Isihloko mayelana lutho

Ngiseyingane, ngayithanda le ndaba, cishe eyaziwa ngabafundi abaningi, mayelana "nesobho esipikili." Ugogo wami (ngekhulu le-XNUMX lokuzalwa) wangitshela lokhu enguqulweni ethi "U-Cossack weza wacela amanzi, ngoba unesipikili futhi uzopheka isobho kuso." Umninikhaya onelukuluku wamnika ibhodwe lamanzi… futhi siyazi ukuthi kwenzekani ngokulandelayo: “isobho kufanele libe nosawoti, i-daitye, ugogo, usawoti”, wabe esegeza inyama “ukuthuthukisa ukunambitheka” nokunye. Ekugcineni, walahla isipikili "esibilisiwe".

Ngakho-ke lesi sihloko bekufanele sibe mayelana nokungabi nalutho kwendawo - futhi lokhu kumayelana nokufika kwemishini yaseYurophu ku-comet 67P / Churyumov-Gerasimenko ngoNovemba 12, 2014. Kodwa ngenkathi ngibhala, nganqotshwa umkhuba omude, Ngiseyisazi sezibalo. Kunjani nge Thandaс Uziro izibalo?

Kanjani Akukho lutho?

Ngeke kushiwo ukuthi Akukho lutho. Ikhona okungenani njengomqondo wefilosofi, wezibalo, wenkolo futhi ovumelana ngokuphelele. U-Zero inombolo evamile, amadigri angu-zero ku-thermometer nawo izinga lokushisa, futhi ibhalansi enguziro ebhange yinto engathandeki kodwa evamile. Qaphela ukuthi awukho unyaka ongu-ziro ekubalweni kwezikhathi, futhi lokhu kungenxa yokuthi i-zero yangeniswa kwizibalo kuphela ngasekupheleni kweNkathi Ephakathi, kamuva kunokulandelana kwezikhathi okwahlongozwa yindela uDionysius (ikhulu lesi-XNUMX).

Okuxakayo ukuthi, besingakwazi ngempela ukwenza ngaphandle kwalo ziro, ngakho-ke, ngaphandle kwezinombolo ezinegethivu. Kwenye yezincwadi zokufunda ezinengqondo, ngithole umsebenzi wokuzivivinya: dweba noma usho ukuthi ucabangani ngokungabi bikho kwezinhlanzi. Kuyamangalisa, akunjalo? Noma ubani angakwazi ukudweba inhlanzi, kodwa hhayi eyodwa?

Manje kafushane Basic mathematics course. Ukunikeza ilungelo lokuba khona kusethi engenalutho ephawulwe ngombuthano onqanyuliwe ∅ kuyinqubo edingekayo efana nokwengeza uziro kusethi yezinombolo. Isethi engenalutho iyona kuphela isethi engaqukethe noma yiziphi izici. Amaqoqo anjalo:

Kodwa awekho amasethi amabili angenalutho ahlukene. Isethi engenalutho ifakiwe kuwo wonke amanye amasethi:

Impela, imithetho yezibalo ithi isethi A iqukethwe kusethi B uma futhi kuphela uma umusho:

kuhlanganisa

Esimeni sesethi engenalutho ethi ∅, isiphakamiso sihlala singamanga, ngakho-ke, ngokuya ngemithetho yengqondo, incazelo ngokuvamile iyiqiniso. Konke kuvela emangeni ("lapha ngizokhula i-cactus uma uthuthela ekilasini elilandelayo ..."). Ngakho-ke, njengoba isethi engenalutho iqukethwe komunye nomunye, khona-ke uma bekungamabili ahlukene, ngayinye yazo ibizobe iqukethwe kwenye. Nokho, uma amasethi amabili equkethwe phakathi kwelinye, ayalingana. Yingakho: kunesethi eyodwa kuphela engenalutho!

I-postulate yokuba khona kwesethi engenalutho ayiphikisani nanoma yimiphi imithetho yezibalo, ngakho kungani ungayiphilisi? Isimiso sefilosofi esibizwa ngokuthiI-razor ka-Occam» Umyalelo wokukhipha imiqondo engadingekile, kodwa kulungile umqondo wesethi engenalutho uwusizo kakhulu kwizibalo. Sicela uqaphele ukuthi isethi engenalutho inobukhulu obungu -1 (minus one) - izakhi ze-zero-dimensional zingamaphuzu kanye nesistimu yazo encane, izakhi zohlangothi olulodwa ziyimigqa, futhi sikhulume ngezinto zezibalo eziyinkimbinkimbi kakhulu ezinobukhulu obuncane esahlukweni. kuma-fractals.

Kuyathakazelisa ukuthi sonke isakhiwo sezibalo: izinombolo, izinombolo, imisebenzi, ama-opharetha, ama-integrated, umehluko, izibalo ... zingatholakala kumqondo owodwa - isethi engenalutho! Kwanele ukucabanga ukuthi kukhona isethi engenalutho, izakhi ezisanda kwakhiwa zingahlanganiswa zibe amasethi ukuze zikwazi yakha zonke izibalo. Yile ndlela uchwepheshe waseJalimane u-Gottlob Frege azakha ngayo izinombolo zemvelo. Uziro isigaba samasethi ama-elementi awo ahambisanayo nezinto zesethi engenalutho. Eyodwa yisigaba samasethi ama-elementi awo ahambisanayo nezinto zesethi okuwukuphela kwayo okuyisethi engenalutho. Okubili yisigaba samasethi ama-elementi awo ahambisana nokukodwa anezici zesethi ehlanganisa isethi engenalutho kanye nesethi okuwukuphela kwayo okuyisethi engenalutho... njalo njalo. Uma uthi nhlá, lokhu kubonakala kuyinto eyinkimbinkimbi kakhulu, kodwa empeleni akunjalo.

Kusabalale okuluhlaza phezu kwami

kunuka iheather kunuke iminti...

Wojciech Mlynarski, Harvest Girl

Kunzima ukucabanga

Akukho okunzima ukukucabanga. Endabeni ka-Stanisław Lem ethi "Indlela Umhlaba Wasindiswa Ngayo", umklami u-Trurl wakha umshini owawuzokwenza yonke into eqala ngohlamvu. Lapho uKlapaucius eyala ukuba yakhiwe Nic, umshini waqala ukususa izinto ezihlukahlukene emhlabeni - ngomgomo omkhulu wokukhipha yonke into. Ngesikhathi u-Klapaucius owayethukile emisa imoto, amagalaji, ama-yews, alenga, ama-hacks, ama-rhyme, ama-beaters, ama-pouf, ama-grinders, ama-skewers, ama-philidrons kanye nesithwathwa kwase kunyamalele emhlabeni unomphela. Futhi ngempela, banyamalala unomphela ...

U-Józef Tischner wabhala kahle kakhulu ngokungabi nalutho encwadini yakhe ethi History of Mountain Philosophy. Phakathi neholide lami lokugcina, nginqume ukuzwa lokhu ukungabi nalutho, okungukuthi, ngaya ezindaweni eziphakeme phakathi kwe-Nowy Targ ne-Jabłonka e-Podhale. Le ndawo ibizwa nangokuthi iPustachia. Uyahamba, uyahamba, kodwa umgwaqo awunciphi - yiqiniso, esikalini sethu esithobekile, sasePoland. Ngolunye usuku ngagibela ibhasi esifundazweni saseCanada iSaskatchewan. Ngaphandle kwakukhona insimu yombila. Ngalala isigamu sehora. Lapho ngiphaphama, sasihamba ngemoto endaweni efanayo yombila ... Kodwa linda, ingabe lokhu akunalutho? Ngomqondo othile, ukungabi bikho koshintsho kuwuze nje.

Sijwayele ukuba khona njalo kwezinto ezihlukahlukene ezisizungezile, futhi kusukela Okuthile awukwazi ukubaleka ngisho uvale amehlo. "Ngicabanga, ngakho-ke nginguye," kusho uDescartes. Uma sengike ngacabanga okuthile, khona-ke ngikhona, okusho ukuthi kukhona okungenani okuthile emhlabeni (okungukuthi, mina). Ngabe lokho ebengikucabanga kukhona? Lokhu kungaxoxwa ngakho, kodwa ku-quantum mechanics yesimanje, isimiso se-Heisenberg siyaziwa: ukubuka ngakunye kuphazamisa isimo sento ebhekiwe. Kuze sikubone Nic alikho, futhi lapho siqala ukubuka, into iyayeka ukuba khona Thanda futhi kuba Okuthile. Sekuyabheda isimiso se-anthropic: Asikho isidingo sokubuza ukuthi ngabe umhlaba unjani ukube besingekho. Umhlaba yilokho okubonakala kithi. Mhlawumbe ezinye izidalwa zizobona uMhlaba njenge-angular?

I-positron (i-electron enjalo enhle) iyimbobo emkhathini, "ayikho i-electron." Ngenqubo yokuqothula, i-electron igxumela kulo mgodi futhi "akukho okwenzekayo" - ayikho imbobo, ayikho i-electron. Ngizokweqa amahlaya amaningi mayelana nezimbobo kushizi waseSwitzerland (“lapho nginokuningi, kuncane lapho ...”). Umqambi odumile uJohn Cage wayesesebenzise imibono yakhe kangangokuthi waqamba (?) ucezu lomculo (?) lapho i-orchestra ihlezi inganyakazi imizuzu emi-4 imizuzwana engu-33 futhi, yiqiniso, ayidlali lutho. "Imizuzu emine nemizuzwana engamashumi amathathu nantathu ingamakhulu amabili namashumi ayisikhombisa nantathu, 273, futhi ukukhishwa kwe-273 degrees kunguziro ophelele, lapho konke ukunyakaza kuma khona," kuchaza umqambi (?)

Hlunga ku-zero, lutho, nick, nick, lutho, zero!

UJerzy efilimini ka-Andrzej Wajda ethi Over the Years,

ziyahamba izinsuku"

Kuthiwani ngabo bonke?

Abantu abaningi (kusukela kubalimi abalula kuya kuzazi zefilosofi ezivelele) bazibuza mayelana nokwenzeka kokuba khona. Ezibalweni, isimo silula: kukhona into engaguquki.

Wanyamalala emasimini aseceleni

Kuzimbali zommbila, ukhula nasemilonyeni yamabhubesi ...

Izinto ezinjengalezi ziyenzeka

Ikakhulukazi ngesikhathi sokuvuna, nangesikhathi sokuvuna

ikakhulukazi...

Wojciech Mlynarski, Harvest Girl

Yonke into ikwelinye i-excess of Nothing. Ezibalweni, siyakwazi lokho Konke akukho. Umbono nje onganembile kakhulu wokuthi ubukhona bakhe ngeke bube nempikiswano. Lokhu kungaqondwa ngesibonelo sendida endala: "Uma uNkulunkulu enamandla onke, dala itshe ozolicosha?" Ubufakazi bezibalo bokuthi angeke kube namasethi awo wonke amasethi busekelwe ku-theoremu umculi-Bershtein, ethi "inombolo engapheli" (izibalo: inombolo eyikhadinali) isethi yawo wonke amalungu esethi enikeziwe inkulu kunenombolo yezakhi zale sethi.

Uma isethi inama-elementi, kusho ukuthi ino-2ⁿ amasethi angaphansi; isibonelo, uma = 3 futhi isethi iqukethe {1, 2, 3} bese kuba khona amasethi angaphansi alandelayo:

• amasethi amathathu ezinto ezimbili: ngayinye yazo ishoda ngeyodwa yezinombolo 1, 2, 3,
• isethi eyodwa engenalutho,
• amasethi amathathu ento eyodwa,
• isethi yonke {1,2,3}

- eziyisishiyagalombili kuphela, 2³Futhi abafundi abasanda kuphothula esikoleni, ngithanda ukukhumbula ifomula ehambisanayo:

Uphawu ngalunye lwe-Newtonian kule fomula inquma inani lamasethi e-k-elementi kusethi ye-elementi.

Kuzibalo, ama-binomial coefficient avela kwezinye izindawo eziningi, njengakumafomula athakazelisayo okuphindaphinda okuncishisiwe:

futhi kusukela esimweni sazo esiqondile, ukuncika kwabo kuyathakazelisa kakhulu.

Kunzima ukuqonda ukuthi yini - ngokuphathelene nengqondo kanye nezibalo - iyini, futhi yini Yonke into engekho. Izingxabano zokungabi khona Kufana nje naleyo kaWinnie the Pooh, owabuza ngesizotha isivakashi sakhe, uTiger, ingabe amaTiger ayaluthanda uju, ama-acorn kanye namakhakhasi? "Ama-Tigers athanda yonke into," kuphendula lowo uKubus aphetha ngokuthi uma ethanda konke, khona-ke athanda nokulala phansi, ngakho-ke, yena, uVinnie, angabuyela embhedeni.

Enye ingxabano Indida kaRussell. Kukhona umgundi edolobheni ogunda wonke amadoda angazigundi. Ingabe uyazishefa? Zombili izimpendulo ziyaphikisana nombandela obekwe phambili wokuthi babulale labo, futhi labo kuphela, abangakwenzi ngokwabo.

Ifuna iqoqo lawo wonke amaqoqo

Sengiphetha, ngizonikeza ubufakazi obuhlakaniphile, kodwa bezibalo bokuthi ayikho isethi yawo wonke amasethi (akufanele kudidaniswe nawo).

Okokuqala, sizobonisa ukuthi kunoma iyiphi isethi engenalutho engu-X, akunakwenzeka ukuthola umsebenzi ohluke ngokuphelele owenza imephu le sethi ibe yisethi yamasethi ayo angaphansi P(X). Ngakho ake sicabange ukuthi lo msebenzi ukhona. Masiyikhombise ngendabuko f. Yini u-f esuka ku-x? Leli yiqoqo. Ingabe i-xf eka-x? Lokhu akwaziwa. Kuphakathi kokuthi kufanele noma cha. Kodwa kwabanye u-x kusafanele abe ngendlela yokuthi akayena eka-f ka-x. Hhayi-ke, bese ucabangela isethi yakho konke okuthi x okuthi x okungeyona eka f(x). Isho (le sethi) ngo-A. Ihambisana nesici esithile esingu-a sesethi X. Ingabe u-a ungeka-A? Ake sicabange ukuthi kufanele. Kodwa u-A uyisethi equkethe kuphela lezo zakhi zika-x ezingezona ezika-f(x) ... Hhayi-ke, mhlawumbe akuyona eka-A? Kodwa isethi A iqukethe zonke izakhi zalesi sakhiwo, futhi yingakho futhi A. Ukuphela kobufakazi.

Ngakho-ke, ukube bekukhona isethi yawo wonke amasethi, bekuyoba ngokwalo isethi engaphansi, okuyinto engenakwenzeka ngokuvumelana nokucabanga kwangaphambilini.

Phew, angicabangi ukuthi abafundi abaningi babubonile lobu bufakazi. Kunalokho, ngayikhuphula ukuze ngibonise lokho izazi zezibalo okufanele zikwenze ekupheleni kwekhulu leshumi nesishiyagalolunye, lapho ziqala ukufunda izisekelo zesayensi yazo. Kuvele ukuthi izinkinga zilele lapho obengazilindele muntu. Ngaphezu kwalokho, kuzo zonke izibalo, lezi zizathu mayelana nezisekelo azinandaba: kungakhathaliseki ukuthi kwenzekani emiphongolweni - sonke isakhiwo sezibalo simi phezu kwedwala eliqinile.

Khonamanjalo, phezulu...

Siphawula okunye ukuziphatha okuhle ezindabeni zikaStanislav Lem. Kolunye uhambo lwakhe, u-Iyon Tichi wafinyelela iplanethi izakhamuzi zayo, ngemva kokuziphendukela kwemvelo isikhathi eside, ekugcineni zafinyelela esigabeni esiphakeme kakhulu sokuthuthuka. Bonke banamandla, bangenza noma yini, banakho konke ezandleni zabo… futhi abenzi lutho. Balala phansi esihlabathini basithele phakathi kweminwe yabo. "Uma konke kungenzeka, akufanelekile," bachazela i-Ijon eshaqisayo. Kwangathi lokhu kungenzeki empucukweni yethu yaseYurophu...