142. Ma hope o nā mea a pau, ʻaʻole wahaheʻe ka helu helu.
Inā manaʻo ka mea heluhelu he hoʻonui wau, a laila ... maikaʻi loa. ʻIke ʻia, ʻaʻole ʻino nā kula Polani e like me, no ka laʻana, ma nā kula Pelekane, kahi o nā mea āpau hiki ole ke ana kahi ma waena o nā moʻolelo moʻolelo.
Ma ka Polani, ʻaʻole weliweli ka huaʻōlelo "irrational" e like me kona hoa ma nā ʻōlelo ʻEulopa. Rational numbers there are rational, rationnel, rational, i.e.
E noʻonoʻo i ke kumu o √2 he helu kuhi hewa, ʻo ia hoʻi, ʻaʻole ia he hakina o ka p/q, kahi o ka p a me q he mau helu. Ma nā huaʻōlelo hou, ua like ia me kēia ... Ina paha ʻo √2 = p / q a ʻaʻole hiki ke hoʻopōkole hou ʻia kēia hakina. ʻO ka mea nui, he ʻokoʻa nā p a me q. Ka huinaha like: 2q2=p2. ʻAʻole hiki ke ʻokoʻa ka helu p, mai ia manawa p2 ʻo ia hoʻi, a ʻo ka ʻaoʻao hema o ka like ʻana he paʻi ia o 2. No laila, p like like, ʻo ia hoʻi, p = 2r, no laila p2= 4r2. Hoemi makou i ka hoohalike 2q2= 4r2. loaʻa iā mākou d2= 2r2 a ke ike nei makou he pono no q, a makou i manao ai aole pela. Loaʻa kuee pau ka hōʻoiaʻiʻo - hiki iā ʻoe ke ʻike i kēia ʻano kumu i kēlā me kēia manawa ma kēlā me kēia puke makemakika. ʻO kēia hōʻike kūʻokoʻa kahi ʻenehana punahele a ka poʻe sophists.
Eia naʻe, ke koʻikoʻi nei au, ʻo kēia ka noʻonoʻo hou - ʻaʻole i loaʻa i ka Pythagoreans kahi mea hana algebraic i kūkulu ʻia. E ʻimi ana lākou i kahi ana maʻamau o ka ʻaoʻao o ka huinahā a me kona diagonal, i alakaʻi iā lākou i ka manaʻo ʻaʻole hiki ke ana like ʻole. ʻO ka manaʻo o kona olaʻana e alakaʻi i kahi kū'ē. Ua paheʻe ka lepo paʻakikī mai lalo o koʻu mau wāwae. Pono e wehewehe ʻia nā mea a pau e nā helu, a ʻo ka diagonal o kahi huinahā, hiki i kekahi ke kaha kiʻi me kahi lāʻau ma ke one, ʻaʻohe lōʻihi (ʻo ia hoʻi, hiki ke ana ʻia, no ka mea ʻaʻohe helu ʻē aʻe). "Ua makehewa ko makou manaoio," wahi a ka Pythagoreans. He aha ka hana?
Ua hoʻāʻo ʻia e hoʻopakele iā lākou iho ma o nā ʻano sectarian. ʻO ka mea e ʻaʻa e ʻike i ke ola ʻana o nā helu irrational e pepehi ʻia ʻo ia, a, ʻoiai, ʻo ka haku ponoʻī - kūʻē i ke kauoha o ke akahai - e hoʻokō i ka ʻōlelo mua. A laila lilo nā mea a pau i pale. Wahi a kekahi manaʻo, ua pepehi ʻia nā Pythagoreans (ua hoʻōla ʻia kekahi mau mea a mahalo iā lākou ʻaʻole i lawe ʻia ka manaʻo holoʻokoʻa i ka lua kupapaʻu), e like me kekahi, ʻo nā haumāna ponoʻī, no ka hoʻolohe ʻana, kipaku aku i ka haku i hoʻomana ʻia a hoʻopau ʻo ia i kona ola. i ke pio ana. Pau ka noho ana o ka secte.
Uaʻike mākou a pau i ka'ōlelo a Winston Churchill: "ʻAʻole loa i loko o ka moʻolelo o ka hakakā kanaka ka nui o nā aie i ka liʻiliʻi." E pili ana ia i nā pailaka i pale iā ʻEnelani mai ka mokulele Kelemania i ka makahiki 1940. Inā mākou e hoʻololi i nā "hakakā kanaka" me nā "manaʻo kanaka", a laila pili ka ʻōlelo i ka lima o nā Pythagoreans i pakele (no ka liʻiliʻi) mai ka pogrom i ka hopena o XNUMXs. VI Keneturi BC.
No laila "ua hala ka manaʻo me ka ʻole." He aha ka hope? E hiki mai ana ka makahiki gula. Ua lanakila nā Helene i nā Peresia (Marathon - 490 BC, Uku - 479). Ke ikaika nei ka Demokala. Ke puka mai nei nā kikowaena noʻonoʻo noʻonoʻo a me nā kula hou. Ke kū nei ka poʻe hahai i ka Pythagoreanism me ka pilikia o nā helu irrational. Wahi a kekahi poe: “Aole makou e hoomaopopo i keia mea pohihihi; hiki iā mākou ke noʻonoʻo a mahalo iā Uncharted." ʻOi aku ka maikaʻi o nā mea hope a ʻaʻole mahalo i ka Mystery: "Inā hewa kekahi mea i kēia mau helu, e waiho wale iā lākou, ma hope o 2500 mau makahiki e ʻike ʻia nā mea āpau. ʻAʻole paha ka helu i ka honua? E hoʻomaka kākou me ka geometric. ʻAʻole ʻo nā helu ka mea nui, akā ʻo kā lākou like a me nā ratios.
ʻO nā mea kākoʻo o ka ʻaoʻao mua i ʻike ʻia e nā mea kākau moʻolelo o ka makemakika e like me nā mea kaniUa ola lākou no kekahi mau kenekulia hou aʻe. Ua kapa aku ka poe hope ia lakou iho makemakika (mai ka Greek mathein = ʻike, aʻo). ʻAʻole pono mākou e wehewehe i kekahi ua lanakila kēia ala: ua ola ʻo ia no iwakāluakūmālima mau kenekulia a lanakila.
Ua hōʻike ʻia ka lanakila o nā mea makemakika ma luna o ka auzmatics, i ka ʻike ʻia ʻana o kahi hōʻailona hou o ka Pythagoreans: mai kēia manawa he pentagram (pentás = ʻelima, gramma = leka, inscription) - he pentagon maʻamau i ke ʻano o kahi. hoku. Kūlike loa kona mau lālā: pili mau ka mea holoʻokoʻa i ka hapa nui, a ʻo ka hapa nui i ka hapa liʻiliʻi. Ua kāhea ʻo ia ka like ana o ke Akua, a laila hoʻolalelale i ke gula. Ua manaʻo ka poʻe Helene kahiko (a me ka honua Eurocentric a pau ma hope o lākou) ʻo kēia ʻāpana ka mea ʻoluʻolu loa i ka maka o ke kanaka, a ua hālāwai me ia ma nā wahi āpau.
(Cyprian Camille Norwid, "Promethidion")
E hoʻopau wau me kahi pauku hou, i kēia manawa mai ka mele "Faust" (unuhi ʻia e Vladislav August Kostelsky). ʻAe, ʻo ka pentagram kekahi kiʻi o nā manaʻo ʻelima a me ka "wāwae kilokilo" kaulana. Ma ka mele a Goethe, ua makemake ʻo Kauka Faust e pale iā ia iho mai ka diabolo ma ke kahakaha ʻana i kēia hōʻailona ma ka paepae o kona hale. Ua hana wale ʻo ia, a penei ka mea i hana ʻia.
Faust
M epistopheles
Faust
A e pili ana kēia i ka pentagon maʻamau i ka hoʻomaka ʻana o ka makahiki kula hou.
