ʻatikala e pili ana i ka mea ʻole
Nā mea
I koʻu wā kamaliʻi, ua hoihoi au i ka moʻolelo, i ʻike ʻia paha e ka poʻe heluhelu he nui, e pili ana i ka "sopa ma ke kui." Ua haʻi mai koʻu kupuna wahine (XNUMXst century o ka hānau ʻana) i kēia ma ka mana "Hele mai ka Cossack a noi i ka wai, no ka mea he kui kona a e kuke ʻo ia i ka sopa ma luna." Hāʻawi ka wahine hoʻokipa hoihoi iā ia i kahi ipu wai ... a ʻike mākou i ka mea i hana ʻia: "ʻo ka sopa e paʻakai, daitye, kupuna kāne, paʻakai", a laila holoi ʻo ia i ka ʻiʻo "e hoʻomaikaʻi i ka ʻono" a pēlā aku. I ka hopena, ua kiola ʻo ia i ke kui "hoʻolapalapa".
No laila ua manaʻo ʻia kēia ʻatikala e pili ana i ka hakahaka o ka lewa - a ʻo kēia e pili ana i ka pae ʻana o kahi mea ʻEulopa ma ka comet 67P / Churyumov-Gerasimenko ma Nowemapa 12, 2014. Akā i ka wā e kākau ana, ua hāʻule au i kahi maʻamau lōʻihi. He kanaka makemakika au. Pehea me Likeс Ole makemakika?
Pehea ka ʻAʻohe mea?
ʻAʻole hiki ke ʻōlelo ʻia ʻAʻohe mea. Aia ia ma ke ʻano he manaʻo noʻonoʻo, makemakika, hoʻomana a me ka manaʻo colloquial maikaʻi loa. He helu maʻamau ʻo Zero, ʻo nā degere ʻaʻohe ma ka thermometer he wela nō hoʻi, a ʻo ke koena ʻole i loko o kahi panakō he mea ʻoluʻolu ʻole akā maʻamau. E hoʻomanaʻo ʻaʻohe makahiki ʻaʻohe o ka chronology, a no ka mea ua hoʻokomo ʻia ka zero i ka makemakika i ka hopena o ka Middle Ages, ma hope o ka chronology i manaʻo ʻia e ka mōneka Dionysius (XNUMXth century).
ʻO ka mea kupanaha, hiki iā mākou ke hana me ka ʻole o kēia zero a, no laila, me ka ʻole o nā helu maikaʻi ʻole. Ma kekahi o nā puke e pili ana i ka loiloi, ua loaʻa iaʻu kahi hoʻomaʻamaʻa: kahakiʻi a ʻōlelo paha pehea ʻoe e noʻonoʻo ai i ka nele o ka iʻa. Kupaianaha, 'a'ole anei? Hiki i kekahi ke huki iʻa, ʻaʻole hoʻokahi?
I kēia manawa pōkole papa makemakika kumu. ʻO ka hāʻawi ʻana i ka pono o ke ola ʻana i ka hoʻonohonoho hakahaka i kaha ʻia me ka pōʻai kea ∅ he hana pono e like me ka hoʻohui ʻana i ka ʻole i ka pūʻulu o nā helu. ʻO ka pūʻulu hakahaka ka pūʻulu wale nō i loaʻa ʻole kekahi mau mea. ʻO ia mau hōʻiliʻili:
Akā, ʻaʻohe ʻelua ʻāpana ʻokoʻa. Hoʻokomo ʻia ka pūʻulu hakahaka i kēlā me kēia pūʻulu ʻē aʻe:
ʻOiaʻiʻo, ʻōlelo nā lula o ka loina makemakika aia ka set A i ka set B inā a inā wale nō ka ʻōlelo:
e komo ana
I ka hihia o ka hoʻonohonoho hakahaka ∅, he wahaheʻe mau ka manaʻo, a no laila, e like me nā kānāwai o ka loiloi, ʻoiaʻiʻo ka manaʻo. ʻO nā mea a pau mai ka wahaheʻe ("eia wau e ulu i kahi cactus inā e neʻe ʻoe i ka papa aʻe ..."). No laila, no ka mea, aia ka pahu hakahaka i loko o nā mea ʻē aʻe, a laila inā ʻelua mau mea ʻokoʻa, e paʻa kēlā me kēia i kekahi. Eia naʻe, inā loaʻa nā pūʻulu ʻelua i loko o kekahi, ua like lāua. ʻO ia ke kumu: hoʻokahi wale nō hoʻonohonoho hakahaka!
ʻAʻole kūʻē ka postulate o ka noho ʻana o kahi pahu hakahaka i nā kānāwai o ka makemakika, no laila no ke aha e hoʻōla ʻole ai? Ua kapa ʻia ka manaʻo filosofiaʻO ka pahi ʻo Occam» He kauoha e kāpae i nā manaʻo pono ʻole, akā pololei ʻO ka manaʻo o kahi hoʻonohonoho hakahaka he mea maikaʻi loa ia ma ka makemakika. E hoʻomanaʻo i ka nui o ka -1 (hoʻemi hoʻokahi) - ʻo nā mea ʻole-dimensional he mau kiko a me kā lākou ʻōnaehana sparse, ʻo nā mea hoʻokahi-dimensional nā laina, a ua kamaʻilio mākou e pili ana i nā mea makemakika paʻakikī me ka nui fractal ma ka mokuna ma nā fractals. .
He mea hoihoi i ka hale a pau o ka makemakika: helu, helu, hana, operator, integrals, differentials, equations ... hiki ke loaʻa mai hoʻokahi manaʻo - he set hakahaka! Ua lawa ka manaʻo ʻana aia kahi hoʻonohonoho kaʻawale, hiki ke hoʻohui ʻia nā mea hou i hana ʻia i nā pūʻulu e hiki ai. kūkulu i ka makemakika a pau. ʻO kēia ke ʻano i kūkulu ʻia ai e ka loea Kelemania ʻo Gottlob Frege i nā helu kūlohelohe. ʻO Zero he papa o nā pūʻulu nona nā mea i pili like me nā mea o ka pūʻulu hakahaka. ʻO kekahi he papa o nā pūʻulu nona nā mea i pili like me nā mea o kahi pūʻulu nona ka mea wale nō ka hoʻonohonoho hakahaka. ʻO ʻelua he papa o nā pūʻulu nona nā mea hoʻokahi i hoʻokahi me nā mea o ka hoʻonohonoho i loaʻa i ka hoʻonohonoho hakahaka a me ka hoʻonohonoho nona ka mea hoʻokahi ʻo ka pahu hakahaka ... a pēlā aku. I ka nānā mua ʻana, he mea paʻakikī loa kēia, akā ʻoiaʻiʻo ʻaʻole ia.
Laha polū ma luna oʻu
honi i ka heather a honi i ka mint...
Wojciech Mlynarski, Kaikamahine ohi
He paʻakikī ke noʻonoʻo
ʻAʻohe mea paʻakikī ke noʻonoʻo. Ma ka moʻolelo a Stanisław Lem "How the World Was Saved", ua hana ka mea hoʻolālā Trurl i kahi mīkini e hana i nā mea āpau e hoʻomaka me kahi leka. I ke kauoha a Klapaucius e kukulu ia Nic, ua hoʻomaka ka mīkini e wehe i nā mea like ʻole mai ka honua - me ka pahuhopu hope loa e wehe i nā mea āpau. I ka wā i hoʻōki ai ʻo Klapaucius makaʻu i ke kaʻa, ua nalowale nā galleys, yews, kawī, hacks, rhymes, beaters, poufs, grinders, skewers, philidrons a me nā hau hau a mau loa aku. A ʻoiaʻiʻo, ua nalowale lākou a mau loa ...
Ua kākau maikaʻi ʻo Józef Tischner e pili ana i ka mea ʻole ma kāna History of Mountain Philosophy. I koʻu wā hoʻomaha hope loa, ua hoʻoholo wau e ʻike i kēia mea ʻole, ʻo ia hoʻi, ua hele au i nā puʻu peat ma waena o Nowy Targ a me Jabłonka ma Podhale. Ua kapa ʻia kēia wahi ʻo Pustachia. Hele ʻoe, hele ʻoe, akā ʻaʻole e emi ke ala - ʻoiaʻiʻo, ma kā mākou ʻano haʻahaʻa, Polani. I kekahi lā ua holo au i kaʻa kaʻa ma ka moku ʻo Kanada ʻo Saskatchewan. Ma waho he kahua kulina. Ua hiamoe au no ka hapalua hola. I koʻu ala ʻana, ke kaʻa nei mākou ma ka pā kulina hoʻokahi... Akā e kali, ʻaʻohe mea kēia? Ma kahi ʻano, ʻo ka nele o ka hoʻololi ʻana he mea ʻole wale.
Ua maʻa mākou i ka noho mau ʻana o nā mea like ʻole a puni mākou, a mai Kekahi mea ʻAʻole hiki iā ʻoe ke holo me ka pani ʻana i kou mau maka. "Manaʻo wau, no laila ʻo wau nō," wahi a Descartes. Inā ua noʻonoʻo mua wau i kekahi mea, aia wau, ʻo ia hoʻi, aia kekahi mea ma ka honua (ʻo ia hoʻi, I). Aia ka mea a'u i manao ai? Hiki ke kūkākūkā ʻia kēia, akā, i loko o nā mechanics quantum hou, ua ʻike ʻia ka loina Heisenberg: hoʻopilikia kēlā me kēia nānā i ke kūlana o ka mea i ʻike ʻia. A ike kakou Nic ʻaʻole ia, a ke hoʻomaka mākou e nānā, pau ka mea Like a lilo ia Kekahi mea. Ke lilo nei i mea lapuwale kuʻuna anthropic: ʻAʻohe kumu o ka nīnau ʻana i ke ʻano o ka honua inā ʻaʻole mākou. ʻO ka honua ka mea i manaʻo ʻia e mākou. E ʻike paha nā mea ʻē aʻe i ka Honua ma ke ʻano he angular?
ʻO kahi positron (ʻo ia ka electron maikaʻi) he puka ma kahi ākea, "ʻaʻohe electron." I ke kaʻina o ka luku ʻana, lele ka electron i loko o kēia lua a "ʻaʻohe mea" - ʻaʻohe puka, ʻaʻohe electron. E hoʻokuʻu wau i nā ʻakaʻaka he nui e pili ana i nā lua i ka cheese Swiss ("ʻo ka nui o kaʻu, ʻoi aku ka liʻiliʻi ma laila ..."). Ua hoʻohana mua ka mea haku mele kaulana ʻo John Cage i kona mau manaʻo a hiki i kona haku ʻana (?) i kahi mele (?) kahi e noho ʻole ai ka mea hoʻokani pila no 4 mau minuke 33 kekona a, ʻoiaʻiʻo, ʻaʻole hoʻokani i kekahi mea. "ʻEhā mau minuke me kanakolukumamākolu kekona he ʻelua haneli kanahikukūmākolu, 273, a ʻo ka emi ʻana o 273 degere ʻo ka ʻole loa, kahi e kū ai nā neʻe a pau," wehewehe ka mea haku mele (?).
E kānana i ka ʻole, ʻaʻohe, nick, nick, ʻaʻohe, ʻole!
Jerzy ma Andrzej Wajda kiʻiʻoniʻoni Over the Years,
hala nā lā"
Pehea nā mea a pau?
Nui ka poʻe (mai ka poʻe mahiʻai maʻalahi a hiki i ka poʻe akeakamai koʻikoʻi) noʻonoʻo i ke ʻano o ke ola. Ma ka makemakika, maʻalahi ke kūlana: aia kekahi mea i kūlike.
Ua nalowale ʻo ia i loko o nā māla marginal
I nā pua kulina, nā nahele a me nā waha o ka liona ...
ʻAe, hiki mai kēia mau mea
ʻOi loa i ka ʻohi ʻana, a i ka wā o ka ʻohi
ʻoi aku…
Wojciech Mlynarski, Kaikamahine ohi
Aia nā mea a pau ma kahi ʻē aʻe o ʻAʻohe mea. Ma ka makemakika, ʻike mākou i kēlā ʻAʻole loaʻa nā mea a pau. ʻO kahi manaʻo pololei ʻole loa e kū ʻole ʻia kona noho ʻana me ka hoʻopaʻapaʻa. Hiki ke hoʻomaopopo ʻia kēia ma ke ʻano o ka paradox kahiko: "Inā he mana ke Akua, a laila hana i pōhaku e ʻohi ai?" ʻO ka hōʻike makemakika ʻaʻole hiki ke loaʻa nā hoʻonohonoho o nā pūʻulu āpau ma luna o ka theorem mele-Bershtein, ka mea i ʻōlelo "he helu pau ʻole" (ka makemakika: helu cardinal) ʻoi aku ka nui o ka pūʻulu o nā lālā a pau o kahi pūʻulu i hāʻawi ʻia ma mua o ka helu o nā mea o kēia pūʻulu.
Inā loaʻa i kahi hoʻonohonoho nā mea, a laila loaʻa iā 2n nā ʻāpana ʻāpana; no ka laʻana, inā = 3 a loaʻa ka pūʻulu o {1, 2, 3} a laila e loaʻa kēia mau ʻāpana:
- ʻekolu mau ʻeleʻele ʻelua: ʻaʻohe o kēlā me kēia o nā helu 1, 2, 3,
- hookahi pahu hakahaka,
- ʻekolu pūʻulu ʻeleʻele hoʻokahi,
- ka pūʻulu holoʻokoʻa {1,2,3}
– ʻewalu wale nō, 23A ʻo ka poʻe heluhelu i puka i ke kula, makemake wau e hoʻomanaʻo i ke ʻano like:
Hoʻoholo kēlā me kēia hōʻailona Newtonian i kēia ʻano hoʻohālikelike i ka helu o nā pūʻulu k-element ma ka set -element.
Ma ka makemakika, ʻike ʻia nā coefficient binomial ma nā wahi ʻē aʻe, e like me nā kumu hoʻohālike hoihoi no ka hoʻonui ʻia ʻana.
a mai ko lakou ano pololei, ua oi aku ka hoihoi.
He mea paʻakikī ke hoʻomaopopo i ka mea - e pili ana i ka loiloi a me ka makemakika - ʻo ia, a he aha nā mea āpau ʻaʻole. ʻO nā ʻōlelo hoʻopaʻapaʻa no ke ola ʻole E like me kā Winnie the Pooh, nāna i nīnau me ka mahalo i kāna hoa kipa, ʻo Tiger, makemake paha nā Tiga i ka meli, nā ʻaʻa a me nā puakala? "Makemake nā tigers i nā mea a pau," wahi a Kubus i hoʻoholo ai inā makemake lākou i nā mea āpau, a laila makemake lākou e hiamoe ma ka papahele, no laila, hiki iā Vinnie ke hoʻi i kahi moe.
ʻO kekahi hoʻopaʻapaʻa ʻO ka paradox a Russell. Aia ma ke kaona kahi mea ʻokiʻoki e kahi i nā kāne a pau ʻaʻole i kahi i ka ʻumi. Ua kahi ʻo ia iā ia iho? Kūʻē nā pane ʻelua i ke ʻano i ʻōlelo ʻia e pepehi ʻia ka poʻe, a ʻo ka poʻe ʻaʻole e hana iā lākou iho.
Ke ʻimi nei i kahi hōʻiliʻili o nā hōʻiliʻili āpau
I ka hopena, e hāʻawi wau i kahi akamai, akā ʻo ka hapa nui o ka makemakika hōʻike ʻaʻohe hoʻonohonoho o nā hoʻonohonoho āpau (ʻaʻole e huikau me ia).
ʻO ka mea mua, e hōʻike mākou no kēlā me kēia pūʻulu ʻole X, ʻaʻole hiki ke loaʻa i kahi hana kūʻokoʻa i palapala ʻāina i kēia hoʻonohonoho i ka pūʻulu o kāna mau ʻāpana P(X). No laila, e manaʻo kākou aia kēia hana. E hōʻike aku kākou ma ka ʻōlelo kuʻuna f. He aha ka f mai x? He hōʻiliʻili kēia. No x ka xf? ʻAʻole ʻike ʻia kēia. Pono ʻoe a ʻaʻole paha. Aka, no kekahi mau x, he mea pono ole ia no f o x. A laila, e noʻonoʻo i ka pūʻulu o nā x a pau nona ka x no f(x). E hōʻike iā ia (keia hoʻonohonoho) e A. Ua pili ia me kekahi ʻano a o ka pūʻulu X. No A? E manaʻo mākou he pono ʻoe. Akā, ʻo A he pūʻulu i loaʻa wale nā mea o x i pili ʻole i ka f(x) ... ʻAe, ʻaʻole paha ia no A? Akā, aia i ka pūʻulu A nā mea a pau o kēia waiwai, a no laila ʻo A. Hoʻopau o ka hōʻoia.
No laila, inā he pūʻulu o nā pūʻulu a pau, he ʻāpana ia nona iho, he mea hiki ʻole e like me ka manaʻo mua.
Phew, manaʻo wau ʻaʻole nui ka poʻe heluhelu i ʻike i kēia hōʻoia. Akā, ua lawe au ia mea e hōʻike i nā mea a ka poʻe makemakika e hana ai i ka hopena o ke kenekulia ʻumikūmāiwa, i ka wā i hoʻomaka ai lākou e aʻo i nā kumu o kā lākou ʻepekema ponoʻī. Ua ʻike ʻia aia nā pilikia ma kahi i manaʻo ʻole ʻia e kekahi. Eia kekahi, no ka makemakika holoʻokoʻa, ʻaʻole pili kēia mau manaʻo e pili ana i nā kumu: ʻaʻohe mea e hana ai i loko o nā hale waihona - kū ka hale makemakika holoʻokoʻa ma luna o ka pōhaku paʻa.
I kēia manawa, ma ka luna ...
Hoʻomaopopo mākou i kahi moʻomeheu hou mai nā moʻolelo o Stanislav Lem. Ma kekahi o kāna huakaʻi, ua hōʻea ʻo Iyon Tichi i kahi honua nona ka poʻe noho, ma hope o ka lōʻihi o ka ulu ʻana, hiki i ka pae kiʻekiʻe o ka hoʻomohala ʻana. He ikaika lākou a pau, hiki iā lākou ke hana i kekahi mea, aia nā mea āpau ma ko lākou manamana lima… ʻaʻole lākou e hana. Moe lākou ma ke one a ninini ma waena o ko lākou manamana lima. "Inā hiki nā mea a pau, ʻaʻole pono ia," wehewehe lākou iā Ijon i haʻalulu. ʻAʻole hiki kēia i ko kākou lāhui ʻEulopa ...
