Lem, Tokarchuk, Krakow, mathematics

NgoSepthemba 3-7, 2019, ingqungquthela yesikhumbuzo ye-Polish Mathematics Society yenzeka eKrakow. Isikhumbuzo, ngenxa yekhulunyaka kwasungulwa iNhlangano. Yayikhona eGalicia kusukela eminyakeni ye-1 (ngaphandle kwesichasiso sokuthi i-Polish-liberalism yombusi FJ1919 yayinemikhawulo yayo), kodwa njengenhlangano yezwe lonke yayisebenza kusukela ku-1919 kuphela. Intuthuko enkulu kuzibalo zasePoland isukela kuma-1939s XNUMX-XNUMX. XNUMX e-Jan Casimir University e-Lviv, kodwa umhlangano awukwazanga ukuba khona - futhi akuwona umqondo omuhle kakhulu.

Umhlangano ubuyinjabulo enkulu, ugcwele imicimbi ehambisanayo (kuhlanganise nomdlalo ka-Jacek Wojcicki enqabeni e-Niepolomice). Izinkulumo eziyinhloko zethulwa izikhulumi ezingama-28. BabengesiPolish ngoba izihambeli ezimenyiwe kwakungamaPoles - hhayi ngomqondo wokuba yisakhamuzi, kodwa bezazi bona njengamaPoles. Oh yebo, abafundisi abayishumi nantathu kuphela abavela ezikhungweni zesayensi zasePoland, abayishumi nanhlanu abasele bavela e-USA (7), France (4), England (2), Germany (1) naseCanada (1). Hhayi-ke, lokhu kuyinto eyaziwayo kumaligi ebhola.

The best njalo enze phesheya. Kuyadabukisa kancane, kodwa inkululeko iyinkululeko. Izazi zezibalo eziningi zasePoland zenze imisebenzi yaphesheya engafinyeleleki ePoland. Imali idlala indima yesibili lapha, kodwa angifuni ukubhala ngezihloko ezinjalo. Mhlawumbe imibono emibili nje.

E-Russia, nangaphambi kwalokho eSoviet Union, lokhu kwaba futhi kusezingeni eliphezulu kakhulu ... futhi ngandlela-thile akekho ofuna ukuthuthela lapho. Ngokulandelayo, eJalimane, cishe ishumi nambili labafundi abafaka izicelo zobuprofesa kunoma iyiphi inyuvesi (ozakwabo baseNyuvesi yaseKonstanz bathi babe nezicelo ezingu-120 ngonyaka, ezingu-50 zazo zazizinhle kakhulu, futhi ezingu-20 zazihamba phambili).

Izinkulumo ezimbalwa zeJubilee Congress zingafingqwa kujenali yethu yanyanga zonke. Izihloko ezifana nokuthi "Imikhawulo Yamagrafu Ambalwa Nezinhlelo Zokusebenza" noma "Isakhiwo Somugqa kanye Nejiyomethri Yezikhala Ezingaphansi Nezikhala Ze-Factor Yezikhala Ezisezingeni Eliphezulu Ezijwayelekile" ngeke zitshele umfundi omaphakathi noma yini. Isihloko sesibili sethulwa umngane wami kusukela ezifundweni zokuqala, UNicole Tomchak.

Eminyakeni embalwa edlule, waqokwa ngempumelelo ethulwa kulesi sifundo. Indondo Yezinkundla liyalingana nezazi zezibalo. Kuze kube manje, uyedwa kuphela owesifazane osethole le ndondo. Okunye okufanele kuqashelwe yinkulumo Anna Marcinyak-Chohra (Heidelberg University) "Indima yamamodeli ezibalo zemishini kwezokwelapha ngesibonelo sokumodela i-leukemia".

wangena umuthi. ENyuvesi yaseWarsaw, iqembu eliholwa nguProf. UJerzy Tyurin.

Isihloko senkulumo ngeke siqonde kubafundi Veslava Niziol (z prestiżowej Higher Pedagogical School) “-i-adic theory ye-Hodge". Noma kunjalo, yilesi sifundo enginqume ukuxoxa ngaso lapha.

I-geometry - imihlaba ye-adic

Iqala ngezinto ezincane ezilula. Uyakhumbula, Mfundi, indlela yokushintshana okubhaliwe? Nakanjani. Cabanga emuva eminyakeni yokungakhathali yasesikoleni samabanga aphansi. Hlukanisa u-125051 ngo-23 (lesi isenzo esingakwesokunxele). Uyazi ukuthi kungaba okuhlukile (isenzo kwesokudla)?

Le ndlela entsha iyathakazelisa. ngisuka ekugcineni. Sidinga ukuhlukanisa u-125051 ngo-23. Sidingani ukuphindaphinda 23 ukuze idijithi yokugcina ibe ngu-1? Isesha ngenkumbulo futhi sine-:=7. Idijithi yokugcina yomphumela ithi 7. Phindaphinda, susa, sithola 489. Uphindaphinda kanjani 23 ukuze ugcine ngo-9? Yebo, ngo-3. Sifika lapho sinquma khona zonke izinombolo zomphumela. Sikuthola kungenangqondo futhi kunzima kakhulu kunendlela yethu evamile - kodwa kuyindaba yokuzijwayeza!

Izinto zithatha inguquko ehlukile uma indoda enesibindi ingahlukaniswanga ngokuphelele ngumhlukanisi. Asenze umehluko futhi sibone ukuthi kwenzekani.

Kwesokunxele kunengoma yesikole ejwayelekile. Kwesokudla "yizimanga zethu".

Singahlola yomibili imiphumela ngokuphindaphinda. Siyaqonda eyokuqala: ingxenye yesithathu yenombolo 4675 iyinkulungwane namakhulu amahlanu namashumi amahlanu nesishiyagalombili, futhi ezintathu esikhathini. Eyesibili ayiwenzi umqondo: iyiphi le nombolo eyandulelwa inombolo engapheli yabayisithupha bese kuba ngu-8225?

Ake sishiye umbuzo wencazelo isikhashana. Asidlale. Ngakho-ke ake sihlukanise u-1 ngo-3 bese u-1 ngo-7 okusho ukuthi ingxenye yesithathu kanye neyodwa isikhombisa. Singathola kalula:

1:3=…6666667, 1/7=…(285714)3.

Lo mugqa wokugcina usho ukuthi: ibhulokhi engu-285714 iphinda unomphela ekuqaleni, futhi ekugcineni kukhona ezintathu zazo. Kulabo abangakholwa, nali isivivinyo:

Manje ake sengeze amafrakshini:

Bese sengeza izinombolo ezingaziwa ezitholiwe, futhi sithola (hlola) inombolo efanayo eyinqaba.

... ....95238095238095238095238010

Singahlola ukuthi lokhu kuyalingana ne

Ingqikithi isazobonakala, kodwa izibalo zilungile.

Esinye isibonelo.

Inombolo evamile, nakuba inkulu, inombolo engu-40081787109376 inendawo ethakazelisayo: isikwele sayo siphetha ngo-40081787109376. inombolo x40081787109376, okungukuthi (x40081787109376)² futhi iphetha ngo-x40081787109376.

Ithiphu. Sine 40081787109376²= 16065496340081787109376, ngakho idijithi elandelayo ihlanganisa okuthathu kuya kweshumi, okungu-7. Ake sihlole: 740081787109376²= 5477210516110077400817 87109376.

Umbuzo wokuthi kungani kunjalo unzima. Kulula: thola iziphetho ezifanayo zezinombolo ezigcina ngo-5. Ngokuqhubeka nenqubo yokuthola amadijithi alandelayo unomphela, sizofika "kuzinombolo" ezinjalo ukuthi ²=²= (futhi ayikho kulezi zinombolo elingana noziro noma eyodwa).

siqonda kahle. Ukuqhela ngemva kwephoyinti ledesimali, inani lenani liba kancane. Ekubalweni kobunjiniyela, idijithi yokuqala emva kwephuzu ledesimali ibalulekile, kanye neyesibili, kodwa ezimweni eziningi kungacatshangwa ukuthi isilinganiso somjikelezo wombuthano kuya kububanzi bawo ngu-3,14. Yebo, izinombolo eziningi zidinga ukufakwa embonini yezindiza, kodwa angicabangi ukuthi zizoba ngaphezu kweshumi.

Igama livele esihlokweni se-athikili Stanislav Lem (1921-2006), kanye nomnqobi wethu omusha weNobel. Ntokazi U-Olga Tokarchuk Ngikhulume lokhu kuphela ngoba ukuklabalasa ngokungabi nabulungisaIqiniso liwukuthi uStanislav Lem akazange athole uMklomelo KaNobel Wezincwadi. Kodwa akukho ekhoneni lethu.

U-Lem wayevame ukubona kusengaphambili ikusasa. Wayezibuza ukuthi kuzokwenzekani uma sezizimele ngaphandle kwabantu. Mangaki amafilimu alesi sihloko avele kamuva nje! U-Lem wabikezela ngokunembile futhi wachaza umfundi obonakalayo kanye ne-pharmacology yesikhathi esizayo.

Wayezazi izibalo, nakuba ngezinye izikhathi wayeziphatha njengomhlobiso, engenandaba nokunemba kwezibalo. Ngokwesibonelo, endabeni ethi "Trial", umshayeli we-Pirks ungena ku-orbit B68 enenkathi yokujikeleza amahora angu-4 nemizuzu engu-29, futhi isiyalo singamahora angu-4 nemizuzu engu-26. Uyakhumbula ukuthi babale ngephutha lika-0,3%. Unikeza idatha ku-Calculator, futhi umshini wokubala uphendule ngokuthi konke kuhamba kahle ... Hhayi-ke, cha. Ingxenye yesithathu yephesenti yemizuzu engama-266 ingaphansi komzuzu. Kodwa ingabe leli phutha liyashintsha? Mhlawumbe bekungamabomu?

Ngibhala ngani ngalokhu? Izazi zezibalo eziningi ziye zaphakamisa lo mbuzo: cabanga umphakathi. Abanayo ingqondo yethu yomuntu. Kithina, 1609,12134 kanye 1609,23245 izinombolo ezisondelene kakhulu - izilinganiso ezinhle zemayela lesiNgisi. Nokho, amakhompyutha angase acabangele izinombolo 468146123456123456 kanye 9999999123456123456 seduze. Zineziphetho ezifanayo ezinamadijithi ayishumi nambili.

Izinombolo ezivame kakhulu ekugcineni, izinombolo zisondelana. Futhi lokhu kuholela kulokho okubizwa ngokuthi ibanga -i-adic. U-p akalingane no-10 okwesikhashana; kungani nje "isikhashana", ngizochaza ... manje. Ibanga lamaphuzu ayi-10 lezinombolo ezibhalwe ngenhla yilo 

noma isigidi esisodwa - ngoba lezi zinombolo zinezinombolo eziyisithupha ezivamile ekugcineni. Wonke izinombolo ziyahluka kuziro ngokukodwa noma ngaphansi. Ngeke ngize ngibhale isifanekiso ngoba akusho lutho. Izinombolo ezifanayo kakhulu ekugcineni, izinombolo eziseduze (kumuntu, ngokuphambene nalokho, izinombolo zokuqala zibhekwa). Kubalulekile ukuthi p kube inombolo eyinhloko.

Bese - bathanda ama-zero kanye nalawo, ngakho babona yonke into kulawa maphethini: 0100110001 1010101101010101011001010101010101111.

Kunoveli ethi Glos Pana, u-Stanisław Lem uqasha ososayensi ukuthi bazame ukufunda umlayezo othunyelwe usuka ekuphileni kwangemva kokufa, onekhodi ethi ziro-one. Ingabe ukhona osibhalelayo? U-Lem uphikisa ngokuthi "noma yimuphi umlayezo ungafundwa uma kungumlayezo othile obefuna ukusitshela okuthile." Kodwa ingabe kunjalo? Ngizoshiya abafundi nale nkinga.

Sihlala esikhaleni se-XNUMXD R³. Incwadi R ikhumbula ukuthi izimbazo zihlanganisa izinombolo zangempela, okungukuthi izinombolo eziphelele, ezinegegethivu nephozithivu, uziro, okunengqondo (okungukuthi amafrakshini) nokungenangqondo, abafundi ababehlangana nabo esikoleni (), nezinombolo ezaziwa ngokuthi izinombolo ezidlulayo, ezingafinyeleleki ku-algebra (lena inombolo u-π , osekuyiminyaka engaphezu kwezinkulungwane ezimbili ihlanganisa ububanzi besiyingi nesiyingi).

Kuthiwani uma izimbazo zesikhala sethu ziyizinombolo ze-adic?

UJerzy Mioduszowski, isazi sezibalo eNyuvesi yaseSilesia, siphikisa ngokuthi lokhu kungase kube njalo, ngisho nokuthi kungase kube njalo. Singakwazi (kusho uJerzy Mioduszewski) ukuhlala endaweni efanayo emkhathini nezidalwa ezinjalo, ngaphandle kokuphazamisa futhi ngaphandle kokubonana.

Ngakho-ke, sinayo yonke i-geometry yomhlaba "yabo" okufanele siyihlole. Akunakwenzeka ukuthi "bona" ​​bacabange ngendlela efanayo ngathi futhi baphinde bafunde i-geometry yethu, ngoba eyethu iyindaba emngceleni wayo yonke imihlaba "yabo". "Them", okungukuthi, yonke imihlaba yesihogo, lapho izinombolo eziyinhloko. Ikakhulukazi, = 2 kanye nalo mhlaba othakazelisayo we-zero-one ...

Lapha umfundi wesihloko angase acasuke aze acasuke. "Ingabe yimbudane lena eyenziwa ongoti bezibalo?" Baphupha ngokuphuza i-vodka ngemva kwesidlo sakusihlwa, nokusebenzisa imali yami (=yomkhokhi wentela). Futhi abahlakaze emimoyeni emine, baye emapulazini kahulumeni ... o, awasekho amapulazi kahulumeni!

Nethezeka. babehlale bethanda amahlaya anjalo. Ake ngivele ngikhulume ngethiyori yesemishi: uma nginesemishi likashizi nesamishi, ngingalisika libe linye ukuze ngihlukanise ingxenye yebhani, iham, noshizi. Lokhu akusizi ekusebenzeni. Iphuzu liwukuthi lokhu kuwuhlelo lokusebenza oludlalayo nje lwethiyori evamile ethakazelisayo evela ekuhlaziyweni kokusebenza.

Kubaluleke kangakanani ukubhekana nezinombolo ze-adic kanye nejometri ehlobene? Ake ngikhumbuze umfundi ukuthi izinombolo ezinengqondo (ngokulula: izingxenyana) ziminyene emgqeni, kodwa ungazigcwaliseli eduze.

Izinombolo ezingenangqondo zihlala "emigodini". Ziningi, ziningi ngokungenamkhawulo, kodwa futhi ungasho ukuthi ukungapheli kwazo kukhulu kunalezo ezilula, lapho sibala khona: eyodwa, ezimbili, ezintathu, ezine ... njalonjalo kuze kufike ku-∞. Lokhu ukugcwalisa kwethu "izimbobo" njengabantu. Lesi sakhiwo somqondo sizuze kuso AmaPythagoreans. 

Kodwa okuthakazelisayo nokubalulekile kusazi sezibalo ukuthi umuntu akakwazi "ukugcwalisa" lezi zimbobo ngezinombolo ezingenangqondo kanye ne-p-adic (kuwo wonke ama-primes p). Kulabo bafundi abakuqondayo lokhu (futhi lokhu kwakufundiswa kuzo zonke izikole zamabanga aphezulu eminyakeni engamashumi amathathu edlule), iphuzu liwukuthi ukulandelana konke okwanelisayo Isimo sikaCauchy, ziyahlangana.

Isikhala lapho lokhu kuyiqiniso sibizwa ngokuthi siphelele ("ayikho into engekho"). Ngizokhumbula inombolo ethi 547721051611007740081787109376.

Ukulandelana okungu-0,5, 0,54, 0,547, 0,5477, 0,54772 nokunye kuguqukela emkhawulweni othile, okungaba ngu-0,5477210516110077400 81787109376.

Kodwa-ke, ngokombono webanga le-10-adic, ukulandelana kwezinombolo 6, 76, 376, 9376, 109376, 7109376 nokunye futhi kuguqukela inombolo "eyinqaba" ... 547721051 611007740081787109376.

Kodwa ngisho nalokho kungase kungabi isizathu esanele sokunikeza ososayensi imali yomphakathi. Ngokuvamile, thina (izazi zezibalo) siyazivikela ngokuthi akunakwenzeka ukubikezela ukuthi ucwaningo lwethu luzoba usizo ngani. Cishe kuqinisekile ukuthi wonke umuntu uzosebenzisa okuthile nokuthi isenzo endaweni ebanzi kuphela esinethuba lokuphumelela.

Enye yezinto ezisunguliwe ezinkulu, umshini we-X-ray, wadalwa ngemva kokutholakala kwe-radioactivity ngephutha Bekkerela. Ukube bekungenjalo, iminyaka eminingi yocwaningo cishe ibingeke ibe nalusizo. "Sibheka indlela yokuthatha i-x-ray yomzimba womuntu."

Ekugcineni, into ebaluleke kakhulu. Wonke umuntu uyavuma ukuthi ikhono lokuxazulula izibalo lidlala indima. Futhi lapha izinombolo zethu eziyinqaba zivikelwe kahle. Ithiyori ehambisanayo (Ngiyamzonda uMinkowski) ithi ezinye zibalo zingaxazululwa ngezinombolo ezinengqondo uma futhi zinezimpande zangempela kanye nezimpande kuwo wonke umzimba we-adic.

Okuningi noma okuncane le ndlela yethuliwe Andrew Wiles, eyaxazulula i-equation yezibalo edume kakhulu yeminyaka engamakhulu amathathu edlule - ngincoma abafundi ukuthi bayifake enjini yokusesha "I-Theorem yokugcina kaFermat".