Blaise Pascal: Inganekwane yesondo le-roulette
Isazi sezibalo esivame ukuthiwa sasungula isondo, kodwa esasizama ukwakha okunye.
UPascal (1623–1662) wenza ucwaningo ngemishini yokunyakaza okungapheli ngama-1650. Isondo elijikelezayo elicishe lingabi nakuhuquzela okuthiwa elakhe lingaba ngukhokho we-rotor ye-roulette; ukuthi elakhe kuyinkolelo yesiko, akubhalwanga phansi ngobufakazi.
Isazi sezibalo
UBlaise Pascal wakha umshini wokubala osebenza ngamagiya eneminyaka eyishumi nesishiyagalolunye, wafakazela imiphumela ku-projective geometry esesemusha, wenza umsebenzi oyisisekelo ngengcindezi nangesikhala esingenalutho, kwathi ngo-1654, ezincwadini abezibhalelana noPierre de Fermat, waxazulula “inkinga yamaphuzu”: indlela yokwahlukanisa ngobulungiswa imali ebhejiwe yomdlalo wenhlanhla ophazamisekile. Impendulo yabo, ukwahlukanisa ngokuya ngamathubaizibaloAmathubaIthuba lomphumela, kusukela ku-0 kuya ku-1 noma ku-0% kuya ku-100%. Inombolo eyodwa: 1/37 = 2.70%.Funda konke → omdlali ngamunye okuwina ukube umdlalo uqhubekile, ingumsuka wenani elilindelekileizibaloInani elilindelekileUmphumela ovamile ekubhejeni ngakunye esikhathini eside. U-−1/37 wenani elibhejwayo kukho konke ukubheja okujwayelekile kwaseYurophu.Funda konke →. Zonke izibalo ze-EV kule sayithi zisuka kulezo zincwadi.
Ingabe wawukhona umshini we-roulette kaBlaise Pascal?
Maphakathi nama-1650 uPascal wasebenza ngomshini wokunyakaza okungapheli futhi kuthiwa wakha isondo elilinganiselwe kahle elalijikeleza isikhathi eside linokuhuquzela okuncane. Indaba yokuthi leli sondo laba yi-rotorokokusebenzaI-rotorIngxenye yesondo ejikelezayo ephethe amagodi.Funda konke → ye-roulette iphindwa emilandweni eminingi kodwa ayibhalwanga kunoma yimuphi umthombo wokuqala. Kungenzeka ukuthi abaqhubi bamakhasino emadolobheni amanzi ashisayo ngekhulu le-18 basebenzisa leli gama ukuheha abantu. Akuyona into iLabhorethri engayamukela ngalobu bufakazi.
Amathuba, ngamazwi akhe nangawethu
Izincwadi zango-1654 azikhulumi nge-roulette, eyayingakabikho ngaleso sikhathi. Ziyabuza: abadlali ababili badinga amaphuzu amathathu ukuze bawine imali ebekiwe; bayeka lapho kungu-2–1; imali kufanele yahlukaniswe kanjani? Impendulo kaPascal isebenzisa lokho esingakubiza manje ngokuthi yi-conditional expectation kanye nendlela yokucabanga eziphindaphindayo eyehla esihlahleni sezindlela umdlalo ongaqhubeka ngazo. UHuygens wafunda lezi zincwadi kwathi ngo-1657 washicilela incwadi yokufunda yokuqala ngenani elilindelekile. Igama elithi “expectation” ngelakhe.
UPascal noFermat baxazulula inkinga yamaphuzu: inani elilindelekile njengentengo efanele yesimo.
UHuygens, De Ratiociniis in Ludo Aleae: incazelo yokuqala ephrintiwe yenani elilindelekile.
UJakob Bernoulli, Ars Conjectandi: umthetho wezinombolo ezinkulu.
I-roulette ichazwa eParis. Yonke inkokhelo ingu-36/n − 1: EV = −1/37 (noma −2/38).
Isivivinyo se-chi-square sikaPearson, siboniswa ngokujikeleza kwe-roulette.
Konke okungenhla, kule sayithi, kusiphequluli.
Ukubheja kukaPascal
Impikiswano kaPascal edume kakhulu ngokubheja ayiphathelene ne-roulette kodwa iphathelene noNkulunkulu: “ukubheja” okusencwadini i-Pensées okubeka ukukholwa njengokubheja okunenkokhelo engapheli. Kuyimpikiswano yenani elilindelekile, futhi kungokokuqala ngqa umuntu esebenzisa i-decision theory (inkolelo yokwenza izinqumo) ukuze asekele umbono othile. Abadlali be-roulette abacaphuna uPascal ngesondo bacaphuna uPascal ongafanele; obalulekile nguye owabonisa ukuthi ukugembula kunqunyelwa kanjani intengo.
Okuxakile
Noma ngabe uPascal wakha isondo lokuqala le-roulette noma cha, umdlalo uwumfanekiso omuhle womsebenzi wakhe wangempela: idivayisi yomuntu owafakazela ukuthi ungeke uthole okuthile ngaphandle kokunikela lutho (ukunyakaza okungapheli kuyehluleka; okulindelekile akuguquki), esetshenziselwa ukubonisa into efanayo kubadlali abayizigidi ezimbalwa ngonyaka.
Imibuzo
Wayehlangana nabagembuli eParis ekuqaleni kwama-1650, yingakho inkinga yamaphuzu yafika kuye ngoChevalier de Méré. Alikho irekhodi lokuthi wake wadlala ngemali ngokuzimisela.
Ngoba kuyindaba enhle futhi ngoba abakhangisi bamakhasino bekhulu le-19 babeyithanda. Uma uyiphinda, yengeze umbhalo waphansi.
Okokuhlekisa
Wafakazela ukuthi ungeke uthole okuthile ngelize. Kwase kwakhiwa ikhasino phezu kwalokho.
Imithombo
- Pascal, B. & Fermat, P. Correspondence on the problem of points.
- Huygens, C. De Ratiociniis in Ludo Aleae.
- Kavanagh, T. M. Dice, Cards, Wheels: A Different History of French Culture.