Mun yi shi!
"Manufar wannan kwas shine don shirya ku don fasaha na gaba."
Hello Habr. Ka tuna labarin mai ban mamaki (+219, 2588 alamun shafi, 429k karanta)?
Don haka Hamming (e, eh, kula da kai da gyara kai ) akwai duka , wanda aka rubuta bisa laccocinsa. Mun fassara shi, saboda mutumin yana magana da ra'ayinsa.
Wannan littafi ne ba game da IT kawai ba, littafi ne game da salon tunani na mutane masu sanyin gaske. “Ba kawai haɓakar kyakkyawan tunani ba ne; yana bayyana yanayin da ke ƙara damar yin babban aiki."
Godiya ga Andrey Pakhomov don fassarar.
Ka'idar Bayani ta C.E. Shannon ta haɓaka a ƙarshen 1940s. Kamfanin Bell Labs ya nace cewa ya kira ta "Ka'idar Sadarwa" saboda ... wannan shine mafi ingancin suna. Don dalilai masu ma'ana, sunan "Theory of Information" yana da tasiri sosai ga jama'a, shi ya sa Shannon ya zaɓe shi, kuma shine sunan da muka sani har yau. Sunan da kansa yana nuna cewa ka'idar tana hulɗar da bayanai, wanda ya sa ya zama mahimmanci yayin da muke zurfafa zurfafa cikin shekarun bayanai. A cikin wannan babi, zan tabo wasu mahimman bayanai daga wannan ka'idar, ba zan ba da ƙarfi ba, amma ingantacciyar shaida na wasu tanadi na wannan ka'idar, don ku fahimci menene ainihin "Ka'idar Bayani", inda zaku iya amfani da shi. kuma inda ba.
Da farko, menene "bayani"? Shannon yana daidaita bayanai da rashin tabbas. Ya zaɓi mummunan logarithm na yuwuwar aukuwa a matsayin ma'auni na bayanin da kuke karɓa lokacin da wani lamari mai yuwuwar p ya faru. Misali, idan na gaya muku cewa yanayin Los Angeles yana da hazo, to p yana kusa da 1, wanda a zahiri ba ya ba mu bayanai da yawa. Amma idan na ce an yi ruwan sama a Monterey a watan Yuni, za a sami rashin tabbas a cikin sakon kuma zai ƙunshi ƙarin bayani. Amintaccen taron bai ƙunshi kowane bayani ba, tun log 1 = 0.
Bari mu dubi wannan dalla-dalla. Shannon ya yi imanin cewa ma'aunin bayanai ya kamata ya zama ci gaba da aiki na yuwuwar aukuwa p, kuma ga abubuwan da suka faru masu zaman kansu yakamata su kasance ƙari - adadin bayanan da aka samu sakamakon faruwar abubuwan da suka faru masu zaman kansu guda biyu yakamata su kasance daidai da adadin bayanan da aka samu sakamakon faruwar taron hadin gwiwa. Misali, sakamakon nadi na dice da nadi tsabar kuɗi yawanci ana ɗaukarsu azaman abubuwan da suka faru masu zaman kansu. Bari mu fassara abin da ke sama zuwa harshen ilimin lissafi. Idan I (p) shine adadin bayanan da ke ƙunshe a cikin wani lamari tare da yiwuwar p, to don taron haɗin gwiwa wanda ya ƙunshi abubuwa biyu masu zaman kansu x tare da yuwuwar p1 da y tare da yiwuwar p2 za mu samu.
(x da y abubuwa ne masu zaman kansu)
Wannan shine ma'aunin Cauchy mai aiki, gaskiya ga duk p1 da p2. Don warware wannan ma'auni na aiki, ɗauka cewa
p1 = p2 = p,
wannan yana bayarwa
Idan p1 = p2 da p2 = p to
da dai sauransu. Ƙaddamar da wannan tsari ta amfani da daidaitaccen hanya don ƙayyadaddun bayanai, ga duk lambobi masu ma'ana m/n mai zuwa gaskiya ne
Daga ci gaban da aka ɗauka na ma'aunin bayanin, yana biye da cewa aikin logarithmic shine kawai ci gaba da mafita ga ma'aunin Cauchy mai aiki.
A cikin ka'idar bayanai, abu ne na kowa don ɗaukar tushen logarithm ya zama 2, don haka zaɓin binary ya ƙunshi daidai 1 bit na bayanai. Saboda haka, ana auna bayanai ta hanyar dabara
Bari mu dakata mu fahimci abin da ya faru a sama. Da farko dai, ba mu ayyana manufar “bayanai” ba, mun fayyace ma’aunin ma’auni ne kawai.
Na biyu, wannan ma'auni yana cikin rashin tabbas, kuma ko da yake ya dace da na'urori - alal misali, tsarin tarho, rediyo, talabijin, kwamfuta, da dai sauransu - ba ya nuna halayen ɗan adam na yau da kullum game da bayanai.
Na uku, wannan ma'auni ne na dangi, ya danganta da yanayin ilimin ku na yanzu. Idan ka kalli rafi na “lambobin bazuwar” daga janareta na lambar bazuwar, za ka ɗauka cewa kowace lamba ta gaba ba ta da tabbas, amma idan ka san dabarar ƙididdige “lambobin bazuwar”, za a san lamba ta gaba, don haka ba za a sani ba. dauke da bayanai.
Don haka ma'anar bayanin Shannon ya dace da na'urori a lokuta da yawa, amma da alama bai dace da fahimtar ɗan adam na kalmar ba. Don haka ne ya kamata a kira "Ka'idar Bayani" "Ka'idar Sadarwa." Duk da haka, ya yi latti don canza ma'anar (wanda ya ba da ka'idar shahararsa ta farko, kuma wanda har yanzu yana sa mutane suyi tunanin cewa wannan ka'idar ta shafi "bayani"), don haka dole ne mu zauna tare da su, amma a lokaci guda dole ne ku kasance tare da su. fahimci a sarari yadda nisa ma'anar bayanin Shannon daga ma'anar da aka saba amfani da ita. Bayanin Shannon ya shafi wani abu daban-daban, wato rashin tabbas.
Ga wani abu da za ku yi tunani a kai lokacin da kuke ba da shawarar kowace kalma. Ta yaya ma'anar da aka gabatar, kamar ma'anar bayanin Shannon, ta yarda da ainihin ra'ayinku kuma yaya ya bambanta? Kusan babu wani lokaci da ke nuna ainihin hangen nesa na ra'ayi na baya, amma a ƙarshe, kalmomin da aka yi amfani da su ne ke nuna ma'anar ra'ayi, don haka tsara wani abu ta hanyar ma'anar ma'ana koyaushe yana gabatar da wasu amo.
Yi la'akari da tsarin da haruffansa ya ƙunshi alamomin q tare da yuwuwar pi. A wannan yanayin matsakaicin adadin bayanai a cikin tsarin (darajar sa da ake sa ran) daidai yake da:
Wannan shi ake kira entropy na tsarin tare da rabon yiwuwar {pi}. Muna amfani da kalmar "entropy" saboda nau'in lissafi iri ɗaya ya bayyana a cikin ma'aunin zafi da sanyio da injiniyoyi. Wannan shine dalilin da ya sa kalmar "entropy" ta haifar da wani abu mai mahimmanci a kusa da kanta, wanda a ƙarshe bai dace ba. Irin wannan nau'i na ƙididdiga ba ya nufin fassarar iri ɗaya na alamomin!
Entropy na rarraba yiwuwar yana taka muhimmiyar rawa a ka'idar coding. Rashin daidaituwar Gibbs don rabon yuwuwar biyu daban-daban pi da qi ɗaya ne daga cikin mahimman sakamakon wannan ka'idar. Don haka dole ne mu tabbatar da hakan
Tabbacin ya dogara ne akan jadawali bayyananne, siffa. 13.I, wanda ke nuna haka
kuma ana samun daidaito ne kawai lokacin x = 1. Bari mu yi amfani da rashin daidaituwa ga kowane lokaci na jimlar daga gefen hagu:
Idan haruffan tsarin sadarwa sun ƙunshi alamomin q, sannan ɗaukar yiwuwar watsa kowace alama qi = 1/q da musanya q, mun samo daga rashin daidaiton Gibbs.
Hoto 13.I
Wannan yana nufin cewa idan yuwuwar watsa duk alamomin q iri ɗaya ne kuma daidai suke - 1 / q, to matsakaicin entropy yana daidai da ln q, in ba haka ba rashin daidaito yana riƙe.
Game da lambar da za a iya yankewa ta musamman, muna da rashin daidaiton Kraft
Yanzu idan muka ayyana yuwuwar yuwuwar
a ina mana = 1, wanda ya biyo baya daga rashin daidaiton Gibbs,
kuma yi amfani da ɗan ƙaramin algebra (tuna cewa K ≤ 1, don haka za mu iya sauke kalmar logarithmic, kuma watakila ƙarfafa rashin daidaituwa daga baya), muna samun
inda L shine matsakaicin tsayin lambar.
Don haka, entropy shine mafi ƙarancin iyaka ga kowane lamba-ta-alama tare da matsakaicin tsayin lambar code L. Wannan shine ka'idar Shannon don tashar da ba ta da tsangwama.
Yanzu la'akari da babban ka'idar game da iyakancewar tsarin sadarwa wanda ake watsa bayanai a cikinsa azaman rafi na raƙuman raƙuma da hayaniya. An fahimci cewa yuwuwar watsawar daidaitaccen bit ɗaya shine P> 1/2, kuma yuwuwar za a juyar da ƙimar bit yayin watsawa (kuskure zai faru) daidai yake da Q = 1 - P. Don dacewa, mu ɗauka cewa kurakurai masu zaman kansu ne kuma yuwuwar kuskure iri ɗaya ne ga kowane ɗan abin da aka aiko - wato, akwai "farar amo" a cikin tashar sadarwa.
Hanyar da muke da dogon rafi na n-bits ɗin da aka sanya su cikin saƙo ɗaya shine ƙarar n - girma na lambar guda-bit. Za mu ƙayyade ƙimar n daga baya. Yi la'akari da saƙo mai kunshe da n-bits a matsayin batu a cikin n-dimensional sarari. Tun da muna da sararin n-dimensional - kuma don sauƙi za mu ɗauka cewa kowane saƙo yana da yiwuwar faruwa iri ɗaya - akwai M saƙonnin da za a iya bayyana (M kuma za a bayyana shi daga baya), don haka yiwuwar duk wani sakon da aka aiko shi ne.
(mai aikawa)
Jadawalin 13.II
Na gaba, la'akari da ra'ayin ikon tashar. Ba tare da shiga cikin cikakkun bayanai ba, ana siffanta ƙarfin tashar a matsayin matsakaicin adadin bayanai waɗanda za a iya dogara da su ta hanyar hanyar sadarwa, la'akari da amfani da mafi inganci codeing. Babu wata hujja cewa ana iya watsa ƙarin bayanai ta hanyar sadarwa fiye da ƙarfinsa. Ana iya tabbatar da wannan don tashoshi mai ma'ana na binary (wanda muke amfani da shi a cikin yanayinmu). Ƙarfin tashar, lokacin aika rago, an ƙayyade azaman
inda, kamar yadda ya gabata, P shine yuwuwar babu kuskure a cikin kowane abin da aka aiko. Lokacin aika n rago masu zaman kansu, ana ba da ƙarfin tashar ta
Idan muna kusa da tashar tashar, to dole ne mu aika kusan wannan adadin bayanai ga kowane alamomin ai, i = 1, ..., M. Ganin cewa yiwuwar faruwar kowace alamar ai shine 1 / M. mun samu
lokacin da muka aika kowane M daidai da saƙon mai yiwuwa ai, muna da
Lokacin da aka aika n bits, muna tsammanin kurakurai nQ zasu faru. A aikace, don saƙon da ya ƙunshi n-bits, za mu sami kusan kurakuran nQ a cikin saƙon da aka karɓa. Don babban n, bambancin dangi (bambanci = faɗin rarraba,)
rarraba adadin kurakurai zai zama ƙara kunkuntar yayin da n karuwa.
Don haka, daga bangaren watsawa, na ɗauki saƙon ai don aikawa da zana yanki kewaye da shi tare da radius.
wanda ya fi girma dan kadan da adadin daidai da e2 fiye da adadin kurakurai da aka sa ran Q, (Hoto 13.II). Idan n ya isa girma, to akwai yuwuwar ƙaramar saƙon bj da ke bayyana a gefen mai karɓa wanda ya wuce wannan fanni. Bari mu zayyana halin da ake ciki kamar yadda na gani ta mahangar mai watsawa: muna da kowane radiyo daga sakon da aka aika ai zuwa saƙon da aka karɓa bj tare da yuwuwar kuskure daidai (ko kusan daidai) zuwa daidaitaccen rarrabawa, ya kai matsakaicin matsakaici. ina nQ. Ga kowane e2 da aka ba, akwai n mai girma wanda yuwuwar sakamakon bj ya kasance a waje da yanki na yana da ƙanƙanta kamar yadda kuke so.
Yanzu bari mu kalli yanayin guda ɗaya daga gefen ku (Fig. 13.III). A gefen receiver akwai wani sphere S (r) na radius iri ɗaya a kusa da wurin da aka karɓa bj a cikin n-dimensional space, ta yadda idan saƙon da aka karɓa bj yana cikin sararin samaniya na, saƙon ai da na aiko yana cikin ku. Sphere.
Ta yaya kuskure zai iya faruwa? Kuskuren na iya faruwa a cikin lamuran da aka kwatanta a cikin tebur da ke ƙasa:
Hoto 13.III
Anan zamu ga cewa idan a cikin filin da aka gina a kusa da wurin da aka karɓa akwai aƙalla ƙarin maki ɗaya daidai da yiwuwar aika saƙon da ba a buɗe ba, to an sami kuskure yayin watsawa, tunda ba za ku iya tantance wane daga cikin waɗannan saƙonnin aka aika ba. Saƙon da aka aiko ba shi da kurakurai kawai idan wurin da ya dace da shi yana cikin filin, kuma babu wasu maki da zai yiwu a cikin lambar da aka bayar waɗanda ke cikin yanki ɗaya.
Muna da lissafin lissafi don yuwuwar kuskure Pe idan an aika saƙon ai
Za mu iya fitar da kashi na farko a cikin zango na biyu, muna ɗaukar shi azaman 1. Ta haka ne muke samun rashin daidaituwa
Babu shakka cewa
don haka
sake neman wa'adi na ƙarshe akan dama
Ɗaukar n babban isa, ana iya ɗaukar kalmar farko ƙarami kamar yadda ake so, a ce ƙasa da wasu lamba d. Don haka muna da
Yanzu bari mu dubi yadda za mu iya gina wani sauƙi musanyawa code to encode M saƙonnin kunshi n bits. Ba tare da sanin ainihin yadda za a gina lamba ba (har yanzu ba a ƙirƙira lambobin gyara kuskure ba), Shannon ya zaɓi bazuwar coding. Juya tsabar kuɗi don kowane n bits a cikin saƙon kuma maimaita tsarin don saƙonnin M. Gabaɗaya, tsabar tsabar nM na buƙatar yin juzu'i, don haka yana yiwuwa
ƙamus na lamba suna da yuwuwar ½nM iri ɗaya. Tabbas, tsarin bazuwar ƙirƙirar kundin kundin yana nufin cewa akwai yuwuwar kwafin kwafin, da kuma maki na lamba waɗanda zasu kasance kusa da juna don haka zama tushen kurakurai masu yiwuwa. Dole ne mutum ya tabbatar da cewa idan wannan bai faru ba tare da yuwuwar mafi girma fiye da kowane ƙaramin matakin kuskure da aka zaɓa, to abin da aka bayar ya isa sosai.
Muhimmin batu shine Shannon ya ƙididdige duk yuwuwar littattafan code don nemo matsakaicin kuskure! Za mu yi amfani da alamar Av[.] don nuna matsakaicin ƙima akan saitin duk yuwuwar littafan lambobin bazuwar. Matsakaicin a kan akai d, ba shakka, yana ba da dindindin, tun da averaging kowane term ɗin daidai yake da kowane lokaci a jimla.
wanda za'a iya ƙarawa (M-1 yana zuwa M)
Ga kowane saƙon da aka bayar, lokacin da ake yin matsakaita a cikin dukkan litattafan code, faifan maɓalli yana gudana cikin dukkan ƙididdiga masu yuwuwa, don haka matsakaicin yuwuwar cewa batu yana cikin yanki shine rabon ƙarar yanki zuwa jimillar ƙarar sarari. Ƙarfin sararin samaniya shine
inda s=Q+e2 <1/2 da ns dole ne su zama lamba.
Ƙarshe na hannun dama shine mafi girma a cikin wannan jimlar. Da farko, bari mu kimanta ƙimarta ta amfani da dabarar Stirling don masana'anta. Za mu dubi raguwar ƙididdiga na kalmar da ke gabansa, lura cewa wannan ƙididdiga yana ƙaruwa yayin da muke matsawa zuwa hagu, don haka za mu iya: (1) taƙaita ƙimar jimlar zuwa jimlar ci gaban geometric tare da. wannan ƙididdiga ta farko, (2) faɗaɗa ci gaban geometric daga sharuɗɗan ns zuwa adadi mara iyaka, (3) ƙididdige jimlar ci gaban geometric mara iyaka (misali algebra, babu wani abu mai mahimmanci) kuma a ƙarshe sami ƙimar iyakance (don isasshe babba). n):
Yi la'akari da yadda entropy H(s) ya bayyana a cikin ainihin binomial. Lura cewa faɗaɗa jerin Taylor H(s)=H(Q+e2) yana ba da ƙididdigewa da aka samu la'akari da abin da aka samo asali kawai kuma yayi watsi da duk wasu. Yanzu bari mu haɗa magana ta ƙarshe:
inda
Duk abin da za mu yi shi ne zaɓi e2 irin wannan e3 <e1, sannan ƙarshen ƙarshe zai zama ƙarami ba bisa ka'ida ba, muddin n ya isa. Sakamakon haka, ana iya samun matsakaicin kuskuren PE ƙarami kamar yadda ake so tare da ikon tashar ba da gangan ba kusa da C.
Idan matsakaita na duk lambobin yana da ƙaramin isashen kuskure, to dole ne aƙalla lamba ɗaya ta dace, don haka akwai aƙalla tsarin coding ɗaya. Wannan wani muhimmin sakamakon da Shannon ya samu - "Shannon's theorem for a m channel", ko da yake ya kamata a lura da cewa ya tabbatar da wannan don wani abu da ya fi girma fiye da sauƙi na binary symmetric tashar da na yi amfani da shi. Ga al'amuran gabaɗaya, ƙididdigar lissafi sun fi rikitarwa, amma ra'ayoyin ba su bambanta ba, don haka sau da yawa, ta yin amfani da misalin wani lamari na musamman, zaku iya bayyana ainihin ma'anar ka'idar.
Mu soki sakamakon. Mun maimaita maimaitawa: "Don isasshe babban n." Amma yaya girman n? Mai girma, babba idan da gaske kuna son kasancewa duka biyu kusa da ƙarfin tashar kuma ku tabbatar da daidaitaccen canja wurin bayanai! Don haka babba, a zahiri, cewa dole ne ku jira dogon lokaci don tara saƙon isassun bugu don ɓoye shi daga baya. A wannan yanayin, girman ƙamus ɗin bazuwar zai zama babba (bayan haka, ba za a iya wakilta irin wannan ƙamus a cikin gajeriyar tsari ba fiye da cikakken jerin duk raƙuman Mn, duk da cewa n da M suna da girma sosai)!
Lambobin gyara kurakurai suna guje wa jiran dogon saƙon sannan a yi rikodin su da kuma yanke shi ta manyan littattafai masu girma saboda suna guje wa littattafan da kansu kuma suna amfani da lissafi na yau da kullun maimakon. A cikin ka'idar sauƙi, irin waɗannan lambobin suna rasa ikon kusanci ikon tashar kuma har yanzu suna kula da ƙananan kuskuren kuskure, amma lokacin da lambar ta gyara babban adadin kurakurai, suna aiki da kyau. A wasu kalmomi, idan kun ware wasu damar tashoshi don gyara kuskure, to dole ne ku yi amfani da damar gyara kuskure mafi yawan lokaci, watau, yawancin kurakurai dole ne a gyara su a cikin kowane sakon da aka aiko, in ba haka ba kuna bata wannan damar.
Hakanan, ka'idar da aka tabbatar a sama har yanzu ba ta da ma'ana! Ya nuna cewa ingantattun tsarin watsawa dole ne su yi amfani da dabarar rufaffiyar wayo don igiyoyi masu tsayi. Misali shi ne tauraron dan adam da suka yi shawagi fiye da na waje; Yayin da suke nisa daga Duniya da Rana, ana tilasta musu gyara kurakurai da yawa a cikin bayanan toshe: wasu tauraron dan adam suna amfani da bangarorin hasken rana, wanda ke samar da kusan 5 W, wasu kuma suna amfani da hanyoyin samar da makamashin nukiliya, wanda ke samar da kusan makamashi iri daya. Ƙarfin wutar lantarki, ƙananan nau'in jita-jita masu watsawa da iyakacin girman jita-jita masu karɓa a duniya, babban nisa da siginar dole ne tayi tafiya - duk wannan yana buƙatar amfani da lambobin tare da babban matakin gyara kuskure don gina ingantaccen tsarin sadarwa.
Bari mu koma ga n-dimensional sarari da muka yi amfani da su a cikin hujja a sama. A cikin tattaunawa game da shi, mun nuna cewa kusan dukkanin girman sararin samaniya yana mayar da hankali ne a kusa da saman waje - don haka, yana da kusan tabbas cewa siginar da aka aika zai kasance kusa da farfajiyar filin da aka gina a kusa da siginar da aka karɓa, ko da tare da ingantacciyar siginar. ƙananan radius na irin wannan yanki. Saboda haka, ba abin mamaki ba ne cewa siginar da aka karɓa, bayan gyara kuskuren da yawa, nQ, ya zama kusa da sigina ba tare da kurakurai ba. Ƙarfin haɗin gwiwar da muka tattauna a baya shine mabuɗin fahimtar wannan lamari. Lura cewa nau'ikan nau'ikan nau'ikan da aka gina don gyara lambobin Hamming ba sa cin karo da juna. Babban adadin kusan ma'auni na orthogonal a cikin girman n-girma yana nuna dalilin da ya sa za mu iya dacewa da sassan M a sararin samaniya tare da ɗan zoba. Idan muka ƙyale ƙarami, ƙarami mai ɗorewa, wanda zai iya haifar da ƙananan kurakurai yayin yanke hukunci, za mu iya samun jeri mai yawa a sararin samaniya. Hamming ya ba da garantin wani matakin gyara kuskure, Shannon - ƙananan yuwuwar kuskure, amma a lokaci guda yana riƙe da ainihin abin da aka samar ba tare da izini ba kusa da ƙarfin tashar sadarwa, wanda lambobin Hamming ba za su iya yi ba.
Ka'idar bayanai ba ta gaya mana yadda za a tsara ingantaccen tsari ba, amma tana nuna hanya zuwa ingantaccen tsarin sadarwa. Kayan aiki ne mai mahimmanci don gina tsarin sadarwa na na'ura zuwa na'ura, amma, kamar yadda muka gani a baya, ba shi da wata mahimmanci ga yadda mutane suke sadarwa da juna. Ba a san iyakar yadda gadon halittu yake kamar tsarin sadarwa na fasaha ba, don haka a halin yanzu ba a fayyace yadda ka'idar bayanai ta shafi kwayoyin halitta ba. Ba mu da wani zaɓi face gwadawa, kuma idan nasara ta nuna mana irin na'ura mai kama da wannan al'amari, to gazawar za ta yi nuni ga wasu mahimman fannoni na yanayin bayanai.
Kada mu yi nisa da yawa. Mun ga cewa duk ma'anoni na asali, zuwa babba ko ƙarami, dole ne su bayyana ainihin imaninmu na asali, amma ana siffanta su da ɗan murɗawa don haka ba su da amfani. An yarda da shi a al'ada cewa, a ƙarshe, ma'anar da muke amfani da ita ita ce ainihin ma'anar; amma, wannan kawai yana gaya mana yadda ake sarrafa abubuwa kuma ba ta wata hanya ta isar mana da wata ma'ana. Hanyar bayana, wanda aka fi so sosai a cikin da'irar lissafi, yana barin abubuwa da yawa da ake so a aikace.
Yanzu za mu dubi misalin gwaje-gwajen IQ inda ma'anar ta kasance madauwari kamar yadda kuke so ta kasance kuma, sakamakon haka, yaudara. An ƙirƙiri gwajin da ya kamata a auna hankali. Daga nan sai a sake bitar shi don daidaita shi yadda ya kamata, sannan a buga shi kuma, a cikin hanya mai sauƙi, a daidaita shi ta yadda "hankali" da aka auna ya zama kamar yadda aka saba rarrabawa (a kan ma'auni na calibration, ba shakka). Dole ne a sake duba duk ma'anar, ba kawai lokacin da aka fara ba da shawara ba, amma kuma da yawa daga baya, lokacin da aka yi amfani da su a cikin yanke shawara. Yaya iyakar ma'anar ta dace don magance matsalar? Sau nawa ake yin ma'anar da aka bayar a cikin saiti ɗaya a cikin saituna daban-daban? Wannan yana faruwa sau da yawa! A cikin ɗan adam, wanda ba makawa za ku ci karo da shi a rayuwar ku, wannan yana faruwa sau da yawa.
Don haka, daya daga cikin makasudin wannan gabatar da ka’idar bayanai, baya ga nuna fa’idarsa, shi ne don fadakar da ku game da wannan hadari, ko kuma a nuna muku daidai yadda ake amfani da shi don samun sakamakon da ake so. An daɗe an lura cewa ma'anar farko sun ƙayyade abin da kuka samu a ƙarshe, zuwa mafi girma fiye da yadda ake tsammani. Ma'anar farko na buƙatar kulawa da yawa daga gare ku, ba kawai a kowane sabon yanayi ba, har ma a yankunan da kuka dade kuna aiki tare da su. Wannan zai ba ku damar fahimtar yadda sakamakon da aka samu shine tautology ba wani abu mai amfani ba.
Shahararren labarin Eddington ya ba da labarin mutanen da suka yi kamun kifi a cikin teku da raga. Bayan sun yi nazarin girman kifin da suka kama, sai suka tantance mafi ƙarancin kifin da ake samu a cikin teku! Na'urar da aka yi amfani da ita ce ta kawo ƙarshen su, ba ta gaskiya ba.
A ci gaba…
Wanene yake son taimakawa tare da fassarar, tsarawa da buga littafin - rubuta a cikin saƙo na sirri ko imel [email kariya]
Af, mun kuma ƙaddamar da fassarar wani littafi mai ban sha'awa - )
Muna nema musamman wadanda zasu taimaka fassara . (canja wuri na minti 10, an riga an ɗauki 20 na farko)
Abubuwan da ke cikin littafin da surori da aka fassara
- Gabatarwa zuwa Fasahar Yin Kimiyya da Injiniya: Koyan Koyo (Maris 28, 1995)
- " Tushen Juyin Juyin Halitta (Masu hankali)" (Maris 30, 1995)
- "Tarihin Kwamfuta - Hardware" (Maris 31, 1995)
- "Tarihin Kwamfuta - Software" (Afrilu 4, 1995)
- "Tarihin Kwamfuta - Aikace-aikace" (Afrilu 6, 1995)
- "Babban Hankali - Sashe na I" (Afrilu 7, 1995)
- "Babban Hankali - Sashe na II" (Afrilu 11, 1995)
- "Harkokin Artificial III" (Afrilu 13, 1995)
- "N-Dimensional Space" (Afrilu 14, 1995)
- "Ka'idar Codeing - Wakilin Bayani, Sashe na I" (Afrilu 18, 1995)
- "Ka'idar Codeing - Wakilin Bayani, Sashe na II" (Afrilu 20, 1995)
- "Lambobin Gyara Kuskure" (Afrilu 21, 1995)
- "Ka'idar Bayani" (Afrilu 25, 1995)
- "Filters Digital, Sashe na I" (Afrilu 27, 1995)
- "Filters Digital, Part II" (Afrilu 28, 1995)
- "Filters Digital, Part III" (Mayu 2, 1995)
- "Filters Digital, Sashe na IV" (Mayu 4, 1995)
- "Simulation, Sashe na I" (Mayu 5, 1995)
- "Simulation, Part II" (Mayu 9, 1995)
- "Simulation, Part III" (Mayu 11, 1995)
- "Fiber Optics" (Mayu 12, 1995)
- "Gudanar da Taimakon Kwamfuta" (Mayu 16, 1995)
- "Lissafi" (Mayu 18, 1995)
- "Kwanta Makanikai" (Mayu 19, 1995)
- "Kirƙirar halitta" (Mayu 23, 1995). Fassara:
- "Masana" (Mayu 25, 1995)
- "Bayanan da ba a dogara ba" (Mayu 26, 1995)
- "Injiniya Tsari" (Mayu 30, 1995)
- "Kuna Samun Abin da Kuke Auna" (Yuni 1, 1995)
- (Yuni 2, 1995) fassara a cikin minti 10 guntu
- Hamming, "Kai da Bincikenku" (Yuni 6, 1995).
Wanene yake son taimakawa tare da fassarar, tsarawa da buga littafin - rubuta a cikin saƙo na sirri ko imel [email kariya]
source: www.habr.com