Sikwenzile!
"Inhloso yalesi sifundo ukukulungiselela ikusasa lakho lobuchwepheshe."
Sawubona, Habr. Khumbula isihloko esimangalisayo (+219, 2588 amabhukumaka, 429k afundiwe)?
So Hamming (yebo, yebo, ukuzibheka nokuzilungisa ) kukhona okuphelele , ebhalwe ngokusekelwe ezinkulumweni zakhe. Siyalihumusha, ngoba indoda ikhuluma okucabangayo.
Le yincwadi hhayi nge-IT kuphela, iyincwadi ekhuluma ngesitayela sokucabanga sabantu abapholile ngendlela emangalisayo. “Akukhona nje ukuthuthukiswa kokucabanga okuhle; ichaza izimo ezandisa amathuba okwenza umsebenzi omkhulu.”
Siyabonga ku-Andrey Pakhomov ngokuhumusha.
I-Information Theory yasungulwa ngu-C. E. Shannon ngasekupheleni kwawo-1940. Abaphathi beBell Labs bagcizelele ukuthi ayibize ngokuthi “I-Communication Theory” ngoba... leli igama elinembe kakhulu. Ngenxa yezizathu ezisobala, igama elithi "Information Theory" linomthelela omkhulu kakhulu emphakathini, yingakho uShannon alikhetha, futhi yigama esilaziyo kuze kube namuhla. Igama ngokwalo liphakamisa ukuthi ithiyori iphathelene nolwazi, okwenza lubaluleke njengoba singena sijula enkathini yolwazi. Kulesi sahluko, ngizothinta iziphetho ezimbalwa eziyinhloko ezivela kulo mbono, ngeke nginikeze ubufakazi obuqinile, kodwa obunembile bamanye amalungiselelo alo mbono, ukuze uqonde ukuthi iyini ngempela "Information Theory", lapho ungayisebenzisa khona. nalapho engekho .
Okokuqala, luyini “ulwazi”? UShannon ulinganisa ulwazi nokungaqiniseki. Ukhethe i-logarithm eyinegethivu yamathuba omcimbi njengesilinganiso sobuningi bolwazi olutholayo uma kwenzeka umcimbi onethuba elingu-p. Isibonelo, uma ngikutshela ukuthi isimo sezulu e-Los Angeles sinenkungu, khona-ke u-p useduze no-1, okungasiniki ngempela ulwazi oluningi. Kodwa uma ngithi lina eMonterey ngoJuni, kuzoba nokungaqiniseki kumlayezo futhi uzoqukatha ulwazi olwengeziwe. Umcimbi onokwethenjelwa awunalo ulwazi, njengoba ulogi 1 = 0.
Ake sibheke lokhu ngokuningiliziwe. UShannon wayekholelwa ukuthi isilinganiso somthamo wolwazi kufanele sibe umsebenzi oqhubekayo wamathuba omcimbi p, futhi ezenzakalweni ezizimele kufanele kube okungeziwe - inani lolwazi elitholwe ngenxa yokwenzeka kwezenzakalo ezimbili ezizimele kufanele lilingane inani lolwazi olutholwe ngenxa yokwenzeka komcimbi ohlanganyelwe. Isibonelo, umphumela we-dice roll kanye ne-coin roll ngokuvamile kuthathwa njengemicimbi ezimele. Ake sihumushe okungenhla olimini lwezibalo. Uma mina (p) kuyinani lolwazi oluqukethwe kumcimbi onamathuba okuthi p, kusho ukuthi ngomcimbi ohlanganyelwe ohlanganisa izehlakalo ezimbili ezizimele x okungenzeka ukuthi u-p1 kanye no-y okungenzeka ukuthi u-p2 esiwutholayo.
(u-x kanye no-y yimicimbi ezimele)
Lena i-equation ye-Cauchy esebenzayo, eyiqiniso kuwo wonke u-p1 no-p2. Ukuze uxazulule le equation yokusebenza, cabanga lokho
p1 = p2 = p,
lokhu kunikeza
Uma p1 = p2 futhi p2 = p ke
njll. Ukunweba le nqubo kusetshenziswa indlela evamile yama-exponentials, kuzo zonke izinombolo ezinengqondo m/n okulandelayo kuyiqiniso
Kusukela ekuqhubekeni okucatshangwayo kwesilinganiso solwazi, kulandela ukuthi umsebenzi we-logarithmic uwukuphela kwesixazululo esiqhubekayo sezibalo ezisebenzayo ze-Cauchy.
Kuthiyori yolwazi, kuvamile ukuthatha isisekelo se-logarithm sibe ngu-2, ngakho ukukhetha kanambambili kuqukethe ncamashi ibhithi eli-1 lolwazi. Ngakho-ke, ulwazi lulinganiswa ngefomula
Ake sime kancane siqonde ukuthi kwenzekeni ngenhla. Okokuqala nje, asiwuchazanga umqondo “wolwazi”; sivele sachaza ifomula yesilinganiso salo sobuningi.
Okwesibili, lesi sinyathelo singaphansi kokungaqiniseki, futhi nakuba siyifanelekela imishini—ngokwesibonelo, izimiso zocingo, umsakazo, ithelevishini, amakhompyutha, njll—asibonisi isimo sengqondo somuntu esivamile ngokwaziswa.
Okwesithathu, lesi isilinganiso esilinganiselwe, kuncike esimweni samanje solwazi lwakho. Uma ubheka ukusakaza "kwezinombolo ezingahleliwe" ezivela ku-generator inombolo engahleliwe, ucabanga ukuthi inombolo ngayinye elandelayo ayinaso isiqiniseko, kodwa uma wazi ifomula yokubala "izinombolo ezingahleliwe", inombolo elandelayo izokwaziwa, ngakho-ke ngeke ziqukethe ulwazi.
Ngakho incazelo yolwazi kaShannon ifanele imishini ezimweni eziningi, kodwa ayibonakali ihambisana nokuqonda komuntu kwegama. Kungalesi sizathu-ke “Ithiyori Yolwazi” bekufanele ibizwe ngokuthi “Ithiyori Yezokuxhumana.” Kodwa-ke, sekwephuzile kakhulu ukushintsha izincazelo (ezanikeza inkolelo-mbono ukuthandwa kwayo kokuqala, futhi okwenza abantu bacabange ukuthi le mbono iphathelene "nolwazi"), ngakho-ke kufanele siphile nabo, kodwa ngesikhathi esifanayo kufanele baqonde ngokucacile ukuthi incazelo kaShannon yolwazi ikude kangakanani nencazelo yayo evame ukusetshenziswa. Ulwazi lukaShannon luphathelene nokuthile okuhluke ngokuphelele, okuwukuthi ukungaqiniseki.
Nakhu okumele ucabange ngakho uma uphakamisa noma yimaphi amagama. Incazelo ehlongozwayo, njengencazelo yolwazi ka-Shannon, ivumelana kanjani nombono wakho wasekuqaleni futhi ihluke kangakanani? Cishe alikho igama eliwubonisa kahle umbono wakho wangaphambilini womqondo, kodwa ekugcineni, yigama elisetshenziswayo elibonisa incazelo yomqondo, ngakho ukwenza okuthile ngokusemthethweni ngezincazelo ezicacile kuhlale kwethula umsindo othile.
Cabangela isistimu amagama ayo aqukethe izimpawu q okungenzeka ukuthi u-pi. Esimweni esinjalo isilinganiso senani lolwazi ohlelweni (inani layo elilindelekile) lilingana no:
Lokhu kubizwa nge-entropy yesistimu enamathuba okusabalalisa {pi}. Sisebenzisa igama elithi "entropy" ngoba ifomu lezibalo elifanayo livela ku-thermodynamics kanye ne-statistical mechanics. Yingakho igama elithi "entropy" lidala i-aura ethile yokubaluleka eduze kwayo, okuyinto ekugcineni engathetheleleki. Indlela efanayo yezibalo yokubhala ayisho incazelo efanayo yezimpawu!
I-entropy yokusatshalaliswa kwamathuba idlala indima enkulu kuthiyori yokubhala ikhodi. Ukungalingani kwe-Gibbs kokuhluka okubili kwamathuba okusatshalaliswa kwe-pi kanye ne-qi kungenye yemiphumela ebalulekile yalo mbono. Ngakho kufanele sikufakazele lokho
Ubufakazi busekelwe kugrafu esobala, Fig. 13.I, okubonisa lokho
futhi ukulingana kufinyelelwa kuphela uma x = 1. Masisebenzise ukungalingani kuthemu ngayinye yesamba ukusuka kwesokunxele:
Uma i-alfabhethi yesistimu yezokuxhumana iqukethe izimpawu ezingu-q, bese sithatha ithuba lokudluliswa kophawu ngalunye qi = 1/q bese kufakwa u-q, sithola ekungalinganini kwe-Gibbs.
Umfanekiso 13.I
Lokhu kusho ukuthi uma ithuba lokudlulisa zonke izimpawu ezingu-q lifana futhi lilingana no - 1 / q, khona-ke i-entropy ephezulu ilingana no-ln q, ngaphandle kwalokho ukungalingani kubambe.
Endabeni yekhodi ehlukanisekayo eyingqayizivele, sinokulingana kuka-Kraft
Manje uma sichaza amathuba mbumbulu
lapho kunjalo = 1, okulandela ukungalingani kukaGibbs,
futhi sisebenzise i-algebra encane (khumbula ukuthi u-K ≤ 1, ukuze sikwazi ukulahla igama le-logarithmic, futhi mhlawumbe siqinise ukungalingani kamuva), sithola
lapho u-L eyisilinganiso sobude bekhodi.
Ngakho, i-entropy iwumkhawulo oboshelwe kunoma iyiphi ikhodi yohlamvu ne-symboli enesilinganiso segama lekhodi L. Lena inkolelo-mbono ka-Shannon yesiteshi esingenaziphazamiso.
Manje cabanga ngethiyori eyinhloko mayelana nemikhawulo yezinhlelo zokuxhumana lapho ulwazi lusakazwa khona njengomfudlana wamabhithi azimele nomsindo okhona. Kuyaqondakala ukuthi amathuba okudluliswa okulungile kwebhithi eyodwa ngu-P > 1/2, futhi amathuba okuthi inani elincane liguqulwe ngesikhathi sokudlulisela (kuzokwenzeka iphutha) lilingana no-Q = 1 - P. Ukuze kube lula, thina cabanga ukuthi amaphutha azimele futhi amathuba ephutha ayafana ebhithi ngalinye elithunyelwe - okungukuthi, kukhona "umsindo omhlophe" esiteshini sokuxhumana.
Indlela esinokusakaza okude ngayo kwamabhithi n afakwe kumlayezo owodwa isandiso sika-n - dimensional sekhodi yebhithi eyodwa. Sizonquma inani lika-n kamuva. Cabangela umlayezo oqukethe ama-n-bits njengephoyinti esikhaleni esingu-n-dimensional. Njengoba sinesikhala esingu-n-dimensional - futhi ukuze sibe lula sizocabanga ukuthi umlayezo ngamunye unethuba elifanayo lokwenzeka - kukhona u-M okungenzeka ukuthi umlayezo (M uzochazwa kamuva), ngakho-ke amathuba anoma yimuphi umlayezo othunyelwe
(umthumeli)
Isheduli 13.II
Okulandelayo, cabanga ngombono womthamo wesiteshi. Ngaphandle kokungena emininingwaneni, umthamo wesiteshi uchazwa njengenani eliphezulu lolwazi elingadluliswa ngendlela enokwethenjelwa ngesiteshi sokuxhumana, kucatshangelwa ukusetshenziswa kombhalo wekhodi osebenza kahle kakhulu. Akukho ukungqubuzana kokuthi ulwazi oluthe xaxa lungadluliswa ngesiteshi sokuxhumana ngaphezu komthamo walo. Lokhu kungafakazelwa isiteshi esilinganisa kanambambili (esisisebenzisa kithi). Umthamo wesiteshi, lapho uthumela izingcezu, ucaciswa ngokuthi
lapho, njengangaphambili, u-P enethuba lokungabikho kwephutha kunoma iyiphi ibhithi ethunyelwe. Uma uthumela amabhithi n ezimele, umthamo wesiteshi unikezwa ngu
Uma siseduze nomthamo wesiteshi, khona-ke kufanele sithumele cishe leli nani lolwazi kuphawu ngalunye ai, i = 1, ..., M. Ngokucabangela ukuthi amathuba okuba khona kophawu ngalunye ai ngu-1 / M, sithola
uma sithumela noma yimiphi imiyalezo engenzeka ngokulinganayo M, sinayo
Uma kuthunyelwa ama-n bits, silindele ukuthi kwenzeke amaphutha e-nQ. Empeleni, kumlayezo oqukethe ama-n-bits, sizoba namaphutha cishe e-nQ kumlayezo owamukelwe. Ku-n enkulu, ukuhluka okuhlobene (ukuhluka = ububanzi bokusabalalisa, )
ukusatshalaliswa kwenani lamaphutha kuzoba kuncane kakhulu njengoba u-n ekhula.
Ngakho-ke, ohlangothini lwesidluliseli, ngithatha umlayezo ai ukuze ngiwuthumele futhi ngidwebe imbulunga ewuzungezile ngerediyasi.
okukhudlwana kancane ngenani elilingana no-e2 kunenani elilindelekile lamaphutha Q, (Umfanekiso 13.II). Uma u-n emkhulu ngokwanele, khona-ke kunethuba elincane ngokunganaki lephuzu lomlayezo bj elivela ohlangothini lomamukeli oludlulela ngale kwale mbulunga. Ake sidwebe isimo njengoba ngisibona ngombono womthumeli: sinanoma iyiphi irediyo esuka kumyalezo odlulisiwe ai ukuya emyalezweni owamukelwe bj namathuba ephutha elilingana (noma elicishe lilingane) nokusatshalaliswa okuvamile, okufinyelela ubuningi. kwe nq. Kunoma iyiphi i-e2 enikeziwe, kukhona u-n omkhulu kangangokuthi amathuba okuthi iphuzu elingumphumela elithi bj libe ngaphandle kwendilinga yami lincane ngendlela othanda ngayo.
Manje ake sibheke isimo esifanayo ohlangothini lwakho (Fig. 13.III). Ehlangothini lomamukeli kukhona i-sphere S(r) yerediyasi efanayo r ezungeze indawo eyamukelwe bj esikhaleni esingu-n-dimensional, ukuze kuthi uma umlayezo owamukelwe bj ungaphakathi kwendilinga yami, khona-ke umlayezo ai othunyelwe yimi ungaphakathi kwakho. i-sphere.
Iphutha lingenzeka kanjani? Iphutha lingenzeka ezimweni ezichazwe kuthebula elingezansi:
Umfanekiso 13.III
Lapha sibona ukuthi uma endaweni eyakhiwe eduze kwendawo etholiwe kukhona okungenani iphuzu elilodwa elihambisana nomlayezo othunyelwe ongekho ikhodi, khona-ke iphutha lenzeke ngesikhathi sokudlulisa, ngoba awukwazi ukucacisa ukuthi iyiphi yale miyalezo edluliselwe. Umlayezo othunyelwe awunaphutha kuphela uma iphuzu elihambisana nawo lisendimeni, futhi awekho amanye amaphuzu angenzeka kukhodi enikeziwe asendimeni efanayo.
Sinezibalo zezibalo zamathuba ephutha elithi Pe uma umlayezo ai uthunyelwe
Singalahla isici sokuqala kwithemu yesibili, siyithathe njengo-1. Ngakho sithola ukungalingani
Ngokusobala,
Ngenxa yalokho
sebenzisa kabusha ithemu yokugcina kwesokudla
Uma uthatha n enkulu ngokwanele, ithemu yokuqala ingathathwa njengencane ngendlela ofisa ngayo, ithi ngaphansi kwenombolo ethile d. Ngakho-ke sinakho
Manje ake sibheke ukuthi singayakha kanjani ikhodi elula yokufaka esikhundleni sekhodi M imilayezo ehlanganisa amabhithi n. Njengoba engazi ukuthi ikhodi yenziwe kanjani kahle (amakhodi okulungisa amaphutha ayengakaqanjwa), u-Shannon wakhetha ukubhala ngekhodi okungahleliwe. Phenya uhlamvu lwemali kumabhithi n ngamunye kumlayezo bese uphinda inqubo yemilayezo engu-M. Sekukonke, ama-nM coin flips adinga ukwenziwa, ngakho-ke kungenzeka
izichazamazwi zekhodi ezinamathuba afanayo ½nM. Yiqiniso, inqubo engahleliwe yokudala i-codebook isho ukuthi kukhona ithuba lokuphindaphinda, kanye namaphoyinti ekhodi azoba eduze komunye nomunye ngakho-ke abe umthombo wamaphutha okungenzeka. Umuntu kufanele afakazele ukuthi uma lokhu kungenzeki ngamathuba amakhulu kunanoma yiliphi izinga elincane elikhethiwe lephutha, khona-ke u-n onikeziwe mkhulu ngokwanele.
Iphuzu elibalulekile ukuthi uShannon wenze i-avareji yawo wonke ama-codebook angaba khona ukuze athole iphutha elimaphakathi! Sizosebenzisa uphawu Av[.] ukuze sibonise inani eliyisilinganiso phezu kwesethi yawo wonke ama-codebook angahleliwe angahleliwe. Ukulinganisa phezu kwe-d engaguquki, yiqiniso, kunikeza ukungaguquguquki, njengoba isilinganiso sethemu ngayinye siyefana nawo wonke amanye amathemu esambeni,
okungandiswa (M–1 iya ku-M)
Kunoma imuphi umlayezo onikeziwe, uma ulinganisa kuwo wonke ama-codebook, umbhalo wekhodi ugijima kuwo wonke amanani angenzeka, ngakho-ke isilinganiso esimaphakathi sokuthi iphoyinti liku-sphere isilinganiso sevolumu ye-sphere nenani eliphelele lesikhala. Umthamo we-sphere ngu
lapho u-s=Q+e2 <1/2 kanye no-ns kumelwe kube inombolo ephelele.
Ithemu yokugcina kwesokudla inkulu kuleli samba. Okokuqala, ake silinganise inani layo sisebenzisa ifomula ye-Stirling yezimboni. Sizobe sesibheka i-coefficient enciphayo yetemu eliphambi kwayo, qaphela ukuthi le coefficient iyanda njengoba siya kwesokunxele, ngakho-ke singakwazi: (1) ukukhawulela inani lesamba kwisamba sokuqhubeka kwejometri nge le coefficient yokuqala, (2) yandise ukuqhubeka kwejiyomethri ukusuka kumatemu angu-ns ukuya enanini elingapheli lamatemu, (3) abale isamba sokuqhubeka kwejometri okungapheli (i-algebra evamile, akukho lutho olubalulekile) futhi ekugcineni uthole inani elikhawulelayo (ngenani elikhulu ngokwanele n):
Qaphela ukuthi i-entropy H(ama) ibonakala kanjani kubunikazi be-binomial. Qaphela ukuthi ukunwetshwa kochungechunge lwe-Taylor H(s)=H(Q+e2) kunikeza isilinganiso esitholiwe kucatshangelwa kuphela okuphuma kokunye kokuqala futhi ungazinaki zonke ezinye. Manje ake sihlanganise isisho sokugcina:
kuphi
Okufanele sikwenze ukukhetha u-e2 ukuthi u-e3 <e1, bese ithemu lokugcina lizoba lincane ngokunganaki, inqobo nje uma u-n emkhulu ngokwanele. Ngakho-ke, iphutha elimaphakathi le-PE lingatholwa lincane ngendlela efunwa ngayo ngomthamo wesiteshi eduze kuka-C.
Uma isilinganiso sawo wonke amakhodi sinephutha elincane ngokwanele, khona-ke okungenani ikhodi eyodwa kufanele ifaneleke, ngakho-ke kukhona okungenani uhlelo olulodwa olufanele lokubhala amakhodi. Lona umphumela obalulekile otholwe u-Shannon - "ithiyori kaShannon yesiteshi esinomsindo", nakuba kufanele kuqashelwe ukuthi wafakazela lokhu ngecala elivamile kakhulu kunesiteshi esilula sika-symmetric kanambambili engasisebenzisa. Ngokwesimo esijwayelekile, izibalo zezibalo ziyinkimbinkimbi kakhulu, kodwa imibono ayifani kangako, ngakho-ke, ngokuvamile, usebenzisa isibonelo secala elithile, ungakwazi ukuveza incazelo yeqiniso ye-theorem.
Ake sigxeke umphumela. Siphinde ngokuphindaphindiwe: "Ngobukhulu ngokwanele n." Kodwa ingakanani i-n? Kakhulu, kukhulu kakhulu uma ufuna ngempela ukusondela kumthamo wesiteshi futhi uqiniseke ngokudluliswa kwedatha okulungile! Kukhulu kakhulu, eqinisweni, ukuthi kuzodingeka ulinde isikhathi eside kakhulu ukuze uqongelele umlayezo wezingcezu ezanele ukuze uwubhale ngekhodi ngokuhamba kwesikhathi. Kulokhu, usayizi wesichazamazwi sekhodi engahleliwe uzoba mkhulu nje (phela, isichazamazwi esinjalo asinakumelwa ngendlela emfishane kunohlu oluphelele lwazo zonke izingcezu zika-Mn, naphezu kweqiniso lokuthi u-n kanye no-M bakhulu kakhulu)!
Amakhodi okulungisa amaphutha agwema ukulinda umlayezo omude kakhulu bese ewubhala futhi ewukhipha ngamakhodi amakhulu kakhulu ngoba agwema ama-codebook ngokwawo futhi esikhundleni salokho asebenzise ukubala okuvamile. Ngombono olula, amakhodi anjalo avame ukulahlekelwa amandla okusondela kumthamo wesiteshi futhi aqhubeke egcina izinga eliphansi lephutha, kodwa lapho ikhodi ilungisa inani elikhulu lamaphutha, enza kahle. Ngamanye amazwi, uma unikeza umthamo othile wesiteshi ekulungiseni amaphutha, kufanele usebenzise amandla okulungisa amaphutha isikhathi esiningi, okungukuthi, inani elikhulu lamaphutha kufanele lilungiswe kumyalezo ngamunye othunyelwe, ngaphandle kwalokho umosha lo mthamo.
Ngesikhathi esifanayo, i-theoem efakazelwe ngenhla ayisho lutho! Kubonisa ukuthi amasistimu okudlulisela asebenza kahle kufanele asebenzise izikimu zokufaka ikhodi ezihlakaniphile kumayunithi ezinhlamvu amabhithi amade kakhulu. Isibonelo amasathelayithi aye andiza ngaphezu kwamaplanethi angaphandle; Njengoba besuka eMhlabeni naseLangeni, baphoqeleka ukuthi balungise amaphutha amaningi nangaphezulu kubhulokhi yedatha: amanye amasathelayithi asebenzisa ama-solar panel, ahlinzeka nge-5 W, amanye asebenzisa imithombo yamandla enyukliya, ehlinzeka ngamandla afanayo. Amandla aphansi okunikezwa kwamandla kagesi, usayizi omncane wezitsha zokudlulisa kanye nosayizi olinganiselwe wezitsha zokwamukela eMhlabeni, ibanga elikhulu okufanele isignali ilihambe - konke lokhu kudinga ukusetshenziswa kwamakhodi anezinga eliphezulu lokulungiswa kwamaphutha uhlelo lokuxhumana olusebenzayo.
Ake sibuyele esikhaleni esingu-n-dimensional esisisebenzisile ebufakazini obungenhla. Lapho sixoxa ngakho, sibonise ukuthi cishe yonke ivolumu ye-sphere igxile eduze kwendawo yangaphandle - ngakho-ke, cishe kuqinisekile ukuthi isignali ethunyelwe izotholakala eduze kwendawo eyakhiwe eduze kwesignali eyamukelwe, ngisho nesilinganiso esilinganiselwe. indawo encane yendilinga enjalo. Ngakho-ke, akumangazi ukuthi isignali etholiwe, ngemva kokulungisa inani elikhulu lamaphutha, i-nQ, ivele isondelene ngokungafanele nesignali ngaphandle kwamaphutha. Amandla okuxhumanisa esikhulume ngawo ekuqaleni ayisihluthulelo sokuqonda lesi simo. Qaphela ukuthi ama-sphere afanayo akhelwe ukulungisa amaphutha amakhodi e-Haming awagqagqani. Inombolo enkulu yobukhulu obucishe bube yi-orthogonal esikhaleni esingu-n-dimensional ibonisa ukuthi kungani singakwazi ukufaka ama-M sphere emkhathini ngokugqagqana okuncane. Uma sivumela ukugqagqana okuncane, okuncane ngokunganaki, okungaholela enanini elincane kuphela lamaphutha ngesikhathi sokukhipha amakhodi, singathola ukubekwa okuminyene kwama-sphere emkhathini. I-Haming iqinisekise izinga elithile lokulungiswa kwamaphutha, i-Shannon - amathuba aphansi ephutha, kodwa ngesikhathi esifanayo ukugcina ukukhishwa kwangempela kusondele ngokungenangqondo kumthamo wesiteshi sokuxhumana, amakhodi we-Hamming angeke akwenze.
Ithiyori yolwazi ayisitsheli ukuthi singaklama kanjani isistimu ephumelelayo, kodwa ikhomba indlela eya ezinhlelweni zokuxhumana eziphumelelayo. Kuyithuluzi elibalulekile lokwakha izinhlelo zokuxhumana ngomshini ngomshini, kodwa, njengoba kuphawuliwe ekuqaleni, akuhlobene kancane nendlela abantu abaxhumana ngayo. Izinga ifa lebhayoloji elifana nezinhlelo zokuxhumana zobuchwepheshe akwaziwa, ngakho-ke akucaci okwamanje ukuthi ithiyori yolwazi isebenza kanjani kuzakhi zofuzo. Akukho okunye esingakwenza ngaphandle kokuthi sizame, futhi uma impumelelo isibonisa imvelo efana nomshini yalesi simo, khona-ke ukwehluleka kuzokhomba ezinye izici ezibalulekile zemvelo yolwazi.
Masingadikibali kakhulu. Sibonile ukuthi zonke izincazelo zasekuqaleni, ngokwezinga elikhulu noma elincane, kufanele ziveze ingqikithi yezinkolelo zethu zasekuqaleni, kodwa zibonakala ngezinga elithile lokuhlanekezelwa ngakho-ke azisebenzi. Kuyavunywa ngokwesiko ukuthi, ekugcineni, incazelo esiyisebenzisayo empeleni ichaza ingqikithi; kodwa, lokhu kusitshela kuphela indlela yokucubungula izinto futhi akudlulisi noma iyiphi incazelo kithina. Indlela ye-postulational, ethandwa kakhulu emibuthanweni yezibalo, ishiya okuningi okufiselekayo ekusebenzeni.
Manje sizobheka isibonelo sokuhlolwa kwe-IQ lapho incazelo iyisiyingi ngendlela othanda ngayo futhi, ngenxa yalokho, iyadukisa. Kwenziwa ukuhlolwa okufanele kukalwe ubuhlakani. Bese ibuyekezwa ukuze yenziwe ingaguquki ngangokunokwenzeka, bese ishicilelwa futhi, ngendlela elula, ilinganiswe ukuze “ubuhlakani” obulinganisiwe buvele bube buvame ukusatshalaliswa (ejikeni lokulinganiswa, kunjalo). Zonke izincazelo kufanele zihlolwe kabusha, hhayi kuphela lapho zihlongozwa okokuqala, kodwa futhi kamuva kakhulu, lapho zisetshenziswa eziphethweni ezithathiwe. Ingabe imingcele yezincazelo ifaneleka kangakanani ukuze inkinga ixazululwe? Kukangaki izincazelo ezinikezwe endaweni eyodwa zisetshenziswe ezilungiselelweni ezihluke kakhulu? Lokhu kwenzeka kaningi! Ezifundweni zesintu, ozohlangana nazo nakanjani empilweni yakho, lokhu kwenzeka kaningi.
Ngakho-ke, enye yezinjongo zalokhu kwethulwa kwethiyori yolwazi, ngaphezu kokubonisa ukuba wusizo kwayo, kwakuwukukuxwayisa ngale ngozi, noma ukukubonisa kahle ukuthi ungayisebenzisa kanjani ukuze uthole umphumela oyifunayo. Sekuyisikhathi eside kuphawulwa ukuthi izincazelo zokuqala zinquma ukuthi yini oyitholayo ekugcineni, ngezinga elikhulu kakhulu kunalokho okubonakala. Izincazelo zokuqala zidinga ukunakwa okuningi kuwe, hhayi kuphela kunoma yisiphi isimo esisha, kodwa nasezindaweni osebenze kuzo isikhathi eside. Lokhu kuzokuvumela ukuthi uqonde ukuthi imiphumela etholiwe ingakanani i-tautology hhayi into ewusizo.
Indaba edumile ka-Eddington isitshela ngabantu ababedoba ngenetha olwandle. Ngemva kokuhlola ubukhulu bezinhlanzi ababezibambile, bathola ukuthi ubuncane kangakanani izinhlanzi ezitholakala olwandle! Isiphetho sabo sasiqhutshwa ithuluzi elisetshenzisiwe, hhayi iqiniso.
Kuzoqhubeka ...
Ubani ofuna ukusiza ngokuhumusha, isakhiwo nokushicilelwa kwencwadi - bhala umlayezo womuntu siqu noma i-imeyili [i-imeyili ivikelwe]
Ngendlela, sethule nokuhunyushwa kwenye incwadi epholile - )
Sifuna ikakhulukazi abazosiza ukuhumusha . (dlulisa imizuzu eyi-10, ama-20 okuqala asethathiwe)
Okuqukethwe yincwadi nezahluko ezihunyushiwe
- Isingeniso Sezobuciko Bokwenza Isayensi Nobunjiniyela: Ukufunda Ukufunda (Mashi 28, 1995)
- "Izisekelo zeDigital (Discrete) Revolution" (March 30, 1995)
- "Umlando Wamakhompiyutha - Hardware" (March 31, 1995)
- "Umlando Wamakhompyutha - Isoftware" (April 4, 1995)
- "Umlando Wamakhompyutha - Izicelo" (April 6, 1995)
- "I-Artificial Intelligence - Ingxenye I" (April 7, 1995)
- "I-Artificial Intelligence - Ingxenye II" (April 11, 1995)
- "I-Artificial Intelligence III" (April 13, 1995)
- "n-Dimensional Space" (April 14, 1995)
- "I-Coding Theory - Ukumelwa Kolwazi, Ingxenye I" (April 18, 1995)
- "I-Coding Theory - Ukumelwa Kolwazi, Ingxenye II" (April 20, 1995)
- "Amakhodi Okulungisa Amaphutha" (April 21, 1995)
- "Information Theory" (April 25, 1995)
- "Izihlungi Zedijithali, Ingxenye I" (April 27, 1995)
- "Izihlungi Zedijithali, Ingxenye II" (April 28, 1995)
- "Izihlungi Zedijithali, Ingxenye III" (May 2, 1995)
- "Izihlungi Zedijithali, Ingxenye IV" (May 4, 1995)
- "Ukulingisa, Ingxenye I" (May 5, 1995)
- "Ukulingisa, Ingxenye II" (May 9, 1995)
- "Ukulingisa, Ingxenye III" (May 11, 1995)
- "Fiber Optics" (May 12, 1995)
- "Imiyalo Yokusiza Ngekhompyutha" (May 16, 1995)
- "Mathematics" (May 18, 1995)
- "I-Quantum Mechanics" (May 19, 1995)
- "Ukudala" (May 23, 1995). Ukuhumusha:
- "Ochwepheshe" (May 25, 1995)
- "Idatha Engathembekile" (May 26, 1995)
- "Ubunjiniyela Bezinhlelo" (May 30, 1995)
- "Uthola Lokho Okulinganisayo" (June 1, 1995)
- (Juni 2, 1995) Humusha ngezingxenye zemizuzu eyi-10
- Hamming, “Wena Nocwaningo Lwakho” (June 6, 1995).
Ubani ofuna ukusiza ngokuhumusha, isakhiwo nokushicilelwa kwencwadi - bhala umlayezo womuntu siqu noma i-imeyili [i-imeyili ivikelwe]
Source: www.habr.com