Lem, Tokarchuk, Krakow, masvomhu

Musi waGunyana 3-7, 2019, musangano wekurangarira wePolish Mathematics Society wakaitwa muKrakow. Anniversary, nekuti makore zana ekuvambwa kweSosaiti. Yakanga iripo muGalicia kubva kumakore e1 (pasina chirevo chokuti Polish-liberalism yamambo FJ1919 yakanga ine miganhu), asi sesangano renyika yose yakashanda kubva ku1919 chete. Kufambira mberi kukuru mumasvomhu echiPolish kubva kuma1939s XNUMX-XNUMX. XNUMX paJan Casimir University muLviv, asi gungano harina kuitika ipapo - uye haisiriyo pfungwa yakanaka.

Musangano uyu waive nemafaro kwazvo, uzere nezviitiko zvinoperekedza (kusanganisira kuita kwaJacek Wojcicki panhare muNiepolomice). Hurukuro huru dzakapiwa nevakurukuri 28. Vaive muPolish nekuti vaenzi vakakokwa vaive Poles - kwete hazvo mupfungwa yekuva vagari vemo, asi vachizviona sePoles. Hongu, vadzidzisi gumi nevatatu chete vakabva kuPoland masangano esainzi, gumi nevashanu vakasara vakabva kuUSA (7), France (4), England (2), Germany (1) neCanada (1). Zvakanaka, ichi chiitiko chinozivikanwa mumitambo yenhabvu.

The best anogara achiita kunze kwenyika. Zvinorwadza zvishoma, asi rusununguko rusununguko. Vanoverengeka vekuPoland masvomhu vakaita mabasa ekunze asingawanikwe muPoland. Mari inotora chikamu chechipiri pano, asi ini handidi kunyora pamisoro yakadai. Pamwe mhinduro mbiri chete.

MuRussia, uye zvisati zvaitika muSoviet Union, izvi zvaive uye zviri pamwero wekuziva ... uye neimwe nzira hapana anoda kutamira ikoko. Zvakare, muGermany, vanenge gumi nevaviri vanonyorera vanonyorera kuti vawane hupurofesa pane chero yunivhesiti (vanoshanda navo kubva kuYunivhesiti yeKonstanz vakati vaive ne120 mafomu pagore, makumi mashanu acho aive akanaka kwazvo, uye makumi maviri aive akanaka).

Hurukuro shoma dzeJubilee Congress dzinogona kupfupikiswa mujenari yedu yepamwedzi. Misoro yakaita se "Miganhu yeSparse Girafu uye Zvishandiso Zvavo" kana "Linear Structure uye Geometry yeSubspaces uye Factor Spaces dzePamusoro-Dimensional Normalized Spaces" haizoudze muverengi wepakati chero chinhu. Musoro wechipiri wakaunzwa neshamwari yangu kubva kumakosi ekutanga, Nicole Tomchak.

Makore mashoma apfuura, akasarudzwa nekuda kwekubudirira kunoratidzwa muhurukuro iyi. Fields Medal ndizvo zvakaenzana kune masvomhu. Kusvika pari zvino, mudzimai mumwe chete ndiye awana mubairo uyu. Zvakare zvakakosha kucherechedzwa ihurukuro Anna Marcinyak-Chohra (Heidelberg University) "Basa remakanika masvomhu modhi mukurapa pamuenzaniso weleukemia modelling".

akapinda mushonga. PaYunivhesiti yeWarsaw, boka rinotungamirirwa naProf. Jerzy Tyurin.

Musoro wehurukuro haunganzwisisike kuVaverengi Veslava Niziol (z prestiżowej Higher Pedagogical School) “-adic dzidziso yeHodge". Zvakadaro, ndiyo hurukuro iyi yandafunga kukurukura pano.

Geometry - adic worlds

Zvinotanga nezvinhu zvidiki zviri nyore. Unorangarira here, Muverengi, nzira yekutsinhanisa yakanyorwa? Zvirokwazvo. Funga shure kumakore okusava nehanya okuchikoro chepuraimari. Gurai 125051 ne23 (ichi ndicho chiito chiri kuruboshwe). Iwe unoziva here kuti inogona kuve yakasiyana (chiito kurudyi)?

Iyi nzira itsva inofadza. Ndiri kuenda kubva kumagumo. Tinofanira kupatsanura 125051 ne 23. Chii chatinoda kuti tiwedzere makumi maviri nenhatu nacho kuti nhamba yekupedzisira iite 23? Kutsvaga mundangariro uye tine:=1. Diji rekupedzisira remugumisiro ndi 7. Wanza, bvisa, tinowana 7. Unowanza sei 489 kusvika pa23? Zvechokwadi, ne 9. Tinosvika panzvimbo yatinosarudza nhamba dzose dzechigumisiro. Isu tinozviona zvisingashande uye zvakanyanya kuoma kupfuura maitiro edu emazuva ese - asi inyaya yekudzidzira!

Zvinhu zvinotora danho rakasiyana kana murume akashinga asina kunyatsopatsanurwa nedivisor. Ngatiitei division tione zvinoitika.

Kuruboshwe kune njanji yechikoro. Kurudyi kune "vatorwa vedu".

Tinogona kutarisa mhinduro dzese nekuwanza. Isu tinonzwisisa yekutanga: chikamu chimwe muzvitatu chenhamba 4675 ichuru nemazana mashanu nemakumi mashanu nesere, uye zvitatu munguva. Chechipiri hachina musoro: nhamba iyi inotangirwa neisingaverengeki nhamba yevatanhatu uyezve 8225?

Ngatisiyei mubvunzo wezvinoreva kwekanguva. Ngatitambe. Saka ngatipatsanurei 1 na 3 tozopatsanura 1 na 7 inova chikamu chimwe muzvitatu chimwe nechinomwe. Tinogona kuwana nyore:

1:3=…6666667, 1/7=…(285714)3.

Uyu mutsara wekupedzisira unoreva: block 285714 inodzokorora nekusingaperi pakutanga, uye pakupedzisira pane matatu acho. Kune avo vasingatendi, heino bvunzo:

Zvino ngatiwedzerei mafractions:

Zvadaro tinowedzera nhamba dzakagamuchirwa dzisinganzwisisiki, uye tinowana (tarisa) nhamba imwe chete isinganzwisisike.

......95238095238095238095238010

Tinogona kutarisa kuti izvi zvakaenzana ne

Iyo pfungwa haisati yaonekwa, asi iyo arithmetic ndeyechokwadi.

Mumwe muenzaniso zvakare.

Iyo yakajairwa, kunyangwe yakakura, nhamba 40081787109376 ine chivakwa chinonakidza: sikweya yayo inoperawo mu40081787109376. nhamba x40081787109376, inova ( x40081787109376)² zvakare inopera mu x40081787109376.

Zano. Tine 40081787109376²= 16065496 57881 XNUMX340081787109376, saka nhamba inotevera ndeyechitatu kusvika gumi mubatsiri, anoti 7. Ngatitarisei: 740081787109376²= 5477210516110077400817 87109376.

Mubvunzo wekuti sei zvakadaro wakaoma. Zviri nyore: tsvaga magumo akafanana enhamba dzinopera muna 5. Kuenderera mberi nehurongwa hwekutsvaga manhamba anotevera nekusingaperi, tichasvika kune "nhamba" dzakadaro ²=²= (uye hapana imwe yenhamba idzi yakaenzana ne zero kana imwe).

tinonzwisisa zvakanaka. Kureba mushure meiyo desimali, ndiko kushomeka kwenhamba. Muchiverengero cheinjiniya, nhamba yekutanga mushure meiyo decimal yakakosha, pamwe neyechipiri, asi muzviitiko zvakawanda zvinogona kufungidzirwa kuti chiyero chedenderedzwa redenderedzwa kusvika padhayamita yayo 3,14. Hongu, nhamba dzakawanda dzinoda kuverengerwa muindasitiri yezvendege, asi handifungi kuti kuchave nevanopfuura gumi.

Zita racho rakabuda mumusoro wechinyorwa chacho Stanislav Lem (1921-2006), pamwe chete nemubairo wedu mutsva weNobel. Mukadzi Olga Tokarchuk Ndakangotaura izvi nekuti kupopota kusaruramisiraIchokwadi ndechokuti Stanislav Lem haana kugamuchira Nobel Prize mu Literature. Asi hazvisi mukona yedu.

Lem aigara achifanoona ramangwana. Aizvibvunza kuti chii chaizoitika kana vakasununguka kubva kuvanhu. Mangani mafirimu pamusoro penyaya iyi akaonekwa munguva pfupi yapfuura! Lem akafanotaura chaizvo uye akatsanangura muverengi wemaziso uye pharmacology yeramangwana.

Aiziva masvomhu, kunyange dzimwe nguva aizvitora sechishongo, asina hanya nekururama kwekuverenga. Semuenzaniso, munyaya ye "Trial", mutyairi wePirks anopinda mu orbit B68 nenguva yekutenderera kwemaawa mana nemaminitsi makumi maviri nepfumbamwe, uye murayiridzo uri maawa mana nemaminitsi makumi maviri nematanhatu. Anoyeuka kuti vakaverenga nemhosho ye4 muzana. Anopa data kuCalculator, uye calculator inopindura kuti zvose zvakanaka ... Zvakanaka, kwete. Zvikamu zvitatu kubva muzana zvemaminitsi 29 zvisingasviki miniti. Asi kukanganisa uku kunoshandura chero chinhu here? Pamwe zvaiva nemaune?

Sei ndiri kunyora pamusoro peizvi? Nyanzvi dzakawanda dzemasvomhu dzakamutsawo mubvunzo uyu: fungidzira nharaunda. Havana pfungwa dzedu dzevanhu. Kwatiri, 1609,12134 uye 1609,23245 nhamba dzepedyo - fungidziro yakanaka kune Chirungu mamaira. Nekudaro, makomputa anogona kufunga kuti nhamba 468146123456123456 uye 9999999123456123456 dziri pedyo. Vane magumo akafanana ane gumi nembiri.

Madijiti akawanda anowanikwa pamagumo, ndiko kuwedzera kwenhamba. Uye izvi zvinotungamirira kune inonzi daro -adic. Rega p aenzane negumi kwechinguvana; sei "kwechinguva", ini ndichatsanangura ... ikozvino. Iyo 10 point distance yenhamba dzakanyorwa pamusoro ndeiyi 

kana miriyoni imwe - nekuti nhamba idzi dzine manhamba matanhatu akafanana pamagumo. Nhamba dzese dzinosiyana kubva ku zero neimwe kana zvishoma. Ini handisi kana kunyora template nekuti hazvina basa. Iyo yakawanda yakafanana nhamba pamagumo, iyo inoswedera pedyo nhamba (kumunhu, pane zvinopesana, nhamba dzekutanga dzinofungidzirwa). Zvakakosha kuti p ive nhamba huru.

Zvadaro - vanoda zero uye imwe, saka vanoona zvose zviri mumapatani aya: 0100110001 1010101101010101011001010101010101111.

Munovhero Glos Pana, Stanisław Lem anohaya masayendisiti kuti aedze kuverenga meseji yakatumirwa kubva kuhupenyu hwepashure perufu, yakanyorwa zero-imwe zvechokwadi. Pane munhu anotinyorera here? Lem anopikisa kuti "chero meseji inogona kuverengwa kana iri meseji yaida kutiudza chimwe chinhu." Asi ndizvo here? Ndichasiya vaverengi vaine dambudziko iri.

Isu tinogara munzvimbo yeXNUMXD R³. Tsamba R inoyeuka kuti matemo acho ane nhamba chaidzo, kureva nhamba dzakakwana, dzisina kunaka uye dzakanaka, zero, zvine musoro (kureva zvikamu zviduku) uye zvisina musoro, izvo zvakasangana nevaverengi muchikoro (), uye nhamba dzinozivikanwa senhamba dzinopfuura, dzisingasvikiki mualgebra (iyi inhamba π , iyo yave ichibatanidza dhayamita yedenderedzwa nedenderedzwa rayo kwemakore anopfuura zviuru zviviri).

Ko kana matemo enzvimbo yedu aive -adic manhamba?

Jerzy Mioduszowski, nyanzvi yemasvomhu paYunivhesiti yeSilesia, inotaura kuti izvi zvingava zvakadaro, uye kunyange kuti zvingadaro. Tinogona (anodaro Jerzy Mioduszewski) kugara panzvimbo imwe chete munzvimbo nezvisikwa zvakadaro, pasina kupindira uye pasina kuonana.

Saka, isu tine ese geometry yenyika "yavo" yekuongorora. Hazvigoneki kuti "ivo" vanofunga nenzira imwechete pamusoro pedu uye zvakare kudzidza geometry yedu, nokuti yedu inyaya yemuganhu we "nyika" dzavo dzose. "Ivo", ndiko kuti, nyika dzese dzegehena, uko dziri nhamba huru. Kunyanya, = 2 uye ino inonakidza nyika ye zero-imwe ...

Apa muverengi wenyaya anogona kutsamwa nekutoshatirwa. "Ndihwo hupenzi hunoitwa nemasvomhu here?" Vanofungidzira nezvekunwa vodka mushure mekudya kwemanheru, nemari yangu (= yemutero). Uye kuvaparadzira kumhepo ina, ngavaende kumapurazi ehurumende ... o, hakusisina mapurazi ehurumende!

Zorora. vaigara vachifarira majee akadaro. Rega ndingotaura nezve sandwich theorem: kana ndine chizi nesangweji yeham, ndinogona kucheka muchidimbu chimwe chete kuganhura bhanzi, ham, uye chizi. Izvi hazvina maturo mukuita. Icho chiripo ndechekuti uku kunongova kwekutamba kwekushandisa kweinonakidza general theorem kubva kuongororo yekushanda.

Zvakakomba zvakadii kubata ne-adic manhamba uye yakabatana geometry? Rega ndiyeuchidze muverengi kuti manhamba anonzwisisika (zvakareruka: mafractions) anorara zvakanyanya pamutsetse, asi usazadze zvakanyanya.

Nhamba dzisina musoro dzinogara mu "makomba". Kune akawanda, asingaverengeki mazhinji acho, asi iwe unogona zvakare kutaura kuti kusakwana kwavo kwakakura pane iyo yakapusa, yatinoverenga: imwe, mbiri, nhatu, ina ... zvichingodaro kusvika ∞. Uku ndiko kuzadza kwedu "maburi". Takagara nhaka chimiro chendangariro ichi kubva pythagoreans. 

Asi chinonakidza uye chakakosha kunyanzvi yemasvomhu ndechekuti munhu haakwanise "kuzadza" maburi aya nenhamba dzisina musoro uye dzep-adic (zvese maprimes p). Kune avo vaverengi vanonzwisisa izvi (uye izvi zvakadzidziswa muchikoro chesekondari chese makore makumi matatu apfuura), poindi ndeyekuti kutevedzana kwese kunogutsa. Cauchy's state, converges.

Nzvimbo umo ichi chiri chokwadi inonzi yakakwana ("hapana chisipo"). Ndicharangarira nhamba 547721051611007740081787109376.

Iyo inoteedzana 0,5, 0,54, 0,547, 0,5477, 0,54772 uye zvichingodaro converges kune imwe muganhu, ingangoita 0,5477210516110077400 81787109376.

Nekudaro, kubva pakuona kwegumi-adic kure, kutevedzana kwenhamba 10, 6, 76, 376, 9376, 109376 uye zvichingodaro zvakare inoshandura kune "zvinoshamisa" nhamba ... 7109376 547721051.

Asi kunyangwe izvo zvingasava chikonzero chakakwana chekupa masayendisiti mari yeruzhinji. Kazhinji, isu (masvomhu) tinozvidzivirira nekutaura kuti hazvibviri kufanotaura kuti tsvakurudzo yedu ichabatsira sei. Zvinenge zveshuwa kuti munhu wese achange achishandiswa uye kuti chiito chete pane yakafara pamberi chine mukana wekubudirira.

Chimwe chezvakanyanya kugadzirwa, muchina weX-ray, wakagadzirwa mushure mekunge radioactivity yawanikwa netsaona Bekkerela. Dai zvisiri zvenyaya iyi, makore mazhinji ekutsvaga angadai asina kubatsira. "Tiri kutsvaga nzira yekutora x-ray yemuviri wemunhu."

Pakupedzisira, chinhu chinonyanya kukosha. Wese munhu anobvuma kuti kugona kugadzirisa equations kune basa. Uye pano nhamba dzedu dzechienzi dzakachengetedzwa zvakanaka. Theorem inoenderana (Ndinovenga minkowski) inotaura kuti mamwe equations anogona kugadziriswa munhamba dzinonzwisisika kana uye chete kana dziine midzi chaiyo nemidzi mune yega-adic muviri.

Zvakawanda kana zvishoma nzira iyi yakaratidzwa Andrew Wiles, iyo yakagadzirisa yakakurumbira masvomhu equation yemakore mazana matatu apfuura - Ndinokurudzira vaverengi kuti vaise iyo injini yekutsvaga. "Fermat's Last Theorem".