Lem, Tokarchuk, Krakow, masamu

Pa Seputembala 3-7, 2019, msonkhano wokumbukira zaka za Polish Mathematics Society unachitika ku Krakow. Chikumbutso, chifukwa chazaka zana kukhazikitsidwa kwa Sosaite. Zinalipo ku Galicia kuyambira zaka za 1 (popanda chiganizo chakuti Polish-liberalism ya mfumu FJ1919 inali ndi malire ake), koma monga bungwe la dziko lonse linagwira ntchito kuchokera ku 1919. Kupita patsogolo kwakukulu mu masamu aku Poland kudayamba m'ma 1939 XNUMX-XNUMX. XNUMX ku yunivesite ya Jan Casimir ku Lviv, koma msonkhano sunathe kuchitikira kumeneko - ndipo si lingaliro labwino kwambiri.

Msonkhanowo unali wosangalatsa kwambiri, wodzaza ndi zochitika zotsatizana nazo (kuphatikizapo sewero la Jacek Wojcicki ku nyumba yachifumu ku Niepolomice). Nkhani zazikulu zidakambidwa ndi okamba 28. Iwo anali mu Chipolishi chifukwa oitanidwawo anali Poles - osati m'lingaliro la nzika, koma kuzindikira okha monga Poles. O inde, ophunzitsa khumi ndi atatu okha adachokera ku mabungwe asayansi aku Poland, otsala khumi ndi asanu adachokera ku USA (7), France (4), England (2), Germany (1) ndi Canada (1). Chabwino, ichi ndi chodziwika bwino m'magulu a mpira.

Zabwino zonse kuchita kunja. Ndizomvetsa chisoni pang'ono, koma ufulu ndi ufulu. Akatswiri angapo a masamu aku Poland apanga ntchito zakunja zomwe sizingatheke ku Poland. Ndalama zimagwira ntchito yachiwiri pano, koma sindikufuna kulemba pamitu yotereyi. Mwina ndemanga ziwiri zokha.

Mu Russia, ndipo izo zisanachitike mu Soviet Union, izi zinali ndipo ndi pa mlingo kwambiri chikumbumtima ... ndipo mwanjira palibe amene akufuna kusamuka kumeneko. Komanso, ku Germany, pafupifupi osankhidwa khumi ndi awiri amafunsira uprofesa ku yunivesite iliyonse (anzake ochokera ku yunivesite ya Konstanz adanena kuti anali ndi mapulogalamu 120 m'chaka, 50 anali abwino kwambiri, ndipo 20 anali abwino kwambiri).

Nkhani zochepa za Jubilee Congress zitha kufotokozedwa mwachidule m'magazini athu apamwezi. Mitu monga "Malire a Zithunzi Zocheperako ndi Ntchito Zawo" kapena "Linear Structure and Geometry of Subspaces and Factor Spaces for High-Dimensional Normalized Spaces" sichiuza owerenga wamba chilichonse. Mutu wachiwiri unayambitsidwa ndi mnzanga kuchokera ku maphunziro oyambirira, Nicole Tomchak.

Zaka zingapo zapitazo, adasankhidwa kuti apindule zomwe zaperekedwa munkhani iyi. Fields Mendulo ndi ofanana ndi masamu. Mpaka pano, mayi mmodzi yekha ndi amene walandira mphoto imeneyi. Komanso chofunika kuzindikira ndi nkhani Anna Marcinyak-Chohra (Heidelberg University) "Udindo wa masamu amakanika muzamankhwala pa chitsanzo cha leukemia modelling".

adalowa mankhwala. Ku Yunivesite ya Warsaw, gulu lotsogozedwa ndi Prof. Jerzy Tyurin.

Mutu wankhaniyo udzakhala wosamvetsetseka kwa Owerenga Veslava Niziol (z prestiżowej Higher Pedagogical School) “-adic chiphunzitso cha Hodge". Komabe, ndi nkhani iyi yomwe ndaganiza kuti tikambirane pano.

Geometry - adic dziko

Zimayamba ndi zinthu zazing'ono zosavuta. Kodi mukukumbukira, Owerenga, njira yolembera? Ndithudi. Ganizirani mmbuyo ku zaka zosadetsa nkhawa za kusukulu ya pulayimale. Gawani 125051 ndi 23 (izi ndizomwe zili kumanzere). Kodi mukudziwa kuti zitha kukhala zosiyana (zochita kumanja)?

Njira yatsopanoyi ndi yosangalatsa. Ine ndikupita kuchokera kumapeto. Tiyenera kugawa 125051 ndi 23. Kodi tiyenera kuchulukitsa 23 ndi chiyani kuti nambala yomaliza ikhale 1? Sakani mu kukumbukira ndikukhala:=7. Nambala yomaliza ya chotsatira ndi 7. Chulukitsani, chotsani, timapeza 489. Kodi mumachulukitsa bwanji 23 kuti muthe 9? Zoonadi, ndi 3. Timafika poti timadziwa manambala onse a zotsatira. Timaona kuti sizothandiza komanso zovuta kwambiri kuposa momwe timachitira masiku onse - koma ndi nkhani yongoyeserera!

Zinthu zimasintha mosiyana pamene munthu wolimba mtima sanagawikane kwathunthu ndi wogawa. Tiyeni tigawane ndikuwona zomwe zikuchitika.

Kumanzere kuli njanji yapasukulu. Kumanja kuli “zachilendo zathu”.

Titha kuwona zotsatira zonse ziwiri pochulukitsa. Timamvetsetsa choyamba: gawo limodzi mwa magawo atatu a chiwerengero cha 4675 ndi chikwi chimodzi ndi mazana asanu ndi makumi asanu ndi atatu, ndi zitatu panthawiyi. Chachiwiri sichimveka: kodi nambala iyi ndi yotani yomwe imatsogozedwa ndi nambala yosawerengeka ya sikisi ndiyeno 8225?

Tiyeni tisiye funso la tanthauzo kwa kanthawi. Tiyeni tisewere. Chifukwa chake tiyeni tigawane 1 ndi 3 kenako 1 ndi 7 zomwe ndi gawo limodzi pachitatu ndi chimodzi chachisanu ndi chiwiri. Titha kupeza mosavuta:

1:3=…6666667, 1/7=…(285714)3.

Mzere wotsirizawu umatanthauza: chipika 285714 chikubwereza kosatha pachiyambi, ndipo pamapeto pake pali atatu mwa iwo. Kwa iwo amene sakhulupirira, nayi mayeso:

Tsopano tiyeni tiwonjezere tizigawo:

Kenako timaphatikiza manambala achilendo omwe adalandira, ndipo timapeza (onani) nambala yachilendo yomweyi.

......95238095238095238095238010

Titha kuwona kuti izi ndizofanana ndi

Zofunikira sizikuwoneka, koma masamu ndi olondola.

Chitsanzo china.

Nthawi zonse, ngakhale yayikulu, nambala 40081787109376 ili ndi malo osangalatsa: lalikulu lake limathera mu 40081787109376. nambala x40081787109376, yomwe ndi (x40081787109376)² imatheranso mu x40081787109376.

Langizo. Tili ndi 40081787109376²= 16065496340081787109376, kotero nambala yotsatira ndi atatu mpaka khumi, omwe ndi 7. Tiyeni tiwone: 740081787109376²= 5477210516110077400817 87109376.

Funso loti chifukwa chiyani zili choncho ndizovuta. Ndizosavuta: pezani malekezero ofanana a manambala omwe amathera mu 5. Kupitiliza njira yopezera manambala otsatirawa mpaka kalekale, tifika ku "manambala" oterowo. ²=²= (ndipo palibe imodzi mwa manambala awa yofanana ndi ziro kapena imodzi).

timamvetsetsa bwino. Kutali kwambiri pambuyo pa decimal, nambalayo ndi yofunika kwambiri. Mu mawerengedwe a uinjiniya, nambala yoyamba pambuyo pa decimal ndi yofunika, komanso yachiwiri, koma nthawi zambiri tingaganize kuti chiŵerengero cha circumference ya bwalo mpaka awiri ake ndi 3,14. Inde, ziwerengero zambiri ziyenera kuphatikizidwa mumakampani oyendetsa ndege, koma sindikuganiza kuti padzakhala oposa khumi.

Dzinali limapezeka pamutu wa nkhaniyo Stanislav Lem (1921-2006), komanso mphotho yathu yatsopano ya Nobel. Dona Olga Tokarchuk Ndinangotchula izi chifukwa kukuwa kupanda chilungamoMfundo ndi yakuti Stanislav Lem sanalandire Nobel Prize mu Literature. Koma siziri mu ngodya yathu.

Lem nthawi zambiri ankaoneratu zam'tsogolo. Anadzifunsa kuti n’ciani cidzacitika akakhala odziimira paokha popanda anthu. Ndi mafilimu angati pamutuwu omwe adawonekera posachedwa! Lem adaneneratu molondola ndikulongosola owerenga owoneka bwino komanso zamankhwala am'tsogolo.

Iye ankadziwa masamu, ngakhale nthawi zina ankaona ngati chokongoletsera, osasamala za kulondola kwa mawerengedwe. Mwachitsanzo, mu "Mayesero" woyendetsa Pirks amapita mu orbit B68 ndi nthawi kasinthasintha wa maola 4 ndi mphindi 29, ndi malangizo 4 hours ndi mphindi 26. Amakumbukira kuti anawerengera ndi cholakwika cha 0,3 peresenti. Amapereka deta kwa Calculator, ndipo chowerengera chimayankha kuti zonse zili bwino ... Chabwino, ayi. Gawo limodzi mwa magawo khumi pa zana la mphindi 266 ndi zosakwana miniti imodzi. Koma kodi cholakwika ichi chimasintha chilichonse? Mwina zinali dala?

Chifukwa chiyani ndikulemba za izi? Akatswiri ambiri a masamu afunsanso funso ili: lingalirani dera. Iwo alibe malingaliro athu aumunthu. Kwa ife, 1609,12134 ndi 1609,23245 ndi manambala oyandikana kwambiri - kuyerekezera kwabwino kwa mtunda wa Chingerezi. Komabe, makompyuta angaganize kuti manambala 468146123456123456 ndi 9999999123456123456 ndi pafupi. Iwo ali ndi mathero ofanana a manambala khumi ndi awiri.

Ziwerengero zodziwika kwambiri pamapeto, zimayandikira manambala. Ndipo izi zimatsogolera ku otchedwa mtunda -adik. Lolani p kukhala wofanana ndi 10 kwa mphindi; bwanji "kwa kanthawi", ndikufotokozera ... tsopano. Mtunda wa 10 wa manambala olembedwa pamwambapa ndi 

kapena miliyoni imodzi - chifukwa manambalawa ali ndi manambala asanu ndi limodzi odziwika kumapeto. Nambala zonse zimasiyana ndi ziro ndi chimodzi kapena zochepa. Sindidzalemba ngakhale template chifukwa zilibe kanthu. Manambala ofanana kwambiri pamapeto, amayandikira manambala (kwa munthu, m'malo mwake, manambala oyambira amaganiziridwa). Ndikofunika kuti p ikhale nambala yoyamba.

Ndiye - amakonda ziro ndi zina, kotero amawona chirichonse muzithunzi izi: 0100110001 1010101101010101011001010101010101111.

M'buku lakuti Glos Pana, Stanisław Lem akulemba asayansi kuti ayese kuwerenga uthenga wotumizidwa kuchokera ku moyo wapambuyo pa imfa, wolembedwa ziro-wani ndithu. Kodi alipo amene amatilembera? Lem akutsutsa kuti "uthenga uliwonse ukhoza kuwerengedwa ngati uli uthenga umene wina akufuna kutiuza chinachake." Koma sichoncho? Ndisiya owerenga ndi vuto ili.

Tikukhala mu danga la XNUMXD R³. Kalata R amakumbukira kuti nkhwangwa zimakhala ndi manambala enieni, kutanthauza kuti manambala, negative ndi positive, ziro, zomveka (i.e. tizigawo) ndi zosamveka, zomwe owerenga anakumana nazo kusukulu (), ndi manambala otchedwa transcendental manambala, osafikirika mu algebra (iyi ndi nambala π , yomwe yakhala ikugwirizanitsa kukula kwa bwalo ndi kuzungulira kwake kwa zaka zoposa zikwi ziwiri).

Bwanji ngati nkhwangwa za malo athu zinali -adic manambala?

Jerzy Mioduszowski, katswiri wa masamu pa yunivesite ya Silesia, akutsutsa kuti izi zikhoza kukhala choncho, ndipo ngakhale kuti zingakhale choncho. Titha (akutero Jerzy Mioduszewski) kukhala malo omwewo mumlengalenga ndi zolengedwa zotere, popanda kusokoneza komanso popanda kuwonana.

Chifukwa chake, tili ndi geometry yonse ya "dziko" lawo loti tifufuze. Ndizokayikitsa kuti "iwo" amaganiza chimodzimodzi za ife ndikuwerenganso geometry yathu, chifukwa yathu ndi malire a maiko "awo" onse. "Iwo", ndiye kuti, maiko onse aku gehena, komwe ali ziwerengero zazikulu. Makamaka, = 2 ndi dziko losangalatsa ili la zero-one ...

Apa wowerenga nkhaniyo akhoza kukwiya ngakhalenso kukwiya. "Kodi izi ndi zopanda pake zomwe akatswiri a masamu amachita?" Amangoganiza za kumwa mowa wa vodka mukatha chakudya chamadzulo, ndikugwiritsa ntchito ndalama zanga (= za olipira msonkho). Ndipo kuwabalalitsa mu mphepo zinayi, apite ku mafamu aboma ... o, kulibenso minda yaboma!

Khazikani mtima pansi. nthawi zonse anali ndi chidwi ndi nthabwala zotere. Ndiloleni ndingotchula za chiphunzitso cha masangweji: ngati ndili ndi sangweji ya tchizi ndi nyama, nditha kuidula mdulidwe umodzi kuti ndichepetse bun, ham, ndi tchizi ndi theka. Izi ndizopanda ntchito. Chowonadi ndi chakuti uku ndikungogwiritsa ntchito mwachisawawa kwa chiphunzitso chambiri chosangalatsa kuchokera ku kusanthula kwamachitidwe.

Ndizovuta bwanji kuthana ndi -adic manambala ndi geometry yofananira? Ndiroleni ndikukumbutseni owerenga kuti manambala omveka (mwachidule: tizigawo) amakhala kwambiri pamzere, koma osadzaza kwambiri.

Manambala opanda nzeru amakhala mu "mabowo". Pali zambiri, zopanda malire, koma mukhoza kunena kuti zopanda malire zawo ndi zazikulu kuposa zosavuta, zomwe timawerengera: chimodzi, ziwiri, zitatu, zinayi ... ndi zina zotero mpaka ∞. Uku ndi kudzazidwa kwathu kwaumunthu "mabowo". Tatengera chikhalidwe chamaganizo ichi kuchokera Pythagoreans. 

Koma chomwe chili chosangalatsa komanso chofunikira kwa katswiri wa masamu ndi chakuti munthu sangathe "kudzaza" mabowowa ndi manambala opanda nzeru komanso p-adic (pazinthu zonse p). Kwa owerenga omwe amamvetsetsa izi (ndipo izi zidaphunzitsidwa kusukulu yasekondale iliyonse zaka makumi atatu zapitazo), mfundo ndikuti mndandanda uliwonse womwe umakwaniritsa Dziko la Cauchy, amakumana.

Malo omwe izi ndi zoona amatchedwa kukwanira ("palibe chomwe chikusoweka"). Ndikumbukira nambala 547721051611007740081787109376.

Zotsatizana 0,5, 0,54, 0,547, 0,5477, 0,54772 ndi zina zotero zimasintha mpaka malire ena, omwe ali pafupifupi 0,5477210516110077400 81787109376.

Komabe, kuchokera pamalingaliro a mtunda wa 10-adic, kutsatizana kwa manambala 6, 76, 376, 9376, 109376, 7109376 ndi zina zotero zimasinthanso ku chiwerengero "chachilendo" ... 547721051 611007740081787109376

Koma ngakhale chimenecho sichingakhale chifukwa chokwanira chopatsa asayansi ndalama zapagulu. Kawirikawiri, ife (akatswiri a masamu) timadziteteza tokha ponena kuti n'zosatheka kufotokozera zomwe kafukufuku wathu angakhale wothandiza. Ndizosakayikitsa kuti aliyense azigwiritsa ntchito ndipo kuti kuchitapo kanthu pazachinthu chilichonse ndikosavuta.

Chimodzi mwazopangidwa zazikulu kwambiri, makina a X-ray, adapangidwa pambuyo poti ma radioactivity apezeka mwangozi Bekerela. Ngati sizinali choncho, zaka zambiri zofufuza zikadakhala zopanda ntchito. "Tikuyang'ana njira yopangira x-ray ya thupi la munthu."

Pomaliza, chinthu chofunika kwambiri. Aliyense amavomereza kuti luso lotha kuthetsa ma equation limagwira ntchito. Ndipo apa ziwerengero zathu zachilendo zimatetezedwa bwino. Theorem yofananira (Ndimadana ndi Minkowski) akuti ma equations ena amatha kuthetsedwa mu ziwerengero zomveka ngati ali ndi mizu yeniyeni ndi mizu m'thupi lililonse la adic.

Zambiri kapena zochepa njira iyi yawonetsedwa Andrew Wiles, yomwe idathetsa masamu odziwika kwambiri azaka mazana atatu zapitazi - ndikupangira owerenga kuti alowe mu injini yosakira "Theorem Yotsiriza ya Fermat".