{"id":38049,"date":"2026-09-11T02:43:00","date_gmt":"2026-09-11T01:43:00","guid":{"rendered":"https:\/\/catalinx.ro\/wordpress\/?p=38049"},"modified":"2026-09-10T19:31:21","modified_gmt":"2026-09-10T18:31:21","slug":"openai-on-navier-stokes-nu-ne-am-inspirat-dar-nu-putem-nega-ca-ai-ul-nostru-ar-putea-trage-cu-ochiul","status":"publish","type":"post","link":"https:\/\/catalinx.ro\/wordpress\/?p=38049","title":{"rendered":"OpenAI on Navier – Stokes > “Nu ne-am inspirat, dar nu putem nega c\u0103 AI-ul nostru ar putea trage cu ochiul\u201d"},"content":{"rendered":"
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V\u00e2lv\u0103 mare c\u0103 au demonstrat OpenAI o ipotez\u0103 \u00een care ecua\u021biile diferen\u021biale propuse Navier-Stokes care modeleaz\u0103 dinamica fluidelor cu v\u00e2scozitate determin\u0103 o stare de \u201dsingularitate\u201d – \u00een condi\u021biile curgerii tridimensionale a unui fluid.<\/p>\n\n\n\n

Ideea presupus\u0103 era c\u0103 dac\u0103 pornim de la un fluid aflat \u00eentr-o stare de curgere incompresibil\u0103 ( \u201dsmooth\u201d – \u00een englez\u0103 – c\u0103 pe la viteza sunetului apar compresibilit\u0103\u021bi \u00een fluide ) \u00een condi\u021bii rezonabile pentru un fluid – f\u0103r\u0103 energie , sau temperatur\u0103 infinite, doar pe un domeniu semi-infinit – pentru a nu opera cu condi\u021bii de frontier\u0103 ( boundaries), ecua\u021biile conduc \u00eentotdeauna o stare stabil\u0103 neted\u0103 pentru tot orizontul de timp viitor.
Presupunerea asta a r\u0103mas \u00een picioare doar pentru c\u0103 p\u00e2n\u0103 a cum nu a venit nimeni cu un contraexemplu, dar nici nu s-a putut demostra vreodat\u0103 c\u0103 e a\u0219a . Dac\u0103 te pasioneaz\u0103 po\u021bi s\u0103 vezi \u00eencercarea de demonstrare din teza de doctorat<\/a> a lui Ionu\u021b Munteanu , de la facultatea de matematic\u0103 – Universitatea din Ia\u0219i. \u00cencearc\u0103 o demonstra\u021bie pentru o curgere bidimensional\u0103, pe care nu m\u0103 pot l\u0103uda c\u0103 reu\u0219esc s-o urm\u0103resc \u00een detaliu p\u00e2n\u0103 la cap ( am \u00eencercat ), pentru c\u0103 \u00een curgere tridimensional\u0103 te bat ecua\u021biile diferen\u021biale cu pula peste gur\u0103, oricine ai fi.

Ia, deschide gura pentru ecua\u021biile \u00een coordonate sferice, gen forma canonic\u0103.
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S\u0103 le calculeze m\u0103-ta pe \u0103stea, analitic, c\u0103 nici nu le pot copia de la un cap la altul f\u0103r\u0103 s\u0103 gre\u0219esc vreun exponent sau simbol pe undeva. Majoritatea celor care le folosesc \u00een inginerie folosesc metode numerice \u0219i calcul discret, iar \u0103stea sunt foarte utile pentru aplica\u021bii practice , dar nu s\u0103 faci inferin\u021be teoretice sau demonstra\u021bii.

Iar OpenAI, av\u00e2nd creieri electronici f\u0103r\u0103-num\u0103r, au g\u0103sit un set de condi\u021bii care probeaz\u0103 un contraexemplu \u0219i arat\u0103 c\u0103 exist\u0103 parametri cu care po\u021bi porni de la un fluid \u00een stare de curgere incompresibil\u0103 – mai exact ei au folosit un \u201dblow up\u201d ( \u00een rom\u00e2ne\u0219te \u201dumfl\u0103tur\u0103\u201d nu sun\u0103 bine, dar asta este – cred c\u0103 e vorba de o divergen\u021b\u0103 \u00een termeni matematici, sau o neacotare ) – pe care l-au alimentat cu un puls periodic \u0219i ajung la o curgere care nu se stabilizeaz\u0103 \u00een repaus \u00eentr-un oriont de timp viitor ci produce o singularitate – cum ar veni gaura neagr\u0103 a fluidelor. E o singularitate matematic\u0103, dar dovede\u0219te c\u0103 po\u021bi avea condi\u021bii care invalideaz\u0103 ipoteza stabiliz\u0103rii curgerii.
Asta e transformarea pe care o urm\u0103resc ei \u0219i anume \u00eentinderea vortexului p\u00e2n\u0103 la singularitate , care contrasteaz\u0103 clar repausului, sau echilibrului.
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Egalitatea de la care se pleac\u0103 e asta:
Evident c\u0103 po\u021bi ob\u021bine o singularitate \/ blow-up dac\u0103 faci for\u021ba aia infinit\u0103, dar tocmai condi\u021biile impun s\u0103 nu ai energie \/ for\u021b\u0103 infinit\u0103 \u0219i demonstra\u021bia OpenAI<\/strong><\/a> se axeaz\u0103 pe asta, s\u0103 arate c\u0103 for\u021ba dat\u0103 de pulsul \u0103la periodic nu e infinit\u0103 . <\/p>\n\n\n\n

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Acuma, eu am \u00eenceput s\u0103 citesc \u0219i s\u0103 analizez demonstra\u021bia aia \u0219i pe la pagina 20 am realizat c\u0103 folosesc un pic cam multe variabile \/ simboluri \u0219i parametri ca s\u0103 pot s\u0103-i \u021bin cont pe to\u021bi, dar am continuat cum am putut, \u00eencerc\u00e2nd s\u0103 \u00een\u021beleg cum vor ei s\u0103 construiasc\u0103 profilele de viteze axisimetrice care alimenteaz\u0103 c\u00e2mpul de concentrare sau \u201dthe concentrating leading field\u201d , dar e \u00een zadar c\u0103 p\u00e2n\u0103 la pagina 28 au folosit deja toate literele din toate alfabetele europene \u0219i \u00een timp ce \u00eencercam s\u0103 \u00eemi aduc aminte calculele cu tupluri \u0219i s\u0103 \u00een\u021beleg ce vor s\u0103 spun\u0103 cu maximul componentelor normate , adic\u0103 maximum din cole\u021bia de elemente a unui tuplu, mi-am adus aminte c\u0103 eu am fost \u0219i corijent la matematic\u0103 \u00eentr-a noua , am mai avut \u0219i restan\u021be prin facultate \u0219i cred c\u0103 nu ar trebui s\u0103 \u00eencerc, nu s\u0103 calculez, dar s\u0103 urm\u0103resc calule de genul \u0103sta c\u0103 exist\u0103 un motiv pentru care Nicu\u0219or Dan conduce Rom\u00e2nia \u0219i nu io.
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Treaba e c\u0103 dac\u0103 <\/strong> calculele sunt corecte, \u0219i-mi este clar c\u0103 n-o s\u0103 fiu eu \u0103la care verific\u0103 \u0219i aprob\u0103, o s\u0103-i fac o \u00eentrebare lui domnu Penrose, dac\u0103 are poft\u0103 dumnealui, c\u0103 pare c\u0103 tr\u0103ie\u0219te tot \u00eentr-o matrice matematic\u0103 \u0219i dac\u0103 au reu\u0219it s\u0103 trimit\u0103 un puls periodic de energie finit\u0103 fluidul cu pricina explodeaz\u0103 \u00eentr-un vortex care se \u00eentinde p\u00e2n\u0103 la o singularitate.
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OK, pe mine nu m\u0103 impresioneaz\u0103 asta prea tare. Gen la ce conteaz\u0103? Pentru fluide, n-am idee, are ceva asem\u0103n\u0103ri cu consmologia \u0219i relativismul la frontiere, dar nu e mai important dec\u00e2t c\u0103 un prieten a fost la \u0219tiuc\u0103 la Sl\u0103tioara c\u00e2t am plecat eu prin Europa \u0219i a prins vreo 20 de \u0219tiuci, de a trebuit s\u0103 mai elibereze din ele, c\u0103 erau prea multe \u0219i m-am ofticat.
Era o problem\u0103 \u201dmilenar\u0103\u201d, pentru c\u0103 era dificil de calculat, nu musai de conceptualizat, dar nu prea avem calculatoare analitice, iar noi oamenii pu\u021bim la matematic\u0103, cum zicea Rocky de pe Eridani.
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Dar. <\/strong>
Ce e impresionant e c\u0103 al\u021bi cercet\u0103tori lucrau la aceea\u0219i problem\u0103 dintr-un alt unghi \u0219i i-au acuzat p-\u0103\u0219tia c\u0103 au tras cu ochiul \u0219i le-au furat solu\u021bia.
Cei de la OpenAI au zis c\u0103 nu, dar au b\u0103gat disclaimer – c\u0103 b\u0103, dac\u0103 ne-a\u021bi folosit AI-ul e posibil s\u0103 fi \u00eenv\u0103\u021bat de la voi.

\u0218i asta e chestia care deschide sau \u00eenchide o lume.
\u00cen noua lume care se contureaz\u0103 patentele , drepturile de autor \u0219i secretele de business sunt pe care s\u0103 fie f\u0103cute inutile – zic la nivel general, comercial \u0219i la metanivel, dac\u0103 ai o inteligen\u021b\u0103 artificial\u0103 care umbl\u0103 prin toate.
Las\u0103 c\u0103 ce ni se poate \u00eent\u00e2mpla nou\u0103 din cauza asta, <\/strong>nu asta e ideea mea acum.

Ci ce fel de lume vrem s\u0103 fim.
Una care \u00eenc\u0103 se \u021bine cu din\u021bii de patente \u0219i drepturi de autor? Cum, \u00een contextul \u00een care dac\u0103 \u00eel \u00eentreb pe Gemini m\u00e2ine ceva ce i-ai \u00eencredin\u021bat tu ieri \u00eem confiden\u021b\u0103 mi-l poate descrie cu maximum de detalii \u0219i \u00eembun\u0103t\u0103\u021biri?
<\/strong><\/em>
Cum ar fi s\u0103 tr\u0103im \u00eentr-o lume f\u0103r\u0103 drepturi de autor?<\/strong>
<\/strong><\/em>Pac, a\u021bi v\u0103zut unde v-am sucit?
<\/p>\n","protected":false},"excerpt":{"rendered":"

V\u00e2lv\u0103 mare c\u0103 au demonstrat OpenAI o ipotez\u0103 \u00een care ecua\u021biile diferen\u021biale propuse Navier-Stokes care modeleaz\u0103 dinamica fluidelor cu v\u00e2scozitate determin\u0103 o stare de \u201dsingularitate\u201d…<\/p>\n","protected":false},"author":2,"featured_media":38062,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[5299],"tags":[7572,7573],"class_list":["post-38049","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-ai-uri","tag-navier-stokes","tag-o-lume-fara-drepturi-de-autor"],"views":76,"jetpack_publicize_connections":[],"jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p4Eq23-9TH","jetpack-related-posts":[],"jetpack_featured_media_url":"https:\/\/catalinx.ro\/wordpress\/wp-content\/uploads\/2026\/09\/image-8.png","_links":{"self":[{"href":"https:\/\/catalinx.ro\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/38049","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/catalinx.ro\/wordpress\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/catalinx.ro\/wordpress\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/catalinx.ro\/wordpress\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/catalinx.ro\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=38049"}],"version-history":[{"count":4,"href":"https:\/\/catalinx.ro\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/38049\/revisions"}],"predecessor-version":[{"id":38071,"href":"https:\/\/catalinx.ro\/wordpress\/index.php?rest_route=\/wp\/v2\/posts\/38049\/revisions\/38071"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/catalinx.ro\/wordpress\/index.php?rest_route=\/wp\/v2\/media\/38062"}],"wp:attachment":[{"href":"https:\/\/catalinx.ro\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=38049"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/catalinx.ro\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=38049"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/catalinx.ro\/wordpress\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=38049"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}