Nkhani za kanthu

Ndili mwana, ndinachita chidwi ndi nkhaniyi, yomwe mwina imadziwika kwa owerenga ambiri, ponena za "supu pa msomali." Agogo anga aakazi (obadwa m'zaka za zana lachisanu ndi chiwiri) adandiuza izi m'mawu akuti "Cossack adabwera kudzapempha madzi, chifukwa ali ndi msomali ndipo adzaphika supu." Mkazi wachidwi adamupatsa mphika wamadzi ... ndipo tikudziwa zomwe zidachitika pambuyo pake: "msuzi uyenera kukhala wamchere, daitye, agogo, mchere", kenako adatsuka nyamayo "kukometsa" ndi zina zotero. Pamapeto pake, adataya msomali "wophika".

Kotero nkhaniyi imayenera kukhala yachabechabe cha danga - ndipo izi ndi za kutsetsereka kwa zida za ku Ulaya pa comet 67P / Churyumov-Gerasimenko pa November 12, 2014. Ine ndidakali katswiri wa masamu. Zili bwanji ndi Mongaс Zero masamu?

Kodi palibe chomwe chilipo bwanji?

Sizinganenedwe kuti Palibe. Lilipo ngati lingaliro la filosofi, masamu, chipembedzo ndi colloquial kwathunthu. Zero ndi nambala wamba, madigiri zero pa thermometer ndi kutentha, ndipo zero bwino mu banki ndi zosasangalatsa koma wamba. Zindikirani kuti palibe chaka chaziro pamawerengedwe anthawi, ndipo izi ndichifukwa chakuti zero adayambitsidwa masamu kumapeto kwa Middle Ages, mochedwa kuposa momwe amonke Dionysius adanenera (zaka za zana la XNUMX).

Zodabwitsa ndizakuti, titha kuchita popanda ziro, chifukwa chake, popanda manambala oyipa. M'mabuku amodzi okhudza malingaliro, ndapeza zolimbitsa thupi: kujambula kapena kunena momwe mukuganizira kusakhalapo kwa nsomba. Zodabwitsa, sichoncho? Aliyense angathe kujambula nsomba, koma osati imodzi?

Tsopano mwachidule Basic masamu maphunziro. Kupereka mwayi wokhalapo pagulu lopanda kanthu lokhala ndi bwalo lodutsa ∅ ndi njira yofunikira yofananira ndi kuwonjezera ziro pagulu la manambala. Seti yopanda kanthu ndi seti yokhayo yomwe ilibe zinthu zilizonse. Zosonkhanitsa zotere:

Koma palibe magulu awiri osiyana opanda kanthu. Seti yopanda kanthu ikuphatikizidwa mu seti ina iliyonse:

Zowonadi, malamulo a masamu amamati seti A ili mu B ngati ndi chiganizo:

zimatengera

Pankhani yopanda kanthu ∅, malingaliro ake amakhala abodza nthawi zonse, motero, molingana ndi malamulo amalingaliro, tanthauzo lake nthawi zambiri limakhala loona. Chilichonse chimachokera ku bodza ("apa ndidzakula cactus ngati mutasamukira ku kalasi yotsatira ..."). Choncho, popeza kuti chopanda kanthu chili m'gulu lililonse la enawo, ndiye kuti akadakhala awiri osiyana, chilichonse chikanakhala mwa china. Komabe, ngati magulu awiri ali pakati pawo, ndi ofanana. Ichi ndichifukwa chake: pali seti imodzi yokha yopanda kanthu!

Lingaliro la kukhalapo kwa seti yopanda kanthu silitsutsana ndi malamulo aliwonse a masamu, ndiye bwanji osagwiritsa ntchito? Mfundo yafilosofi yotchedwaLumo la Occam» Lamulo lochotsa malingaliro osafunikira, koma molondola lingaliro la chopanda kanthu ndi lothandiza kwambiri masamu. Zindikirani kuti chopanda kanthu chili ndi gawo la -1 (kuchotsera limodzi) - zero-dimensional zinthu ndi mfundo ndi kachitidwe kawo kakang'ono, mbali imodzi ndi mizere, ndipo tidakambirana za masamu ovuta kwambiri okhala ndi gawo la fractal mumutu wa fractals. .

Ndizosangalatsa kuti nyumba yonse ya masamu: manambala, manambala, ntchito, ogwira ntchito, ophatikizika, masiyanidwe, ma equation ... atha kutengedwa ku lingaliro limodzi - chopanda kanthu! Ndikokwanira kuganiza kuti pali seti yopanda kanthu, zinthu zomwe zangopangidwa kumene zitha kuphatikizidwa kukhala seti kuti zitheke. pangani masamu onse. Umu ndi momwe katswiri waku Germany Gottlob Frege adapangira manambala achilengedwe. Zero ndi gulu la seti zomwe zinthu zake zimalumikizana molumikizana ndi zinthu zopanda kanthu. Imodzi ndi gulu la seti zomwe zigawo zake zimagwirizana ndi zigawo za seti zomwe chinthu chokhacho chimakhala chopanda kanthu. Awiri ndi gulu la seti zomwe zigawo zake zimakhala chimodzi-ku-chimodzi ndi zinthu za seti zomwe zimakhala zopanda kanthu ndi seti yomwe chinthu chokhacho chimakhala chopanda kanthu ... ndi zina zotero. Poyamba, izi zikuwoneka ngati zovuta kwambiri, koma kwenikweni sizili choncho.

Buluu unafalikira pa ine

ndinamva fungo la heather komanso fungo la timbewu ...

Wojciech Mlynarski, Harvest Girl

Ndizovuta kulingalira

Palibe chovuta kuchilingalira. M'nkhani ya Stanisław Lem "Momwe Dziko Linapulumutsidwira", Trurl wojambula anapanga makina omwe angachite chilichonse kuyambira ndi kalata. Pamene Klapaucius adalamula kuti amangidwe Nic, makinawo anayamba kuchotsa zinthu zosiyanasiyana padziko lapansi - ndi cholinga chachikulu chochotsa chirichonse. Pamene Klapaucius wamantha anaimitsa galimotoyo, ma galleys, yews, kupachikidwa, ma hacks, rhymes, beaters, poufs, grinders, skewers, philidrons ndi frosts zinali zitasowa padziko lapansi kwamuyaya. Ndipo ndithudi, iwo anasowa kosatha ...

Józef Tischner analemba bwino kwambiri zachabe m’buku lake lakuti History of Mountain Philosophy. Patchuthi changa chomaliza, ndinaganiza zokhala opanda kanthu, ndiko kuti, ndinapita kumalo osungiramo madzi pakati pa Nowy Targ ndi Jabłonka ku Podhale. Derali limatchedwanso Pustachi. Mupita, mumapita, koma msewu suchepa - inde, pamlingo wathu wocheperako, waku Poland. Tsiku lina ndinakwera basi m’chigawo cha Canada cha Saskatchewan. Kunja kunali munda wa chimanga. Ndinagona kwa theka la ola. Nditadzuka, tinali kudutsa m'munda wa chimanga womwewo ... Koma dikirani, kodi ichi mulibe? M’lingaliro lina, kusakhalapo kwa kusintha kuli chabe chabe.

Timazolowera kukhalapo kosalekeza kwa zinthu zosiyanasiyana zotizungulira, komanso kuchokera Chinachake sungathe kuthawa ngakhale uli ndi maso otseka. "Ndikuganiza, chifukwa chake ndili," adatero Descartes. Ngati ndaganiza kale, ndiye kuti ndilipo, zomwe zikutanthauza kuti pali china chake padziko lapansi (ndicho, ine). Kodi zomwe ndimaganiza zilipo? Izi zitha kukambidwa, koma mumakanika amakono a quantum, mfundo ya Heisenberg imadziwika: kuyang'ana kulikonse kumasokoneza mkhalidwe wa chinthu chowonedwa. Mpaka ife tiziwona izo Nic kulibe, ndipo tikayamba kuyang'ana, chinthucho chimasiya kukhala Monga ndipo zimakhala Chinachake. Zikukhala zosamveka mfundo ya anthropic: Palibe chifukwa chofunsa kuti dziko likanakhala lotani tikadapanda kukhalapo. Dziko lapansi ndi lomwe likuwoneka kwa ife. Mwina zolengedwa zina zidzawona Dziko Lapansi ngati lozungulira?

Positron (electron yabwino yotere) ndi dzenje mumlengalenga, "palibe electron." M'kati mwa chiwonongeko, electron imalumphira mu dzenje ili ndipo "palibe chomwe chimachitika" - palibe dzenje, palibe electron. Ndidzalumpha nthabwala zambiri za mabowo a tchizi ku Swiss ("ndikakhala ndi zambiri, ndizochepa ..."). Wolemba nyimbo wotchuka John Cage anali atagwiritsa ntchito kale malingaliro ake kotero kuti adalemba (?) nyimbo (?) momwe gulu la oimba limakhala losasunthika kwa mphindi 4 masekondi 33 ndipo, ndithudi, silisewera kalikonse. "Mphindi zinayi ndi masekondi makumi atatu ndi atatu ndi mazana awiri mphambu makumi asanu ndi awiri mphambu zitatu, 273, ndipo minus 273 madigiri ndi zero mtheradi, pomwe mayendedwe onse amasiya," wolemba (?) adalongosola.

Sefa mpaka ziro, palibe, nick, nick, palibe, ziro!

Jerzy mufilimu ya Andrzej Wajda ya Over the Years,

masiku akupita"

Nanga bwanji aliyense?

Anthu ambiri (kuyambira alimi wamba mpaka anthanthi otchuka) adadabwa ndi zochitika za kukhalapo. Mu masamu, zinthu ndi zosavuta: pali chinachake chomwe chimagwirizana.

Anazimiririka m'minda ya m'mphepete mwa nyanja

Mumaluwa a chimanga, udzu ndi mkamwa mwa mikango ...

Chabwino, zinthu ngati izi zimachitika

Makamaka nthawi yokolola, komanso nthawi yokolola

makamaka…

Wojciech Mlynarski, Harvest Girl

Chilichonse chili m'mbali ina ya Palibe. Mu masamu, tikudziwa zimenezo Zonse kulibe. Lingaliro lolakwika kwambiri lakuti kukhalapo kwake kukanakhala kopanda mkangano. Izi zikhoza kumvetsetsedwa ndi chitsanzo cha chododometsa chakale: "Ngati Mulungu ali wamphamvuyonse, ndiye pangani mwala kuti mutenge?" Umboni wamasamu woti sipangakhale magulu amagulu onse umachokera pamalingaliro woimba-Bershtein, yomwe imati "nambala yopanda malire" (masamu: kadinala nambala) gulu la mamembala onse a gulu linalake ndi lalikulu kuposa chiwerengero cha zigawo za seti iyi.

Ngati seti ili ndi zinthu, ndiye kuti ili ndi 2ⁿ kagawo kakang'ono; mwachitsanzo, pamene = 3 ndipo seti imakhala ndi {1, 2, 3} ndiye magawo otsatirawa alipo:

• magawo atatu azinthu ziwiri: iliyonse ikusowa nambala 1, 2, 3,
• seti imodzi yopanda kanthu,
• magawo atatu a chinthu chimodzi,
• gulu lonse {1,2,3}

- eyiti okha, 2³Ndipo owerenga omwe angomaliza kumene sukulu, ndikufuna kukumbukira njira yofananira:

Chizindikiro chilichonse cha Newtonian mu formula iyi chimatsimikizira kuchuluka kwa k-element seti mu -element set.

Mu masamu, ma coefficients a binomial amawoneka m'malo ena ambiri, monga m'njira zosangalatsa zochulutsachulukira:

ndipo kuchokera ku mawonekedwe awo enieni, kudalirana kwawo kumakhala kosangalatsa kwambiri.

Ndizovuta kumvetsetsa zomwe - malinga ndi malingaliro ndi masamu - ndi chiyani, ndi zomwe Chilichonse sichili. Zotsutsana za kusakhalako Monga momwe Winnie wa Pooh adafunsa mwaulemu mlendo wake, Matigari, kodi Matigari amakonda uchi, phala ndi nthula? "Akambuku ngati chirichonse," anayankha amene Kubus ananena kuti ngati amakonda chirichonse, ndiye amakonda kugona pansi, choncho, Vinnie, akhoza kubwerera kukagona.

Mkangano wina Russell chododometsa. Mutauni muli wometa amene amameta amuna onse amene sanamete. Kodi amadzimeta? Mayankho onse awiriwa amatsutsana ndi zomwe zimaperekedwa kuti iwo, ndi okhawo, omwe sachita izi, aphedwe.

Kuyang'ana zosonkhanitsidwa zonse

Pomaliza, ndipereka umboni wochenjera, koma masamu ambiri kuti palibe magulu onse (osasokonezedwa nawo).

Choyamba, tiwonetsa kuti pa seti iliyonse yopanda kanthu X, ndizosatheka kupeza ntchito yapadera yomwe imayika izi ku seti yake ya P(X). Ndiye tiyeni tiyerekeze kuti ntchitoyi ilipo. Tiyeni tifotokoze mwachikhalidwe f. F kuchokera ku x ndi chiyani? Ichi ndi chopereka. Kodi xf ndi ya x? Izi sizikudziwika. Muyenera kutero kapena simukutero. Koma kwa ena x iyenera kukhalabe kuti si ya f wa x. Chabwino, ndiye ganizirani mndandanda wa onse x omwe x sali wa f(x). Fotokozerani (gululi) lolemba A. Limagwirizana ndi chinthu china cha gulu la X. Kodi ndi A? Tiyerekeze kuti muyenera. Koma A ndi gulu lomwe lili ndi maelementi a x omwe sali a f(x) ... Chabwino, mwina si a A? Koma seti A ili ndi zinthu zonse za katunduyu, chonchonso A. Mapeto a umboni.

Chifukwa chake, ngati pangakhale gulu la seti zonse, lingakhale lokhalokha, zomwe sizingatheke malinga ndi malingaliro am'mbuyomu.

Phew, sindikuganiza kuti owerenga ambiri adawona umboniwu. M'malo mwake, ndinabweretsa izo kuti ndisonyeze zomwe akatswiri a masamu ankayenera kuchita kumapeto kwa zaka za zana la khumi ndi zisanu ndi zinayi, pamene anayamba kuphunzira maziko a sayansi yawo. Zinapezeka kuti mavuto ali pomwe palibe amene amawayembekezera. Kuphatikiza apo, pamasamu onse, malingaliro awa okhudza maziko alibe kanthu: ziribe kanthu zomwe zimachitika m'chipinda chapansi pa nyumba - nyumba yonse ya masamu imayima pa thanthwe lolimba.

Pakadali pano, pamwamba ...

Timaonanso makhalidwe ena abwino kuchokera ku nkhani za Stanislav Lem. M’umodzi wa maulendo ake, Iyon Tichi anafikira pulaneti limene okhalamo, pambuyo pa chisinthiko chanthaŵi yaitali, potsirizira pake anafika pamlingo wapamwamba koposa wa chitukuko. Onse ndi amphamvu, amatha kuchita chilichonse, ali ndi chilichonse m'manja mwawo… ndipo sachita kalikonse. Anagona pansi pamchenga ndikuuthira pakati pa zala zawo. "Ngati zonse zili zotheka, sizoyenera," akufotokozera Ijon wodabwa. Izi sizingachitike ku chitukuko chathu cha ku Europe ...