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Enkosi ku-Andrey Pakhomov ngenguqulelo.
Ithiyori yoLwazi yaphuhliswa nguC. E. Shannon ekupheleni koo-1940. Abaphathi beBell Labs banyanzelise ukuba ayibize "Ithiyori yoNxibelelwano" kuba... eli ligama elichaneke ngakumbi. Ngenxa yezizathu ezicacileyo, igama elithi "Information Theory" linempembelelo enkulu kuluntu, yiyo loo nto uShannon wakhetha, kwaye ligama esilaziyo ukuza kuthi ga namhlanje. Igama ngokwalo licebisa ukuba ithiyori ijongene nolwazi, nto leyo eyenza ukuba ibaluleke njengoko singena nzulu kwixesha lolwazi. Kwesi sahluko, ndiza kuchukumiseka kwizigqibo eziphambili eziphuma kule thiyori, andizukubonelela ngokungqongqo, kodwa kunobungqina obuvakalayo bamalungiselelo athile ale thiyori, ukuze uqonde ukuba yintoni kanye kanye “iTheory yoLwazi”, apho ungayisebenzisa khona. nalapho kungekho .
Okokuqala, yintoni “inkcazelo”? UShannon uthelekisa ulwazi kunye nokungaqiniseki. Ukhethe i-logarithm engalunganga yokwenzeka kwesehlo njengomlinganiselo wobungakanani bolwazi olufumanayo xa isiganeko esinokwenzeka ngo-p. Umzekelo, ukuba ndikuxelela ukuba imozulu yaseLos Angeles inenkungu, emva koko u-p usondele ku-1, ongasiniki ulwazi oluninzi. Kodwa ukuba ndithi imvula eMonterey ngoJuni, kuya kubakho ukungaqiniseki kumyalezo kwaye iya kuba nolwazi olungakumbi. Isiganeko esithembekileyo asinalo naluphi na ulwazi, ekubeni ilogi 1 = 0.
Makhe sijonge oku ngokweenkcukacha ngakumbi. UShannon wayekholelwa ukuba umlinganiselo wobungakanani bolwazi kufuneka ube ngumsebenzi oqhubekayo wokunokwenzeka kwesiganeko p, kwaye kwiziganeko ezizimeleyo kufuneka zibe ngezelelo - ubungakanani bolwazi olufunyenweyo ngenxa yokwenzeka kweziganeko ezibini ezizimeleyo kufuneka zilingane isixa solwazi olufunyenweyo ngenxa yokwenzeka kwesiganeko esidibeneyo. Ngokomzekelo, umphumo we-dice roll kunye ne-coin roll idla ngokuphathwa njengeziganeko ezizimeleyo. Oku kungasentla masikuguqulele kulwimi lwemathematika. Ukuba mna (p) sisixa solwazi oluqulethwe kwisiganeko esinamathuba okuthi p, ngoko kwisiganeko esidibeneyo esiquka iziganeko ezibini ezizimeleyo x kunye nokunokwenzeka p1 kunye no-y kunye nokunokwenzeka p2 siyakufumana.
(x kunye no-y ziziganeko ezizimeleyo)
Le yinkqubo yeCauchy equation, yinyani kuzo zonke i p1 kunye ne p2. Ukusombulula le equation esebenzayo, cinga ukuba
p1 = p2 = p,
oku kunika
Ukuba p1 = p2 kunye no-p2 = p ngoko
njl. Ukwandisa le nkqubo kusetyenziswa indlela eqhelekileyo yee-exponentials, kuwo onke amanani a-rational m/n oku kulandelayo kuyinyaniso
Ukususela ekucingeni ukuqhubeka komlinganiselo wolwazi, kulandela ukuba umsebenzi we-logarithmic kuphela kwesisombululo esiqhubekayo kwi-equation Cauchy equation.
Kwithiyori yolwazi, kuqhelekile ukuthatha isiseko se-logarithm sibe ngu-2, ngoko ke ukhetho lokubini luqulethe kanye i-1 bit yolwazi. Ngoko ke, ulwazi lulinganiswa ngefomula
Makhe sinqumame siqonde ukuba kwenzeke ntoni ngasentla. Okokuqala, asiyichazanga ingcamango “yolwazi”; sichaze nje ifomula yomlinganiselo wayo wobungakanani.
Okwesibini, lo mlinganiselo uphantsi kokungaqiniseki, yaye nangona ufanelekile ngokusengqiqweni koomatshini—ngokomzekelo, iinkqubo zemfonomfono, unomathotholo, umabonwakude, iikhompyutha, njl.njl—awubonisi isimo sengqondo esiqhelekileyo sabantu ngokuphathelele inkcazelo.
Okwesithathu, lo ngumlinganiselo ohambelanayo, kuxhomekeke kwimeko yangoku yolwazi lwakho. Ukuba ujonga umlambo "amanani angaqhelekanga" ukusuka kwi-generator inombolo engahleliwe, ucinga ukuba inani ngalinye elilandelayo aliqinisekanga, kodwa ukuba uyayazi indlela yokubala "amanani angaqhelekanga", inombolo elandelayo iya kwaziwa, kwaye ngoko ayiyi kukwazi. ziqulathe ulwazi.
Ke ingcaciso kaShannon yolwazi ifanelekile koomatshini kwiimeko ezininzi, kodwa ayibonakali ihambelana nokuqonda komntu igama. Kungenxa yesi sizathu ukuba “iThiyori yoLwazi” ibifanele ukuba ibizwe ngokuba “yiThiyori yoNxibelelwano.” Nangona kunjalo, kusemva kwexesha kakhulu ukutshintsha iinkcazo (ezanika ithiyori ukuthandwa kwayo okokuqala, kwaye isasenza abantu bacinge ukuba le thiyori ijongana "nolwazi"), ke kufuneka siphile nabo, kodwa kwangaxeshanye kufuneka ukuqonda ngokucacileyo ukuba ikude kangakanani inkcazelo kaShannon yolwazi kwintsingiselo yayo eqhelekileyo. Ulwazi lukaShannon lujongene nento eyahlukileyo ngokupheleleyo, eyile, ukungaqiniseki.
Nantsi into omawucinge ngayo xa uphakamisa nasiphi na isigama. Ngaba inkcazo ecetywayo, efana nengcaciso kaShannon yolwazi, iyavumelana nombono wakho wokuqala kwaye yahluke njani? Phantse akukho gama libonisa ngqo umbono wakho wangaphambili wengqikelelo, kodwa ekugqibeleni, sisigama esisetyenzisiweyo esibonisa intsingiselo yeli gama, ngoko ke ukwenza into ngokusesikweni ngeenkcazo ezicacileyo kuhlala kusazisa ingxolo ethile.
Qwalasela inkqubo enealfabhethi equlathe iisimboli q kunye nezinto ezinokwenzeka pi. Kule meko umndilili wolwazi kwinkqubo (ixabiso layo elilindelekileyo) lilingana no:
Oku kubizwa ngokuba yi-entropy yenkqubo enonikezelo olunokwenzeka {pi}. Sisebenzisa igama elithi "entropy" kuba uhlobo olufanayo lwezibalo luvela kwi-thermodynamics kunye ne-statistical mechanics. Yiyo loo nto igama elithi "entropy" lidala i-aura ethile yokubaluleka kufutshane nalo, nto leyo engathethelelekiyo ekugqibeleni. Kwale ndlela inye yemathematika yokubhala ayithethi kwatoliko leesimboli ezifanayo!
I-entropy ye-probability distribution idlala indima enkulu kwi-coding theory. Ukungalingani kweGibbs kunikezelo olunokwenzeka oluhlukeneyo lwe-pi kunye ne-qi yenye yeziphumo ezibalulekileyo zale thiyori. Ngoko kufuneka siyingqine loo nto
Ubungqina busekelwe kwigrafu ecacileyo, Umzobo. 13.I, ebonisa ukuba
kwaye ukulingana kuphunyezwa kuphela xa x = 1. Masisebenzise ukungalingani kwikota nganye yesamba ukusuka kwicala lasekhohlo:
Ukuba ialfabhethi yenkqubo yonxibelelwano iqulathe iisimboli zika-q, ngoko ke ukuthatha ithuba losasazo lwesimboli nganye qi = 1/q kunye nokubeka endaweni q, sifumana kwiGibbs ukungalingani.
Umfanekiso 13.I
Oku kuthetha ukuba ukuba amathuba okuhambisa zonke iisimboli ze-q ziyafana kwaye zilingana no-1 / q, ngoko ubuninzi be-entropy bulingana no-ln q, ngaphandle koko ukungalingani kubambe.
Kwimeko yekhowudi ekhethekileyo ekwazi ukuqhawuka, sinokungalingani kwe-Kraft
Ngoku ukuba sichaza i-pseudo-enokwenzeka
apho kunjalo = 1, elandela ukungalingani kweGibbs,
kwaye usebenzise i-algebra encinci (khumbula ukuba i-K ≤ 1, ngoko sinokulahla igama le-logarithmic, kwaye mhlawumbi someleze ukungalingani kamva), sifumana
apho L ubude bekhowudi ephakathi.
Ngoko ke, i-entropy yeyona nto incinci ibotshelelwayo kuyo nayiphi na ikhowudi yophawu-nge-symbol ene-avareji yekhowudi yobude L. Le yithiyori kaShannon yesitishi esingenasiphazamiso.
Ngoku qwalasela i-theorem ephambili malunga nokulinganiselwa kweenkqubo zonxibelelwano apho ulwazi luhanjiswa njengomlambo weebhithi ezizimeleyo kunye nengxolo ekhoyo. Kuyaqondwa ukuba amathuba okuhanjiswa okuchanekileyo kwe-bit enye yi-P> 1/2, kwaye amathuba okuba ixabiso elincinci liya kuguqulwa ngexesha lokudluliselwa (impazamo iya kwenzeka) ilingana no-Q = 1 - P. Ukuze kube lula, thina cinga ukuba iimpazamo zizimele kwaye amathuba empazamo ayafana kwinto nganye ethunyelweyo - oko kukuthi, kukho "ingxolo emhlophe" kumjelo wonxibelelwano.
Indlela esinomjelo omde wamasuntswana afakwe kwikhowudi kumyalezo omnye lulwandiso lwe-n-dimensional yekhowudi yebit enye. Siza kugqiba ixabiso le-n kamva. Qwalasela umyalezo oquka i-n-bits njengenqaku kwisithuba esingu-n-dimensional. Kuba sinesithuba esine-n-dimensional - kwaye ukwenza lula siyakuthatha ukuba umyalezo ngamnye unethuba elifanayo lokwenzeka - kukho imiyalezo enokwenzeka engu-M (M iyakuchazwa kamva), ngoko ke amathuba okuba nawuphi na umyalezo othunyelweyo
(umthumeli)
IShedyuli 13.II
Okulandelayo, qwalasela umbono womthamo wetshaneli. Ngaphandle kokungena kwiinkcukacha, umthamo wejelo uchazwa njengobuninzi bolwazi olunokudluliselwa ngokuthembekileyo kumjelo wonxibelelwano, kuthathelwa ingqalelo ukusetyenziswa kweyona khowudi isebenzayo. Akukho ngxoxo yokuba ulwazi oluninzi lunokuhanjiswa ngejelo lonxibelelwano kunomthamo walo. Oku kunokungqinwa kwitshaneli ye-symmetric yokubini (esiyisebenzisa kwimeko yethu). Umthamo wetshaneli, xa uthumela amasuntswana, uchazwe njenge
apho, njengangaphambili, i-P inokuba kungabikho mpazamo kuyo nayiphi na intwana ethunyelweyo. Xa uthumela n amasuntswana azimeleyo, umthamo wejelo unikwa ngu
Ukuba sisondele kumthamo wejelo, ngoko ke kufuneka sithumele phantse lo mthamo wolwazi kwisimboli nganye ai, i = 1, ..., M. Ukuqwalasela ukuba amathuba okuba ukwenzeka kwesimboli ngasinye ai yi-1 / M, sifumana
xa sithumela nawuphi na ka M ngokulinganayo imiyalezo enokwenzeka ai, siye
Xa i-n bits ithunyelwa, silindele ukuba iimpazamo ze-nQ zenzeke. Ngokwesiqhelo, kumyalezo oquka i-n-bits, siya kuba neempazamo ezimalunga ne-nQ kumyalezo ofunyenweyo. Kwi-n enkulu, iyantlukwano ezalanayo (utshintsho = ububanzi bokusabalalisa, )
unikezelo lwenani leempazamo liya kuba lincinci kakhulu njengoko i-n inyuka.
Ke, kwicala lomthumeli, ndithatha umyalezo ai ukuwuthumela kwaye ndizobe ingqukuva ejikeleze iradius.
enkulu kancinane ngexabiso elilingana ne-e2 kunenani elilindelekileyo leempazamo Q, (Umfanekiso 13.II). Ukuba u-n mkhulu ngokwaneleyo, ngoko kukho ithuba elincinci lokuzikhethela lenqaku lomyalezo bj elivela kwicala lomamkeli elidlulela ngaphaya kwale ngqukuva. Makhe sizobe imeko njengoko ndiyibona ukusuka kwindawo yokujonga umthumeli: sinayo nayiphi na i-radii evela kumyalezo ogqithisiweyo ai ukuya kumyalezo ofunyenweyo bj kunye namathuba empazamo alinganayo (okanye aphantse alingane) ukuya kunikezelo oluqhelekileyo, ukufikelela kwiqondo eliphezulu. kwi nQ. Kuyo nayiphi na i-e2 enikiweyo, kukho i-n enkulu kangangokuba amathuba okuba inqaku lesiphumo bj libe ngaphandle kwendawo yam lincinci ngendlela othanda ngayo.
Ngoku makhe sijonge imeko efanayo ukusuka kwicala lakho (Fig. 13.III). Kwicala lomamkeli kukho ingqukuva S(r) yeradiyasi efanayo r engqonge indawo efunyenweyo bj kwisithuba se-n-dimensional, ukuze ukuba umyalezo ofunyenweyo bj ungaphakathi kwendawo yam, ngoko umyalezo ai othunyelwe ndim ungaphakathi kwakho. ingqukuva.
Inokwenzeka njani impazamo? Impazamo inokwenzeka kwiimeko ezichazwe kwitheyibhile engezantsi:
Umfanekiso 13.III
Apha sibona ukuba kwi-sphere eyakhiwe malunga nenqaku elifunyenweyo kukho ubuncinane enye inqaku elihambelana nomyalezo othunyelweyo ongathunyelwanga, emva koko kwenzeke impazamo ngexesha logqithiso, kuba awukwazi ukugqiba ukuba yeyiphi le miyalezo ethunyelwe. Umyalezo othunyelweyo awunampazamo kuphela ukuba inqaku elihambelana nalo likwi-sphere, kwaye akukho manqaku athile anokwenzeka kwikhowudi enikiweyo ekwindawo efanayo.
Sinenxaki yezibalo malunga nokuba nokwenzeka kwemposiso Pe ukuba umyalezo ai uthunyelwe
Singaphosa into yokuqala kwikota yesibini, siyithathe njenge-1. Ngaloo ndlela sifumana ukungalingani
Ngokucacileyo,
kungoko
faka isicelo kwakhona kwikota yokugqibela ekunene
Ukuthatha i-n enkulu ngokwaneleyo, ikota yokuqala inokuthatyathwa njengencinci njengoko ufunwa, yithi ngaphantsi kwenani elithile d. Ngoko ke sinalo
Ngoku makhe sijonge indlela esingayenza ngayo ikhowudi yokutshintsha elula ukubethelela imiyalezo engu-M equka amasuntswana e-n. Engenalo nofifi lwendlela yokwakhiwa kwekhowudi (iikhowudi zokulungisa impazamo zazingekayilwa), uShannon wakhetha ukukhowudwa okungacwangciswanga. Flip ingqekembe kwibhithi nganye ye-n kumyalezo kwaye uphinda inkqubo yemiyalezo kaM. Lilonke, ii-nM coin flips kufuneka zenziwe, ngoko kunokwenzeka
ikhowudi yesichazi-magama esinethuba elifanayo ½nM. Ngokuqinisekileyo, inkqubo engahleliweyo yokudala i-codebook ithetha ukuba kukho ukuphindaphinda okuphindaphindiweyo, kunye namanqaku ekhowudi aya kusondela omnye komnye kwaye ngoko ke abe ngumthombo weempazamo ezinokwenzeka. Umntu kufuneka angqine ukuba oku akwenzeki ngokunokwenzeka okukhulu kunalo naliphi na inqanaba lemposiso encinci ekhethiweyo, ngoko ke u-n onikiweyo mkhulu ngokwaneleyo.
Inqaku elibalulekileyo kukuba uShannon wenze i-avareji kuzo zonke iikhowudi iincwadi ezinokubakho ukufumana impazamo ephakathi! Siza kusebenzisa isimboli Av[.] ukubonisa umndilili wexabiso phezu kweseti yazo zonke iicodebooks ezingakhethiyo ezinokwenzeka. I-avareji ngaphezu kwe-d eqhubekayo, ngokuqinisekileyo, inika into ezinzileyo, kuba i-avareji yekota nganye ifana nayo yonke enye ikota kwisibalo,
enokwandiswa (M–1 iya ku-M)
Kuwo nawuphi na umyalezo onikiweyo, xa kusenziwa i-avareji kuzo zonke ii-codebooks, i-encoding ibaleka kuwo onke amaxabiso anokwenzeka, ngoko ke umndilili wokwenzeka ukuba inqaku likwi-sphere ngumlinganiselo womthamo we-sphere ukuya kumthamo opheleleyo wendawo. Umthamo wesphere ngu
apho u-s=Q+e2 <1/2 kunye no-ns kufuneka abe yinani elipheleleyo.
Ikota yokugqibela ekunene lelona likhulu kwesi sixa. Okokuqala, masiqikelele ixabiso layo sisebenzisa ifomula ye-Stirling yeefektri. Emva koko siya kujonga i-coefficient ehlayo yegama eliphambi kwayo, qaphela ukuba lo mlinganiso uyanyuka njengoko sisiya ngasekhohlo, kwaye ngoko sinokuthi: (1) sithintele ixabiso lesamba kwisambuku sokuqhubela phambili kwejometri nge. lo mlinganiso wokuqala, (2) ukwandisa ukuqhubela phambili kwejometri ukusuka kwimiqathango ye-ns ukuya kwinani elingenasiphelo lamagama, (3) bala isixa senkqubela yejometri engapheliyo (i-algebra eqhelekileyo, akukho nto ibalulekileyo) kwaye ekugqibeleni ufumane ixabiso elisikelwe umda (ubukhulu ngokwaneleyo n):
Qaphela indlela i-entropy H(s) evele ngayo kwisazisi se-binomial. Qaphela ukuba iTaylor series expansion H(s)=H(Q+e2) inika uqikelelo olufunyenweyo kuthathelwa ingqalelo kuphela iderivative yokuqala kunye nokungahoyi zonke ezinye. Ngoku makhe sidibanise intetho yokugqibela:
apho
Ekuphela kwento ekufuneka siyenzile kukukhetha u-e2 ukuba u-e3 <e1, kwaye ke ixesha lokugqibela liya kuba lincinci ngokungenasizathu, ukuba nje u-n mkhulu ngokwaneleyo. Ngenxa yoko, i-avareji yempazamo ye-PE inokufunyanwa incinci njengoko ifunwa kunye nomthamo wetshaneli ngokungenasizathu kufutshane ne-C.
Ukuba i-avareji yazo zonke iikhowudi zinempazamo encinci ngokwaneleyo, ngoko ke ubuncinane ikhowudi enye kufuneka ifaneleke, ngoko ke kukho ubuncinane enye inkqubo yekhowudi efanelekileyo. Esi sisiphumo esibalulekileyo esifunyenwe nguShannon - "ithiyori kaShannon yetshaneli enengxolo", nangona kufanele kuqatshelwe ukuba wangqina oku kwimeko eqhelekileyo ngakumbi kunejenali ye-symmetric elula yokubini endiyisebenzisileyo. Kwimeko eqhelekileyo, izibalo zemathematika zinzima kakhulu, kodwa iingcamango azifani, ngoko kaninzi, usebenzisa umzekelo wemeko ethile, unokutyhila intsingiselo yokwenene yethiyori.
Masigxeke umphumo. Siye saphinda ngokuphindaphindiweyo: "Kubukhulu ngokwaneleyo n." Kodwa ungakanani u-n? Kakhulu, inkulu kakhulu ukuba ufuna ngokwenene ukuba nobabini kufutshane nomthamo wetshaneli kwaye uqiniseke ngokugqithiselwa kwedatha okuchanekileyo! Inkulu kakhulu, eneneni, kuya kufuneka ulinde ixesha elide kakhulu ukuqokelela umyalezo wamasuntswana awaneleyo ukuze uyifake ikhowudi kamva. Kule meko, ubungakanani bekhowudi yesichazi-magama esingenamkhethe buya kuba bukhulu kakhulu (emva kwayo yonke loo nto, isichazi-magama esinjalo asinakumelwa ngendlela emfutshane kunoluhlu olupheleleyo lwazo zonke iibits zika-M, nangona u-n kunye no-M zikhulu kakhulu)!
Iikhowudi zokulungisa iimpazamo zinqanda ukulinda umyalezo omde kakhulu kwaye emva koko zikhowudwe kwaye ziwuguqulele kwiikhowudi ezinkulu kakhulu zekhowudi kuba ziphepha ngokwazo iincwadi zekhowudi kwaye endaweni yoko zisebenzisa ikhompyutha eqhelekileyo. Kwithiyori elula, iikhowudi ezinjalo zivame ukulahlekelwa ukukwazi ukusondela kumthamo wetshaneli kwaye zigcine izinga eliphantsi lephutha, kodwa xa ikhowudi ilungisa inani elikhulu leempazamo, zenza kakuhle. Ngamanye amazwi, ukuba unikezela umthamo wetshaneli ekulungiseni iimpazamo, ngoko kufuneka usebenzise amandla okulungisa impazamo amaxesha amaninzi, oko kukuthi, inani elikhulu leempazamo kufuneka lilungiswe kumyalezo ngamnye othunyelweyo, kungenjalo uchitha lo mthamo.
Kwangaxeshanye, ithiyori engqinwe ngasentla ayikabi nantsingiselo! Ibonisa ukuba iisistim zothumelo ezisebenzayo kufuneka zisebenzise izikimu zokukhowuda ezikrelekrele kwiintambo zebit ezinde kakhulu. Umzekelo ziisathelayithi eziye zabhabha ngaphaya kweeplanethi zangaphandle; Njengoko behamba kude noMhlaba kunye neLanga, baphoqeleka ukuba balungise iimpazamo ezininzi ngakumbi kwibhloko yedatha: ezinye iisathelayithi zisebenzisa iipaneli zelanga, ezibonelela malunga ne-5 W, ezinye zisebenzisa imithombo yamandla enyukliya, enika malunga namandla afanayo. Amandla aphantsi obonelelo lwamandla, ubungakanani obuncinci bezitya zokuhambisa kunye nobungakanani obulinganiselweyo besitya esamkelayo eMhlabeni, umgama omkhulu ekufuneka uwuhambile umqondiso - konke oku kufuna ukusetyenziswa kweekhowudi ezinomgangatho ophezulu wokulungiswa kwempazamo inkqubo yonxibelelwano esebenzayo.
Masibuyele kwisithuba esingu-n-dimensional esisisebenzisileyo kubungqina obungasentla. Ekuxoxeni ngayo, sibonise ukuba phantse yonke ivolumu yesphere igxininiswe kufuphi nomphezulu ongaphandle - ngoko ke, kuphantse kube yinto eqinisekileyo ukuba isibonakaliso esithunyelweyo siya kuba kufuphi nomphezulu we-sphere eyakhiwe malunga nomqondiso ofunyenweyo, nangona Iradiyasi encinci yesphere enjalo. Ngoko ke, akumangalisi ukuba isignali efunyenweyo, emva kokulungiswa kwenani elikhulu leempazamo, i-nQ, ijika ibe kufuphi nomqondiso ngaphandle kweempazamo. Umthamo wekhonkco esixubushe ngawo ngaphambili uyisitshixo sokuqonda le nto. Qaphela ukuba imimandla efanayo eyenzelwe ukulungisa impazamo iikhowudi zeHaming azithungelani enye kwenye. Inani elikhulu lemilinganiselo ye-orthogonal ephantse ilingane kwisithuba esingu-n-dimensional ibonisa ukuba kutheni sinokulingana ii-M spheres ngokudibana okuncinci. Ukuba sivumela ukugqithelana okuncinci, okuncinci, okunokuthi kukhokelela kwinani elincinci leempazamo ngexesha lokudibanisa, sinokufumana ukubekwa okuxineneyo kweengqukuva kwisithuba. I-Haming iqinisekise umgangatho othile wokulungiswa kwempazamo, u-Shannon - amathuba aphantsi empazamo, kodwa kwangaxeshanye ukugcina eyona mveliso ikhoyo ngokungekho mthethweni kufutshane nomthamo wejelo lonxibelelwano, apho iikhowudi zeHaming azinakwenza.
Ithiyori yolwazi ayisixeleli ukuba siyila njani inkqubo esebenzayo, kodwa isalatha indlela eya kwiinkqubo ezisebenzayo zonxibelelwano. Sisixhobo esixabisekileyo sokwakha iinkqubo zonxibelelwano ngomatshini ukuya kumatshini, kodwa, njengoko kuphawulwe ngaphambilana, akunamsebenzi kangako kwindlela abantu abanxibelelana ngayo. Ubungakanani belifa lebhayoloji elifana neenkqubo zonxibelelwano zobugcisa akwaziwa, ngoko ke akukacaci okwangoku ukuba ithiyori yolwazi isebenza njani kwimizila yemfuza. Asinakho ukukhetha ngaphandle kokuzama, kwaye ukuba impumelelo isibonisa ubume obufana nomatshini wale nto, ukusilela kuya kukhomba eminye imiba ebalulekileyo yolwazi.
Masingaphambuki kakhulu. Siye sabona ukuba zonke iinkcazo zangaphambili, kumlinganiselo omkhulu okanye omncinci, kufuneka zibonise ingundoqo yeenkolelo zethu zangaphambili, kodwa zibonakaliswe kwinqanaba elithile lokugqwesa kwaye ngoko azisebenzi. Kuyavunywa ngokwesiko ukuba, ekugqibeleni, inkcazo esiyisebenzisayo ichaza undoqo; kodwa, oku kusixelela kuphela indlela yokwenza izinto kwaye nangayiphi na indlela ayidlulisi nayiphi na intsingiselo kuthi. Indlela ye-postulational, ethandwa kakhulu kwizangqa zemathematika, ishiya okuninzi okufunekayo ekusebenzeni.
Ngoku siza kujonga umzekelo weemvavanyo ze-IQ apho inkcazo injengesetyhula njengoko uthanda kwaye, ngenxa yoko, iyalahlekisa. Kwenziwa uvavanyo olufanele ukulinganisa ubukrelekrele. Emva koko ihlaziywa ukuze ihambelane ngokusemandleni, kwaye emva koko ipapashwe kwaye, ngendlela elula, ilinganiswe ukuze "ubulumko" obulinganisiweyo buvele buhanjiswe ngokuqhelekileyo (kwi-curve calibration, kunjalo). Zonke iinkcazo kufuneka ziqwalaselwe kwakhona, kungekuphela nje xa zicetywa okokuqala, kodwa kamva kakhulu, xa zisetyenziswa kwizigqibo ezithatyathiweyo. Ingaba imida echazayo ifanelekile kangakanani kwingxaki esonjululwayo? Kukangaphi iinkcazelo ezinikelwe kwisimo esinye zisetyenziswa kwiimeko ezahlukeneyo? Oku kwenzeka rhoqo! Kubuntu, oya kudibana nabo ebomini bakho, oku kwenzeka rhoqo.
Ngaloo ndlela, enye yeenjongo zale nkcazo-bungcali yolwazi, ukongezelela ekuboniseni ukuba luncedo kwayo, yayikukulumkisa ngale ngozi, okanye ukukubonisa ngokuthe ngqo indlela yokuyisebenzisa ukuze ufumane isiphumo esifunekayo. Sekukudala kuqatshelwe ukuba iinkcazo zokuqala zigqiba ukuba yintoni oyifumanayo ekugqibeleni, ukuya kwinqanaba elikhulu kunokuba kubonakala ngathi. Iinkcazo zokuqala zifuna ingqwalasela eninzi kuwe, kungekhona nje kuyo nayiphi na imeko entsha, kodwa nakwiindawo oye wasebenza nazo ixesha elide. Oku kuya kukuvumela ukuba uqonde ukuba iziphumo ezifunyenweyo ziyi-tautology kwaye hayi into eluncedo.
Ibali elidumileyo lika-Eddington lisixelela ngabantu ababeloba elwandle ngomnatha. Emva kokuba befunde ubungakanani beentlanzi abazibambisileyo, bafumanisa eyona ntlanzi incinane ifumaneka elwandle! Isigqibo sabo sasiqhutywa sisixhobo esisetyenzisiweyo, kungekhona ngokwenyani.
Iza kuqhubeka…
Ngubani ofuna ukunceda ngoguqulelo, uyilo kunye nokupapashwa kwencwadi - bhala kumyalezo wobuqu okanye i-imeyile [imeyile ikhuselwe]
Ngendlela, siye saqalisa ukuguqulelwa kwenye incwadi epholileyo - )
Sikhangele ngokukodwa abo baya kunceda ukuguqulela . (ukudluliselwa kwemizuzu ye-10, i-20 yokuqala sele ithathwe)
Iziqulatho zencwadi kunye nezahluko eziguqulelweyo
- Intshayelelo kuBugcisa bokwenza iNzululwazi nobuNjineli: Ukufunda ukuFunda (ngoMatshi 28, 1995)
- "Iziseko zeDigital (Discrete) Revolution" (ngoMatshi 30, 1995)
- "Imbali yeeKhompyutha - i-Hardware" (ngoMatshi 31, 1995)
- "Imbali yeeKhompyutha-Isoftware" (NgoAprili 4, 1995)
- "Imbali yeeKhompyutha-Izicelo" (NgoAprili 6, 1995)
- "I-Artificial Intelligence-Icandelo I" (Aprili 7, 1995)
- "I-Artificial Intelligence-Icandelo II" (Aprili 11, 1995)
- "I-Artificial Intelligence III" (ngoAprili 13, 1995)
- "n-Dimensional Space" (ngoAprili 14, 1995)
- "Ithiyori yeKhowudi - Ukumelwa koLwazi, iCandelo I" (Aprili 18, 1995)
- "Ithiyori yeKhowudi - Ukumelwa koLwazi, iCandelo II" (ngoAprili 20, 1995)
- "Iikhowudi zokulungisa impazamo" (ngomhla wama-21 kuEpreli 1995)
- "Ithiyori yoLwazi" (ngoAprili 25, 1995)
- "Izihluzi zeDigital, iCandelo I" (Aprili 27, 1995)
- "Izihluzi zeDijithali, iCandelo II" (ngoAprili 28, 1995)
- "Izihluzi zeDigital, iCandelo III" (Meyi 2, 1995)
- "Izihluzi zeDigital, iCandelo IV" (ngoMeyi 4, 1995)
- "Ukulinganisa, Icandelo I" (ngoMeyi 5, 1995)
- "Ukulinganisa, Icandelo II" (ngoMeyi 9, 1995)
- "Ukulinganisa, Icandelo III" (ngoMeyi 11, 1995)
- "I-Fiber Optics" (ngoMeyi 12, 1995)
- "Umyalelo woNcedo lweKhompyutha" (ngoMeyi 16, 1995)
- "IMathematika" (ngoMeyi 18, 1995)
- "I-Quantum Mechanics" (ngoMeyi 19, 1995)
- "Ukudala" (ngoMeyi 23, 1995). Inguqulelo:
- "Iingcali" (ngoMeyi 25, 1995)
- "Idatha engathembekanga" (ngoMeyi 26, 1995)
- "Ubunjineli beeNkqubo" (ngoMeyi 30, 1995)
- "Ufumana Oko Ukulinganisayo" (Juni 1, 1995)
- (Juni 2, 1995) guqulela kwimizuzu eli-10
- Hamming, “Wena Nophando Lwakho” (Juni 6, 1995).
Ngubani ofuna ukunceda ngoguqulelo, uyilo kunye nokupapashwa kwencwadi - bhala kumyalezo wobuqu okanye i-imeyile [imeyile ikhuselwe]
umthombo: www.habr.com