Ngiyithole kanjani le ncwadi?
NgoMeyi 2017, ngathola i-imeyili evela kuthisha wami omdala wesikole samabanga aphezulu okuthiwa uGeorge Rutter lapho abhala khona: “Nginekhophi yencwadi enhle ka-Dirac ngesiJalimane ( Die Prinzipien der Quantenmechanik ), okwakungeka-Alan Turing, nangemva kokufunda incwadi yakho. , kwakubonakala kimina ukuthi nguwe kanye umuntu oyidingayo" Wangichazela ukuthi le ncwadi wayithola komunye uthisha wami wesikole (owayengasekho ngaleso sikhathi). , engangimazi ukuthi wayengumngane ka-Alan Turing. UGeorge waphetha incwadi yakhe ngala mazwi: "Uma ufuna le ncwadi, ngingakunika yona ngokuzayo uma ufika eNgilandi".
Ngemva kweminyaka embalwa, ngoMashi 2019, ngafika ngempela eNgilandi, ngemva kwalokho ngahlela ukuhlangana noGeorge ukuze sidle isidlo sasekuseni ehhotela elincane e-Oxford. Sadla, saxoxa salinda ukuthi kungene ukudla. Kwabe sekuyisikhathi esihle sokuxoxa ngencwadi. UGeorge wafaka isikhwama sakhe esikhwameni futhi wakhipha ivolumu yezemfundo eklanywe ngesizotha kusukela maphakathi nawo-1900.
Ngavula isembozo, ngizibuza ukuthi kungenzeka yini ukuthi kukhona okuthile ngemuva okufundeka kanje: “Izindlu zika-Alan Turing noma into enjalo. Kodwa, ngeshwa, lokhu akuzange kube njalo. Kodwa-ke, ibihambisana nenothi elinamakhasi amane elivela kuNorman Routledge liya kuGeorge Rutter, elabhalwa ngo-2002.
Ngamazi uNorman Rutledge ngisengumfundi в ekuqaleni kwawo-1970. Wayenguthisha wezibalo obizwa ngokuthi "Nutty Norman." Wayenguthisha okahle ngayo yonke indlela futhi exoxa izindaba ezingapheli ngezibalo kanye nazo zonke izinhlobo zezinto ezithokozisayo. Ubenomthwalo wemfanelo wokuqinisekisa ukuthi isikole sithola ikhompuyutha (ehlelwe kusetshenziswa itheyiphu epunchwe edeskini) - kwaba .
Ngaleso sikhathi, ngangingazi lutho ngesizinda sikaNorman (khumbula, lokhu kwakusasele isikhathi eside ngaphambi kwe-Internet). Engangikwazi nje ukuthi wayengu "Dkt. Rutledge." Utshele izindaba ngabantu baseCambridge kaningi, kodwa akazange akhulume ngo-Alan Turing ezindabeni zakhe. Vele, uTuring wayengakadumi kakhulu (yize, njengoba kuvela, ngase ngizwile ngaye kumuntu owayemazi (indlu enkulu lapho isikhungo sokubethela sasikhona phakathi neMpi Yezwe II)).
U-Alan Turing akazange adume kwaze kwaba ngo-1981, lapho ngiqala khona , nakuba ngaleso sikhathi kusesemongweni we-automata yeselula, futhi cha .
Lapho kungazelelwe ngolunye usuku, ngenkathi ngibheka ikhathalogi yamakhadi emtatsheni wezincwadi , ngazithela phezu kwencwadi , eyabhalwa unina uSara Turing. Le ncwadi yayiqukethe ulwazi oluningi, kuhlanganise nezincwadi zesayensi zikaTuring ezingakashicilelwa zesayensi yezinto eziphilayo. Kodwa-ke, angizange ngifunde lutho ngobuhlobo bakhe noNorman Routledge, njengoba kungekho lutho olushiwo ngaye encwadini (nakuba, njengoba ngitholile, uSara Turing , futhi uNorman waze wagcina ebhale ).
Eminyakeni eyishumi kamuva, nganginelukuluku lokwazi ngoTuring neyakhe (ngaleso sikhathi eyayingashicilelwe) , ngavakashela в . Ngokushesha, ngemva kokujwayelana nalokho ababenakho ngomsebenzi kaTuring, futhi sengichithe isikhathi esithile kuwo, ngacabanga ukuthi ngingase ngicele ukubona nezincwadi zakhe. Ngithe ngisabheka ngathola ukusuka ku-Alan Turing kuya eNorman Routledge.
Ngaleso sikhathi yashicilelwa U-Andrew Hodges, owenza okuningi kakhulu ukuze aqinisekise ukuthi uTuring wagcina esedumile, waqinisekisa ukuthi u-Alan Turing noNorman Routledge babengabangane ngempela, nokuthi uTuring wayengumeluleki wesayensi kaNorman. Ngangifuna ukubuza i-Routledge mayelana ne-Turing, kodwa ngaleso sikhathi u-Norman wayesevele ethathe umhlalaphansi futhi ephila impilo yokucasha. Kodwa-ke, lapho ngiqeda umsebenzi wencwadi "” ngo-2002 (ngemuva kokuhlala ngizihlalele iminyaka eyishumi), ngamthola ngase ngimthumelela ikhophi yale ncwadi namagama-ncazo athi “Kuthisha wami wokugcina wezibalo.” Bese mina naye kancane , futhi ngo-2005 ngabuyela eNgilandi futhi ngahlela ukuhlangana noNorman ukuze ngithole itiye ehhotela eliwubukhazikhazi enkabeni yeLondon.
Sibe nengxoxo emnandi ngezinto eziningi, okuhlanganisa no-Alan Turing. UNorman waqala ingxoxo yethu ngokusitshela ukuthi wayemazi ngempela uTuring, ikakhulukazi ngokukha phezulu, eminyakeni engu-50 edlule. Kodwa noma kunjalo wayenokuthile ayefuna ukukutshela ngaye ngokwakhe: “Wayengenabudlelwane". "Wagigitheka kakhulu". "Wayengakwazi ngempela ukukhuluma nabangezona izibalo". "Wayehlale esaba ukucasula unina". "Waphuma emini futhi wagijima i-marathon". "Wayengazimisele kakhulu" Ingxoxo yabe isiphendukela ebuntwini bukaNorman. Uthe yize esethathe umhlalaphansi iminyaka engu-16 kodwa usabhala izihloko ezithi ""ukuze, ngamazwi akhe,"qedela yonke imisebenzi yakho yesayensi ngaphambi kokudlulela emhlabeni olandelayo", lapho, njengoba engeza ngokumamatheka kancane,"wonke amaqiniso ezibalo azokwembulwa nakanjani" Lapho umcimbi wetiye usuphelile, uNorman wagqoka ijakhethi yakhe yesikhumba waqonda ku-moped yakhe, enganakile nhlobo ukuthi ngalolosuku.
Ngaleso sikhathi ngangigcina ukubona uNorman; washona ngo-2013.
Eminyakeni eyisithupha kamuva ngangihlezi ekudleni kwasekuseni noGeorge Rutter. Ngangiphethe inothi elivela ku-Rutledge, elibhalwe ngo-2002 ngombhalo wakhe wesandla ohlukile:
Ngiqale ngaphenya inothi. Wayeveza njengokujwayelekile:
Ngathola incwadi ka-Alan Turing kumngane wakhe nomabi wefa (eKing's College kwakuwumyalelo wosuku wokunikeza izincwadi ezivela eqoqweni labafileyo, futhi ngakhetha iqoqo lezinkondlo kusukela ezincwadini njengesipho esifanele (wayengumfundisi futhi weqa ethempelini [ngo-1956])…
Kamuva ngenothi elifushane uyabhala:
Ubuza ukuthi le ncwadi kufanele igcine kuphi - ngokubona kwami kufanele iye kumuntu owazisa konke okuhlobene nomsebenzi kaTuring, ngakho-ke isiphetho sayo sincike kuwe.
UStephen Wolfram ungithumelele incwadi yakhe ehlaba umxhwele, kodwa angizange ngijule ngokwanele kuyo...
Uphethe ngokuhalalisela uGeorge Rutter ngokuba nesibindi sokuthuthela (isikhashana, njengoba kwenzeka) e-Australia ngemuva kokuthatha umhlalaphansi, wathi yena ngokwakhe "uzodlala ngokuthuthela eSri Lanka njengesibonelo sokuphila okushibhile nokufana ne-lotus", kodwa wengeza ngokuthi "izehlakalo ezenzeka khona manje zikhomba ukuthi bekungafanele akwenze lokhu"(ngokusobala okushoyo eSri Lanka).
Pho yini efihlwe ekujuleni kwencwadi?
Ngenzenjani-ke ngekhophi yencwadi yesiJalimane eyabhalwa uPaul Dirac eyake yaba eka-Alan Turing? Angisifundi isiJalimane, kodwa ngifundile ngesiNgisi (okuwulimi lwayo lwangempela) kusukela ngeminyaka yawo-1970s. Nokho, ngolunye usuku ngesikhathi sokudla kwasekuseni kwabonakala kulungile ukuba ngihlole ngokucophelela incwadi ikhasi nekhasi. Phela, lokhu kuwumkhuba ovamile lapho usebenza nezincwadi zakudala.
Kufanele kuqashelwe ukuthi ngahlatshwa umxhwele ubuhle besethulo sikaDirac. Le ncwadi yanyatheliswa ngo-1931, kodwa ukuhleleka kwayo okumsulwa (futhi, yebo, naphezu kwesithiyo solimi, ngangikwazi ukufunda izibalo encwadini) kucishe kufane nokuthi kulotshiwe namuhla. (Angifuni ukugcizelela kakhulu i-Dirac lapha, kodwa umngane wami wangitshela ukuthi, okungenani ngokombono wakhe, ukuvezwa kukaDirac kuyi-monosyllabic. UNorman Rutledge wangitshela ukuthi wayengumngane eCambridge , owaba isazi sezibalo. UNorman wayevakashela umuzi kaDirac kaningi futhi wathi “indoda enkulu” ngezinye izikhathi yayizithela ngasemuva, kuyilapho eyokuqala yayihlale igcwele izindida zezibalo. Mina ngokwami, ngeshwa, angikaze ngihlangane noPaul Dirac, nakuba ngatshelwa ukuthi ngemva kokushiya kwakhe eCambridge eFlorida, walahlekelwa ukuqina kwakhe kwangaphambili futhi waba umuntu onobungane.
Kodwa ake sibuyele encwadini kaDirac, okwakungekaTuring. Ekhasini 9, ngiphawule ukudwebela namanothi amancane emaceleni, ebhalwe ngepensela. Ngaqhubeka ngiphenya amakhasi. Ngemva kwezahluko ezimbalwa, amanothi anyamalala. Kodwa-ke, kungazelelwe, ngathola inothi elinamathiselwe ekhasini 127 elithi:
Yayibhalwe ngesiJalimane ngendlela yokubhala ngesandla yesiJalimane. Futhi kubonakala sengathi kukhona akwenzayo . Ngacabanga ukuthi mhlawumbe othile wayenale ncwadi ngaphambi kwe-Turing, futhi lokhu kumelwe kube inothi elibhalwe yilowo muntu.
Ngaqhubeka ngiphefa incwadi. Ayengekho amanothi. Futhi ngacabanga ukuthi angitholi lutho olunye. Kodwa-ke, ekhasini 231, ngathola ibhukhimakhi enophawu - enombhalo ophrintiwe:
Ngabe ngizogcina ngitholile okunye? Ngaqhubeka ngiphefa incwadi. Khona-ke, ekupheleni kwencwadi, ekhasini 259, esigabeni se-relativistic electron theory, ngathola lokhu okulandelayo:
Ngembula leli phepha:
Ngaqaphela ngokushesha ukuthi kwakuyini ihlanganiswe ne , kodwa leli qabunga laphelela kanjani lapha? Masikhumbule ukuthi le ncwadi iyincwadi ekhuluma nge-quantum mechanics, kodwa ipheshana elifakiwe likhuluma ngezibalo ezinengqondo, noma lokho manje okubizwa ngokuthi inkolelo yokubala. Lokhu kujwayelekile emibhalweni kaTuring. Ngazibuza ukuthi ngabe uTuring ulibhale yena mathupha leli nothi?
Ngisho nangesikhathi sasekuseni, ngicinge ku-inthanethi ukuze ngithole izibonelo zombhalo wesandla ka-Turing, kodwa angitholanga zibonelo ngendlela yokubala, ngakho angikwazanga ukufinyelela esiphethweni mayelana nokuthi ungubani ngempela umbhalo wesandla. Futhi ngokushesha kwadingeka sihambe. Ngayipakisha kahle le ncwadi, ngilungele ukuveza imfihlakalo yokuthi yayiyiliphi ikhasi nokuthi yayibhalwe ubani, ngahamba nayo.
Mayelana nencwadi
Okokuqala, ake sixoxe ngencwadi ngokwayo. "» Imikhakha kaDirac yashicilelwa ngesiNgisi ngo-1930 futhi yahunyushelwa ngokushesha esiJalimane. (Isandulelo sikaDirac sangomhla zingama-29 kuNhlaba 1930; ngesomhumushi - - Agasti 15, 1930.) Le ncwadi yaba ingqopha-mlando ekuthuthukisweni kwe-quantum mechanics, isungula ngokuhlelekile ukuhleleka okucacile kokwenza izibalo, futhi, phakathi kwezinye izinto, ichaza ukubikezela kukaDirac , ezovulwa ngo-1932.
Kungani u-Alan Turing enencwadi yesiJalimane hhayi isiNgisi? Angikwazi lokhu ngokuqinisekile, kodwa ngalezo zinsuku isiJalimane sasiwulimi oluhamba phambili lwesayensi, futhi siyazi ukuthi u-Alan Turing wayekwazi ukusifunda. (Phela, egameni lodumo lwakhe работы « (Entscheidungsproblem)" kwakuyigama lesiJalimane elide kakhulu - futhi engxenyeni eyinhloko ye-athikili usebenza ngezimpawu zesiGothic ezingacacile ngendlela "yezinhlamvu zesiJalimane" azisebenzise esikhundleni, isibonelo, izimpawu zesiGreki).
Ingabe u-Alan Turing uzithengele yena le ncwadi noma wayinikwa? Angazi. Kukhava yangaphakathi yencwadi ka-Turing kunombhalo wepensela othi "20/-", okwakuwuphawu oluvamile "losheleni abangama-20", olufana no-£1. Ekhasini elingakwesokudla kunegama elithi "26.9.30" elisuliwe, okungenzeka ukuthi lisho uSepthemba 26, 1930, okungenzeka usuku incwadi eyathengwa ngalo okokuqala. Bese, ngakwesokudla, inombolo esuliwe “20.” Mhlawumbe yintengo futhi. (Kungaba yintengo lena , ucabanga ukuthi le ncwadi yathengiswa eJalimane? Ngalezo zinsuku, i-1 Reichsmark yayibiza cishe i-schilling engu-1, intengo yesiJalimane cishe yayizobhalwa ngokuthi "RM20" isibonelo.) Ekugcineni, ngaphakathi kwekhava yangemuva kukhona "c 5/-" - mhlawumbe lokhu, (ngesikhulu esikhulu. discount) intengo yencwadi esetshenzisiwe.
Ake sibheke izinsuku ezibalulekile empilweni ka-Alan Turing. Alan Turing (ngokweqile, eminyakeni engama-76 ngaphambili ). Ekwindla ka-1931 wangena eKing's College, eCambridge. Uthole iziqu zakhe ze-bachelor ngemuva kweminyaka emithathu yokufunda ngo-1934.
Ngawo-1920 nasekuqaleni kwawo-1930, i-quantum mechanics kwakuyisihloko esishisayo, futhi u-Alan Turing wayenesithakazelo kuso. Kusukela ezinqolobaneni zakhe siyazi ukuthi ngo-1932, ngokushesha nje lapho incwadi ishicilelwe, wathola "» UJohn von Neumann (ku ). Siyazi futhi ukuthi ngo-1935 uTuring wathola isabelo kudokotela wesayensi yemvelo waseCambridge esihlokweni sokufunda i-quantum mechanics. (U-Fowler uphakamise ukubala , empeleni okuyinkinga eyinkimbinkimbi kakhulu edinga ukuhlaziywa okugcwele nge-quantum field theory esebenzisanayo, engakaxazululwa ngokuphelele).
Nokho, uTuring wayithola nini futhi kanjani ikhophi yakhe yencwadi kaDirac? Uma kubhekwa ukuthi le ncwadi inenani elimakiwe, kungenzeka ukuthi u-Turing ulithenge ngamasekeni. Ubani umnikazi wokuqala wencwadi? Amanothi encwadini abonakala ekhuluma ngokuyinhloko ngesakhiwo esinengqondo, ephawula ukuthi ubudlelwano obuthile obunengqondo kufanele buthathwe njenge-axiom. Khona-ke kuthiwani ngenothi elifakwe ekhasini 127?
Hhayi-ke, mhlawumbe kumane kwaqondana, kodwa khona kanye ekhasini 127 - UDirac ukhuluma nge-quantum futhi ubeka isisekelo - okuyisisekelo sayo yonke i-quantum formalism yesimanje. Iquketheni inothi? Iqukethe isandiso se-Equation 14, okuyisibalo sokuguquguquka kwesikhathi kwe-quantum amplitude. Umbhali wenothi umiselele i-Dirac A ngobude wafaka u-ρ, mhlawumbe ngaleyo ndlela ebonisa amazwibela aseJalimane angaphambilini (isifaniso sokuminyana koketshezi). Umbhali ube esezama ukwandisa isenzo ngamandla ka-ℏ (, ihlukaniswe ngo-2π, ngezinye izikhathi ebizwa ngokuthi ).
Kodwa akubonakali kunolwazi oluningi oluwusizo olungatholwa kulokho okusekhasini. Uma uphakamisela ikhasi ekukhanyeni, liqukethe isimanga esincane - i-watermark ethi “Z f. Physik. I-Chem. B":
Lena inguqulo efushanisiwe - ijenali yesiJalimane ephathelene namakhemikhali omzimba, eyaqala ukunyatheliswa ngo-1928. Mhlawumbe inothi labhalwa umhleli kamagazini? Nasi isihloko semagazini sango-1933. Kalula, abahleli bahlelwa ngendawo, futhi oyedwa uyagqama: "Bourne · Cambridge".
Yilokho okuyikhona ngubani umbhali nokunye okuningi kuthiyori ye-quantum mechanics (kanye nomkhulu womculi ). Ngakho-ke, leli nothi kungenzeka ukuthi libhalwe nguMax Born? Kodwa, ngeshwa, akunjalo, ngoba umbhalo wesandla awuhambisani.
Kuthiwani ngebhukhimakhi esekhasini 231? Nansi izinhlangothi zombili:
Ibhukhimakhi ayijwayelekile futhi yinhle impela. Kodwa yenziwa nini? ECambridge kukhona , nakuba manje isiyingxenye yeBlackwell. Iminyaka engaphezu kuka-70 (kuze kube ngu-1970), u-Heffers wayetholakala ekhelini, njengoba ibhukhimakhi ibonisa, и .
Le thebhu iqukethe ukhiye obalulekile - lena inombolo yocingo “Tel. 862". Njengoba kwenzeka, ngo-1939 iningi laseCambridge (kuhlanganise noHeffers) lashintshela ezinombolweni ezinezinombolo ezine, futhi ngokuqinisekile ngo-1940 amabhukumaka ayenyatheliswa ngezinombolo zocingo "zesimanje". (Izinombolo zocingo zesiNgisi kancane kancane zaba zinde; lapho ngisakhula eNgilandi ngawo-1960, izinombolo zethu zocingo zazithi "Oxford 56186" kanye nethi "Kidmore End 2378". Ingxenye yesizathu esenza ngikhumbule lezi zinombolo ingoba, njengoba kuyinqaba manje. bekungabonakali ukuthi ngihlale ngifona inombolo yami uma ngiphendula ucingo olungenayo).
Ibhukhimakhi yanyatheliswa ngaleli fomu kwaze kwaba ngu-1939. Kodwa isikhathi esingakanani ngaphambi kwalokho? Kukhona izikena ezimbalwa zezikhangiso ze-Heffers ezindala ku-inthanethi, ezisukela emuva okungenani ngo-1912 (kanye nokuthi "Sicela ukuthi uhlangabezane nezicelo zakho...") baqedela "Ifoni 862" ngokungeza "(imigqa emi-2)." Kukhona futhi amabhukhimakhi anemiklamo efanayo angatholakala ezincwadini kusukela ngo-1904 (yize kungacaci ukuthi ezangempela yini kulezi zincwadi (okungukuthi zanyatheliswa ngesikhathi esifanayo). Ngezinjongo zophenyo lwethu, kubonakala sengathi singaphetha ngokuthi Le ncwadi yavela ku-Heffer's (okuyinto, ngendlela, eyayiyisitolo sezincwadi esikhulu eCambridge) phakathi kuka-1930 no-1939.
Ikhasi le-Lambda calculus
Ngakho manje siyazi okuthile mayelana nokuthi incwadi yathengwa nini. Kodwa kuthiwani “ngekhasi le-lambda calculus”? Kwabhalwa nini lokhu? Yebo, ngokwemvelo, ngaleso sikhathi i-lambda calculus kufanele ngabe isivele yasungulwa. Kwase kwenziwa , isazi sezibalo esivela , esimweni sawo sokuqala ngo-1932 futhi esimweni sawo sokugcina ngo-1935. (Kukhona imisebenzi yososayensi bangaphambilini, kodwa abazange basebenzise notation λ).
Kunokuxhumana okuyinkimbinkimbi phakathi kuka-Alan Turing kanye ne-lambda calculus. Ngo-1935, uTuring waba nesithakazelo "emishinini" yokusebenza kwezibalo, futhi wasungula umqondo womshini weTuring, ukuwusebenzisa ukuxazulula izinkinga zezibalo eziyisisekelo. U-Turing uthumele i-athikili ngalesi sihloko kumagazini wesiFulentshi (), kodwa lalahleka eposini; kwabe sekuvela ukuthi owayeyithunyelelwe wayengekho vele, wayethuthele eChina.
Kodwa ngoMeyi 1936, ngaphambi kokuba uTuring athumele iphepha lakhe kwenye indawo, . UTuring wayekade ekhononda ngokuthi lapho enza ubufakazi ngo-1934 , ngabe sengithola ukuthi kukhona isazi sezibalo saseNorway esasisenaso kakade ngonyaka we-1922.
Akunzima ukubona ukuthi imishini ye-Turing kanye ne-lambda calculus ilingana ngempumelelo ezinhlotsheni zezibalo abangazimelela (futhi lokho kuyisiqalo ). Nokho, uTuring (nothisha wakhe ) babeqiniseka ukuthi indlela kaTuring yayihluke ngokwanele ukuze ifaneleke ukushicilelwa kwayo. NgoNovemba 1936 (futhi ngama-typos alungiswa ngenyanga elandelayo) ngo Iphepha elidumile likaTuring lashicilelwa .
Ukugcwalisa umugqa wesikhathi kancane: kusukela ngoSepthemba 1936 kuya kuJulayi 1938 (nekhefu lezinyanga ezintathu ehlobo lika-1937), uTuring wayesePrinceton, eye lapho ngenhloso yokuba ngumfundi oneziqu ze-Alonzo Church. Phakathi nalesi sikhathi ePrinceton, uTuring ngokusobala wayegxile ngokuphelele ku-logic yezibalo, ebhala ezimbalwa , - futhi, cishe, wayengenayo incwadi ye-quantum mechanics naye.
UTuring wabuyela eCambridge ngoJulayi 1938, kodwa ngoSepthemba walowo nyaka wayesebenza itoho e- , futhi ngemva konyaka wathuthela eBletchley Park ngenhloso yokusebenza lapho isikhathi esigcwele ezindabeni ezihlobene ne-cryptanalysis. Ngemva kokuphela kwempi ngo-1945, uTuring wathuthela eLondon ukuze ayosebenzela khona ekuthuthukisweni kwephrojekthi ezokwakhiwa . Uchithe unyaka wezifundo we-1947-8 eCambridge kodwa wabe esethuthela eManchester ukuze athuthuke .
Ngo-1951, uTuring waqala ukufunda ngokuzimisela . (Kimina ngokwami, leli qiniso liyayindida ngandlela thize, ngoba kimina kubonakala sengathi i-Turing ihlale ikholelwa ngokunganaki ukuthi amasistimu ebhayoloji kufanele amodelwe ngama-equations ahlukene, hhayi ngokuthile okuhlukile njengemishini ye-Turing noma i-automata yeselula). Wabuye wabuyisela intshisekelo yakhe ku-physics, futhi ngo-1954 ngisho , Ini: "Ngizamile ukusungula i-quantum mechanics entsha" (yize enezela: "kodwa empeleni akulona iqiniso ukuthi kuzosebenza"). Kodwa ngeshwa, yonke into yaphela kungazelelwe ngo-June 7, 1954, lapho uTuring efa ngokuzumayo. (Ngicabanga ukuthi kwakungekona ukuzibulala, kodwa leyo enye indaba.)
Ngakho-ke ake sibuyele ekhasini le-lambda calculus. Masiyiphakamisele ekukhanyeni futhi sibone i-watermark futhi:
Kubonakala kuyisiqephu sephepha elenziwe eBrithani, futhi kubonakala kungenakwenzeka kimi ukuthi ngabe lisetshenziswe ePrinceton. Kodwa ingabe singayishela ngokunembile? Hhayi-ke, ngaphandle kosizo oluthile , siyazi ukuthi umkhiqizi osemthethweni wephepha kwakunguSpalding & Hodge, Papermakers, Drury House Wholesale and Export Company, Russell Street, Drury Lane, Covent Garden, London. Lokhu kungase kusisize, kodwa hhayi kakhulu, njengoba kungase kucatshangwe ukuthi uhlobo lwabo lwephepha lwe-Excelsior lubonakala lufakiwe kumakhathalogi wokuhlinzeka kusukela ngawo-1890 kuya ku-1954.
Lithini leli khasi?
Ngakho-ke, ake sihlolisise lokho okusezinhlangothini zombili zephepha. Ake siqale ngama-lambdas.
Nansi indlela yokunquma , futhi ziwumqondo oyisisekelo ku-logic yezibalo, futhi manje kusekuhlelweni okusebenzayo. Le misebenzi ivame kakhulu olimini , futhi umsebenzi wabo kulula kakhulu ukuwuchaza. Ngokwesibonelo, othile uyabhala f[x] ukukhombisa umsebenzi f, kusetshenziswe impikiswano x. Futhi kunemisebenzi eminingi ebizwa ngokuthi f njenge noma noma . Kodwa kuthiwani uma umuntu efuna f[x] kwaba 2x +1? Alikho igama eliqondile lalo msebenzi. Kodwa ingabe kukhona olunye uhlobo lomsebenzi, f[x]?
Impendulo inguyebo: esikhundleni salokho f siyabhala Function[a,2a+1]. Futhi ngolimi lweWolfram Function [a,2a+1][x] isebenzisa imisebenzi ku-agumenti x, iyakhiqiza 2x+1. Function[a,2a+1] kuwumsebenzi "ohlanzekile" noma "ongaziwa" omele ukusebenza okumsulwa kokuphindaphinda ngo-2 bese wengeza u-1.
Ngakho-ke, u-λ ku-lambda calculus uyi-analogue ngqo ngolimi lweWolfram - ngakho-ke, ngokwesibonelo, λa.(2 a+1) kulingana Function[a, 2a + 1]. (Kubalulekile ukuqaphela ukuthi umsebenzi, uthi, Function[b,2b+1] okulinganayo; "okuguquguqukayo okuboshiwe" a noma b ama-agumenti asebenza esikhundleni - futhi ngolimi lwe-Wolfram angagwenywa ngokusebenzisa ezinye izincazelo zemisebenzi emsulwa (2# +1)&).
Ezibalweni ezivamile, imisebenzi ngokuvamile icatshangwa njengezinto ezimele okokufaka (okuphinde kube izinombolo eziphelele, isibonelo) kanye nokuphumayo (okubuye, isibonelo, izinombolo eziphelele). Kodwa hlobo luni lwento lena? (noma λ)? Empeleni, i-opharetha yesakhiwo esithatha izisho futhi iziguqule zibe imisebenzi. Lokhu kungase kubonakale kuyinqaba kancane ngokombono wezibalo zendabuko kanye nezibalo, kodwa uma umuntu edinga ukwenza ukukhohlisa kwezimpawu ngokunganaki, kungokwemvelo kakhulu, ngisho noma kubonakala kungabonakali ekuqaleni. (Kufanele kuqashelwe ukuthi lapho abasebenzisi befunda Ulimi lweWolfram, ngingahlala ngitshela ukuthi badlule umkhawulo othile wokucabanga okungacacile lapho bethola ukuqonda ).
Ama-Lambda ayingxenye kuphela yalokho okukhona ekhasini. Kukhona omunye umqondo, ngisho nangokwengeziwe abstract - lokhu . Cabangela umucu ocashile PI1IIx? Lokhu kungasho ukuthini? Empeleni, lokhu ukulandelana kwezihlanganisi, noma ukwakheka okuthile okungaqondakali kwemisebenzi engokomfanekiso.
I-superposition evamile yemisebenzi, ejwayeleke kakhulu kwizibalo, ingabhalwa ngolimi lweWolfram ngokuthi: f[g[x]] - okusho ukuthi "sebenzisa" f kumphumela wesicelo g к x" Kodwa ingabe abakaki bayadingeka ngempela kulokhu? Ngolimi lwe-Wolfram f@g@ x - enye indlela yokuqopha. Kulokhu okuthunyelwe, sithembele encazelweni yolimi lwe-Wolfram: opharetha @ uhlotshaniswa nohlangothi olungakwesokudla, ngakho-ke. f@g@x kulingana f@(g@x).
Kodwa kuzosho ukuthini ukuqoshwa? (f@g)@x? Lokhu kuyalingana f[g][x]. Futhi uma f и g bekuyimisebenzi ejwayelekile kuzibalo, bekungeke kusho lutho, kodwa uma f - , khona-ke f[g] ngokwawo kungase kube umsebenzi ongase usetshenziswe kuwo x.
Qaphela ukuthi kusenezingqinamba lapha. IN f[х] - f kuwumsebenzi wempikiswano eyodwa. KANYE f[х] lilingana nokubhala Function[a, f[a]][x]. Kodwa kuthiwani ngomsebenzi onezimpikiswano ezimbili, yithi f[x,y]? Lokhu kungabhalwa ngokuthi Function[{a,b},f[a, b]][x, y]. Kodwa kuthiwani uma Function[{a},f[a,b]]? Kuyini lokhu? Kukhona "okuguquguqukayo kwamahhala" lapha b, emane idluliselwe kumsebenzi. Function[{b},Function[{a},f[a,b]]] izobopha lokhu okuguquguqukayo bese kuthi-ke Function[{b},Function[{a},f [a, b]]][y][x] unika f[x,y] futhi. (Ukucacisa umsebenzi ukuze ube ne-agumenti eyodwa kubizwa ngokuthi "currying" ukuhlonipha ungqondongqondo oqanjwe ).
Uma kukhona okuguquguqukayo kwamahhala, kunezindlela eziningi eziyinkimbinkimbi zokuthi imisebenzi ingachazwa kanjani, kodwa uma sizikhawulela ezintweni. noma λ, ezingenakho okuguquguqukayo kwamahhala, ngakho-ke zingacaciswa ngokukhululekile. Izinto ezinjalo zibizwa ngokuthi ama-combinator.
Izihlanganisi zinomlando omude. Kuyaziwa ukuthi baqale bahlongozwa ngo-1920 ngumfundi - .
Ngaleso sikhathi, kwakusanda kutholwa ukuthi sasingekho isidingo sokusebenzisa izinkulumo , и ukumela izinkulumo ngomqondo ojwayelekile wesiphakamiso: bekwanele ukusebenzisa u-opharetha oyedwa, esizombiza manje (ngoba, isibonelo, uma ubhala njengoba · ke Or[a,b] uzothatha ifomu ). U-Schoenfinkel wayefuna ukuthola ukumelwa okuncane okufanayo kwe-logic ye-predicate, noma, empeleni, ingqondo ehlanganisa imisebenzi.
Uqhamuke “nabadidiyeli” ababili u-S no-K. Olimini lweWolfram lokhu kuzobhalwa ngokuthi
K[x_][y_] → x kanye ne-S[x_][y_][z_] → x[z][y[z]].
Kuyamangaza ukuthi kube nokwenzeka ukusebenzisa lezi zihlanganisi ezimbili ukwenza noma yisiphi isibalo. Ngokwesibonelo,
S[K[S]][S[K[S[K[S]]]][S[K[K]]]]
ingasetshenziswa njengomsebenzi wokwengeza izinombolo ezimbili.
Lezi zonke izinto ezingasho lutho ezingasho lutho, kodwa manje njengoba sesiqonda ukuthi iyini imishini ye-Turing kanye ne-lambda calculus, siyabona ukuthi abahlanganisi be-Schoenfinkel empeleni bebelindele umqondo wekhompuyutha yendawo yonke. (Futhi okuphawuleka nakakhulu ukuthi izincazelo zango-1920 zika-S no-K zilula kancane, zisikhumbuza , engaphakamisa ngawo-1990, ukuguquguquka kwayo okwakukhona ).
Kodwa ake sibuyele eqabungeni lethu nomugqa PI1IIx. Izimpawu ezibhalwe lapha ziyizihlanganisi, futhi zonke zenzelwe ukucacisa umsebenzi. Lapha incazelo iwukuthi i-superposition yemisebenzi kufanele ishiywe ihlangene, ukuze fgx akufanele kuhunyushwe ngokuthi f@g@x noma f@(g@x) noma f[g[x]], kodwa kunalokho ngokuthi (f@g)@x noma f[g][x]. Ake sihumushe lokhu kufakwa efomini elilungele ukusetshenziswa yiWolfram Language: PI1IIx uzothatha ifomu p[i][one][i][i][x].
Kungani ubhala into enjalo? Ukuchaza lokhu, sidinga ukuxoxa ngomqondo wezinombolo zeBandla (eziqanjwe nge-Alonzo Church). Ake sithi sisebenza nje ngezimpawu nama-lambda noma izihlanganisi. Ingabe ikhona indlela yokuwasebenzisa ukuze ucacise izinombolo?
Kanjani sivele sithi inombolo n соответствует Function[x, Nest[f,x,n]]? Noma, ngamanye amazwi, ukuthi (ngenothi elifushane):
1 ngi f[#]&
2 ngi f[f[#]]&
3 ngi f[f[f[#]]]& nokunye.
Konke lokhu kungase kubonakale kungacacile, kodwa isizathu esithakazelisayo ukuthi kusivumela ukuthi senze yonke into ibe ngumfanekiso ngokuphelele futhi ingabonakali, ngaphandle kokuthi sikhulume ngokusobala ngento efana nezinombolo.
Ngale ndlela yokucacisa izinombolo, cabanga, isibonelo, ukwengeza izinombolo ezimbili: 3 ingamelwa njenge f[f[f[#]]]& futhi u2 u f[f[#]]&. Ungazingeza ngokumane usebenzise enye yazo kwenye:
Kodwa yini into? f? Kungaba noma yini! Ngomqondo othile, "iya ku-lambda" yonke indlela futhi umele izinombolo usebenzisa imisebenzi ethathayo f njengengxabano. Ngamanye amazwi, asimele u-3, isibonelo, njenge Function[f,f[f[f[#]]] &] noma Function[f,Function[x,f[f[f[x]]]]. (udinga nini futhi kanjani ukuqamba okuguquguqukayo ukuhlikihla ku-lambda calculus).
Cabanga ngocezu lwephepha lika-Turing lango-1937 , ehlela izinto ngendlela esisanda kuxoxa ngayo:
Yilapho okuqoshiwe kungase kudideke khona. x I-Turing ingeyethu f, Nezakhe x' (umshini wokuthayipha wenze iphutha ngokufaka isikhala) - lena eyethu x. Kodwa indlela efanayo ncamashi isetshenziswa lapha.
Ngakho ake sibheke umugqa ngemva nje kokugoqa ngaphambili kwephepha. Lokhu I1IIYI1IIx. Ngokusho kwe-Wolfram Language notation, lokhu kungaba i[one][i][i][y][i][one][i][i][x]. Kodwa nansi i identity function, ngakho i[one] imane ibonise one. Okwamanje, one ukumelwa kwezinombolo kweSonto koku-1 noma Function[f,f[#]&]. Kodwa ngale ncazelo one[а] iyaba a[#]& и one[a][b] iyaba a[b]. (Konje, i[а][b], noma Identity[а][b] nayo а[b]).
Kuzocaca kakhulu uma sibhala phansi imithetho yokushintsha i и one, esikhundleni sokusebenzisa ngokuqondile i-lambda calculus. Umphumela uzoba okufanayo. Sebenzisa le mithetho ngokucacile, sithola:
Futhi lokhu kufana ncamashi nalokho okwethulwe ekufakweni kokuqala okufushanisiwe:
Manje ake sibheke iqabunga futhi, phezulu:
Kukhona izinto ezididayo nezididayo "E" kanye "D" lapha, kodwa ngalawa sisho "P" kanye "Q", ukuze sikwazi ukubhala inkulumo futhi siyihlole (qaphela ukuthi lapha - ngemva kokudideka okuthile ne uphawu lokugcina - “usosayensi ongaqondakali” ubeka […] futhi (...) ukumela ukusetshenziswa komsebenzi):
Ngakho lesi isifinyezo sokuqala esibonisiwe. Ukuze ubone okwengeziwe, ake sixhume izincazelo ze-Q:
Sithola ncamashi ukuncishiswa okulandelayo okubonisiwe. Kwenzekani uma sishintsha amagama athi P?
Nawu umphumela:
Futhi manje, sisebenzisa iqiniso lokuthi i ngingumsebenzi okhipha ingxabano uqobo, sithola:
Hawu! Kodwa lokhu akuwona umugqa olandelayo oqoshiwe. Ingabe kunephutha lapha? Akucacile. Ngoba, ngemva kwakho konke, ngokungafani nezinye izimo eziningi, awukho umcibisholo obonisa ukuthi umugqa olandelayo ulandela kowangaphambili.
Kukhona okungaqondakali lapha, kodwa ake siqhubekele phansi eshidini:
Lapha u-2 inombolo yeBandla, enqunywa, isibonelo, ngephethini two[a_] [b_] → a[a[b]]. Qaphela ukuthi lokhu kuyindlela yomugqa wesibili uma u-a ethathwa njengo Function[r,r[р]] и b kanjani q. Ngakho silindele ukuthi umphumela wokubala ube kanjena:
Nokho, inkulumo ngaphakathi а[b] ingabhalwa ngokuthi x (mhlawumbe ihluke ku-x ebhalwe ngaphambili ephepheni) - ekugcineni sithola umphumela wokugcina:
Ngakho-ke, singakwazi ukucacisa okuncane okwenzekayo kuleli phepha, kodwa okungenani imfihlakalo eyodwa esasele yilokho okufanele u-Y abe yikho.
Eqinisweni, ku-logic yokuhlanganisa kukhona i-Y-combinator evamile: okuthiwa . Ngokusemthethweni, kuchazwa iqiniso lokuthi u-Y[f] kufanele zilingane f[Y[f]], noma, ngamanye amazwi, ukuthi Y[f] ayishintshi uma u-f esetshenziswa, ngakho-ke iphoyinti eligxilile f. (Inhlanganisela Y ihlotshaniswa ne #0 ngolimi lweWolfram.)
Njengamanje, i-Y-combinator isidumile ngenxa , eqanjwe kanjalo (osebe ngumlandeli isikhathi eside и futhi sasebenzisa isitolo sewebhu sokuqala ngqa ngokususelwe kulolu limi). Wake wangitshela ukuthi "akekho oqondayo ukuthi iyini inhlanganisela engu-Y" (Kumele kuqashelwe ukuthi i-Y Combinator iyona kanye evumela izinkampani ukuthi zigweme ukuthengiselana okugxilile...)
Isihlanganisi esingu-Y (njengesihlanganisi samaphuzu angashintshi) sisungulwe izikhathi ezimbalwa. UTuring waqhamuka nokuqaliswa kwayo ngo-1937, ayibiza ngokuthi Θ. Kodwa ingabe uhlamvu oluthi "Y" ekhasini lethu lungumhlanganisi odumile wamaphuzu angaguquki? Mhlawumbe akunjalo. Ngakho uyini u-“Y wethu”? Cabangela lesi sifinyezo:
Kodwa lolu lwazi ngokusobala alwanele ukucacisa ngokucacile ukuthi u-Y uyini. Kuyacaca ukuthi u-Y akasebenzi nje ngempikiswano eyodwa; Kubonakala sengathi kunezimpikiswano ezimbili okungenani ezihilelekile, kodwa akucaci (okungenani kimi) ukuthi mangaki ama-agumenti athathayo njengokufakwayo nokuthi yenzani.
Okokugcina, nakuba singenza umqondo ezingxenyeni eziningi zephepha, kufanele sisho ukuthi emhlabeni wonke akucaci ukuthi kwenziwani kulo. Noma kunokuningi okuchazwayo okuhilelekile kulokho okuseshidini lapha, kuyisisekelo esihle ku-lambda calculus kanye nokusebenzisa izihlanganisi.
Cishe lokhu kuwumzamo wokudala "uhlelo" olulula - usebenzisa i-lambda calculus nezihlanganisi ukwenza okuthile. Kodwa njengoba lokhu kuyinkomba yobunjiniyela obuhlehlayo, kunzima ngathi ukusho ukuthi leyo "nto" kufanele ibe yini nokuthi ithini inhloso "echazekayo" isiyonke.
Kunesici esisodwa esethulwe eshidini okufanele siphawule ngaso lapha - ukusetshenziswa kwezinhlobo ezahlukene zabakaki. Izibalo zendabuko ngokuvamile zisebenzisa abakaki kuyo yonke into - kanye nezinhlelo zokusebenza (njengaku f (x)), kanye namaqembu amalungu (njengaku (1+x) (1-x), noma, ngokusobala, a(1-x)). (Olimini lweWolfram, sihlukanisa ukusetshenziswa okuhlukile kwabakaki—kubakaki abayisikwele ukuchaza imisebenzi f [x] - futhi abakaki basetshenziselwa ukuqoqa kuphela).
Lapho i-lambda calculus ibonakala okokuqala, kwakunemibuzo eminingi mayelana nokusetshenziswa kobakaki. U-Alan Turing kamuva uzobhala wonke umsebenzi (ongashicilelwe) onesihloko”, kodwa kakade ngo-1937 waba nomuzwa wokuthi udinga ukuchaza izincazelo zesimanje (ezinye ze-hacky) ze-lambda calculus (okuyinto, ngendlela, eyavela ngayo ngenxa yeBandla).
Washo lokho f, kufakwe ku g, kufanele kubhalwe {f}(g), Uma kuphele f akuyena uhlamvu kuphela, kulokhu kungaba f(g). Wabe esethi lambda (as in Function[a, b]) kufanele ibhalwe njengo-λ a[b] noma, ngokunye, λ a.b.
Kodwa-ke, mhlawumbe ngo-1940 wonke umqondo wokusebenzisa {...} kanye […] nokumela izinto ezahlukene wawusushiywe, ikakhulukazi kwavuna abakaki besitayela sezibalo.
Bheka phezulu kwekhasi:
Kuleli fomu kunzima ukuliqonda. Ezincazelweni zeBandla, abakaki abayisikwele bahloselwe ukuhlanganisa, kunobakaki ovulekile othatha indawo yenkathi. Kusetshenziswa le ncazelo, kuyacaca ukuthi i-Q (egcine ibhalwe ukuthi D) efakwe kubakaki ekugcineni yiyona yonke i-lambda yokuqala esebenza kuyo.
Ubakaki oyisikwele lapha empeleni awubeki umkhawulo womzimba we-lambda; esikhundleni salokho, imele okunye ukusetshenziswa komsebenzi, futhi akukho nkomba ecacile yokuthi umzimba we-lambda uphelela kuphi. Ekugcineni, kungabonakala ukuthi “usosayensi ongaqondakali” uguqule ubakaki oyisikwele wokuvala waba ubakaki oyindilinga, ngaleyo ndlela wasebenzisa incazelo yeSonto ngokuphumelelayo - ngaleyo ndlela ephoqelela inkulumo ukuba ibalwe njengoba kukhonjisiwe eshidini.
Ngakho-ke lesi siqeshana esincane sisho ukuthini? Ngicabanga ukuthi lokhu kusikisela ukuthi leli khasi labhalwa ngeminyaka yawo-1930, noma kungakabiphi, njengoba imihlangano yabakaki yayingakahlali ngaleso sikhathi.
Pho kwakubhalwe ngesandla sikabani lesi?
Ngakho, ngaphambi kwalokhu sikhulume ngalokho okubhalwe ekhasini. Kodwa kuthiwani ngobani ngempela owayibhala?
Umuntu ozokhethwa kakhulu kule ndima kuzoba ngu-Alan Turing ngokwakhe, ngoba, ngemuva kwakho konke, leli khasi lalingaphakathi kwencwadi yakhe. Mayelana nokuqukethwe, kubonakala sengathi akukho lutho olungahambisani nombono wokuthi u-Alan Turing wayengawubhala - ngisho nalapho eqala ukubamba i-lambda calculus ngemva kokuthola iphepha leSonto ekuqaleni kuka-1936.
Kuthiwani ngokubhala ngesandla? Ingabe eka-Alan Turing? Ake sibheke izibonelo ezimbalwa ezisekhona esazi ngokuqinisekile ukuthi zabhalwa u-Alan Turing:
Umbhalo owethulwe ngokusobala ubukeka uhluke kakhulu, kodwa kuthiwani ngombhalo osetshenziswe embhalweni? Okungenani, ngokubona kwami, akubukeki kusobala - futhi umuntu angacabanga ukuthi noma yimuphi umehluko ungase ubangelwe ngokunembile ukuthi amasampula akhona (avezwe ezinqolobaneni) abhaliwe, ngomqondo ongokomfanekiso, "phezu, ” kuyilapho elethu ikhasi liwukubonakaliswa ngokunembile komsebenzi womcabango.
Kube lula ophenyweni lwethu ukuthi ingobo yomlando kaTuring iqukethe ikhasi abhala kulo , okudingekayo ukuze kubhalwe phansi. Futhi lapho uqhathanisa lezi zimpawu uhlamvu nohlamvu, zibukeka zifana kakhulu nami (la manothi enziwe ngo Turing ngenkathi efunda , yingakho ilebula ethi “leaf area”):
Bengifuna ukuhlola lokhu ngokuqhubekayo, ngakho ngithumele amasampula , uchwepheshe wokubhala ngesandla ochwepheshile (nombhali wezinkinga ezisekelwe ekubhaleni) engijabulele ukuhlangana naye kanye - ngokumane sethule iphepha lethu "njengesampula 'A'" kanye nesampula ekhona yombhalo wesandla ka-Turing njengokuthi "Isampula 'B'." Impendulo yakhe yayingeyokugcina futhi yayingeyinhle: "Isitayela sokubhala sihluke ngokuphelele. Mayelana nobuntu, umbhali wesampula "B" unesitayela sokucabanga esisheshayo nesinembile kunesampula "A" yombhali.".
Bengingakaqiniseki ngokuphelele okwamanje, kodwa nginqume ukuthi sekuyisikhathi sokubheka ezinye izinketho.
Ngakho-ke uma kuvela ukuthi uTuring akazange abhale, ubani owabhala? UNorman Routledge wangitshela ukuthi le ncwadi wayithola kuRobin Gandy, owayengumabi wamafa kaTuring. Ngakho ngithumele "Isampula "C"" kusuka ku-Gandhi:
Kodwa isiphetho sokuqala sikaSheila sasiwukuthi amasampula amathathu cishe abhalwa abantu abathathu abahlukene, futhi waphawula ukuthi isampula "B" ivela ku-"umcabango oshesha kakhulu—ongase azimisele kakhulu ukufuna amakhambi angavamile ezinkingeni" (Ngikuthola kuqabula ukuthi uchwepheshe wesimanje wokubhala ngesandla anganikeza lokhu kuhlola kokubhala kwesandla kuka-Turing, uma kubhekwa ukuthi wonke umuntu wayekhononda kangakanani ngokubhala kwakhe ngesandla esabelweni sesikole sika-Turing sika-1920s.)
Nokho, ngalesi sikhathi bekubonakala sengathi bobabili uTuring noGandhi sebekhishwe "njengabasolwa". Pho ngubani obengabhala lokhu? Ngaqala ukucabanga ngabantu okungenzeka uTuring waboleka incwadi yakhe. Yebo, kufanele futhi bakwazi ukwenza izibalo besebenzisa i-lambda calculus.
Ngicabange ukuthi lo muntu kumele abe ngowaseCambridge, noma okungenani eNgilandi, anikezwe i-watermark ephepheni. Ngakuthatha njengombono osebenzayo wokuthi i-1936 noma ngaphezulu kwakuyisikhathi esihle sokubhala lokhu. Ngakho-ke uTuring wayazi futhi waxhumana nobani ngaleso sikhathi? Ngalesi sikhathi, sithole uhlu lwabo bonke abafundi nothisha bezibalo eKing's College. (Kwakunabafundi abaziwayo abangu-13 abafunda kusukela ngo-1930 kuya ku-1936.)
Futhi kubo, kubonakale ikhandidethi ethembisa kakhulu . Wayelingana noTuring, umngane wakhe wesikhathi eside, futhi wayenesithakazelo nasezifundweni eziyisisekelo zezibalo - ngo-1933 waze washicilela iphepha ngalokho esikubiza manje. : 0.12345678910111213… (itholwe ngu 1, 2, 3, 4,…, 8, 9, 10, 11, 12,…, kanye neyodwa yezinombolo ezimbalwa kakhulu ngomqondo wokuthi ibhulokhi ngayinye yamadijithi iyenzeka ngamathuba alinganayo).
Ngo-1937, waze wasebenzisa u-Dirac's gamma matrices, njengoba kushiwo encwadini kaDirac, ukuze axazulule. . (Njengoba kwenzeka, ngemva kweminyaka ngaba umlandeli omkhulu wezibalo ze-gamma matrix).
Njengoba eseqale ukufunda izibalo, uChampernowne waba ngaphansi kwethonya (naseKing's College) futhi ekugcineni waba isazi sezomnotho esivelele, ikakhulukazi esenza umsebenzi wokungalingani kweholo. (Nokho, ngo-1948 waphinde wasebenza noTuring ukudala - Uhlelo lwe-chess, olwaba ngowokuqala emhlabeni ukuthi lusetshenziswe kukhompyutha).
Kodwa ngingalitholaphi isampula lombhalo wesandla ka-Champernowne? Ngokushesha ngathola indodana yakhe u-Arthur Champernowne ku-LinkedIn, okwathi ngokuxakile, wayeneziqu ku-logic yezibalo futhi wasebenzela iMicrosoft. Uthe uyise wakhuluma naye kancane ngomsebenzi kaTuring, nakuba engazange akhulume ngezinhlanganisela. Ungithumele isampula lombhalo wesandla kayise (ucezu olumayelana nokwakheka komculo we-algorithmic):
Ungasho ngokushesha ukuthi imibhalo yesandla ayizange ihambisane (ama-curls nemisila kuzinhlamvu f embhalweni wesandla ka-Champernowne, njll.)
Pho kungaba ubani omunye? Bengilokhu ngibabaza , ngezindlela eziningi umeluleki ku-Alan Turing. U-Newman waqala ukuthanda uTuring "umshini wezibalo"Kwakungumngane wakhe wesikhathi eside, futhi eminyakeni kamuva waba umphathi wakhe emsebenzini wekhompyutha eManchester. (Naphezu kwesithakazelo sakhe ekubaleni, uNewman ubonakala ehlala ezibona njengesazi sezibalo eziphezulu, nakuba iziphetho zakhe zazisekelwa ubufakazi obuyiphutha abuthola kubo. ).
Akubanga nzima ukuthola isampula yombhalo wesandla ka-Newman - futhi futhi, cha, imibhalo yesandla yayingahambisani neze.
"Trace" yencwadi
Ngakho-ke, umqondo wokukhomba ukubhala ngesandla wehlulekile. Futhi nganquma ukuthi isinyathelo esilandelayo okufanele ngisithathe kwakuwukuzama ukulandelela ngokuningiliziwe okwengeziwe ukuthi empeleni kwakwenzekani ngencwadi engangiyiphethe ngezandla zami.
Okokuqala nje, yayiyini indaba ende noNorman Rutledge? Ufunde eKing's College, eCambridge ngo-1946 futhi wahlangana noTuring (yebo, bobabili babeyizitabane). Uthole iziqu ekolishi ngo-1949, wabe eseqala ukubhala ithisisi yakhe ye-PhD noTuring njengomeluleki wakhe. Wathola i-PhD yakhe ngo-1954, esebenza nge-mathematical logic kanye ne-recursion theory. Wathola umfundaze wakhe eKing's College, kwathi ngo-1957 waba inhloko yomnyango wezibalo lapho. Lokhu wayengakwenza impilo yakhe yonke, kodwa wayenezithakazelo ezibanzi (umculo, ubuciko, izakhiwo, izibalo zokuzilibazisa, uhlu lozalo, njll.). Ngo-1960 washintsha indlela yakhe yokufunda futhi waba uthisha e-Eton, lapho izizukulwane zabafundi (kuhlanganise nami) zazisebenza (futhi zafunda) futhi zachayeka olwazini lwakhe lwe-eclectic futhi ngezinye izikhathi ngisho oluyinqaba.
Kungenzeka yini ukuthi uNorman Routledge uzibhalele yena leli khasi eliyimfihlakalo? Wayazi i-lambda calculus (yize, kwaqondana, wayisho ngesikhathi siphuza itiye ngo-2005 ukuthi wayehlale eyithola "ididekile"). Nokho, umbhalo wakhe wesandla awumfaki ngaphandle nje “njengososayensi ongaqondakali” okungenzeka.
Ingabe leli khasi lingaxhunyaniswa ngandlela thize nomfundi kaNorman, mhlawumbe kusukela lapho eseseCambridge? Ngiyangabaza. Ngoba angicabangi ukuthi uNorman wake wafunda i-lambda calculus nanoma yini efana naleyo. Ngenkathi ngibhala lesi sihloko, ngathola ukuthi uNorman wayebhale iphepha ngo-1955 mayelana nokudala i-logic "kumakhompiyutha kagesi" (nokwakha amafomu ajwayelekile ahlangene, njengoba umsebenzi owakhelwe ngaphakathi manje wenza. ). Lapho ngimazi uNorman, wayenesithakazelo esikhulu ekubhaleni izinsiza zamakhompiyutha wangempela (iziqalo zakhe zazithi "NAR", futhi wabiza izinhlelo zakhe ngokuthi "NAR...", isibonelo, "NARLAB", uhlelo lokudala amalebula ombhalo usebenzisa i-punched. imbobo "amaphethini" "ephepheni tape). Kodwa akakaze akhulume ngamamodeli etiyetha wokubala.
Masifunde inothi likaNorman ngaphakathi encwadini eduze kakhudlwana. Into yokuqala esizoyibona ukuthi ukhuluma ngayo "ukunikeza izincwadi ezivela kumtapo wolwazi womuntu oshonile" Futhi kusukela ekubhalweni kwamagama kuzwakala sengathi konke kwenzeka ngokushesha ngemva kokushona kwale ndoda, okusikisela ukuthi uNorman wathola le ncwadi ngemva nje kokushona kukaTuring ngo-1954, nokuthi uGandhi wayesenesikhathi eside eyikhumbula. U-Norman uqhuba ngokuthi empeleni uthole izincwadi ezine, ezimbili zezibalo ezihlanzekile nezimbili ze-theoretical physics.
Wabe esethi uyanikela"enye evela encwadini ye-physics (uhlobo, )»«KuSebag Montefiore, insizwa emnandi ongase uyikhumbule [uGeorge Rutter]" Kulungile, pho ungubani? Ngamba Uhlu Lwami Lwamalungu olwalungavamile ukusetshenziswa . (Kumele ngibike ukuthi lapho ngiyivula angikwazanga ukuzibamba kodwa ngabona imithetho yayo kusukela ngo-1902, eyokuqala yayo, ngaphansi kwesihloko esithi "Amalungelo Amalungu", yazwakala ihlekisa: "Gqoka ngemibala yeNhlangano").
Kufanele kwengezwe ukuthi mhlawumbe bengingeke ngijoyine lo mphakathi noma ngithole le ncwadi ukube bekungengenxa yokunxenxwa umngane ka-Eton ogama lakhe lingu-Eton. , owayehlela kusukela eneminyaka engu-12 ukuba ngelinye ilanga abe uNdunankulu, kodwa ngokudabukisayo washona eneminyaka engu-21 ubudala).
Kodwa kunoma yikuphi, kwakukhona abantu abahlanu kuphela ababalwe nesibongo Sebag-Montefiore, abanezinsuku eziningi zokufunda. Kwakungenzima ukuqonda ukuthi yayifaneleka . Umhlaba omncane, njengoba kwenzeka, umndeni wakhe wawuphethe iBletchley Park ngaphambi kokuyithengisa kuhulumeni waseBrithani ngo-1938. Futhi ngo-2000, uSebag-Montefiore wabhala - lokhu kungenxa yokuthi ngo-2002 uNorman wanquma ukumnika incwadi uTuring ayenayo.
Kulungile, kuthiwani ngezinye izincwadi uNorman azithola eTuring? Njengoba ngangingenayo enye indlela yokuthola ukuthi kwenzekani kubo, nga-oda ikhophi yencwadi yefa kaNorman. Isigatshana sokugcina sefa sasicacile ngesitayela sikaNorman:
Incwadi yefa ibithi izincwadi zikaNorman kumele zishiywe eKing's College. Futhi nakuba iqoqo lakhe eliphelele lezincwadi libonakala lingatholakali ndawo, izincwadi ezimbili zikaTuring zezibalo ezimsulwa, azishilo encwadini yakhe, manje sezigcinwe kungobo yomlando eKing's College Library.
Umbuzo olandelayo: kwenzekani kwezinye izincwadi zikaTuring? Ngabheka incwadi yefa kaTuring, eyabashiya bonke kuRobin Gandy.
UGandhi wayengumfundi wezibalo eKing's College, eCambridge, owaba umngane no-Alan Turing ngonyaka wakhe wokugcina ekolishi ngo-1940. Ekuqaleni kwempi, uGandhi wasebenza emsakazweni kanye ne-radar, kodwa ngo-1944 wabelwa endaweni efanayo ne-Turing futhi wasebenza ekubetheleni kwenkulumo. Futhi ngemva kwempi, uGandhi wabuyela eCambridge, ngokushesha wathola iziqu zakhe zobudokotela, futhi uTuring waba umeluleki wakhe.
Umsebenzi wakhe kwezempi ngokusobala wamholela ekubeni abe nesithakazelo kusayensi yemvelo, futhi incwadi yakhe, eyaqedwa ngo-1952, yayinesihloko esithi. . Okwabonakala sengathi uGandhi uzama ukukwenza mhlawumbe kwakuwukuhlukanisa imibono yezemvelo ngokomqondo wezibalo. Ukhuluma ngayo и , kodwa hhayi mayelana nemishini ye-Turing. Futhi ngokwalokho esikwaziyo manje, ngicabanga ukuthi singaphetha ngokuthi uphuthelwe iphuzu. Futhi ngempela, uye waphikisana kusukela ekuqaleni kwawo-1980 ukuthi izinqubo zomzimba kufanele zithathwe "njengezibalo ezihlukahlukene" -isibonelo, njengemishini ye-Turing noma i-automata yamaselula - kunokuba kube yimibono okufanele ithathwe. (UGandhi uxoxa kahle ngokuhleleka kwezinhlobo ezithintekayo kumathiyori aphathekayo, ngokwesibonelo ukuthi "Ngikholwa ukuthi ukuhleleka kwanoma iyiphi inombolo yedesimali esebenza kufomu kanambambili ingaphansi kwesishiyagalombili"). Wathi "Esinye sezizathu ezenza ithiyori yesimanje ye-quantum field ibe yinkimbinkimbi kangaka yingoba ikhuluma ngezinto zohlobo oluyinkimbinkimbi - ukusebenza kwemisebenzi...", okusho ukuthi ekugcineni"singase sithathe uhlobo olukhulu kakhulu lokusetshenziswa okuvamile njengesilinganiso sokuqhubeka kwezibalo".)
UGandhi ukhuluma ngoTuring izikhathi eziningi encwadini, ephawula esingenisweni ukuthi ukweleta u-A. M. Turing, owathi "waqala wadonsela ukunaka kwakhe okungatheni ekubaleni kweBandla” (okungukuthi lambda calculus), nakuba eqinisweni ithisisi yakhe inobufakazi be-lambda obuningi.
Ngemva kokuvikela incwadi yakhe, uGandhi waphendukela ekubeni nengqondo yezibalo ehlanzekile futhi iminyaka engaphezu kwamashumi amathathu ebhala izindatshana ngenani elilodwa ngonyaka, futhi lezi zihloko zacashunwa ngempumelelo emphakathini wezibalo zamazwe ngamazwe. Wathuthela e-Oxford ngo-1969 futhi ngicabanga ukuthi kumelwe ukuba ngahlangana naye ebusheni bami, nakuba ngingakukhumbuli lokho.
Ngokusobala uGandhi wayemkhulekela kakhulu uTuring futhi wakhuluma kakhulu ngaye eminyakeni eyalandela. Lokhu kuphakamisa umbuzo weqoqo eliphelele lemisebenzi kaTuring. Ngemva nje kokushona kukaTuring, uSarah Turing noMax Newman bacela uGandhi - njengomabi wefa lakhe - ukuba ahlele ukushicilelwa kwezincwadi zikaTuring ezingakashicilelwa. Yahamba iminyaka futhi kubonisa ukukhungatheka kukaSarah Turing ngalolu daba. Kodwa ngandlela thize uGandhi akakaze abonakale ehlele ukuhlanganisa amaphepha kaTuring.
UGandhi ushone ngo-1995 ngaphandle kokuhlanganisa imisebenzi eqediwe. - umhlaziyi wemibhalo kanye nombhali wempilo yabantu , uTuring ahlangana naye eKing's College, wayengumenzeli wezincwadi kaTuring, futhi ekugcineni waqala umsebenzi wezincwadi zikaTuring eziqoqwe. Okwaba nempikiswano kakhulu kwabonakala kuwumthamo wezibalo zezibalo, lapho aheha khona umfundi wakhe wokuqala oneziqu ezijulile, uRobin Gandy, umfundi othile. , owathola izincwadi eziya kuGandhi mayelana nemisebenzi eqoqiwe eyayineminyaka engama-24 iqalisiwe. ( ekugcineni uvele ngo-2001 - eminyakeni engama-45 ngemuva kokukhululwa kwabo).
Kodwa kuthiwani ngezincwadi uTuring ayenazo? Ngiqhubeka nokuzama ukubalandela, indawo yami elandelayo kwakuwumndeni wakwaTuring, futhi ikakhulukazi indodana encane yomfowabo kaTuring, (empeleni onguSir Dermot Turing, ngenxa yokuthi wayenjalo , lesi sihloko asizange sidlule kuye ngo-Alan emndenini wakwaTuring). UDermot Turing (osanda kubhala ) wangitshela mayelana "nogogo kaTuring" (owaziwa nangokuthi uSarah Turing), indlu yakhe ngokusobala yabelana ngomnyango wengadi nomndeni wakhe, nezinye izinto eziningi ngo-Alan Turing. Wangitshela ukuthi izincwadi zika-Alan Turing azikaze zibe semkhayeni wabo.
Ngakho ngabuyela ekufundeni izincwadi zefa futhi ngathola ukuthi umabi wamafa kaGandhi kwakuwumfundi wakhe uMike Yates. Ngifunde ukuthi uMike Yates uthathe umhlalaphansi njengoprofesa eminyakeni engama-30 edlule futhi manje uhlala eNorth Wales. Uthe emashumini eminyaka asebenza ku-mathematical logic kanye ne-computational theory, akazange ayithinte ngempela ikhompiyutha - kodwa ekugcineni wakwenza lapho esethatha umhlalaphansi (futhi, lokhu kwenzeka, ngemva nje kokuthola uhlelo. ). Uthe kumnandi kanjani ukuthi uTuring usedume kangaka, wathi efika eManchester ngemuva kweminyaka emithathu nje uTuring eshonile, akekho owayekhuluma ngoTuring, ngisho uMax Newman ngesikhathi efundisa izifundo zelogic. Kodwa-ke, uGandy wayezokhuluma ngokuhamba kwesikhathi ngokuthi ungene kanjani ekubhekaneni neqoqo lemisebenzi kaTuring, futhi ekugcineni wayishiya yonke kuMike.
Wayazini uMike ngezincwadi zikaTuring? Wathola enye yezincwadi zikaTuring ezibhalwe ngesandla, uGandhi angazange ayinike iKing's College ngoba (okuxakayo) uGandhi wayisebenzisa njengesifihlo samanothi ayewagcina ngamaphupho akhe. (UTuring wabuye wagcina amanothi amaphupho akhe, ashabalala ngemva kokufa kwakhe.) UMike uthe incwajana yokubhalela isanda kuthengiswa endalini ngemali elinganiselwa ku-$1 million. Futhi ukuthi ngaphandle kwalokho wayengeke acabange ukuthi phakathi kwezinto zikaGandhi kwakukhona izinto zeTuring.
Kwakubonakala sengathi zonke izinketho zethu zase zomile, kodwa uMike wangicela ukuba ngibheke lelo pheshana eliyimfihlakalo. Futhi ngokushesha wathi: ".Lona umbhalo wesandla ka-Robin Gandy!» Uthe usebone izinto eziningi kule minyaka edlule. Futhi wayeqinisekile. Uthe akanalo ulwazi oluningi nge-lambda calculus futhi akakwazi ngempela ukufunda leli khasi, kodwa unesiqiniseko sokuthi uRobin Gandy ulibhalile.
Sibuyele kuchwepheshe wethu wokubhala ngesandla namasampula engeziwe futhi wavuma ukuthi yebo, okwakukhona kufana nombhalo wesandla ka-Gandhi. Ngakho ekugcineni sikutholile: URobin Gandy wabhala lelo pheshana eliyimfihlakalo. Ayibhalwanga ngu-Alan Turing; yabhalwa umfundi wakhe uRobin Gandy.
Yebo, ezinye izimfihlakalo zisekhona. Kuthiwa uTuring waboleka uGandhi le ncwadi, kodwa nini? Indlela ye-lambda calculus notation yenza kubonakale sengathi yayingawo-1930s. Kodwa ngokususela ekuphawuleni kwencwadi kaGandhi, cishe wayengeke enze lutho nge-lambda calculus kuze kube sekupheleni kweminyaka yawo-1940. Umbuzo ube usuphakama ukuthi kungani uGandhi abhala lokhu. Lokhu akubonakali kuhlobene ngokuqondile nethisisi yakhe, ngakho-ke kungenzeka ukuthi kwaba ngenkathi eqala ukuzama ukuthola i-lambda calculus.
Ngiyangabaza ukuthi sizoke silazi iqiniso, kodwa ngokuqinisekile bekumnandi ukuzama ukulithola. Lapha kufanele ngisho ukuthi lonke lolu hambo lwenze lukhulu ekwandiseni ukuqonda kwami ukuthi inkimbinkimbi kangakanani imilando yezincwadi ezifanayo zamakhulu eminyaka adlule, okungaba, ikakhulukazi engiphethe. Lokhu kungenza ngicabange ukuthi kungcono ngenze isiqiniseko sokuthi ngibheka wonke amakhasi abo - ukuze nje ngibone ukuthi yini engase ithandeke lapho...
Siyabonga ngosizo ku-: Jonathan Gorard (Cambridge Private Studies), Dana Scott (Mathematical Logic), kanye no-Matthew Szudzik (Mathematics Logic).
Mayelana nokuhumushaUkuhunyushwa kokuthunyelwe kukaStephen Wolfram "".
Ngizwakalisa ukubonga kwami okujulile и ukuze uthole usizo ekuhumusheni nasekulungiseleleni ukushicilelwa.
Uyafuna ukufunda ukuthi ungahlela kanjani ngolimi lweWolfram?
Buka masonto onke .
... Ilungile .
ngolimi lweWolfram.
Source: www.habr.com