Richard Hamming. "Chitsauko Chisipo": Maziviro Atinoita Zvatinoziva (yakazara shanduro)


(Kune avo vakatoverenga zvikamu zvakapfuura zveshanduro yehurukuro iyi, dzokera ku nguva kodhi 20:10)

[Hamming inotaura zvisinganzwisisike munzvimbo, saka kana uine chero mazano ekuvandudza dudziro yezvimedu zvega, ndapota nyora mune yako meseji.]

Hurukuro iyi yanga isiri pahurongwa, asi yaifanira kuwedzerwa kudzivirira hwindo pakati pemakirasi. Hurukuro yacho ndeye maziviro atinoita zvatinoziva, kana, chokwadi, tichizviziva. Nyaya iyi ndeyekare senguva - yakakurukurwa kwemakore 4000 apfuura, kana kwete. Muhuzivi, izwi rakakosha rakagadzirwa kuti riratidze - epistemology, kana sainzi yeruzivo.

Ndinoda kutanga nemadzinza ekare ekare. Zvakakosha kuziva kuti mune imwe neimwe yadzo maive nenhema pamusoro pekusikwa kwenyika. Maererano nechimwe chitendero chekare cheJapan, mumwe munhu aimutsa madhaka, kubva pamapako ezvitsuwa zvakabuda. Mamwe marudzi aivawo nengano dzakafanana: somuenzaniso, vaIsraeri vaidavira kuti Mwari akasika nyika kwemazuva matanhatu, achibva azoneta ndokupedza kusika. Idzi ngano dzese dzakafanana - kunyangwe zvirongwa zvavo zvakasiyana, vese vanoedza kutsanangura kuti sei nyika ino iripo. Ndichadaidza nzira iyi yedzidziso yebhaibheri nekuti haibatanidzi tsananguro kunze kwekuti “yakaitika nekuda kwevamwari; vakaita zvavaifunga kuti zvakakodzera, uye ndiwo masikirwo akaita nyika.”

Munenge muzana remakore rechitanhatu BC. e. Vazivi veGreece yekare vakatanga kubvunza mibvunzo yakananga - kuti nyika ino inei, ndezvipi zvikamu zvayo, uye zvakare vakaedza kutaura navo zvine musoro pane zvebhaibheri. Sezvinozivikanwa, vakasimbisa zvinhu: pasi, moto, mvura nemhepo; vaiva nedzimwe pfungwa nezvitendero zvakawanda, uye zvishoma nezvishoma asi zvechokwadi zvose izvi zvakashandurwa kuva pfungwa dzedu dzemazuva ano dzezvatinoziva. Zvisinei, nyaya iyi yakavhiringidza vanhu munguva yose, uye kunyange vaGiriki vekare vakashamisika kuti vaiziva sei zvavaiziva.

Sezvaunorangarira kubva mukukurukura kwedu masvomhu, vaGiriki vekare vaidavira kuti geometry, uko masvomhu avo akanga akaganhurirwa, yakanga iri zivo yakavimbika uye isingarambiki chose chose. Zvisinei, seizvo Maurice Kline, munyori webhuku rinonzi “Mathematics,” akaratidzira. Kurasikirwa nechokwadi,” uko nyanzvi dzakawanda dzemasvomhu dzaizobvuma, hakuna chokwadi chipi nechipi mumasvomhu. Masvomhu inopa chete kuenderana kwakapihwa yakatarwa seti yemitemo yekufunga. Kana iwe ukashandura iyi mitemo kana fungidziro inoshandiswa, masvomhu achave akasiyana zvakanyanya. Hapana chokwadi chakakwana, kunze kweMitemo Gumi (kana uri muKristu), asi, maiwe, hapana chine chekuita nenyaya yehurukuro yedu. Hazvinakidze.

Asi iwe unogona kushandisa dzimwe nzira uye kuwana mhedziso dzakasiyana. Descartes, achifunga nezvekufungidzira kwevazivi vakawanda pamberi pake, akatora danho shure ndokubvunza mubvunzo: "Ndingave nechokwadi zvishoma sei?"; Semhinduro, akasarudza kutaura kwokuti “Ndinofunga, naizvozvo ndiri.” Kubva mukutaura uku akaedza kuwana huzivi uye kuwana ruzivo rwakawanda. Uzivi uhwu hwakanga husina kunyatsotsigirwa, saka hatina kumbowana ruzivo. Kant akapokana kuti munhu wese anozvarwa aine ruzivo rwakasimba rweEuclidean geometry, nezvimwe zvakasiyana-siyana, zvinoreva kuti kune ruzivo rwekuzvarwa narwo rwunopihwa, kana uchida, naMwari. Nehurombo, Kant paainyora pfungwa dzake, nyanzvi dzemasvomhu dzaigadzira dzisiri dzeEuclidean geometries dzaingoenderana senge prototype yavo. Zvinoitika kuti Kant aikanda mazwi kumhepo, kungofanana nemunhu wese akaedza kufunga kuti anoziva sei zvaanoziva.

Iyi inyaya inokosha, nokuti sayenzi inogara yakashandurwa kune inosimbisa: iwe unogona kazhinji kunzwa kuti sainzi yakaratidza izvi, zvichiratidza kuti zvichave seizvi; tinoziva izvi, tinoziva izvo - asi isu tinoziva here? Une chokwadi here? Ndichatarisa mibvunzo iyi zvakadzama. Ngatiyeukei mutemo kubva kune biology: ontogeny inodzokorora phylogeny. Zvinoreva kuti kukura kwemunhu, kubva pazai rakasangana nembeu kusvika kumudzidzi, zvine hurongwa kunodzokorora muitiro wose wekare wemhindumupindu. Nokudaro, masayendisiti anopikisa kuti panguva yekukura kwe embryonic, gill slits inooneka uye inonyangarika zvakare, uye saka vanofunga kuti madzitateguru edu ari kure aiva hove.

Zvinonzwika zvakanaka kana ukasafunga nezvazvo zvakanyanya. Izvi zvinopa zano rakanaka rekuti evolution inoshanda sei, kana uchitenda. Asi ini ndichaenda mberi zvishoma ndobvunza: vana vanodzidza sei? Vanowana sei zivo? Zvichida vanoberekwa vaine ruzivo rwakafanorongwa, asi izvozvo zvinonzwika kuremara zvishoma. Kutaura chokwadi, zvakanyanya kusagutsikana.

Saka vana vanoita sei? Vane mamwe masikirwo, vachiteerera izvo, vana vanotanga kuita manzwi. Vanoita manzwi ese aya atinowanzo kudaidza kuti kubvotomoka, uye kutaura uku kunenge kusingaenderane nekuti mwana anozvarirwa kupi - kuChina, Russia, England kana America, vana vanongobwairawo saizvozvo. Nekudaro, kubhuroka kuchakura zvakasiyana zvichienderana nenyika. Somuenzaniso, kana mwana wokuRussia akataura shoko rokuti “mama” kakawanda, anogamuchira mhinduro yakanaka uye nokudaro anodzokorora manzwi aya. Kuburikidza neruzivo, anoona kuti ndezvipi zvinonzwika zvinobatsira kuita zvaanoda uye izvo zvisingaite, uye nekudaro anodzidza zvinhu zvakawanda.

Rega ndikuyeuchidze zvandambotaura kakawanda - hapana izwi rekutanga muduramazwi; izwi rimwe nerimwe rinotsanangurwa kuburikidza nemamwe, zvinoreva kuti duramazwi rine denderedzwa. Nenzira imwecheteyo, kana mwana akaedza kugadzira kutevedzana kwakabatana kwezvinhu, ane dambudziko rekusangana nekusawirirana kwaanofanira kugadzirisa, sezvo pasina chinhu chekutanga chekuti mwana adzidze, uye "amai" haashande nguva dzose. Kuvhiringidzika kunomuka, semuenzaniso, sezvandicharatidza zvino. Heino joke rakakurumbira reAmerica:

mazwi erwiyo runozivikanwa ( nerufaro muchinjikwa ndichatakura, nemufaro kutakura muchinjikwa wako)
uye manzwire azvinoita vana (nomufaro bere rakachinjika, nerufaro bere rakachinjika)

(MuchiRussian: violin-fox/creak of a vhiri, ini ndiri kudonha emerald/cores emerald yakachena, kana iwe uchida bhuru plums/kana uchida kufara, bvisa shit-dhongi yako/ nhanho zana kumashure.)

Ndakavawo nezvinetso zvakadaro, kwete muichi chinoitika chaicho, asi pane zvinoitika zvinoverengeka muupenyu hwangu izvo ndaigona kuyeuka apo ndaifunga kuti zvandairava nokutaura zvimwe zvakanga zvakarurama, asi avo vakandipoteredza, zvikurukuru vabereki vangu, vakanzwisisa chimwe chinhu. .. izvo zvakasiyana zvachose.

Pano iwe unogona kuona zvikanganiso zvakakomba uye zvakare kuona kuti zvinoitika sei. Mwana akatarisana nekudikanwa kwekuita fungidziro pamusoro pezvinoreva mazwi mumutauro uye zvishoma nezvishoma anodzidza sarudzo dzakakodzera. Zvisinei, kugadzirisa zvikanganiso zvakadaro zvinogona kutora nguva yakareba. Hazvibviri kuva nechokwadi chokuti vakaruramiswa zvakakwana kunyange iye zvino.

Unogona kuenda kure usinganzwisise zvauri kuita. Ndakatotaura nezve shamwari yangu, chiremba wemasvomhu kubva kuHarvard University. Paakapedza kudzidza kuHarvard, akati aigona kuverenga zvakatorwa netsanangudzo, asi haanyatso kuzvinzwisisa, anongoziva maitirwo acho. Izvi ndezvechokwadi kune zvakawanda zvatinoita. Kuti tichovha bhasikoro, skateboard, kushambira, nezvimwe zvinhu zvakawanda, hatifaniri kuziva maitirwo azvo. Zvinoita sokuti zivo yakawanda kupfuura inogona kutaurwa nemashoko. Ndinozeza kutaura kuti hauzivi kuchovha bhasikoro, nyangwe usingakwanise kundiudza kuti sei, asi unokwira pamberi pangu pavhiri rimwe chete. Nokudaro, zivo inogona kuva yakasiyana zvikuru.

Ngatimbopfupisa zvishoma zvandataura. Kune vanhu vanotenda kuti tine ruzivo rwekuzvarwa narwo; Kana ukatarira mugariro wacho chose chose, ungabvumirana naikoku, uchirangarira, somuenzaniso, kuti vana vane kombamiro yomuzvarirwo yokutaura manzwi. Kana mwana akaberekerwa kuChina, achadzidza kududzira manzwi akawanda kuti aite zvaanoda. Kana akaberekerwa muRussia, achaitawo manzwi akawanda. Kana akaberekerwa muAmerica, acharamba achiita manzwi akawanda. Mutauro pachawo hauna kukosha zvakanyanya pano.

Kune rumwe rutivi, mwana ane mano okuberekwa nawo okudzidza mutauro upi noupi, kungofanana nemimwewo zvayo. Anoyeuka kutevedzana kwemanzwi uye anoona zvaari kureva. Iye anofanira kuisa revo muaya manzwi amene, sezvo pasina rutivi rwokutanga rwaaigona kuyeuka. Ratidza mwana wako bhiza womubvunza kuti: “Shoko rokuti “bhiza” ndiro zita rebhiza here? Kana kuti izvi zvinoreva kuti ane makumbo mana? Zvichida iri ndiro ruvara rwake? Kana ukaedza kuudza mwana kuti bhiza chii nokuriratidza, mwana wacho haakwanisi kupindura mubvunzo iwoyo, asi ndizvo zvauri kureva. Mwana haazive kuti oisa izwi iri muchikamu chipi. Kana, semuenzaniso, tora izwi rechiito "kumhanya." Inogona kushandiswa paunenge uchifamba nekukurumidza, asi iwe unogona zvakare kutaura kuti mavara ari pahembe yako apera mushure mekugeza, kana kunyunyuta pamusoro pekumhanya kwewachi.

Mwana anosangana nematambudziko makuru, asi nokukurumidza kana kuti gare gare anogadzirisa zvikanganiso zvake, achibvuma kuti akanzwisisa chimwe chinhu chisina kururama. Nokufamba kwemakore, vana vanova vashoma uye vasingachakwanisi kuita izvi, uye kana vakura zvakakwana, havachagoni kuchinja. Zviri pachena kuti vanhu vanogona kukanganisa. Rangarira, somuenzaniso, avo vanodavira kuti iye Napoleon. Hazvina mhosva kuti ufakazi hwakawanda sei hwaunopa kumunhu akadaro kuti izvi hazvina kudaro, acharamba achitenda mazviri. Munoziva, kune vanhu vakawanda vane zvitendero zvakasimba zvausingabvumirani nazvo. Sezvo ungadavira kuti zvitendero zvavo zvinopenga, kutaura kuti kune nzira yechokwadi yokuwana nayo zivo itsva hakusi kwechokwadi chose chose. Iwe uchati kune izvi: "Asi sainzi yakanaka kwazvo!" Ngatitarisei nzira yesainzi uye tione kana ichi chiri chokwadi.

Kutenda kuna Sergei Klimov neshanduro.

10-43: Mumwe munhu anoti: “Musayendisiti anoziva sayenzi sezvinoita hove inoziva hydrodynamics.” Hapana tsanangudzo yeScience pano. Ndakaona (ndinofunga ndakambokuudza izvi) kumwe kusekondari vadzidzisi vakasiyana vaindiudza nezvezvidzidzo zvakasiyana uye ndaigona kuona kuti vadzidzisi vakasiyana vaitaura nezvezvidzidzo zvakafanana nenzira dzakasiyana. Uyezve, panguva imwe chete ndakatarisa zvatakanga tichiita uye chaiva chimwe chinhu chakasiyana zvakare.

Iye zvino, iwe wakamboti, "tinoita zviedzo, iwe unotarisa data uye gadzira dzidziso." Izvi zvinogona kunge zvisina musoro. Usati watora data raunoda, iwe unofanirwa kuve uine dzidziso. Iwe haugone kungounganidza isina kurongeka seti yedata: mavara ari mukamuri ino, mhando yeshiri yaunoona inotevera, nezvimwe, uye tarisira kuti itakure zvimwe zvazvinoreva. Iwe unofanirwa kuve neimwe dzidziso usati watora data. Uyezve, haugone kududzira mhedzisiro yezviyedzo zvaunogona kuita kana iwe usina dzidziso. Miedzo idzidziso dzakaenda kure kubva kwekutanga kusvika kwekupedzisira. Une mafungiro ekare uye unofanira kududzira zviitiko uchifunga izvozvo.

Iwe unowana huwandu hukuru hwekufungidzira kubva ku cosmogony. Madzinza ekare anotaura nyaya dzakasiyana-siyana dzakatenderedza moto, uye vana vanodzinzwa uye vanodzidza tsika netsika (Ethos). Kana iwe uri musangano rakakura, unodzidza mitemo yemaitiro zvakanyanya nekuona vamwe vanhu vachizvibata. Sezvaunokura, haugone kumira nguva dzose. Ndinofunga kuti kana ndikatarisa madzimai ezera rangu, ndinoona kapfungwa kekuti madhirezi akanga ari mufashoni mazuva apo madzimai aya ari kukoreji. Ndinogona kunge ndichizvinyengera, asi ndizvo zvandinofunga kufunga. Mese makaona maHippies ekare achiri kupfeka uye kuita sezvavaiita panguva iyo hunhu hwavo hwakaumbwa. Zvinoshamisa kuti unowana sei nenzira iyi uye hautombozvizivi, uye zvakaoma sei kuti chembere dzisununguke uye dzisiye tsika dzadzo, dzichiziva kuti havachatenderwi maitiro.

Zivo chinhu chine ngozi zvikuru. Zvinouya nerusaruro rwese rwawakambonzwa. Somuenzaniso, une rusaruro rwokuti A anotangira B uye A ndiye anokonzera B. Okay. Zuva rinogara richitevera usiku. Usiku ndicho chikonzero chemasikati here? Kana kuti masikati ndiwo anokonzera usiku here? Aihwa. Uye mumwe muenzaniso wandinoda chaizvo. Poto'mac Rwizi mazinga anowirirana zvakanyanya nehuwandu hwekufona. Nhare dzenhare dzinoita kuti mvura ikwire saka tinogumbuka. Kufona hakukonzerese kuti nzizi dzikwire. Mvura iri kunaya uye nechikonzero ichi vanhu vanodaidza tekisi nguva zhinji uye nekuda kwezvimwe zvikonzero, semuenzaniso, kuzivisa vadikani kuti nekuda kwekunaya kwemvura vanozononoka kana zvimwe zvakadaro, uye mvura inoita kuti rwizi rwuyerere. simuka.

Pfungwa yekuti unogona kutaura chikonzero nemhedzisiro nekuti imwe inouya pamberi peimwe inogona kunge isiriyo. Izvi zvinoda kuchenjerera mukuongorora kwako uye kufunga kwako uye zvinogona kukutungamira iwe munzira isiriyo.

Munguva yeprehistoric nguva, vanhu sezviri pachena vairatidzira miti, nzizi nematombo, zvese nekuti vaisakwanisa kutsanangura zviitiko zvakaitika. Asi Mweya, munoona, ine rusununguko rwokusarudza, uye nenzira iyi zvaiitika zvaitsanangurwa. Asi nekufamba kwenguva takaedza kuganhurira midzimu. Kana iwe wakaita mhepo inodiwa ichipfuura nemaoko ako, zvino midzimu yakaita ichi neicho. Kana iwe ukakanda zvitsinga zvakanaka, mweya wemuti uchaita ichi neicho uye zvese zvinozvidzokorora. Kana kuti iwe wakadyara mukati memwedzi wakakwana, kukohwa kuchava nani kana chimwe chinhu chakadaro.

Zvichida pfungwa idzi dzichiri kuremedza zvitendero zvedu. Tine zvakawanda zvavo. Isu tinoita zvakanaka nevamwari kana vamwari vanotipa zvikomborero zvatinokumbira, chero, chokwadika, kuti tinoita zvakanaka nevatinoda. Nokudaro, vamwari vazhinji vekare vakava Mwari Mumwe, pasinei zvapo neidi rokuti kuna Mwari wechiKristu, Allah, Buddha mumwe, kunyange zvazvo zvino vane nhevedzano yavaBuddha. Zvizhinji kana zvishoma zvaro zvakabatanidzwa kuva Mwari mumwe, asi tichine mashiripiti mazhinji akatipoteredza. Tine mashiripiti mazhinji muchimiro chemazwi. Somuenzaniso, une mwanakomana anonzi Charles. Munoziva, ukamira uchifunga, Charles haasi mwana wacho. Charles izita remwana, asi hazvina kufanana. Nekudaro, kazhinji mashiripiti akasviba akabatana nekushandiswa kwezita. Ndinonyora zita romumwe munhu ndoripisa kana kuita chimwe chinhu, uye rinofanira kuva nezvarinoita pamunhu wacho neimwe nzira.

Kana kuti tine mashiripiti anonzwira tsitsi, apo chimwe chinhu chinotaridzika chakafanana kune chimwe, uye kana ndikachitora ndikachidya, zvimwe zvinhu zvichaitika. Yakawanda yemishonga mumazuva ekutanga yaive homeopathy. Kana chimwe chinhu chichitaridzika zvakafanana kune chimwe, chichaita zvakasiyana. Zvakanaka, iwe unoziva izvo hazvishande zvakanyanya.

Ndakadudza Kant, uyo akanyora bhuku rose, The Critique of Pure Reason, iro akaita nevhoriyamu huru, gobvu mumutauro wakaoma kunzwisisa, pamusoro pemaziviro atinoita zvatinoziva uye kuti tinofuratira sei nhau yacho. Handifungi kuti idzidziso yakakurumbira pamusoro pekuti ungave sei nechokwadi chechinhu chipi nechipi. Ndichapa muenzaniso wenhaurirano yandakashandisa kakawanda apo mumwe munhu anoti ane chokwadi chechimwe chinhu:

- Ndiri kuona kuti une chokwadi?
- Pasina kusava nechokwadi.
- Hapana mubvunzo, zvakanaka. Tinogona kunyora pasi papepa kuti kana iwe usina kururama, chokutanga, iwe uchapa mari yako yose uye, chechipiri, iwe uchazviuraya.

Kamwe kamwe, havadi kuzviita. Ndinoti: asi wanga uine chokwadi! Vanotanga kutaura zvisina maturo ndofunga munoona chikonzero. Kana ndikabvunza chimwe chinhu chawanga uine chokwadi nacho, wobva wati, "Zvakanaka, zvakanaka, pamwe handisi 100% chokwadi."
Unoziva mapoka ezvitendero akati kuti anofunga kuti mugumo wava pedyo. Vanotengesa zvinhu zvavo zvose voenda kumakomo, uye nyika inoramba iripo, vanodzoka votanga patsva. Izvi zvakaitika kakawanda uye kakawanda muupenyu hwangu. Mapoka akasiyana siyana akaita izvi aive nechokwadi chekuti nyika yave kusvika kumagumo uye izvi hazvina kuitika. Ndinoedza kukupwisa kuti zivo yakakwana haipo.

Ngatinyatsoongororai zvinoita sainzi. Ndakakuudza kuti, chokwadi, usati watanga kuyera iwe unofanirwa kugadzira dzidziso. Ngationei kuti zvinoshanda sei. Mimwe miedzo inoitwa uye mimwe mibairo inowanikwa. Sainzi inoedza kugadzira dzidziso, kazhinji iri muchimiro chefomula, inovhara nyaya idzi. Asi hapana kana chimwe chezvazvino mhedzisiro chinogona kuvimbisa chinotevera.

Mumasvomhu kune chimwe chinhu chinonzi mathematical induction, iyo, kana ukaita fungidziro dzakawanda, inokubvumira kuratidza kuti chimwe chiitiko chichagara chichiitika. Asi kutanga iwe unofanirwa kubvuma akawanda akasiyana ane musoro uye mamwe fungidziro. Hongu, nyanzvi dzemasvomhu dzinogona, mumamiriro ezvinhu aya ekugadzira zvakanyanya, kuratidza huchokwadi hwenhamba dzese dzechisikigo, asi haugone kutarisira kuti nyanzvi yefizikisi igone kuratidza kuti izvi zvinogara zvichiitika. Hazvina mhosva kuti kangani iwe ukadonhedza bhora, hapana vimbiso yekuti iwe uchaziva chinotevera chinhu chemuviri chaunodonhedza zviri nani pane chekupedzisira. Kana ndikabata chibharumu ndikachisunungura, chinobhururuka chichikwira. Asi iwe unobva wangove nealibi: "Ah, asi zvese zvinodonha kunze kweizvi. Uye iwe unofanirwa kuita kusarudzika kune ichi chinhu.

Sayenzi izere nemienzaniso yakafanana. Uye iri idambudziko rine miganhu isiri nyore kutsanangura.

Zvino zvataedza nekuyedza izvo zvaunoziva, takatarisana nekudiwa kwekushandisa mazwi kutsanangura. Uye mashoko aya anogona kuva nezvaanoreva zvakasiyana neawaunoapa nawo. Vanhu vakasiyana vanogona kushandisa mazwi mamwechete ane zvirevo zvakasiyana. Imwe nzira yokubvisa nayo kusanzwisisana kwakadaro ndeyokuti mune vanhu vaviri murabhoritari vachiitirana nharo pamusoro peimwe nyaya. Kusanzwisisa kunovamisa uye kuvamanikidza kuti vanyatsojekesa zvavanoreva kana vachitaura nezvezvinhu zvakasiyana. Kazhinji ungawana kuti havarevi chinhu chimwe chete.

Vanokakavadzana pamusoro pekududzira kwakasiyana. Nharo inobva yaenda kune zvinorehwa izvi. Mushure mekujekesa zvinorehwa nemashoko, iwe unonzwisisana zviri nani, uye iwe unogona kukakavadzana pamusoro pezvinoreva - hongu, kuedza kunotaura chinhu chimwe kana iwe uchinzwisisa nenzira iyi, kana kuedza kunotaura imwe kana iwe uchinzwisisa neimwe nzira.

Asi wakangonzwisisa mazwi maviri chete ipapo. Mazwi anotishandira zvisina kunaka.

Kutenda kuna Artem Nikitin neshanduro


20:10… Mitauro yedu, sekuziva kwangu, yose inosimbisa “hongu” na “kwete,” “dema” na “chena,” “chokwadi” uye “nhema.” Asi pane zvakare zvinoreva goridhe. Vamwe vanhu varefu, vamwe vapfupi, uye vamwe vari pakati pevarefu nevapfupi, i.e. nokuti mamwe anogona kuva akakwirira, uye zvimwewo. Ivo vari pakati nepakati. Mitauro yedu yakaoma zvekuti tinowanzo kukakavara pamusoro pezvinoreva mazwi. Izvi zvinotungamirira kuchinetso chokufunga.
Kwaive nevazivi vaipikisa kuti unongofunga nemazwi chete. Nokudaro, kune maduramazwi anotsanangura, anozivikanwa kwatiri kubva pauduku, ane zvinoreva zvakasiyana-siyana zvemashoko mamwe chete. Uye ndinofungidzira kuti munhu wese ave neruzivo rwekuti kana uchidzidza ruzivo rutsva, haugone kutaura chimwe chinhu mumashoko (haukwanise kuwana mazwi akakodzera ekutaura). Isu hatinyatso funga mumashoko, tinongoedza kuita, uye izvo chaizvo zvinoitika ndizvo zvinoitika.

Ngatiti wanga uri pazororo. Unouya kumba woudza mumwe munhu nezvazvo. Zvishoma nezvishoma, zororo rawakatora rinova chinhu chaunotaura kune mumwe munhu. Mazwi, sekutonga, anotsiva chiitiko uye chando.
Rimwe zuva, ndiri pazororo, ndakataura navanhu vaviri vandakaudza zita rangu nekero, uye ini navadzimai vangu takaenda kunotenga, ipapo takaenda kumba, uye ipapo, pasina kukurukura nomunhu upi noupi, ndakanyora pasi sezvandaigona. zvakaitika zviitiko nhasi. Ndakanyora zvese zvandaifunga uye ndakatarisa mazwi akave chiitiko. Ndakaedza nepese pandaigona kuti chiitiko chitore mazwi. Nekuti ini ndinonyatsoziva nguva iyoyo kana iwe uchida kutaura chimwe chinhu, asi usingawane mazwi akakodzera. Zvinoita sekuti zvese zviri kuitika sezvandakataura, kuti zororo rako riri kuita sekutsanangurwa kwazvinoitwa mumashoko. Zvakawanda kupfuura zvaungave uine chokwadi. Dzimwe nguva unofanira kubhuya pamusoro pehurukuro pachayo.

Chimwe chinhu chakabuda mubhuku pamusoro pe quantum mechanics ndechokuti kunyange kana ndine boka re data yesayenzi, vanogona kuva netsanangudzo dzakasiyana zvachose. Kune zvitatu kana zvina zvakasiyana dzidziso dze quantum mechanics izvo zvakawanda kana zvishoma zvinotsanangura chiitiko chimwe chete. Sezvakangoita isiri-Euclidean geometry uye Euclidean geometry inodzidza chinhu chimwe chete asi inoshandiswa nenzira dzakasiyana. Iko hakuna nzira yekuwana yakasarudzika dzidziso kubva kune seti yedata. Uye nekuti iyo data inopera, iwe wakanamatira pairi. Iwe hauzove nedzidziso iyi yakasiyana. Never. Kana kune ese 1+1=2, saka kutaura kwakafanana mukodhi yeHamming (iyo inonyanya kuzivikanwa yekutanga yekuzviongorora uye yekuzvigadzirisa macode) ichave 1+1=0. Hapana ruzivo rwechokwadi rwaungada kuva narwo.

Ngatitaurei nezvaGalileo (mufizikisi wekuItaly, makanika, nyanzvi yenyeredzi yezana ramakore rechi XNUMX), uyo akatanga naye quantum mechanics. Aifungidzira kuti mitumbi inodonha inowira nenzira imwe chete, pasinei nokuti inokurumidza kukurumidza sei, kukwesha kusingachinji, uye simba remhepo. Izvo zvakanaka, muvacuum, zvese zvinowira nekumhanya kwakafanana. Ko kana mumwe muviri ukabata mumwe pakudonha. Vachadonha nespeed imwechete here nekuti vava vamwe? Kana kubata kusingaverengeki, ko kana mitumbi yakasungwa netambo? Miviri miviri yakabatanidzwa netambo inodonha semurenga mumwe here kana kuti icharamba ichidonha semirwi miviri yakasiyana? Zvakadini kana miviri yakasungwa kwete netambo, asi netambo? Ko kana vakanamirana? Ndirini apo miviri miviri inganzi muviri mumwe? Uye mutumbi uyu unodonha nespidhi ipi? Patinowedzera kufunga nezvazvo, ndipo patinogadzira mibvunzo "yeupenzi" zvakanyanya. Galileo akati: “Miviri yose ichawira pasi pamwero wakafanana, kana zvisina kudaro, ndichabvunza mubvunzo “webenzi”, miviri iyi inoziva sei kuti inorema sei? Pamberi pake, zvaitendwa kuti miviri inorema inowira nokukurumidza, asi akakakavara kuti kukurumidza kwekudonha hakubvi pahuwandu uye zvinhu. Gare gare tichaona nekuedza kuti anga ari mugwara, asi hatizive kuti sei. Uyu mutemo waGalileo, muchokwadi, haunganzi mutemo wenyama, asi wekutaura-unonzwisisika. Izvo zvinobva pakuti haudi kubvunza mubvunzo, "Ndeipi miviri miviri imwe?" Hazvinei kuti miviri inorema zvakadii chero ingangonzi muviri mumwe chete. Ngokudaro, vanozowe ngekumhanya kwakafanana.

Kana iwe ukaverenga zvechinyakare mabasa pamusoro pehukama, uchaona kuti kune yakawanda yedzidziso yebhaibheri uye idiki yeinonzi chaiyo sainzi. Sezvineiwo zvakadaro. Sayenzi chinhu chinoshamisa kwazvo, chisingadi kutaura!

Sezvandakataura muhurukuro nezve mafirita edhijitari, tinogara tichiona zvinhu kuburikidza ne "hwindo". Hwindo haisi pfungwa yenyama chete, asiwo yehungwaru, iyo yatino "kuona" zvimwe zvinoreva. Isu tinogumira kuona mamwe mazano chete, uye saka isu takamira. Nekudaro, isu tinonzwisisa zvakanaka kuti izvi zvingave sei. Zvakanaka, ndinofungidzira maitiro ekutenda zvinogona kuitwa nesainzi kwakafanana nemwana ari kudzidza mutauro. Mwana anoita fungidziro pamusoro pezvaanenge anzwa, asi anozogadzirisa uye anowana dzimwe mhedziso (akanyorwa pabhodhi: “Ndinofara muchinjikwa ndingatakura/Ndinofara, bere rakachinjika.” Pun: se“Takura muchinjikwa wangu/Nemufaro , bere duku”) . Tinoedza zvimwe zviedzo, uye kana zvikasashanda, tinoita dudziro yakasiyana yezvatinoona. Sezvinongoita mwana anonzwisisa hupenyu hwakangwara uye mutauro waari kudzidza. Zvakare, vaongorori, vane mukurumbira mudzidziso nefizikisi, vakabata imwe pfungwa inotsanangura chimwe chinhu, asi haina kuvimbiswa kuti ichokwadi. Ndiri kuisa pamberi penyu chokwadi chiri pachena, dzidziso dzese dzataive nadzo musainzi dzakashanduka dzisiridzo. Takavatsiva nedzidziso dzazvino uno. Zvine musoro kufunga kuti tave kuuya kuzoongororazve sainzi yese. Zvakaoma kufungidzira kuti dzinenge dzidziso dzese dzatiinadzo parizvino dzinenge dziri dzenhema neimwe nzira. Mupfungwa yekuti classical mechanics yakave yenhema kana ichienzaniswa nequantum mechanics, asi paavhareji nhanho yatakaedza, ingangove ndiyo yakanakisa chishandiso chatiinacho. Asi maonero edu ehuzivi ezvinhu akasiyana zvachose. Saka tiri kufambira mberi zvinoshamisa. Asi pane chimwe chinhu chisingafungirwe uye icho chine musoro, nekuti iwe hauna kupihwa zvakawanda zvine musoro.

Ndinofunga ndakakuudza kuti avhareji yemasvomhu anowana PhD yake nekukurumidza anoona kuti anofanirwa kunatsiridza humbowo hweiyo thesis yake. Semuenzaniso, izvi ndizvo zvakaitika kuna Gauss uye humbowo hwake hwemudzi wepolynomial. Uye Gauss aive nyanzvi yemasvomhu. Tiri kusimudza mwero wekuomarara muhumbowo. Maonero edu kune kuomarara ari kuchinja. Tave kutanga kuona kuti logic haisi iyo yakachengeteka yataifunga kuti yaive. Pane zvakawanda zvinokanganisa mariri sezviri mune zvimwe zvese. Mitemo yepfungwa ndeye maitiro aunofunga kufunga nenzira yaunoda: "hongu" kana "kwete", "zvimwe-uye-izvo" uye "zvimwe izvo." Hatizi pamahwendefa amabwe akaburutswa naMosesi paGomo reSinai. Isu tiri kuita fungidziro dzinoshanda zvakanaka nguva zhinji, asi kwete nguva dzose. Uye mu quantum mechanics, haugone kutaura nechokwadi kuti zvimedu zvimedu, kana zvimedu mafungu. Panguva imwe chete, zviri zviviri here, kana kuti kwete?

Isu taizofanira kutora nhanho yakapinza kumashure kubva pane zvatiri kuyedza kuwana, asi tichienderera mberi nezvatinofanira. Panguva ino, sainzi inofanirwa kutenda izvi pane dzidziso dzakasimbiswa. Asi marudzi aya ekugadzirisa akareba uye anofinha. Uye vanhu vanonzwisisa nyaya yacho vanonyatsonzwisisa kuti hatiiti uye hatizombofa takaita, asi isu tinogona, semwana, kuva nani uye nani. Nokufamba kwenguva, kubvisa kupesana kwakawanda. Asi mwana uyu achanzwisisa zvakakwana zvose zvaanonzwa uye haazovhiringidziki nazvo here? Aihwa. Tichifunga kuti ingani fungidziro dzinogona kududzirwa nenzira dzakasiyana kwazvo, izvi hazvishamise.

Iye zvino tiri kurarama munguva umo sainzi inotonga nezita, asi chaizvoizvo haisi iyo. Mazhinji mapepanhau nemagazini, anoti Vogue (magazini yefashoni yevakadzi), anoburitsa fungidziro yezvenyeredzi yezviratidzo zvezodhiac mwedzi wega wega. Ndinofunga kuti anenge masayendisiti ose anoramba kuongorora nyeredzi, kunyange panguva imwe chete, isu tose tinoziva kuti Mwedzi unobata sei Pasi, zvichikonzera kupera uye kuyerera kwemafungu.

30:20
Zvisinei, tinopokana kuti mwana achangoberekwa achave neruoko rworudyi kana rworuboshwe, zvichienderana nenzvimbo iri mudenga yenyeredzi iri kure nechiedza kwemakore makumi maviri nemashanu. Kunyangwe takaona kakawanda kuti vanhu vanozvarwa pasi penyeredzi imwe chete vanokura zvakasiyana uye vane mafambiro akasiyana. Saka, hatizivi kana nyeredzi dzichipesvedzera vanhu.

Tine nzanga inovimba zvakanyanya nesainzi nehuinjiniya. Kana kuti zvimwe zvakanyanya kutsamira apo Kennedy (Mutungamiri wechimakumi matatu neshanu weUnited States) akazivisa kuti mukati memakore gumi tinenge tave paMwedzi. Paive nemazano akawanda makuru ekutora imwe chete. Waigona kupa mari kuchechi wonamata. Kana, shandisa mari kumasvikiro. Vanhu vangadai vakagadzira nzira yavo yekuenda kuMwedzi kuburikidza nedzimwe nzira dzakasiyana, dzakadai sepiramidhi (pseudoscience). Senge, ngativake mapiramidhi kuti vashandise simba ravo uye kuzadzisa chinangwa. Asi kwete. Isu tinovimba neinjiniya yakanaka yechinyakare. Hatina kuziva kuti ruzivo rwataifunga kuti tinoruziva, taingofunga kuti tinoziva. Asi damn it, takaenda kumwedzi nekudzoka. Tinotsamira pakubudirira kumwero mukuru zvikuru kupfuura nesayenzi pachayo. Asi hapana chimwe cheizvi chine basa. Tine zvinhu zvakakosha zvekuita kupfuura engineering. Uku ndiko kugara zvakanaka kwevanhu.

Uye nhasi tine nyaya dzakawanda dzekukurukura, dzakadai seUFOs nezvimwe zvakadaro. Ini handisi kutaura kuti CIA yakaronga kuurayiwa kwaKennedy kana kuti hurumende yakabhomba Oklahoma kuti iite kutya. Asi vanhu nguva dzose vanobatirira kuzvitendero zvavo kunyange mukutarisana noufakazi. Tinozviona izvi nguva dzose. Zvino, kusarudza kuti ndiani anoonekwa sechitsotsi uye asiri iye hazvisi nyore.

Ndine mabhuku akati wandei pamusoro pekuparadzanisa sainzi chaiyo kubva kupseudoscience. Isu takararama kuburikidza akati wandei emazuva ano pseudoscientific theories. Isu takasangana nechiitiko che "polywater" (inofungidzira polymerized fomu yemvura inogona kuumbwa nekuda kwezviitiko zvepasi uye ine yakasarudzika yemuviri zvimiro). Isu takasangana nechando chenyukireya fusion (inofungidzirwa mukana wekuita nuclear fusion reaction mumakemikari masisitimu pasina kupisa kwakakosha kwechinhu chinoshanda). Zvikumbiro zvakakura zvinoitwa musainzi, asi chikamu chidiki chete chazvo chiri chokwadi. Muenzaniso unogona kupihwa nehungwaru hwekugadzira. Iwe unogara uchinzwa nezve izvo michina ine artificial intelligence ichaita, asi iwe hauone mhedzisiro. Asi hapana anogona kuvimbisa kuti izvi hazviitiki mangwana. Sezvo ndakaita nharo dzokuti hapana munhu anogona kubvumikisa chinhu chipi nechipi musayenzi, ndinofanira kubvuma kuti ini handigoni kuzvibvumikisa. Handikwanise kana kuratidza kuti hapana chandinogona kuratidza. Idenderedzwa rakashata, handizvo here?

Pane zvirambidzo zvakakura zvekuti tinoona zvisingaite kuti titende chero chinhu, asi isu tinofanirwa kubvumirana nazvo. Kunyanya, nezvandakatodzokorora kwauri kakawanda, uye izvo zvandaratidza ndichishandisa muenzaniso wekukurumidza kushandurwa kweFourier (algorithm yekuverenga komputa kweiyo discrete Fourier shanduko, iyo inoshandiswa zvakanyanya pakugadzirisa masaini uye kuongorora data) . Ndiregerereiwo nekusaziva kwangu, asi ndini ndakatanga kuisa pfungwa pamusoro pezvakanakira. Ndakasvika pamhedziso yekuti "Butterfly" (nhanho yekutanga mukumhanya kweFourier kushandura algorithm) hazvigoneke kuita nemidziyo yandaive nayo (programmable Calculator). Gare gare, ndakarangarira kuti tekinoroji yachinja, uye kune akakosha makomputa andinogona kupedzisa kuita kweiyo algorithm. Kugona kwedu uye ruzivo rwedu zvinogara zvichichinja. Zvatisingakwanisi kuita nhasi, tinogona kuita mangwana, asi panguva imwe chete, kana iwe ukanyatsotarisa, "mangwana" haipo. Mamiriro acho ezvinhu ari paviri.

Ngatidzokerei kusainzi. Kwemakore anenge mazana matatu, kubva muna 1700 kusvika nhasi, sainzi yakatanga kutonga uye kukura mune zvakawanda. Nhasi, hwaro hwesainzi ndiyo inonzi reductionism (iyo methodological musimboti maererano nezvinoitika zvakaoma zvinogona kutsanangurwa zvizere uchishandisa mitemo inovapo mune zviri nyore zviitiko). Ndinogona kupatsanura muviri kuita zvikamu, kuongorora nhengo uye kutora mhedziso pamusoro pese. Ndakambotaura kuti vanhu vakawanda vechitendero vakati, “Hamugoni kukamura Mwari muzvikamu, kudzidza nhengo dzake uye kunzwisisa Mwari.” Uye vatsigiri vepfungwa yeGestalt vakati: “Unofanira kutarira chose chose. Iwe haugone kupatsanura chinhu chose kuita zvidimbu usina kuchiparadza. Zvose zvakawanda kupfuura zvikamu zvaro.

Kana mutemo mumwe uchishandiswa mune rimwe bazi resainzi, saka mutemo mumwechete haugone kushanda muchikamu chebazi rimwechete. Motokari dzine mavhiri matatu hadzishande munzvimbo dzakawanda.

Naizvozvo, tinofanira kurangarira mubvunzo wokuti: “Sayenzi yose ingarangarirwa seinopedza simba zvikuru kupfurikidza nokuvimba nemiuyo inowanwa mumativi makuru here?”

VaGiriki vekare vaifunga nezvepfungwa dzakadai seChokwadi, Runako uye Ruramisiro. Sayenzi yakawedzera chimwe chinhu kupfungwa idzi munguva yose iyi here? Aihwa. Iye zvino hatichina ruzivo rwepfungwa idzi sezvaiitwa nevaGiriki vekare.

Mambo weBhabhironi Hammurabi (akatonga munenge muna 1793-1750 BC) akasiya Bumbiro reMitemo raiva nemutemo wakadaro, somuenzaniso, “Ziso neziso, zino nezino.” Uku kwaive kuedza kuisa Justice mumashoko. Kana tikazvienzanisa nezviri kuitika muLos Angeles (zvinoreva mhirizhonga yemarudzi muna 1992), saka iyi haisi kururamisira, asi mutemo. Hatikwanise kuisa Ruramisiro mumashoko, uye kuedza kuzviita kunongopa pamutemo. Hatikwanisi kuisa Chokwadi mumashoko. Ndinoedza nepandinogona napo kuita izvi muzvidzidzo izvi, asi muchokwadi handikwanise kuzviita. Ndizvo zvimwe chete naBeauty. John Keats (mudetembi wechizvarwa chiduku cheChirungu Romantics) akati: “Runako ichokwadi, uye chokwadi runako, uye ndizvo zvoga zvaunogona kuziva uye zvose zvaunofanira kuziva.” Nyanduri akadoma Chokwadi naRunako sechinhu chimwe chete. Kubva pakuona kwesainzi, tsananguro yakadaro haina kugutsikana. Asi sainzi haipe mhinduro yakajeka zvakare.

Ndinoda kupfupisa hurukuro tisati taenda nenzira dzedu dzakasiyana. Sayenzi haingobudisi zivo yakati yatinoda. Chinetso chedu chikuru ndechokuti tinoda kuva nechimwe chokwadi, saka tinofungidzira kuti tinacho. Kushuvira kufunga ndiko kutukwa kukuru kwemunhu. Ndakaona izvi zvichiitika pandakashanda kuBell Labs. Dzidziso yacho inoita seine musoro, tsvakiridzo inopa tsigiro, asi kumwe kutsvagurudza hakupi humbowo hutsva hwayo. Masayendisiti ari kutanga kufunga kuti vanogona kuita pasina humbowo hutsva hwedzidziso. Uye vakatanga kuvatenda. Uye zvakanyanya, vanongotaura zvakanyanya uye zvakanyanya, uye chishuwo chinoita kuti vatende nesimba ravo rose kuti ichokwadi zvavanotaura. Uyu ndiwo hunhu hwevanhu vese. Unobvuma kuda kutenda. Nokuti unoda kutenda kuti uchawana chokwadi, unopedzisira wava kugara uchichiwana.

Sainzi haina zvakawanda zvokutaura pamusoro pezvinhu zvauri kufunga nezvazvo. Izvi zvinoshanda kwete chete kuChokwadi, Runako uye Ruramisiro, asiwo kune zvimwe zvinhu zvese. Sayenzi inogona chete kuita zvakawanda. Nezuro chaiye ndakaverenga kuti mamwe ma geneticists akawana mamwe mhedzisiro kubva mukutsvagisa kwavo, nepo panguva imwecheteyo, mamwe ma geneticist akagamuchira mhedzisiro inoramba mhedzisiro yekutanga.

Zvino, mazwi mashoma nezve kosi iyi. Yekupedzisira lecture inonzi "Iwe netsvakurudzo yako", asi zvingava nani kungoidana kuti “Iwe Noupenyu Hwako.” Ndinoda kupa hurukuro inoti “Iwe Nekutsvagisa Kwako” nekuti ndapedza makore akawanda ndichidzidza nyaya iyi. Uye neimwe nzira, hurukuro iyi ichave iri pfupiso yekosi yese. Uku kuedza kutsanangura nenzira yakanakisa zvaunofanira kuita zvinotevera. Ndakasvika pamhedziso idzi ndega; hapana akandiudza nezvadzo. Uye pakupedzisira, mushure mokunge ndakuudza zvose zvaunoda kuita uye maitirwo azvo, iwe uchakwanisa kuita zvakawanda uye zviri nani kupfuura zvandakaita. Sara mushe!

Kutenda kuna Tilek Samiev neshanduro.

Ndiani anoda kubatsira kushandura, marongerwo nekutsikiswa kwebhuku - nyora muPM kana email [email inodzivirirwa]

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

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) Zvaitwa, zvese zvaunofanirwa kuita kuzviburitsa
  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

Ndiani anoda kubatsira kushandura, marongerwo nekutsikiswa kwebhuku - nyora muPM kana email [email inodzivirirwa]

Source: www.habr.com

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