Ua haʻohaʻo nā ʻepekema Helene kahiko inā paha i hana kekahi i ka makemakika a i ʻole aia a alakaʻi i ka hoʻomohala ʻana o ka Universe e ia iho, a hiki i ke kanaka ke hoʻomaopopo i ka makemakika i kekahi ʻano. Ua manaʻo ʻo Platon lāua ʻo Aristotle ʻaʻole hiki i nā kānaka ke hoʻololi a hoʻohuli paha i ka makemakika. Me ka hoʻomohala hou ʻana o ka ʻepekema, ka postulate i ka makemakika kahi mea i hāʻawi ʻia iā mākou mai luna mai, ua hoʻoikaika ʻia me ka paradoxically. Ua kākau pololei ʻo Thomas Hobbes i ke kenekulia 18 i ka mōʻaukala e like me ka ʻepekema i mōhai ʻia i ke kanaka e ke Akua. ʻO ka laureate Nobel ʻo Eugene Wigner i ke kenekulia iwakālua i kapa ʻia ka ʻōlelo makemakika he "makana", eia naʻe, ʻaʻole ʻo ke Akua i ke ʻano hou, a e like me Wigner, ua loaʻa iā mākou ka makana mai ka hopena.
Ua kapa ʻia ʻo Eugene Wigner "ke akamai noho mālie"
ʻO ka paio ma waena o ka hoʻomohala ʻana o ka makemakika ma ke ʻano he ʻepekema a me ka hoʻoikaika ʻana o ka manaʻoʻiʻo i ke ʻano o ko mākou honua, i ʻike mua ʻia mai luna mai. Inā aʻo ka hapanui o ke koena o ka ʻepekema e pili ana i ka honua, maʻamau, empirically - loaʻa i nā meaolaola kahi ʻano hou a wehewehe iā ia, wehewehe nā chemist a hana paha i nā mea, a pēlā aku - a laila waiho ka makemakika i ka ʻike hoʻokolohua ma mua loa. Eia kekahi, hiki iā ia ke pale i kāna ulu ʻana. Inā ʻo Galileo Galilei, Newton a Kepler paha, ma kahi o ka hana kuhiakau e pili ana i ka neʻe ʻana o nā paneta a me nā satellite, i nānā ʻia ma o ka teleskope i ka pō, ʻaʻole hiki iā lākou ke loaʻa. Ma ke kōkua wale nō o ka helu makemakika i helu ai lākou i kahi e kuhikuhi ai i ka teleskopa, a loaʻa ka hōʻoia o kā lākou kuhiakau a me nā helu. A i ka loaʻa ʻana o kahi manaʻo kuʻikahi, makemakika nani o ka neʻe ʻana o nā kino lani, pehea e hiki ai ke hōʻoia i ka noho ʻana o ke Akua, nāna i hoʻonohonoho kūleʻa a kūpono hoʻi i ka Universe?
No laila, ʻo ka nui o ka ʻepekema e aʻo e pili ana i ka honua a wehewehe iā ia e nā ʻano makemakika, ʻoi aku ka pīhoihoi i ka leka ʻana o ka mīkini makemakika i nā kānāwai o ke kūlohelohe. Ua ʻike ʻo Newton i ka ikaika o ka pilina gravitational i kūlike kūlike i ka square o ka mamao ma waena o nā kino. ʻO ke kumumanaʻo o "square", ʻo ia hoʻi, ke kekelē ʻelua, ua ʻike ʻia i ka makemakika i ka wā ma mua, akā ua hana kupanaha ʻia ka wehewehe ʻana o ke kānāwai hou. Ma lalo iho kahi laʻana o kahi noi kamahaʻoi aʻe o ka makemakika i ka wehewehe o nā hana olaola.
1. Maliʻa paha, ua hoʻokumu ʻia ka manaʻo a puni ka honua i ka makemakika i ka manaʻo mua o Archimedes. ʻAʻole ia e pili ana i ka ʻōlelo kaulana e pili ana i ka fulcrum a me ke kipi o ka honua. ʻAʻole hiki iā Archimedes ke hōʻoia i ka hoʻokumu ʻia o ke ao ma ka makemakika (a ʻaʻohe hiki i kekahi). Manaʻo ka makemakika i nā mea āpau i ke kūlohelohe e hiki ke wehewehe ʻia e nā ʻano o ka makemakika (eia ka fulcrum!), A ʻo nā ʻike makemakika e hiki mai ana ua hōʻike ʻia i ke ʻano ma kahi ʻē. ʻO ke kuhi ke loaʻa wale kēia mau hana.
2. Ua nui ka ʻiʻini o ka makemakika Pelekane Godfrey Hardy e lilo i ʻepekema noho lima wale e noho ana i ke ao kiʻekiʻe o nā kiʻi matematika i loko o kāna puke ponoʻī, i kapa ʻia ʻo "The Apology of a Matematika," ua kākau ʻo ia i kāna hana maikaʻi ʻole i ke ola. ʻIno, ʻoiaʻiʻo nō - he makemakika maoli wale nō. Eia nō naʻe, i ka manawa i hoʻokolokolo ai ke kauka Kelemania ʻo Wilhelm Weinberg i nā waiwai genetics o kēlā me kēia kanaka i hānau ʻia me ka nui o ka lehulehu me ka ʻole o ka neʻe ʻana, ua hōʻoia ʻo ia ʻaʻole e loli ke ʻano o nā holoholona. Ua hoʻolaʻa ʻia ka hana i nā waiwai o nā helu kūlohelohe, a ua kapa ʻia ke kānāwai ʻo Weinberg-Hardy Law. ʻO kā Weinberg co-mea kākau ka mea maʻamau i ke kiʻi hele ʻana o ka puke kākau "ʻoi aku ka hāmau". Ma mua o ka hoʻomaka ʻana o ka hana ma ka hōʻoia, ka mea i kapa ʻia. ʻO ka pilikia binary o Goldbach a i ʻole ko Euler pilikia (hiki i kekahi helu ke kū i ke ʻano o ka helu o nā prime ʻelua) Ua ʻōlelo ʻo Hardy: e kuhi paha kekahi mea lapuwale i kēia. Ua make ʻo Hardy i ka makahiki 1947; ʻaʻole i loaʻa ka hōʻoia o ke kākau manaʻo.
ʻOiai ʻo kāna mau eccentricities, ʻo Godfrey Hardy kahi makemakika ikaika loa.
3. Ua kākau pololei ʻo Galileo Galilei kaulana i kāna puke moʻolelo "Assaying Master" i ka Universe, e like me kahi puke, wehe ʻia i nā maka o kekahi, akā hiki i kēia puke ke heluhelu wale ʻia e ka poʻe ʻike i ka ʻōlelo i kākau ʻia ai. A kākau ʻia i ka ʻōlelo o ka makemakika. I kēlā manawa, ua ʻike ʻo Galileo i nā satellite o Jupiter a helu i ko lākou mau kaʻina, a ua hōʻoia ʻia aia nā kiko o ka Lā ma luna pono o ka hōkū, e hoʻohana ana i hoʻokahi kūkulu geometric. ʻO ka hoʻomāinoino ʻia o Galileo e ka Ekalesia Katolika ma muli o kāna hilinaʻi ʻana i ka heluhelu ʻana i ka puke o ka Universe kahi hana e ʻike ai i ka manaʻo akua. ʻO Cardinal Bellarmine, ka mea i noʻonoʻo i ka hihia o ka ʻepekema i ka Hui Hemolele Nui, ua hoʻomaopopo koke ʻo ia i ka makaʻu o ia mau manaʻo. Ma muli o kēia makaʻu loa ua kipaku ʻia ʻo Galiono mai ke ʻae ʻana ʻo ke kikowaena o ke ao ka Honua. Ma nā huaʻōlelo hou aku, ʻoi aku ka maʻalahi o ka wehewehe ʻana i nā haʻiʻōlelo e pili ana ʻo Galileo i ka Palapala Hemolele ma mua o ka wehewehe ʻana i nā kumumanaʻo o ka hoʻokokoke ʻana i ka Universe no ka manawa lōʻihi.
Galileo i kona hoʻokolokolo ʻia
4. ʻO kahi loea i ka physics physics Mitch Feigenbaum i ʻike ʻia ma 1975 inā ʻoe e hana hou me ka mīkini i ka helu ʻana o kekahi mau hana makemakika ma kahi microcalculator, hiki i ka hopena o nā helu ke 4.669 ... ʻAʻole hiki iā Feigenbaum ke wehewehe i kēia ʻano ʻē, akā kākau ʻo ia i kahi ʻatikala e pili ana iā ia. Ma hope o ka loiloi ʻeono mahina, ua hoʻihoʻi ʻia ka ʻatikala iā ia, e aʻoaʻo ana iā ia e hoʻolohe iki i ka hanana wale - ka makemakika ma hope o nā mea āpau. A ma hope ua hoʻololi ʻia kēlā ʻano helu i ke ʻano o ka helium wai ke hoʻomehana ʻia mai lalo, ka wai i loko o kahi paipu e lilo i ʻano kūpikipiki (ʻo kēia ke kahe ka wai mai ka piula me nā huʻa ea) a ʻo ka wai e kahe ana ma muli o ka piula pani paʻa.
He aha ka mea i ʻike ʻia e Mitchell Feigenbaum inā loaʻa iā ia he iPhone i kona wā ʻōpio?
5. ʻO ka makuakāne o nā makemakika a pau, koe wale nō ka helu, ʻo Rene Descartes me ka ʻōnaehana hoʻohui i kapa ʻia ma hope ona. Hoʻohui ʻo Descartes i ka algebra me ka geometry, e lawe ana iā lākou i kahi pae qualitative hou. Ua hana ʻo ia i ka makemakika i kahi ʻepekema puni honua āpau. Ua wehewehe ka Euclid nui i kahi kiko me he mea waiwai ʻole a hiki ʻole ke hoʻokaʻawale ʻia i nā ʻāpana. I Descartes, ua lilo ka piko i hana. I kēia manawa, e hoʻohana nei i nā hana, wehewehe mākou i nā kaʻina hana ʻole laina laina mai ka ʻai ʻana o ka penehine i nā loli i kou kaumaha pono - pono ʻoe e ʻike i ka piko pololei. Eia nō naʻe, ākea ka launa o nā makemake o Descartes. Eia hou, ua hāʻule ka wā pīhoihoi o kāna mau hana i ka manawa o Galileo, a ʻo Descartes, e like me kāna ʻōlelo ponoʻī, ʻaʻole makemake e paʻi i hoʻokahi huaʻōlelo i kūʻē i ke aʻo ʻana o ka hale pule. A me ka ʻole o ia, me ka ʻae ʻia o Cardinal Richelieu, ua hōʻino ʻia ʻo ia e nā Katolika a me nā Protestant. Ua haʻalele ʻo Descartes i ke ao o ka akeakamai maʻemaʻe a laila make koke ia ma Suedena.
ʻO Rene Descartes
6. I kekahi manawa me he mea lā, ʻo ke kauka Lākana a me ka antiquarian ʻo William Stukeley, i manaʻo ʻia he hoaaloha na Isaac Newton, pono e hoʻokau ʻia i kekahi o nā kaʻina hana mai ka arsenal o ka Inquisance Hemolele. Me kona lima māmā i hele a kaʻao ka kaʻao o ka apple Newtonian a puni ka honua. Me he mea lā, ua hele au i kaʻu hoaaloha ʻo ʻIsaʻaka ma ka ʻelima-o-clok, hele mākou i waho i ka māla, a ma laila e hāʻule ai nā ʻāpala. Lawe iā ʻIsaʻaka, a noʻonoʻo: no ke aha e hāʻule wale ai nā ʻoma? Pēlā i hānau ʻia ai ke kānāwai gravitation ākea ma ke alo o kāu kauā haʻahaʻa. Hoʻopau profanation o ka ʻepekema noiʻi. ʻO ka ʻoiaʻiʻo, ua kākau pololei ʻo Newton i kāna "Matematika Kumumanaʻo o Philosophy Kūlohelohe" i loaʻa i ka makemakika nā ikaika o ka umekaumaha mai nā hanana lani. ʻO ka pālākiō o ka loaʻa ʻana o Newton he paʻakikī loa e noʻonoʻo. Ma hope o nā mea āpau, ʻike mākou i kēia manawa ua pili ka ʻike āpau o ka honua i ke kelepona, a ma laila e loaʻa ai kahi lumi. Akā e waiho iā mākou iā mākou iho i nā kāmaʻa o ke kanaka o ke kenekulia 17, nāna i wehewehe i ka neʻe ʻana o nā kino lani like ʻole me ka ʻike ʻole ʻia a me ka launa pū ʻana o nā mea me nā ʻano makemakika maʻalahi. E hōʻike i ka makemake akua i nā helu. ʻAʻole i pau ke ahi o ka Inekuisitio i kēlā manawa, akā ma mua o ke ʻano kanaka he 100 mau makahiki a ʻoi paha. Ua makemake paha ʻo Newton iā ia iho no ka nui he mālamalama akua ia ma ke ʻano he ʻāpala, a ʻaʻole ia i hōʻole i ka moʻolelo - he haipule loa ʻo ia.
ʻO Newton a me ka ʻāpala ka papahele kāhiko. Hōʻike pololei ʻia nā makahiki o ka ʻepekema - i ka manawa i loaʻa ai, 23 mau makahiki o Newton
7. Hiki iā ʻoe ke ʻike pinepine i kahi ʻōlelo e pili ana i ke Akua e ka makemakika poʻokela ʻo Pierre-Simon Laplace. I ka nīnau ʻana a Napoleon no ke aha e ʻōlelo ʻole ai ke Akua i hoʻokahi manawa i loko o nā puke ʻelima o Celestial Mechanics, ua pane ʻo Laplace ʻaʻole pono ia i kahi kuhiakau. He mea hoʻomaloka ʻo Laplace, akā ʻaʻole pono e unuhi ʻia kāna pane i kahi ʻano atheistic koʻikoʻi. I loko o kahi polemikena me kekahi makemakika, ʻo Joseph-Louis Lagrange, ua koʻikoʻi ʻo Laplace ua wehewehe kahi kuhiakau i nā mea āpau, akā ʻaʻole wānana i kekahi mea. Ua ʻōlelo ʻoiaʻiʻo ka makemakika: ua wehewehe ʻo ia i ke ʻano o nā hihia, akā pehea ka ulu a me kahi e hele ai, ʻaʻole hiki iā ia ke wānana. A ʻike maoli ʻo Laplace i ka hana o ka ʻepekema i kēia.
ʻO Pierre-Simon Laplace
