Bhuku iri ndakariwana sei?
Muna Chivabvu 2017, ndakagamuchira email kubva kumudzidzisi wangu wechikoro chesekondari ainzi George Rutter paakanyora kuti: “Ndine kopi yebhuku guru raDirac muchiGerman ( Die Prinzipien der Quantenmechanik), raive raAlan Turing, uye mushure mekuverenga bhuku renyu. , ndakazviona kuti ndiwe munhu arikuda" Akanditsanangurira kuti akagamuchira bhuku racho kune mumwe mudzidzisi wangu wechikoro (panguva iyoyo akanga afa). , wandaiziva kuti yaiva shamwari yaAlan Turing. George akapedzisa tsamba yake nemashoko anoti: "Kana muchida bhuku iri, ndinogona kukupai nguva inotevera pamunouya kuEngland".
Makore akati wandei gare gare, muna Kurume 2019, ndakasvika muEngland, mushure mezvo ndakaronga kusangana naGeorge kwekudya kwemangwanani pane imwe hotera diki muOxford. Takadya hedu nyaya ndokumirira kuti chikafu chigare. Ipapo yakanga yava nguva yakanaka yokukurukura bhuku racho. George akapinza ruoko mubhegi rake ndokuburitsa rakagadzirwa zvine mwero, rakafanana neredzidzo kubva pakati pemakore ekuma1900.
Ndakavhura butiro, ndichinetseka kana pangava nechimwe chinhu kuseri chaiti: “Property yaAlan Turing" kana chimwe chinhu chakadaro. Asi, zvinosuruvarisa, izvi hazvina kuitika. Nekudaro, yaiperekedzwa neinoratidziro yemapeji mana kubva kuna Norman Routledge kuenda kuGeorge Rutter, yakanyorwa muna 2002.
Ndaiziva Norman Rutledge pandaiva mudzidzi в mukutanga kwema1970. Aive mudzidzisi wemasvomhu ainzi "Nutty Norman." Akanga ari mudzidzisi aifadza munzira dzose uye aitaura nyaya dzisingaperi pamusoro pemasvomhu nezvimwe zvakasiyana-siyana zvezvimwe zvinhu zvinonakidza. Aive nebasa rekuona kuti chikoro chawana komputa (yakarongedzwa nedesk-wide punched tepi) - yaive .
Panguva iyoyo, hapana chandaiziva nezvekwakabva Norman (rangarirai, iyi yakanga iri nguva refu Internet isati yavapo). Chandaiziva ndechekuti aiva "Dr. Rutledge." Akataura nyaya nezvevanhu veCambridge kazhinji, asi haana kumbotaura nezveAlan Turing munyaya dzake. Ehe, Turing anga asati anyanya mukurumbira (kunyangwe, sezvazvinozoitika, ndakanga ndatonzwa nezvake kubva kune mumwe munhu aimuziva mukati. (iyo imba iyo iyo encryption centre yaive panguva yeHondo Yenyika Yechipiri)).
Alan Turing haana kuita mukurumbira kutozosvikira muna 1981, pandakatanga , kunyangwe zvakadaro zvichiri muchimiro che cellular automata, uye kwete .
Kana kamwe kamwe rimwe zuva, ndichitarisa kuburikidza nekabhuku kadhi muraibhurari , ndakasangana nebhuku , rakanyorwa naamai vake Sarah Turing. Iri bhuku raive neruzivo rwakawanda, kusanganisira nezve Turing asina kudhindwa mabasa esainzi nezve biology. Zvisinei, handina kudzidza chero chinhu pamusoro pehukama hwake naNorman Routledge, sezvo pasina chakataurwa pamusoro pake mubhuku (kunyange, sezvandakaona, Sarah Turing , uye Norman akatozopedzisa kunyora ).
Makore gumi gare gare, ndichida zvikuru kuziva nezveTuring neyake (yakazove isina kudhindwa) , Ndakashanya в . Nenguva isipi, pandakanga ndajairana nezvavaiva nazvo pabasa raTuring, uye ndambopedza nguva ndichizviita, ndakafunga kuti ndaizokumbirawo kuona tsamba dzake. Ndichiri kudongorera ndakaona kubva kuAlan Turing kuenda kuNorman Routledge.
Panguva iyoyo rakabudiswa Andrew Hodges, akaita zvakawanda kuti ave nechokwadi chekuti Turing akazova nemukurumbira, zvakasimbisa kuti Alan Turing naNorman Routledge vaive shamwari, uyezve kuti Turing aive chipangamazano chaNorman sainzi. Ndaida kubvunza Routledge nezveTuring, asi panguva iyoyo Norman akanga atova pamudyandigere uye achirarama upenyu hwakavanzika. Zvisinei, pandakapedza basa rebhuku "” muna 2002 (pashure pokunge ndava ndoga kwemakore gumi), ndakamutsvaga ndokumutumira bhuku racho rine mashoko okuti “Kumudzidzisi wangu wokupedzisira wemasvomhu.” Ipapo iye neni zvishoma , uye muna 2005 ndakadzokera kuEngland ndokuronga kusangana naNorman kuti tinwe tii pahotera youmbozha iri pakati peLondon.
Takakurukura zvakanaka nezvezvinhu zvakawanda, kusanganisira Alan Turing. Norman akatanga kurukurirano yedu nokutiudza kuti iye aiziva zvomenemene Turing, zvikurukuru pamusoro, makore 50 apfuura. Asi zvakadaro aive nechimwe chinhu chekutaura nezvake pachezvake: “Akanga asina kushamwaridzana". "Akaseka zvakanyanya". "Akanga asisakwanise kutaura nevasiri vemasvomhu". "Aigara achitya kugumbura mai vake". "Akabuda masikati ndokumhanya marathon". "Akanga asina kunyanya kuda chinzvimbo" Hurukuro yakazoenda kuhunhu hwaNorman. Anoti kunyangwe anga ava nemakore 16 ari pamudyandigere, achiri kunyora zvinyorwa zve“"kuti, mumashoko ake,"pedzisa mabasa ako ese esainzi usati waenda kune imwe nyika", apo, sezvaakawedzera nenyemwerero isina simba,"chokwadi chesvomhu chese chichaburitswa pachena" Pakapera mutambo wetii, Norman akapfeka bhachi rake redehwe akananga kumope yake, asina kana hanya nazvo. nezuva iroro.
Aka kaive kekupedzisira kuona Norman; akafa muna 2013.
Makore matanhatu gare gare ndakanga ndakagara pakudya kwemangwanani naGeorge Rutter. Ndakanga ndine katsamba kubva kuRutledge, yakanyorwa muna 2002 murunyoro rwake rwakasiyana:
Ndakatanga nekusvetukira pasi. Aitaura semazuva ese:
Ndakagamuchira bhuku raAlan Turing kubva kushamwari yake uye muurayi wake (kuKing's College kwaive kurongeka kwezuva rekupa mabhuku kubva muunganidzwa wevakafa, uye ndakasarudza muunganidzwa wenhetembo. kubva mumabhuku sechipo chakakodzera (aive dhiani uye akasvetuka kubva pachapel [muna 1956])…
Gare gare muchidimbu chipfupi anonyora kuti:
Iwe unobvunza kuti bhuku iri rinofanira kugumira kupi - mumaonero angu rinofanira kuenda kune mumwe munhu anoonga zvese zvine chekuita nebasa raTuring, saka magumo aro anoenderana newe.
Stephen Wolfram akanditumira bhuku rake rinonakidza, asi handina kunyura zvakaringana mariri...
Akapedzisa nekukorokotedza George Rutter nekuva neushingi hwekutama (kwechinguva, sezvazvakazoitika) kuenda kuAustralia mushure mekusiya basa, achiti iye pachake "yaizotamba nekuenda kuSri Lanka semuenzaniso wehupenyu hwakachipa uye hwakafanana nelotus", asi akawedzera kuti "zviri kuitika ikoko zvinoratidza kuti aisafanirwa kuita izvi"(sezviri pachena zvichireva muSri Lanka).
Saka chii chakavigwa mukatikati mebhuku?
Saka ndakaita sei nekopi yebhuku rechiGerman rakanyorwa naPaul Dirac raimbove raAlan Turing? Ini handiverengi chiGerman, asi ndaverenga muChirungu (unova ndiwo mutauro wavo wekutanga) edition kubva kuma1970s. Zvisinei, rimwe zuva pakudya kwemangwanani kwakaratidzika kuva kwakarurama kuti ndinofanira kunzvera nokungwarira peji nepeji. Mushure mezvose, izvi zvinowanzoitika kana uchibata nemabhuku ekare.
Zvinofanira kucherechedzwa kuti ndakabatwa nekunaka kwemharidzo yaDirac. Bhuku racho rakabudiswa muna 1931, asi muitiro waro wakachena (uye, hungu, pasinei zvapo nemhinganidzo yomutauro, ndaigona kurava masvomhu mubhuku) zvakada kufanana sokunge kuti zvakanyorwa nhasi. (Handidi kunyanya kukoshesa Dirac pano, asi shamwari yangu akandiudza kuti, zvirinani mumaonero ake, kuburitswa kwaDirac ndeye monosyllabic. Norman Rutledge akandiudza kuti aive shamwari paCambridge , uyo akazova nyanzvi yemagirafu. Norman akashanyira imba yaDirac kakawanda uye akataura kuti “murume mukuru” pane dzimwe nguva aidzokera kumashure, nepo yekutanga yaigara yakazara nemasvomhu. Ini pachangu, zvinosuruvarisa, handina kumbosangana naPaul Dirac, kunyangwe ndakaudzwa kuti mushure mekunge abva kuCambridge achienda kuFlorida, akarasikirwa nekuoma kwake kwepakutanga uye akave munhu anoshamwaridzana).
Asi ngatidzokere kubhuku raDirac, raiva raTuring. Papeji 9, ndakaona kutara uye zvinyorwa zviduku mumicheto, zvakanyorwa nepenzura. Ndakaramba ndichivhura mapeji. Pashure pezvitsauko zvishomanana, zvinyorwa zvacho zvakanyangarika. Asi ipapo, kamwe kamwe, ndakawana chinyorwa chakabatanidzwa papeji 127 chaiti:
Yakanyorwa muchiGerman murunyoro rwechiGerman. Uye zvinoita sekunge ane chekuita naye . Ndakafunga kuti zvichida mumwe munhu aiva nebhuku iri Turing asati auya, uye ichi chinofanira kunge chiri chinyorwa chakanyorwa nemunhu iyeye.
Ndakaramba ndichivhura bhuku. Pakanga pasina zvinyorwa. Uye ndakafunga kuti hapana chimwe chandaiwana. Asi zvino, papeji 231, ndakawana bhukimaki ine mhando - ine mavara akadhindwa:
Ndichapedzisira ndawana chimwe chinhu here? Ndakaramba ndichivhura bhuku. Zvino, pakupera kwebhuku, papeji 259, muchikamu cherelativistic electron theory, ndakawana zvinotevera:
Ndakabhedhenura bepa iri:
Ndakabva ndangoziva kuti chaiva chii yakasanganiswa ne , asi shizha iri rakasvika sei pano? Ngatiyeukei kuti bhuku iri ibhuku rinotaura nezve quantum mechanics, asi kapepa kakavharirwa kanotaura nezvemasvomhu, kana izvo zvave kunzi dzidziso yekombuta. Izvi zvinongoitika muzvinyorwa zvaTuring. Ndakashamisika kana Turing pachake akanyora chinyorwa ichi?
Kunyangwe panguva yekudya kwemangwanani, ndakatsvaga paInternet kuti ndiwane mienzaniso yerunyoro rwaTuring, asi handina kuwana mienzaniso muchimiro chekuverenga, saka handina kukwanisa kuita mhedziso pamusoro pekuzivikanwa chaiko kwerunyoro. Uye munguva pfupi taifanira kuenda. Ndakanyatsorongedza bhuku riya, ndagadzirira kuburitsa chakavanzika chepeji ripi uye ndiani akanyora, ndokuenda naro.
Nezve bhuku
Kutanga, ngatikurukurei bhuku racho pacharo. "» Minda yeDirac yakabudiswa muChirungu muna 1930 uye munguva pfupi yakashandurirwa muchiGermany. (Sumo yeDirac yakanyorwa muna Chivabvu 29, 1930; ndeyemuturikiri - - 15 Nyamavhuvhu 1930.) , iyo ichavhurwa muna 1932.
Sei Alan Turing aine bhuku rechiGerman kwete Chirungu? Ini handizive izvi zvechokwadi, asi mumazuva iwayo chiGerman ndicho chaitungamira mutauro wesainzi, uye tinoziva kuti Alan Turing aikwanisa kuuverenga. (Mushure mezvose, muzita remukurumbira wake работы « (Entscheidungsproblem)" rakanga riri izwi refu rechiGerman - uye muchikamu chikuru chechinyorwa anoshandisa neasina kujeka zviratidzo zveGothic muchimiro che "mabhii echiGerman" aakashandisa pachinzvimbo che, semuenzaniso, zviratidzo zvechiGiriki).
Alan Turing akatenga bhuku iri pachake here kana kuti akapiwa kwaari? Handizive. Pabutiro remukati rebhuku raTuring pane chinyorwa chepenzura "20/-", chaive chinyoreso che "20 shilingi", yakafanana ne£1. Papeji rekurudyi pane zvakadzimwa "26.9.30", zvichida zvichireva kuti Gunyana 26, 1930, pamwe zuva rakatanga kutengwa bhuku. Ipapo, kurudyi, ndiyo nhamba yakadzimwa “20.” Pamwe ndiwo mutengo zvakare. (Unogona kunge uri mutengo mu , tichifunga kuti bhuku racho rakatengeswa muGermany? Mumazuva iwayo, 1 Reichsmark yaive yakakosha nezve 1 schilling, mutengo weGerman ungangonyorwa se "RM20" semuenzaniso.) Pakupedzisira, mukati mukati mebutiro rekuseri kune "c 5/-" - pamwe ichi, (ine hombe. discount) mutengo webhuku rakashandiswa.
Ngatitarisei mazuva makuru muhupenyu hwaAlan Turing. Alan Turing (sezvineiwo, makore 76 apfuura ) Mumatsutso a1931 akapinda muKing's College, Cambridge. Akagamuchira dhigirii rake reBachelor mushure memakore matatu ekudzidza muna 1934.
Muma1920 nekutanga 1930s, quantum mechanics yaive nyaya inopisa, uye Alan Turing aifarira mazviri. Kubva muzvinyorwa zvake tinoziva kuti muna 1932, pakangobudiswa bhuku, akagamuchira "»John von Neumann (pa ) Isu tinoziva zvakare kuti muna 1935 Turing akagamuchira basa kubva kuCambridge nyanzvi yefizikisi pamusoro penyaya yekudzidza quantum mechanics. (Fowler akakurudzira kuverenga , iro chairo dambudziko rakaoma kwazvo rinoda kuongororwa kwakazara nekudyidzana quantum field theory, iyo isati yanyatsogadziriswa).
Uye zvakadaro, Turing akawana rini uye sei bhuku rake rebhuku raDirac? Tichifunga kuti bhuku racho rine mutengo wamaka, Turing angangoritenga rakamboshandiswa. Ndiani akanga ari muridzi webhuku rokutanga? Zvinonyorwa zviri mubhuku zvinoita sezvinobata zvakanyanya nechimiro chine musoro, tichiona kuti humwe hukama hune musoro hunofanira kutorwa seaxiom. Ko zvakadini netsamba inobatanidzwa papeji 127?
Zvakanaka, pamwe zvangoitika, asi pane peji 127 - Dirac inotaura nezve quantum uye anoisa hwaro hwe - inova hwaro hwemazuva ano quantum formalism. Ko chinyorwa chinei? Iine wedzero yeEquation 14, inova equation yenguva yekushanduka kwe quantum amplitude. Munyori wenoti akatsiva iyo Dirac A yeamplitude ne ρ, zvichida zvichiratidza yepakutanga (fluid density analogy) German notation. Munyori anobva aedza kuwedzera chiito nemasimba e ℏ (, yakakamurwa na 2π, dzimwe nguva inodanwa ).
Asi zvinoita kunge pasina ruzivo rwakawanda runobatsira rwunotorwa kubva pane zviri papeji. Kana iwe ukabata peji kusvika kuchiedza, rine kakushamisika - watermark inoti "Z f. Physik. Chem. B":
Iyi ndiyo vhezheni yakapfupikiswa - pepanhau reGermany pamusoro pemakemikari emuviri, iyo yakatanga kubudiswa muna 1928. Zvichida chinyorwa chakanyorwa nemupepeti wemagazini? Heino musoro wemagazini kubva muna 1933. Zviri nyore, vapepeti vakanyorwa nenzvimbo, uye imwe inomira pachena: "Bourne · Cambridge."
Ndizvo zvazviri munyori ndiani uye nezvimwe zvakawanda mudzidziso ye quantum mechanics (pamwe chete nasekuru vemuimbi ) Saka, chinyorwa ichi chinogona kunge chakanyorwa naMax Born? Asi, zvinosuruvarisa, izvi handizvo, nokuti runyoro haruenderani.
Zvakadini nebhukimaki riri papeji 231? Hezvino zviri kubva kumativi maviri:
Iyo bookmark inoshamisa uye yakanaka chaizvo. Asi yakaitwa rini? MuCambridge pane , kunyange zvazvo ikozvino chikamu cheBlackwell. Kwemakore anopfuura makumi manomwe (kusvika 70), Heffers aive pakero, sezvinoratidzwa nebhukimaki, и .
Iyi tebhu ine kiyi yakakosha - iyi ndiyo nhamba yefoni "Tel. 862". Sezvazvakaitika, muna 1939 vazhinji veCambridge (kusanganisira Heffers) vakashandura kune nhamba dzemanhamba mana, uye zvechokwadi muna 1940 mabhukumaki akanga achidhindwa nenhamba dzefoni "yemazuva ano". (Nhamba dzenhare dzechiRungu dzakarebesa zvishoma nezvishoma; pandakanga ndichikura muEngland kuma1960, nhamba dzedu dzorunhare dzakanga dziri “Oxford 56186” uye “Kidmore End 2378.” Chimwe chikonzero nei ndirangarira nhamba idzi imhaka yokuti, zvinoshamisa sezvazviri iye zvino. zvaisaita sekuti ndaigara ndichifona panumber dzangu kana ndichidaira incoming call).
Bookmark rakadhindwa iri fomu kusvika 1939. Asi nguva yakareba sei izvozvo zvisati zvaitika? Kune akatiwandei akati wandei ekare ekare Heffers kushambadzira pamhepo, inotangira kusvika 1912 (pamwe ne "Tinokumbira kuti usangane nezvikumbiro zvako ...") vanozadzisa "Phone 862" nekuwedzera "(2 mitsara)." Kune zvakare mamwe mabhukimaki ane magadzirirwo akafanana anogona kuwanikwa mumabhuku kumashure kumakore a1904 (kunyangwe zvisiri pachena kuti aive ekutanga kumabhuku aya (kureva akadhindwa panguva imwe chete). Nechinangwa chekuongorora kwedu, zvinoita sekunge isu anogona kugumisa kuti Iri bhuku rakabva kuna Heffer's (iyo, nenzira, yaive chitoro chikuru muCambridge) imwe nguva pakati pa1930 na1939.
Lambda calculus peji
Saka zvino tinoziva chimwe chinhu pamusoro penguva yakatengwa bhuku racho. Asi zvakadini ne "lambda calculus peji"? Izvi zvakanyorwa rini? Zvakanaka, sezvazviri, panguva iyoyo lambda calculus inofanira kunge yakatogadzirwa. Uye zvakaitwa , nyanzvi yemasvomhu kubva , muchimiro chayo chepakutanga muna 1932 uye muchimiro chayo chokupedzisira muna 1935. (Paive nemabasa nemasayendisiti apfuura, asi havana kushandisa notation λ).
Pane hukama hwakaoma pakati peAlan Turing uye lambda calculus. Muna 1935, Turing akatanga kufarira "mechanization" yekushanda kwemasvomhu, uye akagadzira pfungwa yeTuring machine, achiishandisa kugadzirisa matambudziko mumasvomhu anokosha. Turing akatumira chinyorwa nezvenyaya iyi kumagazini yechiFrench (), asi yakarasika mutsamba; uye zvakazoonekwa kuti munhu waakatumira kwaari akanga asipo, sezvo akanga atamira kuChina.
Asi muna Chivabvu 1936, Turing asati atumira bepa rake chero kupi zvako, . Turing akambonyunyuta kuti paakagadzira humbowo muna 1934 , ndakabva ndaona kuti paiva neimwe nyanzvi yemasvomhu yekuNorway yakanga yatova nayo muna 1922 gore.
Hazvina kuoma kuona kuti Turing michina uye lambda calculus yakanyatso kuenzana mumhando dzemakomputa dzavanogona kumiririra (uye ndiko kutanga. ) Zvisinei, Turing (nemudzidzisi wake ) vaiva nechokwadi chokuti maitiro aTuring akanga akasiyana zvokuti akakodzera kubudiswa. MunaNovember 1936 (uye nematypos akagadziriswa mwedzi unotevera) mukati Pepa raTuring rine mukurumbira rakabudiswa .
Kuzadza rondedzero yenguva zvishoma: kubva munaGunyana 1936 kusvika Chikunguru 1938 (nezororo remwedzi mitatu muzhizha ra1937), Turing aive kuPrinceton, aenda ikoko aine chinangwa chekuve mudzidzi akapedza kudzidza weChechi yeAlonzo. Munguva iyi paPrinceton, Turing sezviri pachena ainyanya kufunga nezvemasvomhu, achinyora akati wandei , - uye, zvichida, akanga asina bhuku pamusoro pe quantum mechanics naye.
Turing akadzokera kuCambridge muna July 1938, asi pakazosvika September wegore iroro akanga achishanda nguva isina kuzara pa , uye gore rakatevera akatamira kuBletchley Park nechinangwa chekushanda ikoko nguva yakazara panyaya dzine chokuita necryptanalysis. Pashure pokunge hondo yapera muna 1945, Turing akatamira kuLondon kunoshandira pakuvandudzwa kweprojekti yekugadzira . Akapedza 1947-8 gore redzidzo kuCambridge asi ndokuzotamira kuManchester kunosimudzira .
Muna 1951, Turing akatanga kunyatsodzidza . (Kwandiri pachangu, chokwadi ichi chinotoshamisa, nekuti kwandiri zvinoita sekunge Turing aigara achitenda zvisingaite kuti biological masisitimu anofanirwa kuenzanisirwa nekusiyanisa equation, uye kwete nechinhu chakajeka seTuring muchina kana cellular automata). Akadzoreredza kufarira kwake kufizikisi, uye ne1954 kunyangwe , Chii: "Ndakaedza kugadzira imwe quantum mechanics"(kunyangwe akawedzera: "asi chokwadi hachisi chokwadi kuti zvichabuda"). Asi zvinosuruvarisa kuti zvinhu zvose zvakangoerekana zvapera pana June 7, 1954, apo Turing akafa kamwe kamwe. (Ndiri kufungidzira kuti kwaisava kuzviuraya, asi ndiyo imwe nyaya.)
Saka ngatidzokerei kune lambda calculus peji. Ngatisimudzei kumusoro kuchiedza uye tione watermark zvakare:
Inoratidzika kunge chidimbu chebepa rakagadzirwa neBritish, uye zvinoita sezvisingaite kwandiri kuti ringadai rakashandiswa kuPrinceton. Asi tinogona kufambidzana nayo zvakarurama here? Zvakanaka, kwete pasina rubatsiro , tinoziva kuti mugadziri wepamutemo webepa aive Spalding & Hodge, Papermakers, Drury House Wholesale and Export Company, Russell Street, Drury Lane, Covent Garden, London. Izvi zvinogona kutibatsira, asi kwete zvakanyanya, sezvo zvichigona kufungidzirwa kuti bepa ravo reExcelsior rinoratidzika kunge rakaverengerwa mumabhuku ekupa kubva kuma1890 kusvika 1954.
Peji iri rinoti kudii?
Saka, ngatitarisei zvakanyanya pane zviri kumativi ese epepa. Ngatitangei ne lambdas.
Heino nzira yekuziva , uye iwo ipfungwa yekutanga mune masvomhu logic, uye ikozvino mune inoshanda hurongwa. Aya mabasa anowanikwa zvakanyanya mumutauro , uye basa ravo riri nyore kutsanangura. Somuenzaniso, mumwe munhu anonyora f[x] kuratidza basa f, inoshandiswa kune nharo x. Uye kune akawanda ane mazita mabasa f zvakaita se kana kana . Asi zvakadini kana mumwe munhu achida f[x] aiva 2x +1? Hapana zita rakananga rebasa iri. Asi pane imwe nzira yebasa, f[x]?
Mhinduro ndeyekuti hongu: pane kudaro f tiri kunyora Function[a,2a+1]. Uye mumutauro weWolfram Function [a,2a+1][x] inoshandisa mabasa kunharo x, kugadzira 2x+1. Function[a,2a+1] ibasa "rakachena" kana "risina zita" rinomiririra kushanda kwakachena kwekuwanza ne2 uye kuwedzera 1.
Saka, λ mu lambda calculus ianalogue chaiyo muWolfram Mutauro - uye saka, semuenzaniso, λa.(2 a+1) yakaenzana Function[a, 2a + 1]. (Zvakakosha kuziva kuti basa, taura, Function[b,2b+1] equivalent; "zvakasungirirwa zvakasiyana" a kana b anongori mashandisirwo enharo - uye muWolfram Mutauro anogona kudzivirirwa nekushandisa mamwe akachena basa tsanangudzo (2# +1)&).
Mumasvomhu echinyakare, mabasa anowanzo fungwa sezvinhu zvinomiririra zvinopinda (zvinovawo zvikamu zvakakwana, semuenzaniso) uye zvinobuda (izvo zvakare, semuenzaniso, nhamba dzese). Asi rudzii rwechinhu ichi? (kana λ)? Chaizvoizvo, inyanzvi yekugadzira iyo inotora mazwi uye inoashandura kuita mabasa. Izvi zvingaita sezvisinganzwisisike kubva pamaonero echinyakare masvomhu uye masvomhu notation, asi kana munhu achida kuita zvehumbimbindoga chiratidzo chemanipulation, zvinongoitika, kunyangwe zvikaita sezvisinganzwisisike pakutanga. (Izvo zvinofanirwa kucherechedzwa kuti kana vashandisi vakadzidza Mutauro weWolfram, ndinogona kugara ndichitaura kuti vakapfuura imwe chikumbaridzo chekufunga zvisiri izvo pavanowana kunzwisisa kwe. ).
Lambdas inongova chikamu chezviripo pane peji. Pane imwe, inotonyanya kujeka pfungwa - iyi . Funga nezvetambo isina kujeka PI1IIx? Izvi zvingarevei? Chaizvoizvo, uku ndiko kutevedzana kwevanobatanidza, kana kumwe kuumbwa kwemaitiro ekufananidzira.
Iyo yakajairwa superposition yemabasa, yakajairika mumasvomhu, inogona kunyorwa muWolfram Mutauro se: f[g[x]] - zvinoreva kuti "shandisa" f kune mhedzisiro yekushandisa g к x" Asi maparentheses anodiwa zvechokwadi here kune izvi? Mumutauro weWolfram f@g@ x - imwe nzira yekurekodha. Mune ino post, isu tinovimba netsananguro muWolfram Mutauro: iyo @ opareta inosanganiswa nekurudyi-ruoko, saka f@g@x yakaenzana f@(g@x).
Asi kurekodha kunorevei? (f@g)@x? Izvi zvakaenzana f[g][x]. Uye kana f и g aiva mabasa akajairika mumasvomhu, zvinenge zvisina zvazvinoreva, asi kana f - , ipapo f[g] pachayo inogona kunge iri basa rinogona kushandiswa kwariri x.
Ziva kuti pachine zvimwe zvinonetsa apa. IN f[х] - f ibasa renharo imwe. UYE f[х] zvakaenzana nekunyora Function[a, f[a]][x]. Asi zvakadini nebasa rine nharo mbiri, taura f[x,y]? Izvi zvinogona kunyorwa se Function[{a,b},f[a, b]][x, y]. Asi zvakadini kana Function[{a},f[a,b]]? Ichi chii? Pane "free variable" pano b, iyo inongopfuudzwa kune basa. Function[{b},Function[{a},f[a,b]]] achasunga ichi chinja uye ipapo Function[{b},Function[{a},f [a, b]]][y][x] anopa f[x,y] zvakare. (Kutsanangura basa kuitira kuti rive nenharo imwe chete inonzi "curry" mukuremekedza nyanzvi inonzi ).
Kana paine mahara vhezheni, saka kune akawanda akasiyana akaomesesa ekuti mabasa anogona kutsanangurwa sei, asi kana tikangozvidzora kune zvinhu. kana λ, iyo isina mavara emahara, saka anogona kunyatso kutsanangurwa zvakasununguka. Zvinhu zvakadai zvinonzi combinators.
Combinators vane nhoroondo refu. Zvinozivikanwa kuti vakatanga kutaurwa muna 1920 nemudzidzi - .
Panguva iyoyo, kwakanga kuri nguva pfupi yapfuura apo kwakaonekwa kuti pakanga pasina chikonzero chokushandisa mashoko acho , и kumiririra mataurirwo mune yakajairwa propositional logic: zvaive zvakakwana kushandisa mushandisi mumwechete, watichadaidza zvino (nekuti, semuenzaniso, kana ukanyora se · ipapo Or[a,b] achatora fomu ) Schoenfinkel aida kuwana imwechete inomiririrwa ye predicate logic, kana, chaizvo, pfungwa dzinosanganisira mabasa.
Akauya ne "combinators" maviri S uye K. Mumutauro weWolfram izvi zvichanyorwa se
K[x_][y_] → x uye S[x_][y_][z_] → x[z][y[z]].
Zvinoshamisa kuti zvakazove zvichigoneka kushandisa aya maviri macombinator kuita chero kuverenga. Semuyenzaniso,
S[K[S]][S[K[S[K[S]]]][S[K[K]]]]
inogona kushandiswa sebasa rekuwedzera nhamba mbiri.
Izvi zvese zviri zvinhu zvisinganzwisisike kutaura zvishoma, asi ikozvino zvatiri kunzwisisa kuti Turing muchina uye lambda calculus chii, tinogona kuona kuti Schoenfinkel combinators aitarisira pfungwa yeuniversal computing. (Uye chinotonyanya kushamisa ndechekuti tsananguro dze1920 dzeS uye K dziri nyore, dzinoyeuchidza nezve. , iyo yandakakurudzira muma1990, kushandiswa kwakasiyana-siyana kwaiva ).
Asi ngatidzokere kushizha nemutsara wedu PI1IIx. Zviratidzo zvakanyorwa pano zvinosanganisa, uye zvese zvakagadzirirwa kutsanangura basa. Pano tsananguro ndeyokuti superposition yemabasa inofanira kusiiwa yakabatana, kuitira kuti fgx haifanire kududzirwa sef@g@x kana f@(g@x) kana f[g[x]], asi kuti (f@g)@x kana f[g][x]. Ngatishandure chinyorwa ichi kuita fomu rakakodzera kushandiswa neWolfram Mutauro: PI1IIx achatora fomu p[i][mumwe][i][i][x].
Sei kunyora chinhu chakadaro? Kuti titsanangure izvi, tinofanira kukurukura pfungwa yenhamba dzeChechi (dzinotumidzwa zita reChechi yeAlonzo). Ngatitii tiri kungoshanda nezviratidzo uye lambdas kana combinators. Pane nzira yekuashandisa kudoma nhamba dzakakwana here?
Ko isu tongoti nhamba yacho n соответствck Function[x, Nest[f,x,n]]? Kana, nemamwe mazwi, izvo (mune pfupiso notation):
1 iri f[#]&
2 iri f[f[#]]&
3 iri f[f[f[#]]]& uye zvichingodaro.
Izvi zvese zvingaite sezvisinganzwisisike, asi chikonzero chinonakidza ndechekuti zvinotitendera kuti tiite zvese zvinofananidzira uye zvisinganzwisisiki, pasina kutaura zvakajeka nezve chimwe chinhu senge nhamba.
Neiyi nzira yekutsanangura nhamba, fungidzira, semuenzaniso, kuwedzera nhamba mbiri: 3 inogona kumiririrwa se f[f[f[#]]]& uye 2i f[f[#]]&. Iwe unogona kuzviwedzera nekungoshandisa imwe yadzo kune imwe:
Asi chii chiri chinhu? f? Inogona kuva chero chinhu! Neimwe nzira, "enda ku lambda" nzira yese uye unomiririra nhamba uchishandisa mabasa anotora f senharo. Mune mamwe mazwi, ngatimirirei 3, semuenzaniso, se Function[f,f[f[f[#]]] &] kana Function[f,Function[x,f[f[f[x]]]]. (rini uye sei paunoda kutumidza zvinosiyana ndiyo rub mu lambda calculus).
Funga nezvechidimbu chebepa raTuring ra1937 , iyo inomisikidza zvinhu chaizvo sezvatabva kukurukura:
Apa ndipo apo kurekodha kunogona kuwana kuvhiringika zvishoma. x Turing ndeyedu f, Uye yake x' (taipa akakanganisa nekuisa nzvimbo) - iyi ndeyedu x. Asi nzira imwecheteyo ndiyo inoshandiswa pano.
Saka ngatitarisei mutsara mushure mekupeta kumberi kwebepa. Izvi I1IIYI1IIx. Zvinoenderana neWolfram Mutauro notation, izvi zvingave i[one][i][i][y][i][one][i][i][x]. Asi heino identity basa, saka i[one] zvinongoratidza mumwe. Zvichakadaro, mumwe inomiririra nhamba yeChechi ye1 kana Function[f,f[#]&]. Asi netsanangudzo iyi one[а] kuri kuitika a[#]& и one[a][b] kuri kuitika a[b]. (Zviya, i[а][b], kana Identity[а][b] iri zvakare а[b]).
Zvichava zvakanyanya kujeka kana tikanyora pasi mitemo yekutsiva ye i и mumwe, pachinzvimbo chekushandisa zvakananga lambda calculus. Chigumisiro chichave chakafanana. Shandisa mitemo iyi zvakajeka, tinowana:
Uye izvi zvakangofanana nezvakaratidzwa mune yekutanga yakapfupikiswa yekupinda:
Ngatitarisei shizha zvakare, kumusoro kwaro:
Pane zvimwe zvinovhiringa nekuvhiringa zvinhu "E" na "D" pano, asi neizvi tinoreva "P" na "Q", saka tinogona kunyora chirevo nekuchiongorora (ona kuti pano - mushure mekuvhiringidzika ne chiratidzo chekupedzisira - "musayendisiti asinganzwisisike" anoisa […] uye (...) kumiririra mashandisirwo ebasa):
Saka iyi ndiyo pfupiso yekutanga kuratidzwa. Kuti tione zvimwe, ngatibayei tsananguro dzeQ:
Isu tinowana chaizvo kuderedzwa kunotevera kunoratidzwa. Chii chinoitika kana tikatsiva mazwi ekuti P?
Heino mhedzisiro:
Uye ikozvino, tichishandisa chokwadi chekuti ini ibasa rinoburitsa iyo nharo pachayo, tinowana:
Oooooops! Asi iyi haisi iyo inotevera yakanyorwa mutsara. Pane kukanganisa here apa? Unclear. Nekuti, mushure mezvose, kusiyana nemamwe akawanda kesi, hapana museve unoratidza kuti mutsara unotevera unotevera kubva kune yapfuura.
Pane chakavanzika pano, asi ngatiendererei kuzasi kwebepa:
Pano 2 ndiyo nhamba yeChechi, inotarwa, semuenzaniso, nemaitiro two[a_] [b_] → a[a[b]]. Ziva kuti ichi ndicho chaicho chimiro chemutsara wechipiri kana a achionekwa se Function[r,r[р]] и b sei q. Saka isu tinotarisira kuti mhedzisiro yekuverenga iite seinotevera:
Zvisinei, kutaura mukati а[b] inogona kunyorwa se x (zvichida zvakasiyana neiyo x yakambonyorwa pabepa) - pakupedzisira tinowana mhedzisiro:
Saka, tinogona kududzira zvishoma zviri kuitika pabepa iri, asi chakavanzika chimwe chete chasara ndicho chinonzi Y.
Muchokwadi, mune combinatorial logic pane yakajairwa Y-combinator: iyo inonzi . Pakare, zvinotsanangurwa nekuti Y[f] inofanira kuenzana f[Y[f]], kana, nemamwe mazwi, kuti Y[f] haichinje kana f ikaiswa, saka inzvimbo yakatarwa ye f. (Iyo musanganiswa Y inosanganiswa ne #0 mumutauro weWolfram.)
Parizvino, iyo Y-combinator yave yakakurumbira kuvonga , zita rakadaro (uyo anga ari fan kwenguva yakareba и uye kushandisa chitoro chekutanga chewebhu maererano nemutauro uyu). Akambondiudza ega"hapana anonzwisisa kuti Y combinator chii" (Izvo zvinofanirwa kucherechedzwa kuti Y Combinator ndiyo chaiyo inobvumira makambani kudzivirira yakagadziriswa-poindi transaction...)
Iyo Y combinator (seyakagadziriswa-point combinator) yakagadzirwa kakawanda. Turing yakauya nekuitwa kwayo muna 1937, iyo yaakadaidza kuti Θ. Asi iyo tsamba "Y" papeji yedu ndiyo ine mukurumbira fixed-point combinator? Zvichida kwete. Saka "Y" yedu chii? Chimbofunga chidimbu ichi:
Asi ruzivo urwu haruna kukwana kuti utarise zvisina kujeka kuti Y chii. Zviri pachena kuti Y inoshanda kwete negakava rimwe chete; Zvinoita sekunge pane anokwana kupokana maviri anobatanidzwa, asi hazvina kujeka (zvishoma kwandiri) kuti ingani nharo dzinotora sekuisa uye zvazvinoita.
Pakupedzisira, kunyange zvazvo tichikwanisa kuita pfungwa dzezvikamu zvakawanda zvepepa, tinofanira kutaura kuti pamwero wepasi rose hazvisi pachena kuti chii chakaitwa pairi. Kunyangwe paine kutsanangura kwakawanda kunobatanidzwa mune zviri pabepa pano, zvakaringana mu lambda calculus uye kushandisa ma combinator.
Zvichida uku kuedza kugadzira "chirongwa" chiri nyore - kushandisa lambda calculus uye combinator kuita chimwe chinhu. Asi sekuwanda kwazvakaita zveinjiniya, zvakatiomera kuti titaure kuti "chimwe chinhu" ichocho chinofanira kunge chiri chii uye kuti chinangwa "chinotsanangurwa" chii.
Pane chimwezve chimiro chinoratidzwa papepa icho chakakodzera kutaura pano - kushandiswa kwemhando dzakasiyana dzemaparentheses. Masvomhu echinyakare anonyanya kushandisa maparentheses ezvese - uye mashandisirwo emabasa (semu f (x)), uye mapoka enhengo (semuna (1+x) (1-x), kana, zvishoma zviri pachena, a(1-x)) (Mumutauro weWolfram, tinopatsanura mashandisirwo akasiyana ezvibodzwa-mumabhuraketi akaenzana kutsanangura mabasa f [x] - uye maparentheses anoshandiswa chete kuita mapoka).
Pakatanga kuoneka lambda calculus, paive nemibvunzo mizhinji nezvekushandiswa kwezvibodzwa. Alan Turing aizonyora basa rose (risina kudhindwa) rine musoro”, asi kare muna 1937 akanzwa kuti aifanira kutsanangura tsananguro yemazuva ano (panzvimbo yehacky) yelambda calculus (iyo, nenzira, yakaonekwa nekuda kweChechi).
Akadaro f, inoshandiswa ku g, inofanira kunyorwa {f}(g), Kana chete f harisi iro chete hunhu, muchiitiko ichi zvinogona kuva f(g). Akabva ati lambda (as in Function[a, b]) inofanira kunyorwa se λ a[b] kana, neimwe nzira, λ a.b.
Nekudaro, pamwe pakasvika 1940 pfungwa yese yekushandisa {...} uye […]
Tarisa kumusoro kwepeji:
Mune chimiro ichi zvakaoma kunzwisisa. Mutsananguro dzeChechi, mabhuraketi amativi mana anoitirwa kubatanidza, aine chibhuraketi chakavhurika chinotsiva nguva. Uchishandisa tsananguro iyi, zvinova pachena kuti Q (inozonyorwa kuti D) yakavharirwa mumaparentheses kumagumo ndiyo iyo yekutanga lambda inoshanda kwairi.
Sikweya bracket pano hainyatso kuganhura muviri welambda; pachinzvimbo, rinomiririra kumwe kushandiswa kwechishandiso, uye hapana chinoratidza pachena panoperera muviri welambda. Pakupedzisira, zvinogona kuonekwa kuti "musayendisiti asinganzwisisike" akashandura bhaketi rekuvhara rekuvhara kuita bhaketi rakatenderera, nekudaro kushandisa zvinobudirira tsananguro yeChechi - uye nekudaro kumanikidza kutaura kuverengerwa sezvakaratidzwa papepa.
Saka chidimbu chidiki ichi chinorevei zvakadaro? Ini ndinofunga izvi zvinoratidza kuti peji rakanyorwa muma1930s, kana kuti kwete nguva refu yapfuura, sezvo kokorodzano dzemaparentheses dzakanga dzisati dzagadzikana kusvika panguva iyoyo.
Saka izvi zvaive nerunyoro rwaani?
Saka, izvi zvisati zvaitika takataura pamusoro pezvakanyorwa papeji. Asi zvakadiniko nezvaakanyora chaizvoizvo?
Mumiriri ari pachena weichi basa angave Alan Turing pachake, sezvo, shure kwezvose, peji iri mukati mebhuku rake. Panyaya yezviri mukati, zvinoita sekunge pasina chinhu chisingaenderane nepfungwa yekuti Alan Turing angadai akazvinyora - kunyangwe paakatanga kubata lambda calculus mushure mekugamuchira bepa reChechi mukutanga kwa1936.
Zvakadini nekunyora nemaoko? NdezvaAlan Turing here? Ngatitarisei mienzaniso mishoma yasara yatinoziva zvechokwadi yakanyorwa naAlan Turing:
Rugwaro rwunopihwa sezviri pachena runotaridzika rwakasiyana kwazvo, asi zvakadiniko nezvechinyorwa chinoshandiswa murugwaro? Zvirinani, mukuona kwangu, hazviratidzike sezviri pachena - uye munhu anogona kufunga kuti chero mutsauko unogona kukonzerwa chaizvo nenyaya yekuti masampuli aripo (anoratidzwa mudura) akanyorwa, sekutaura, "pamusoro, ” nepo redu peji rinonyatsoratidza basa rekufunga.
Zvakazotinakira kuferefeta kwedu kuti dura raTuring rine peji raakanyora , inodiwa pakunyorwa. Uye kana tichienzanisa aya mavara mavara netsamba, anotaridzika akafanana neni (aya manotsi akagadzirwa mukati Turing paaidzidza , saka pakanyorwa kuti “nzvimbo yemashizha”):
Ini ndaida kuongorora izvi zvakare, saka ndakatumira samples , nyanzvi yekunyora nemaoko (uye munyori wezvinetso zvekunyora) wandakafara kusangana naye kamwe chete - nekungopa bepa redu se "Sample 'A'" uye muenzaniso uripo wekunyora kwaTuring se "Sample 'B'." Mhinduro yake yaive yekupedzisira uye yakaipa: "Nzira yekunyora yakasiyana zvachose. Panyaya yehunhu, sampuli "B" munyori ane kukurumidza uye intuitive kufunga maitiro pane muenzaniso "A" munyori.".
Ndakanga ndisati ndanyatsogutsikana, asi ndakafunga kuti yakanga yava nguva yekutarisa dzimwe nzira.
Saka kana zvikaitika kuti Turing haana kuinyora, saka ndiani akazvinyora? Norman Routledge akandiudza kuti akagamuchira bhuku racho kubva kuna Robin Gandy, uyo akanga ari muurayi waTuring. Saka ndakatumira "Sample "C"" kubva kuGandhi:
Asi mhedziso yekutanga yaSheila yaive yekuti masampuli matatu angangove akanyorwa nevanhu vatatu vakasiyana, zvakare achicherekedza kuti sampuli "B" yakabva ku "mufungo unokurumidza zvikuru—uyo sezvingabvira angava anodisa zvikuru kutsvaka mhinduro dzisina kujairika dzezvinetso" (Ndinoona zvichizorodza kuti nyanzvi yekunyora nemaoko yemazuva ano yaizopa ongororo yerunyoro rwaTuring, zvichipihwa kuti munhu wese akanyunyuta sei nezvekunyora kwake mumabasa echikoro eTuring 1920s.)
Zvakanaka, panguva ino zvaiita sekunge Turing naGandhi vange vanzi "vafungidzirwe". Saka ndiani angadai akanyora izvi? Ndakatanga kufunga vanhu vangave vakweretwa naTuring bhuku rake. Ehe, ivo vanofanirwawo kukwanisa kuita masvomhu vachishandisa lambda calculus.
Ndakafunga kuti munhu wacho anofanira kunge achibva kuCambridge, kana kuEngland, akapihwa watermark pabepa. Ndakazvitora sefungidziro inoshanda yekuti 1936 kana zvakadaro yaive nguva yakanaka yekunyora izvi. Saka Turing aiziva uye kutaurirana ndiani panguva iyoyo? Kwenguva ino yenguva, takawana runyorwa rwevadzidzi vese nevadzidzisi vemasvomhu kuKing's College. (Paiva nevadzidzi 13 vaizivikanwa vakadzidza kubva muna 1930 kusvika muna 1936.)
Uye kwavari, mumiriri ainyanya kuvimbisa airatidzika . Aive zera naTuring, shamwari yake yenguva refu, uye aifarirawo zvemasvomhu - muna 1933 akatoburitsa bepa rezvatiri kudaidza zvino. : 0.12345678910111213… (yakatorwa na 1, 2, 3, 4,…, 8, 9, 10, 11, 12,…, uye imwe yenhamba shoma mupfungwa yekuti bhuroka yega yega yemanhamba inoitika ine mukana wakaenzana).
Muna 1937, akatoshandisa Dirac's gamma matrices, sezvakataurwa mubhuku raDirac, kugadzirisa. . (Sezvinoitika, makore gare gare ndakava fan hombe yekuverenga gamma matrix).
Sezvo atanga kudzidza masvomhu, Champernowne akave pasi pesimba (zvakare kuKing's College) uye akazova nyanzvi yezvehupfumi, kunyanya kuita basa pakusaenzana kwemari. (Zvisinei, muna 1948 akashandawo naTuring kugadzira - chirongwa che chess, chakazova chekutanga munyika kuti chiitwe pakombuta).
Asi ndaigona kuwana kupi muenzaniso werunyoro rwaChampernowne? Nenguva isipi ndakawana mwanakomana wake Arthur Champernowne paLinkedIn, uyo, zvisingaite, aive nedhigirii remasvomhu uye aishandira Microsoft. Akataura kuti baba vake vakataura naye zvishoma nezvebasa raTuring, kunyangwe iye asina kutaura nezve combinators. Akanditumira sampuli yerunyoro rwababa vake (chidimbu che algorithmic mimhanzi yekuumbwa):
Unogona kukurumidza kutaura kuti zvinyorwa hazvina kuenderana (macurls nemiswe mune mavara f murunyoro rwaChampernowne, nezvimwewo)
Saka angave ani mumwe? Ndagara ndichiyemura , munzira dzakawanda murairidzi kuna Alan Turing. Newman akatanga kufarira Turing "mechanization yemasvomhu"Aive shamwari yake yenguva refu, uye makore akazotevera akazova mukuru wake pane chimwe chirongwa chekombuta muManchester. (Zvisinei nekufarira kwake kuverenga, Newman anogara anoratidzika kunge akazviona semuongorori wepamusoro, kunyangwe mhedziso dzake dzakatsigirwa nehumbowo husina kururama hwaakatora kubva. ).
Zvakanga zvisina kunetsa kuwana sampuli yerunyoro rwaNewman - uye zvakare, aiwa, zvinyorwa zvemawoko zvaisaenderana.
"Trace" yebhuku
Saka, pfungwa yekuzivisa runyoro yakakundikana. Uye ndakafunga kuti nhanho yaitevera yaifanira kutora kwaiva kuedza kuronda nekamwe muudzame kuti chii chaizvo chaiitika nebhuku randakanga ndakabata mumaoko angu.
Saka chekutanga pane zvese, ndeipi yaive nyaya refu naNorman Rutledge? Akapinda King's College, Cambridge muna 1946 uye akasangana naTuring (hongu, vese vaive ngochani). Akapedza koreji muna 1949, akabva atanga kunyora thesis yake yePhD naTuring sechipangamazano wake. Akagamuchira PhD yake muna 1954, achishanda pane masvomhu logic uye recursion theory. Akagamuchira bhezari kuKing's College, uye pakazosvika 1957 akava mukuru wedhipatimendi remasvomhu ikoko. Angadai akaita izvi hupenyu hwake hwose, asi aive nezvakawanda zvaanofarira (mimhanzi, unyanzvi, zvivakwa, masvomhu ekuvaraidza, dzinza, nezvimwewo). Muna 1960 akachinja gwara rake redzidzo ndokuva mudzidzisi paEton, uko mazera evadzidzi (kusanganisira ini) akashanda (uye akadzidza) uye akaratidzirwa kune yake eclectic uye dzimwe nguva kunyange ruzivo rwechienzi.
Norman Routledge angave akanyora peji iyi isinganzwisisike iye pachake? Aiziva lambda calculus (asi, zvakangoitika, akazvitaura patakanga tichinwa tii muna 2005 kuti aigara achizviona "zvichivhiringidza"). Zvisinei, manyorero ake anomusiya pakarepo se“musayendisiti asinganzwisisike” anobvira.
Iri peji ringave rakabatana neimwe mudzidzi waNorman, pamwe kubva paakanga achiri kuCambridge? Ndinokahadzika. Nekuti handifunge kuti Norman akambodzidza lambda calculus kana chero zvakadaro. Ndichiri kunyora chinyorwa ichi, ndakaona kuti Norman akange anyora bepa muna 1955 nezve kugadzira pfungwa pa "electronic computers" (uye kugadzira conjunctive normal forms, sebasa rakavakirwa-mukati izvozvi. ) Pandakaziva Norman, aifarira zvikuru kunyora zvishandiso zvemakomputa chaiwo (matangiro ake aive "NAR", uye akadana zvirongwa zvake "NAR...", semuenzaniso, "NARLAB", chirongwa chekugadzira zvinyorwa zvemavara uchishandisa punched. gomba "patterns" "pabepa tepi). Asi haana kumbotaura nezve theoretical modhi yekombuta.
Ngativerengei chinyorwa chaNorman mukati mebhuku zvishoma. Chekutanga chatichaona ndechekuti anotaura nezve ".tichigovera mabhuku anobva muraibhurari yomushakabvu" Uye kubva pamazwi zvinoita sekunge zvese zvakaitika nekukurumidza mushure mekufa kwemurume uyu, zvichiratidza kuti Norman akagamuchira bhuku nguva pfupi Turing afa muna 1954, uye kuti Gandhi akange arishaya kwenguva yakareba. Norman anoenderera mberi achiti akawana mabhuku mana zvechokwadi, maviri esvomhu dzakachena uye maviri ezvidzidzo zvefizikisi.
Akabva ati akapa"imwe kubva mubhuku refizikisi (rudzi rwe, )»«Kuna Sebag Montefiore, jaya rinofadza raungarangarira [George Rutter]" Zvakanaka, saka ndiani? Ndakachera List yangu isingawanzo shandiswa . (Ndinofanira kutaura kuti pakuivhura handina kukwanisa kuita asi kucherechedza mitemo yayo kubva 1902, yekutanga iyo, pasi pemusoro wekuti "Kodzero dzeVatendi", yakanzwika kusetsa: "Pfeka nemavara eSangano").
Zvinofanira kuwedzerwa kuti pamwe ndingadai ndisina kumbobatana nesangano iri kana kugamuchira bhuku iri dai pasina kukurudzirwa kweshamwari yeEton inonzi , akanga achironga kubvira aine makore 12 kuti rimwe zuva azova Prime Minister, asi zvinosuruvarisa kuti akafa aine makore 21 ezera).
Asi chero zvakadaro, kwaingova nevashanu vevanhu vakanyorwa nesurname Sebag-Montefiore, vaine huwandu hwakawanda hwemazuva ekudzidza. Zvakanga zvisina kuoma kunzwisisa kuti zvakanga zvakakodzera . Nyika diki, sezvazvinozoitika, mhuri yake yaive neBletchley Park isati yaitengesa kuhurumende yeBritish muna 1938. Uye muna 2000, Sebag-Montefiore akanyora - izvi ndizvo, zvingangoita, nei muna 2002 Norman akasarudza kumupa bhuku iro Turing aiva naro.
Zvakanaka, zvakadini nemamwe mabhuku aNorman akawana kubva kuTuring? Ndisina imwe nzira yokuziva nayo zvakaitika kwavari, ndakaodha kopi yewiro yaNorman. Chikamu chekupedzisira chechido chaive zvakajeka muchimiro chaNorman:
Wiri yaiti mabhuku aNorman ngaasiiwe kuKing's College. Uye kunyangwe muunganidzwa wake wakazara wemabhuku uchiita kunge usipo, mabhuku maviri aTuring ezvemasvomhu chaiwo, aakataura mutsamba yake, zvino akachengetwa muKing's College Library.
Mubvunzo unotevera: chii chakaitika kune mamwe mabhuku aTuring? Ndakatarisa kuda kwaTuring, kwakazoita kuvasiya vese kuna Robin Gandy.
Gandhi aive mudzidzi wemasvomhu paKing's College, Cambridge, uyo akave shamwari naAlan Turing mugore rake rekupedzisira kukoreji muna 1940. Pakutanga kwehondo, Gandhi akashanda muredhiyo uye radar, asi muna 1944 akagoverwa kuchikamu chimwe chete neTuring uye akashanda pakunyora kwekutaura. Uye pashure pehondo, Gandhi akadzokera Cambridge, nokukurumidza kugamuchira doctorate yake, uye Turing akava chipangamazano wake.
Basa rake rechiuto sezviri pachena rakamuita kuti afarire physics, uye rondedzero yake, yakapedzwa muna 1952, yakanzi . Zvaiita senge Gandhi ari kuyedza kuita zvimwe kuratidza dzidziso dzemuviri maererano nemasvomhu. Anotaura nezvazvo и , asi kwete nezveTuring michina. Uye kubva pane zvatinoziva iye zvino, ndinofunga tinogona kugumisa kuti akapotsa pfungwa yacho. Uye zvechokwadi, yakapokana kubva pakutanga kwe1980s kuti maitiro emuviri anofanirwa kutorwa se "akasiyana computations" -somuenzaniso, seTuring muchina kana cellular automata-panzvimbo pekuti dzidziso dzinofanirwa kutorwa. (Gandhi anokurukura zvakanaka kurongeka kwemhando dzakabatanidzwa mudzidziso dzemuviri, achiti semuenzaniso "Ini ndinotenda kuti kurongeka kwechero nhamba yedesimali inogoneka mubhinari fomu isingasviki masere"). Akataura kuti "Chimwe chezvikonzero nei yemazuva ano quantum field theory yakaoma kudaro ingori nekuti inobata nezvinhu zverudzi rwakaoma kunzwisisa - functionals of function...", izvo zvinoreva kuti "isu tinogona kutora mhando huru yekushandiswa kwakajairika sechiyero chekufambira mberi kwemasvomhu".)
Gandhi anotaura Turing kakawanda mudissertation, achitaura musumo kuti ane chikwereti kuna A. M. Turing, uyo "akatanga akwevera pfungwa dzake dzisina kunanga kukuverenga kweChechi” (kureva lambda calculus), kunyange hazvo rondedzero yake ine humbowo hwakawanda hwe lambda.
Mushure mekudzivirira dissertation yake, Gandhi akatendeukira kune akachena masvomhu logic uye kweanopfuura makumi matatu emakore akanyora zvinyorwa pamwero weimwe chete pagore, uye zvinyorwa izvi zvakabudirira kutorwa munharaunda yepasi rose mathematical logic. Akatamira kuOxford muna 1969 uye ndinofunga kuti ndinofanira kunge ndakasangana naye muhuduku hwangu, kunyange zvazvo ndisingazviyeuki.
Gandhi sezviri pachena akanamata Turing zvakanyanya uye akataura kazhinji nezvake mumakore akazotevera. Izvi zvinomutsa mubvunzo wekuunganidzwa kwakazara kwemabasa aTuring. Nguva pfupi Turing afa, Sarah Turing naMax Newman vakakumbira Gandhi - semutongi wake - kuti aronge kuburitswa kwemabhuku aTuring asina kudhindwa. Makore akafamba uye ratidza kushushikana kwaSarah Turing panyaya iyi. Asi neimwe nzira Gandhi haana kumbobvira aita kunge akaronga kuisa mapepa aTuring pamwechete.
Gandhi akafa muna 1995 asina kuunza pamwechete mabasa akapedzwa. - mutsoropodzi wezvinyorwa uye munyori wehupenyu , uyo akasangana naTuring kuKing's College, aive mumiriri wezvinyorwa waTuring, uye akazotanga kushanda pamabasa akaunganidzwa aTuring. Chinonyanya kukakavara chaiita sevhoriyamu yemasvomhu, yaakakwezva mudzidzi wake wekutanga akapedza kudzidza, Robin Gandy, mumwe mudzidzi. , akawana tsamba kuna Gandhi pamusoro pemabasa akaunganidzwa akanga asina kutangwa kwemakore 24. ( pakupedzisira akaonekwa muna 2001 - 45 makore mushure mekusunungurwa kwavo).
Asi zvakadini nemabhuku aiva naTuring pachake? Ndichiramba ndichiedza kuvatsvaga, kwandakazomira kwaive nemhuri yekwaTuring, uye kunyanya mwanakomana wemukoma waTuring, (uyo ari chaizvo Sir Dermot Turing, nekuda kwekuti aive , zita iri harina kupfuudza kwaari kuburikidza naAlan mumhuri yeTuring). Dermot Turing (uyo achangonyora ) akandiudza nezve "ambuya vaTuring" (aka Sarah Turing), imba yake sezviri pachena yakagovera gonhi rebindu nemhuri yake, uye zvimwe zvinhu zvakawanda pamusoro paAlan Turing. Akandiudza kuti mabhuku aAlan Turing akanga asati ambovapo mumhuri yavo.
Saka ndakadzokera kukuverenga zvidikanwi uye ndakaona kuti muurayi waGandhi aive mudzidzi wake Mike Yates. Ndakadzidza kuti Mike Yates akasiya basa sepurofesa makore makumi matatu apfuura uye zvino anogara kuNorth Wales. Akataura kuti mumakumi emakore aakashanda pamasvomhu uye computational theory, haana kumbobvira abata komputa - asi pakupedzisira akazviita paakaenda pamudyandigere (uye, izvi zvakaitika, nguva pfupi mushure mekunge awana chirongwa ichi. ) Akataura kuti zvaishamisa sei kuti Turing akange ave nemukurumbira, uye kuti paakasvika kuManchester makore matatu chete mushure mekufa kwaTuring, hapana aitaura nezvaTuring, kunyangwe Max Newman paakadzidzisa kosi yepfungwa. Nekudaro, Gandy akazotaura nezvekufara kwaakaita nezve kubata nekuunganidzwa kwemabasa kwaTuring, uye pakupedzisira akasiya ese kuna Mike.
Mike aizivei nezvemabhuku aTuring? Akawana rimwe remabhuku akanyorwa nemaoko aTuring, ayo Gandhi asina kupa kuKing's College nokuti (zvinoshamisa) Gandhi akaishandisa sechifukidziro chezvinyorwa zvaakachengeta pamusoro pezviroto zvake. (Turing akachengetawo zvinyorwa zvezviroto zvake, izvo zvakaparadzwa mushure mekufa kwake.) Mike akati bhuku rekunyorera rakanga richangobva kutengeswa paauction yeinenge miriyoni yemadhora. Uye kuti zvimwe angadai asina kufunga kuti pakati pezvinhu zvaGandhi paive neTuring materials.
Zvaiita sokuti zvose zvataizosarudza zvakanga zvaoma, asi Mike akandikumbira kuti nditarise bepa riya rakanga risinganzwisisike. Uye pakarepo akati: ".Uku ndiko kunyora kwaRobin Gandy!»Akataura kuti akange aona zvinhu zvakawanda mumakore apfuura. Uye aiva nechokwadi. Akataura kuti akanga asingazivi zvakawanda nezve lambda calculus uye akanga asingagoni kunyatsoverenga peji, asi aiva nechokwadi chokuti Robin Gandy akanga anyora.
Takadzokera kuna mazvikokota wedu wekunyora nemaoko nemasamples akawanda achibva abvuma kuti hongu, zvaivepo zvaienderana nerunyoro rwaGandhi. Saka takazofunga kuti: Robin Gandy akanyora kuti bepa risinganzwisisike. Harina kunyorwa naAlan Turing; yakanyorwa nemudzidzi wake Robin Gandy.
Chokwadi, zvimwe zvakavanzika zvichiripo. Turing anonzi akakweretesa Gandhi bhuku racho, asi riini? Chimiro che lambda calculus notation chinoita kuti zviite sekunge zvaive zvakapoteredza 1930s. Asi zvichibva pane zvakataurwa pamusoro peDissertation yaGandhi, angangodaro aisazoita chero chinhu nelambda calculus kusvika mukupera kwema1940. Mubvunzo unobva wamuka kuti sei Gandhi akanyora izvi. Izvi hazviratidzike kunge zvine hukama zvakananga nedzidziso yake, saka zvinogona kunge zviri paakatanga kuyedza kufunga lambda calculus.
Ndinokahadzika kuti tichazomboziva chokwadi, asi chokwadi chaive chinonakidza kuyedza kuzvifunga. Pano ndinofanira kutaura kuti rwendo urwu rwose rwakaita zvakawanda kuwedzera kunzwisisa kwangu kwekuoma kwenhoroondo dzemabhuku akafanana emazana emakore apfuura, izvo, kunyanya, ini zvangu, zvinogona kuva. Izvi zvinoita kuti ndifunge kuti zvirinani ndiite chokwadi chekuti ndinotarisa pamapeji avo ese - kuti ndingoona zvingave zvinonakidza ipapo...
Tinotenda nerubatsiro kuna: Jonathan Gorard (Cambridge Private Studies), Dana Scott (Mathematical Logic), naMatthew Szudzik (Mathematical Logic).
NezvekushanduraDudziro yechinyorwa chaStephen Wolfram "".
Ndinotaura kutenda kwangu kwakadzama и kuti vabatsirwe mukushandura nekugadzirira kuburitswa.
Unoda kudzidza kuronga muWolfram Mutauro?
Tarisa vhiki nevhiki .
... Ready .
paWolfram Mutauro.
Source: www.habr.com