Richard Hamming: Chitsauko 13. Ruzivo rwedzidziso

Tazviita!

"Chinangwa chekosi iyi kugadzirira iwe ramangwana rako rehunyanzvi."

Mhoro, Habr. Rangarira chinyorwa chinokatyamadza "Iwe nebasa rako" (+219, 2588 mabhukumaki, 429k inoverengwa)?

Saka Hamming (hongu, hongu, kuzviongorora uye kuzvigadzirisa Hamming codes) pane zvakakwana bhuku, yakanyorwa zvichibva pahurukuro dzake. Tinorishandura, nokuti murume anotaura zvaanofunga.

Iri ibhuku kwete zveIT chete, ibhuku rine chekuita nemafungiro evanhu vanotonhorera zvinoshamisa. “Hakusi kungowedzera kufunga kwakanaka; rinotsanangura mamiriro ezvinhu anowedzera mikana yokuita basa guru.”

Kutenda kuna Andrey Pakhomov neshanduro.

Dzidziso yeRuzivo yakagadziridzwa naC. E. Shannon mukupera kwema1940. Bell Labs manejimendi akasimbirira kuti adaidze "Communication Theory" nekuti... iri izita rakanyatsojeka. Nezvikonzero zviri pachena, zita rokuti "Information Theory" rine simba guru kune veruzhinji, ndosaka Shannon akarisarudza, uye ndiro zita ratinoziva nanhasi. Zita racho pacharo rinoratidza kuti dzidziso inobata neruzivo, izvo zvinoita kuti ive yakakosha sezvatinofamba zvakadzama muzera reruzivo. Muchitsauko chino, ini ndichabata pane akati wandei mhedziso kubva mudzidziso iyi, ini handipe humbowo hwakasimba, asi humbowo hwehumwe hunopihwa hwedzidziso iyi, kuti iwe unzwisise kuti "Information Theory" chii chaizvo, paunogona kuishandisa. uye pasina .

Kutanga, chii chinonzi “ruzivo”? Shannon anoenzanisa ruzivo nekusava nechokwadi. Akasarudza negative logarithm yemukana wechiitiko sechiyero chehuwandu hweruzivo rwaunogamuchira kana chiitiko chine mukana p chikaitika. Semuenzaniso, kana ndikakuudza kuti mamiriro ekunze muLos Angeles ane mhute, ipapo p iri pedyo ne1, iyo isingatipi ruzivo rwakawanda. Asi kana ndikataura kuti kunaya muMonterey munaChikumi, pachave nekusagadzikana mumeseji uye ichave neruzivo rwakawanda. Chiitiko chakavimbika hachina chero ruzivo, sezvo log 1 = 0.

Ngatitarisei izvi zvakadzama. Shannon aitenda kuti chiyero chehuwandu hwemashoko chinofanira kunge chiri chiitiko chinopfuurira chechiitiko chechiitiko p, uye nokuda kwezviitiko zvakasununguka zvinofanira kuwedzera - huwandu hwemashoko akawanikwa nekuda kwekuitika kwezviitiko zviviri zvakasununguka zvinofanira kuenzana ne huwandu hwemashoko akawanikwa semugumisiro wekuitika kwechiitiko chekubatana. Semuenzaniso, mhedzisiro yedhayisi roll uye coin roll zvinowanzobatwa sezviitiko zvakazvimirira. Ngatishandure zviri pamusoro mumutauro wemasvomhu. Kana ini (p) iri huwandu hweruzivo rwuri muchiitiko chine mukana p, saka chechiitiko chemubatanidzwa chine zviitiko zviviri zvakazvimiririra x zvine mukana p1 uye y pamwe pamwe p2 watinowana.

(x uye y zviitiko zvakazvimirira)

Iyi ndiyo inoshanda Cauchy equation, yechokwadi kune ese p1 uye p2. Kugadzirisa iyi inoshanda equation, fungidzira izvozvo

p1 = p2 = p,

izvi zvinopa

Kana p1 = p2 uye p2 = p ipapo

etc. Kuwedzera hurongwa uhu uchishandisa nzira yakajairwa yekutsanangura, kune ese manhamba anonzwisisika m/n zvinotevera ndezvechokwadi

Kubva pane zvinofungidzirwa kuenderera kweyero yeruzivo, zvinotevera kuti logarithmic basa ndiyo yega inoenderera mhinduro kuCauchy functional equation.

Muchidzidzo cheruzivo, zvakajairika kutora iyo logarithm base kuita 2, saka sarudzo yebhinari ine chaiyo 1 bit yeruzivo. Nokudaro, ruzivo runoyerwa nefomula

Ngatimbomirai tinzwisise zvakaitika pamusoro. Chekutanga, isu hatina kutsanangura pfungwa ye "ruzivo"; isu takangotsanangura fomula yechiyero chayo chehuwandu.

Chechipiri, chiyero ichi chinokonzerwa nokusava nechokwadi, uye kunyange zvazvo chakakodzera michina—somuenzaniso, gadziriro dzorunhare, redhiyo, terevhizheni, makombiyuta, zvichingodaro—hachiratidzi zvimiro zvendangariro zvavanhu zvenguva dzose kumashoko.

Chechitatu, ichi chiyero chinoenderana, zvinoenderana nemamiriro azvino eruzivo rwako. Kana iwe ukatarisa rukova rwe "random manhamba" kubva kune isina kujairika nhamba jenareta, iwe unofunga kuti imwe neimwe inotevera nhamba haina chokwadi, asi kana iwe uchiziva fomuro yekuverenga "random manhamba", iyo inotevera nhamba ichazivikanwa, uye saka haizo. zvine ruzivo.

Saka tsananguro yaShannon yeruzivo inokodzera michina muzviitiko zvakawanda, asi inoita seisingakwane manzwisisiro evanhu veizwi. Ndicho chikonzero nei "Information Theory" inofanira kunge yakanzi "Communication Theory." Nekudaro, yanonoka kushandura tsananguro (iyo yakapa dzidziso kufarirwa kwayo kwekutanga, uye izvo zvichiri kuita kuti vanhu vafunge kuti dzidziso iyi inobata ne "ruzivo"), saka isu tinofanirwa kugara navo, asi panguva imwe chete iwe unofanirwa. nyatsonzwisisa kuti tsananguro yaShannon yeruzivo iri papi kubva kune zvarinowanzo shandiswa. Ruzivo rwaShannon runobata nechimwe chinhu chakasiyana zvachose, kureva kusavimbika.

Hechino chimwe chinhu chekufunga nezvacho kana iwe uchikurudzira chero mazwi. Tsanangudzo yakatsanangurwa, senge tsananguro yaShannon yeruzivo, inobvumirana sei nepfungwa yako yepakutanga uye yakasiyana sei? Iko kunenge kusina izwi rinonyatsoratidza chiono chako chekare chepfungwa, asi pakupedzisira, ndiro izwi rinoshandiswa rinoratidza zvinoreva pfungwa, saka kugadzira chimwe chinhu kuburikidza netsananguro dzakajeka nguva dzose kunosuma imwe ruzha.

Funga nezvechirongwa chine mavara ane mavara q ane zvingangoitika pi. Panyaya iyi avhareji yehuwandu hwemashoko muhurongwa (ukoshi hwayo hunotarisirwa) hwakaenzana ne:

Izvi zvinodaidzwa kuti entropy ye system ine mukana wekugovera {pi}. Isu tinoshandisa izwi rekuti "entropy" nekuti iyo yakafanana fomu yemasvomhu inoonekwa mune thermodynamics uye statistical mechanics. Ichi ndicho chikonzero izwi rekuti "entropy" rinogadzira imwe aura yekukosha kwakatenderedza pachayo, iyo inozopedzisira isina kurongeka. Imwe nzira yemasvomhu yenotation hairevi kududzira kumwe chete kwezviratidzo!

Iyo entropy yekugoneka kugovera inoita basa rakakura mukukodha dzidziso. Kusaenzana kweGibbs kune maviri akasiyana mukana wekugovera pi uye qi ndeimwe yemhedzisiro yakakosha yedzidziso iyi. Saka tinofanira kuratidza izvozvo

Humbowo hwakavakirwa pagirafu riri pachena, Fig. 13.I, izvo zvinoratidza izvozvo

uye kuenzana kunowanikwa chete kana x = 1. Ngatishandise kusaenzana patemu yega yega yehuwandu kubva kuruboshwe:

Kana iyo alphabet yehurongwa hwekutaurirana ine q zviratidzo, zvino kutora mukana wekufambiswa kwechiratidzo chega chega qi = 1/q nekutsiva q, tinowana kubva kuGibbs kusaenzana.

Mufananidzo 13.I

Izvi zvinoreva kuti kana mukana wekutumira zviratidzo zvese q zvakafanana uye zvakaenzana ne - 1 / q, saka iyo entropy yakakura yakaenzana ne ln q, zvikasadaro kusaenzana kunobata.

Panyaya yekodhi yakasarudzika, isu tine kusaenzana kwaKraft

Zvino kana tikatsanangura pseudo-zvingaitika

kupi hazvo = 1, iyo inotevera kubva kuGibbs 'kusaenzana,

uye shandisa algebra diki (rangarira kuti K ≤ 1, kuti tigone kudonhedza izwi relogarithmic, uye pamwe kusimbisa kusaenzana gare gare), tinowana.

apo L ndiyo avhareji urefu hwekodhi.

Saka, entropy ndiyo idiki inosungirwa kune chero mavara-ne-chiratidzo kodhi ine avhareji codeword kureba L. Iyi ndiyo theorem yaShannon yechiteshi chisina kukanganisa.

Zvino funga iyo huru theorem pamusoro pezvipimo zvehurongwa hwekutaurirana umo ruzivo rwunofambiswa serukova rwemabhiti akazvimirira uye ruzha rwuripo. Zvinonzwisiswa kuti mukana wekutapurirana kwakaringana kwechimwe chikamu ndiP> 1/2, uye mukana wekuti iyo bhiti kukosha ichave inverted panguva yekufambisa (kukanganisa kuchaitika) yakaenzana Q = 1 - P. Kuti zvive nyore, isu fungidzira kuti zvikanganiso zvakazvimiririra uye mukana wekukanganisa wakafanana kune imwe neimwe yakatumirwa bit - ndiko kuti, pane "ruzha ruchena" muchiteshi chekutaurirana.

Nzira yatine rwizi rwakareba rwe n bits yakavharidzirwa mune imwe meseji ndeye n - dimensional yekuwedzera yeiyo-bit kodhi. Tichaona kukosha kwe n gare gare. Funga nezve meseji ine n-bits sepoindi mune n-dimensional nzvimbo. Sezvo isu tine n-dimensional nzvimbo - uye nekureruka isu tichafunga kuti meseji yega yega ine mukana wakafanana wekuitika - kune M inogoneka meseji (M ichatsanangurwa zvakare gare gare), saka mukana wechero meseji inotumirwa ndeye

(mutumi)
Chirongwa 13.II

Tevere, funga zano rekugona kwechiteshi. Pasina kupinda muhuwandu, chiteshi chechiteshi chinotsanangurwa sehuwandu hwehuwandu hweruzivo hunogona kufambiswa zvakavimbika pamusoro penzira yekutaurirana, tichifunga nezvekushandiswa kwekodha inoshanda zvakanyanya. Hapana nharo yekuti ruzivo rwakawanda runogona kufambiswa kuburikidza nechiteshi chekukurukurirana kupfuura kugona kwayo. Izvi zvinogona kuratidzwa kune binary symmetric chiteshi (iyo yatinoshandisa kwatiri). Iyo chiteshi simba, kana uchitumira bits, inotsanangurwa se

uko, sepakutanga, P ndiyo mukana wekuti hapana chikanganiso mune chero chidimbu chakatumirwa. Pakutumira n mabhiti akazvimirira, chiteshi chechiteshi chinopihwa na

Kana isu tave padhuze neiyo chiteshi huwandu, saka tinofanira kutumira hunenge huwandu uhu hweruzivo kune chimwe nechimwe chezviratidzo ai, i = 1, ..., M. Tichifunga kuti mukana wekuitika kwechiratidzo chega chega ai 1 / M, tinowana

patinotumira chero yeM zvakaenzana mameseji anogona kuitika ai, tine

Kana n bits ikatumirwa, tinotarisira kuti nQ zvikanganiso zviitike. Mukuita, kune meseji ine n-bits, isu tichave neangangoita nQ zvikanganiso mune yakagamuchirwa meseji. Kune yakakura n, kusiyana kwakasiyana (kusiyana = kugovera hupamhi,)
kugoverwa kwenhamba yekukanganisa kuchawedzera kutetepa sezvo n inowedzera.

Saka, kubva kudivi rekutapurirana, ini ndinotora meseji ai kutumira uye kudhirowa denderedzwa rakatenderedza neradius.

iyo yakakura zvishoma nehuwandu hwakaenzana ne2 pane inotarisirwa nhamba yezvikanganiso Q, (Mufananidzo 13.II). Kana n yakakura zvakakwana, saka pane mukana wekuti meseji poindi bj ibude padivi rekugamuchira inoenda kupfuura chikamu ichi. Ngatitorei mamiriro ezvinhu sezvandinozviona kubva pamaonero eanotapurirana: isu tine chero radii kubva kune yakafambiswa meseji ai kune yakagamuchirwa meseji bj ine mukana wekukanganisa kwakaenzana (kana kupotsa kuenzana) kune yakajairwa kugovera, inosvika pakakwirira. zve nq. Kune chero ipi zvayo yakapihwa e2, pane n n yakakura zvekuti mukana wekuti mhedzisiro bj kuve kunze kwechikamu changu idiki sezvaunoda.

Iye zvino ngatitarisei mamiriro akafanana kubva parutivi rwako (Fig. 13.III). Kudivi rekugamuchira kune sphere S(r) yeradius yakafanana r yakatenderedza nzvimbo yakagamuchirwa bj mu n-dimensional space, zvekuti kana meseji yakagamuchirwa bj iri mukati mesphere yangu, ipapo meseji inotumirwa neni iri mukati mako. sphere.

Chikanganiso chingaitika sei? Iko kukanganisa kunogona kuitika mumakesi anotsanangurwa mutafura pazasi:

Mufananidzo 13.III

Pano tinoona kuti kana munzvimbo yakavakirwa yakatenderedza nzvimbo yakagamuchirwa paine imwe imwe pfungwa inoenderana neinogona kutumirwa meseji isina kuvharwa, ipapo kukanganisa kwakaitika panguva yekutapurirana, nekuti haugone kuona kuti ndeipi yemeseji iyi yakafambiswa. Mharidzo yakatumirwa haina kukanganisa chete kana poindi inoenderana nayo iri mundima, uye pasina mamwe mapoinzi anogoneka mukodhi yakapihwa iri muchikamu chimwe chete.

Tine equation yemasvomhu yemukana wekukanganisa Pe kana meseji ai yakatumirwa

Tinogona kukanda chinhu chekutanga muchikamu chechipiri, tichichitora se 1. Nokudaro tinowana kusaenzana

Zviri pachena kuti

saka

nyorera zvakare kune yekupedzisira temu kurudyi

Kutora n yakakura zvakakwana, temu yekutanga inogona kutorwa sediki sezvaunoda, taura zvishoma pane imwe nhamba d. Naizvozvo tine

Zvino ngatitarisei kuti tingagadzira sei kodhi yakareruka yekutsiva kuti encode M mameseji anosanganisira n bits. Sezvo asina ruzivo rwekugadzira kodhi chaiyo (kukanganisa-kugadzirisa makodhi akange asati agadzirwa), Shannon akasarudza zvisina tsarukano coding. Flip coin kune yega yega n bits mumeseji uye dzokorora maitiro eM meseji. Pakazara, nM coin flips inoda kugadzirwa, saka zvinogoneka

kodhi dictionaries ane mukana wakafanana ½nM. Ehe, maitiro asina kujairika ekugadzira bhuku rekodhi zvinoreva kuti pane mukana wekudzokororwa, pamwe nekodhi mapoinzi ayo achave ari padhuze kune mumwe nemumwe uye nekudaro ave sosi yezvingangoitika zvikanganiso. Munhu anofanirwa kuratidza kuti kana izvi zvikasaitika nemukana wakakura kupfuura chero diki yakasarudzwa kukanganisa level, ipapo iyo yakapihwa n yakakura zvakakwana.
Chinhu chakakosha ndechekuti Shannon akaverengera ese anokwanisika macodebook kuti awane avhareji kukanganisa! Tichashandisa chiratidzo Av[.] kuratidza kukosha kweavhareji pamusoro peseti yezvose zvingangoitika macodebooks. Avhareji pamusoro penguva dzose d, hongu, inopa isingachinji, sezvo paavhareji temu yega yega yakafanana neimwe temu yese muhuwandu,

inogona kuwedzerwa (M-1 inoenda kuM)

Kune chero meseji yakapihwa, paavhareji yemabhuku ekodhi ese, iyo encoding inofamba kuburikidza nemhando dzese dzinogoneka, saka avhareji mukana wekuti poindi iri muchikamu ndiyo reshiyo yevhoriyamu yesphere kusvika kuhuwandu hwenzvimbo. Kuwanda kwedenderedzwa ndiko

apo s=Q+e2 <1/2 uye ns inofanira kuva nhamba yakazara.

Temu yekupedzisira kurudyi ndiyo yakakura pane iyi mari. Chekutanga, ngatitarisei kukosha kwayo tichishandisa iyo Stirling formula yemafekitari. Isu tichazotarisa kuderera kweiyo temu iri pamberi payo, cherechedza kuti iyi coefficient inowedzera sezvatinoenda kuruboshwe, uye saka tinogona: (1) kudzora kukosha kwehuwandu kusvika kuhuwandu hwekufambira mberi kwejometri ne. iyi yekutanga coefficient, (2) wedzera kufambira mberi kwejometri kubva pamatemu ens kusvika kunhamba isingaverengeki yematemu, (3) verenga hwerengedzo yeasingagumi geometric kufambira mberi (standard algebra, hapana chakakosha) uye pakupedzisira kuwana kukosha kwekumisikidza (kune yakakura zvakakwana. n):

Cherechedza kuti entropy H (s) yakaonekwa sei mune binomial identity. Ziva kuti Taylor akateedzera kuwedzera H(s)=H(Q+e2) inopa fungidziro yakawanikwa uchifunga chete yekutanga kubva uye kufuratira mamwe ese. Zvino ngatiise pamwe chete chirevo chekupedzisira:

apo

Chatinofanira kuita kusarudza e2 sekuti e3 <e1, uyezve temu yekupedzisira ichava diki zvisina tsarukano, chero n yakakura zvakakwana. Nekuda kweizvozvo, avhareji yekukanganisa kwePE inogona kuwanikwa idiki sezvaidiwa nechiteshi chechiteshi chiri padyo neC.
Kana avhareji yemakodhi ese aine kakanganiso kadiki, saka kanenge kodhi imwe chete inofanirwa kunge yakakodzera, saka paine kanenge imwe yakakodzera yekodhi system. Uyu ndiwo mugumisiro wakakosha wakawanikwa naShannon - "Shannon's theorem yechiteshi chine ruzha", kunyangwe hazvo zvichifanira kucherechedzwa kuti airatidza izvi kune imwe nyaya yakajairika kupfuura iyo yakapfava binary symmetric chiteshi chandakashandisa. Panyaya yakajairika, kuverenga kwemasvomhu kwakaoma zvakanyanya, asi pfungwa hadzina kusiyana, saka kazhinji, uchishandisa muenzaniso weimwe nyaya, unogona kuburitsa chokwadi cheiyo theorem.

Ngatishorei mugumisiro. Isu takadzokorora zvakare: "Kune yakakura zvakakwana n." Asi n yakakura sei? Yakanyanya, yakakura kwazvo kana iwe uchinyatsoda kuve mese padhuze nechiteshi chiteshi uye uve nechokwadi cheiyo chaiyo yekufambisa data! Yakakura kwazvo, kutaura zvazviri, zvekuti uchafanirwa kumirira nguva yakareba kuti uunganidze meseji yemabhiti akakwana kuti uiise gare gare. Muchiitiko ichi, saizi yeduramazwi rekodhi inongove yakakura (mushure mezvose, duramazwi rakadaro harigone kumiririrwa nechimiro chipfupi pane runyoro rwese Mn bits, zvisinei nekuti n uye M zvakakura kwazvo)!

Kukanganisa-kugadzirisa makodhi kudzivirira kumirira meseji refu kwazvo wobva waisa kodhi nekuinyora kuburikidza nemabhuku makuru ekodhi nekuti ivo vanodzivirira macodebook pachavo uye vanoshandisa yakajairwa computation pachinzvimbo. Muchirevo chakareruka, makodhi akadaro anowanzorasikirwa nekukwanisa kusvika kuchiteshi chechiteshi uye achiri kuchengetedza yakaderera yekukanganisa mwero, asi kana iyo kodhi inogadzirisa nhamba yakakura yezvikanganiso, inoita zvakanaka. Mune mamwe mazwi, kana iwe ukagovera imwe chiteshi kugona kugadzirisa kukanganisa, saka iwe unofanirwa kushandisa iko kukanganisa kugadzirisa kugona nguva zhinji, kureva kuti, nhamba huru yezvikanganiso zvinofanirwa kugadziriswa mune yega meseji inotumirwa, zvikasadaro iwe unopambadza iyi simba.

Panguva imwecheteyo, theorem yakaratidzwa pamusoro haisati iri isina maturo! Zvinoratidza kuti masisitimu ekufambisa anoshanda anofanirwa kushandisa akangwara encoding zvirongwa zvetambo refu refu. Muenzaniso ndewe satellites akabhururuka kupfuura mapuraneti ekunze; Sezvo ivo vachifamba kubva kuPasi neZuva, vanomanikidzwa kugadzirisa zvikanganiso zvakawanda uye zvakanyanya mu data block: mamwe ma satellite anoshandisa solar panels, iyo inopa anenge 5 W, mamwe anoshandisa magetsi enyukireya, ayo anopa simba rakafanana. Iyo yakaderera simba remagetsi emagetsi, diki saizi yedhishi dzekutapurirana uye saizi shoma yekugamuchira ndiro paPasi, chinhambwe chakakura icho chiratidzo chinofanirwa kufamba - zvese izvi zvinoda kushandiswa kwemakodhi ane yakakwira nhanho yekururamisa kuvaka hurongwa hwekukurukurirana hunobudirira.

Ngatidzokere kune n-dimensional nzvimbo yatakashandisa muhumbowo huri pamusoro. Mukukurukura nezvazvo, takaratidza kuti rinenge vhoriyamu yese yedenderedzwa yakatarisana nechekunze - nekudaro, zvine chokwadi chekuti chiratidzo chakatumirwa chichave chiri padhuze nepamusoro penzvimbo yakavakirwa kutenderedza chiratidzo chakagamuchirwa, kunyangwe paine diki radius yedenderedzwa rakadaro. Nokudaro, hazvishamisi kuti chiratidzo chakagamuchirwa, mushure mekugadzirisa nhamba yakawanda yezvikanganiso, nQ, inoshanduka kuva nechisimba pedyo nechiratidzo pasina zvikanganiso. Iyo yekubatanidza simba yatakakurukura pakutanga ndiyo kiyi yekunzwisisa ichi chiitiko. Ziva kuti masipiramu akafanana akagadzirirwa kukanganisa-kugadzirisa Hamming macode haapindirane. Huwandu hukuru hweakada kuita orthogonal dimensions munzvimbo yen-dimensional inoratidza kuti nei tichigona kukwana M spheres muchadenga nekupindirana kushoma. Kana isu tikabvumira kudiki, kudiki kudiki kupindirana, izvo zvinogona kutungamira kune diki nhamba yezvikanganiso panguva yekudhirodha, tinogona kuwana yakaomesesa yekuiswa kwenzvimbo muchadenga. Hamming yakavimbisa imwe nhanho yekururamisa kukanganisa, Shannon - mukana wakaderera wekukanganisa, asi panguva imwe chete kuchengetedza iyo chaiyo yekufambisa iri padhuze nekugona kwenzira yekutaurirana, iyo Hamming macode asingakwanisi kuita.

Dzidziso yeruzivo haitiudzi magadzirirwo ehurongwa hunoshanda, asi inonongedza nzira yekuenda kuhurongwa hwekutaurirana hunoshanda. Icho chishandiso chakakosha chekuvaka muchina-kune-muchina masisitimu ekutaurirana, asi, sezvambotaurwa, ine zvishoma zvine chekuita nematauriro anoita vanhu kune mumwe nemumwe. Mwero wekuti nhaka yebhayoloji yakaita senge tekinoroji yekukurukurirana masisitimu haingozivikanwe, saka parizvino hazvisi pachena kuti dzidziso yeruzivo inoshanda sei kune majini. Hatina sarudzo kunze kwekuedza, uye kana budiriro ichitiratidza chimiro-semuchina wechiitiko ichi, ipapo kukundikana kunongedza kune zvimwe zvakakosha zvemhando yeruzivo.

Ngatirege kunyura zvakanyanya. Takaona kuti tsananguro dzose dzepakutanga, pamwero mukuru kana muduku, dzinofanira kuratidza hunhu hwezvitendero zvedu zvepakutanga, asi dzinoratidzirwa nemwero wakati wokukanganiswa uye naizvozvo hadzishandiswi. Zvinogara zvichigamuchirwa kuti, pekupedzisira, tsananguro yatinoshandisa inotsanangura izvo chaizvo; asi, izvi zvinongotiudza magadzirisiro ezvinhu uye hapana nzira inoburitsa chero zvazvinoreva kwatiri. Iyo postulational maitiro, anofarirwa zvakanyanya mumasvomhu madenderedzwa, anosiya zvakanyanya kudiwa mukuita.

Iye zvino tichatarisa muenzaniso weIQ bvunzo apo tsananguro iri sedenderedzwa sezvaunoda kuti ive uye, semhedzisiro, inotsausa. Muedzo unogadzirwa unofungidzirwa kuyera hungwaru. Inobva yadzokororwa kuti iite kuti ienderane sezvinobvira, uye yobva yadhindwa uye, nenzira iri nyore, yakagadziriswa kuitira kuti "njere" yakayerwa iite kuti igove yakagovaniswa (pane calibration curve, hongu). Tsanangudzo dzese dzinofanirwa kutariswa, kwete chete padzinotanga kutaurwa, asiwo pave paya, padzashandiswa mumhedziso dzakatorwa. Miganhu yetsanangudzo yakakodzera kusvika papi padambudziko riri kugadziriswa? Kangani kangani tsananguro dzinopiwa mune imwe mamiriro ezvinhu dzinosvika pakushandiswa mumamiriro akasiyana kwazvo? Izvi zvinoitika kazhinji! Muvanhu, izvo zvauchasangana nazvo muhupenyu hwako, izvi zvinoitika kazhinji.

Saka, chimwe chezvinangwa zveiyi mharidzo yedzidziso yeruzivo, pamusoro pekuratidza kubatsira kwayo, kwaive kukuyambira nezvenjodzi iyi, kana kukuratidza mashandisiro aungaita kuti uwane mhedzisiro yaunoda. Izvo zvave zvichicherechedzwa kuti tsananguro dzekutanga dzinosarudza chaunowana pakupedzisira, kusvika pamwero mukuru kupfuura zvaunoratidzika. Tsanangudzo dzekutanga dzinoda kutariswa kwakawanda kubva kwauri, kwete chete mune chero mamiriro matsva, asiwo munzvimbo dzawave uchishanda nadzo kwenguva yakareba. Izvi zvinokutendera kuti unzwisise kuti kusvika papi mhedzisiro inowanikwa ndeye tautology uye kwete chinhu chinobatsira.

Nyaya yakakurumbira yaEddington inotaura nezvevanhu vairedza mugungwa nemambure. Pashure pokuongorora ukuru hwehove dzavakabata, vakaziva kuti hove dukuduku sei inowanikwa mugungwa! Mhedziso yavo yakasundwa nechiridzwa chakashandiswa, kwete nechokwadi.

Zvichaenderera mberi…

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Nenzira, isu takatangisawo kududzira kwerimwe bhuku rinotonhorera - "The Dream Machine: Nyaya yeComputer Revolution")

Tiri kunyanya kutsvaga avo vanogona kubatsira kushandura bhonasi chitsauko, chiri chete pavhidhiyo. (kutamisa kwemaminetsi gumi, makumi maviri ekutanga atotorwa)

Zviri mukati mebhuku nezvitsauko zvakashandurwaForeword

1. Nhanganyaya kune Iyo Art yeKuita Sayenzi neInjiniya: Kudzidza Kudzidza (Kurume 28, 1995) Dudziro: Chitsauko 1
2. "Nheyo dzeDhijitari (Discrete) Revolution" (Kurume 30, 1995) Chitsauko 2. Zvinokosha zve digital (discrete) revolution
3. "Nhoroondo yeKombuta - Hardware" (Kurume 31, 1995) Chitsauko 3. History of Computers - Hardware
4. "Nhoroondo yeMakomputa - Software" (Kubvumbi 4, 1995) Chitsauko 4. History of Computers - Software
5. "Nhoroondo yeMakomputa - Zvikumbiro" (Kubvumbi 6, 1995) Chitsauko 5: Nhoroondo Yemakombuta - Inoshanda Zvishandiso
6. "Artificial Intelligence - Chikamu I" (Kubvumbi 7, 1995) Chitsauko 6. Artificial Intelligence - 1
7. "Artificial Intelligence - Chikamu II" (Kubvumbi 11, 1995) Chitsauko 7. Artificial Intelligence - II
8. "Artificial Intelligence III" (Kubvumbi 13, 1995) Chitsauko 8. Artificial Intelligence-III
9. "n-Dimensional Space" (Kubvumbi 14, 1995) Chitsauko 9. N-dimensional nzvimbo
10. "Coding Theory - The Representation of Information, Part I" (Kubvumbi 18, 1995) Chitsauko 10. Coding Theory - I
11. "Coding Theory - The Representation of Information, Part II" (Kubvumbi 20, 1995) Chitsauko 11. Coding Theory - II
12. "Kukanganisa-Kururamisa Makodhi" (Kubvumbi 21, 1995) Chitsauko 12. Makodhi Error Correction
13. "Information Theory" (Kubvumbi 25, 1995) Chitsauko 13. Ruzivo rwedzidziso
14. "Digital Filters, Chikamu I" (Kubvumbi 27, 1995) Chitsauko 14. Digital Filters - 1
15. "Digital Filters, Chikamu II" (Kubvumbi 28, 1995) Chitsauko 15. Digital Filters - 2
16. "Digital Filters, Chikamu III" (Chivabvu 2, 1995) Chitsauko 16. Digital Filters - 3
17. "Digital Filters, Chikamu IV" (Chivabvu 4, 1995) Chitsauko 17. Digital Filters - IV
18. "Simulation, Chikamu I" (May 5, 1995) Chitsauko 18. Modelling - I
19. "Simulation, Chikamu II" (Chivabvu 9, 1995) Chitsauko 19. Modelling - II
20. "Simulation, Chikamu III" (Chivabvu 11, 1995) Chitsauko 20. Modelling - III
21. "Fiber Optics" (Chivabvu 12, 1995) Chitsauko 21. Fiber optics
22. "Computer Aided Instruction" (Chivabvu 16, 1995) Chitsauko 22: Computer Assisted Instruction (CAI)
23. "Masvomhu" (Chivabvu 18, 1995) Chitsauko 23. Masvomhu
24. "Quantum Mechanics" (Chivabvu 19, 1995) Chitsauko 24. Quantum mechanics
25. "Kusika" (May 23, 1995). Shanduro: Chitsauko 25. Creativity
26. "Nyanzvi" (Chivabvu 25, 1995) Chapter 26. Nyanzvi
27. "Data Risingavimbike" (Chivabvu 26, 1995) Chitsauko 27. Data isina kuvimbika
28. "Systems Engineering" (Chivabvu 30, 1995) Chitsauko 28. Systems Engineering
29. "Iwe Unowana Zvaunoyera" (June 1, 1995) Chitsauko 29: Iwe unowana zvaunoyera
30. "Tinoziva Sei Zvatinoziva" (June 2, 1995) shandura muzvikamu zvemaminitsi gumi
31. Hamming, "Iwe uye Tsvakurudzo Yako" (June 6, 1995). Dudziro: Iwe nebasa rako

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