URichard Hamming. “Isahluko esingekho”: Sazi kanjani esikwaziyo (imizuzu eyi-1-10 kwengama-40)


Lesi sifundo besingekho ohlelweni, kodwa bekufanele sengezwe ukuze kugwenywe iwindi phakathi kwamakilasi. Inkulumo empeleni imayelana nendlela esikwazi ngayo esikwaziyo, uma, kunjalo, sikwazi ngempela. Lesi sihloko sidala njengesikhathi - sekuxoxiwe ngaso iminyaka engu-4000 edlule, uma kungesona isikhathi eside. Kufilosofi, igama elikhethekile lenziwe ukulichaza - i-epistemology, noma isayensi yolwazi.

Ngingathanda ukuqala ngezizwe zakudala zakudala. Kuyaphawuleka ukuthi ngamunye wabo kwakukhona inganekwane mayelana nokudalwa kwezwe. Ngokwenkolelo ethile yaseJapane yasendulo, othile wavusa udaka, okwavela eziqhingini ezivuvuzayo. Ezinye izizwe nazo zazinezinganekwane ezifanayo: ngokwesibonelo, ama-Israyeli ayekholelwa ukuthi uNkulunkulu wadala umhlaba izinsuku eziyisithupha, okwathi ngemva kwalokho wakhathala waqeda ukudala. Zonke lezi zinganekwane ziyefana - nakuba iziza zabo zihluke kakhulu, zonke zizama ukuchaza ukuthi kungani lo mhlaba ukhona. Le ndlela ngizoyibiza ngemfundiso yenkolo ngoba ayibandakanyi izincazelo ngaphandle kokuthi “kwenzeka ngentando yonkulunkulu; benza lokho ababecabanga ukuthi kudingekile, futhi kwaba kanjalo izwe.”

Cishe ngekhulu lesi-XNUMX BC. e. Izazi zefilosofi zaseGreece lasendulo zaqala ukubuza imibuzo eqondile - ukuthi leli zwe liquketheni, yiziphi izingxenye zalo, futhi bazama ukusondela kubo ngokunengqondo kunezimfundiso zenkolo. Njengoba kwaziwa, bagqamisa izakhi: umhlaba, umlilo, amanzi nomoya; babeneminye imibono nezinkolelo eziningi, futhi kancane kancane konke lokhu kwaguqulwa kwaba imibono yethu yesimanje yalokho esikwaziyo. Nokho, lesi sihloko siye sabaxaka abantu isikhathi eside, ngisho namaGreki asendulo ayezibuza ukuthi akwazi kanjani ayekwazi.

Njengoba uzokhumbula engxoxweni yethu yezibalo, amaGreki asendulo ayekholelwa ukuthi i-geometry, izibalo zabo zazilinganiselwe, iwulwazi oluthembekile nolungenakuphikiswa nhlobo. Nokho, njengoba uMaurice Kline, umbhali wencwadi ethi “Mathematics,” abonisa. Ukulahlekelwa isiqiniseko,” izazi zezibalo eziningi ezingavuma ngazo, akuqukethe noma yiliphi iqiniso ezibalweni. Izibalo zihlinzeka ngokungaguquguquki kuphela uma kunikezwe isethi yemithetho yokucabanga. Uma ushintsha le mithetho noma okucatshangwayo okusetshenzisiwe, izibalo zizohluka kakhulu. Alikho iqiniso eliphelele, ngaphandle kweMithetho Eyishumi (uma ungumKristu), kodwa, maye, akukho lutho mayelana nesihloko sengxoxo yethu. Akumnandi.

Kodwa ungasebenzisa ezinye izindlela futhi uthole iziphetho ezahlukene. UDescartes, ngemva kokucabangela imibono yezazi zefilosofi eziningi ngaphambi kwakhe, wathatha isinyathelo emuva futhi wabuza umbuzo: "Kuncane kangakanani engingaqiniseka ngakho?"; Njengempendulo, wakhetha inkulumo ethi “Ngicabanga, ngakho-ke nginguye.” Kule nkulumo wazama ukuthola ifilosofi futhi azuze ulwazi oluningi. Le filosofi ayizange ifakazelwe kahle, ngakho asikaze sithole ulwazi. UKant waphikisa ngokuthi wonke umuntu uzalwa enolwazi oluqinile lwe-Euclidean geometry, nezinye izinto ezihlukahlukene, okusho ukuthi kukhona ulwazi oluzalwa nalo olunikezwa nguNkulunkulu, uma uthanda. Ngeshwa, ngesikhathi uKant ebhala imicabango yakhe, izazi zezibalo zazidala amajiyometri angewona awe-Euclidean ayefana nje ne-prototype yawo. Kuvele ukuthi uKant wayejikijela amazwi emoyeni, cishe njengawo wonke umuntu owayezama ukucabanga ukuthi wazi kanjani lokho akwaziyo.

Lesi yisihloko esibalulekile, ngoba isayensi ihlale iphendulwa ukuze kuqinisekiswe: ungavame ukuzwa ukuthi isayensi ibonise lokhu, kufakazelwe ukuthi kuzoba kanje; siyakwazi lokhu, siyakwazi lokho - kodwa siyakwazi na? Uqinisekile? Ngizobheka le mibuzo kabanzi. Masikhumbule umthetho ovela kubhayoloji: i-ontogeny iphinda i-phylogeny. Kusho ukuthi ukukhula komuntu, kusukela eqandeni elivundisiwe kuya kumfundi, kuphinda ngohlelo yonke inqubo yangaphambili yokuziphendukela kwemvelo. Ngakho-ke, ososayensi bathi ngesikhathi sokuthuthukiswa kwe-embryonic, ama-gill slits avela futhi aphinde anyamalale, ngakho-ke bacabanga ukuthi okhokho bethu abakude babeyizinhlanzi.

Kuzwakala kukuhle uma ungacabangi ngakho kakhulu. Lokhu kunikeza umbono omuhle kakhulu wokuthi ukuziphendukela kwemvelo kusebenza kanjani, uma ukukholelwa. Kodwa ngizoqhubekela phambili futhi ngibuze: izingane zifunda kanjani? Baluthola kanjani ulwazi? Mhlawumbe bazalwa benolwazi olunqunywe kusengaphambili, kodwa lokho kuzwakala kuwukukhubazeka okuncane. Ukukhuluma iqiniso, akugculisi neze.

Zenzani-ke izingane? Banemizwa ethile engokwemvelo, elalela lokho, izingane ziqala ukwenza imisindo. Benza yonke le misindo esivame ukuyibiza ngokuthi ukubhibhidla, futhi lokhu kubhuqa akubonakali kuncike ekutheni ingane izalelwa kuphi - eShayina, eRussia, eNgilandi noma eMelika, izingane zizobhavumula ngendlela efanayo. Nokho, ukubhibhidla kuzokhula ngendlela ehlukile kuye ngezwe. Isibonelo, lapho ingane yaseRussia isho igama elithi "mama" izikhathi ezimbalwa, izothola impendulo enhle futhi ngenxa yalokho izophinda le misindo. Ngokusebenzisa isipiliyoni, uthola ukuthi yimiphi imisindo esiza ukufeza lokho akufunayo nokuthi yini engakwenzi, futhi ngaleyo ndlela ufunda izinto eziningi.

Ake nginikhumbuze engikushilo izikhathi eziningana - alikho igama lokuqala kusichazamazwi; igama ngalinye lichazwa ngamanye, okusho ukuthi isichazamazwi siyisiyingi. Ngendlela efanayo, lapho ingane izama ukwakha ukulandelana okuhambisanayo kwezinto, iba nenkinga yokubhekana nokungqubuzana okufanele ikuxazulule, ngoba ayikho into yokuqala okufanele ingane ifunde, futhi "umama" akasebenzi ngaso sonke isikhathi. Ukudideka kuvela, isibonelo, njengoba ngizokukhombisa manje. Nali ihlaya elidumile laseMelika:

amazwi eculo elidumile (ngiyajabula isiphambano ngingasithwala, ngithwale isiphambano sakho ngentokozo)
kanye nendlela izingane ezizizwa ngayo (ngokujabula ibhere eliphambanayo, ngenjabulo ibhere eliphambanayo)

(Ngesi-Russian: i-violin-fox/creak of a wheel, I am a wanking emerald/cores are a pure emerald, uma ufuna inkunzi plums/uma ufuna ukujabula, stosh shit-ass/ikhulu izinyathelo emuva.)

Ngaphinde ngabhekana nobunzima obunjalo, hhayi kulesi simo, kodwa kunezimo eziningana ekuphileni kwami ​​engangizikhumbula lapho ngicabanga ukuthi engangikufunda nengikusho cishe kwakuyiqiniso, kodwa labo ababengizungezile, ikakhulukazi abazali bami, babekuqonda okuthile. .. lokho kuhluke ngokuphelele.

Lapha ungabona amaphutha amakhulu futhi ubone ukuthi kwenzeka kanjani. Ingane ibhekene nesidingo sokucabanga ukuthi amagama asho ukuthini olimini futhi kancane kancane ifunda izinketho ezifanele. Nokho, ukulungisa amaphutha anjalo kungathatha isikhathi eside. Akunakwenzeka ukuqiniseka ukuthi zilungiswe ngokuphelele ngisho namanje.

Ungaya kude kakhulu ungaqondi ukuthi wenzani. Sengike ngakhuluma ngomngane wami, udokotela wesayensi yezibalo wase-Harvard University. Lapho ethweswa iziqu eHarvard, wathi angakwazi ukubala okuphumayo ngencazelo, kodwa akakuqondi ngempela, uyazi nje ukuthi kwenziwa kanjani. Lokhu kuyiqiniso ezintweni eziningi esizenzayo. Ukuze ugibele ibhayisikili, i-skateboard, ukubhukuda, nezinye izinto eziningi, akudingeki sazi ukuthi sizenza kanjani. Kubonakala sengathi ulwazi lungaphezu kwalokho olungavezwa ngamazwi. Ngimanqika ukusho ukuthi awazi ukugibela ibhayisikili, noma ungangitsheli ukuthi kanjani, kodwa uhamba phambi kwami ​​ngesondo elilodwa. Ngakho, ulwazi lungahluka kakhulu.

Ake sifingqe kancane engikushilo. Kunabantu abakholelwa ukuthi sinolwazi esizalwa nalo; Uma ubheka isimo sisonke, ungase uvumelane nalokhu, ucabangela, ngokwesibonelo, ukuthi izingane zinokuthambekela okungokwemvelo kokuphimisa imisindo. Uma ingane yazalelwa eChina, izofunda ukuphimisela imisindo eminingi ukuze ifinyelele lokho akufunayo. Uma wazalelwa eRussia, uzophinde enze imisindo eminingi. Uma ezalelwe eMelika, usazokhipha imisindo eminingi. Ulimi ngokwalo alubalulekile kangako lapha.

Ngakolunye uhlangothi, ingane inekhono lemvelo lokufunda noma yiluphi ulimi, njengazo zonke ezinye. Ukhumbula ukulandelana kwemisindo futhi athole ukuthi isho ukuthini. Kumelwe ayichaze ngokwakhe le misindo, njengoba ingekho ingxenye yokuqala ayengayikhumbula. Bonisa ingane yakho ihhashi bese uyibuza: “Ingabe igama elithi “ihhashi” igama lehhashi? Noma lokhu kusho ukuthi unemilenze emine? Mhlawumbe umbala wakhe lona? Uma uzama ukutshela ingane ukuthi ihhashi liyini ngokulikhombisa, ingane ngeke ikwazi ukuphendula lowo mbuzo, kodwa yilokho okushoyo. Ingane ngeke yazi ukuthi leli gama izolihlukanisa ngasiphi isigaba. Noma, isibonelo, thatha isenzo "ukugijima." Ingasetshenziswa uma uhamba ngokushesha, kodwa futhi ungasho ukuthi imibala yehembe lakho isiphelile ngemva kokugeza, noma ukhononda ngokugijima kwewashi.

Umntwana ubhekana nobunzima obukhulu, kodwa ngokushesha noma kamuva uyawalungisa amaphutha akhe, avume ukuthi wayeqonda okuthile okungalungile. Ngokuhamba kweminyaka, izingane ziya ngokuya ziba ncane amandla okwenza lokhu, futhi lapho sezikhule ngokwanele, azisakwazi ukushintsha. Ngokusobala, abantu bangenza iphutha. Khumbula, isibonelo, labo abakholelwa ukuthi unguNapoleon. Akukhathalekile ukuthi uveza ubufakazi obungakanani kumuntu onjalo ukuthi akunjalo, uzoqhubeka ekholelwa kukho. Uyazi, kunabantu abaningi abanezinkolelo eziqinile ongavumelani nazo. Njengoba ungase ukholelwe ukuthi izinkolelo zabo ziyasangana, ukusho ukuthi kunendlela eqinisekile yokuthola ulwazi olusha akulona iqiniso ngokuphelele. Uzothi kulokhu: "Kodwa isayensi icocekile kakhulu!" Ake sibheke indlela yesayensi futhi sibone ukuthi lokhu kuyiqiniso yini.

Siyabonga ku-Sergei Klimov ngokuhumusha.

Kuzoqhubeka ...

Ubani ofuna ukusiza ukuhumusha, ukwakheka kanye nokushicilelwa kwencwadi - bhala ku-PM noma nge-imeyili [i-imeyili ivikelwe]

Ngendlela, sethule nokuhunyushwa kwenye incwadi epholile - "Umshini Wamaphupho: Indaba Ye-Computer Revolution")

Sifuna ikakhulukazi abazosiza ukuhumusha isahluko sebhonasi, esikuvidiyo kuphela. (dlulisa imizuzu eyi-10, ama-20 okuqala asethathiwe)

Okuqukethwe yincwadi nezahluko ezihunyushiweIsibikezelo

  1. Isingeniso Sezobuciko Bokwenza Isayensi Nobunjiniyela: Ukufunda Ukufunda (Mashi 28, 1995) Ukuhumusha: Isahluko 1
  2. "Izisekelo zeDigital (Discrete) Revolution" (March 30, 1995) Isahluko 2. Okuyisisekelo kwenguquko yedijithali (ehlukile).
  3. "Umlando Wamakhompiyutha - Hardware" (March 31, 1995) Isahluko 3. Umlando Wamakhompyutha - Izingxenyekazi zekhompuyutha
  4. "Umlando Wamakhompyutha - Isoftware" (April 4, 1995) Isahluko 4. Umlando Wamakhompyutha - Isofthiwe
  5. "Umlando Wamakhompyutha - Izicelo" (April 6, 1995) Isahluko 5: Umlando Wamakhompyutha - Izicelo Ezisebenzayo
  6. "I-Artificial Intelligence - Ingxenye I" (April 7, 1995) Isahluko 6. I-Artificial Intelligence - 1
  7. "I-Artificial Intelligence - Ingxenye II" (April 11, 1995) Isahluko 7. I-Artificial Intelligence - II
  8. "I-Artificial Intelligence III" (April 13, 1995) Isahluko 8. I-Artificial Intelligence-III
  9. "n-Dimensional Space" (April 14, 1995) Isahluko 9. Isikhala esingu-N-dimensional
  10. "I-Coding Theory - Ukumelwa Kolwazi, Ingxenye I" (April 18, 1995) Isahluko 10. Ithiyori yokubhala ikhodi - I
  11. "I-Coding Theory - Ukumelwa Kolwazi, Ingxenye II" (April 20, 1995) Isahluko 11. I-Coding Theory - II
  12. "Amakhodi Okulungisa Amaphutha" (April 21, 1995) Isahluko 12. Amakhodi Wokulungisa Amaphutha
  13. "Information Theory" (April 25, 1995) Kwenziwe, okumele ukwenze nje ukuyishicilela
  14. "Izihlungi Zedijithali, Ingxenye I" (April 27, 1995) Isahluko 14. Izihlungi Zedijithali - 1
  15. "Izihlungi Zedijithali, Ingxenye II" (April 28, 1995) Isahluko 15. Izihlungi Zedijithali - 2
  16. "Izihlungi Zedijithali, Ingxenye III" (May 2, 1995) Isahluko 16. Izihlungi Zedijithali - 3
  17. "Izihlungi Zedijithali, Ingxenye IV" (May 4, 1995) Isahluko 17. Izihlungi Zedijithali - IV
  18. "Ukulingisa, Ingxenye I" (May 5, 1995) Isahluko 18. Ukumodela - I
  19. "Ukulingisa, Ingxenye II" (May 9, 1995) Isahluko 19. Ukumodela - II
  20. "Ukulingisa, Ingxenye III" (May 11, 1995) Isahluko 20. Ukumodela - III
  21. "Fiber Optics" (May 12, 1995) Isahluko 21. Fiber optics
  22. "Imiyalo Yokusiza Ngekhompyutha" (May 16, 1995) Isahluko 22: I-Computer Assisted Instruction (CAI)
  23. "Mathematics" (May 18, 1995) Isahluko 23. Izibalo
  24. "I-Quantum Mechanics" (May 19, 1995) Isahluko 24. I-Quantum mechanics
  25. "Ukudala" (May 23, 1995). Ukuhumusha: Isahluko 25. Ukudala
  26. "Ochwepheshe" (May 25, 1995) Isahluko 26. Ongoti
  27. "Idatha Engathembekile" (May 26, 1995) Isahluko 27. Idatha engathembekile
  28. "Ubunjiniyela Bezinhlelo" (May 30, 1995) Isahluko 28. Ubunjiniyela Bezinhlelo
  29. "Uthola Lokho Okulinganisayo" (June 1, 1995) Isahluko 29: Uthola lokho okulinganisayo
  30. "Sikwazi Kanjani Esikwaziyo" (Juni 2, 1995) Humusha ngezingxenye zemizuzu eyi-10
  31. Hamming, “Wena Nocwaningo Lwakho” (June 6, 1995). Ukuhumusha: Wena nomsebenzi wakho

Ubani ofuna ukusiza ukuhumusha, ukwakheka kanye nokushicilelwa kwencwadi - bhala ku-PM noma nge-imeyili [i-imeyili ivikelwe]

Source: www.habr.com

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