Lem, Tokarczuk, Krakow, makemakika

Ma Kepakemapa 3-7, 2019, ua mālama ʻia ka ʻaha hoʻomanaʻo makahiki o ka Polish Mathematic Society ma Krakow. Makahiki, no ka mea, ka makahiki o ka hookumu ana o ka Ahahui. Ua noho ia ma Galicia mai ka makahiki 1 (me ka ʻole o ka huaʻōlelo ʻo ka Polish-liberalism o ka mōʻī FJ1919 i kona palena), akā ma ke ʻano he hui holoʻokoʻa ua hana ia mai 1919 wale nō. ʻO nā holomua nui ma ka makemakika Polani mai ka 1939s XNUMX-XNUMX. ʻO XNUMX ma ke Kulanui ʻo Jan Casimir ma Lviv, akā ʻaʻole hiki ke hana ʻia ka ʻaha kūkā ma laila - a ʻaʻole ia ka manaʻo maikaʻi loa.

Ua hauʻoli loa ka hālāwai, piha i nā hanana e pili ana (me kahi hana a Jacek Wojcicki ma ka hale kākela ma Niepolomice). Ua hāʻawi ʻia nā haʻiʻōlelo nui e 28 mau mea haʻiʻōlelo. Aia lākou ma Polani no ka mea he pole ka poʻe i kono ʻia - ʻaʻole ma ke ʻano he kupa, akā ʻike lākou iā lākou iho he pole. ʻAe, he ʻumikūmākolu mau kumu aʻo i hele mai mai nā kula ʻepekema Polani, ʻo ke koena he ʻumikumamālima mai USA (7), Farani (4), ʻEnelani (2), Kelemānia (1) a me Kanada (1). ʻAe, he mea kaulana kēia i nā līpika pôpeku.

ʻO ka mea maikaʻi loa e hana mau ma waho. He mea kaumaha iki, akā ʻo ke kūʻokoʻa ke kūʻokoʻa. Ua hana kekahi mau mea makemakika Polani i nā ʻoihana ma waho i hiki ʻole ke loaʻa ma Polani. ʻO ke kālā ke kuleana lua ma aneʻi, akā ʻaʻole wau makemake e kākau ma ia mau kumuhana. ʻElua wale nō manaʻo.

Ma Rūsia, a ma mua o ka Soviet Union, aia kēia a aia ma ka pae ʻike loa ... a ʻaʻohe mea makemake e neʻe i laila. I ka huli ʻana, ma Kelemania, ma kahi o ka ʻumi mau moho e noi ana i ke kaukaʻi ma kekahi kulanui (ua ʻōlelo nā hoa hana mai ke Kulanui o Konstanz he 120 mau noi i ka makahiki, 50 o ia mau mea maikaʻi loa, a he 20 maikaʻi loa).

Hiki ke hōʻuluʻulu ʻia nā haʻiʻōlelo o ka Ahaolelo Iubile ma kā mākou puke pai mahina. ʻO nā poʻomanaʻo e like me "Limits of Sparse Graphs and Their Applications" a i ʻole "Linear Structure and Geometry of Subspaces and Factor Spaces for High-Dimensional Normalized Spaces" ʻaʻole e haʻi i ka mea heluhelu maʻamau. ʻO ke kumuhana ʻelua i hoʻolauna ʻia e koʻu hoa mai nā papa mua, Nicole Tomchak.

He mau makahiki i hala aku nei, ua koho ʻia ʻo ia no ka holomua i hōʻike ʻia ma kēia haʻiʻōlelo. Medal Fields ʻo ia ka mea like no ka poʻe makemakika. I kēia manawa, hoʻokahi wale nō wahine i loaʻa kēia makana. He mea pono ke hoʻomaopopo ʻia ka haʻiʻōlelo Anna Marciniak-Chokhra (Heidelberg University) "ʻO ke kuleana o nā hiʻohiʻona makemakika mechanistic i ka lāʻau lapaʻau ma ka laʻana o ka hoʻohālike leukemia".

komo i ka laau lapaau. Ma ke Kulanui o Warsaw, kahi hui i alakaʻi ʻia e Prof. Jerzy Tyurin.

ʻAʻole hiki ke hoʻomaopopo ʻia ke poʻo o ka haʻiʻōlelo i ka poʻe heluhelu ʻO Veslava Niziol (z prestiżowej Kula Hoʻonaʻauao Kiʻekiʻe) “-adic Hodge theory". Eia naʻe, ʻo kēia haʻiʻōlelo kaʻu i hoʻoholo ai e kūkākūkā ma ʻaneʻi.

Geometry -adic honua

Hoʻomaka me nā mea liʻiliʻi maʻalahi. Ke hoʻomanaʻo nei ʻoe, e ka mea heluhelu, ke ʻano o ka hoʻololi kākau ʻana? ʻOiaʻiʻo. E noʻonoʻo i nā makahiki mālama ʻole o ke kula haʻahaʻa. E puunaue i ka 125051 me 23 (eia ka hana ma ka hema). ʻIke paha ʻoe he ʻokoʻa paha ia (hana ma ka ʻākau)?

He mea hoihoi kēia ʻano hou. E hele ana au mai ka hopena. Pono kākou e puunaue i ka 125051 me ka 23. He aha ka mea e pono ai e hoonui i ka 23 me ka 1 ka huahelu hope? Huli ma ka hoʻomanaʻo a loaʻa iā mākou :=7. ʻO ka huahelu hope o ka hopena he 7. E hoʻonui, e unuhi, e loaʻa iā mākou ka 489. Pehea ʻoe e hoʻonui ai i ka 23 a pau i ka 9? ʻOiaʻiʻo, ma ka 3. Hiki mākou i kahi e hoʻoholo ai i nā helu a pau o ka hopena. ʻIke mākou he mea paʻakikī a ʻoi aku ka paʻakikī ma mua o kā mākou hana maʻamau - akā he mea hoʻomaʻamaʻa!

He ʻokoʻa nā mea i ka wā ʻaʻole i māhele ʻia ke kanaka koa e ka mea hoʻokaʻawale. E hana kāua i ka mahele a ʻike i ka hopena.

Aia ma ka hema he ala kula maʻamau. Aia ma ka ʻaoʻao ʻākau "ʻo kā mākou mau malihini".

Hiki iā mākou ke nānā i nā hopena ʻelua ma ka hoʻonui ʻana. Hoʻomaopopo mākou i ka mua: ʻo ka hapakolu o ka helu 4675 he hoʻokahi tausani ʻelima haneri me kanalimakumamāwalu, a ʻekolu i ka manawa. ʻAʻole kūpono ka lua: he aha kēia helu ma mua o ka helu pau ʻole o ʻeono a laila 8225?

E haʻalele kākou i ka nīnau o ke ʻano no kekahi manawa. E pāʻani kāua. No laila, e puunaue kakou i ka 1 me ka 3 a me ka 1 me ka 7, oia ka hapakolu a me ka hiku. Hiki iā mākou ke loaʻa maʻalahi:

1:3=…6666667, 1/7=…(285714)3.

ʻO ke ʻano o kēia laina hope: ʻo ka poloka 285714 e hoʻomau mau loa i ka hoʻomaka, a ma hope he ʻekolu o lākou. No ka poʻe manaʻoʻiʻo ʻole, eia kahi hoʻāʻo:

E hoʻohui kākou i nā hakina:

A laila hoʻohui mākou i nā helu ʻano ʻē i loaʻa, a loaʻa iā mākou (nānā) i ka helu ʻano like ʻole.

......95238095238095238095238010

Hiki iā mākou ke nānā ua like kēia me

ʻAʻole ʻike ʻia ke kumu nui, akā pololei ka helu helu.

Hoʻokahi laʻana hou.

He waiwai hoihoi ko ka helu 40081787109376 maʻamau: pau kona huinaha ma 40081787109376. ʻO ka helu x40081787109376, ʻo ia ( x40081787109376)² e pau ana ma x40081787109376.

Manaʻo kōkua. Loaʻa iā mākou 40081787109376²= 16065496340081787109376, no laila, ʻekolu a ʻumi ka hoʻokō o ka huahelu hou, ʻo ia ka 7. E nānā kākou: 740081787109376²= 5477210516110077400817 87109376.

He mea paʻakikī ka nīnau no ke kumu o kēia. ʻOi aku ka maʻalahi: e ʻimi i nā hopena like no nā helu e pau ana i ka 5. Ke hoʻomau nei i ke kaʻina hana o ka loaʻa ʻana o nā huahelu aʻe no ka pau ʻole, e hele mākou i kēlā "helu" ²=²= (a ʻaʻohe o kēia mau helu i like me ka ʻole a i ʻole hoʻokahi).

maopopo mākou. ʻO ka lōʻihi ma hope o ka helu decimal, ʻoi aku ka liʻiliʻi o ka helu. Ma ka helu ʻenekinia, he mea nui ka huahelu mua ma hope o ka helu decimal, a me ka lua, akā i nā manawa he nui hiki ke manaʻo ʻia he 3,14 ka ratio o ke anapuni o ka pōʻai i kona anawaena. ʻOiaʻiʻo, pono e hoʻokomo ʻia nā helu hou aku i ka ʻoihana mokulele, akā manaʻo wau ʻaʻole e ʻoi aku ma mua o ʻumi.

Aia ka inoa ma ke poʻo o ka ʻatikala ʻO Stanislav Lem (1921-2006), a me kā mākou Nobel laureate hou. Wahine Olga Tokarchuk Ua ʻōlelo wale au i kēia no ka mea uwao pono oleʻO ka ʻoiaʻiʻo ʻaʻole i loaʻa iā Stanislav Lem ka makana no ka Nobel ma ka palapala. Akā ʻaʻole ia ma ko mākou kihi.

ʻIke pinepine ʻo Lem i ka wā e hiki mai ana. Ua noʻonoʻo ʻo ia i ka mea e hiki mai ana ke kūʻokoʻa lākou i ke kanaka. ʻEhia mau kiʻiʻoniʻoni ma kēia kumuhana i hōʻike ʻia i kēia mau lā! Ua wānana pololei a wehewehe ʻo Lem i ka mea heluhelu optical a me ka pharmacology o ka wā e hiki mai ana.

Ua ʻike ʻo ia i ka makemakika, ʻoiai i kekahi manawa ua hana ʻo ia i mea hoʻonani, me ka mālama ʻole i ka pololei o nā helu. No ka laʻana, ma ka moʻolelo "Trial", hele ka Pirks pilot i ka orbit B68 me kahi manawa hoʻololi o 4 mau hola 29 mau minuke, a ʻo ke aʻo ʻana he 4 mau hola 26 mau minuke. Hoʻomanaʻo ʻo ia ua helu lākou me ka hapa o 0,3 pakeneka. Hāʻawi ʻo ia i ka ʻikepili i ka Calculator, a pane ka calculator ua maikaʻi nā mea āpau ... ʻAe, ʻaʻole. ʻEkolu hapaʻumi o ka pākēneka o 266 mau minuke i emi iho ma mua o hoʻokahi minuke. Akā, hoʻololi paha kēia hewa i kekahi mea? Malia paha ma ke kumu?

No ke aha wau e kākau nei no kēia? He nui nā mea makemakika i hāpai i kēia nīnau: e noʻonoʻo i kahi kaiāulu. ʻAʻohe o lākou manaʻo kanaka. No mākou, ʻo 1609,12134 a me 1609,23245 nā helu kokoke loa - nā hoʻohālikelike maikaʻi i ka mile Pelekane. Eia nō naʻe, hiki i nā kamepiula ke noʻonoʻo i nā helu 468146123456123456 a me 9999999123456123456 kokoke. Loaʻa iā lākou nā hopena he ʻumikumamālua.

ʻO nā huahelu maʻamau ma ka hopena, ʻoi aku ka pili o nā helu. A alakaʻi kēia i ka mea i kapa ʻia he mamao -adic. E like ka p me 10 no kekahi manawa; no ke aha "no kekahi manawa", e wehewehe wau ... i kēia manawa. ʻO ka mamao 10 mau helu o nā helu i kākau ʻia ma luna 

a i ʻole hoʻokahi miliona - no ka mea he ʻeono mau huahelu maʻamau i ka hopena. 'Oko'a nā helu helu a pau mai ka 'ole ma ka ho'okahi a emi mai paha. ʻAʻole wau e kākau i kahi mamana no ka mea ʻaʻohe mea nui. ʻO ka nui o nā helu like ma ka hopena, ʻoi aku ka pili o nā helu (no ke kanaka, ʻaʻole, noʻonoʻo ʻia nā helu mua). He mea nui ka p he helu prima.

A laila - makemake lākou i nā zeros a me nā mea, no laila ʻike lākou i nā mea āpau i kēia mau hiʻohiʻona: 0100110001 1010101101010101011001010101010101111.

Ma ka puke moʻolelo Glos Pana, hoʻolimalima ʻo Stanisław Lem i nā ʻepekema e hoʻāʻo e heluhelu i kahi leka i hoʻouna ʻia mai ke ola hope, i helu ʻia ʻaʻole hoʻokahi. Ke palapala mai nei kekahi iā mākou? Ua hoʻopaʻapaʻa ʻo Lem "hiki ke heluhelu ʻia kēlā me kēia memo inā he memo i makemake kekahi e haʻi mai iā mākou." Akā ʻo ia? E waiho au i ka poe heluhelu me keia pilikia.

Noho mākou i ka lewa XNUMXD R³. Palapala R Hoʻomanaʻo ʻo ia he mau helu maoli nā koʻi, ʻo ia hoʻi, integers, negative and positive, zero, rational (i.e. fractions) and irrational, i hui ai ka poʻe heluhelu ma ke kula (), a me nā helu i ʻike ʻia he mau helu transcendental, hiki ʻole ke loaʻa i ka algebra (ʻo ia ka helu π , ka mea i hoʻohui i ke anawaena o ka pōʻai me kona anapuni no ʻelua kaukani makahiki).

He aha inā inā he helu -adic nā koʻi o kā mākou wahi?

Jerzy Mioduszowski, he mea makemakika ma ke Kulanui o Silesia, ke hoʻopaʻapaʻa nei he hiki ke hana pēlā, a ʻo ia nō hoʻi. Hiki iā mākou (wahi a Jerzy Mioduszowski) ke noho i ka wahi like ma ka lewa me ia mau mea, me ke keakea ʻole a ʻike ʻole kekahi i kekahi.

No laila, loaʻa iā mākou nā geometry āpau o "ko lākou" honua e makaʻala. ʻAʻole paha e like ka manaʻo o "lākou" e pili ana iā mākou a e aʻo pū i kā mākou geometry, no ka mea, ʻo kā mākou kahi hihia palena o nā "lākou" honua āpau. "ʻO lākou", ʻo ia hoʻi, nā honua pōʻino a pau, kahi i helu nui ai lākou. ʻO ka mea kūikawā, = 2 a me kēia honua hoihoi o zero-one ...

Ma ʻaneʻi e huhū a huhū paha ka mea heluhelu i ka ʻatikala. "ʻO kēia ke ʻano o ka naʻaupō a ka poʻe makemakika?" Manaʻo lākou e inu i ka vodka ma hope o ka ʻaina ahiahi, me kaʻu kālā (= ʻauhau ʻauhau). A hoʻopuehu iā lākou i ʻehā makani, e hoʻokuʻu iā lākou e hele i nā mahiʻai mokuʻāina ... ʻe, ʻaʻohe mahiʻai mokuʻāina!

Hoʻomaha. Ua makemake mau lākou i ia mau ʻakaʻaka. E ʻae mai iaʻu e haʻi wale aku i ka theorem sanwiti: inā loaʻa iaʻu kahi paʻakai a me ka sanwiti ham, hiki iaʻu ke ʻokiʻoki i hoʻokahi ʻoki e ʻoki ʻia i ka ʻāpana o ka bun, ka ham, a me ka paʻakai. He mea ole keia ma ka hana. ʻO ka manaʻo, he noi pāʻani wale nō kēia o kahi theorem maʻamau mai ka loiloi hana.

Pehea ka koʻikoʻi o ka hana ʻana i nā helu -adic a me nā geometry pili? E hoʻomanaʻo mai au i ka mea heluhelu e moe paʻapū ana nā helu kūpono (ma ka maʻalahi: nā hakina) ma ka laina, akā mai hoʻopiha piha.

Noho nā helu irrational i loko o nā "puka". Nui ka nui o ia mau mea, akā hiki iā ʻoe ke ʻōlelo he ʻoi aku ko lākou palena ʻole ma mua o nā mea maʻalahi, a mākou e helu ai: hoʻokahi, ʻelua, ʻekolu, ʻehā ... a pēlā aku a hiki i ∞. ʻO kēia kā mākou hoʻopiha kanaka i nā "puka". Ua hoʻoili ʻia kēia ʻano noʻonoʻo iā mākou mai ʻ .liʻi. 

Akā, ʻo ka mea hoihoi a koʻikoʻi no ka mea makemakika, ʻaʻole hiki i kekahi ke "hoʻopiha" i kēia mau puka me nā helu noʻonoʻo a me nā helu p-adic (no nā p prime a pau). No kēlā poʻe heluhelu i hoʻomaopopo i kēia (a ua aʻo ʻia kēia ma kēlā me kēia kula kiʻekiʻe he kanakolu makahiki i hala aku nei), ʻo ka manaʻo o kēlā me kēia kaʻina e māʻona ai. ʻO ke kūlana o Cauchy, converges.

Ua kapa ʻia kahi hakahaka ʻoiaʻiʻo ("ʻaʻohe mea e nalowale"). E hoʻomanaʻo wau i ka helu 547721051611007740081787109376.

Hoʻololi ke kaʻina 0,5, 0,54, 0,547, 0,5477, 0,54772 a pēlā aku i kekahi palena, ʻo ia ma kahi o 0,5477210516110077400 81787109376.

Eia naʻe, mai ka manaʻo o ka mamao 10-adic, ke kaʻina o nā helu 6, 76, 376, 9376, 109376, 7109376 a pēlā aku e hui pū ai i ka helu "ʻano" ... 547721051 611007740081787109376.

Akā ʻaʻole lawa paha ia kumu e hāʻawi ai i nā ʻepekema kālā lehulehu. Ma keʻano laulā, pale mākou (māthematicians) iā mākou iho ma ka ʻōlelo ʻana he hiki ʻole ke wānana i ka mea e pono ai kā mākou noiʻi. Aneane maopopo loa e hoʻohana nā mea a pau a ʻo ka hana ma ke alo ākea ka manawa e kūleʻa ai.

ʻO kekahi o nā mea nui loa, ʻo ka mīkini X-ray, i hana ʻia ma hope o ka ʻike ʻia ʻana o ka radioactivity becquerel. Inā ʻaʻole no kēia hihia, ʻaʻole pono paha nā makahiki he nui o ka noiʻi. "Ke ʻimi nei mākou i kahi ala e lawe ai i kahi x-ray o ke kino kanaka."

ʻO ka hope, ka mea nui loa. Ua ʻae nā kānaka a pau he kuleana ko ka hiki ke hoʻoponopono i nā hoohalike. A maanei ua pale pono ia ko kakou heluna malihini. ʻO ka theorem pili (Ke inaina nei au iā Minkowski) 'ōlelo 'ia e hiki ke ho'oholo 'ia kekahi mau hoohalike ma nā helu ku'una inā he mau a'a maoli ko lākou a me nā a'a ma kēlā me kēia kino -adic.

ʻOi aku a liʻiliʻi paha kēia ala i hōʻike ʻia Andrew Wiles, ka mea i hoʻoholo i ka hoʻohālikelike makemakika kaulana loa o nā makahiki ʻekolu haneli i hala - Paipai au i ka poʻe heluhelu e hoʻokomo iā ia i loko o kahi ʻenekini huli. "Ka Theorem hope o Fermat".