Lem, Tokarchuk, Krakow, lissafi

A ranar 3-7 ga Satumba, 2019, taron ranar tunawa da Ƙungiyar Lissafi ta Poland ya faru a Krakow. Bikin cika shekaru 1 da kafuwar Al'umma. Ya wanzu a Galicia daga shekaru 1919st (ba tare da siffa cewa Polish-liberalism na sarki FJ1919 yana da iyaka), amma a matsayin ƙungiyar ƙasa baki ɗaya tana aiki ne kawai daga 1939. Babban ci gaba a cikin ilimin lissafin Poland ya koma XNUMXs XNUMX-XNUMX. XNUMX a Jami'ar Jan Casimir a Lviv, amma taron ba zai iya faruwa a can ba - kuma ba shine mafi kyawun ra'ayi ba.

Taron ya kasance mai ban sha'awa sosai, cike da abubuwan da suka faru (ciki har da wasan kwaikwayo na Jacek Wojcicki a gidan sarauta a Niepolomice). Masu jawabai 28 ne suka gabatar da manyan laccoci. Sun kasance a cikin Yaren mutanen Poland saboda baƙi da aka gayyata sun kasance Poles - ba lallai ba ne a cikin ma'anar zama ɗan ƙasa, amma sun amince da kansu a matsayin Poles. Eh, malamai goma sha uku ne kawai suka fito daga cibiyoyin kimiyya na Poland, sauran goma sha biyar sun fito daga Amurka (7), Faransa (4), Ingila (2), Jamus (1) da Kanada (1). To, wannan sanannen lamari ne a wasannin ƙwallon ƙafa.

Mafi kyawu kullum yi a kasashen waje. Yana da ɗan baƙin ciki, amma 'yanci shine 'yanci. Masana ilimin lissafin Poland da yawa sun sa ba a iya samun ayyukan ƙasashen waje a Poland. Kudi yana taka rawa ta biyu a nan, amma ba na son yin rubutu akan irin waɗannan batutuwa. Wataƙila kawai sharhi biyu ne.

A cikin Rasha, kuma kafin wannan a cikin Tarayyar Soviet, wannan ya kasance kuma yana cikin mafi girman matakin ... kuma ko ta yaya ba wanda yake so ya yi hijira a can. Bi da bi, a Jamus, kimanin 'yan takara goma sha biyu ne suka nemi takardar shaidar digiri a kowace jami'a (abokan aiki daga Jami'ar Konstanz sun ce sun sami aikace-aikacen 120 a cikin shekara guda, 50 na da kyau sosai, kuma 20 sun yi kyau).

Kadan daga cikin laccoci na Jubilee Congress za a iya taƙaita a cikin mujallarmu ta wata-wata. Kanun labarai irin su "Iyakokin Zane-zane da Aikace-aikacensu" ko "Tsarin Tsarin Layi da Geometry na Wuraren Ƙaƙwalwa da Factors Factors for High-Dimensional Normalized Spaces" ba za su gaya wa matsakaicin mai karatu komai ba. Maudu'i na biyu abokina ne ya gabatar da shi daga darasi na farko, Nicole Tomchak asalin.

A 'yan shekarun da suka gabata, an zabe ta ne don nasarar da aka gabatar a cikin wannan lacca. Lambar Filaye daidai yake da masu ilimin lissafi. Ya zuwa yanzu dai mace daya ce ta samu wannan lambar yabo. Hakanan abin lura shine karatun Anna Marcinyak-Chohra (Jami'ar Heidelberg) "Ayyukan na'urorin lissafi na injiniyoyi a cikin likitanci akan misalin cutar sankarar bargo".

shiga magani. A Jami'ar Warsaw, ƙungiyar da Prof. Jerzy Tyurin.

Taken karatun ba zai gagara fahimtar masu karatu ba Veslava Niziol (z prestiżowej Higher Pedagogical School) "-adic ka'idar Hodge". Duk da haka, wannan lacca ce na yanke shawarar tattaunawa a nan.

Geometry - duniya adices

Yana farawa da ƙananan abubuwa masu sauƙi. Ka tuna, Mai karatu, hanyar musayar rubutu? Tabbas. Ka yi tunani baya ga shekarun rashin kulawa na makarantar firamare. Raba 125051 ta 23 (wannan shine aikin hagu). Shin kun san cewa zai iya bambanta (aiki a hannun dama)?

Wannan sabuwar hanyar tana da ban sha'awa. Zan tafi daga ƙarshe. Muna buƙatar raba 125051 zuwa 23. Menene muke buƙatar ninka 23 ta yadda lambobi na ƙarshe ya zama 1? Neman ƙwaƙwalwar ajiya kuma muna da: = 7. Lambobin ƙarshe na sakamakon shine 7. ninka, cirewa, muna samun 489. Ta yaya kuke ninka 23 don ƙare da 9? Tabbas, ta hanyar 3. Mun isa wurin da muke ƙayyade duk lambobin sakamakon. Mun same shi ba shi da amfani kuma yana da wahala fiye da yadda muka saba - amma lamari ne na aiki!

Al'amura suna canza salo daban-daban yayin da jarumin bai gama raba shi da masu rarrabawa ba. Mu yi rabo mu ga abin da ya faru.

A hagu akwai waƙa ta makaranta. A dama shine "baƙinmu".

Za mu iya duba sakamakon biyu ta hanyar ninkawa. Mun fahimci na farko: daya bisa uku na lamba 4675 shi ne dubu daya da dari biyar da hamsin da takwas, da uku a cikin zamani. Na biyun ba shi da ma'ana: menene wannan lambar da ke gaba da adadi mara iyaka na shida sannan 8225?

Bari mu bar tambayar ma'ana na ɗan lokaci. Mu yi wasa. Don haka mu raba 1 da 3 sannan mu raba 1 da 7 wato kashi uku da na bakwai. Za mu iya samun sauƙi:

1:3=…6666667, 1/7=…(285714)3.

Wannan layi na ƙarshe yana nufin: toshe 285714 yana maimaita har abada a farkon, kuma a ƙarshe akwai uku daga cikinsu. Ga wadanda ba su yi imani ba, ga gwaji:

Yanzu bari mu ƙara ɓangarorin:

Sa'an nan kuma mu tara baƙon lambobin da aka karɓa, kuma muna samun (duba) lambar baƙon iri ɗaya.

......95238095238095238095238010

Za mu iya duba cewa wannan daidai yake da

Har yanzu ba a ga ainihin abin ba, amma lissafin daidai ne.

Misali guda daya.

Al'ada, ko da yake babba, lamba 40081787109376 yana da dukiya mai ban sha'awa: filinsa kuma yana ƙare a 40081787109376. lambar x40081787109376, wato (x40081787109376)² kuma ya ƙare a x40081787109376.

Tukwici. Muna da 40081787109376²= 16065496340081787109376, don haka lamba ta gaba ita ce ta uku zuwa goma, wato 7. Mu duba: 740081787109376²= 5477210516110077400817 87109376.

Tambayar me yasa haka yake abu ne mai wahala. Yana da sauƙi: nemo ƙarewar irin wannan don lambobin da ke ƙarewa a cikin 5. Ci gaba da aiwatar da gano lambobi na gaba har abada, za mu zo ga irin waɗannan "lambobi" waɗanda ²=²= (kuma babu ɗayan waɗannan lambobin da ya kai sifili ko ɗaya).

mun fahimta da kyau. Mafi nisa bayan maki goma, ƙarancin mahimmancin lambar shine. A cikin lissafin injiniya, lambobi na farko bayan ma'aunin ƙima yana da mahimmanci, haka kuma na biyu, amma a yawancin lokuta ana iya ɗauka cewa rabon da'irar da'irar zuwa diamita shine 3,14. Tabbas, akwai bukatar a saka adadin da yawa a harkar sufurin jiragen sama, amma ba na jin za a samu fiye da goma.

Sunan ya bayyana a cikin taken labarin Stanislav Lem (1921-2006), da kuma sabuwar lambar yabo ta Nobel. Uwargida Olga Tokarchuk Na ambaci wannan kawai saboda kururuwa rashin adalciGaskiyar ita ce Stanislav Lem bai sami lambar yabo ta Nobel a adabi ba. Amma ba a cikin kusurwar mu ba.

Lem sau da yawa ya hango abin da zai faru nan gaba. Ya yi mamakin abin da zai faru sa’ad da suka ’yantar da ’yan Adam. Fina-finai nawa ne kan wannan batu suka fito kwanan nan! Lem yayi annabta daidai kuma ya bayyana mai karatu na gani da ilimin likitanci na gaba.

Ya san ilimin lissafi, ko da yake wani lokacin yana ɗaukar shi a matsayin kayan ado, ba ya damu da daidaiton lissafin ba. Alal misali, a cikin labarin "Trial", matukin jirgin Pirks ya shiga cikin kewayawa B68 tare da lokacin jujjuyawar sa'o'i 4 da minti 29, kuma umarnin shine 4 hours da minti 26. Ya tuna cewa sun kirga da kuskuren kashi 0,3. Ya ba da bayanai ga Kalkuleta, kuma kalkuleta ya amsa cewa komai yana da kyau ... To, a'a. Kashi uku cikin goma na kashi dari na mintuna 266 bai wuce minti daya ba. Amma wannan kuskuren ya canza wani abu? Wataƙila da gangan ne?

Me yasa nake rubutu akan wannan? Masana ilmin lissafi da yawa ma sun yi wannan tambayar: tunanin al'umma. Ba su da tunanin mu na ɗan adam. A gare mu, 1609,12134 da 1609,23245 lambobi ne masu kusanci sosai - kyakkyawan kusanci zuwa mil na Ingilishi. Koyaya, kwamfutoci na iya ɗaukar lambobi 468146123456123456 da 9999999123456123456 kusa. Suna da ƙarshen lambobi goma sha biyu iri ɗaya.

Yawancin lambobi gama gari a ƙarshen, mafi kusancin lambobi. Kuma wannan yana haifar da abin da ake kira nisa -adi. Bari p ya zama daidai da 10 na ɗan lokaci; me yasa kawai "na ɗan lokaci", zan bayyana ... yanzu. Tazarar maki 10 na lambobin da aka rubuta a sama shine 

ko miliyan ɗaya - saboda waɗannan lambobin suna da lambobi guda shida na gama-gari a ƙarshen. Duk lamba sun bambanta daga sifili ta ɗaya ko ƙasa da haka. Ba zan ma rubuta samfuri ba saboda ba komai. Yawancin lambobi masu kama da juna a ƙarshen, mafi kusancin lambobin (ga mutum, akasin haka, ana la'akari da lambobin farko). Yana da mahimmanci cewa p ya zama babban lamba.

Sa'an nan - suna son sifili da waɗanda, don haka suna ganin komai a cikin waɗannan alamu: 0100110001 1010101101010101011001010101010101111.

A cikin labari na Glos Pana, Stanisław Lem ya dauki hayar masana kimiyya don kokarin karanta sakon da aka aiko daga lahira, wanda aka sanya sifili-daya ba shakka. Akwai wanda ya rubuta mana? Lem yayi jayayya cewa "kowane sako za a iya karantawa idan saƙo ne da wani ya so ya gaya mana wani abu." Amma shi ne? Zan bar masu karatu da wannan matsala.

Muna rayuwa a sararin XNUMXD R³. Wasika R yana tuna cewa gatari ya ƙunshi lambobi na gaske, watau lamba, korau da tabbatacce, sifili, ma'ana (watau ɓangarori) da rashin hankali, waɗanda masu karatu suka hadu a makaranta (), da lambobi waɗanda aka sani da lambobi masu wuce gona da iri, waɗanda ba za su iya shiga cikin algebra (wannan ita ce lambar π). , wanda ya kasance yana haɗa diamita na da'ira tare da kewayenta fiye da shekaru dubu biyu).

Idan gatari na sararin samaniyanmu ya kasance - lambobin adic?

Jerzy Mioduszowski, Masanin lissafi a Jami'ar Silesia, yayi jayayya cewa hakan na iya zama haka, har ma yana iya zama haka. Za mu iya (in ji Jerzy Mioduszewski) a cikin sararin samaniya tare da irin waɗannan halittu, ba tare da tsoma baki ba kuma ba tare da ganin juna ba.

Don haka, muna da dukkan jumlolin “su” ɗin duniya don bincika. Yana da wuya "su" suyi tunani iri ɗaya game da mu kuma su yi nazarin ilimin lissafin mu, domin namu lamari ne na iyaka na dukan "su" duniya. "Su", wato, duk duniyar jahannama, inda suke manyan lambobi. Musamman, = 2 da wannan duniyar mai ban sha'awa ta sifili-daya ...

Anan mai karanta labarin zai iya yin fushi har ma ya yi fushi. "Shin wannan irin shirmen da masana lissafi suke yi?" Suna sha'awar shan vodka bayan abincin dare, tare da kuɗin (= mai biyan haraji). Kuma a watsar da su iska guda hudu, a bar su su tafi gonakin jaha...o, babu sauran gonakin jaha!

Huta. kullum suna da sha'awar irin wannan barkwanci. Bari in ambaci ka'idar sanwici kawai: idan ina da cuku da sanwici na naman alade, zan iya yanke shi a yanka guda ɗaya don raba bun, naman alade, da cuku. Wannan ba shi da amfani a aikace. Ma'anar ita ce wannan kawai aikace-aikacen wasa ne na ƙa'idar gabaɗaya mai ban sha'awa daga nazarin aiki.

Yaya tsanani yake yin mu'amala da -adic lambobi da lissafi masu alaƙa? Bari in tunatar da mai karatu cewa lambobi masu hankali (a sauƙaƙe: ɓangarorin) suna kwance sosai akan layi, amma kar a cika su sosai.

Lambobin rashin hankali suna rayuwa a cikin "ramuka". Akwai da yawa, da yawa ba su da iyaka, amma kuma kana iya cewa rashin iyakansu ya fi na masu sauki, a cikinsa muke kirga: daya, biyu, uku, hudu ... da sauransu har zuwa ∞. Wannan shine cikawar ɗan adam na "ramuka". Mun gaji wannan tsarin tunani daga gare shi Pythagoreans. 

Amma abin da ke da ban sha'awa da mahimmanci ga mai ilimin lissafi shine mutum ba zai iya "cika" waɗannan ramukan tare da lambobi marasa ma'ana da p-adic (ga duk primes p). Ga masu karatun da suka fahimci hakan (kuma an koyar da wannan a kowace makarantar sakandare shekaru talatin da suka gabata), abin lura shine duk jerin abubuwan da suka gamsar da su. Jihar Cauchy, haduwa.

Wurin da wannan gaskiya ne ana kiransa cikakke ("babu abin da ya ɓace"). Zan tuna da lamba 547721051611007740081787109376.

Matsakaicin 0,5, 0,54, 0,547, 0,5477, 0,54772 da sauransu yana haɗuwa zuwa ƙayyadaddun iyaka, wanda shine kusan 0,5477210516110077400 81787109376.

Duk da haka, daga ra'ayi na 10-adic nisa, jerin lambobi 6, 76, 376, 9376, 109376, 7109376 da sauransu kuma suna haɗuwa zuwa lambar "baƙon" ... 547721051 611007740081787109376.

Amma ko da hakan bazai isa dalilin baiwa masana kimiyya kudaden jama'a ba. Gabaɗaya, mu (masu ilimin lissafi) suna kare kanmu ta hanyar cewa ba zai yiwu a faɗi abin da bincikenmu zai yi amfani da shi ba. Yana da kusan tabbas cewa kowa zai yi amfani da shi kuma kawai aiki akan faffadan gaba yana da damar samun nasara.

Ɗaya daga cikin manyan abubuwan ƙirƙira, na'urar X-ray, an ƙirƙira shi ne bayan da aka gano aikin rediyo bisa kuskure Bakkerela. Idan ba don wannan yanayin ba, da yawancin shekaru na bincike da ƙila ba su da amfani. "Muna neman hanyar daukar hoton x-ray na jikin mutum."

A ƙarshe, abu mafi mahimmanci. Kowa ya yarda cewa ikon warware daidaito yana taka rawa. Kuma a nan baƙon lambobinmu suna da kariya sosai. Ka'idar da ta dace (Ina ƙin minkowski) ya ce za a iya warware wasu ma'auni a cikin lambobi masu ma'ana idan kuma kawai idan suna da tushen asali da tushe a cikin kowane jiki.

An gabatar da wannan hanya ko žasa Andrew Wiles ne adam wata, wanda ya warware mafi shahararren lissafin lissafin lissafin shekaru dari uku da suka gabata - Ina ba da shawarar masu karatu su shigar da shi a cikin injin bincike. "Fermat's Last Theorem".