Masamu ndi makina
Anthu ambiri amaganiza kuti kumanga makina masamu? ndipo kwenikweni makompyuta? ndi mainjiniya okha omwe adathandizira. Izi sizowona, akatswiri a masamu athandizira ntchitoyi kuyambira pachiyambi. Ndipo awa ndi omwe ali ndi chiphunzitso chokha. Ndithudi, kodi ena a iwo anali ndi lingaliro laling’ono chabe lakuti zimene anatulukira tsiku lina zidzagwiritsiridwa ntchito m’bizinesi wamba monga kupanga maakaunti?
Lero ndikuwuzani za masamu awiri akale. Wina (ndiwo, John von Neumann), popanda ntchito yake ndi malingaliro ake makompyuta sakanapangidwa nkomwe, ndikusiya mtsogolo; ndi yayikulu kwambiri komanso yofunika kwambiri kuti isaphatikizidwe ndi zina munkhani imodzi. Ndimalumikizanso awiriwa chifukwa anali mabwenzi apamtima, ngakhale adasiyana ndi kusiyana kwa zaka.
Njira ina ndi mgwirizano
Koma awiriwa nawonso sali oyenera kuposa Neumann. Komabe, tisanapitirire ku mbiri yawo, ndikupereka ntchito yosavuta. Ganizirani chiganizo chilichonse chokhala ndi ziganizo ziwiri zochepa zomwe zimagwirizanitsidwa ndi mgwirizano (chiganizo choterocho, yemwe sakumbukira, amatchedwa njira ina). Tinene kuti:. Vuto ndi kutsutsa ganizoli. Ndiye izi zikutanthauza chiyani:
Chabwino, lamulo ndi ili: tidzalowa m'malo mwa mgwirizano ndikutsutsana ndi ziganizo zambiri, choncho:.
Osati zovuta. Chabwino, tiyeni tiyese kutsutsa chiganizo chokhala ndi ziganizo ziwiri zogwirizanitsidwa ndi mgwirizano (kachiwiri, yemwe sakumbukira mawuwa: Mgwirizano). Mwachitsanzo: Lamulo lofanana, mwachitsanzo, kusinthidwa ndi ziganizo zophatikizana? ndimakana kotero timapeza :, zikutanthauza chimodzimodzi monga
Kaŵirikaŵiri: (1) kukana njira ina ndiko kugwirizana kwa kusagwirizana, ndipo (2) kukana kwa mgwirizano ndi mgwirizano wa kusagwirizana. Izi? chofunika kwambiri? malamulo awiri a Morgan a propositional calculus.
Wopanda mphamvu
August de Morgan, woyamba mwa akatswiri a masamu amene tawatchula poyamba paja, amene analemba malamulowa, anabadwira ku India m’chaka cha 1806 m’banja la mkulu wa asilikali atsamunda a ku Britain. Mu 1823-27 adaphunzira ku Cambridge? ndipo atangomaliza maphunziro ake anakhala pulofesa pa yunivesite yodabwitsa imeneyi. Anali mnyamata wofooka, wamanyazi komanso wosalemera kwambiri, koma wanzeru kwambiri. Zokwanira kunena kuti adalemba ndikusindikiza mabuku 30 a masamu ndi zolemba zasayansi zopitilira 700; ndi cholowa chochititsa chidwi. Kodi panthaŵiyo panali ophunzira ake ambiri? tikanati bwanji lero? anthu otchuka komanso otchuka. Kuphatikizapo mwana wamkazi wa ndakatulo wamkulu Wachikondi Lord Byron? wotchuka Ada Lovelace (1815-1852), amaonedwa kuti lero ndi wolemba mapulogalamu woyamba m'mbiri (iye analemba mapulogalamu a makina a Charles Babbage, omwe ndikambirana mwatsatanetsatane). Mwa njira, kodi chinenero chodziwika bwino cha ADA chimatchedwa dzina lake?
Ntchito ya De Morgan (anamwalira ali wamng'ono mu 1871) chinali chiyambi cha kuphatikiza maziko zomveka za masamu. Kumbali ina, malamulo ake omwe tawatchulawa adapeza kukhazikitsidwa kokongola kwamagetsi (ndiyeno zamagetsi) pamapangidwe a zipata zomveka zomwe zimagwira ntchito ya purosesa iliyonse.
Ndisanayiwale. Ngati tinyalanyaza chiganizocho: timapeza chiganizo: Momwemonso, ngati tinyalanyaza chiganizocho:, timapeza chiganizo: Awanso ndi malamulo a De Morgan, koma a quantifier calculus. Zosangalatsa ? pali paliponse kuti tiwonetse? kodi uku ndikosavuta kunena kwa malamulo a de Morgan a propositional calculus?
Mwana wamphatso ya wopanga nsapato
Zoposa lero, wina mwa ngwazi zathu amakhala ndi de Morgan, ndiye kuti, George Bull. Banja la a Boules linali banja la alimi ang'onoang'ono ndi amalonda ochokera kumpoto chakum'mawa kwa England. Banjali silinali lapadera asanafike John Bull? ngakhale kuti anali wosoka nsapato wamba? adakonda masamu, zakuthambo ndi? nyimbo mpaka ngati wosoka nsapato? adasokonekera. Chabwino, mu 1815, John anali ndi mwana wamwamuna, George (ndiko kuti, George).
Bambo ake atasokonekera, George wamng'ono anayenera kuchotsedwa sukulu. Masamu? zidatheka bwanji? atate wake mwini anamphunzitsa; koma iyi sinali phunziro loyamba lomwe Yurek wamng'ono anaphunzira kunyumba. Poyamba panali Latin, kenako zinenero: Greek, French, German ndi Italy. Koma chopambana kwambiri chinali chiphunzitso cha mnyamata wa masamu: ali ndi zaka 19, mnyamatayo adasindikizidwa? mu Cambridge Journal of Mathematics? ? ntchito yanga yoyamba yayikulu mdera lino. Kenako otsatirawo anabwera.
Chaka chotsatira, George, pokhala wopanda maphunziro apamwamba, anatsegula sukulu yakeyake. Ndipo mu 1842 anakumana ndi De Morgan ndipo anakhala naye pa ubwenzi.
De Morgan anali ndi mavuto panthawiyo. Malingaliro ake adanyozedwa ndikutsutsidwa kwambiri ndi akatswiri afilosofi omwe sakanatha kuganiza kuti katswiri wa masamu anayamba kunena chinachake mu chilango mpaka pano chomwe chimaganiziridwa kuti ndi nthambi ya filosofi yoyera, mwachitsanzo mu logic (mwa njira, asayansi ambiri amakono amaona kuti logic ndi imodzi yokha. za nthambi za masamu koyera, zomwe ziribe kanthu kochita ndi filosofi, ndithudi, zimapandukira afilosofi pafupifupi mofanana ndi nthawi ya de Morgan?). Buhl, ndithudi, adathandizira bwenzi? ndipo mu 1847 analemba kabuku kakang'ono kamutu. Nkhani imeneyi ndi yochititsa chidwi.
De Morgan adayamikira ntchitoyi. Patangopita miyezi ingapo itatulutsidwa, adamva za uprofesa wopanda munthu pa King's College, University of Cork ku Ireland. Buhl adapikisana nawo paudindowu koma adachotsedwa ndipo mpikisanowo sunaloledwe. Patapita nthawi, mnzake anamuthandiza? ndi Boole, komabe, adalandira mpando wa masamu pa yunivesite iyi; osaphunzira konse masamu kapena gawo lina lililonse?
Zaka zingapo pambuyo pake, nkhani yofananayo inachitika kwa mnzathu wanzeru Stefan Banach. Komanso, maphunziro ake asanalowe pulofesa ku Lviv anali ochepa kwa undergraduate ndi semesita imodzi ya polytechnic?
Koma kubwerera ku booleans. Kukulitsa malingaliro ake kuchokera ku monograph yoyamba, adasindikiza mu 1854 ntchito yake yotchuka komanso yamakono? (mutuwo, mogwirizana ndi mafashoni a nthawiyo, unali wautali kwambiri). M'bukuli, Boolev adawonetsa kuti kuganiza momveka bwino kumatha kuchepetsedwa kukhala kosavuta? kugwiritsa ntchito masamu odabwitsa (binary!)? Akaunti. Zaka mazana awiri zisanachitike, Leibniz wamkulu anali ndi lingaliro lofananalo, koma lingaliro ili linalibe nthawi yomaliza nkhaniyi.
Koma ndani akuganiza kuti dziko lagwa pansi Boole asanayambe ntchito yake ndikudabwa ndi kuzama kwa luntha lake? si bwino. Ngakhale kuti Boole anali kale membala wa Royal Academy kuyambira 1857 komanso katswiri wa masamu wolemekezeka komanso wotchuka, maganizo ake omveka ankaganiziridwa kuti ndizovuta kwambiri. Ndipotu, sizinali mpaka 1910 pamene asayansi akuluakulu a ku Britain Bertrand Russell i Alfred North Whitehead, posindikiza voliyumu yoyamba ya ntchito yawo yabwino kwambiri (), adawonetsa malingaliro a Boolean - osati kukhala ndi ubale wofunikira ndi malingaliro? koma ngakhale pali logics. Kupitilira malingaliro a George Boole, kodi malingaliro akale osavuta? ndi kukokomeza pang'ono? kulibe konse. Aristotle, wodziwika bwino wamalingaliro, adangokhala chidwi chofuna kudziwa mbiri yakale patsiku lofalitsidwa.
Mwa njira, chidziwitso chimodzi chochititsa chidwi: pafupifupi theka la zaka pambuyo pake, malingaliro onse amafuta atsimikiziridwa mosamala ndi mawerengedwe a Boolean kwa zaka zambiri? m'mphindi zisanu ndi zitatu zidapezeka kuti ndi kompyuta yopanda mphamvu, yokonzedwa mwaluso ndi katswiri waku China waku America Wang Hao.
Mwa njira, Boole anali ndi mwayi pang'ono: ngati akanachotsa Aristotle pampando wachifumu zaka mazana atatu zapitazo, akanawotchedwa pamtengo.
Ndiyeno zinapezeka kuti otchedwa Boolean algebras? sikuti ndi gawo lofunika kwambiri komanso lolemera la masamu, lomwe likukulabe mpaka pano, komanso maziko abwino opangira makina a masamu. Komanso, ziphunzitso za Boolean, popanda kusintha kulikonse, sizigwira ntchito pamalingaliro okha, pomwe zimalongosola kawerengedwe kakale, komanso mawerengedwe a binary (mu dongosolo la manambala lomwe limagwiritsa ntchito manambala awiri okha - ziro ndi imodzi, yomwe ili maziko a masamu apakompyuta), koma amagwiritsidwanso ntchito mu chiphunzitso chokhazikitsidwa, chomwe chinapangidwa pambuyo pake. Zikuwonekeratu kuti mu chiphunzitso ichi banja lamagulu amtundu uliwonse likhoza kuchitidwa ngati algebra ya Boolean.
mtengo wa boolean? bwanji de morgan? anali ndi thanzi labwino. Tinenenso zoona kuti sanali kusamala za thanzi limeneli nkomwe: ankagwira ntchito molimbika kwambiri komanso molimbikira kwambiri, ndipo anali wolimbikira kwambiri. Pa October 24, 1864, kodi ankakaphunzitsa liti? Anali wonyowa kwambiri. Posafuna kuchedwetsa makalasi, sanasinthe kapena kuvula. Chotulukapo chake chinali chimfine choopsa, chibayo, ndi imfa miyezi ingapo pambuyo pake. Anamwalira ali ndi zaka 49 zokha.
Boole anakwatiwa ndi Mary Everest, mwana wamkazi wa wofufuza malo wotchuka wa ku Britain ndi katswiri wa geographer (inde, inde? mmodzi wochokera ku phiri lalitali kwambiri padziko lonse lapansi) zaka 17 ali wamng'ono wake. Chikondi? anathera m’banja lopambana kwambiri? anayamba ndi? Maphunziro a ma acoustics operekedwa ndi wasayansi kwa mtsikana wokongola. Anali ndi ana aakazi asanu, atatu mwa iwo adalandira udindo wapamwamba: Alice adakhala katswiri wa masamu, Lucy anali pulofesa woyamba wa chemistry ku England, Ethel Lillian adadziwika mu nthawi yake ngati wolemba.
