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

Fassarar asali akan bulogi na

Ta yaya wannan littafin ya shigo hannuna?

A watan Mayun 2017, na sami imel daga tsohon malamin makarantar sakandare na mai suna George Rutter, inda ya rubuta:Ina da kwafin babban littafin Dirac a cikin Jamusanci (Die Prinzipien der Quantenmechanik), wanda mallakar Alan Turing ne, kuma bayan na karanta littafinka. Masu Shirya Ra'ayi, ya bayyana a gare ni cewa kai ne mutumin da take buƙata"Ya bayyana mini cewa ya karɓi littafin daga wani malamin makaranta na (wanda a lokacin ya rasu). Norman Rutledge, wanda na san abokin Alan Turing ne. George ya ƙare wasiƙarsa da jumlar:Idan kana buƙatar wannan littafin, zan iya ba ka shi a lokaci na gaba da ka zo Ingila.".

Bayan 'yan shekaru, a watan Maris na 2019, na isa Ingila, inda na shirya ganawa da George don karin kumallo a wani ƙaramin otal a Oxford. Mun ci abinci, muka yi hira, kuma muka jira abincin ya lafa. Sai lokacin da ya dace ya zo don tattauna littafin. George ya miƙa hannu cikin jakarsa ya fito da wani littafi mai sauƙi, wanda aka saba amfani da shi a tsakiyar shekarun 1900.

Na buɗe murfin, ina mamakin ko akwai rubutu a baya:"Mallakar Alan Turing" ko wani abu makamancin haka. Amma, abin takaici, hakan bai kasance ba. Duk da haka, an haɗa shi da wani rubutu mai shafuka huɗu mai bayyana ra'ayi daga Norman Rutledge ga George Rutter, wanda aka rubuta a shekara ta 2002.

Na san Norman Rutledge tun ina ɗalibi makarantar sakandare в Eton a farkon shekarun 1970. Malamin lissafi ne wanda ake wa lakabi da "Nutty Norman." Malami ne mai daɗi ta kowace hanya kuma yana ba da labarai marasa iyaka game da lissafi da sauran abubuwa masu ban sha'awa iri-iri. Shi ne ke da alhakin samar wa makarantar kwamfuta (wanda za a iya tsara shi ta amfani da tef mai kaifi kamar faɗin tebur)—shi ne kwamfuta ta farko da na taɓa amfani da ita.

A lokacin, ban san komai game da tarihin Norman ba (ku tuna, wannan ya daɗe kafin intanet). Na san kawai cewa shi "Dr. Rutledge ne." Sau da yawa yana ba da labarai game da mutanen Cambridge, amma a cikin labaransa bai taɓa ambaton Alan Turing ba. Tabbas, Turing ba shi da shahara sosai a lokacin (kodayake, kamar yadda ya bayyana, na riga na ji labarinsa daga wani wanda ya san shi a cikin Filin shakatawa na Bletchley (wani babban gida wanda ke ɗauke da cibiyar ɓoye sirri a lokacin Yaƙin Duniya na Biyu).

Alan Turing bai shahara ba sai a shekarar 1981, lokacin da na fara Na fara koyon shirye-shirye masu sauƙi, kodayake har yanzu a cikin mahallin tantanin halitta ta atomatik, kuma ba Injin Turing.

Sai kwatsam wata rana, yayin da yake duba kundin kati a ɗakin karatu Cibiyar Fasaha ta CaliforniaNa ci karo da wani littafi Alan M. Turing, wanda mahaifiyarsa, Sarah Turing, ta rubuta. Littafin ya ƙunshi bayanai da yawa, ciki har da takardun kimiyya na Turing da ba a buga ba kan ilmin halitta. Duk da haka, ban koyi komai game da dangantakarsa da Norman Routledge ba, domin littafin bai ambaci shi ba (kodayake, kamar yadda na gano, Sarah Turing Na yi rubutu da Norman game da wannan littafin., kuma Norman har ma ya ƙare rubutawa sake dubawa game da shi).

Shekaru goma bayan haka, da tsananin sha'awar Turing da nasa (wanda a lokacin ba a buga shi ba) yana aiki a ilmin halitta, na ziyarci Taskar bayanai ta Turing в Kwalejin King's, CambridgeBa da daɗewa ba, bayan na saba da abubuwan da suka shafi ayyukan Turing, kuma bayan na ɗan ɓata lokaci a kai, na yi tunanin zan iya neman ganin wasiƙunsa na sirri. Na duba ta, na gano haruffa da dama daga Alan Turing zuwa Norman Routledge.

A lokacin an buga shi biography Andrew Hodges, wanda ya yi abubuwa da yawa don a ƙarshe ya shahara da Turing, ya tabbatar da cewa Alan Turing da Norman Routledge abokai ne, kuma Turing shi ne mai ba da shawara kan kimiyya na Norman. Ina so in tambayi Routledge game da Turing, amma a lokacin Norman ya yi ritaya kuma yana rayuwa cikin kaɗaici. Duk da haka, lokacin da na kammala littafin,Sabuwar Nau'in Kimiyya"A shekara ta 2002 (bayan na shafe shekaru goma ina killace kaina), na bi sawunsa na aika masa da kwafin littafin mai rubutu "Ga malamin lissafi na ƙarshe." Sai muka yi ɗan tattaunawa. ya dace, kuma a shekarar 2005 na sake dawowa Ingila kuma na shirya ganawa da Norman don shan shayi a wani otal mai tsada a tsakiyar London.

Mun yi tattaunawa mai daɗi game da abubuwa da yawa, ciki har da Alan Turing. Norman ya fara tattaunawarmu da bayyana cewa ya san Turing, galibi a zahiri, shekaru 50 da suka gabata. Amma har yanzu yana da abubuwa da yawa da zai faɗa game da shi da kansa:Bai kasance mai son jama'a ba". "Ya yi dariya sosai.". "Bai iya magana da waɗanda ba su da ilimin lissafi ba.". "Kullum yana jin tsoron ɓata wa mahaifiyarsa rai.". "Zai fita da rana ya yi gudun marathon.". "Bai kasance mai himma sosai ba."Sannan tattaunawar ta koma kan halayen Norman. Ya ce, duk da cewa ya yi ritaya na tsawon shekaru 16, har yanzu yana rubuta labarai donJaridar lissafi", don haka, a cikin kalmominsa,"don kammala dukkan ayyukan kimiyya na kafin in wuce zuwa duniya mai zuwa", inda, kamar yadda ya ƙara da murmushin da ba a iya gani sosai ba,"duk gaskiyar lissafi ba makawa za a bayyana ta"Lokacin da bikin shayi ya ƙare, Norman ya saka jaket ɗin fata ya nufi babur ɗinsa, ba tare da ya sani ba." fashewar da ta kawo cikas ga zirga-zirgar ababen hawa a Landan a wannan ranar.

Wannan shine karo na ƙarshe da na ga Norman, ya mutu a shekarar 2013.

Shekaru shida bayan haka, ina cin abincin safe tare da George Rutter. Na riƙe da wata takarda daga Rutledge, wadda aka rubuta a shekarar 2002 a cikin rubutun hannunsa na musamman:

Na fara rage bayanin. Kamar yadda aka saba, yana da ma'ana:

Na karɓi littafin Alan Turing daga abokinsa kuma mai aiwatarwa. Robina Gandy (Aikin da aka saba yi a Kwalejin King's shine a raba littattafai daga tarin matattu, kuma na zaɓi tarin waƙoƙi. A. E. Hausman daga littattafai Ivor Ramsay a matsayin kyauta mai dacewa (shi shugaban coci ne kuma ya yi tsalle daga ɗakin ibada [a cikin 1956])…

Daga baya a cikin ɗan gajeren rubutu ya rubuta:

Kana tambaya inda wannan littafin zai ƙare a ƙarshe - a ganina ya kamata ya ƙare da wanda ke yaba duk abin da ya shafi aikin Turing, don haka ƙaddararsa ta rage gare ka.

Stephen Wolfram ya aiko min da littafinsa mai ban sha'awa, amma ban zurfafa cikinsa ba...

Ya kammala da taya George Rutter murna bisa samun ƙarfin gwiwar ƙaura (na ɗan lokaci, kamar yadda ya bayyana) zuwa Ostiraliya bayan ritayarsa, yana mai cewa shi da kansa "Zan yi wasa da ƙaura zuwa Sri Lanka a matsayin misali na rayuwa mai araha da kama da ta lotus", amma ya ƙara da cewa"abubuwan da ke faruwa a can yanzu suna nuna cewa bai kamata ya yi hakan ba"(a bayyane yake ma'ana yakin basasa a Sri Lanka).

To mene ne yake ɓoye a cikin zurfin littafin?

To, me na yi da kwafin littafin Jamusanci da Paul Dirac ya rubuta wanda a da mallakar Alan Turing ne? Ba na karanta Jamusanci, amma ina da akwai kwafin wannan littafin a Turanci (harshensa na asali) daga bugu na shekarun 1970. Duk da haka, wata rana bayan karin kumallo, ya zama daidai in duba littafin a hankali shafi bayan shafi. Bayan haka, wannan ita ce hanyar da aka yarda da ita wajen mu'amala da littattafan tarihi.

Ya kamata a lura cewa kyawun gabatarwar Dirac ya burge ni. An buga littafin a shekarar 1931, amma tsantsar tsarinsa (kuma, eh, duk da cewa akwai shingen harshe, na iya karanta lissafin da ya gabatar) kusan iri ɗaya ne da wanda aka rubuta a yau. (Ba na son in fifita Dirac a nan, amma abokina Richard Feynman ya gaya min cewa, aƙalla a ra'ayinsa, gabatarwar Dirac ba ta da tsari ɗaya. Norman Routledge ya gaya mini cewa shi abokina ne a Cambridge Ɗan da Dirac ya ɗauka, wanda ya zama masanin zane-zane. Norman ya ziyarci gidan Dirac sau da yawa kuma ya ba da labarin yadda "babban mutum" wani lokacin yake ɓacewa a bango, yayin da yawancin wasanin lissafi suka zama babban mataki. Abin takaici, ban taɓa haɗuwa da Paul Dirac da kaina ba, kodayake an gaya mini cewa bayan ya bar Cambridge zuwa Florida, ya rasa yawancin tsanarsa ta baya kuma ya zama mutum mai son jama'a.

Amma bari mu koma ga littafin Dirac, wanda mallakar Turing ne. A shafi na 9, na lura da layi a ƙasa da ƙananan bayanai a gefen gefe, an rubuta su da fensir. Na ci gaba da juya shafukan. Bayan surori kaɗan, bayanan sun ɓace. Amma, ba zato ba tsammani, na gano wata takarda da aka ɓoye a shafi na 127 wadda ta ce:

An rubuta shi da Jamusanci a cikin rubutun hannu na Jamusanci na yau da kullun. Kuma da alama yana da alaƙa da shi ta wata hanya. Makanikan LagrangianNa yi tunanin cewa wataƙila wani ya mallaki wannan littafin kafin Turing, kuma wannan dole ne ya zama bayanin da wannan mutumin ya rubuta.

Na ci gaba da duba littafin. Bayanan sun ɓace. Kuma na yi tunanin ban sami wani abu ba. Amma, a shafi na 231, na sami alamar alama—wanda aka buga da rubutu mai zuwa:

Zan iya gano wani abu daga baya? Na ci gaba da duba littafin. Sannan, a ƙarshen littafin, a shafi na 259, a cikin sashin da ke kan ka'idar relativistic of electrons, na sami wannan:

Na buɗe wannan takardar:

Nan da nan na fahimci menene abin lissafin lambda tare da wani abu mai kauri masu makirci, amma ta yaya wannan bayanin ya ƙare a nan? Ka tuna, wannan littafin yana game da makanikan kwantum ne, amma bayanin da aka saka ya tattauna dabarun lissafi, ko abin da ake kira ka'idar lissafi yanzu. Wannan abu ne da aka saba gani a aikin Turing. Na yi mamakin ko Turing da kansa ne ya rubuta wannan bayanin.

Ko da ina cin abincin karin kumallo, na bincika intanet don neman samfuran rubutun hannun Turing, amma ban sami wani misali a cikin lissafin ba, don haka ban iya yanke shawara game da ainihin asalin rubutun hannu ba. Kuma ba da daɗewa ba dole na tafi. Na tattara littafin a hankali, a shirye nake don bayyana sirrin abin da wannan shafin yake da kuma wanda ya rubuta shi, na tafi da shi.

Game da littafin

Da farko, bari mu tattauna littafin da kansa.Ka'idojin makanikan kwantum"An buga Dirac's Fields a Turanci a shekarar 1930 kuma ba da daɗewa ba aka fassara shi zuwa Jamusanci. (An rubuta gabatarwar Dirac a ranar 29 ga Mayu, 1930; na mai fassara ne - Werner Bloch (Agusta 15, 1930) Littafin ya kasance wani muhimmin ci gaba a cikin ci gaban makanikan kwantum, wanda aka tsara shi bisa tsari don yin lissafi, da kuma wasu abubuwa, yana bayanin hasashen Dirac game da positron, wanda za a buɗe a shekarar 1932.

Me ya sa Alan Turing ya sami littafi a cikin Jamusanci ba a cikin Turanci ba? Ban sani ba tabbas, amma Jamusanci shine babban harshen kimiyya a wancan lokacin, kuma mun san cewa Alan Turing zai iya karanta shi. (Bayan haka, taken littafinsa mai suna injin работы Turing «Akan Lambobin Kwamfuta tare da Aikace-aikacen Matsalar Warwarewa (Entscheidungsproblem)" kalma ce mai tsayi sosai a Jamusanci - kuma a cikin babban ɓangaren labarin yana aiki da alamomin Gothic marasa ma'ana a cikin nau'in "haruffan Jamusanci", wanda ya yi amfani da shi, maimakon, misali, alamomin Girkanci).

Shin Alan Turing ne ya sayi wannan littafin da kansa ko kuma an ba shi? Ban sani ba. A cikin murfin littafin Turing akwai rubutun "20/-," wanda shine ma'aunin "shillings 20," kamar £1. A shafin dama akwai "26.9.30" da aka goge, wanda ake tsammanin yana nufin Satumba 26, 1930 - wataƙila ranar da aka fara siyan littafin. Sannan, a kusurwar dama ta nesa, akwai "20" da aka goge. Wataƙila wannan shine farashin kuma. (Shin wannan shine farashin a cikin Alamun Reichs(Ana ɗauka cewa an sayar da littafin a Jamus? A wancan lokacin, 1 Reichsmark ya kai kimanin schilling 1; farashin Jamus wataƙila an rubuta shi kamar, misali, "20 RM.") A ƙarshe, a cikin murfin baya akwai "c 5/-"—wataƙila wannan shine farashin (wanda aka rage sosai) na littafin da aka yi amfani da shi.

Bari mu kalli muhimman ranakun rayuwar Alan Turing. Alan Turing An haife shi a ranar 23 ga Yuni, 1912 (haka dai, daidai shekaru 76 da suka gabata fitowar Mathematica 1.0A lokacin kaka na shekarar 1931, ya shiga Kwalejin King's, Cambridge. Ya sami digirin BA bayan shekaru uku na karatu a shekarar 1934.

A shekarun 1920 da farkon shekarun 1930, ilimin kimiyyar lissafi ya zama ruwan dare gama gari, kuma Alan Turing ya yi sha'awar hakan. Mun san daga tarihinsa cewa a shekarar 1932, da zarar an buga littafin, ya samu karbuwa.Tushen Lissafi na Kwatancen Makanikai"John von Neumann (a kan cikin JamusanciMun kuma san cewa a shekarar 1935 Turing ya sami aiki daga wani masanin kimiyyar lissafi na Cambridge. Ralph Fowler kan batun nazarin makanikan kwantum. (Fowler ya gabatar da shawarar yin lissafi ma'aunin dielectric na ruwa, wanda a zahiri matsala ce mai sarkakiya da ke buƙatar cikakken bincike tare da ka'idar filin quantum mai hulɗa, wanda har yanzu ba a warware ta gaba ɗaya ba).

To, yaushe kuma ta yaya Turing ya sami kwafin littafin Dirac? Ganin farashin da aka buga a littafin, Turing ya yi tsammanin ya saya shi da hannu biyu. Wanene ainihin mai littafin? Bayanan da ke cikin littafin sun fi mayar da hankali kan tsarin ma'ana, suna lura cewa ya kamata a ɗauki wata alaƙa ta ma'ana a matsayin ma'ana. To fa game da bayanin da ke cikin shafi na 127?

To, yana iya zama daidaituwa, amma a shafi na 127 ne Dirac ya yi magana game da quantum ƙa'idar aiki mafi ƙarancin aiki kuma yana shimfida harsashin ginin Hanyar Feynman mai hadewa — wanda shine tushen duk tsarin kwantum na zamani. Me bayanin ya ƙunsa? Ya ƙunshi faɗaɗa lissafi na 14, wanda shine lissafin juyin halittar lokaci na girman kwantum. Marubucin bayanin ya maye gurbin A na Dirac don girman da ρ, wataƙila yana nuna bayanin Jamusanci na baya (kwatancen da yawa na ruwa). Sannan marubucin ya yi ƙoƙarin faɗaɗa aikin zuwa ikon ℏ (Planck ta akai-akai, an raba shi da 2π, wanda wani lokacin ake kira Dirac constant).

Amma da alama akwai ƙarancin bayanai masu amfani da za a samu daga abin da ke kan shafin. Idan ka riƙe shafin zuwa haske, yana ɗauke da ƙaramin abin mamaki—wani alamar ruwa mai rubutu "Z f. Physik. Chem. B":

Wannan sigar gajeriyar hanya ce Zeitschrift für physikalische Chemie, Abteilung B — mujallar Jamus kan ilmin sunadarai ta jiki wadda ta fara bugawa a shekarar 1928. Wataƙila editan mujallar ne ya rubuta bayanin? Ga taken mujallar na shekarar 1933. Da sauƙi, an jera editocin ta wurin da suke zaune, kuma ɗaya daga cikinsu ya yi fice: "An haifi Cambridge."

Shi ke nan Max Haihuwar wanene marubucin Dokokin Bourne da ƙari mai yawa a cikin ka'idar makanikan kwantum (da kuma kakan mawaƙin Olivia Newton-John) To, Max Born ne ya rubuta wannan bayanin? Amma abin takaici, ba haka lamarin yake ba, domin rubutun hannu bai yi daidai ba.

Yaya batun alamar da ke shafi na 231? Ga shi daga ɓangarorin biyu:

Alamar shafin abin mamaki ne kuma tana da kyau sosai. Amma yaushe aka yi ta? Akwai ɗaya a Cambridge. Shagon Littattafai na Heffer, kodayake yanzu ɓangare ne na Blackwell. Fiye da shekaru 70 (har zuwa 1970), Heffers yana nan a adireshin, kamar yadda alamar ta nuna, 3 и 4 ta Petty Cury.

Wannan alamar ta ƙunshi wata muhimmiyar alama: lambar wayar "Tel. 862." Hakan ya faru cewa a shekarar 1939, yawancin Cambridge (ciki har da Heffers) sun koma lambobi huɗu, kuma tabbas zuwa 1940, ana buga alamun shafi da lambobin wayar "na zamani". (Lambobin wayar Turanci sun yi tsayi a hankali; lokacin da nake girma a Ingila a shekarun 1960, lambobin wayarmu sune "Oxford 56186" da "Kidmore End 2378." Wani ɓangare, ina tuna waɗannan lambobin domin, kamar yadda yake a yanzu, koyaushe ina ba da lambata lokacin da nake amsa kira mai shigowa.)

An buga wannan nau'in alamar shafi har zuwa 1939. Amma tsawon lokacin da aka ɗauka kafin hakan? Akwai hotunan tsoffin tallace-tallace na Heffers a yanar gizo, tun daga aƙalla 1912 (tare da "Muna roƙon ku da ku biya buƙatunku..."), sun ƙara "Telephone 862" da "(layuka 2)." Akwai kuma wasu alamomin shafi masu irin wannan ƙira da aka samu a cikin littattafai tun farkon 1904 (kodayake ba a san ko asalin waɗannan littattafan ne ba (watau, an buga su a lokaci guda). Don dalilan bincikenmu, da alama za mu iya kammala cewa wannan littafin ya fito ne daga Heffers (wanda, ba zato ba tsammani, shine babban kantin sayar da littattafai a Cambridge) wani lokaci tsakanin 1930 da 1939.

Shafin Lissafi na Lambda

To yanzu mun san wani abu game da lokacin da aka sayi littafin. Amma fa game da "shafin lissafin lambda"? Yaushe aka rubuta hakan? To, ba shakka, dole ne a ƙirƙira lissafin lambda a lokacin. Kuma haka ne. Cocin Alonzo, masanin lissafi daga Princeton, a cikin siffarsa ta asali a 1932 da kuma a cikin siffarsa ta ƙarshe a 1935. (Akwai ayyukan da masana kimiyya na baya suka yi, amma ba su yi amfani da alamar λ ba.)

Akwai wata alaƙa mai sarkakiya tsakanin Alan Turing da kalkuletin lambda. A shekara ta 1935, Turing ya fara sha'awar "injiniya" ayyukan lissafi kuma ya ƙirƙiro ra'ayin injin Turing don magance matsalolin da ke cikin tushen lissafi. Turing ya gabatar da takarda kan batun ga wata mujallar Faransa (Gasar cin kofin), amma an ɓace a cikin wasiƙa; sannan sai ya zama cewa wanda aka aika masa da adireshin bai nan ko ta yaya, tunda ya ƙaura zuwa China.

Amma a watan Mayu na shekarar 1936, kafin Turing ya iya aika takardarsa zuwa wani wuri, Aikin Cocin Alonzo ya iso daga AmurkaTuring ya yi korafin cewa lokacin da ya ƙirƙiro hujjar a shekarar 1934 ka'idar iyaka ta tsakiya, sai na gano cewa akwai wani masanin lissafi ɗan ƙasar Norway wanda ya riga ya gabatar da shaida a 1922 shekara.
Ba abu ne mai wahala a ga cewa injunan Turing da lissafin lambda suna daidai gwargwado a cikin nau'ikan lissafin da za su iya wakilta ba (kuma wannan shine farkon Rubutun Cocin-TuringDuk da haka, Turing (da malaminsa Max Newman) ya gamsu cewa hanyar Turing ta bambanta sosai don ta cancanci a buga ta daban. A watan Nuwamba na 1936 (kuma tare da gyara kurakurai a watan da ya biyo baya) a cikin Takardun Ƙungiyar Lissafi ta London An buga sanannen labarin Turing Akan Lambobin da Za a Iya Kwafi.

Domin cike jadawalin lokaci kaɗan: daga Satumba 1936 zuwa Yuli 1938 (tare da hutun watanni uku a lokacin bazara na 1937), Turing yana Princeton, bayan ya je can don zama ɗalibi na digiri na biyu a Cocin Alonzo. A wannan lokacin a Princeton, Turing ya fi mai da hankali kan dabarun lissafi, yana rubuta da yawa. wahalar karantawa labarai cike da lissafin lambda na cocin, - kuma, wataƙila, bai da littafi kan makanikan kwantum tare da shi.

Turing ya koma Cambridge a watan Yulin 1938, amma a watan Satumba na wannan shekarar yana aiki na ɗan lokaci a Makarantar Gwamnati ta Lambobi da Siphers, kuma bayan shekara guda ya koma Bletchley Park don yin aiki na cikakken lokaci kan batutuwan da suka shafi nazarin cryptanalysis. Bayan yaƙin ya ƙare a 1945, Turing ya koma Landan don yin aiki a Dakin Gwaji na Ƙasa kan ci gaban aikin ƙirƙira kwamfutaYa yi shekarar karatu ta 1947-8 a Cambridge, amma daga baya ya koma Manchester don ci gaba da karatu akwai kwamfuta ta farko.

A shekarar 1951, Turing ya fara karatu sosai. ilmin halitta na ka'ida(Ni da kaina na ga wannan gaskiyar abin mamaki ne, domin a gare ni, Turing koyaushe yana da ra'ayin cewa ya kamata a yi amfani da tsarin halittu ta hanyar lissafin bambanci, ba ta hanyar wani abu daban kamar injinan Turing ko na'urorin tantanin halitta ba.) Ya kuma mayar da sha'awarsa ga kimiyyar lissafi, kuma har zuwa 1954 har ma ya kai ga ya rubuta wa abokinsa kuma ɗalibi Robin Gandy, Menene: "Na yi ƙoƙarin ƙirƙiro sabuwar fasahar kwantum"(kodayake ya ƙara da cewa:"amma a zahiri ba gaskiya ba ne cewa zai yi aiki"). Amma, abin takaici, komai ya ƙare ba zato ba tsammani a ranar 7 ga Yuni, 1954, lokacin da Turing ya mutu ba zato ba tsammani. (Ina tsammanin ba kashe kansa ba ne, amma wannan wani labari ne daban.)

To, bari mu koma shafin lissafin lambda. Riƙe shi har zuwa haske, za mu sake ganin alamar ruwa:

Wannan takarda a bayyane take an yi ta ne daga Birtaniya, kuma a gare ni da alama ba za a yi amfani da ita a Princeton ba. Amma za mu iya yin kwanan wata daidai? To, ba tare da wani taimako ba. Ƙungiyar Masana Tarihi na Masu Kera Takardu ta BurtaniyaMun san cewa kamfanin da ke kera takardu na hukuma shine Spalding & Hodge, Papermakers, Wholesale and Export Company, Drury House, Russell Street, Drury Lane, Covent Garden, London. Wannan na iya taimakawa, amma ba sosai ba, domin da alama an haɗa takardar Excelsior ɗinsu a cikin kundin kayayyaki daga shekarun 1890 zuwa 1954.

Me wannan shafin ya ce?

Don haka, bari mu yi nazari sosai kan abin da ke gefen takardar biyu. Bari mu fara da lambdas.

Ga wata hanya don tantancewa ayyuka na "tsarkakakku" ko "marasa suna", kuma su ne ginshiƙi na asali a cikin dabarun lissafi, kuma yanzu a cikin shirye-shiryen aiki. Waɗannan ayyuka sun zama ruwan dare a cikin harshen Yaren Wolfram, kuma manufarsu tana da sauƙin bayyanawa. Misali, wani ya rubuta f[x] don nuna aiki f, an yi amfani da shi ga hujjar x. Kuma akwai ayyuka da yawa masu suna f kamar Abs ko zunubi ko blurAmma fa idan wani yana son f[x] ya kasance 2x + 1Babu wani suna kai tsaye ga wannan aikin. Amma akwai wani nau'in aikin, 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] yana amfani da ayyuka ga hujjar x, yana samar da sakamako 2x+1. Function[a,2a+1] aiki ne na "tsarkakakke" ko "ba a san shi ba", wanda shine aikin tsarkakewa na ninkawa da 2 da ƙara 1.

Don haka, λ a cikin lissafin lambda ainihin analog ne aiki a cikin Harshen Wolfram—saboda haka, misali, λa.(2 a+1) daidai Function[a, 2a + 1](Yana da kyau a lura cewa aikin, kamar, Function[b,2b+1] daidai; "masu canjin da aka ɗaure" a ko b kawai wurare ne da za a maye gurbin hujjar aiki - kuma a cikin Yaren Wolfram ana iya guje musu ta hanyar amfani da wasu ma'anoni na tsarkakken aiki (2# +1)&).

A cikin ilmin lissafi na gargajiya, yawanci ana ɗaukar ayyuka a matsayin abubuwa waɗanda ke wakiltar shigarwa (misali, lambobi) da fitarwa (waɗanda kuma, misali, lambobi). Amma wane irin abu ne wannan? aiki (ko λ )? Ainihin tsarin aiki ne wanda ke ɗaukar maganganu ya mayar da su ayyuka. Wannan na iya zama kamar abin mamaki daga mahangar lissafi na gargajiya da kuma bayanin lissafi, amma idan mutum yana buƙatar yin amfani da alamomin da ba a saba gani ba, ya fi dacewa, koda kuwa da farko yana kama da ɗan ƙaramin abu. (Ya kamata a lura cewa lokacin da masu amfani suka koyi Harshen Wolfram, koyaushe zan iya cewa sun ketare wani matakin tunani mai zurfi da zarar sun fahimci aiki).

Lambdas wani ɓangare ne kawai na abin da ke shafin. Akwai wani ra'ayi, wanda ya fi rikitarwa— masu haɗakaBari mu kalli wani layi mai duhu PI1IIxMe wannan zai iya nufi? Ainihin, jerin masu haɗa abubuwa ne, ko kuma wani tsari mai kama da na ayyukan alamu.

Za a iya rubuta wani tsari mai sauƙi na ayyuka, wanda aka saba da shi a lissafi, cikin Harshen Wolfram kamar haka: f[g[x]] - me ake nufi da "amfani"? f sakamakon aikace-aikacen g к x"Amma da gaske kuna buƙatar maƙallan don wannan? A cikin Harshen Wolfram f@g@ x — wani madadin rubutu. A cikin wannan bayanin, mun dogara ne akan ma'anar Harshen Wolfram: mai aiki @ yana da alaƙa da gefen dama, don haka f@g@x daidai f@(g@x).

Amma mene ne ma'anar rikodin? (f@g)@xWannan daidai yake f[g][x]Kuma idan f и g ayyuka ne na yau da kullun a cikin lissafi, da ba shi da ma'ana, amma idan f - aiki mafi girma, to, f[g] zai iya zama aiki wanda za a iya amfani da shi sosai x.

Bari mu lura cewa har yanzu akwai wani sarkakiya a nan. f[х] - f aiki ne na hujja ɗaya. Kuma f[х] daidai da shigarwar Function[a, f[a]][x]Amma idan akwai hujjoji guda biyu a cikin wani aiki, misali, f[x,y]? Ana iya rubuta wannan kamar haka Function[{a,b},f[a, b]][x, y]Amma fa idan ya faru Function[{a},f[a,b]]Menene wannan? Akwai "canjin kyauta" a nan. b, wanda kawai ake miƙawa ga aikin. Function[{b},Function[{a},f[a,b]]] zai ɗaure wannan canjin sannan Function[{b},Function[{a},f [a, b]]][y][x] bayarwa f[x,y] kuma. (Bayani game da aiki don ya sami hujja ɗaya ana kiransa "currying," wanda aka sanya wa suna bayan masanin dabaru mai suna Haskell Curry).

Idan akwai masu canji kyauta, to akwai matsaloli daban-daban game da yadda za a iya bayyana ayyuka, amma idan muka takaita kanmu ga abubuwa aiki ko kuma λ, waɗanda ba su da masu canji masu 'yanci, gabaɗaya ana iya bayyana su cikin 'yanci. Irin waɗannan abubuwa ana kiransu masu haɗuwa.

Masu haɗaka suna da dogon tarihi. An san cewa ɗalibi ne ya fara gabatar da su a shekarar 1920. Dauda Gilbert - Musa Schonfinkel.

A wancan lokacin, kwanan nan ne aka gano cewa babu buƙatar amfani da maganganu kuma, Or и ba don wakiltar maganganu a cikin tsarin dabaru na yau da kullun: ya isa a yi amfani da mai aiki ɗaya, wanda yanzu za mu kira shi Nan (domin, misali, idan ka rubuta Nan yaya ·, sannan Or[a,b] zai ɗauki fom ɗin (a·a)·(b·b)Schönfinkel yana son samun irin wannan ƙaramin wakilci na dabaru na predicate, ko, a zahiri, dabaru gami da ayyuka.

Ya fito da "haɗawa" guda biyu S da K. A cikin Harshen Wolfram, ana iya rubuta wannan kamar haka
K[x_][y_] → x da S[x_][y_][z_] → x[z][y[z]].

Abin mamaki ne cewa ya zama mai yiwuwa a yi amfani da waɗannan mahaɗan guda biyu don yin kowace lissafi. Misali,

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

ana iya amfani da shi azaman aiki don ƙara lambobi biyu.

Waɗannan duk abubuwa ne marasa ma'ana, a taƙaice, amma yanzu da muka fahimci menene injunan Turing da lissafin lambda, za mu iya ganin cewa masu haɗa Schoenfinkel sun yi hasashen manufar lissafi na duniya baki ɗaya. (Kuma abin da ya fi ban mamaki shi ne cewa ma'anonin S da K na 1920 ba su da sauƙi, kuma suna kama da juna. injin Turing mai sauƙi sosai a duniya, wanda na gabatar a shekarun 1990, wanda ya kasance na duniya baki ɗaya an tabbatar da shi a shekarar 2007).

Amma bari mu koma ga takardarmu da layinmu PI1IIxAlamomin da aka rubuta a nan masu haɗaka ne, kuma duk an yi su ne don ayyana aiki. Ma'anar a nan ita ce cewa haɗin ayyuka dole ne ya kasance mai alaƙa da hagu, don haka fgx bai kamata a fassara shi da f@g@x ko f@(g@x) ko f[g[x]] ba, sai dai a fassara shi da (f@g)@x ko f[g][x]. Bari mu fassara wannan zuwa tsari mai dacewa don amfani a cikin Harshen Wolfram: PI1IIx zai ɗauki fom ɗin p[i][one][i][i][x].

Me yasa za a rubuta wani abu kamar haka? Domin bayyana wannan, muna buƙatar tattauna manufar lambobin coci (wanda aka sanya wa suna bayan Cocin Alonzo). Bari mu ce kawai muna aiki da alamomi da lambdas ko masu haɗa lambobi. Akwai wata hanyar da za a yi amfani da su don wakiltar lambobi?

Yaya za a ce kawai lambar ce n соответствует Function[x, Nest[f,x,n]]Ko kuma, a wata ma'anar, me (a takaice):

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

Wannan duk yana iya zama kamar ba a san shi sosai ba, amma dalilin da ya sa yake da ban sha'awa shi ne cewa yana ba mu damar yin komai gaba ɗaya a matsayin alama da kuma abin da ba a iya fahimta ba, ba tare da yin magana a sarari game da abubuwa kamar lambobi ba.

Da wannan hanyar rarraba lambobi, bari mu yi tunanin, misali, ƙara lambobi biyu: 3 za a iya wakilta shi kamar haka f[f[f[#]]]& kuma 2 shine f[f[#]]&Za ka iya ƙara su ta hanyar amfani da ɗaya kawai ga ɗayan:

Amma menene abin? f? Zai iya zama komai! A wata ma'ana, "je lambda" gaba ɗaya kuma yana wakiltar lambobi ta amfani da ayyuka waɗanda ke ɗaukar f a matsayin hujja. A wata ma'anar, bari mu wakilci 3, misali, kamar Function[f,f[f[f[#]]] &] ko Function[f,Function[x,f[f[f[x]]]](Yaushe da kuma yadda ake buƙatar ambaton masu canji shine ɓangaren da ke da wahala a cikin lissafin lambda).

Bari mu kalli wani ɓangare na labarin Turing na 1937 Kwarewa da bambancin λ, wanda ke daidaita abubuwa daidai kamar yadda muka tattauna yanzu:

Shigarwa a nan na iya zama ɗan rikitarwa. x Turing namu ne f, Kuma nasa x' (mai rubuta rubutu ya yi kuskure ta hanyar saka sarari) - wannan namu ne xAmma daidai wannan hanyar ana amfani da ita a nan.

Don haka bari mu kalli layin bayan naɗewa a gaban takardar. Wannan shine I1IIYI1IIxA cikin rubutun Wolfram Language, wannan zai zama i[one][i][i][y][i][one][i][i][x]Amma ga ni aikin asali ne, saboda haka i[one] kawai yana bayarwa daya. A halin yanzu, daya Shin wakilcin lambar Ikilisiya ne ga 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 bayyana idan muka rubuta ƙa'idodin maye gurbin don i и daya, maimakon amfani da lissafin lambda kai tsaye. Sakamakon zai zama iri ɗaya. Yi amfani da waɗannan ƙa'idodi a sarari, kuma za mu sami:

Kuma wannan daidai yake da abin da aka gabatar a cikin taƙaitaccen shigarwar farko:

Bari mu sake duba takardar, a samanta:

Akwai wasu abubuwa masu rikitarwa da ba a san su ba "E" da "D" a nan, amma suna nufin "P" da "Q", don haka za mu iya rubuta furucin kuma mu kimanta shi (lura cewa a nan - bayan wasu rikicewa da alamar ƙarshe - "masanin kimiyya mai ban mamaki" yana sanya […] da (…) don wakiltar aikace-aikacen aikin):

Don haka, wannan shine taƙaitaccen bayani na farko da aka nuna. Domin ganin ƙarin bayani, bari mu maye gurbin ma'anar Q:

Mun sami ainihin taƙaitaccen bayanin da aka nuna. Me zai faru idan muka maye gurbin kalmomin da P?

Ga sakamakon:

Kuma yanzu, ta amfani da gaskiyar cewa i aiki ne wanda ke samar da hujjar kanta a matsayin fitarwa, mun sami:

Kai! Amma ba wannan ne layin da aka rubuta na gaba ba. Akwai kuskure a nan? Ba a fayyace shi ba. Domin kuwa, ba kamar sauran lokuta ba, babu kibiya da ke nuna cewa layi na gaba ya biyo baya daga wanda ya gabata.

Akwai ɗan sirri a nan, amma bari mu ci gaba zuwa ƙasan takardar:

Ga lambar Cocin 2, misali, an ƙaddara ta hanyar tsari. two[a_] [b_] → a[a[b]]Lura cewa wannan shine ainihin sigar layi na biyu idan an yi la'akari da a a matsayin Function[r,r[р]] и b yadda qDon haka, muna sa ran sakamakon lissafin zai kasance kamar haka:

Duk da haka, ma'anar da ke ƙasa а[b] za a iya rubuta shi a matsayin x (mai yiwuwa ya bambanta da x da aka rubuta a baya akan takardar) - sakamakon haka mun sami sakamakon ƙarshe:

Don haka za mu iya fahimtar kaɗan daga cikin abubuwan da ke faruwa a wannan takarda, amma aƙalla wani sirri da ya rage shi ne abin da ake tsammanin Y zai kasance.

A zahiri, a cikin dabaru masu haɗaka akwai daidaitaccen haɗin Y: abin da ake kira mai haɗa maƙallin gyarawaA hukumance, ana bayyana shi ta hanyar gaskiyar cewa Y[f] ya kamata ya zama daidai f[Y[f]], ko kuma, a wata ma'anar, cewa Y[f] baya canzawa lokacin da aka yi amfani da f, don haka wuri ne da aka ƙayyade don f(Mai haɗa Y yana da alaƙa da #0 a cikin Yaren Wolfram.)

A halin yanzu, Y-combinator ya shahara saboda Mai hanzarta ƙaddamar da Y-Combinator, mai suna haka Paul Graham (wanda ya daɗe yana sha'awar shirye-shiryen aiki и Harshen shirye-shirye na LISP kuma ya aiwatar da shagon yanar gizo na farko bisa ga wannan harshe). Ya taɓa gaya mini da kaina, “Babu wanda ya fahimci menene haɗin Y"(Ya kamata a lura cewa Y Combinator shine ainihin abin da ke bawa kamfanoni damar gujewa ayyukan da aka tsara…)

An ƙirƙiro haɗin Y (a matsayin mai haɗa maki mai tsayi) sau da yawa. Turing ya fito da aiwatarwa a shekarar 1937, wanda ya kira Θ. Amma shin harafin "Y" a shafinmu sanannen mai haɗa maki mai tsayi? Wataƙila a'a. To menene "Y" ɗinmu? Yi la'akari da wannan taƙaitaccen bayani:

Amma wannan bayanin a bayyane yake bai isa ya tantance ainihin abin da Y yake nufi ba. A bayyane yake cewa Y yana aiki akan fiye da hujja ɗaya kawai; da alama yana aiki akan aƙalla biyu, amma ba a san (aƙalla a gare ni) adadin muhawarar da ake buƙata da abin da yake yi ba.

A ƙarshe, duk da cewa za mu iya fahimtar sassa da yawa na takardar, dole ne mu ce, a matakin duniya, ba a san abin da aka yi a can ba. Ko da yake ana buƙatar bayani mai yawa game da abin da aka gabatar a nan, yana da matuƙar sauƙi ta amfani da lambda calculus da combinators.

Wataƙila, wannan yana wakiltar yunƙurin ƙirƙirar "shiri" mai sauƙi—ta amfani da lissafin lambda da masu haɗa abubuwa don cimma wani abu. Amma dangane da injiniyan baya, yana da wuya a faɗi menene "wani abu" ya kamata ya kasance da kuma menene babban burin "wanda za a iya bayyanawa".

Akwai wani fasali da aka gabatar a takardar da ya cancanci yin tsokaci a kai a nan: amfani da nau'ikan baka daban-daban. A cikin lissafin gargajiya, galibi ana amfani da baka don komai - da kuma aikace-aikacen aiki (kamar yadda yake a cikin f (x)), da kuma rukunonin membobi (kamar yadda yake a cikin (1+x) (1-x), ko kuma, ƙasa da haka a bayyane yake, a(1-x)(A cikin Harshen Wolfram, mun bambanta tsakanin amfani daban-daban na baka - a cikin maƙallan murabba'i don bayyana ayyuka f [x] - kuma ana amfani da maƙallan zagaye ne kawai don haɗa rukuni).

Lokacin da lissafin lambda ya fara bayyana, akwai tambayoyi da yawa game da amfani da baka. Daga baya Alan Turing zai rubuta cikakken takarda (wanda ba a buga ba) mai taken "Canjin tsarin rubutu da kuma tsarin jumla", amma tun a shekarar 1937 ya ji cewa yana buƙatar bayyana ma'anar zamani (wani lokacin hackish) ga lambda calculus (wanda, ta hanyar, saboda Cocin ne).

Yace haka f, an yi amfani da shi g, ya kamata a rubuta shi {f}(g), idan kawai f ba shine kawai alamar ba, a wannan yanayin yana iya zama f(g)Sai ya ce lambda (kamar yadda yake a cikin Function[a, b]) ya kamata a rubuta shi kamar λ a[b] ko kuma, a madadin haka, λ a.b.

Duk da haka, wataƙila zuwa 1940 an yi watsi da duk ra'ayin amfani da {…} da […] don nuna abubuwa daban-daban, galibi don fifita maƙallan a cikin salon lissafi na yau da kullun.

Duba saman shafin:

Yana da wuya a fahimta a wannan tsari. A cikin ma'anonin Church, ana amfani da maƙallan murabba'i don haɗa rukuni, tare da maƙallin buɗewa wanda ke maye gurbin lokacin. Idan aka yi amfani da wannan ma'anar, ya bayyana cewa Q (wanda aka yiwa lakabi da D daga ƙarshe), wanda aka haɗa a cikin maƙallan a ƙarshe, shine abin da dukkan lambda na farko ya shafi.

A gaskiya ma, maƙallin murabba'i a nan bai iyakance jikin lambda ba; maimakon haka, yana wakiltar wani aikace-aikacen aiki yadda ya kamata, kuma babu wata alama a fili game da inda jikin lambda ya ƙare. A ƙarshe, a bayyane yake cewa "masanin kimiyya mai ban mamaki" ya canza maƙallin murabba'i na rufewa zuwa bakan gizo, yana amfani da ma'anar Church yadda ya kamata - don haka ya tilasta a kimanta kalmar kamar yadda aka nuna a takardar.

To me wannan ƙaramin guntun yake nufi a zahiri? Ina tsammanin yana nuna cewa an rubuta shafin a shekarun 1930, ko kuma aƙalla ba da daɗewa ba bayan haka, domin ba a riga an kafa ƙa'idodin maƙallan ba tukuna.

To, rubutun hannun wa ne ko ta yaya?

To, zuwa yanzu mun yi magana game da abin da aka rubuta a shafin. Amma fa game da wanda ya rubuta shi?

Wanda ya fi bayyana a fili a wannan matsayin shine Alan Turing da kansa, tunda, bayan haka, shafin yana cikin littafinsa. Daga mahangar abun ciki, babu wani abu da ya saba wa ra'ayin cewa Alan Turing zai iya rubuta shi - ko da lokacin da ya fara yin amfani da kalkuletin lambda bayan ya karɓi takardar Church a farkon 1936.

Yaya batun rubutun hannu? Shin na Alan Turing ne? Bari mu dubi misalai da dama da suka tsira waɗanda muka san tabbas Alan Turing ne ya rubuta su:

Rubutun da aka gabatar a bayyane yake ya bambanta sosai, amma me game da bayanan da aka yi amfani da su a cikin rubutun? Aƙalla, a ganina, bai yi kama da a bayyane ba - kuma mutum zai iya ɗauka cewa duk wani bambanci na iya kasancewa saboda gaskiyar cewa an rubuta misalan da ke akwai (wanda aka gabatar a cikin tarihin), a ce, "a bayyane," yayin da shafinmu yake nuna aikin tunani na gaske.

Ya zama abin da ya dace a bincikenmu cewa a cikin tarihin Turing akwai shafi wanda ya rubuta a kai teburin hali, wanda ake buƙata don sunayen. Kuma idan aka kwatanta waɗannan alamomin harafi-harafi, suna kama da ni sosai (an yi waɗannan shigarwar a cikin lokacin Turing lokacin da aka ɗaura masa aure nazarin girman tsirrai, don haka aka rubuta "yankin takardar"):

Ina so in ci gaba da bincike a kan wannan, don haka na aika da samfura Sheila Lowe, ƙwararren masanin rubutun hannu (kuma marubucin matsalolin rubutun hannu) wanda na taɓa haɗuwa da shi—kawai ina gabatar da takardarmu a matsayin "samfurin 'A'" da kuma samfurin rubutun Turing da ke akwai a matsayin "samfurin 'B'." Amsarta ta kasance tabbatacce kuma mara kyau:Salon rubutu ya bambanta gaba ɗaya. Dangane da halayen mutum, marubucin samfurin "B" yana da salon tunani mai sauri da fahimta fiye da marubucin samfurin "A."".

Ban gamsu sosai ba tukuna, amma na yanke shawarar cewa lokaci ya yi da zan nemi wasu zaɓuɓɓuka.

To idan Turing bai rubuta wannan ba, to wa ya rubuta? Norman Routledge ya gaya mini cewa ya karɓi littafin daga Robin Gandy, wanda shi ne mai aiwatar da Turing. Don haka na aika wa Gandy "Sample C":

Amma ƙarshen farko na Sheila shine cewa samfuran uku wataƙila mutane uku ne suka rubuta su, kuma lura cewa samfurin "B" ya fito ne daga "mafi saurin tunani - wanda ya fi yiwuwa ya nemi mafita marasa kyau ga matsaloli" (Ina ganin abin farin ciki ne cewa ƙwararren rubutun hannu na zamani zai ba da irin wannan kimantawa game da rubutun hannu na Turing, ganin yadda kowa ya yi korafi game da rubutun hannu a cikin ayyukan makarantar Turing na shekarun 1920.)

To, a lokacin, da alama an cire Turing da Gandhi daga jerin "wanda ake zargi". To wa zai iya rubuta shi? Na fara tunanin mutanen da Turing zai iya ba da rancen littafinsa. Tabbas, dole ne su iya yin lissafi ta amfani da lambda calculus.

Na yi zaton mutumin ya fito ne daga Cambridge, ko kuma aƙalla daga Ingila, idan aka yi la'akari da alamar da ke kan takardar. Na ɗauka cewa 1936 ko makamancin haka lokaci ne mai kyau don rubuta wannan. To, wa Turing ya san kuma ya yi mu'amala da shi a wancan lokacin? Mun sami jerin duk ɗaliban lissafi da malamai a Kwalejin King's na wannan lokacin. (Akwai ɗalibai 13 da aka sani waɗanda suka yi karatu tsakanin 1930 da 1936.)

Kuma daga cikinsu, ɗan takarar da ya fi samun nasara shine David ChampernowShekarunsa ɗaya ne da Turing, wani abokinsa na dogon lokaci, kuma yana da sha'awar tushen lissafi - a shekarar 1933 ma ya buga wata takarda kan abin da muke kira yanzu. Lambar Champernowne (lambar "al'ada"): 0.12345678910111213… (wanda aka samu ta haɗa lambobi 1, 2, 3, 4,…, 8, 9, 10, 11, 12,…, kuma ɗaya daga cikin lambobi kaɗan, wanda aka sani da "al'ada" a ma'anar cewa kowace toshewar lambobi mai yiwuwa tana faruwa da daidaiton yuwuwar).

A shekarar 1937 ma ya yi amfani da Dirac gamma matrices, kamar yadda aka ambata a littafin Dirac, don warware matsalar. matsalar lissafi ta hutawa(Hakan ya faru ne bayan shekaru da yawa na zama babban mai sha'awar lissafin gamma matrix.)

Lokacin da ya fara karatun lissafi, Champernowne ya sami kansa a ƙarƙashin tasirin John Maynard Keynes (har ila yau a Kwalejin King's) kuma daga ƙarshe ya zama ƙwararren masanin tattalin arziki, musamman yana yin aiki kan rashin daidaiton samun kuɗi. (Duk da haka, a shekarar 1948 ya kuma yi aiki tare da Turing kan ƙirƙirar Turbochamp - shirin dara wanda ya zama kusan na farko a duniya da aka aiwatar akan kwamfuta).

Amma ina zan iya samun samfurin rubutun hannu na Champernowne? Ba da daɗewa ba na sami ɗansa, Arthur Champernowne, a LinkedIn, wanda, abin mamaki, yana da digiri a fannin dabaru na lissafi kuma yana aiki a Microsoft. Ya ce mahaifinsa ya yi masa magana sosai game da aikin Turing, kodayake bai ambaci mahaɗan ba. Ya aiko min da samfurin rubutun hannu na mahaifinsa (wani sashi game da rubutun kiɗa na algorithmic):

Nan take za a iya cewa rubutun hannu bai yi daidai ba (launi da wutsiyoyin da ke cikin haruffan f a cikin rubutun hannu na Champernowne, da sauransu)

To, wanene kuma zai iya zama? Na daɗe ina yabawa Max Newman, ta hanyoyi da yawa jagora ne ga Alan Turing. Newman ya fara sha'awar Turing atsarin lissafi", abokinsa ne na dogon lokaci, kuma shekaru bayan haka ya zama shugabansa a aikin kwamfuta na Manchester. (Duk da sha'awarsa ga kwamfuta, Newman koyaushe yana ganin kansa a matsayin masanin ilimin halittu, kodayake ƙarshen bincikensa ya sami goyon baya daga wata shaida mara kyau da ya samo daga Zato na Poincaré).

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

"Babbar" littafin

Don haka, aikin tantance rubutun hannu ya gaza. Na yanke shawarar cewa mataki na gaba shine in yi ƙoƙarin bin diddigin abin da ya faru da littafin da nake riƙe da shi a hannuna.

To, da farko, menene dogon labarin game da Norman Routledge? Ya halarci Kwalejin King's, Cambridge, a shekarar 1946 kuma ya haɗu da Turing (eh, dukkansu 'yan luwaɗi ne). Ya kammala karatunsa a shekarar 1949, sannan ya fara rubuta takardar digirin digirgir ɗinsa tare da Turing a matsayin mai ba shi shawara. Ya sami digirin digirgir a shekarar 1954, yana aiki akan ka'idar lissafi da kuma ka'idar recursion. Ya sami tallafin karatu a Kwalejin King's, kuma zuwa 1957, ya zama shugaban sashen lissafi a can. Da ya iya yin wannan duk rayuwarsa, amma yana da sha'awa iri-iri (kiɗa, fasaha, gine-gine, lissafi na nishaɗi, asalin tarihi, da sauransu). A shekarar 1960 ya canza mayar da hankali kan ilimi ya zama malami a Eton, inda tsararraki da yawa na ɗalibai (ciki har da ni) suka yi aiki (kuma suka yi karatu), suna fuskantar iliminsa na musamman da kuma wani lokacin ma na ban mamaki.

Shin Norman Rutledge ne ya rubuta wannan shafin mai ban mamaki da kansa? Ya san lissafin lambda (kodayake, bisa ga kuskure, ya ambaci hakan lokacin da muka sha shayi a shekarar 2005, yana cewa koyaushe yana ganin yana "rikitarwa"). Duk da haka, rubutun hannunsa na musamman nan da nan ya hana shi zama "masanin kimiyya mai ban mamaki."

Shin wannan shafin zai iya kasancewa yana da alaƙa ta wata hanya da ɗalibin Norman, wataƙila tun lokacin da yake Cambridge? Ina shakkar hakan. Domin ban yi tsammanin Norman ya taɓa yin nazarin kalkuleta na lambda ko wani abu makamancin haka ba. Yayin rubuta wannan labarin, na gano cewa Norman ya rubuta takarda a shekarar 1955 kan ƙirƙirar dabaru kan "kwamfutocin lantarki" (da ƙirƙirar siffofi na yau da kullun masu haɗawa, kamar yadda aikin da aka gina a ciki yake yi a yau). Rage girman Boolean). Lokacin da na san Norman, yana da sha'awar rubuta kayan aiki na kwamfutoci na gaske (sunan farko na farko shine "NAR," kuma ya kira shirye-shiryensa "NAR...," kamar "NARLAB," wani shiri ne na ƙirƙirar lakabin rubutu ta amfani da ramukan da aka huda a cikin tef ɗin takarda. Amma bai taɓa tattauna samfuran ka'idoji na kwamfuta ba.

Bari mu karanta bayanin Norman a cikin littafin sosai. Abu na farko da za mu lura shi ne yana magana game da "bayar da littattafai daga ɗakin karatu na wani mamaci"Kuma daga kalmomin, da alama komai ya faru da sauri bayan mutuwar mutumin, yana nuna cewa Norman ya sami littafin jim kaɗan bayan mutuwar Turing a 1954, kuma Gandhi ya daɗe yana ɓatar da shi. Norman ya ci gaba da cewa ya sami littattafai huɗu, biyu akan lissafi tsantsa da biyu akan kimiyyar lissafi.

Sai ya ce ya bayar"wani daga cikin littattafan kimiyyar lissafi (ina tsammanin, Zuwa ga Hermann Weyl)»«Ga Sebag Montefiore, saurayi mai kirki da za ku iya tunawa [George Rutter]"To, to wanene shi? Na tono Jerin Membobina da ba a cika amfani da su ba." Ƙungiyar Tsohon Eton(Dole ne in faɗi cewa, lokacin da na buɗe shi, ban iya daina lura da ƙa'idodinsa daga 1902 ba, wanda na farko, a ƙarƙashin taken "Hakkokin Membobi," an karanta cikin ban dariya: "Riga da launukan Ƙungiyar").

Ya kamata a ƙara da cewa da ban taɓa shiga wannan ƙungiyar ba ko kuma na sami wannan littafin idan ba don nacewar abokina daga Eton mai suna ba. Nicholas Kermack, wanda ya daɗe yana shirin zama firayim minista tun yana ɗan shekara 12 zuwa wata rana, amma abin baƙin ciki ya mutu yana da shekara 21).

Amma a kowane hali, mutane biyar ne kawai daga cikin waɗanda aka lissafa suna da sunan ƙarshe Sebag-Montefiore, tare da lokutan horo iri-iri. Abu ne mai sauƙi a ga cewa wanda ya dace shi ne wanda ya dace. Hugh Sebag-MontefioreKamar yadda aka bayyana, ƙaramar duniya ce ta iyalinsa ta mallaki Bletchley Park kafin ta sayar da ita ga gwamnatin Birtaniya a shekarar 1938. Kuma a shekarar 2000, Sebag-Montefiore ya rubuta littafi game da karya Enigma (injin ɓoye bayanai na Jamus) — wannan shine, a dukkan alamu, dalilin da ya sa a shekarar 2002 Norman ya yanke shawarar ba shi littafin da Turing ya mallaka.

To, to fa sauran littattafan da Norman ya karɓa daga Turing fa? Da yake ban sami wata hanyar gano abin da ya same su ba, sai na yi odar kwafin wasiyyar Norman. Sashe na ƙarshe ya yi kama da na Norman:

Wasiyyar ta ƙayyade cewa a bar littattafan Norman ga Kwalejin King. Duk da cewa babu cikakken tarin littattafansa a ko'ina, littattafai biyu kan lissafi na gaskiya na Turing, waɗanda ya ambata a cikin bayaninsa, yanzu an ajiye su a cikin taskar ɗakin karatu na Kwalejin King.

Tambaya ta gaba: Me ya faru da sauran littattafan Turing? Na kalli wasiyyar Turing, wadda ta zama kamar ta bar wa Robin Gandy duka.

Gandy ɗalibi ne na lissafi a Kwalejin King's, Cambridge, wanda ya yi abota da Alan Turing a shekararsa ta ƙarshe a can a shekarar 1940. A farkon yaƙin, Gandy ya yi aiki a rediyo da radar, amma a shekarar 1944, an tura shi zuwa wannan sashe da Turing, yana aiki a kan ɓoye magana. Bayan yaƙin, Gandy ya koma Cambridge, ba da daɗewa ba ya sami digirin digirgir, kuma Turing ya zama mai ba shi shawara.

Aikinsa a soja ya sa ya fara sha'awar tambayoyi a fannin kimiyyar lissafi, kuma takardar digirinsa ta digiri, wadda aka kammala a shekarar 1952, an yi mata taken "President of the Dissertation". Akan Tsarin Axiomatic a Lissafi da Ka'idoji a fannin LissafiAbin da Gandhi yake ƙoƙarin yi shi ne wataƙila ya siffanta ka'idojin zahiri ta fuskar dabaru na lissafi. irin theories и ƙa'idodin ƙididdiga, amma ba game da injunan Turing ba. Kuma daga abin da muka sani yanzu, ina tsammanin za mu iya yanke hukuncin cewa ya rasa ma'anar. Kuma hakika, aikina na kaina tun farkon shekarun 1980 ya yi jayayya cewa ya kamata a ɗauki hanyoyin jiki a matsayin "ƙididdiga iri-iri" - kamar injinan Turing ko na'urorin tantanin halitta, misali - maimakon a matsayin ka'idoji da za a iya fahimta. (Gandhi ya tattauna tsarin nau'ikan da ke cikin ka'idojin zahiri da kyau, yana cewa, misali, cewa "Ina ganin cewa tsarin kowace lambar adadi mai lissafi a cikin nau'in binary bai kai takwas ba"). Ya ce "Ɗaya daga cikin dalilan da ya sa ka'idar filin kwantum ta zamani take da rikitarwa shine kawai saboda tana hulɗa da abubuwa masu nau'in rikitarwa - ayyukan ayyuka ...", wanda a ƙarshe yana nuna cewa"Za mu iya ɗaukar mafi girman nau'in amfani na yau da kullun a matsayin alamar ci gaban lissafi".)

Gandhi ya ambaci Turing sau da yawa a cikin rubutun digiri, yana mai cewa a cikin gabatarwar cewa yana bin A. M. Turing bashi, wanda "da farko ya jawo hankalinsa ga lissafin cocin da ba a mayar da hankali ba"(watau lissafin lambda), kodayake a zahiri rubutunsa yana da hujjoji da yawa na lambda.

Bayan kare rubutunsa na digiri, Gandhi ya koma ga tsararren dabaru na lissafi kuma, tsawon shekaru sama da talatin, ya rubuta takardu a kan adadin guda ɗaya a kowace shekara, wanda aka yi la'akari da shi sosai a cikin al'ummar dabaru na lissafi ta duniya. A shekarar 1969, ya ƙaura zuwa Oxford, kuma ina tsammanin na haɗu da shi tun ina ƙarami, kodayake ban tuna da shi ba.
A bayyane yake Gandhi ya bauta wa Turing kuma yana yawan magana game da shi a shekarun baya. Wannan ya haifar da tambayar cikakken tarin ayyukan Turing. Jim kaɗan bayan mutuwar Turing, Sarah Turing da Max Newman sun nemi Gandhi - a matsayin wanda zai aiwatar da shi - ya shirya buga takardun Turing da ba a buga ba. Yayin da shekaru suka shude, wasiƙu daga taskar tarihi ya nuna rashin jin daɗin Sarah Turing game da wannan batu. Amma ta wata hanya, Gandhi bai taɓa shirin tattara takardun Turing ba.

Gandhi ya mutu a shekarar 1995 ba tare da ya tattara ayyukansa da ya kammala ba. Nick Furbank - mai sukar adabi da kuma mai rubuta tarihin rayuwa E. M. Forster, wanda Turing ya haɗu da shi a Kwalejin King's, shine wakilin adabi na Turing, kuma a ƙarshe ya fara aiki akan tarin ayyukan Turing. Kundin da aka yi kan dabarun lissafi ya zama mafi tayar da hankali, kuma saboda haka ya jawo hankalin ɗalibi na farko na digiri na biyu na Robin Gandy, wani takamaiman Mike Yates, wanda ya sami wasiƙu zuwa ga Gandhi game da ayyukan da aka tattara waɗanda ba a fara su ba tsawon shekaru 24.Ayyukan da aka Tara a ƙarshe ya bayyana a shekarar 2001 - shekaru 45 bayan fitowarsu).

Amma fa game da littattafan da Turing ya mallaka da kansa? A ci gaba da ƙoƙarina na gano su, na gaba da na je gidan Turing, musamman ƙaramin ɗan ɗan'uwan Turing. Dermot Turing (wanda a zahiri shine Sir Dermot Turing, saboda gaskiyar cewa shi ne baronet, wannan lakabin bai zo masa ta hanyar zuriyar Alan a cikin dangin Turing ba). Dermot Turing (wanda ya rubuta kwanan nan Tarihin Alan Turing) ya gaya min game da "kakar Turing" (wanda aka fi sani da Sarah Turing), wacce a bayyane yake cewa gidanta yana da ƙofar shiga lambu tare da iyalinsa, da kuma wasu abubuwa da yawa game da Alan Turing. Ya gaya mini cewa iyalin ba su taɓa samun ɗaya daga cikin littattafan Alan Turing ba.

Don haka na koma karanta wasiyyar kuma na gano cewa mai aiwatar da Gandhi shine ɗalibinsa, Mike Yates. Na ji cewa Mike Yates ya yi ritaya daga aikin farfesa shekaru 30 da suka gabata kuma yanzu yana zaune a Arewacin Wales. Ya ce a cikin shekarun da suka gabata yana aiki akan dabaru na lissafi da ka'idar lissafi, bai taɓa taɓa kwamfuta ba - amma a ƙarshe ya yi hakan lokacin da ya yi ritaya (wanda jim kaɗan bayan ya gano shirin). Ilmin lissafiYa ce abin mamaki ne cewa Turing ya shahara sosai, kuma lokacin da ya isa Manchester shekaru uku kacal bayan mutuwar Turing, babu wanda ya yi magana game da Turing, har ma Max Newman lokacin da yake koyar da darasi kan dabaru. Duk da haka, Gandy daga baya ya ba da labarin yadda ya ji daɗin gogewarsa da ayyukan Turing da aka tattara, kuma daga ƙarshe ya bar su duka ga Mike.

Me Mike ya sani game da littattafan Turing? Ya sami ɗaya daga cikin littattafan Turing da aka rubuta da hannu, waɗanda Gandhi bai ba wa Kwalejin King ba saboda (abin mamaki) Gandhi ya yi amfani da shi a matsayin ɓoye bayanan mafarkin da ya ajiye. (Turing kuma ya ajiye bayanan mafarki, waɗanda aka lalata bayan mutuwarsa.) Mike ya ce an sayar da littafin kwanan nan a gwanjon kusan dala miliyan 1. Kuma in ba haka ba, da bai yi tsammanin cewa kayan Gandhi sun haɗa da kayan Turing ba.

Da alama duk zaɓuɓɓukanmu sun ƙare, amma Mike ya ce in duba wannan takarda mai ban mamaki. Nan da nan ya ce:Wannan rubutun hannun Robin Gandhi ne!"Ya ce ya ga abubuwa da yawa tsawon shekaru. Kuma ya tabbata. Ya ce bai san abubuwa da yawa game da lissafin lambda ba kuma ba zai iya karanta shafin ba, amma yana da tabbacin cewa Robin Gandy ne ya rubuta shi."

Mun koma ga ƙwararren rubutun hannunmu da ƙarin samfura, kuma ta yarda cewa, eh, abin da ke wurin ya yi daidai da rubutun hannun Gandhi. Don haka, a ƙarshe muka gano: Robin Gandy ya rubuta wannan takarda mai ban mamaki.Ba Alan Turing ne ya rubuta wannan ba, ɗalibinsa Robin Gandy ne ya rubuta shi.

Ba shakka, akwai wasu asirai har yanzu. Ana zargin Turing ya ba Gandhi littafin, amma yaushe? Yadda aka rubuta lambda calculus yana nuna cewa ya kasance a kusa da shekarun 1930. Amma bisa ga sharhin da Gandhi ya yi kan rubutun digiri, da alama ba zai yi komai da lambda calculus ba har zuwa ƙarshen shekarun 1940. Wannan ya haifar da tambayar dalilin da yasa Gandhi ya rubuta shi. Da alama ba shi da alaƙa kai tsaye da rubutun digirinsa, don haka wataƙila lokacin ne ya fara ƙoƙarin fahimtar lambda calculus.

Ina shakkar za mu taɓa sanin gaskiya, amma tabbas abin sha'awa ne ƙoƙarin gano ta. Ya kamata in ce wannan tafiya gaba ɗaya ta yi matuƙar amfani wajen faɗaɗa fahimtara game da yadda labaran da ke bayan littattafai makamantan su na ƙarni da suka gabata, kamar waɗanda nake da su, za su iya zama masu sarkakiya. Yana sa ni tunanin cewa ya kamata in tabbatar na duba dukkan shafukansu, kawai don ganin abubuwan ban sha'awa da za su iya kasancewa a can…

Ina so in gode wa Jonathan Gorard (karatun sirri a Cambridge), Dana Scott (dabarun lissafi), da Matthew Shudzik (dabarun lissafi) saboda taimakonsu.

Game da fassararFassarar sakon Stephen Wolfram"Littafi daga Alan Turing… da kuma takarda mai ban mamaki".

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