Littafin Alan Turing da bayanin kula mai ban mamaki - Binciken Kimiyya

Fassarar asali akan bulogi na

Ta yaya na sami wannan littafin?

A watan Mayu 2017, na sami imel daga tsohon malamina na sakandare mai suna George Rutter wanda a ciki ya rubuta: “Ina da kwafin babban littafin Dirac a cikin Jamusanci (Die Prinzipien der Quantenmechanik), wanda na Alan Turing ne, kuma bayan karanta littafinku. Ra'ayi Maker, Ya zama a gare ni kai tsaye cewa kai ne ainihin mutumin da ke bukata" Ya bayyana mani cewa ya karbi littafin daga wurin wani malamina (wanda ya rasu a lokacin). Norman Rutledge, wanda na san abokin Alan Turing ne. George ya ƙare wasiƙarsa da jimlar: "Idan kuna son wannan littafin, zan iya ba ku lokacin da kuka zo Ingila na gaba".

Bayan shekaru biyu, a cikin Maris 2019, na isa Ingila a zahiri, bayan haka na shirya saduwa da George don karin kumallo a wani ƙaramin otal a Oxford. Muka ci, muna ta hira muna jiran abinci ya daidaita. Bayan haka, lokaci ne mai kyau don tattauna littafin. George ya shiga cikin jakarsa kuma ya fitar da wani tsari mai kyau da aka tsara, na al'ada na ilimi daga tsakiyar 1900s.

Na bude murfin, ina mamakin ko akwai wani abu a bayansa da ya karanta: “Dukiyar Alan Turing" ko wani abu makamancin haka. Amma, abin takaici, wannan ya zama ba haka lamarin yake ba. Duk da haka, an haɗa shi da bayanin rubutu mai shafuka huɗu daga Norman Routledge zuwa George Rutter, wanda aka rubuta a cikin 2002.

Na san Norman Rutledge lokacin da nake ɗalibi makarantar sakandare в Eton a farkon shekarun 1970. Malamin lissafi ne da ake yi wa lakabi da "Nutty Norman." Ya kasance malami mai daɗi ta kowace hanya kuma yana ba da labarai marasa iyaka game da ilimin lissafi da sauran abubuwa masu ban sha'awa iri-iri. Shi ne ke da alhakin tabbatar da cewa makarantar ta sami kwamfuta (wanda aka tsara ta amfani da tef mai faɗin naushi) - ya kasance. kwamfuta ta farko da na taba amfani da ita.

A lokacin, ban san kome ba game da tarihin Norman (tuna, wannan ya dade kafin Intanet). Abin da na sani shi ne "Dr. Rutledge." Ya sha ba da labarai game da mutanen Cambridge sau da yawa, amma bai taɓa ambata Alan Turing a cikin labarunsa ba. Tabbas, har yanzu Turing bai shahara sosai ba (ko da yake, kamar yadda ya bayyana, na riga na ji labarinsa daga wani wanda ya san shi a ciki). Bletchley Park (gidan da cibiyar boye bayanan ta kasance a lokacin yakin duniya na biyu)).

Alan Turing bai yi suna ba sai 1981, lokacin da na fara zama ya fara koyon shirye-shirye masu sauki, ko da yake to har yanzu a cikin mahallin salula automata, kuma ba Turing inji.

Lokacin ba zato ba tsammani wata rana, yayin duba ta cikin kundin katunan a cikin ɗakin karatu Caltech, Na ci karo da wani littafi "Alan M. Turing", mahaifiyarsa Sarah Turing ce ta rubuta. Littafin ya ƙunshi bayanai da yawa, ciki har da game da ayyukan kimiyya da ba a buga ba a Turing kan ilmin halitta. Duk da haka, ban koyi wani abu game da dangantakarsa da Norman Routledge ba, tun da yake ba a ambaci wani abu game da shi a cikin littafin ba (ko da yake, kamar yadda na gano, Sarah Turing. yayi magana da Norman game da wannan littafi, kuma Norman ma ya gama rubutawa bita don shi).

Shekaru goma bayan haka, mai tsananin sha'awar Turing da nasa (sa'an nan ba a buga ba) aikin ilmin halitta, Na ziyarci Turing archive в Yin Karatu a King's College Cambridge. Ba da daɗewa ba, da na san abin da suke da shi na aikin Turing, kuma na ɗan ɗauki lokaci a kai, na yi tunanin cewa ma zan iya neman ganin wasiƙunsa na kansa. Yayin duba ta, na gano wasu haruffa daga Alan Turing zuwa Norman Routledge.

A lokacin an buga shi biography Andrew Hodges, wanda ya yi yawa don tabbatar da cewa a ƙarshe Turing ya zama sananne, ya tabbatar da cewa Alan Turing da Norman Routledge abokai ne, kuma Turing shi ne mashawarcin kimiyya na Norman. Ina so in tambayi Routledge game da Turing, amma a lokacin Norman ya riga ya yi ritaya kuma ya jagoranci rayuwa ta keɓe. Duk da haka, lokacin da na kammala aiki a kan littafin "Wani sabon nau'in kimiyya” a shekara ta 2002 (bayan keɓe ni na shekara goma), na bi sawun shi kuma na aika masa da kwafin littafin mai taken “Ga malamin lissafi na na ƙarshe.” Sai ni da shi kadan rubuta, kuma a cikin 2005 na dawo Ingila na shirya saduwa da Norman don shan shayi a wani otal mai alfarma a tsakiyar London.

Mun yi hira mai daɗi game da abubuwa da yawa, ciki har da Alan Turing. Norman ya fara tattaunawarmu ta hanyar gaya mana cewa a zahiri ya san Turing, galibi a zahiri, shekaru 50 da suka gabata. Amma duk da haka yana da abin da zai faɗa game da shi da kansa: “Ya kasance ba shi da alaƙa". "Ya kyalkyace da dariya". "Ba zai iya magana da masu ilimin lissafi ba". "Ya kasance yana tsoron batawa mahaifiyarsa rai". "Ya fita da rana ya yi gudun fanfalaki". "Bai kasance mai kishi ba" Tattaunawar ta koma ga halin Norman. Ya ce duk da cewa ya yi ritaya shekaru 16, har yanzu yana rubuta labarai don "Jaridar lissafi"saboda haka, a cikin kalmominsa,"gama duk ayyukan kimiyyar ku kafin tafiya zuwa duniya ta gaba", Inda ya k'ara da wani lallausan murmushi."duk gaskiyar ilimin lissafi tabbas za a bayyana" Lokacin da liyafar shayi ta ƙare, Norman ya sa jaket ɗin fata ya nufi wajen moped ɗinsa, gaba ɗaya ya manta fashe-fashen da suka kawo cikas ga zirga-zirga a London a wannan rana.

Wannan shine karo na ƙarshe da na ga Norman; ya mutu a cikin 2013.

Bayan shekaru shida ina zaune a karin kumallo tare da George Rutter. Ina da wata sanarwa daga Rutledge tare da ni, wanda aka rubuta a cikin 2002 a cikin rubutun hannu na musamman:

Na farko na zazzage bayanin kula. Ta fad'a kamar yadda ta saba:

Na karɓi littafin Alan Turing daga abokinsa kuma mai zartarwa Robina Gandy (a Kwalejin King ya kasance tsari na yau da kullun don ba da littattafai daga tarin matattu, kuma na zaɓi tarin wakoki. A. E. Houseman daga littattafai Ivor Ramsay a matsayin kyauta mai dacewa (shi shugaban kasa ne kuma ya yi tsalle daga ɗakin sujada [a cikin 1956])…

Daga baya a takaice ya rubuta:

Kuna tambaya inda wannan littafi ya ƙare - a ganina ya kamata ya je wurin wanda ya yaba duk abin da ke da alaka da aikin Turing, don haka makomarsa ta dogara da ku.

Stephen Wolfram ya aiko mani da littafinsa mai ban sha'awa, amma ban nutse cikinsa sosai ba.

Ya kammala da taya George Rutter murna don samun ƙarfin hali don ƙaura (na ɗan lokaci, kamar yadda ya faru) zuwa Ostiraliya bayan ya yi ritaya, yana mai cewa shi da kansa "zai yi wasa tare da ƙaura zuwa Sri Lanka a matsayin misali na arha kuma mai kama da lotus"amma ya kara da cewa"abubuwan da ke faruwa a yanzu suna nuni da cewa bai kamata ya yi haka ba"(a fili ma'ana yakin basasa in Sri Lanka).

To me ke boye a cikin zurfafan littafin?

To me na yi da kwafin littafin Jamus da Paul Dirac ya rubuta wanda ya taɓa kasancewa na Alan Turing? Ba na karanta Jamusanci, amma ina da akwai kwafin littafi guda a cikin Turanci (wanda shine asalin harshensa) bugun daga 1970s. Duk da haka, wata rana a karin kumallo ya yi kama da cewa ya kamata in shiga cikin littafin a hankali a shafi na shafi. Bayan haka, wannan al'ada ce ta kowa lokacin da ake hulɗa da littattafan antiquarian.

Ya kamata a lura cewa kyawun gabatarwar Dirac ya burge ni. An buga littafin a shekara ta 1931, amma tsarinsa tsantsa (kuma, a, duk da shingen harshe, zan iya karanta lissafin lissafi a cikin littafin) kusan daidai yake da an rubuta shi a yau. (Ba na so in ba da fifiko ga Dirac a nan, amma abokina Richard Feynman ya gaya mani cewa, aƙalla a ra'ayinsa, nunin Dirac shine monosyllabic. Norman Rutledge ya gaya mani cewa abokansa ne a Cambridge ɗan Dirac, wanda ya zama graph theorist. Norman ya ziyarci gidan Dirac sau da yawa kuma ya ce "babban mutum" wani lokacin da kansa ya ɓace a bango, yayin da wuri na farko yana cike da wasanin gwada ilimi. Ni kaina, da rashin alheri, ban taɓa saduwa da Paul Dirac ba, kodayake an gaya mini cewa bayan ya bar Cambridge daga ƙarshe zuwa Florida, ya rasa yawancin taurinsa na farko kuma ya zama ɗan adam).

Amma bari mu koma littafin Dirac, wanda na Turing ne. A shafi na 9, na lura da jakunkuna da ƙananan rubutu a cikin gefe, an rubuta da fensir. Na ci gaba da jujjuya shafukan. Bayan surori kaɗan, bayanin kula ya ɓace. Amma sai, ba zato ba tsammani, na sami wani rubutu a maƙalla shafi na 127 da ke cewa:

An rubuta shi cikin Jamusanci a daidaitaccen rubutun Jamusanci. Kuma da alama tana da wani abu da zai yi da ita Lagrangian makanikai. Na yi tunanin cewa mai yiwuwa wani ya mallaki wannan littafi kafin Turing, kuma wannan dole ne ya zama bayanin kula da mutumin ya rubuta.

Na ci gaba da lefe cikin littafin. Babu bayanin kula. Kuma na yi zaton ba zan iya samun wani abu dabam. Amma sai, a shafi na 231, na gano alamar alamar alama - tare da rubutun da aka buga:

Zan kawo karshen gano wani abu dabam? Na ci gaba da lefe cikin littafin. Sannan, a karshen littafin, a shafi na 259, a sashen nazarin ka'idar electron, na gano kamar haka:

Na buɗe wannan takarda:

Nan take na gane mene ne lambda calculus gauraye da masu haɗawa, amma ta yaya wannan ganye ya ƙare a nan? Bari mu tuna cewa wannan littafi littafi ne game da makanikan ƙididdiga, amma ƙayyadaddun ƙayyadaddun ya yi magana game da ilimin lissafi, ko abin da yanzu ake kira ka'idar lissafi. Wannan shi ne yanayin rubuce-rubucen Turing. Na yi mamaki ko Turing da kansa ya rubuta wannan bayanin?

Ko da lokacin karin kumallo, na bincika Intanet don misalan rubutun hannu na Turing, amma ban sami misalai ta hanyar ƙididdiga ba, don haka ba zan iya yanke shawara game da ainihin ainihin rubutun hannu ba. Kuma nan da nan sai da mu tafi. Na tattara littafin a hankali, na shirya don tona asirin wane shafi ne da wanda ya rubuta, na tafi da shi.

Game da littafin

Da farko, bari mu tattauna littafin da kansa. "Ƙa'idodin Ƙimar Makanikai» An buga filayen Dirac a cikin Turanci a cikin 1930 kuma ba da daɗewa ba aka fassara su zuwa Jamusanci. (Mukaddamar Dirac ta kasance ranar 29 ga Mayu, 1930; na mai fassara ne - Werner Bloch - Agusta 15, 1930.) Littafin ya zama wani ci gaba a cikin ci gaban ƙididdiga makanikai, tsare-tsare kafa bayyananne ka'idar don yin lissafin, da kuma, a tsakanin sauran abubuwa, bayyana Dirac ta Hasashen na positron, wanda zai bude a 1932.

Me yasa Alan Turing ya sami littafi a cikin Jamusanci ba Ingilishi ba? Ban san wannan tabbas ba, amma a wancan lokacin Jamusanci shine babban harshen kimiyya, kuma mun san cewa Alan Turing yana iya karanta shi. (Bayan haka, da sunan shahararren sa inji работы Turing «A kan lambobi masu ƙididdigewa tare da aikace-aikacen zuwa Matsalolin Ƙimar Ƙaddamarwa (Enscheidungsproblem)" kalma ce ta Jamusanci mai tsayi sosai - kuma a cikin babban ɓangaren labarin yana aiki tare da alamomin Gothic mara kyau a cikin nau'in "haruffa na Jamusanci" waɗanda ya yi amfani da su maimakon, alal misali, alamun Girkanci).

Shin Alan Turing ya sayi wannan littafi da kansa ko kuwa aka ba shi? Ban sani ba. A cikin murfin littafin Turing akwai alamar fensir "20/-", wanda shine ma'auni na "shilling 20", kama da £ 1. A shafi na dama akwai "26.9.30" da aka goge, mai yiwuwa ma'ana 26 ga Satumba, 1930, watakila ranar da aka fara siyan littafin. Sannan, a hannun dama, lambar gogewa ta “20.” Wataƙila farashin kuma. (Shin wannan shine farashin a Reichsmarks, zato cewa an sayar da littafin a Jamus? A cikin waɗannan kwanaki, 1 Reichsmark ya kai kimanin 1 schilling, farashin Jamus zai yiwu a rubuta shi a matsayin "RM20" misali.) A ƙarshe, a kan murfin baya na ciki akwai "c 5/-" - watakila wannan, (tare da babban girma). rangwame) farashin littafin da aka yi amfani da shi.

Bari mu kalli manyan kwanakin rayuwar Alan Turing. Alan Turing an haife shi ranar 23 ga Yuni, 1912 (kwatsam, daidai shekaru 76 da suka gabata Mathematica 1.0 saki). A cikin kaka na 1931 ya shiga King's College, Cambridge. Ya sami digirinsa na farko bayan kammala karatun shekaru uku a 1934.

A cikin 1920s da farkon 1930s, injiniyoyin ƙididdiga ya kasance batu mai zafi, kuma tabbas Alan Turing yana sha'awar hakan. Daga ma’ajiyar tarihinsa mun san cewa a shekarar 1932, da zarar an buga littafin, ya samu”.Tushen lissafi na injiniyoyi masu yawa» John von Neumann (a kan Jamusanci). Mun kuma san cewa a cikin 1935 Turing ya sami aiki daga wani masanin kimiyyar lissafi na Cambridge Ralph Fowler ne adam wata a kan batun nazarin injiniyoyin ƙididdiga. (Fowler ya ba da shawarar yin lissafi dielectric akai na ruwa, wanda a zahiri matsala ce mai sarƙaƙƙiya wacce ke buƙatar cikakken bincike tare da ma'amala da ka'idar filin ƙira, wanda har yanzu ba a warware gaba ɗaya ba).

Duk da haka, yaushe kuma ta yaya Turing ya sami kwafin littafin Dirac? Ganin cewa littafin yana da ƙayyadaddun farashi, tabbas Turing ya siya ta hannu ta biyu. Wanene farkon mai littafin? Bayanan kula da ke cikin littafin da alama sun yi magana da farko tare da tsari mai ma'ana, lura da cewa ya kamata a ɗauki wasu alaƙar ma'ana a matsayin axiom. To, bayanin da ke shafi na 127 fa?

To, watakila hakan ya kasance kwatsam, amma daidai a shafi na 127 - Dirac yayi magana game da adadi. ka'idar mafi ƙarancin aiki kuma ya kafa harsashin ginin Hanyar Feynman mai mahimmanci - wanda shine ginshiƙi na duk tsarin ƙididdiga na zamani. Menene bayanin ya kunsa? Yana ƙunshe da tsawo na Equation 14, wanda shine ma'auni na lokacin juyin halittar jimla. Marubucin bayanin kula ya maye gurbin Dirac A don amplitude tare da ρ, watakila don haka yana nuna wani abu na farko (misali yawan ruwa) na Jamusanci. Daga nan marubucin yayi ƙoƙarin faɗaɗa aikin ta ikon ℏ (Planck ta akai-akai, raba ta 2π, wani lokaci ana kiransa Dirac akai-akai).

Amma da alama ba a sami bayanai masu fa'ida da yawa da za a tattara daga abin da ke shafin ba. Idan ka riƙe shafin har zuwa haske, yana ɗauke da ƙaramin abin mamaki - alamar ruwa da ke cewa “Z f. Physik. Chem. B":

Wannan ita ce taqaitaccen sigar Zeitschrift für physikalische Chemie, Abteilung B - Mujallar Jamus kan ilmin sunadarai ta jiki, wacce ta fara bugawa a 1928. Wataƙila editan mujallu ne ya rubuta bayanin? Ga kanun mujallar daga 1933. Da kyau, an jera editocin ta wuri, kuma ɗayan ya fito fili: “Bourne · Cambridge.”

Haka abin yake Max Haihuwar wanene marubucin Burne dokokin da ƙari sosai a cikin ka'idar injiniyoyin ƙididdiga (da kuma kakan mawaƙa Olivia Newton-John). Don haka, wataƙila Max Born ne ya rubuta wannan bayanin kula? Amma, abin takaici, wannan ba haka lamarin yake ba, saboda rubutun hannu bai dace ba.

Me game da alamar shafi a shafi na 231? Ga shi daga bangarorin biyu:

Alamar tana da ban mamaki kuma kyakkyawa ce sosai. Amma yaushe aka yi shi? A Cambridge akwai Heffers kantin sayar da littattafai, ko da yake yanzu yana cikin Blackwell. Sama da shekaru 70 (har zuwa 1970), Heffers ya kasance a adireshin, kamar yadda alamar ta nuna, 3 и 4 ta Petty Cury.

Wannan shafin ya ƙunshi maɓalli mai mahimmanci - wannan ita ce lambar wayar “Tel. 862 " ku. Kamar yadda ya faru, a cikin 1939 yawancin Cambridge (ciki har da Heffers) sun canza zuwa lambobi huɗu, kuma tabbas a cikin 1940 ana buga alamomi tare da lambobin wayar "zamani". (Lambobin tarho na turanci a hankali sun ƙara tsayi; lokacin da nake girma a Ingila a cikin 1960s, lambobin mu sune "Oxford 56186" da "Kidmore End 2378" Wani ɓangare na dalilin da yasa na tuna waɗannan lambobin shine, ban mamaki kamar yadda yake a yanzu ba kamar koyaushe ina kiran lambata ba lokacin amsa kira mai shigowa).

An buga alamar ta cikin wannan fom har zuwa 1939. Amma sai yaushe kafin wannan? Akwai 'yan sikanin tsoffin tallace-tallacen Heffers akan layi, tun daga aƙalla 1912 (tare da "Muna rokon ku don Allah ku cika buƙatun ku...") sun kammala "Wayar 862" ta ƙara "(2 Lines)." Haka kuma akwai wasu alamomi masu irin wannan zane da za a iya samu a cikin littattafai tun a shekarar 1904 (ko da yake ba a san ko asalinsu ne na waɗannan littattafan ba (wato an buga su a lokaci ɗaya) don dalilan bincikenmu, da alama mun kasance. na iya kammala cewa Wannan littafi ya fito ne daga Heffer's (wanda, a hanya, shine babban kantin sayar da littattafai a Cambridge) wani lokaci tsakanin 1930 zuwa 1939.

Lambda calculus page

Don haka yanzu mun san wani abu game da lokacin da aka sayi littafin. Amma menene game da "shafin lissafin lambda"? Yaushe aka rubuta wannan? To, a zahiri, a wancan lokacin ya kamata a riga an ƙirƙira lissafin lambda. Kuma aka yi Alonzo Church, masanin lissafi daga Princeton, a cikin sigarsa ta asali a cikin 1932 kuma a cikin tsari na ƙarshe a 1935. (Akwai ayyukan da masana kimiyyar da suka gabata suka yi, amma ba su yi amfani da bayanin λ ba).

Akwai hadaddun haɗi tsakanin Alan Turing da lambda calculus. A cikin 1935, Turing ya zama sha'awar "injin" na ayyukan lissafi, kuma ya ƙirƙira ra'ayin Turing na'ura, yana amfani da shi don magance matsaloli a cikin ilimin lissafi. Turing ya aika da labarin kan wannan batu ga wata mujallar Faransanci (Comptes rendus), amma an rasa a cikin wasiku; daga nan sai ya zama cewa wanda ya aika masa ba ya nan, tunda ya koma kasar Sin.

Amma a watan Mayu 1936, kafin Turing ya aika da takarda a ko'ina. Aikin Alonzo Church ya zo daga Amurka. A baya Turing ya koka da cewa lokacin da ya samar da hujja a cikin 1934 ka'idar iyaka ta tsakiya, sa'an nan na gano cewa akwai wani Norwegian mathematician wanda ya riga bayar da shaida a 1922 shekara.
Ba shi da wahala a ga cewa injunan Turing da lissafin lambda suna daidai daidai a cikin nau'ikan lissafin da za su iya wakilta (kuma wannan farawa ne. Rubutun Church-Turing). Duk da haka, Turing (da malaminsa Max Newman) sun gamsu cewa tsarin Turing ya bambanta sosai don ya cancanci buga kansa. A cikin Nuwamba 1936 (kuma tare da typos gyara a wata mai zuwa) in Abubuwan da aka gabatar na Ƙungiyar Lissafi ta London An buga shahararren takarda na Turing "Game da lambobi masu ƙididdigewa...".

Don cika tsarin lokaci kaɗan: daga Satumba 1936 zuwa Yuli 1938 (tare da hutun watanni uku a lokacin rani na 1937), Turing ya kasance a Princeton, bayan ya tafi can tare da burin zama ɗalibin digiri na Cocin Alonzo. A wannan lokacin a Princeton, a fili Turing ya mayar da hankali ga ilimin lissafi, yana rubuta da yawa labarai masu wuyar karantawa cike da lissafin lambda na Church, - kuma, mai yiwuwa, ba shi da wani littafi akan injiniyoyin ƙididdiga tare da shi.

Turing ya koma Cambridge a watan Yuli 1938, amma a watan Satumba na wannan shekarar yana aiki na ɗan lokaci a Makarantar Lambobin Gwamnati da Ciphers, kuma bayan shekara guda ya koma Bletchley Park tare da burin yin aiki a can cikakken lokaci akan batutuwan da suka shafi cryptanalysis. Bayan karshen yakin a 1945, Turing ya koma London don yin aiki Laboratory Jiki na Kasa a kan ci gaban aikin da za a ƙirƙira kwamfuta. Ya ciyar da shekarar ilimi ta 1947 – 8 a Cambridge amma sannan ya koma Manchester don haɓaka akwai kwamfuta ta farko.

A 1951, Turing ya fara karatu sosai ilmin halitta na ka'idar. (A gare ni da kaina, wannan gaskiyar tana da ɗan ban mamaki, saboda a gare ni cewa Turing ko da yaushe ya yi imani da cewa ya kamata a tsara tsarin ilimin halitta ta hanyar daidaitawa daban-daban, kuma ba ta wani abu mai hankali kamar na'urorin Turing ko na'urar salula ba). Ya kuma mayar da sha'awarsa zuwa kimiyyar lissafi, kuma a 1954 ma ya rubuta wa abokinsa kuma dalibi Robin Gandy, Menene:"Na yi ƙoƙari na ƙirƙira sabon injin ƙira(ko da yake ya kara da cewa:)amma a gaskiya ba gaskiya ba ne cewa zai yi aiki"). Amma abin takaici, komai ya zo ga ƙarshe a ranar 7 ga Yuni, 1954, lokacin da Turing ya mutu ba zato ba tsammani. (Ina tsammanin ba kisan kai ba ne, amma wannan wani labari ne.)

Don haka mu koma shafin lambda calculus. Bari mu riƙe shi har zuwa haske kuma mu sake ganin alamar ruwa:

Ya bayyana kamar takarda ce ta Biritaniya, kuma da alama ba zai yiwu a gare ni ba da an yi amfani da ita a Princeton. Amma za mu iya kwanan wata daidai? To, ba tare da wani taimako ba Ƙungiyar Marubuta Tarihi ta Biritaniya, Mun san cewa mai sana'a na takarda shine Spalding & Hodge, Papermakers, Drury House Wholesale and Export Company, Russell Street, Drury Lane, Covent Garden, London. Wannan na iya taimaka mana, amma ba sosai ba, tunda ana iya ɗauka cewa alamar takardar su ta Excelsior tana da alama an haɗa su a cikin kasidar wadata daga 1890s zuwa 1954.

Menene wannan shafin ke cewa?

Don haka, bari mu kalli abin da ke bangarorin biyu na takardar. Bari mu fara da lambdas.

Anan akwai hanyar tantancewa ayyuka "tsabta" ko "marasa sani"., kuma su ne ainihin ra'ayi a cikin ilimin lissafi, kuma yanzu a cikin shirye-shiryen aiki. Waɗannan ayyuka sun zama ruwan dare gama gari a cikin harshe Yaren Wolfram, kuma aikinsu yana da sauƙin bayyanawa. Misali, wani ya rubuta f[x] don nuna wani aiki f, amfani da hujjar x. Kuma akwai ayyuka masu suna da yawa f kamar Abs ko zunubi ko blur. Amma idan wani yana so f[x] ya kasance 2x +1 ku? Babu suna kai tsaye don wannan aikin. Amma akwai wani nau'i na assignment, f[x]?

Amsar ita ce eh: maimakon haka f muna rubutu Function[a,2a+1]. Kuma a cikin harshen Wolfram Function [a,2a+1][x] ya shafi ayyuka zuwa gardama x, samarwa 2x+1. Function[a,2a+1] aiki ne na "tsarkake" ko "marasa sani" wanda ke wakiltar aiki mai tsabta na ninkawa ta 2 da ƙara 1.

Don haka, λ a cikin lissafin lambda ainihin analog ne aiki a cikin Harshen Wolfram - don haka, alal misali, λa.(2 a+1) daidai Function[a, 2a + 1]. (Yana da kyau a lura cewa wani aiki, ka ce, Function[b,2b+1] daidai; "masu canzawa" a ko b su ne kawai musanya muhawarar aiki - kuma a cikin Yaren Wolfram ana iya guje musu ta amfani da madadin ma'anar ayyuka masu tsafta (2# +1)&).

A cikin ilimin lissafi na al'ada, yawanci ana ɗaukar ayyuka azaman abubuwa waɗanda ke wakiltar abubuwan shigarwa (waɗanda suma lamba ne, alal misali) da abubuwan fitarwa (waɗanda suma, misali, lamba). Amma wannan wane irin abu ne? aiki (ko λ)? Mahimmanci, ma'aikacin tsari ne wanda ke ɗaukar maganganu kuma ya juya su zuwa ayyuka. Wannan na iya zama ɗan ban mamaki daga mahangar ilimin lissafi na gargajiya da na lissafi, amma idan mutum yana buƙatar yin magudin alamomin sabani, ya fi dabi'a sosai, koda kuwa da alama kaɗan ne da farko. (Ya kamata a lura cewa lokacin da masu amfani suka koyi Harshen Wolfram, koyaushe zan iya faɗi cewa sun ƙetare wani madaidaicin madaidaicin tunani lokacin da suka sami fahimta. aiki).

Lambdas wani ɓangare ne kawai na abubuwan da ke akwai akan shafin. Akwai wani, ma mafi m ra'ayi - wannan masu haɗawa. Yi la'akari da igiyar da ba ta da kyau PI1IIx? Menene wannan zai iya nufi? Mahimmanci, wannan jeri ne na masu haɗawa, ko wasu abubuwan da ba za a iya gani ba na ayyuka na alama.

Babban matsayi na yau da kullun na ayyuka, wanda aka saba da shi a cikin ilimin lissafi, ana iya rubuta shi cikin Yaren Wolfram kamar: f[g[x]] - wanda ke nufin "yi amfani" f zuwa sakamakon aikace-aikace g к x" To amma shin da gaske ne allunan ya zama dole don wannan? A cikin harshen Wolfram f@g@ x - madadin nau'i na rikodi. A cikin wannan sakon, mun dogara da ma'anar a cikin Harshen Wolfram: mai aiki @ yana da alaƙa da gefen dama, don haka f@g@x daidai f@(g@x).

Amma me rikodin zai nufi? (f@g)@x? Wannan yayi daidai f[g][x]. Kuma idan f и g ayyuka ne na yau da kullun a cikin lissafi, zai zama mara ma'ana, amma idan f - aikin oda mafi girma, to, f[g] kanta na iya zama aikin da za a iya amfani da shi sosai x.

Lura cewa har yanzu akwai wasu rikitarwa a nan. IN f[х] - f aiki ne na hujja ɗaya. KUMA f[х] yayi daidai da rubutu Function[a, f[a]][x]. Amma menene game da aiki tare da jayayya guda biyu, ka ce f[x,y]? Ana iya rubuta wannan kamar yadda Function[{a,b},f[a, b]][x, y]. Amma idan Function[{a},f[a,b]]? Menene wannan? Akwai "mai canzawa kyauta" anan b, wanda kawai aka wuce zuwa aikin. Function[{b},Function[{a},f[a,b]]] zai daure wannan canjin sannan Function[{b},Function[{a},f [a, b]]][y][x] bayarwa f[x,y] sake. (Kayyade aiki don ya sami hujja guda ɗaya ana kiransa "currying" don girmama mai hankali mai suna. Haskell Curry).

Idan akwai sauye-sauye na kyauta, to akwai abubuwa da yawa daban-daban game da yadda za a iya siffanta ayyuka, amma idan muka taƙaita kanmu ga abubuwa. aiki ko λ, waɗanda ba su da sauye-sauye na kyauta, to ana iya fayyace su da sauƙi. Irin waɗannan abubuwa ana kiran su masu haɗawa.

Masu haɗawa suna da dogon tarihi. An san cewa an fara gabatar da su a cikin 1920 ta hanyar ɗalibi David Gilbert - Musa Shenfinkel.

A wancan lokacin, ba da jimawa ba ne aka gano cewa ba a buƙatar yin amfani da maganganun kuma, Or и ba don wakiltar maganganu a cikin daidaitattun dabaru na tunani: ya isa ya yi amfani da ma'aikata guda ɗaya, wanda za mu kira yanzu Nan (saboda, misali, idan ka rubuta Nan kamar haka · Or[a,b] zai dauki form (a·a) · (b·b)). Schoenfinkel yana so ya sami ɗan ƙaramin wakilci ɗaya na dabaru na tsinkaya, ko, da gaske, dabaru gami da ayyuka.

Ya fito da “haɗuwa” S da K. A cikin Harshen Wolfram za a rubuta wannan azaman
K[x_][y_] → x da S[x_][y_][z_] → x[z][y[z]].

Yana da ban mamaki cewa ya zama mai yiwuwa a yi amfani da waɗannan mahaɗa biyu don yin kowane lissafi. Misali,

S[K[S]] [S[K[S]]]

za a iya amfani da shi azaman aiki don ƙara lamba biyu.

Waɗannan duk wasu abubuwa ne da ba za a iya faɗi ba, amma yanzu da muka fahimci menene injin Turing da lissafin lambda, zamu iya ganin cewa masu haɗin gwiwar Schoenfinkel a zahiri suna tsammanin manufar lissafin duniya. (Kuma abin da ya fi ban mamaki shi ne cewa ma'anar 1920 na S da K ba su da sauƙi, suna tunawa da su. injin Turing mai sauƙaƙan duniya, wanda na ba da shawara a cikin 1990s, wanda ya dace da shi tabbatar a 2007).

Amma mu koma ga ganye da layinmu PI1IIx. Alamomin da aka rubuta anan masu haɗawa ne, kuma duk an ƙirƙira su don tantance aiki. Anan ma'anar shine cewa dole ne a bar babban matsayi na ayyuka masu alaƙa, don haka fgx bai kamata a fassara shi da f@g@x ko f@(g@x) ko f[g[x]] ba, amma a matsayin (f@g)@x ko f[g][x]. Bari mu fassara wannan shigarwar zuwa wani nau'i mai dacewa don amfani da Harshen Wolfram: PI1IIx zai dauki form p[i][one][i][i][x].

Me yasa rubuta wani abu makamancin haka? Don bayyana wannan, muna buƙatar tattaunawa game da manufar lambobin Ikilisiya (mai suna bayan Cocin Alonzo). Bari mu ce kawai muna aiki tare da alamomi da lambdas ko masu haɗawa. Shin akwai hanyar da za a yi amfani da su don tantance lamba?

Yaya za mu ce kawai lambar n соответствует Function[x, Nest[f,x,n]]? Ko, a wasu kalmomi, (a takaice dai):

1 da f[#]&
2 da f[f[#]]&
3 da f[f[f[#]]]& da sauransu.

Wannan na iya zama kamar ɗan ƙarami, amma dalilin da ya sa yana da ban sha'awa shi ne cewa yana ba mu damar yin komai gabaɗaya na alama da ƙima, ba tare da yin magana a sarari game da wani abu kamar lamba ba.

Tare da wannan hanyar tantance lambobi, yi tunanin, misali, ƙara lambobi biyu: 3 ana iya wakilta azaman f[f[f[#]]]& kuma 2 ne f[f[#]]&. Kuna iya haɗa su ta hanyar amfani da ɗaya daga cikinsu zuwa ɗayan:

Amma menene abin? f? Yana iya zama wani abu! A wata ma'ana, "je zuwa lambda" gabaɗaya kuma wakiltar lambobi ta amfani da ayyukan da suke ɗauka f a matsayin hujja. A wasu kalmomi, bari mu wakilci 3, misali, kamar Function[f,f[f[f[#]]] &] ko Function[f,Function[x,f[f[f[x]]]]. (lokacin da kuma yadda kuke buƙatar suna masu canji shine rub a lissafin lambda).

Yi la'akari da guntun takarda na Turing na 1937 "Ƙidaya da λ-bambanci", wanda ke tsara abubuwa daidai kamar yadda muka tattauna yanzu:

Wannan shi ne inda rikodin zai iya samun ɗan ruɗani. x Turing namu ne f, Kuma nasa x' (mai bugawa yayi kuskure ta hanyar saka sarari) - wannan shine namu x. Amma ana amfani da daidai wannan hanya a nan.

Don haka bari mu kalli layin bayan ninka a gaban takardar. Wannan I1IIYI1IIx. Dangane da bayanin Harshen Wolfram, wannan zai kasance i[one][i][i][y][i][one][i][i][x]. Amma a nan ni ne aikin ainihi, don haka i[one] yana nunawa kawai daya. A halin yanzu, daya shine wakilcin lambobi na Church na 1 ko Function[f,f[#]&]. Amma da wannan ma'anar one[а] zama a[#]& и one[a][b] zama a[b]. (AF, i[а][b], ko Identity[а][b] shine kuma а[b]).

Zai fi haske sosai idan muka rubuta ƙa'idodin maye gurbin i и daya, maimakon yin amfani da lissafin lambda kai tsaye. Sakamakon zai kasance iri ɗaya. Aiwatar da waɗannan ƙa'idodin a sarari, muna samun:

Kuma wannan daidai yake kamar yadda aka gabatar a farkon taƙaitaccen shigarwa:

Bari yanzu mu sake kallon ganyen, a samansa:

Akwai wasu abubuwa masu rikitarwa da rikicewa "E" da "D" a nan, amma da waɗannan muna nufin "P" da "Q", don haka za mu iya rubuta kalmar kuma mu kimanta shi (lura cewa a nan - bayan wasu rikice tare da alama ta ƙarshe - "masanin masanin kimiyya" ya sanya […] da (...) don wakiltar aikace-aikacen aikin):

Don haka wannan shi ne gajarta ta farko da aka nuna. Don ƙarin ganin, bari mu shigar da ma'anar Q:

Muna samun daidai raguwar da aka nuna. Me zai faru idan muka musanya magana ga P?

Ga sakamakon:

Kuma yanzu, ta amfani da gaskiyar cewa ni aiki ne wanda ke fitar da hujjar kanta, muna samun:

Ooooops! Amma wannan ba shine layi na gaba da aka yi rikodin ba. Akwai kuskure a nan? Ba a bayyana ba. Domin, bayan haka, ba kamar sauran lokuta ba, babu wata kibiya da ke nuna cewa layi na gaba yana zuwa daga baya.

Akwai ɗan sirri a nan, amma bari mu matsa zuwa kasan takardar:

Anan 2 shine lambar Ikilisiya, an ƙaddara, misali, ta tsari two[a_] [b_] → a[a[b]]. Lura cewa wannan shine ainihin nau'in layi na biyu idan an dauki a matsayin Function[r,r[р]] и b yadda q. Don haka muna sa ran sakamakon lissafin ya kasance kamar haka:

Duk da haka, magana a ciki а[b] ana iya rubuta shi azaman x (wataƙila ya bambanta da x ɗin da aka rubuta a baya akan takardar) - a ƙarshe muna samun sakamako na ƙarshe:

Don haka, za mu iya fayyace kaɗan daga abin da ke faruwa akan wannan takarda, amma aƙalla asiri ɗaya da ya rage shine abin da Y ya kamata ya kasance.

A gaskiya ma, a cikin ma'anar haɗakarwa akwai daidaitattun Y-combinator: abin da ake kira kafaffen batu mai haɗawa. A bisa ka'ida, an siffanta shi da cewa Y[f] dole ne ya zama daidai f[Y[f]], ko, a wasu kalmomi, cewa Y[f] ba ya canzawa lokacin da aka yi amfani da f, don haka yana da ƙayyadadden wuri don f. (An haɗa haɗin Y tare da #0 a cikin Harshen Wolfram.)

A halin yanzu, Y-combinator ya zama sananne godiya ga Y-Combinator farawa mai sauri, mai suna Paul Graham (wanda ya dade yana fanka shirye-shirye masu aiki и Harshen shirye-shirye na LISP kuma ya aiwatar da kantin yanar gizo na farko dangane da wannan harshe). Ya taba gaya mani da kaina"babu wanda ya fahimci abin da mai haɗa Y yake" (Ya kamata a lura cewa Y Combinator shine ainihin abin da ke ba da damar kamfanoni su guje wa ma'amala mai mahimmanci ...)

Mai haɗa Y (a matsayin ƙayyadadden mai haɗawa) an ƙirƙira sau da yawa. Turing ya fito da aiwatar da shi a cikin 1937, wanda ya kira Θ. Amma shin harafin "Y" a shafin namu shine sanannen mai haɗa madaidaicin wuri? Wataƙila ba. To, menene "Y" namu? Yi la'akari da wannan gajarta:

Amma wannan bayanin a fili bai isa ba don tantance menene Y yake ba tare da shakka ba. A bayyane yake cewa Y yana aiki ba kawai da hujja ɗaya ba; Da alama akwai aƙalla gardama guda biyu, amma ba a sani ba (aƙalla a gare ni) yawan muhawarar da ake ɗauka a matsayin shigarwa da abin da yake aikatawa.

A ƙarshe, ko da yake za mu iya yin ma'anar sassa da yawa na takarda, dole ne mu ce a kan sikelin duniya ba a bayyana abin da aka yi a kai ba. Ko da yake akwai bayani da yawa da ke tattare da abin da ke kan takardar a nan, yana da kyakkyawan asali a lissafin lambda da amfani da masu haɗawa.

Mai yiwuwa wannan yunƙuri ne na ƙirƙirar "shiri" mai sauƙi - ta yin amfani da lissafin lambda da masu haɗawa don yin wani abu. Amma kamar yadda wannan ya kasance irin na injiniya na baya, yana da wuya a gare mu mu faɗi abin da "wani abu" ya kamata ya zama da kuma menene maƙasudin "masu bayani" gaba ɗaya.

Akwai ƙarin fasalin da aka gabatar akan takardar wanda ya cancanci yin sharhi a nan - yin amfani da nau'ikan nau'ikan baka. Ilimin lissafi na gargajiya galibi yana amfani da baka don komai - da aikace-aikacen aiki (kamar a cikin f (x)), da kuma ƙungiyoyin membobin (kamar a cikin (1+x) (1-x), ko, žasa a fili, a (1-x)). (A cikin Harshen Wolfram, muna raba fa'idodi daban-daban na baka-a cikin madauri don ayyana ayyuka f [x] - kuma ana amfani da baka ne kawai don haɗawa).

Lokacin da lissafin lambda ya fara bayyana, an yi tambayoyi da yawa game da amfani da baka. Daga baya Alan Turing zai rubuta gaba dayan aikin (ba a buga ba) mai sunaJuyawa bayanin ilimin lissafi da kuma jimla”, amma tuni a cikin 1937 ya ji cewa yana buƙatar bayyana ma’anar zamani (maimakon hacky) don lissafin lambda (wanda, ta hanyar, ya bayyana saboda Coci).

Yace haka f, shafi zuwa g, ya kamata a rubuta {f} (g), Idan kawai f ba shine kawai halin ba, a cikin wannan yanayin yana iya zama f(g). Sai yace lambda (kamar in Function[a, b]) ya kamata a rubuta kamar λ a[b] ko, a madadin, λ a.b.

Koyaya, watakila a cikin 1940 gabaɗayan ra'ayin amfani da {...} da […] don wakiltar abubuwa daban-daban an yi watsi da su, galibi don goyon bayan daidaitaccen salon lissafi.

Dubi saman shafin:

A cikin wannan nau'i yana da wuyar fahimta. A cikin fassarori na Coci, an yi niyya ga maƙallan murabba'i don haɗawa, tare da buɗaɗɗen sashi mai maye gurbin lokacin. Yin amfani da wannan ma'anar, zai bayyana a sarari cewa Q (wanda aka yiwa lakabi da D) wanda ke kewaye a cikin baƙaƙe a ƙarshen shine abin da duk farkon lambda ya shafi.

Bakin murabba'i a nan ba ya keɓe jikin lambda a zahiri; a maimakon haka, a zahiri yana wakiltar wani amfani da aikin, kuma babu wani takamaiman alamar inda jikin lambda ya ƙare. A ƙarshe, ana iya ganin cewa “masanin masanin kimiyya mai ban mamaki” ya canza madaidaicin madauri na rufewa zuwa madaidaicin sashi, ta haka ya yi amfani da ma’anar Church yadda ya kamata - kuma ta haka ne ya tilasta yin lissafin furci kamar yadda aka nuna akan takardar.

To mene ne ma'anar wannan ƙaramin yanki? Ina tsammanin wannan yana nuna cewa an rubuta shafin ne a cikin 1930s, ko kuma ba a daɗe ba, tun da har yanzu ba a kai ga taron gunduma ba har zuwa lokacin.

To, rubutun hannun wane ne wannan?

Don haka, kafin wannan, mun yi magana game da abin da aka rubuta a shafi. Amma menene game da wanda a zahiri ya rubuta shi?

Dan takarar da ya fi dacewa ga wannan rawar zai kasance Alan Turing da kansa, tun da yake, bayan haka, shafin yana cikin littafinsa. Dangane da abun ciki, da alama babu wani abu da ya dace da ra'ayin cewa Alan Turing zai iya rubuta ta - ko da lokacin da ya fara samun lambda calculus bayan ya karɓi takardar Coci a farkon 1936.

Game da rubutun hannu fa? Shin na Alan Turing ne? Bari mu kalli wasu misalan da suka tsira waɗanda muka sani tabbas Alan Turing ne ya rubuta:

Rubutun da aka gabatar a fili ya bambanta sosai, amma menene game da bayanin da aka yi amfani da shi a cikin rubutun? Aƙalla, a ra'ayi na, bai yi kama da a bayyane ba - kuma mutum zai iya ɗauka cewa kowane bambanci na iya haifar da shi daidai ta gaskiyar cewa an rubuta samfurorin da ake ciki (wanda aka gabatar a cikin ɗakunan ajiya), don yin magana, "a saman, ” yayin da shafin namu ke nuni da aikin tunani.

Ya zama dacewa ga bincikenmu cewa tarihin Turing yana ƙunshe da shafi wanda ya rubuta tebur alama, wajibi ne don sanarwa. Kuma lokacin kwatanta waɗannan haruffan haruffa ta wasiƙa, suna kama da ni (an yi waɗannan bayanan a ciki lokacin Turing lokacin yana karatu nazarin girma shuka, don haka alamar "yankin ganye"):

Ina so in kara bincika wannan, don haka na aika samfurori Sheila Lowe, ƙwararren ƙwararren ƙwararren rubutun hannu (kuma marubucin matsalolin rubutun hannu) wanda na ji daɗin saduwa da ita sau ɗaya - kawai ta hanyar gabatar da takardanmu a matsayin "Sample 'A'" da kuma samfurin da ya kasance na rubutun hannun Turing a matsayin "Sample 'B'." Amsar ta ta ƙarshe ce kuma mara kyau: "Salon rubutun ya bambanta. Dangane da mutuntaka, samfurin “B” marubucin yana da saurin tunani da fahimta fiye da samfurin marubucin “A”.".

Ban tabbata ba tukuna, amma na yanke shawarar lokaci ya yi da zan duba wasu zaɓuɓɓuka.

To, idan ya zama cewa Turing bai rubuta ba, to wa ya rubuta? Norman Routledge ya gaya mani cewa ya karbi littafin daga Robin Gandy, wanda shi ne jami'in Turing. Don haka na aika "Sample"C" daga Gandhi:

Amma abin da Sheila ta fara yi shi ne, wataƙila mutane uku ne suka rubuta samfuran uku, kuma suna lura cewa samfurin "B" ya fito daga "mafi saurin tunani-wanda zai yuwu ya fi son neman hanyoyin magance matsalolin da ba a saba gani ba" (Na ga abin farin ciki ne cewa ƙwararren rubutun hannu na zamani zai ba da wannan kimantawar rubutun hannun Turing, idan aka yi la'akari da yadda kowa ya koka game da rubutun hannunsa a ayyukan makaranta na Turing na 1920.)

To, a wannan lokacin da alama an cire Turing da Gandhi a matsayin "masu tuhuma". To wa zai iya rubuta wannan? Na fara tunanin mutanen da Turing zai iya aron littafinsa. Tabbas, dole ne su kuma iya yin lissafi ta amfani da lambda calculus.

Na ɗauka dole ne mutumin ya fito daga Cambridge, ko kuma aƙalla Ingila, da aka ba da alamar ruwa akan takarda. Na ɗauki shi azaman hasashe mai aiki cewa 1936 ko makamancin haka shine lokacin da ya dace don rubuta wannan. To, wa ya sani kuma ya yi magana da Turing a lokacin? A wannan lokacin, mun sami jerin sunayen duk ɗalibai da malaman lissafi a Kwalejin King. (Akwai sanannun ɗalibai 13 waɗanda suka yi karatu daga 1930 zuwa 1936.)

Kuma a cikin su, ɗan takarar da ya fi dacewa ya zama kamar David Champernow. Yana da shekaru ɗaya da Turing, abokinsa da ya daɗe, kuma yana sha'awar ilimin lissafi - a cikin 1933 har ma ya buga takarda akan abin da muke kira yanzu. Tsawanin Champernow (lambar "al'ada"): 0.12345678910111213… hada lambobi 1, 2, 3, 4,…, 8, 9, 10, 11, 12,…, da ɗayan lambobi kaɗan. aka sani da "al'ada" a cikin ma'anar cewa kowane yuwuwar toshe lambobi yana faruwa tare da yuwuwar daidai).

A cikin 1937, har ma ya yi amfani da Dirac's gamma matrices, kamar yadda aka ambata a littafin Dirac, don warwarewa. matsalar nishaɗin lissafi. (Kamar yadda ya faru, shekaru daga baya na zama babban mai sha'awar lissafin gamma matrix).

Da ya fara karatun lissafi, Champernowne ya sami tasiri John Maynard Keynes (har ila yau a Kwalejin King) kuma a ƙarshe ya zama fitaccen masanin tattalin arziki, musamman yin aiki akan rashin daidaiton kuɗin shiga. (Duk da haka, a cikin 1948 ya kuma yi aiki tare da Turing don ƙirƙirar Turbochamp - shirin dara, wanda a zahiri ya zama na farko a duniya da aka aiwatar akan kwamfuta).

Amma a ina zan iya samun samfurin rubutun hannun Champernowne? Ba da daɗewa ba na sami ɗansa Arthur Champernowne akan LinkedIn, wanda, abin ban mamaki, ya sami digiri a ilimin lissafi kuma ya yi aiki ga Microsoft. Ya ce mahaifinsa ya yi magana da shi sosai game da aikin Turing, kodayake bai ambaci masu haɗawa ba. Ya aiko mani da samfurin rubutun hannun mahaifinsa (wani guntu game da haɗaɗɗun kiɗan algorithmic):

Nan da nan za ku iya faɗi cewa rubutun hannu bai yi daidai ba (ƙuƙumma da wutsiya a cikin haruffa f a cikin rubutun hannun Champernowne, da sauransu.)

To wanene kuma zai iya zama? A koyaushe ina sha'awar Max Newman, ta hanyoyi da yawa mai ba da shawara ga Alan Turing. Newman ya fara sha'awar Turing"injiniyoyin lissafi" Abokinsa ne na dogon lokaci, kuma bayan shekaru da yawa ya zama shugabansa a aikin kwamfuta a Manchester. (Duk da sha'awar lissafi, Newman koyaushe yana da alama ya ga kansa da farko a matsayin masanin kimiyyar yanayi, kodayake ra'ayinsa ya sami goyan bayan wata hujja ta kuskure da ya samo asali. Poincare zato).

Ba abu mai wahala ba ne a sami samfurin rubutun hannu na Newman - kuma kuma, a'a, rubutun hannu babu shakka bai dace ba.

"Trace" na littafin

Don haka, ra'ayin gano rubutun hannu ya gaza. Kuma na yanke shawarar cewa mataki na gaba da za a dauka shi ne in yi kokarin gano ainihin abin da ke faruwa da littafin da na rike a hannuna.

Don haka da farko, menene dogon labari tare da Norman Rutledge? Ya halarci Kwalejin King, Cambridge a 1946 kuma ya sadu da Turing (e, dukansu sun kasance gayu). Ya sauke karatu daga kwaleji a 1949, sannan ya fara rubuta karatun digirinsa na PhD tare da Turing a matsayin mai ba shi shawara. Ya sami digirin digirgir a shekarar 1954, inda ya yi aiki kan ilimin lissafi da ka'idar recursion. Ya sami gurbin karatu na sirri a Kwalejin King, kuma a shekara ta 1957 ya zama shugaban sashen lissafi a can. Zai iya yin haka gabaɗayan rayuwarsa, amma yana da buƙatu masu yawa (kiɗa, fasaha, gine-gine, lissafi na nishaɗi, tarihin sassa, da sauransu). A cikin 1960 ya canza hanyarsa ta ilimi kuma ya zama malami a Eton, inda tsararrun ɗalibai (ciki har da ni) suka yi aiki (kuma na yi karatu) kuma aka fallasa su ga haɓakar iliminsa da wasu lokuta ma ban mamaki.

Shin Norman Routledge zai iya rubuta wannan shafi mai ban mamaki da kansa? Ya san lambda calculus (ko da yake, kwatsam, ya ambata shi lokacin da muke shan shayi a 2005 cewa koyaushe yana samun "rikitarwa"). Koyaya, rubutun halayensa nan da nan ya keɓe shi a matsayin mai yuwuwar “masanin kimiyya mai ban mamaki.”

Za a iya danganta shafin ko ta yaya da dalibin Norman, watakila daga lokacin da yake Cambridge? Ina shakka. Domin bana jin Norman ya taba karatun lambda calculus ko makamancin haka. Yayin rubuta wannan labarin, na gano cewa Norman ya rubuta takarda a cikin 1955 game da ƙirƙirar dabaru akan "kwamfutar lantarki" (da ƙirƙirar nau'i na al'ada, kamar yadda aikin da aka gina a yanzu yake yi. Boolean rage girman). Lokacin da na san Norman, yana da sha'awar rubuta abubuwan amfani ga kwamfutoci na gaske (baƙaƙen sa na farko sune "NAR", kuma ya kira shirye-shiryensa "NAR...", misali, "NARLAB", shirin ƙirƙirar rubutun rubutu ta amfani da naushi. rami "samfurin" "a kan tef na takarda). Amma bai taɓa magana game da ƙirar ƙididdiga na ƙididdiga ba.

Bari mu karanta bayanin Norman a cikin littafin kadan a hankali. Abu na farko da za mu lura shi ne cewa ya yi magana game da ".bayar da littattafai daga ɗakin karatu na mutumin da ya rasu" Kuma daga lafazin yana jin kamar duk ya faru da sauri bayan mutumin ya mutu, yana nuna cewa Norman ya karɓi littafin jim kaɗan bayan Turing ya mutu a 1954, kuma Gandhi ya daɗe yana ɓacewa. Norman ya ci gaba da cewa a zahiri ya karbi litattafai hudu, biyu akan tsantsar lissafi, biyu kan ilimin kimiyyar lissafi.

Sai ya ce ya bayar"wani daga littafin physics (irin, Herman Weil)»«Zuwa Sebag Montefiore, saurayi mai daɗi wanda zaku iya tunawa [George Rutter]" Lafiya, to wanene shi? Na tono Jerin Membobi na da ba a cika amfani da su ba Ƙungiyar tsohuwar Eton. (Dole ne in ba da rahoton cewa lokacin buɗe shi ba zan iya taimakawa ba sai dai lura da ƙa'idodinta tun 1902, wanda na farko, a ƙarƙashin taken "Haƙƙin Membobi", ya kasance mai ban dariya: "Tufafi a cikin launuka na Ƙungiyar").

Yakamata a kara da cewa tabbas bazan taba shiga wannan al'umma ba ko kuma na sami wannan littafi in ba don kwadaitar da wani abokin Eton mai suna ba. Nicholas Kermack, wanda tun yana dan shekara 12 yake shirin zama Firayim Minista, amma cikin bakin ciki ya mutu yana da shekaru 21).

Amma a kowane hali, akwai biyar kawai daga cikin mutanen da aka jera sunayensu da sunan mai suna Sebag-Montefiore, tare da fa'idar kwanakin karatu. Ba shi da wuya a gane cewa ya dace Hugh Sebag-Montefiore. Ƙananan duniya, kamar yadda ya fito, danginsa sun mallaki Bletchley Park kafin su sayar da ita ga gwamnatin Birtaniya a 1938. Kuma a cikin 2000, Sebag-Montefiore ya rubuta littafi game da karya Enigma (na'urar ɓoye bayanan Jamus) - Wannan shi ne, a kowane hali, dalilin da ya sa a cikin 2002 Norman ya yanke shawarar ba shi littafin da Turing ya mallaka.

To, yaya game da sauran littattafan Norman ya samu daga Turing? Ba ni da wata hanya ta gano abin da ya same su, sai na ba da umarnin kwafin wasiyyar Norman. Sashe na ƙarshe na wasiyyar ya fito fili a cikin salon Norman:

Wasiyyar ta bayyana cewa ya kamata a bar littattafan Norman a Kwalejin King. Kuma ko da yake ba a iya samun cikakken tarin littattafansa ba, littattafan Turing guda biyu kan ƙididdiga masu tsafta, waɗanda ya ambata a cikin bayaninsa, yanzu an adana su sosai a ɗakin karatu na Kwalejin King.

Tambaya ta gaba: me ya faru da sauran littattafan Turing? Na kalli wasiyyar Turing, wanda ya juya ya bar su duka ga Robin Gandy.

Gandhi dalibin lissafi ne a Kwalejin King, Cambridge, wanda ya zama abokai da Alan Turing a shekararsa ta karshe ta kwaleji a 1940. A farkon yakin, Gandhi ya yi aiki a rediyo da radar, amma a cikin 1944 an sanya shi a cikin sashin Turing kuma ya yi aiki a kan ɓoye bayanan. Kuma bayan yakin, Gandhi ya koma Cambridge, ba da daɗewa ba ya sami digiri na uku, kuma Turing ya zama mashawarcinsa.

Aikin soja a fili ya kai shi sha'awar ilimin kimiyyar lissafi, kuma karatun nasa, wanda aka kammala a 1952, yana da taken. "A kan tsarin axiomatic a cikin lissafi da ka'idojin a physics". Abin da Gandhi ya yi kamar yana ƙoƙari ya yi shi ne watakila ya siffanta ka'idodin jiki ta fuskar ilimin lissafi. Yayi magana akai irin theories и dokokin janyewa, amma ba game da injin Turing ba. Kuma daga abin da muka sani a yanzu, ina tsammanin za mu iya yanke shawarar cewa ya fi rasa batun. Kuma lallai, aikina ya yi jayayya tun farkon 1980s cewa ya kamata a dauki matakan jiki a matsayin "ƙididdigar lissafi" -misali, a matsayin na'urorin Turing ko automata cellular - maimakon a matsayin ka'idodin da za a iya cirewa. (Gandhi yayi magana sosai game da tsarin nau'ikan da ke cikin ka'idodin zahiri, yana mai cewa misali cewa "Na yi imani cewa tsarin kowane lamba na ƙididdigewa a cikin nau'in binary bai wuce takwas ba"). Yace"Ɗaya daga cikin dalilan da ya sa ka'idar filin ƙididdiga ta zamani ta kasance mai sarƙaƙƙiya shine kawai saboda tana hulɗa da abubuwa na nau'i mai mahimmanci - ayyuka na ayyuka ...", wanda a ƙarshe yana nufin cewa "za mu iya ɗaukar mafi girman nau'in amfani gama gari azaman ma'aunin ci gaban lissafi".)

Gandhi ya ambaci Turing sau da yawa a cikin karatun, yana lura a cikin gabatarwar cewa yana da bashi ga A.M. Turing, wanda "da farko ya jawo hankalinsa da ba a maida hankali ba ga lissafin Ikilisiya"(watau lambda calculus), ko da yake a gaskiya kasidarsa tana da hujjojin lambda da dama.

Bayan kare karatun nasa, Gandhi ya juya zuwa mahangar lissafi mai tsafta kuma sama da shekaru 1969 yana rubuta kasidu a kan adadin daya a shekara, kuma an ci gaba da nakalto wadannan kasidu cikin nasara a cikin al'ummar duniya na mathematics dabaru. Ya koma Oxford a XNUMX kuma ina tsammanin tabbas na hadu da shi a lokacin kuruciyata, ko da yake ba ni da abin tunawa.
Gandhi ya kasance yana bautar Turing sosai kuma ya yi magana akai-akai game da shi a cikin shekaru masu zuwa. Wannan ya haifar da tambayar cikakken tarin ayyukan Turing. Jim kadan bayan mutuwar Turing, Sarah Turing da Max Newman sun tambayi Gandhi - a matsayinsa na zartarwa - don shirya buga ayyukan Turing da ba a buga ba. Shekaru sun shude kuma haruffa daga rumbun adana bayanai nuna takaicin Sarah Turing akan wannan batu. Amma ko ta yaya Gandhi bai taɓa shirin haɗa takaddun Turing tare ba.

Gandhi ya mutu a shekara ta 1995 ba tare da hada ayyukan da aka kammala ba. Nick Furbank - marubucin adabi da tarihin rayuwa E. M. Forster, wanda Turing ya sadu da shi a Kwalejin King, shine wakilin wallafe-wallafen Turing, kuma a ƙarshe ya fara aiki a kan ayyukan Turing da aka tattara. Babban abin da ya fi jawo cece-kuce shine ƙarar ilimin lissafi, wanda ya jawo hankalin ɗalibinsa na farko da ya kammala karatun digiri, Robin Gandy, wani takamaiman. Mike Yates, wanda ya samo wasiƙu ga Gandhi game da ayyukan da aka tattara waɗanda ba a fara ba har tsawon shekaru 24. (Ayyukan da aka tattara a ƙarshe ya bayyana a cikin 2001 - shekaru 45 bayan sakin su).

Amma menene game da littattafan da Turing da kansa ya mallaka? Ci gaba da ƙoƙarin gano su, tasha ta gaba ita ce dangin Turing, kuma musamman ɗan ƙaramin ɗan'uwan Turing. Dermot Turing (wanda shine ainihin Sir Dermot Turing, saboda gaskiyar cewa ya kasance baronet, wannan lakabi bai wuce shi ta hanyar Alan a cikin dangin Turing ba). Dermot Turing (wanda ya rubuta kwanan nan biography na Alan Turing) ya gaya mani game da " kakar Turing" (aka Sarah Turing), gidanta a fili ya raba hanyar shiga lambu tare da iyalinsa, da sauran abubuwa da yawa game da Alan Turing. Ya gaya mani cewa littattafan sirri na Alan Turing ba su taɓa kasancewa a cikin danginsu ba.

Don haka na koma karanta wasiyoyin na gano cewa wanda ya zartar da Gandhi shi ne dalibinsa Mike Yates. Na koyi cewa Mike Yates ya yi ritaya a matsayin farfesa shekaru 30 da suka wuce kuma yanzu yana zaune a Arewacin Wales. Ya ce a cikin shekarun da suka gabata ya yi aiki a kan ilimin lissafi da ka'idar lissafi, bai taɓa taɓa kwamfuta da gaske ba - amma a ƙarshe ya yi lokacin da ya yi ritaya (kuma hakan ya faru, jim kaɗan bayan gano shirin. Ilmin lissafi). Ya ce abin mamaki ne cewa Turing ya shahara sosai, kuma lokacin da ya isa Manchester shekaru uku bayan mutuwar Turing, babu wanda ke magana game da Turing, har ma Max Newman lokacin da yake koyar da kwas kan dabaru. Duk da haka, daga baya Gandy zai yi magana game da yadda ya sami farin ciki game da mu'amala da tarin ayyukan Turing, kuma a ƙarshe ya bar su duka ga Mike.

Menene Mike ya sani game da littattafan Turing? Ya sami ɗaya daga cikin littattafan rubutu na Turing da hannu, wanda Gandhi bai bai wa Kwalejin King ba saboda (baƙon abu) Gandhi ya yi amfani da shi azaman ɓoyayyiyar bayanan da ya ajiye game da mafarkinsa. (Turing ya kuma ajiye bayanan mafarkinsa, wadanda aka lalata bayan mutuwarsa.) Mike ya ce kwanan nan an sayar da littafin a gwanjon dalar Amurka miliyan daya. Kuma in ba haka ba, ba zai yi tunanin cewa a cikin abubuwan Gandhi akwai kayan Turing ba.

Da alama duk zaɓukanmu sun bushe, amma Mike ya ce in kalli wannan takarda mai ban mamaki. Kuma nan take ya ce: “Wannan shine rubutun hannun Robin Gandy!» Ya ce ya ga abubuwa da yawa a cikin shekaru. Kuma ya tabbata. Ya ce bai san da yawa game da lissafin lambda ba kuma ba zai iya karanta shafin da gaske ba, amma ya tabbata Robin Gandy ya rubuta.

Mun koma wurin gwanin rubutun hannu tare da ƙarin samfurori kuma ta yarda cewa eh, abin da ke wurin ya yi daidai da rubutun hannun Gandhi. Don haka a ƙarshe mun gano shi: Robin Gandy ya rubuta wannan takarda mai ban mamaki. Ba Alan Turing ne ya rubuta ba; dalibinsa Robin Gandy ne ya rubuta.

Tabbas, wasu asirai har yanzu suna nan. Turing da ake zaton ya ba Gandhi littafin, amma yaushe? Siffar lissafin lissafin lambda ya sa ya zama kamar yana kusa da 1930s. Amma dangane da sharhi kan rubutun Gandhi, mai yiwuwa ba zai yi wani abu da lissafin lambda ba har zuwa ƙarshen 1940s. Tambayar ta taso dalilin da yasa Gandhi ya rubuta wannan. Wannan ba alama yana da alaƙa kai tsaye da rubutunsa, don haka yana iya kasancewa lokacin da ya fara ƙoƙarin gano lissafin lambda.

Ina shakka ba za mu taɓa sanin gaskiya ba, amma tabbas yana da daɗi ƙoƙarin gano ta. A nan dole ne in ce wannan tafiya gaba ɗaya ta yi tasiri sosai don faɗaɗa fahimtar yadda tarihin littattafan makamantansu na ƙarnin da suka gabata suka bambanta, waɗanda, musamman, na mallaka, na iya zama. Wannan ya sa na yi tunanin cewa na fi dacewa in tabbatar da cewa na kalli duk shafukansu - don ganin abin da zai iya zama mai ban sha'awa a can ...

Godiya da taimako ga: Jonathan Gorard (Nazarin Masu Zaman Kansu na Cambridge), Dana Scott (Logic Mathematical), da Matthew Szudzik (Logic Logic).

Game da fassararFassarar sakon Stephen Wolfram"Littafi daga Alan Turing… da wani Bahaushe Na Takarda".

Ina matukar godiya ta Galina Nikitina и Peter Tenishev don taimako a cikin fassarar da shirye-shiryen bugawa.

Kuna so ku koyi yadda ake tsara shirye-shirye a cikin Yaren Wolfram?
Kalli mako-mako webinars.
rajista don sababbin darussa... Shirya kan layi kwas.
Oda yanke shawara akan Harshen Wolfram.

source: www.habr.com