Inguxa yokuCikiza nobuHlakani

" **Inguxa yokuCikiza nobuHlakani** " kwakuyisihloko sephepha elinethonya elabhalwe ngu-Alan Turing ngesihloko sohlakahlisombulu. Lesi sibhalwa sakhe, esashicilelwa ngowezi-1950 kumagazini obizwa Mind, kwaba ngesokuqala ukungenisa emphakathini isibangelo namuhla esaziwa ngokuthi isivivinyo sika-Turing.

Isibhalwa sika-Turing sicubungula umbuzo othi "ingabe izinguxa ziyakwazi ukucabanga?" UTuring uthi, njengoba izwi elithi "ukucabanga"nelithi "inguxa" lingenakuchasiswa ngokucacileyo kufanele "sinane umbuzo ngelinye, elihlobene eduze nalo futhi elikhulunywa ngamazwi angathinziyeli."  Ukuze enze lokho, kufanele aqale ngokufumana isu elilula nelingathinziyeli azonana ngalo izwi elithi "ukucabanga", okwesibili kufanele achaze ngokuqondile ukuthi yiziphi "izinguxa" azicubungulayo, okokugcina, lapho sekahlone ngalamaqiniso, uzocabaya umbuzo omusha, ohlobene nowokuqala nakholelwa ukuthi ungaphendula ngokuqinisekile.

## Isivivinyo sika-Turing

Kunokuthi sizame ukunqumela ukuba inguxa iyacabanga yini, uTuring usikisela ukuthi sibuze ukuba ingabe inguxa ingawunqoba umfeketho obizwa ngokuthi "uMfeketho wokuLingisa". UMfeketho wokuLingisa wendabuko, lowo uTuring awuchazisayo, ungumdlalo weqembu olula obandakanya abadlali abathathu. Umdlali A kuba ngowesilisa, umdlali B kuba ngowesifazane bese umdlali C (obuye abe ngumphenyi) angaba ngowanoma ibuphi ubulili. EMfekethweni wokuLingisa, umdlali C akakwazi ukubona umdlali A nomdlali B (wazi nje ukuthi babizwa X no-Y), futhi ukuxhumana nabo kuphela ngesiqoshwana noma ezinye izindlela ezingayivezi imininingwane yobulili babo. Ngokubuza umdlali A nomdlali B imibuzo, ulinga ukunqumela ukuthi yimuphi kulabadlali ababili ongowesilisa kanye nongowesifazane. Iqhaza lomdlali A ukugila umphenyi ukuze enze isinqumelo esiyiphutha, kuyilapho umdlali B ezama ukulekelela umphenyi ekwenzeni esilungile.
  
UTuring uphakamisa umxhantela walomdlalo obandakanya isiCikizi:  
Ngakho umfeketho oguquliwe kuba ngobandakanya abadlali abathathu abasemagumbini aqhingiwe: isiCikizi (okuyisona esivivinywayo), isothamlilo kanye nesothamlilo esingumgwebi. UMgwebi oyisothamlilo uyakwazi ukuxoxa kokubili nesothamlilo kanye nesicikizi ngokuchofa esiqhafazeni. Kokubili isiCikizi nesothamlilo zilinga ukukholisa umgwebi ukuba bobabili bayizothamlilo. Uma umgwebi ehluleka ukugagula ngokuphindelela ukuthi ini iyini, khona isiCikizi siyawunqoba umfeketho.

Kunjengoba kwaphawula u-Stevan Harna, ukuthi umbuzo usuphendukile waba ngothi "ingabe izinguxa zingakwenza lokho esikwaziyo ukukwenza?" Ngamanye amazwi, uTuring akasabuzi ukuthi inguxa iyakwazi "ukucabanga"; ubuza ukuthi iyakwazi *ukwenza* ngokufanayo  nendlela isothamlilo esicabangayo esenza ngayo. Lombuzo ugwema inkinga enzima yenjulalwazi yokuchasisa kusengaphambili isenzo esithi "ukucabanga" futhi ugxila emakhonweni wokwenza awumphumela wokucabanga, nokuthi isimiso esingunobangela singawaphehla kanjani.

Abanye baye bathatha imibuzo ka-Turing njengebuza ukuthi "ingabe isiCikizi, lapho sixhumana ngesichilelakude, singakwazi ukukhohlisa isothamlilo sikholwe ukuthi naso siyisothamlilo?" kodwa sekuyacaca ukuba uTuring wayengakhulumi ngokukhohlisa abantu kodwa ngokuphathelene nokuphehla ikhono lokuqonda elinjengelomuntu.

## IziNguxa zezezibhangqiwe

UTuring uphinde aqaphele ukuthi sidinga ukunqumela ngokuthi yiziphi "izinguxa" esifisa ukuzicubungula. Uveza ukuthi umuntu oluswempu, nakuba ekhandwe umuntu, akanakuba ilyisibonelo esihle. UTuring wasikisela ukuba sigxile emakhonweni ezinguxa zezezibhangqiwe—izinguxa ezilumba amanani angamabhangqa (1 kanye ne-0), siwabhale kabusha kube yinkumbulo sisebenzisa imithetho elula. Wanikela ngezizathu ezimbili.

Okokuqala, asikho isizathu sokuqagula ukuba zikhona noma cha. Kakade zazikhona ngowe-1950.

Okwesibili, inguxa yezezibhangqiwe "indawozonke". Ucwaningo luka-Turing ngezisekelo zokucikiza lwafakaza ukuthi isiCikizi sezezibhangqiwe singafefenyeka, ngokombono, ukucondoza kwanoma iyiphi inguxa yezezibhangqiwe, uma sinikwe inkumbulo nesikhathi esanele. (Lokhu ukuqonda okuyingqikithi kombono ka-Church no-Turing nokwenguxa ka-Turing.) Ngenxa yalokho, uma *noma iyiphi* inguxa yezezibhangqiwe "yenzisa sengathi iyacabanga" khona ke, *zonke* izinguxa zezezibhangqiwe ezinamandla ngokwanele zingakwenza. UTuring wabhala wathi, "zonke izicikizi zezezibhangqiwe ngomqondo othile ziyalingana."

Lokhu kuvumela ukuba umbuzo wendabuko wenziwe uqonde kakhudlwana. uTuring manje ulungisa umbuzo wendabuko njengothi "Ake sigxilise ukunaka kwethu esicikizini esikhethekile esizosibiza C. Ingabe kuyiqiniso ukuthi ngokuguqula lesicikizi sisenze sibe nesibeko esanele, sandise ngokulingene ijubane laso lokusebenza, futhi sisihlinzeke ngenhleleliso efanele, u-C angenziwa ukuba afekethe ngokugculisayo ingxenye ka-A emfekethweni wokulingisa, lapho ingxenye ka-B yenziwa isothamlilo?"

Ingakho, njengoba kuveza uTuring, singagxilile ekutheni "ingabe zonke izicikizi zezezibhangqiwe zizoganya emfekethweni noma ingabe izicikizi ezitholakalayo kwamanje zizoganya, kodwa ekutheni kunezicikizi ezingenakubalwa ezizoganya". Into ebaluleke kakhulu ukuba sicubungule izimpokozelo ezingenziwa ngesimo sezinguxa zethu namuhla kungakhathaliseki ukuba sinensizakusebenza yokuzakha noma cha.

## Izimpikiso ezilithoba ezivamile

Emva kokucasisa umbuzo, uTuring waqhubeka nokuwuphendula: ecubungula izimpikiso ezilithoba ezivamile ezilandelayo, ezihlanganisa yonke imizakuzakwana emikhulu emelene nohlakahlisombulu eyaphakanyiswa iminyaka kusukela isibhalwa sakhe sishicilelwa okokuqala.

#*Impikiso yezenkolo*: Yona ithi ukucabanga kuyinsebenzo yomphefumulo ongafiyo wesothamlilo; ngalokho, inguxa ayikwazi ukucabanga. "Ekulingeni ukukhanda izinguxa ezinjalo," kubhala uTuring, "akufanele sigabadele ngokungahloniphi amandla Wakhe wokudala imiphefumulo, ngendlela efanayo nalapho sizala izingane: kunalokho, kunoma yisiphi isimo, singamathuluzi entando Yakhe ahlinzeka imiphefumulo ayidalayo ngezithabathaba.
#* 'Impikiso yokuzithela ngabandayo' *: "Imiphumela yokucabanga kwezinguxa ingaba yingozi kakhulu. Masithembe futhi sikholwe soze zikwenze lokho." Le ndlela yokucabanga inesibunge phakathi kwabantu abafundile, njengoba becabanga ukuthi ukuphakama kuvela ebuhlakanini obuphakeme nasekutheni uhlakahlisombulu lunobungozi (ngoba izinguxa zinengcinankumbulo efanele nejubane elifanele lokudludlunga, futhi izinguxa zinekhono lokufunda nolwazi elikhulu). Lempikiso ingukuvezwa kwemiphumela okukhohlisayo, futhi ididanisa okungafanele kube khona nalokho okungaba khona noma okungenakuba khona. (Wardrip-Fruin, 56).
#*Impikiso yomchazazibalo*: Lempikiso isebenzisa izibalosiminya zomchazazibalo, ezifana nesibalasiminya sokungapheleli sikaGödel, ukuveza ukuthi kunemikhawulo emibuzweni isimiso sesiCikizi esisekwe kumhluzangqondo esingayiphendula. UTuring usikisela ukuthi izothamlilo zivame ukuba nemaphosiso ngokwazo futhi ziyawathokozela amaphutha wenguxa. (Lempikiso yaphinde yenziwa ngusonjulalwazi uJohn Lucas ngowe-1961 nomchazindalo uRoger Penrose ngowe-1989.) 
#*Umzakuzakwana ngokwe[[Mpaphamo]]*: Lomzakuzakwana, wasikiselwa ngoSolwazi Geoffrey Jefferson esifundisweni sakhe sangowe-1949 esasithi "kuze kube yilapho inguxa ikwazi ukubhala inshumasine *(sonnet)* noma iqambe umkhenqeziso *(concerto)*  ngenxa yemizindlo nemizwa eyizwayo, hhayi ngenxa yezimpawu, soze sivumelane ukuthi izinguxa zilingana nobuchopho."  UTuring waphendula ngokuthi asinayo indlela yokugagula ukuba ezinye ozinto ngaphandle kwethu aziyingcwethi imizwa, futhi ngalokho kufanele sisamukele isivivinyo. Wajobelela ngokuthi, "angifisi ukuvela sengathi ngicabanga ukuthi akunamfihlakalo ngempaphamo... kodwa angicabangi ukuthi lezi zimfihlakalo zidinga ukuxazululwa ngaphambi kokuba siphendule othi ingabe izinguxa zingakwazi ukucabanga." (Lomzakuzakwana, othi isiCikizi soze sibe *nobungcethi bempaphamo* noma *ukuqonda*, waphinde wenziwa futhi ngowe-1980 wenziwa usonjulalwazi uJohn Searle kumzakuzakwana wakhe weGumbi lamaShayina. Impendulo ka-Turing namuhla yaziwa ngokuthi "impendulo yenkinga yeminye imiqondo".)
#*Imizakuzakwana ngemiqhina ehlukahlukene*. Lemizakuzakwana yonke inesimo esithi "isiCikizi soze yenze okungu-*X*". UTuring unikela ngezinketho:Yiba ngonomusa, onosizo, omuhle, onobungane, yiba yingqalabutho, yiba namahlaya, hlukanisa okuhle nokubi, yenza amaphutha, yona sothandweni, thokozela amajingijolo nolaza, yenza othile athandane nawe, funda ebungcwethini, sebenzisa amazwi ngokufanele, zindla ngawe, condoza ngokuhlukahluka njengesothamlilo, yenza into entsha sha. UTuring uqaphela ukuthi "akukho ukwesekwa okuvame ukunikelwa ngenxa yalemisho," nokuthi ixhomeke emizindlekelweni yobungane ngokuphathelene nokuthi zizobhengcezeka kanjani izinguxa enkathini ezayo, noma "ziyimizakuzakwana ethubileyo yempaphamo." Futhi uyaziphendula ezinye zazo:

## Imithombo