Izazi zezibalo nemishini
Okuqukethwe
Abantu abaningi bacabanga ukuthi ukwakhiwa kwemishini yezibalo? futhi ngempela amakhompyutha? onjiniyela kuphela abanikele. Lokhu akulona iqiniso, izazi zezibalo ziye zaba nesandla kulo msebenzi kusukela ekuqaleni. Futhi laba yilabo abanombono kuphela. Ngempela, ingabe abanye babo babenombono omncane wokuthi ababekutholile ngolunye usuku kwakuyosetshenziswa ebhizinisini elivamile lapho kwakhiwa ama-akhawunti?
Namuhla ngizokutshela ngezibalo ezimbili zasendulo. Omunye (okungukuthi, uJohn von Neumann), ngaphandle komsebenzi nemibono yakhe amakhompyutha ayengeke adalwe nhlobo, ngishiya kamuva; inkulu kakhulu futhi ibaluleke kakhulu ukuthi ingahlanganiswa nezinye endabeni eyodwa. Ngiphinde ngibaxhumanise laba ababili ngoba babengabangani abakhulu, nakuba babehlukaniswa ngokwehlukana kweminyaka ethile.
Okunye kanye nenyunyana
Kodwa laba ababili nabo abafaneleki kancane kunoNeumann. Kodwa-ke, ngaphambi kokuthi singene ku-biography yabo, nginikeza inselele elula. Cabangela noma yimuphi umusho onezigatshana ezimbili ezingaphansi ezixhunywe inyunyana (umusho onjalo, ongakhumbuli, ubizwa ngokuthi okunye). Ake sithi:. Inselelo iwukuphikisa lesi siphakamiso. Ngakho kusho ukuthini lokhu:
Hhayi-ke, umthetho yilokhu: sizofaka inyunyana esikhundleni futhi siphikisane nemisho ehlanganisiwe, ngakho-ke:.
Akunzima. Hhayi-ke, ake sizame ukuphikisa umusho onemisho emibili exhunywe inyunyana (futhi, ongalikhumbuli leli gama: Isihlanganiso). Isibonelo: Umthetho ofanayo, okungukuthi ukushintshwa kwemisho embaxambili? ngiyaphika ukuze sithole:, kusho kufana ncamashi ne
Ngokuvamile: (1) ukunganaki kokunye kuwukuhlangana kokuphika, futhi (2) ukunganaki kwesihlanganiso kuyinhlanganisela yokuphika. Lezi ? kubaluleke kakhulu? imithetho emibili kaMorgan yokubala okuhlongozwayo.
I-aristocrat ebuthakathaka
Augustus de Morgan, owokuqala wezazi zezibalo okukhulunywe ngazo ekuqaleni, umlobi wale mithetho, wazalelwa eNdiya ngo-1806 emkhayeni wesikhulu sebutho lamakoloni aseBrithani. Ngo-1823-27 wafunda eCambridge? futhi ngokushesha ngemva kokuthweswa iziqu waba uprofesa kule nyuvesi emangalisayo. Wayeyinsizwa ebuthakathaka, enamahloni futhi engacebile kakhulu, kodwa enekhono ngokwedlulele ngokobuhlakani. Kwanele ukusho ukuthi wabhala futhi washicilela izincwadi ze-30 zezibalo kanye nezihloko zesayensi ezingaphezu kuka-700; kuyifa elihlaba umxhwele. Ingabe babebaningi abafundi bakhe ngaleso sikhathi? singasho kanjani namuhla? osaziwayo nabantu abavelele. Kuhlanganisa indodakazi imbongi enkulu Romantic Lord Byron? odumile Ada Lovelace (1815-1852), ebhekwa namuhla njengomhleli wokuqala emlandweni (wabhala izinhlelo zemishini kaCharles Babbage, engizokhuluma ngayo ngokuningiliziwe). Kodwa-ke, ingabe ulimi lwezinhlelo oludumile lwe-ADA luqanjwe ngaye?
Umsebenzi ka-De Morgan (wafa esemncane ngokuqhathaniswa ngo-1871) waphawula ukuqala kokuhlanganiswa kwezisekelo ezinengqondo zezibalo. Ngakolunye uhlangothi, imithetho yakhe okukhulunywe ngayo ngenhla ithole ukuqaliswa okuhle kagesi (bese kuba nge-elekthronikhi) ekwakhiweni kwamasango anengqondo angaphansi kokusebenza komprosesa ngamunye.
Konje. Uma siwuphika umusho: sithola umusho: Ngokufanayo, uma siphika umusho:, sithola umusho: Lena futhi imithetho kaDe Morgan, kodwa yezibalo zokubala. Kuyathakazelisa ? kukhona lapho ongakukhombisa khona? ingabe lokhu ukujwayela okulula kwemithetho ka-de Morgan yokubala okuhlongozwayo?
Indodana yomkhandi wezicathulo enesiphiwo esihle
Namuhla, elinye lamaqhawe ethu lalihlala no-de Morgan, okungukuthi, George Bull. AbakwaBoules bekuwumndeni wabalimi abancane nabahwebi abavela eNyakatho Mpumalanga yeNgilandi. Umndeni wawungelutho olukhethekile ngaphambi kokufika kukaJohn Bull? nakuba ayemane nje engumkhandi wezicathulo ovamile? wathandana nezibalo, isayensi yezinkanyezi kanye? umculo uze ufane nomthungi wezicathulo? waqothuka. Nokho, ngo-1815, uJohn waba nendodana, uGeorge (okunguGeorge).
Ngemva kokuba uyise ecwile, uGeorge omncane kwadingeka akhishwe esikoleni. Izibalo? iphumelele kanjani? uyise wamfundisa; kodwa lesi kwakungesona isifundo sokuqala uYurek omncane asifunda ekhaya. Okokuqala kwakukhona isiLatini, kwase kuba izilimi: isiGreki, isiFulentshi, isiJalimane nesiNtaliyane. Kodwa okuphumelele kakhulu kwaba ukufundisa komfana kwezibalo: eneminyaka engu-19, umfana wanyathelisa? ku-Cambridge Journal of Mathematics? ? umsebenzi wami wokuqala obalulekile kule ndawo. Kwabe sekufika abalandelayo.
Ngemva konyaka, uGeorge, engafundile, wavula esakhe isikole. Futhi ngo-1842 wahlangana no-De Morgan futhi waba umngane naye.
UDe Morgan wayenezinkinga ezithile ngaleso sikhathi. Imibono yakhe yahlekwa usulu futhi yagxekwa kakhulu izazi zefilosofi ezazingakwazi ukucabanga ukuthi isazi sezibalo sizoqala ukusho okuthile ngesiyalo kuze kube manje esithathwa njengegatsha lefilosofi emsulwa, okungukuthi, kunengqondo (ngendlela, ososayensi abaningi banamuhla bacabanga ngalowo mqondo. ingenye yamagatsha ezibalo ezihlanzekile, kodwa ayihlangene nhlobo nefilosofi, yebo, ivukela izazi zefilosofi cishe ngokufanayo nangesikhathi sika-de Morgan?). U-Buhl, kunjalo, wasekela umngane? kwathi ngo-1847 wabhala incwadi encane enesihloko esithi. Lesi sihloko siyiqiniso.
UDe Morgan uwuthokozele lo msebenzi. Ezinyangeni ezimbalwa ngemva kokukhululwa kwayo, wezwa ngoprofesa owayengenamuntu e-King's College eyayisanda kusungulwa, e-University of Cork e-Ireland. UBuhl ubehlabana ngalesi sikhundla kodwa wakhishwa futhi umncintiswano wangavunyelwa. Ngemva kwesikhathi esithile, umngane wamsiza ngokumsekela? no-Boole, nokho, wathola usihlalo wezibalo kule nyuvesi; awunayo nhlobo imfundo esemthethweni yezibalo nanoma yimuphi omunye umkhakha?
Eminyakeni embalwa kamuva, kwenzeka indaba efanayo kumuntu wakithi okhaliphile uStefan Banach. Ngokulandelayo, izifundo zakhe ngaphambi kokujoyina i-professorship e-Lviv zazilinganiselwe ku-undergraduate kanye ne-semester eyodwa ye-polytechnic?
Kodwa emuva ku-booleans. Enweba emibonweni yakhe kusukela ku-monograph yokuqala, washicilela ngo-1854 umsebenzi wakhe odumile futhi wanamuhla? (isihloko, ngokuhambisana nemfashini yangaleso sikhathi, sasiside kakhulu). Kulo msebenzi, uBoolev wabonisa ukuthi umkhuba wokucabanga okunengqondo ungancishiswa ube lula? noma ngabe usebenzisa i-arithmetic eyinqaba (kanambambili!)? Ama-akhawunti. Eminyakeni engamakhulu amabili ngaphambi kwakhe, uLeibniz omkhulu wayenombono ofanayo, kodwa lesi sihloko sokucabanga sasingenaso isikhathi sokuqedela lolu daba.
Kodwa ubani ocabanga ukuthi umhlaba waguqa ngamadolo ngaphambi komsebenzi kaBoole futhi wamangala ngokujula kobuhlakani bakhe? okungalungile. Nakuba uBoole wayesevele eyilungu leRoyal Academy kusukela ngo-1857 futhi eyisazi sezibalo esihlonishwa kakhulu nesidumile, imibono yakhe enengqondo yayibhekwa isikhathi eside njengelukuluku lokufuna ukwazi okungabalulekile kangako. Eqinisweni, kwaze kwaba ngo-1910 lapho ososayensi abakhulu baseBrithani Bertrand Russell i Alfred North Whitehead, ngokushicilela ivolumu yokuqala yomsebenzi wabo ogqamile (), babonisa ukuthi imibono ye-Boolean - futhi ayinakho nje kuphela ukuhlobana okubalulekile kunengqondo? kodwa futhi kukhona logics. Ngaphandle kwemibono kaGeorge Boole, ingabe i-logical yakudala ilula? ngehaba kancane? alikho nhlobo. U-Aristotle, i-classic ye-logic, waba nje ilukuluku lomlando ngosuku lokushicilelwa.
Ngendlela, olunye ulwazi oluthakazelisayo: cishe isigamu sekhulu leminyaka kamuva, wonke ama-theorems amafutha afakazelwe ngokucophelela yi-Boolean calculus iminyaka eminingi? emizuzwini eyisishiyagalombili kuvele ukuthi ikhompuyutha enamandla kancane, ehlelwe ngobuchule yingcweti yaseShayina yaseMelika u-Wang Hao.
Ngendlela, u-Boole wayenenhlanhla encane: ukube waketula u-Aristotle esihlalweni sobukhosi emakhulwini amathathu eminyaka ngaphambili, ngabe washiswa esigxotsheni.
Futhi-ke kwavela ukuthi lokho okubizwa ngokuthi ama-algebra e-Boolean? lena akuyona nje indawo ebaluleke kakhulu futhi ecebile yezibalo, esathuthuka nanamuhla, kodwa futhi isisekelo esinengqondo sokwakhiwa kwemishini yezibalo. Ngaphezu kwalokho, izithiyori ze-Boolean, ngaphandle kwanoma yiziphi izinguquko, azisebenzisi kuphela ku-logic, lapho zichaza i-calculus ye-propositional yakudala, kodwa futhi nokubala kanambambili (ohlelweni lwezinombolo olusebenzisa amadijithi amabili kuphela - zero kanye neyodwa, okuyisisekelo sezibalo zekhompyutha. ), kodwa zibuye zisetshenziswe ku-set theory eyathuthukiswa kamuva kakhulu. Kuvele ukuthi kulo mbono umndeni wamasethi angaphansi kwanoma iyiphi isethi ungaphathwa njenge-algebra ye-Boolean.
inani le-boolean? unjani u-de morgan? wayenempilo ebuthaka. Masikhulume iqiniso futhi ukuthi wayengenandaba nale mpilo nhlobo: wayesebenza kanzima futhi ekhuthele kakhulu, futhi wayekhuthele kakhulu. Ngo-Okthoba 24, 1864, wayezokhuluma nini? Wayemanzi te. Engafuni ukubambezela amakilasi, akazange ashintshe noma akhumule. Umphumela waba umkhuhlane omubi, inyumoniya, nokufa ezinyangeni ezimbalwa kamuva. Washona eneminyaka engu-49 kuphela.
U-Boole wayeshade noMary Everest, indodakazi yomhloli wamazwe odumile waseBrithani kanye nesazi sezwe (yebo, yebo? lowo ovela entabeni ephakeme kunazo zonke emhlabeni) iminyaka engu-17 ubudala bakhe. Ezothando? waphetha ngomshado ophumelela kakhulu? waqala nge? ukufundisa nge-acoustics okunikezwe usosayensi intombazanyana enhle. Wayenamadodakazi amahlanu naye, amathathu kuwo athola isihloko esivelele: U-Alice waba isazi sezibalo esikhulu, uLucy wayenguprofesa wokuqala we-chemistry eNgilandi, u-Ethel Lillian waqashelwa ngesikhathi sakhe njengomlobi.
