Blaise Pascal: tamucuha n uḍebsi n rulit
Amussnaw n tusnakt i wumi ttaken s waṭas aḍebsi, yerna yella yeɛreḍ ad yebnu kra nniḍen.
Pascal (1623–1662) yexdem tirmiyin ɣef tmacinin n umussu ur nettḥebbis deg yiseggasen 1650. Aḍebsi yettezzin qrib war aḥukku i s-ttaken yezmer ad yili d jeddi n uqerru yettezzin n rulit; tilin-is d ayla-s d awal n tradisyun, mačči d ayen yettwarun deg yisemmaden.
Amussnaw n tusnakt
Blaise Pascal yebna tamsiḍent tamikanikt di tseɛṭac n yiseggasen, yesbeggen-d igmaḍ n tjumiṭrit tasenfalt mi yella d ilemẓi, yexdem axeddim n llsas ɣef uḍeɣḍeɣ d ilem n waḍu, yerna deg 1654, deg tebratin yuran akked Pierre de Fermat, yefra «ugur n tneqqiḍin»: amek ara yebḍu s lḥeqq adrim n rrehn n wurar n zzher i yettwagezmen. Tiririt-nsen, ad yettwabḍu wedrim i yal amurar akken tella taprubabilittusnaktTaprubabilitAzal n yiwen ugmuḍ ad d-yeḍru, seg 0 ɣer 1 neɣ seg 0% ɣer 100%. Yiwen wuṭṭun: 1/37 = 2,70%.Ɣer akk →-is ad yerbeḥ lukan ikemmel wurar, d aẓar n wazal yettwaṛǧantusnaktAzal yettwaṛǧanAlemmas n ugmuḍ n yal rrehn deg uɣawas aɣezfan. −1/37 n rrehn i yal rrehn amagnu awrupi.Ɣer akk →. Yal aḥsab n EV deg usmel-a yekka-d seg tebratin-a.
Yella s tidet waḍebsi n rulit n Blaise Pascal?
Di tlemmast n yiseggasen 1650, Pascal yexdem ɣef tmacint n umussu ur nettḥebbis, qqaren yebna aḍebsi yettwasemsawan akken iwata, yettezzin aṭas n wakud s waḥukku amecṭuḥ. Taqsiḍt i yeqqaren belli aḍebsi-a yuɣal d aqerru yettezzin (rotor)ibenkanAqerru yettezzin (rotor)Aḥric n uḍebsi yettezzin i yeṭṭfen tixxamin.Ɣer akk → n rulit tettwales-d deg waṭas n yimezruyen, yerna ur tettwaru ara deg yiwen seg yisemmaden imezwura. Yezmer d tidet belli wid yessedduyen lkazinu n temdinin n waman iḥman deg tasut wis 18 sseqdacen isem-is akken ad d-jebden imuraren. Maca d ayen ur yettqebbil ara Tanarit s yibeggnen i yellan.
Taprubabilit, s wawalen-is d wawalen-nneɣ
Tibratin n 1654 ur d-bedrent ara rulit, imi mazal ur d-tban ara. Steqsayent: sin n yimuraren ḥwaǧen kraḍ n tneqqiḍin akken ad rebḥen adrim yellan di tlemmast; ḥebsen ɣef 2–1; amek ara yettwabḍu wedrim? Tiririt n Pascal tesseqdac ayen i nsemma ass-a azal yettwaṛǧan s tewtilt, d ubeggen yettuɣalen ɣef yiman-is ɣef useklu n wayen i yezmren ad d-yeḍru. Huygens yeɣra tibratin-a, deg 1657 yessufeɣ-d adlis amezwaru n uselmed ɣef wazal yettwaṛǧan. Awal «expectation» d ayla-s.
Pascal d Fermat fran ugur n tneqqiḍin: azal yettwaṛǧan d ssuma n lḥeqq n yiwen n wadeg deg wurar.
Huygens, De Ratiociniis in Ludo Aleae: tasleḍt tamezwarut yettwaḍebɛen ɣef wazal yettwaṛǧan.
Jakob Bernoulli, Ars Conjectandi: alugen n wuṭṭunen imeqqranen.
Rulit tettwaglem deg Paris. Yal lexlaṣ d 36/n − 1: EV = −1/37 (neɣ −2/38).
Akayad χ² n Pearson, yettwasbeggen ɣef tuzzyiwin n rulit.
Akk ayen d-yezrin, deg usmel-a, deg yiminig.
Rrehn
Abeggen n Pascal yettwassnen akk ɣef rrehn ur yelli ɣef rulit, yella ɣef Ṛebbi: «rrehn» deg Pensées i deg-s yettwali liman am rrehn s lexlaṣ ur nesɛi taggara. D abeggen n wazal yettwaṛǧan, yerna d tikkelt tamezwarut ideg yesseqdec yiwen tiẓri n tegtin akken ad yesbeggen kra. Imuraren i d-yettbedren Pascal ɣef uḍebsi bedren-d Pascal ur nelli d win ilaqen; win yesɛan azal d win yeskanen amek ara yettwasbedd ssuma n yiwen n lqmer.
Taḍsa n wakud
Ama yebna Pascal aḍebsi amezwaru n rulit ama ala, urar-a d amedya yelhan n uxeddim-is n tidet: d allal n wergaz yesbeggnen belli yiwen ur yezmir ad yawi kra seg ulac (amussu ur nettḥebbis ur iteddu ara; azal yettwaṛǧan yettwaḥrez), yettwasqedcen akken ad yesken ayen-nni kan i kra n yimelyunen n yimuraren yal aseggas.
Isteqsiyen
Yella yettemlil d yimqemmren deg Paris deg tazwara n yiseggasen 1650; akka i s-d-yewweḍ ugur n tneqqiḍin s Chevalier de Méré. Ulac aɣbalu i d-yeqqaren yella yettqemmir s yedrimen s tidet.
Imi d taqsiḍt yelhan, yerna wid yessedduyen lkazinu n tasut wis 19 ḥemmlen-tt. Ɛawdet-tt s tamawt deg ukessar.
Taḍsa i usgunfu
Yesbeggen belli yiwen ur yezmir ad yawi kra seg ulac. Syin yebna yiwen lkazinu fell-as.
Iɣbula
- 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.