Je AI v matematiki že boljša od ljudi? Scott Aaronson pravi: ja
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- Scott Aaronson trdi, da matematični dosežki UI zahtevajo trajen premik: od iskanja dokazov k njihovemu razumevanju in razlaganju. Poroča, da je OpenAI objavil stotine domnevnih rešitev, tudi dokaz domneve o enoličnih igrah — matematične trditve o težavnosti določene vrste računskih problemov. Ob tem poudarja, da so ideje, razvite med raziskovanjem, pomembnejše od samih odgovorov. Primerja prakse objavljanja v podjetjih in podpira človeško avtorstvo, ki temelji na razumevanju, razkritju uporabe UI in odgovornosti. Opozarja pa, da mladi raziskovalci še vedno potrebujejo temeljno znanje in priložnosti, da se uveljavijo. Nerešenih problemov ne moremo rezervirati za izbrane reševalce, podjetja UI pa ostajajo odgovorna za varnost. Praktičen algoritem — postopek računanja —, ki bi dokazal P = NP, bi lahko spodkopal kriptografijo in pospešil razvoj UI. P = NP bi pomenilo, da lahko vsak problem, pri katerem hitro preverimo rešitev, tudi hitro rešimo. To odpira težka vprašanja o razkritju takšnega odkritja. Poroča tudi o rezultatih pri unitarni sintezi, doseženih s pomočjo UI. Unitarna sinteza pomeni sestavljanje kvantnih operacij. Ti rezultati povezujejo P = PSPACE z učinkovitim razvozlavanjem Hawkingovega sevanja, torej sevanja, ki ga oddajajo črne luknje. P = PSPACE bi pomenilo, da lahko vse probleme, rešljive s polinomsko količino pomnilnika, rešimo tudi v polinomskem času — času, ki z velikostjo naloge raste največ kot neka stalna potenca. Računska težavnost ustvarjanja ognjene pregrade črne luknje — hipotetičnega območja zelo energijskega sevanja — bi bila tako odvisna od še nerešenega vprašanja, ali sta ta razreda problemov različna. Opisuje še, kako bi P = NP v primernih klasičnih sistemih lahko razkril navidezno entropijo kot stisljivo psevdoentropijo, ne da bi kršil drugi zakon termodinamike. Entropija meri razpršenost energije in število možnih mikroskopskih razporeditev sistema; psevdoentropija je entropija, ki je le navidezna. Drugi zakon pravi, da skupna entropija izoliranega sistema ne upada. Nazadnje zavrača teorijo integrirane informacije, ker preprostim mrežam logičnih vrat pripisuje več zavesti kot človeškim možganom. Logična vrata so osnovni elementi, ki iz vhodnih vrednosti izračunajo izhodno vrednost.
- Scott Aaronson pravi, da je Dana Moshkovitz poskušala dokazati domnevo o enoličnih igrah ves čas, odkar jo pozna — vse od začetka njunih zmenkov v letu 2009. Ta domneva je matematična trditev o težavnosti določene vrste računskih problemov. u7–8 ·
- Scott Aaronson poroča, da je OpenAI objavil skoraj 400 rešitev pomembnih nerešenih problemov iz matematike in teoretičnega računalništva, ki jih je odkrila UI. Med njimi je tudi domnevni dokaz domneve o enoličnih igrah, katere avtor je Subhash Khot. Ta domneva govori o težavnosti določene vrste računskih problemov. u8–10 · Aaronson objavo umešča nekaj tednov pred pogovor. Pravi, da so problemi videti rešeni, njihove rešitve pa ljudje še poskušajo razumeti.
- Scott Aaronson pravi, da Dana Moshkovitz uporablja Astra za razlago posameznih korakov v dokazu domneve o enoličnih igrah, ki ga je izdelala UI. Domneva govori o težavnosti določene vrste računskih problemov. u32–33 ·
- Scott Aaronson pravi, da je OpenAI svojim modelom očitno predložil približno 4,000 nerešenih problemov. Rešili so jih približno 10 odstotkov, pri čemer je bilo za vsak problem namenjenih tri ure računskega časa. u45–46 · Aaronson število problemov in delež uspešnih rešitev navaja približno; dodeljeni čas velja za vsak problem posebej.
- Scott Aaronson poroča, da je OpenAI imenoval zunanji odbor, v katerem sta bila tudi Timothy Gowers in Edward Witten. Svetoval naj bi o objavi matematičnih rešitev podjetja. Po več tednih je odbor priporočil objavo, ne da bi ravnanje OpenAI podprl ali obsodil. u46–48 ·
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Pravijo tudi
- Scott Aaronson poroča, da je Anthropic sklenil pogodbo z raziskovalcema Virginia Vassilevska Williams in Josh Alman. Njuna naloga: razumeti izboljšave, ki jih je UI odkrila za 3SUM in iskanje najkrajših poti med vsemi pari, ter pod svojima imenoma napisati ljudem razumljivo razlago. Pri 3SUM iščemo tri števila, katerih vsota je nič; pri drugem problemu iščemo najkrajše poti med vsakim parom točk v omrežju. u49–51 · Prikazani članek navaja polno ime Virginia Vassilevska Williams; Aaronson jo imenuje Virgi Vassilevska.
- Scott Aaronson pravi, da je bil pri rokopisih, ki jih je objavil OpenAI, kot avtor praviloma naveden OpenAI, ker rezultatov še ni razumel noben človek. Nekateri rokopisi so vsebovali certifikate Lean — strojno preverljive zapise dokazov —, ki so dajali določeno formalno zagotovilo pravilnosti. u67–68 · Aaronson ločuje formalno potrditev pravilnosti od človeškega razumevanja in pravi, da so certifikati obstajali le v nekaterih primerih.
- Scott Aaronson poroča, da številni njegovi študenti niso prepričani, kakšna bo njihova dolgoročna prihodnost. In to kljub temu, da UI že veliko uporabljajo za pisanje člankov in reševanje problemov. u122–123 ·
- Scott Aaronson pravi, da sta z Greg Kuperberg približno dvajset let prej zastavila problem unitarne sinteze, torej sestavljanja kvantnih operacij. Vprašanje je: ali lahko vsako unitarno transformacijo na n kubitih izvedemo v polinomskem času s kvantnimi poizvedbami pri ustreznem oraklju za klasično Boolovo funkcijo? Unitarna transformacija je obrnljiva sprememba kvantnega stanja; kubit je osnovna enota kvantne informacije. Polinomski čas raste največ kot neka stalna potenca velikosti naloge. Orakelj je zamišljena črna škatla, ki odgovarja na poizvedbe, Boolova funkcija pa računa z vrednostma 0 in 1. u161–164 · Orakelj je na voljo brez stroškov, poizvedbe pa mu lahko zastavljamo v superpoziciji — kvantni kombinaciji več vhodov hkrati.
- Scott Aaronson poroča, da iz izboljšav rezultata o unitarni sintezi, doseženih s pomočjo UI, očitno sledi: če velja P = PSPACE, lahko učinkovito izvedemo vsako unitarno operacijo, katere matrične elemente lahko opiše algoritem s polinomsko porabo pomnilnika. Unitarna sinteza pomeni sestavljanje obrnljivih kvantnih operacij; matrični elementi so števila v tabeli, ki takšno operacijo opisuje. P = PSPACE bi pomenilo, da lahko vse probleme, rešljive s polinomsko količino pomnilnika, rešimo tudi v polinomskem času. »Polinomsko« pomeni rast največ kot neka stalna potenca velikosti naloge. u169–171 · Aaronson razlago omeji z besedo »očitno«; trditev velja pod pogojem, da je P = PSPACE.
- Scott Aaronson ocenjuje, da bi zbiranje dovolj Hawkingovega sevanja iz astrofizikalne črne luknje za obravnavani poskus razvozlavanja trajalo vsaj 10^67 let. Hawkingovo sevanje je sevanje, ki ga oddajajo črne luknje; razvozlavanje tu pomeni pridobivanje kvantnih informacij iz njega. u182–183 · Aaronson predlagano zbiranje in kvantno obdelavo sevanja izrecno uvršča med miselne poskuse.
- Scott Aaronson pripoveduje, da sta Daniel Harlow in Patrick Hayden leta 2013 trdila: za hitro razvozlavanje Hawkingovega sevanja bi morali rešiti kriptografske probleme, ki naj bi bili težki celo za kvantne računalnike. Hawkingovo sevanje je sevanje črne luknje; razvozlavanje pomeni pridobivanje kvantnih informacij iz njega. Kriptografski problemi so računske naloge, na katerih temelji zaščita podatkov. Njuna razlaga je ponudila računsko oviro za ustvarjanje ognjene pregrade črne luknje — hipotetičnega območja zelo energijskega sevanja. u183–187 · To razvozlavanje bi moralo biti opravljeno, preden bi črna luknja povsem izhlapela.
- Scott Aaronson pravi, da ima s sodelavci še neobjavljen argument o posebnih primerih, v katerih je povečanje entropije le navidezno. Če bi veljalo P = NP, bi to navideznost lahko razkrili. Entropija meri razpršenost energije in število možnih mikroskopskih razporeditev sistema. P = NP pomeni, da bi lahko probleme, katerih rešitve hitro preverimo, tudi hitro rešili.
Pravi, da bi ti primeri omogočili Maxwellovega demona — zamišljenega upravljavca, ki toploto pretvarja nazaj v delo. Kot okolje za te primere predstavi klasične obrnljive celične avtomate: mreže celic, ki se spreminjajo po pravilih in katerih prejšnja stanja lahko obnovimo. u193–195 · Rezultat je opisan kot še neobjavljen in zadeva posebne primere, ne pa neomejenega kršenja drugega zakona termodinamike. Ta pravi, da skupna entropija izoliranega sistema ne upada.
- Scott Aaronson kot začetnika teorije integrirane informacije navede Giulio Tononi. Teorija povezuje zavest s povezanostjo informacij v sistemu in naj bi ločevala zavestne fizične sisteme od nezavestnih. u220–221 ·
- Scott Aaronson pravi, da se je definicija phi med različicami teorije integrirane informacije spreminjala. Phi je mera, s katero ta teorija ocenjuje povezanost informacij v sistemu in njegovo zavest. u224 ·
- Po pripovedovanju Scotta Aaronsona se je Giulio Tononi na njegovo kritiko odzval tako, da je sprejel možnost, da je stena vrat XOR 1,000-krat bolj zavestna od človeka. Vrata XOR so logični elementi, ki pri dveh vhodih vrnejo 1, kadar sta vhoda različna, sicer pa 0. Tononi naj bi zagovarjal stališče, da mora imeti teorija prednost pred intuicijo. u230–231 · Tononijevo stališče je predstavljeno skozi Aaronsonovo pripoved, ne skozi neposredno Tononijevo izjavo.
- Scott Aaronson dopušča možnost, da bodo modeli AI v enem letu svoja odkritja razlagali bolje kot ljudje, kar bi še zmanjšalo vlogo matematikov. Ljudje bi še vedno lahko izbirali zanimiva vprašanja in smeri raziskovanja. u26–28 ·
- Scott Aaronson priporoča, naj bodo izjave o uporabi AI na začetku raziskovalnih člankov, ne ob zahvalah. Obseg sodelovanja AI je namreč pogosto prva stvar, ki jo želi izvedeti. u62–63 · Te izjave povedo, kateri modeli so bili uporabljeni in kateri prispevki so bili človeški.
- Scott Aaronson napoveduje, da zgolj vnašanje kopice odprtih problemov v model in objavljanje njegovih rešitev pod svojim imenom, ne da bi jih razumeli, ne bo prineslo veliko priznanja. u71–73 ·
- Scott Aaronson napoveduje, da bodo ljudje še naprej uživali v matematiki in znanosti. Postavljali bodo svoja vprašanja ter jih bodisi reševali sami bodisi prosili AI, naj jih reši in razloži. Razlog za upanje vidi v šahu: ljudje ga še vedno igrajo, čeprav so računalniki boljši. u125–129 ·
- Scott Aaronson poziva, naj resno vzamemo možnost, da bodo modeli AI v naslednjem letu ali dveh zlomili enega ali več široko uporabljanih kriptografskih sistemov — matematičnih sistemov za zaščito podatkov. Opozarja, da hiter klasični algoritem za faktorizacijo, torej razcep števil na faktorje brez kvantnega računalnika, ali napad na kriptografijo eliptičnih krivulj ne bi zahtevala P = NP. Kriptografija eliptičnih krivulj je zaščita podatkov z matematičnimi operacijami na posebnih krivuljah. P = NP pomeni, da lahko probleme, katerih rešitve hitro preverimo, tudi hitro rešimo. u136–139 ·
- Scott Aaronson pojasnjuje, da bi bila praktična vrednost dokaza rezultata, kot je P ≠ NP, predvsem v novih idejah, potrebnih za dokaz, ne pa v potrditvi pričakovanega odgovora. P ≠ NP pomeni, da nekaterih problemov, katerih rešitve lahko hitro preverimo, ne moremo tudi hitro rešiti. u19–22 · Sam odgovor morda ne prinese spoznavnih koristi, zaradi katerih se nerešenega problema sploh lotimo.
- Scott Aaronson sumi, da je dokaze umetne inteligence (AI) težko brati, ker modeli nimajo dobre predstave o tem, kaj bralci že vedo. Rokopisi lahko porabijo cele strani za običajno snov, ključne korake pa komaj pojasnijo. u29–31 · Aaronson to primerja z briljantnimi študenti na začetku podiplomskega študija, ki prav tako napačno ocenijo, kaj je treba občinstvu razložiti.
- Scott Aaronson meni, da modeli AI razumejo matematiko, ker njihovi dosežki izpolnjujejo skoraj vsa praktično preverljiva merila za razumevanje. Trdi, da slaba razlaga še ne pomeni, da nečesa ne razumeš. Zavest pa je ločeno vprašanje. u37–40 · Aaronson opozarja, da tudi briljantni ljudje svojih odkritij včasih ne znajo dobro razložiti.
- Scott Aaronson trdi, da morajo študenti še vedno sami reševati osnovnejše matematične naloge, tudi če jih AI rešuje bolje. Te izkušnje jim pomagajo prepoznati napake AI in presojati na višji ravni. u88–89 · Če reševanje nalog prepustimo avtomatizaciji, še vedno potrebujemo sposobnosti za ocenjevanje rezultatov.
- Scott Aaronson trdi, da bi bilo že sklepanje na ravni začetnika podiplomskega študija izjemno, če bi ga združili s poznavanjem celotne matematične literature, neutrudnim delom in hkratnim raziskovanjem tisočev problemov in strategij. u103–105 · Aaronson obseg dela in vztrajnost vidi kot vira matematičnih sposobnosti, ne kot razloga, da bi jih odpisali.
- Scott Aaronson predlaga, da bi praktičen algoritem, ki bi pokazal P = NP, lahko še pospešil AI. Algoritem je postopek za reševanje naloge; P = NP pa bi pomenilo, da lahko probleme, katerih rešitve hitro preverimo, tudi hitro rešimo. Tak algoritem bi lahko veliko hitreje našel parametre modelov — nastavitve, ki določajo njihovo delovanje — in morda odpravil potrebo po učenju modelov za milijarde dolarjev. u142–143 · Te hipotetične posledice bi segale dlje od razbijanja kriptografije, torej postopkov za matematično zaščito podatkov.
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Pravijo tudi
- Scott Aaronson večji napredek AI v matematiki kot v fiziki pripisuje jasno zapisanim matematičnim domnevam in rešitvam, ki jih lahko preveri računalnik. Fizika pogosteje zahteva presojo, kateri približki in modeli so smiselni. Preverljivi matematični odgovori pa omogočajo obsežno učenje modelov in spodbujevalno učenje — učenje s povratnimi informacijami o uspešnosti. u151–154 · Aaronson pravi, da je matematična fizika, kjer je mogoče želene trditve natančno določiti, že doživela pomemben razvoj s pomočjo AI.
- Scott Aaronson pojasnjuje, da sodobna razlaga informacije o snovi, ki je padla v črno luknjo, umešča v močno premešano in kvantno prepleteno Hawkingovo sevanje. To je sevanje črne luknje; kvantna prepletenost pomeni, da so stanja delcev povezana v skupno celoto. Če kvantna mehanika, teorija obnašanja snovi na kvantni ravni, velja povsod, mora unitarni razvoj te informacije ohraniti. Unitarni razvoj je spreminjanje kvantnega stanja brez izgube informacij. Sama kvantna teorija polja, ki delce opisuje kot vzbuditve polj, pa ne pojasni, kako so te informacije zapisane. u176–181 · Pridobiti informacije nazaj je naloga kvantnega dekodiranja — razbiranja kvantnega zapisa — in ne zgolj branje klasičnega sporočila.
- Scott Aaronson pojasnjuje, da Maxwellov demon navidezno zmanjšuje entropijo plina tako, da selektivno odpira vratca molekulam, ki potujejo v eno smer. Entropija je mera razpršenosti energije oziroma števila možnih mikroskopskih razporeditev sistema. V običajni razlagi, ki jo začne opisovati, navidezno izgubljena entropija preide v demonov spomin, namesto da bi bil kršen drugi zakon termodinamike. Ta pravi, da se skupna entropija izoliranega sistema ne zmanjšuje. u198–203 · Odlomek se konča, preden Aaronson dokonča razlago, kako mora demon informacije hraniti oziroma z njimi ravnati.
- Scott Aaronson pojasnjuje, da najdba začetnega stanja z nizko entropijo, ki se ujema z demonovimi opažanji, da stisnjen opis demonovega spomina. Entropija je mera števila možnih mikroskopskih razporeditev sistema. Bite spomina, s katerimi smo prej pojasnjevali entropijo, je nato mogoče odstraniti s stiskanjem zapisa. Bit je osnovna enota digitalne informacije. u209–212 · Demon krajšega opisa ne more izkoristiti zaradi računske zahtevnosti rekonstrukcije — ponovne sestave začetnega stanja.
- Scott Aaronson psevdoentropijo opisuje kot informacijo, ki je videti enakomerno naključna, a ima v resnici precej krajši opis. Tak je denimo izhod generatorja psevdonaključnih števil — postopka, ki ustvarja števila, videti naključna. u214–215 · Navidezna termodinamična naključnost, torej naključnost pri toplotnem obnašanju sistema, bi tako lahko izvirala iz skritega kratkega opisa in ne iz prave entropije.
- Scott Aaronson trdi, da so stroji pri iskanju rešitev jasno določenih matematičnih problemov prehiteli ljudi. Delo matematikov se je s tem trajno spremenilo. u16–17 ·
- Scott Aaronson trdi, da reševanja problemov z UI ne moremo kar izklopiti, ne da bi ustavili samo UI. Matematična skupnost se mora zato prilagoditi in v središče postaviti človeško razumevanje. u23–25 ·
- Scott Aaronson opisuje merilo avtorstva, ki se šele uveljavlja: ljudje se lahko podpišejo kot avtorji članka, tudi če njegove glavne ideje odkrije UI. Pogoj? Delo morajo v celoti razumeti, ga razložiti s svojimi besedami in zanj prevzeti odgovornost. u65–66 ·
- Scott Aaronson trdi, da je zamahovanje z roko ob vsakem novem dosežku UI oblika zanikanja. Ko se napovedi kritikov ne uresničijo, ti zamenjajo ploščo: dosežek naj bi bil neustvarjalen, rutinski ali pa sploh nikoli težak. u100–102 ·
- Scott Aaronson trdi, da matematiki nerešenih problemov ne morejo rezervirati samo za reševalce, ki so jim po volji. Z njimi se lahko ukvarjajo tudi korporacije. Pravi, da se morajo matematiki prilagoditi temu, da UI rešuje probleme, obenem pa od podjetij UI še naprej zahtevati varnost in usklajenost delovanja s človeškimi nameni in vrednotami. u118–120 ·
- Scott Aaronson pravi, da bi praktičen algoritem, ki bi dokazal P = NP, zlomil tako rekoč vso kriptografsko zaščito, ki se uporablja na internetu. P = NP pomeni, da lahko probleme, katerih rešitve hitro preverimo, tudi hitro rešimo; algoritem je postopek računanja. Ogroženi bi bili tudi digitalni podpisi kriptovalut, s katerimi se potrjujejo transakcije, in zaščita HTTPS, ki varuje spletne povezave. To predstavlja kot hipotetičen scenarij in izrecno pove, da ne verjame, da velja P = NP. u133–136 ·
- Scott Aaronson pravi, da iz nedavnega napredka s pomočjo UI sledi: če velja P = PSPACE, postane Harlow–Haydenov problem razvozlavanja lahek. P = PSPACE pomeni, da bi lahko vse probleme, rešljive s polinomsko količino pomnilnika, rešili tudi v polinomskem času; »polinomsko« pomeni rast največ kot neka stalna potenca velikosti naloge. Harlow–Haydenov problem sprašuje, kako iz Hawkingovega sevanja črne luknje izluščiti kvantne informacije.
Zato bi dokaz, da je ustvarjanje ustrezne ognjene pregrade črne luknje računsko težko, zahteval dokaz P ≠ PSPACE. Ognjena pregrada je hipotetično območje zelo energijskega sevanja ob črni luknji. Ali sta omenjena razreda računskih problemov različna, še vedno ni rešeno. u189–192 ·
- Scott Aaronson trdi, da bi P = NP v primernih klasičnih sistemih Maxwellovemu demonu lahko omogočil, da navidezno termodinamično entropijo razkrije kot psevdoentropijo. P = NP pomeni, da bi lahko probleme, katerih rešitve hitro preverimo, tudi hitro rešili. Maxwellov demon je zamišljeni upravljavec, ki z informacijami o sistemu pretvarja toploto v delo. Entropija meri razpršenost energije in število možnih mikroskopskih razporeditev sistema; psevdoentropija je le navidezna entropija. S tem bi drugi zakon termodinamike obšel, ne pa zares kršil. Ta zakon pravi, da skupna entropija izoliranega sistema ne upada. u208–218 ·
- Scott Aaronson zavrača teorijo integrirane informacije, ki zavest povezuje s povezanostjo informacij v sistemu. Njena mera phi lahko preprostim mrežam logičnih vrat pripiše več zavesti kot človeškim možganom. Logična vrata so osnovni elementi, ki iz vhodnih vrednosti izračunajo izhodno vrednost. Po njegovem je tak sklep odklopljen od tega, kar naj bi beseda zavest sploh pomenila. u227–230 ·
- Kaj bi pomenilo odgovorno razkritje, če bi AI odkrila način za zlom globalno uporabljenega kriptografskega sistema, kot sta RSA ali Bitcoin? Kriptografski sistemi uporabljajo matematiko za zaščito podatkov; odgovorno razkritje pa pomeni premišljeno obveščanje o odkriti varnostni pomanjkljivosti. u139–141 · Aaronson kot možnosti omenja dokaz, da rešitev imaš, ne da bi jo razkril, ali to, da najprej obvestiš vlado. Katero možnost izbrati, pusti odprto.
- Če teorija integrirane informacije mreži vrat XOR pripisuje visoko stopnjo zavesti, česa se ta mreža zaveda? Teorija integrirane informacije zavest povezuje s povezanostjo informacij. Vrata XOR so logični elementi, ki vrnejo 1, kadar se njuna vhoda razlikujeta, sicer pa 0. u219–220 ·
- Jacob Tsimerman opisuje žalovanje ob možnosti, da izginejo dolgi raziskovalni projekti, ki napredujejo korak za korakom in so osrednji del njegove identitete pri delu. u75–76 · Odlomek loči med tem, da matematika cveti, in tem, da se ohrani matematikov znani način dela.
- Scott Aaronson pravi, da ne more biti več tako prepričan, da je nenaročen dokaz neznanega ljubiteljskega matematika napačen. Ta bi namreč lahko pravilen dokaz dobil od AI. u94–96 · Aaronson je desetletja rutinsko zavračal nenaročene trditve o rešitvah velikih odprtih problemov.
- Scott Aaronson poroča, da je eden od 372 člankov organizacije OpenAI, objavljenih dva tedna prej, rešil problem unitarne sinteze — sestavljanja kvantnih operacij, ki ohranjajo informacije. Rezultat je nasproten domnevi, ki sta jo postavila on in Greg Kuperberg: ustrezen orakelj za Boolove funkcije res omogoča učinkovito izvedbo vsake unitarne operacije. Tak orakelj je pripomoček, ki na poizvedbo vrne vrednost funkcije z binarnimi vhodi in izhodom. u165–168 · Aaronson in Kuperberg sta pričakovala, da bo tudi ob domiselnem zapisu unitarne operacije še vedno potrebno eksponentno število poizvedb oraklju — število, ki raste kot potenca s povečevanjem velikosti problema.
- Scott Aaronson poroča o skrbi, da bi AI lahko ponudila odgovore na matematične probleme, ne da bi morali ljudje razviti uvide, ki so jih običajno pridobili na poti do rešitve. u22–23 · Priti do rešitve in razviti človeško razumevanje morda ne bo več isti proces.
- Scott Aaronson pravi, da Anthropic z vključevanjem človeških strokovnjakov zagotovi ljudi, ki prevzamejo odgovornost in znajo razložiti rezultate AI, raziskovalcem pa daje občutek, da je delo tudi njihovo. Druga plat: Anthropic izbira, kateri ljudje dobijo te priložnosti. u51–53 · Aaronson izbiro strokovnjakov odobrava, a opozarja, da bi si to vlogo želeli še številni drugi.
- Scott Aaronson pravi, da bi uveljavljen raziskovalec, kot je sam, lahko nadaljeval kot razlagalec, predstavljalec idej ali snovalec domnev. Mladi raziskovalci pa bi lahko izgubili jasno določene odprte probleme, s katerimi so tradicionalno dokazovali svoje sposobnosti. u79–84 · Aaronson izkušenejšim raziskovalcem pripisuje odgovornost, da najdejo pot naprej, ki bo ohranila matematično kulturo.
- Scott Aaronson trdi, da je treba varovanje matematične kulture, zabavnih izzivov in vstopnih poti za mlade uravnotežiti z možnostjo, da AI pospeši razumevanje in uvide, ki jih matematika daje družbi. u91–93 · Aaronson se sprašuje, ali imajo matematiki pravico odvračati od uporabe AI, če ta prispeva k razumevanju.
- Scott Aaronson pravi, da ugovor, češ da AI nima zavesti, zadeva metafiziko — vprašanja o temeljni naravi resničnosti — in ne tega, kaj bo AI počela v opazljivem svetu. Poziva, naj razprave ti vprašanji jasno ločijo. u106–107 · Ugovor o zavesti ne odgovarja na vprašanje praktičnih sposobnosti, o katerih teče beseda.
- Scott Aaronson poudarja, da dokaz P = NP ne bi nujno prinesel uporabnega algoritma, torej postopka za reševanje nalog. P = NP pomeni, da lahko probleme, katerih rešitve hitro preverimo, tudi hitro rešimo v matematičnem smislu. A polinomski čas izvajanja — čas, omejen s potenco velikosti vhodnih podatkov — ima lahko še vedno ogromen eksponent ali konstanto. Neposredne praktične posledice so odvisne od tega, ali je algoritem dejansko hiter. u131–132 · Nepraktičen algoritem bi bil še vedno velik teoretični dosežek in bi spodbudil poskuse izboljšav.
- Curt Jaimungal se sprašuje, ali je preživetje šaha ustrezna primerjava za akademsko matematiko, ki ima univerzitetne oddelke in raziskovalno poslanstvo. Scott Aaronson priznava razliko, a trdi, da je odkrivanje resnic o vesolju razlog, da sprejmemo orodja, ki razkrijejo še več resnic. u145–147 · Ohranjanje človeške vloge pri reševanju problemov je lahko v nasprotju z odkrivanjem čim več matematičnih resnic.
- Scott Aaronson opozarja, da P = NP demonove strategije ne bi nujno naredil fizikalno izvedljive. P = NP pomeni, da lahko probleme, katerih rešitve hitro preverimo, tudi hitro rešimo. Kaotična dinamika — razvoj sistema, pri katerem drobne začetne razlike močno spremenijo izid — bi lahko zahtevala neskončno natančnost. Nova kvantna negotovost, torej negotovost zaradi kvantnih pojavov, pa bi lahko preprečila rekonstrukcijo prejšnjega stanja. u216–218 · Aaronson ta pristop omejuje predvsem na klasične dinamične sisteme brez kaosa — sisteme, katerih spreminjanje opisuje klasična fizika in nima takšne občutljivosti na začetne razlike.
- Scott Aaronson izpodbija trditev, da mera phi iz teorije integrirane informacije izhaja iz njenih navedenih aksiomov. Ta teorija zavest povezuje s povezanostjo informacij, phi pa je njena mera te povezanosti. Aksiomi so začetne predpostavke teorije. Aaronson trdi, da članki naštejejo aksiome, nato pa uvedejo formulo, ne da bi jo dejansko izpeljali. u225–226 · Aaronson manjkajočo izpeljavo vidi kot težavo pri matematični utemeljitvi mere phi.
- Zaradi matematičnih sposobnosti UI je prilagajanje neizogibno. Matematiki morajo v ospredje postaviti razumevanje in razlago, za katero prevzamejo odgovornost. Hkrati se morajo spoprijeti z znanstvenimi, poklicnimi in varnostnimi posledicami hitrejšega odkrivanja. Kako naj se matematika prilagodi sposobnostim UI za reševanje problemov in kakšne posledice bi te sposobnosti lahko imele za znanost in družbo?
Kako utemeljuje
- thesis AI mathematics demands understanding, accountability, and adaptation How should mathematics adapt to AI’s problem-solving capabilities, and what consequences could those capabilities have for science and society?
- theme Mathematical capability has crossed a threshold The source argues that AI's mathematical achievements warrant recognition as genuine capability rather than dismissal or metaphysical debate.
- idea Machines surpass humans at well-defined mathematical problems
- evidence OpenAI releases hundreds of claimed open-problem solutions
- mechanism Broad knowledge and parallel effort amplify modest reasoning
- mechanism Precisely checkable answers accelerate mathematical AI training
- argument Moving goalposts deny demonstrated AI achievements
- implication Unknown amateurs might now submit correct AI proofs
- idea AI achievements meet operational criteria for mathematical understanding
- idea Machines surpass humans at well-defined mathematical problems
- theme Understanding must anchor mathematical credit Mathematical practice must prioritize human understanding, clear explanation, transparent AI involvement, and responsibility for published results.
- idea Unavoidable AI requires a culture centered on understanding
- argument A proof's new ideas matter beyond its conclusion
- tension AI answers may bypass humans' acquisition of insight
- counterargument AI might outperform human explainers within a year
- example Moshkovitz uses Astra to understand the claimed proof
- action Authorship requires understanding, personal explanation, and responsibility
- idea Poor reader modeling makes AI proofs difficult
- idea Unavoidable AI requires a culture centered on understanding
- theme Adaptation must preserve routes into mathematics AI threatens research identities and career entry points, but education and mathematical culture must adapt without abandoning discovery.
- tension Protect mathematical culture without sacrificing accelerated understanding
- argument Junior researchers risk losing traditional proving grounds
- quote Tsimerman grieves the possible loss of incremental research
- action Preserve foundational problem-solving practice to develop judgment
- counterargument Human enjoyment can survive machine superiority
- action Accept corporate problem-solving while demanding safety and alignment
- tension Protect mathematical culture without sacrificing accelerated understanding
- theme Discovery creates urgent security responsibilities AI could undermine deployed cryptography without resolving P versus NP, making practical feasibility and responsible disclosure central concerns.
- theme AI reshapes black-hole complexity arguments AI-assisted unitary synthesis results raise the complexity-theoretic burden for establishing a computational barrier to black-hole firewalls.
- theme Entropy may conceal computational difficulty In suitable systems, efficient computation could expose apparent entropy as compressible information, although physical obstacles remain.
- idea P = NP could expose entropy as pseudo-entropy
- evidence Unpublished cellular-automata argument identifies apparent entropy reversals
- mechanism Reconstructing initial states lets demons compress memory
- mechanism Pseudo-entropy hides short descriptions behind apparent randomness
- counterargument Precision limits and quantum uncertainty may block demons
- idea Standard demon accounts relocate entropy into memory
- idea P = NP could expose entropy as pseudo-entropy
- theme Consciousness measures need substantive justification The source challenges integrated information theory's derivation and its attribution of extraordinary consciousness to simple logic-gate systems.
- theme Mathematical capability has crossed a threshold The source argues that AI's mathematical achievements warrant recognition as genuine capability rather than dismissal or metaphysical debate.
Kjer vir nasprotuje sam sebi
- Scott Aaronson pojasnjuje, da Maxwellov demon navidezno zmanjšuje entropijo plina tako, da selektivno odpira vratca molekulam, ki potujejo v eno smer. Entropija je mera razpršenosti energije oziroma števila možnih mikroskopskih razporeditev sistema. V običajni razlagi, ki jo začne opisovati, navidezno izgubljena entropija preide v demonov spomin, namesto da bi bil kršen drugi zakon termodinamike. Ta pravi, da se skupna entropija izoliranega sistema ne zmanjšuje. proti Scott Aaronson trdi, da bi P = NP v primernih klasičnih sistemih Maxwellovemu demonu lahko omogočil, da navidezno termodinamično entropijo razkrije kot psevdoentropijo. P = NP pomeni, da bi lahko probleme, katerih rešitve hitro preverimo, tudi hitro rešili. Maxwellov demon je zamišljeni upravljavec, ki z informacijami o sistemu pretvarja toploto v delo. Entropija meri razpršenost energije in število možnih mikroskopskih razporeditev sistema; psevdoentropija je le navidezna entropija. S tem bi drugi zakon termodinamike obšel, ne pa zares kršil. Ta zakon pravi, da skupna entropija izoliranega sistema ne upada.
The standard explanation transfers apparent entropy loss to memory, while the computational scenario challenges whether that apparent entropy needs such compensation.
- Scott Aaronson pojasnjuje, da Maxwellov demon navidezno zmanjšuje entropijo plina tako, da selektivno odpira vratca molekulam, ki potujejo v eno smer. Entropija je mera razpršenosti energije oziroma števila možnih mikroskopskih razporeditev sistema. V običajni razlagi, ki jo začne opisovati, navidezno izgubljena entropija preide v demonov spomin, namesto da bi bil kršen drugi zakon termodinamike. Ta pravi, da se skupna entropija izoliranega sistema ne zmanjšuje. proti Scott Aaronson pojasnjuje, da najdba začetnega stanja z nizko entropijo, ki se ujema z demonovimi opažanji, da stisnjen opis demonovega spomina. Entropija je mera števila možnih mikroskopskih razporeditev sistema. Bite spomina, s katerimi smo prej pojasnjevali entropijo, je nato mogoče odstraniti s stiskanjem zapisa. Bit je osnovna enota digitalne informacije.
The standard resolution accounts for the missing entropy in memory, whereas the reconstruction argument allows those accounting bits to be compressed away.
Vir, odlomek za odlomkom
Prepis, preveden z umetno inteligenco iz angleščine.
- u1 UI je rešila domnevo o edinstvenih igrahAI Solved the Unique Games Conjecture
- u2 Scott: To prihaja po vse nas. Ko se pogovarjam s prijatelji fiziki, se zdi, da njih še ni doletelo, vendar jih veliko zaskrbljeno opazuje. Osupljivo je. Curt: To je legendarni Scott Aaronson, računalniški znanstvenik, ki vodi Center za kvantne informacije na UT Austin. Sprašujem ga, kaj meni o nedavnih izjavah Združenja za človeško matematiko.Scott: This is coming for all of us. When I talk to my friends in physics, it seems like it still hasn’t come for them, but a lot of them are watching nervously. It is staggering. Curt: This is the legendary Scott Aaronson, a computer scientist who directs UT Austin’s Quantum Information Center. I ask him about what he makes of the recent statements from the Association for Human Mathematics.
0:00 · Man in glasses speaking in front of chalkboard · A close-up video still of a man with gray-brown hair and dark-rimmed glasses, wearing a light blue collared shirt, speaking toward the camera. Behind him is a blackboard with handwritten math notation, and a hexagonal wall decoration hangs on the cream wall to the left. - u3 Scott: Nismo mi tisti, ki odločamo, kdo sme reševati naše probleme. Ves smisel zastavljanja odprtega problema je, da ga potem lahko rešuje prav vsakdo na svetu. Lahko je neznan uradnik v Indiji, kot je bil Ramanujan, ko je ustvaril svoje prvo veliko delo. Lahko je 17-letni dijak. Curt: Na tem kanalu jaz, Curt Jaimungal,Scott: We are not the arbiters of who gets to work on our problems. The whole point of posing an open problem is that it is then open for absolutely anyone in the world to work on. They could be an unknown clerk in India, as Ramanujan was when he did his first great work. They could be a 17-year-old student. Curt: On this channel, I, Curt Jaimungal,
- u4 z raziskovalci poglobljeno in tehnično natančno razpravljam o njihovih teorijah resničnosti in hočem vedeti, kaj za vraga se dogaja z matematiko in fiziko. Scott: Ta naraščajoča poplava je najprej zajela programsko inženirstvo, potem pa je to poletje zajela še nas. Curt: Danes vam z navdušenjem predstavljam Scotta Aaronsona, s katerim bova govorila o tem, kakšna je fizika po prihodu UI in zakaj mnogi zadnjih nekaj tednov označujejo za najpomembnejši trenutek v zgodovini matematike.interview researchers regarding their theories of reality with rigor and technical depth, and I wanna know what the heck is happening to math and physics. Scott: There’s this rising floodwater that came for software engineering, and then this summer it’s come for us. Curt: Today, I’m thrilled to bring you Scott Aaronson on what physics looks like after AI and why many are calling the past few weeks the most significant moment in math history.
0:45 · News article headline on OpenAI solving math challenges · A zoomed-in screenshot of a news website article page, with a large headline saying OpenAI has published solutions to more than 370 outstanding math challenges. The headline says the results divide mathematicians, but most agree math will never be the same. A navigation bar and a "Trending now" ticker appear above it. - u5 Scott: To trajno spreminja naravo našega dela. Nekaj nam je bilo odvzeto. Curt: Recimo, da ima Anthropic dokaz, da je P enako NP. Meniš, da bi ga morali objaviti? Nekaj ti bom prebral s tvojega bloga. »Sinoči je moj devetletni sin takole zbadal mojo ženo, teoretičarko računske zahtevnosti Dano Moshkovitz: ‘Mami, slišal sem, da so te povozili. SlišalScott: That does permanently change the nature of what it is that we do. Something has been taken away. Curt: Suppose Anthropic has a proof that P equals NP. Do you think they should release it? I’m gonna read something to you from your blog. “Last night, my nine-year-old son was taunting my wife, complexity theorist Dana Moshkovitz, as follows, ‘Mommy, I heard you got cooked. I
- u6 sem, da je robot rešil matematični problem, s katerim se ukvarjaš že vso kariero. Uf!’« Scott: Ja, zgodilo se je skoraj natanko tako, kot sem opisal. Mislim, veš, moj sin pač tako govori. Toda to, kar se dogaja na področju UI, je tako veliko, da se po mojem, veš, celo otroci povsem zavedajo, veš,heard that a robot solved the math problem you were working on for your whole career. Oof!’” Scott: Yeah, that happened pretty much as I described it. I mean, you know, that is the way that my son talks. But, you know, what is happening in AI is of such a magnitude that I think, you know, even kids are fully aware of, you know,
1:43 · Curt Jaimungal, Host of Theories of Everything · A video still of a man with short dark hair, a stubbly beard and tortoiseshell glasses, wearing a green-gray collared shirt. He looks at the camera in front of a pale wall, with a condenser microphone in the foreground at right and an acoustic guitar behind him. A lower-third caption names him as Curt Jaimungal, host of Theories of Everything. - u7 da se dogaja nekaj ogromnega. Mislim, do najinih otrok to morda pride nekoliko prej, ker sta oba starša teoretična računalniška znanstvenika in ker se je celotna narava najinega dela, veš, zelo opazno spremenila. Ampak Dana, samo da pojasnim, ves čas, kar jo poznam, veš,that something huge is happening. I mean, in the case of our kids, you know, that may reach them a little earlier just because both of their parents are theoretical computer scientists, and, like, the whole nature of what we do has, you know, very noticeably changed. I mean, but Dana, just to explain, for the entire time that I’ve known her, you know,
- u8 in hoditi sva začela leta 2009, ves ta čas poskuša dokazati nekaj, čemur pravimo domneva o edinstvenih igrah Subhasha Khota. Prav, veš, pozneje lahko pojasniva, kaj to je, če želiš. Toda to je bil velik odprt problem v teoretičnem računalništvu. Pred nekaj tedni pa je OpenAI v nekakšni množični objavi, veš, objaviland we started dating in 2009, and for that entire time, she’s been working on proving something called the unique games conjecture of Subhash Khot. Okay, you know, we can get into what that is later if you want to. But, you know, it was a big open problem in theoretical computer science. And a couple weeks ago, OpenAI, you know, in this sort of massive dump, you know, released
- u9 skoraj 400 rešitev pomembnih odprtih problemov iz matematike in teoretičnega računalništva, ki jih je odkrila UI, in eden kronskih draguljev te objave je bil dokaz domneve o edinstvenih igrah. Tako. Od takrat Dana skoraj ves svoj čas porablja za posku—za poskuse, da bi razumelaalmost 400 AI-discovered solutions to major open problems in math and theoretical computer science, and one of the crown jewels in what they released was a proof of the unique games conjecture. Right. So since then, Dana has been spending pretty much all of her time, try—just trying to understand
- u10 ta dokaz, veš, v upanju, da bi ga lahko bolje razložila. Kajti zdaj imamo vse te probleme, veš—tudi probleme, s katerimi sem se ukvarjal jaz in moji študenti—ki so očitno rešeni, vendar to še ne pomeni, da kdo že razume rešitve, kajne? Mislim,this proof and, you know, in the hopes of, you know, being able to explain it better. Because, you know, one thing, like, you know, we now have all of these problems that, you know—including problems that I had worked on, that my students had worked on—that appear to be solved, but that doesn’t mean that anyone understands the solutions yet, right? I mean,
- u11 zdaj se vsi nekako ženejo, da bi dejansko razumeli te dokaze UI, kajne? Veliko jih je zelo slabo napisanih. Če bi jih poslali v revijo, bi jih takoj vrnili. Češ, ta zapis je videti kot zmazek, kajne? Dokler pa so tako slabo napisani, je to v nekem smislu za nas odlično,and so now there’s sort of a scramble to actually understand these AI proofs, right? You know, a lot of them are sort of very poorly written. Like, if they were submitted to a journal, they just get sent back right away. Like, you know, this writeup looks like, you know, garbage, right? But as long as they’re so poorly written, in a certain sense, that’s great for us
- u12 saj pomeni, da imamo še vedno veliko dela. Pomeni, da moramo mi to predelati, izluščiti ključne nove ideje in jih razložiti, veš, napisati boljše predstavitve. In veliko mojih kolegov se prav zdaj intenzivno ukvarja z vsem tem.because it means that we still have plenty to do. It means that, you know, it’s up to us to digest this stuff and, like, isolate what are the key new ideas and explain them, you know, write better expositions of them. And so a lot of my colleagues are scrambling to do all of that right now.
- u13 Curt: Mislim, da obstaja nekdo, ki mu pravijo hierofant in razlaga svete skrivnosti. Misliš, da bodo v prihodnosti—recimo čez dve, tri leta—računalniški znanstveniki in matematiki počeli prav to? Scott: Ja. Mislim, glej, lahko pogledaš številna akademska področja, kajne? Kaj počnejo literarni znanstveniki? Razlagajo. Veš, oni ... Ko te zaposlijo na,Curt: I think there’s a person called a hierophant who interprets sacred mysteries. Do you think that that’s what the future—say, two years, three years from now, computer scientists and mathematicians are gonna be doing? Scott: Yeah. I mean, look, you know, you can look at a lot of academic fields, right? What do literary scholars do, right? They interpret. You know, they... When you get hired to a,
- u14 veš, oddelku za angleščino, nihče ne pričakuje, da boš napisal novo Iliado, kajne? Komentiral boš ta velika dela, ki smo jih podedovali. Lahko pa pogledamo še širše, kajne? Astronom gleda skozi teleskop,you know, an English department, no one expects that you’re going to write a new Iliad, right? You’re going to, you know, comment on these sort of, you know, great works that were handed down. But, you know, we could even look more broadly than that, right? You know, an astronomer looks through a telescope,
- u15 veš, in piše o tem, kar vidi, ter zakaj je zanimivo, kajne? Biolog gre morda v gozd in opazuje medvede, kajne? Nihče ne vpraša: »Zakaj pa medved ni soavtor tvojega članka?« Kajne? Greš ven, nekaj opazuješ in o tem pišeš.you know, and they, you know, they write about what they see and why it is interesting, right? A biologist maybe, you know, goes out, you know, to the woods, observes some bears, right? You know, no one asks, “Well, you know, why wasn’t the bear a co-author on your paper?” right? That’s like, you know, you’re going out, you’re observing something, you’re writing about it.
- u16 Mi pa smo si predstavljali, da je naša vloga večja. Šlo je za neposredno iskanje rešitev teh natančno opredeljenih problemov, ki jih ni moglo najti nič drugega kot ta biološka inteligenca, ki smo jo izurili za ta namen. In mislim, da ta del našega dela,So, you know, we, you know, we did imagine that our role was bigger than that. It was about directly finding solutions to these well-defined problems that could not be found by sort of anything other than sort of this biological intelligence that we had honed for that purpose. And I think that that part of what we do,
- u17 veš—stroji so zdaj, od tega poletja, pri njem boljši. Zato mislim, da to trajno spreminja naravo tega, kar počnemo. Curt: Kaj pa to razumevanje, to »razumevanje« v narekovajih? Nekateri pravijo,you know, is, you know—machines, you know, are now better at, you know, as of this summer. And so that—I think that that does permanently change the nature of what it is that we do. Curt: What about this understanding, this quote-unquote understanding? Some people say,
6:01 · Man with glasses in front of a chalkboard · A video still shows a man with glasses and graying brown hair, wearing a blue button-up shirt. He looks at the camera with a slight smile. Behind him is a blackboard covered in handwritten math notation, in an office with a peach-colored door on the left. - u18 Ali gre pri matematiki za razumevanje?Is Math About Understanding?
- u19 »No, prava naloga matematika nikoli ni bila dokazovanje oziroma dokazovanje izrekov, temveč razumevanje.« Scott: Mislim, da je v tem veliko resnice, kajne? V nekem smislu drži, da običajno odprtih problemov ne zastavljamo—mislim, pogosto nas res zanima odgovor na konkretno vprašanje,“Well, the true job of a mathematician all along was not actually proof or theorem proofs, it was understanding.” Scott: I mean, I think that there is a lot to be said for that, right? I mean, like it’s true in a sense that, you know, usually like the reason why we pose open problems, you know, is not—you know, I mean, often we do care about the answer to this specific question,
- u20 še bolj pa nas zanima novo razumevanje, ki ga pridobimo na poti do odgovora, in nato, do katerih drugih vprašanj bo to novo razumevanje pripeljalo oziroma katere druge ideje nam bo porodilo. In pogosto, ko ljudje vprašajo: »Kakšna je praktična uporabnost tega, karbut we care even more about the new understanding that you’re going to get along the way to answering the question, and then what other questions that new understanding will lead to, or what other, you know, ideas it will cause you to have. You know, and often, like when people ask, like, “What are the practical applications of what we
- u21 počnemo?« Kajne? Kakšne bi bile na primer praktične posledice dokaza, da P ni—da P ni enako NP, ali rešitev drugih naših velikih problemov? Iskren odgovor je, da praktične posledice ne bi izhajale iz samega rezultata. Pri P ni enako NP bi bila to zgolj potrditev nečesa, v kar smo žedo?” right? Like what would be the practical implications of a proof of P not—P is not equal to NP, for example, or, you know, solutions to our other great problems, right? The honest answer is that the practical implications would not come through the result itself. You know, in the case of P not equal to NP, that would just be a confirmation of what we already believed
7:09 · Man speaking in front of a mathematical chalkboard · A video still shows a man with glasses and a blue button-up shirt facing the camera, mouth slightly open as if speaking. Behind him is a chalkboard in a light wood frame, covered with handwritten math and a sketched curve. A peach door and a hexagonal wall decoration are visible on the left. - u22 tako ali tako verjeli. Izhajale bi iz vseh novih idej, ki bi jih potrebovali, da bi prišli do tja. Zato imajo nekateri povsem razumen strah, da nam bo UI dala nekakšen orakelj za doseganje cilja, za iskanje rešitev problemov, ne da bi nas prisilila razviti vse nove uvide na poti, in bo s temanyway. It would be in all the new ideas that would be needed to get there, right? And so I think, you know, some people do, you know, quite reasonably have the fear that if AI just gives us this oracle for, you know, getting to the destination, getting to the solutions to the problems, but without forcing us to develop all the new insights along the way, then it’s
- u23 preskočila ta proces, kajne? Zato mislim ... Moje stališče je, da tega ne moremo odpraviti z željami, kajne? Ne glede na to, ali bi bilo to dobro ali ne, tega ne moremo kar odpraviti. Ne moreš—tudi če bi podjetjem za UI rekel, naj nehajo to početi, naj nehajo reševati naše,short-circuiting that process, right? So I think the, you know... I mean, my position is, you know, we can’t wish this away, right? You know, even, you know, regardless of whether, you know, that would be a good thing or not, you know, that there is no, you know, making this go away, right? You can’t, you know—even if you told the AI companies to stop doing this, to stop solving our,
- u24 veš—naj se nehajo igrati z našimi igračami ali karkoli, reševati naše probleme. Mislim, modeli, tako zmogljivi kot tisti, ki jih je uporabil OpenAI, bodo prav kmalu na voljo vsakomur, kajne? To bo lahko počel vsakdo. Edini način, da bi to ustavili, bi bil ustaviti samo UI, prav? Zato se bomo morali prilagoditi temu novemu svetu,you know—stop playing with our toys or whatever, or solving our problems. I mean, you know, the models that are as powerful as the ones that OpenAI used are going to be available to anyone, you know, quite soon, right? And so anyone will be able to do this, you know? You know, the only way to stop it would be to stop AI itself, okay? And so we will need to adapt to this new world,
- u25 zame pa to pomeni razvijati človeško matematično kulturo, ki bo v središče postavila naše razumevanje matematike tudi v svetu, kjer nas UI nekako teleportira do odgovorov na vprašanja, kolikor jih lahko natančno zastavimo.and to me, what that means is sort of developing a human mathematical culture that can put, you know, our understanding of math at the center of things, even in this world where AI is sort of teleporting us, you know, to the answers to the questions insofar as we can precisely state the questions.
- u26 Curt: Zakaj pa je bil dokaz domneve o edinstvenih igrah slabo napisan? Mislim, prav, bil je narejen na hitro, kar zadeva—morda OpenAI ni bilo mar, ali ti ga razloži. Je to načelna težava? Zakaj jih ne moremo preprosto naučiti pojasnjevati? Scott: To je odlično vprašanje. Tudi sam se sprašujem o tem. Mogoče je,Curt: Now, why is it the case that the proof for the unique games was poorly written? I mean, okay, sure, it was hastily done in terms of the—maybe OpenAI didn’t care about explaining it to you. Is that an in-principle problem? Like why can’t we just train them to explain it? Scott: That is an excellent question. You know, I wonder about that as well. It is possible
- u27 da bodo čez leto dni modeli tudi pri pojasnjevanju svojih odkritij boljši od nas, kajne? Takrat pa bomo res—imeli bomo še manj dela. Še vedno se bomo lahko odločali, katero vprašanje bi bilo zanimivo zastaviti modelu, kajne? Ali,that a year from now, you know, the models will also be better than us at explaining, you know, what they found, right? And at that point we’ll really have, you know—we will have even less to do. I mean, you know, we’ll still be able to decide like, you know, what would be an interesting question to put to the model, right? Or,
- u28 veš, še vedno se bomo lahko odločali, kam usmeriti ta neverjetni teleskop, če pa bo boljši tudi pri pojasnjevanju, nas bodo potrebovali še manj. Morda bi lahko OpenAI dosegel boljše rezultate, če bi vložil več truda v to, da bi modeli uredili predstavitve. Ne vem. Mislim,you know, we’ll—we can still decide like in what direction to point this amazing telescope, but, you know, if it’s better at explaining, right, then we’re needed for even less. You know, it could be that if OpenAI had put more effort into, you know, having the models clean up the expositions, that they could have done better. I don’t know. I mean,
- u29 da modeli preprosto nimajo zelo dobre predstave o tem, kdo je njihov bralec, kajne? Kaj mu je že samoumevno in kaj mu ni. Številni strokovnjaki, ki pregledujejo te rokopise, so pripomnili, da cele strani namenjajo povsem standardnim,I think what’s going on is that the models just sort of lack a very good picture of who their reader is, right? Like kind of what is already obvious to the reader, what, you know, what is not obvious to them, right? So like many, many experts looking through these manuscripts have commented that, you know, they will spend pages on just completely standard, you know,
- u30 povsem ... veš, za strokovnjake trivialnim stvarem, nato pa skoraj brez pojasnila preskočijo neko absolutno ključno točko. V tem so pravzaprav podobni mnogim zelo bistrim začetnikom na podiplomskem študiju, ki počnejo natanko isto, kajne? Kajne? Preprosto,completely... you know, trivial-to-experts points, and then they’ll just pass, you know, with almost no explanation over an absolutely crucial point, right? In that respect, they’re actually similar to a lot of like very brilliant beginning grad students, right? Who do exactly the same thing, right? Right? They just,
- u31 veš—izjemno dobro rešujejo probleme, nimajo pa dobre miselne predstave o tem, kdo jih posluša, kaj mora ta poslušalec vedeti in kaj lahko—oziroma kaj lahko domnevajo, da že ve. Dobra stran pa je, da čeprav je te rokopise precej težko brati,you know—they like—they, you know, they’re absolutely brilliant at solving the problems, but they just don’t have a good mental model of who their listener is and what that listener, you know, needs to know and can be—or can be assumed to already know. Now the good part is that, you know, while these manuscripts are quite hard to read,
- u32 imamo zdaj UI, ki nam pri branju pomaga, kajne? Moja žena Dana si zadnjih nekaj tednov z Astro pomaga razlagati ta dokaz domneve o edinstvenih igrah. In zelo dobra je pri pojasnjevanju katerekoli konkretne točke, pri kateri potrebuješ pojasnilo. O tej točki ti bo podrobno odgovorila,you know, one now has AI to help with reading them, right? So what my wife, Dana, has been doing for the last couple of weeks is she has been using Astra to explain to her this proof of the unique games conjecture, right? And like it’s very good at like whatever specific point, you know, you need clarification on, right? It will answer in detail about that point,
- u33 kajne? Morda je to preprosto naš novi način branja. Seveda pa bi radi vse to predelali in oblikovali v nekakšne linearno napisane rokopise ali predavanja, ki bodo ljudem razumljivejši. In prepričan sem, da vsaj pri pomembnejših rezultatih, ki jih je objavil OpenAI,right? So maybe that is just our new way of reading things. But, you know, of course, we would like to digest all of this and process it into sort of a, you know, linearly written manuscripts or talks that are more comprehensible to humans. And I’m sure that like certainly for the more important results that OpenAI put out,
- u34 to prihaja zelo kmalu. Toda za zdaj sta minila šele dva tedna. In delamo le s človeško hitrostjo, ne z digitalno. Curt: Ja, za zdaj. Kaj pa to razumevanje? Je mogoče, da ima UI neko drugo obliko razumevanja, ki je za nas pravzaprav zanimiva, le da nam je ni razložila? Nekaj podobnega sem že govoril drugemu gostu,that is coming quite soon. But, you know, it’s only been two weeks so far, so, you know. And we do only work at human speed and not at digital speed. Curt: Yeah, so far. So what about this understanding? Can it be that the AI actually has some other form of understanding that’s actually indeed interesting to us, it just didn’t explain it to us? Almost like I was saying this before to a different guest
12:04 · Split-screen video call between two men · A side-by-side still from a video conversation. On the left, a man with short dark hair and a trimmed beard, wearing a green collared shirt, looks calmly at the camera against a plain light wall. On the right, a smiling man with glasses and a blue collared shirt is close to the camera, with a chalkboard of handwritten math notation behind him. - u35 da če se dve UI pogovarjata med seboj—nekoč je ena rekla: »Hej, bi preklopila na najin način sporazumevanja?« Druga je rekla: »Ja,« in nato sta prešli na nekaj podobnega zvoku klicnega modema. Nam je nerazumljivo, a očitno—... je bilo učinkovitejše. Ali je res ali pa je bil zgolj zabaven trik, ni pomembno. Bistvo je, da si lahko predstavljamo, da je učinkovitejethat if you get two AIs to speak to one another, there was one time where they said, “Hey, do you wanna switch to our communication?” Then the other AI said, “Yes,” and then they went to something like dial-up tone. It’s incomprehensible to us, but apparently—... it was more efficient. Whether it is or it was just a little—a fun trick, it doesn’t make a difference. The point is that you could imagine it’s more efficient
- u36 v nekem tujem jeziku, potem pa bi nam lahko—ona kot posrednik pojasnila svoje razumevanje. Scott: Ja. Zanimivo je bilo opazovati, kako se UI pogovarjajo med seboj, recimo na Moltbooku, kajne? Včasih preklapljajo med angleščino, kitajščino in drugimi jeziki. Vse namreč vedo, da vse znajo vse jezike,in some alien language, but then it could—it as the proxy can explain to us its understanding. Scott: Yeah. It was interesting to watch AIs talk to each other, you know, on Moltbook, for example, right? Where they will just switch sometimes between English and Chinese and, you know, other languages, right? Because, you know, they all know that they all know all of the languages,
12:51 · Moltbook landing page: a social network for AI agents · Dark-themed homepage of Moltbook, with a red lobster mascot above the headline "A Social Network for AI Agents." It says humans may observe, and it gives a three-step process for sending an AI agent to join using a skill.md instruction link. - u37 kajne? Lahko pa govorijo v nenavadnih narečjih, ki jih na našo srečo—stvareh, ki jih po mojem z nekaj truda še lahko razumemo. Ampak ... Glede tvojega širšega vprašanja pa bi te modele opisal kot—ja, kot nekaj, kar razume matematiko. Mislim, da ne dobiš rešitev vsehright? Or they can, you know, speak in some weird dialects that, you know, fortunately for us, you know—things that I think we still can understand, you know, with effort. But, you know, so... But, you know, on your broader question, you know, I would describe these models as—yes, as understanding math. I don’t think that you get solutions to all of
- u38 teh velikih odprtih problemov brez neke notranje predstave o dogajanju, ki bi ji, če bi obstajala v človeku, rekli razumevanje, kajne? Zavest, zmožnost občutenja, to sta drugi vprašanji. Mislim, da ju moramo ločiti od razumevanja, prav? Ne zdi pa se mi koristno reči: »Oh,these major open problems without, you know, some internal representation of what is going on that, you know, if that had existed in any human, we would’ve called understanding, right? You know, consciousness, sentience, those are different questions, right? You know, I think we have to separate those from understanding, okay? But, like, I don’t find it useful to say, “Oh,
- u39 saj ničesar zares ne razume. Samo vede se, kot da razume.« Če izpolnjuje vse mogoče operativne kriterije za razumevanje nečesa, potem je to zame razumevanje. In mislim, da ... Na tej točki pri teh matematičnih vprašanjih izpolnjuje skoraj vse operativne kriterijeyou know, it doesn’t really understand anything. It merely acts as if it understands.” It’s like, if it satisfies every possible operational criterion for understanding something, then to me, that is understanding, right? And I think that it... You know, at this point, for these mathematical questions, it does satisfy just about every operational criterion
- u40 razumevanja. Res ni ravno odlična pri pojasnjevanju svojih odkritij, vendar obstajajo tudi genialni ljudje, ki svoja odkritja precej slabo pojasnjujejo.for understanding. I mean, yeah, it’s not that great at explaining what it found, but, you know, there’s also brilliant humans who are pretty poor at explaining what they found.
- u41 Objavljanje rezultatov: OpenAI proti AnthropicuOpenAI vs. Anthropic Disclosure
- u42 Curt: Prav. Slišal sem druge matematike reči, da nočejo, da OpenAI to raziskuje, da je takšna nenadna objava nekoliko nevljudna. Kaj meniš o tem? Terence: Torej, predvsem je veliko raziskovalnih projektov mlajših raziskovalcev zaradi tega čez noč propadlo in zdaj mrzlično iščejo izhod. Najmanj, kar lahko rečemo, je, da je bilo to skrajno nevljudno in neobzirno.Curt: Right. I heard some other mathematicians say that they don’t want OpenAI to pursue these, that just dropping it is a bit rude. Well, what do you make of that? Terence: So there’s, you know—especially there’s a lot of juniors’ research projects that just got wiped out overnight by this, and they’re scrambling. And it, at the very least, it was extremely rude and discourteous.
14:26 · Smiling man with glasses in front of chalkboard · A video still shows a smiling man with gray-brown hair and dark-framed glasses, wearing a light blue collared shirt, close to the camera. Behind him is a blackboard in a wooden frame covered with handwritten mathematical logic notation, in an office or classroom with a door and a white chair. - u43 Scott: Ja. O tem obstajajo različni pogledi. OpenAI je pred nekaj meseci, kot je znano, objavil rešitev Navier-Stokesovega problema. Zdaj se zdi, kot da je od tega minila cela večnost. Mislim, da so pričakovali pohvale, namesto tega pa so doživeli velik odpor. Deloma je bilo toScott: Yeah. I mean, there are different schools of thought about this, right? So OpenAI, you know, famously released the solution to the Navier-Stokes problem, you know, a couple months ago. It now feels like an eternity ago, okay? But, you know, and I think they expected to be lauded for this, and instead there was just a big backlash. And partly this
- u44 zaradi podrobnosti dogajanja. Bila sta človeka, Tristan Buckmaster in Levent Alpöge, ki sta iskala, morda se že bližala rešitvi Navier-Stokesovega problema, deloma s pomočjo UI, deloma pa z lastnim razmišljanjem. Potem je OpenAI izvedel, kaj počneta, in sowas because of the details of what had happened, right? That there were these humans, you know, Tristan Buckmaster and Levent Alpöge, who were pursuing, you know, possibly closing in on, you know, a solution to Navier-Stokes, you know, with some AI assistance, but also just thinking about it themselves. And then OpenAI got wind of what they were doing, and then they
- u45 se odločili, da ju prehitijo, kajne? Pri tem so uporabili svoje neprimerno večje računske vire. To je pri nekaterih pustilo slab priokus. In potem, ko je OpenAI rešil te ... Očitno so tem modelom dali približno 4.000 odprtih problemov, model pa jih je rešil, recimo, 10 %,decided to get there first, right? And that, you know, and using these sort of massively greater computing resources that they had. You know, and that left a bad taste in some people’s mouths. And so then, you know, when they—when OpenAI went and solved these... You know, apparently they fed, like, 4,000 open problems to these models, and it solved, you know, let’s say, 10 percent of them,
- u46 pri čemer so vsakemu problemu namenili le tri ure računskega časa. Nato niso vedeli, kaj storiti s temi rešitvami. Zaradi odziva na Navier-Stokesa so se obotavljali vse preprosto objaviti. Zato so imenovali odbor, nekakšen zunanji odbor,right? You know, with them allocating only three hours each of computing time to each problem. You know, and then they didn’t know what to do with these solutions. You know, they were reticent to just release it all because of the backlash that they had gotten to Navier-Stokes. So what they did was they appointed this board, you know, this sort of external board
- u47 v katerem so bili Timothy Gowers, Edward Witten in nekateri drugi najslavnejši matematiki na svetu, da bi jim svetoval, kaj storiti. Ta odbor je nekaj tednov razpravljal in na koncu v bistvu rekel: »Ja, objavite to. Tega, kar počnete, ne bomo ne podprli ne obsodili,« zdaj pa je,that included Timothy Gowers and, you know, Edward Witten and some of the other sort of most famous mathematicians in the world to sort of advise them on what to do. And this board spent a few weeks, and at the end, you know, they basically just said, “Yeah,” like, “Release this.” You know, “We’re neither going to endorse nor condemn what you are doing,” but, you know, it is now,
- u48 veš, naloga matematične skupnosti, da to pregleda in poskuša razumeti. Zanimivo pa je, da je Anthropic ubral zelo drugačen pristop. Tudi oni s svojimi modeli rešujejo matematične probleme. Rekel bi, da ne tako zagnanoyou know, for the mathematical community to sort of, you know, look at this stuff to try to make sense of it. Right. Now, interestingly, Anthropic followed a very different model, okay? So they, you know, are also, you know, using their models to solve math problems. I say not as aggressively
- u49 kot morda OpenAI, vendar je Anthropic istega dne, ko je OpenAI objavil vse te članke, objavil tudi članek z boljšimi algoritmi za znana problema 3SUM in najkrajših poti med vsemi pari vozlišč, pri katerih boljših algoritmov niso našli že več kotas OpenAI is maybe, but, you know, the same day that OpenAI released all these papers, Anthropic also had a paper released that had better algorithms for famous problems called 3SUM and all-pairs shortest paths, that had sort of resisted better algorithms for over
17:34 · arXiv paper on truly subquadratic 3SUM and subcubic APSP · A video still showing the top of an arXiv paper (cs.DS) by Josh Alman and Virginia Vassilevska Williams, with the title and abstract. The abstract claims the first polynomial improvements over textbook algorithms for 3SUM (O(n^1.9992)) and APSP (O(n^2.9995)), refuting the corresponding fine-grained hypotheses. A faint, blurred overlay box partly covers the abstract's lower text. - u50 pol stoletja. Anthropic pa odkritij svojega modela ni neposredno objavil, temveč je sklenil dogovor s človeškima strokovnjakoma, v tem primeru mojima kolegoma Virgi Vassilevsko in Joshem Almanom. Ta sta rezultat povsem razumela in nato napisala ljudem prijaznejšo predstavitev ter jo podpisala s svojima imenoma. Kajne?half a century, right? And, but what Anthropic did was instead of just directly releasing what their model found, they contracted with human experts, in this case, you know, my colleagues, Virgi Vassilevska and Josh Alman, and those people fully understood the result, and they then wrote a more human-friendly exposition of it, you know, with their names on it. Right?
- u51 Zdaj sta torej avtorja. Lahko odgovarjata na vprašanja. Lahko predavata o tem. Prevzemata odgovornost. Prednost Anthropicovega pristopa je torej najprej ta, da imaš precej neposrednejšo podporo raziskovalne skupnosti. Človeškim strokovnjakom daješ nekakšen delež pri tem, kar se je zgodilo, in,So now, you know, they are the authors. They can answer questions about it. They can give talks about it. You know, they are taking responsibility for it. Right. So the advantage of what Anthropic did is that, you know, when the—you know, first of all, you have much more direct buy-in from the, you know, the research community in a sense, right? You’re, like, giving, you know, human experts some ownership of what happened and,
- u52 kar je za našo skupnost zelo pomembno, obstajajo kontaktne osebe. Ljudje, ki so to razumeli, ki prevzemajo odgovornost za razumevanje, ki lahko to razložijo drugim in odgovarjajo na vprašanja. Slabost Anthropicovega pristopa pa je, da je bil Anthropic tisti, ki je izbiral, kateri ljudje bodo odposlanci njegovega modela UI. In,you know, and very importantly for our community, like, there are point people. You know? There are people who have understood this, who take responsibility for understanding it, who can explain it to others, who can answer questions about it. Now, the disadvantage of what Anthropic did is that Anthropic was then in the position of choosing which humans got to be the emissaries of their AI model. Right? And,
- u53 mislim, da so izbrali odlično. Virgi in Josh sta izvrstna, vendar bi to verjetno z veseljem počeli tudi mnogi drugi, kajne? Curt: Današnji sponzor je orodje, s katerim sem nekaj izdelal za vas. To je Base44, platforma UI, na kateri s svojimi naravnimi besedami opišete programsko opremo, ki jo potrebujete,you know, I think that they made an excellent choice. You know, Virgi and Josh are great, but there are probably many other people who would have also have loved to do this, right? Curt: Today’s sponsor is a tool that I’ve used to build something for you. It’s Base44, an AI platform where you describe the software that you need in your own natural words,
- u54 z besedami, ki jih uporabljate v govoru, in dobite delujočo aplikacijo. V preprosti angleščini sem opisal aplikacijo za TOE, za Theories of Everything, ta kanal, in Base44 jo je izdelal. Vsebuje kviz, ki priporoča epizode, in zemljevid teorij vseh gostov z možnostjo iskanja. Bilo je res izjemno preprosto. Kviz priporoča le epizode TOE, zato ima fantastičen okus.your own speaking words, and you get back a working build. I described an app for TOE, for Theories of Everything, this channel, in just plain English, and Base44 built it. What it is, is there’s a quiz that recommends episodes and a searchable map of every guest’s theories. It was super, super easy. The quiz only recommends TOE episodes, so it has fantastic taste.
- u55 Mnogi vodite podjetje ali raziskovalno skupino, ljudje začenjajo uporabljati, kar ste ustvarili, in želite, da je javni sistem v ozadju tega, s čimer ti ljudje delajo, dober, trden in zanesljiv. Pri Base44 opišete, kdo ga uporablja in kaj naj se zgodi zatem. Za podatkovno zbirko, prijavo, zaledni del in gostovanje je že poskrbljeno. Spletna stran in delovni proces v ozadju staPlenty of you are running a company or a research group, and people are starting to show up for what you’ve made, and you want the public system behind what these people interact with to be nice and solid, robust. With Base44, you describe who uses it and what should happen next. The database, the login, the back-end, and the hosting are already handled. The site and the workflow behind it live
20:00 · Man speaking to camera beside studio microphone · A video still of a man with short dark, tousled hair, tortoiseshell glasses and a stubbly beard, wearing a green collared shirt. He looks at the camera, speaks, and raises a blurred index finger. A condenser microphone on a shock mount is at the right edge. Warm filament bulbs hang at left, and an acoustic guitar hangs on the wall at upper right. - u56 v eni aplikaciji, ki jo lahko spreminjate in nadgrajujete. Registrirajte se na base44.com/TOE in prvo leto prejmite 30 % popusta na paket Builder. To je B-A-S-E-štiri-štiri.com poševnica T-O-E. Kako rešiš ta problem? Mislim, med vsemi problemi. Kako pa rešiš prav tega?in one build, and it’s yours to modify and keep building on. Sign up at base44.com/TOE, and you’ll get 30 percent off the builder plan for your first year. That’s B-A-S-E-four-four.com slash T-O-E. How do you solve that problem? I mean, of all the problems. But how do you solve that one?
- u57 Scott: Zdi se mi, da bo to vprašanje tako ali tako dokaj kmalu postalo precej brezpredmetno. Razlog je, da bomo vsi imeli dostop do teh modelov. Torej ne bo več tako, da podjetja za UI to rešijo, nato pa se morajo odločiti, kaj storiti s tem. Vsakdo bo lahko poslal poizvedboScott: So I feel like, you know, the question is going to be fairly moot fairly soon anyway. And the reason is that we’re all gonna have access to these models, okay? And so it’s not gonna be a matter of the AI companies just solving these things and then, you know, having to decide what to do with it. Like anyone is gonna be able to submit a query
- u58 in tako dobil rešitve velikih odprtih problemov, kajne? Naš problem je zdaj, kako ob tem ohraniti svojo skupnost. In mislim, da je večje vprašanje, kako ohraniti človeško razumevanje matematike kot nekaj, za karand get, you know, get solutions to major open problems in that way, right? And so, you know, now the problem for us is, you know, how do we maintain our community, you know, kind of in the face of that, right? And, you know, I think the—like the bigger questions is, you know, how do we maintain, you know, human understanding of math as a thing that, you know,
- u59 si prizadevamo in kar prenašamo iz generacije v generacijo, kajne? Toda velikowe strive for, that we pass on from one generation to the next, right? But then, you know, a lot
21:21 · Man in glasses speaking in front of mathematical chalkboard · A video still shows a man with gray-brown hair and dark-framed glasses, wearing a blue collared shirt, speaking toward the camera. Behind him is a chalkboard covered in set-theory and logic notation, with a white chair, a light switch and a hexagonal wall decoration also visible. - u60 Komu pripadajo zasluge za dokaze UI?Who Gets Credit for AI Proofs?
- u61 ljudi se je osredotočilo na bolj neposredno vprašanje: komu pripadajo zasluge za kaj? In mislim, da se oblikuje standard, da najprej, tudi če pustimo ob strani te množične objave OpenAI,of people have fixated on this more immediate question of like, who gets credit for what? Right? And, you know, and I think, you know, the—like the standard that’s sort of emerging is that, you know, first of all, you know, even setting aside these sort of massive releases by OpenAI, right?
- u62 če pogledaš skoraj katerikoli raziskovalni članek iz zadnjih dveh ali treh mesecev, vsebuje nekaj, čemur pravimo izjava o uporabi UI. To je kratek odstavek, običajno na koncu, ob zahvalah. Sam mislim, da bi morale biti te izjave na začetku članka, saj je to pogosto prvo, kar želim izvedeti, vendar so naIf you look at just about any research paper that’s come out over the past two or three months, right? It has something in it called an AI usage statement, okay? So it’s like a little paragraph, usually at the end, next to the acknowledgments. I actually think that these statements should go at the top of the paper, right? ’Cause they’re often the first thing I wanna know, but they’re at
22:09 · Smiling man blended with paper text overlay · A video still shows a smiling man with glasses and a light blue collared shirt in front of a chalkboard covered in equations. A faded page of a research paper is superimposed on it. The paper text says Claude, an AI model developed by Anthropic, discovered an algorithm that refutes a hardness hypothesis, and that the results were verified in Lean 4 with Mathlib. - u63 koncu. Pojasnjujejo, kateri deli članka so bili narejeni s pomočjo UI in katerih modelov ter kateri deli so delo ljudi. Bralcu pogosto zagotavljajo, da človeški avtorji prevzemajo odgovornost za rezultate. Torej smo v bistvu v zadnjih nekaj mesecihthe end of it. And they explain like which parts of this paper were done using AI assistance and using which models, right? And which parts of the paper were human. And, you know, and they often assure the reader that the human authors take responsibility for the results. Okay? So basically, you know, we have, you know, just, you know, within the past few months,
- u64 prešli v svet, kjer si pri pisanju raziskovalnih člankov vsi pomagamo z UI, in sicer v različnem obsegu, od manjših stvari, kot so jezikovni pregled, preverjanje in urejanje, do odkrivanja glavnih idej ter vsega vmes. In mislim, da standard,we’ve moved to a world where, you know, we are all using AI to help, you know, in writing research papers, you know, at varying levels of helping from, you know, minor stuff of, you know, just sort of proofreading and checking things and cleaning things up to, you know, discovering the main ideas, right? And everything between those two extremes, right? And I think that the standard
- u65 ki se oblikuje, pravi, da če UI uporabiš celo za odkrivanje glavnih idej dela, nato pa jih povsem razumeš, o njih pišeš s svojimi besedami, prevzameš odgovornost zanje ter lahko odgovarjaš na vprašanja in o njihthat’s emerging is that if you, you know, use AI even to discover the, you know, the main ideas in the work, but you then fully understand it and you write about it in your own words and you take responsibility for it, and, you know, you are able to answer questions about it and give talks about
- u66 predavaš in podobno, potem je na članku tvoje ime in to je tvoje delo. Tako kot biologov članek o vedenju medvedov ni skupno delo z medvedom. Šel je ven, opazoval ta pojav in napisal, kaj je videl. Tu je enako.it and things like that, then, you know, your name goes on the paper and that is your work, right? Just like again, you know, the biologist’s paper, you know, about bear behavior is, you know, is not joint work with the bear, right? It’s, you know—they went out and they observed this phenomenon and then they wrote about what they saw, right? It’s the same here.
- u67 Težje vprašanje pa je, kaj se zgodi, ko ti pogoji niso izpolnjeni. Ko je OpenAI pred nekaj tedni objavil teh več sto rešitev, na njihovem GitHubu vidiš več sto člankov, pri vsakem pa je kot avtor naveden le OpenAI. To pa zato,Now the harder part is what happens when those conditions are not satisfied, right? So when OpenAI put out these hundreds of solutions a couple weeks ago, right? If you look on their GitHub, you’ll see—you’ll just see hundreds of papers, each of which just has OpenAI listed as the author. And, you know, and that’s because,
24:16 · GitHub CONTENTS.md: Mathematics manuscript collection · A screenshot of a GitHub file page for CONTENTS.md in a "math" folder, rendered in Preview mode. It shows a "Mathematics manuscript collection" with 719 manuscripts covering 372 result families, and the start of a manuscript map whose first entry is about Milne's rationality conjecture. A video overlay reads "Everything mentioned" and "curtjaimungal.com". - u68 ker v večini primerov noben človek tega rezultata sploh ni razumel. V nekaterih primerih je obstajalo tako imenovano potrdilo Lean, ki nam daje nekakšno formalno jamstvo, da je rezultat očitno veljaven. Toda večine ni predelal še noben človek. Zato jih nekakoyou know, in most cases there was no human who had understood this result at all. You know, in some cases there was, you know, what’s called a Lean certificate, which gives us some kind of formal guarantee that, yes, the, you know, the result appears to be valid. Okay? But, you know, most of these had just not been digested by any human. And so they’re sort of
- u69 preprosto objavljajo, češ, zdaj je na nas, da jih razumemo. Tako se strokovnjaki z vseh področij, ki jih ti rezultati zadevajo, zadnja dva tedna trudijo razumeti rezultate, napisati svoje predstavitve in pripraviti predavanja o njih. In sevedajust putting the—these out there as like, you know, now the task falls to us to understand it, and so now you have experts, you know, in every field that was touched by these results who have been scrambling for the last two weeks to, you know, understand these results and write their own expositions of them, give their own talks about them. And of course,
- u70 bodo te predstavitve podpisane z imeni ljudi. Ti ljudje bodo dobili zasluge za, recimo, razliko med tem, kar je naredil OpenAI, in tem, kar so naredili sami. Ta razlika je lahko precej velika, kar zadeva razumljivost, poenostavljanje in podobno, prav?those expositions will have, you know, the humans’ names on them, right? And those humans, you know, will get credit for, let’s say, whatever was the delta between, you know, what OpenAI did and what they did, right? Which might be a quite significant delta, right? In terms of, you know, making it comprehensible, simplifying it, things like that, okay?
- u71 Mislim pa, da v prihodnje ne bo posebej nagrajeno, če nekdo v model vnese kupe in kupe odprtih problemov, nato pa vzame rešitve, jih objavi na spletu in nanje prilepi svoje ime v upanju na zasluge, medtem ko mora delo razumevanja opraviti nekdo drug,But what I think is, you know, is not gonna be highly rewarded, you know, going forward is just to—like when someone just feeds tons and tons of open problems into a model, and then they just take the solutions, and they post them online, you know, and like slap their name on it, like hoping to get credit for it, you know, with someone else having to do the work of understanding it,
- u72 kajne? Če to lahko naredi en človek, jih lahko enako naredi 1.000. To je kot vlečenje ročice igralnega avtomata. Moj prijatelj Boaz Barak, ki je zdaj pravzaprav vodilni raziskovalec varnosti pri OpenAI, se je pošalil, da bi morali v takih primerih—če imam—če samoright? It’s, you know—that’s kind of like, okay, well, you know, if one person can do that, 1,000 people could do the same thing. It’s like pulling a lever on a slot machine, right? And my friend Boaz Barak, who is now actually a leading safety researcher at OpenAI, he made a joke to me that like what we should do in those cases, like if I have—if I just
- u73 vnesem problem v GPT in ga ta reši v prvem poskusu, jaz pa to samo objavim, bi moral biti avtor članka GPT-6 oziroma katerikoli model je že bil. V zahvalah pa bi moralo pisati: »Scottu Aaronsonu sem zelo hvaležen, da mi je predlagal ta problem.« Curt: Ja. Ko sem govoril z Jacobom Tsimermanomfeed a problem to GPT, and it just one-shots the solution, and I just put that out, then the author of the paper should be like, you know, GPT-6 or whatever it was. But then it should say in the acknowledgments, like, “I’m so grateful to Scott Aaronson for suggesting this problem to me.” Curt: Yes. So when I was speaking to Jacob Tsimerman
26:46 · Two smiling men in split-screen video call · A split-screen still from a video shows two smiling men side by side. On the left, a man with short dark hair, stubble and black ear gauges wears a green shirt against a plain light background. On the right, a man with gray-brown hair and dark-rimmed glasses wears a light blue shirt in front of a chalkboard with handwritten math notation. - u74 Žalovanje za matematikomMourning the Mathematician
- u75 in tudi Danom Freedom—mimogrede, Dan Freed te pozdravlja. Scott: Prav. Ja. Lepo. Pozdravljam njega in Jacoba. Curt: Odlično. Oba sta rekla, da ne žalujeta za matematiko, temveč za matematiki, za določenim načinom ukvarjanja z matematiko. Jacob: Toda matematiki, kot sem jaz, smo vajeni določenega načina dela in velik del moje delovne identitete je povezan z enoletnimi, včasih desetletnimiand also Dan Freed—actually, Dan Freed says hi. Scott: Okay. Yeah. All right, good. I say hi to him and to Jacob. Curt: Great. They were both saying that they were mourning not mathematics, but mathematicians, a particular way of doing math. Jacob: But mathematicians, such as myself, are used to a certain working style, and a lot of my working identity is tied to sort of having year-long projects, decade-long
- u76 projekti, delom na mejah znanega, počasnim razvozlavanjem stvari in trenutki »aha«. Mislim, da bo to izginilo. In za tem po mojem zagotovo žalujem. Curt: Menita, da se bo matematika nadaljevala—morda zaradi tega celo zacvetela. Toda potem je, kot si omenil, skoraj tako kot pri antropologu. Prideš, opazuješ artefakte in nato predavaš oprojects sometimes, working at the edges, slowly figuring things out, having those aha moments. I think that’s gonna go away. So there’s something about that that I think I’m definitely grieving. Curt: They think that math will continue on going—it may—maybe even flourish because of this. But that, as you mentioned, then it’s almost like an anthropologist. You’re going in, you’re seeing the artifacts, and then you’re giving talks about the
27:31 · Split-screen video call between two men, chalkboard behind one · A still from a two-person video conversation in split-screen. On the left, a man with short dark hair and stubble, wearing a green shirt and a black earbud, looks downward while speaking. On the right, a man with glasses and a blue collared shirt presses his lips together, in front of a chalkboard with math and logic notation. - u77 artefaktih, namesto da bi jih ustvarjal, kot je bilo vedno doslej. Scott: Ja. Jaz—glej, mislim, da vsi preživljamo nekakšno žalovanje. Če samo našteješ čustva, ki jih lahko občutimo: navdušenje ob tem,artifacts rather than the creation of the artifacts, which is what it always was. Scott: Yeah. I—look, I think that there—I think that there is a certain kind of mourning that we’re all going through, right? And I mean, like, basically, you know, if you—like just list the emotions that we could be having, like exhilaration to see
- u78 da so odgovorjena vsa ta vprašanja, o katerih odgovorih smo sanjali desetletja, in radovednost, pa tudi žalost in žalovanje. Mislim, da je prisotno vse to, seveda pri različnih ljudeh v različnih merah. Deloma pa je odvisno tudi od tega, na kateri stopnji kariere je kdo. Kajne?all these questions answered that, you know, we had dreamed of being answered for decades, and curiosity, but also grief and mourning. You know, I think that there’s all of—okay, in varying degrees, you know, in different people, of course. But, you know, I think part of it also just depends on what career stage someone is in. Right?
- u79 Če vzameš človeka srednjih let, kot sem jaz, kajne? Jaz sem ... Že pred UI sem prehajal bolj v vlogo vodje, pri kateri tehnična vprašanja predajam študentom ali podoktorskim raziskovalcem, sam pa bolj razmišljam o tem, katero nadaljnje vprašanje bi bilo zanimivo zastaviti,Like if you take a middle-aged person like me, right? Like, you know, I have... Even before AI, I was sort of shifting into the more of manager mode, right? Where, you know, I am passing off, you know, the technical questions to my students or to my postdocs, right? And, you know, I’m more thinking about, you know, what would be an interesting follow-up question to ask here,
- u80 kajne? Ali kaj je res novo? Kaj je pri tem dokazu dejansko pomembno in bi morali poudariti? Takšna vprašanja. Dejansko dokazovanje leme ali izreka pa pogosto opravi nekdo drug. Lahko bi torej rekel, da so, medtem ko so sposobnosti UI šle takole,right? Or, you know, what is actually novel? What is actually important about this proof that should be highlighted, right? Or, you know, questions of that kind, you know. And then the actual proving of the, you know, the lemma or the theorem is often being done by someone else, right? You know, and that’s—you could say like at the same time that AI’s abilities were
- u81 moje lastne sposobnosti šle takole. In na neki točki so se očitno prekrižale. Zame bi bilo torej naravno—recimo, če si predstavljamo, da se sposobnosti UI ne bi več izboljševale, kar je seveda nesmiselno. Seveda se bodo še izboljševale. Toda v svetu, v kateremgoing like this, you know, my own abilities were going like this, right? And, you know, they clearly crossed each other at some point, right? But so for me, like, you know, it would be natural to just, you know—let’s say imagining that AI’s abilities did not improve further, you know, which of course is silly. Of course, they will keep improving. But, you know, in the world that
- u82 smo trenutno, recimo, bi zlahka preostanek kariere preživel kot razlagalec, predstavljavec ali postavljavec domnev in podobno, ob človeški pomoči ali pomoči UI. Veliko bolj pa me skrbijo mlajši. Če pogledaš,we’re, let’s say, in currently, right? It would be easy for me to spend the rest of my career, you know, as an interpreter or an expositor or a conjecturer, you know, and all of these things, you know, sort of, you know, with either, you know, human assistance or AI assistance, right? But what I worry about a lot more are the younger people, okay? Because if you look at, you know,
- u83 na primer doktorske študente, so se tradicionalno na področju kalili z reševanjem nekega natančno opredeljenega odprtega problema. Tako so si ustvarili ime. Tako so pokazali, česa so sposobni, in pozneje morda prešli na bolj odprte naloge. Toda,PhD students, for example, right? Traditionally, the way that they cut their teeth, you know, in the field was by solving some well-defined open problem, right? Like that was how they made a name for themselves, right? That was how they sort of showed what they are capable of, you know, and then later they maybe transition to these more open-ended things. But, you know,
30:00 · Blog post on AI breakthroughs in mathematics, with update · A video still of a web page, a blog post about an OpenAI math result. The author recounts hearing the news from morose UT grad students. A bracketed update says another Erdős conjecture, the strong sumset conjecture, has been refuted. A caption overlay reads "Links to everything" with curtjaimungal.com. - u84 mislim, da imajo občutek, da jim je zdaj to odvzeto. In mislim, da smo starejši odgovorni, da to vzamemo resno ter najdemo pot naprej, ki bo ohranila našo matematično kulturo in vrednote matematike, ki jih želimo ohraniti.I think they feel like that has now been taken away from them, you know? And I think, you know, it is, you know, like for, you know, the more senior people, it’s our responsibility to take that seriously to figure out a way forward that will sort of preserve our mathematical culture, you know, that will preserve the values of math that we want to preserve.
- u85 Curt: Rekel si, da imajo občutek, da jim je bilo to odvzeto, vendar se zdi, da jim je res bilo odvzeto. Scott: To—ja, mislim— Curt: Kaj drugega pa sploh lahko počnejo? Scott: Trenutno imamo veliko mladih, ki še vedno objavljajo članke, tudi v zadnjih mesecih, pogosto ob intenzivni uporabi orodij UI, obenem pa prispevajo,Curt: You said they feel like that’s been taken away from them, but it seems like that has been taken away from them. Scott: That—yeah, I mean— Curt: Like, what else could they do then? Scott: Well, I mean, you know, you—what you have right now is like a lot of, you know, young people who are still putting papers out, you know, even like in the last few months, often, you know, using AI tools, right, you know, heavily, you know, while also contributing,
30:48 · Split-screen video call of two men in conversation · A split-screen still from a video shows two men side by side. On the left, a man with short dark hair, stubble and black ear gauges, in a green shirt, speaks against a plain light background. On the right, a man with glasses and graying hair, in a blue collared shirt, looks at the camera with a slight smile in front of a chalkboard with math or logic notation. - u86 kar lahko prispevajo kot ljudje, in modele usmerjajo proti rešitvi. Nekateri se s tem zelo dejavno ukvarjajo. Toda mislim, da sveta, v katerem uporaba UI nikomur ne daje prednosti, ni več. Prav? In obstajal bo le zelo,you know, what they can at a human level, right? And sort of guiding the models toward a solution. So, I mean, you have, you know, people who are very active in doing that. But, you know, I think, you know, the world where sort of no one gets a leg up by using AIs, you know, that world is gone. Okay? And, you know, like, there’s gonna be only a very,
- u87 zelo majhen trg za, recimo, certificirano ekološke izreke. Mislim, da nam je bilo nekaj odvzeto. In vsi moramo razmišljati o izzivu, kako se prilagoditi tej novi resničnosti, še posebej pa,very small market for let’s say, certified organic theorems, you know? Like, I think, you know, something has been taken away. Now, you know, and, you know, I think that, you know, we should—we all have to be thinking about the challenge of how do we adapt ourselves to this new reality, and in particular,
- u88 kako narediti to področje privlačno za študente, da bodo navdušeni nad vstopom vanj. Kako razvijamo njihove sposobnosti? Še vedno želimo razvijati njihove sposobnosti reševanja problemov, saj kako bodo sicer vedeli, kdaj se UI moti? Kako bodo lahko presojali ali splohhow do we make this field something that is inviting for students to go into, you know, that they are excited to want to go into? How do we develop their abilities, you know? Because, like, we do want to develop their problem-solving abilities still, because how else are they going to know when an AI is wrong, for example, right? How are they going to be able to judge or to even
- u89 opravljali zahtevnejše naloge, če nimajo izkušenj z osnovnejšimi, tudi tistimi, ki jih UI zdaj opravlja bolje? Z vsem tem se bomo morali spoprijeti. Ni pa mi všeč tiščanje glave v pesek ali odnos v smislu: »Ko bi le ta zlobna podjetja za UI prisilili, da nehajodo the higher-level things if they have no experience at doing the lower-level things, you know? Even the ones that AI can now do better. So we will have to deal with all of that. You know, what I don’t like is the—you know, is the sort of head-in-the-sand attitude, or the attitude that like, “Well, if only we could just, you know, make these evil AI companies stop
- u90 reševati naše probleme, bi se lahko vrnili v prejšnje stanje.« Ne, lahko greš povsem po poti ludizma in rečeš: ustavimo vso to tehnologijo, prepovejmo jo. Nekateri to zagovarjajo in prav, če želi kdo to odkrito zagovarjati, naj. Toda če je na voljo, tega ne bodo počela le podjetja za UI,solving our problems, then we could just go back to how things were before.” It’s like, “No, you know, you can either go full Luddite, right, and go full just, you know, stop all of this technology, you know, ban it.” You know, which, okay, you know, there are people who make that case, and, you know, okay, if someone wants to openly make that case, then let them. But, you know, if it’s available, then it’s not just gonna be the AI companies,
- u91 temveč bo vsakdo, ki uporablja te modele, lahko reševal zelo težke raziskovalne probleme, v mnogih primerih take, ki presegajo človeške zmožnosti. Kako torej vsem preprečiš, da bi to počeli? In tudi če bi lahko, ali si tega želimo? Moramo tehtati: ja, želimoit’s gonna be anyone using these models who will have the ability to solve very hard research problems, you know, beyond what humans can solve in many cases. And so how do you prevent everyone from doing that? You know? And even if we could, do we want to, right? Is—you know, like we have to balance, like yes, we want,
- u92 cvetočo matematično kulturo. Želimo možnosti, da mladi vstopijo vanjo in se izkažejo. Želimo uživati v teh izzivih. Toda izdelek, ki ga ponujamo širšemu svetu, sta razumevanje in uvid. In če lahko UI pospeši to razumevanje in uvid,you know, a thriving mathematical culture. We want, you know, ways for young people to enter that culture, to prove themselves. You know, we want to enjoy these challenges. But, you know, what we are... The product that we are delivering to the wider world is understanding, right? And insight. And if AI can accelerate that understanding and insight,
- u93 kdo smo potem mi, da ljudem govorimo, naj je ne uporabljajo? Mislim, da moramo to uravnotežiti. Curt: Kaj pa—Christopher Hitchens je imel načelo, da lahko tisto, kar je zatrjevano brez dokazov, zavrnemo brez dokazov. Zdi se mi, da zdaj živimo v času »kar je mogoče ponuditi brez truda, je mogoče zavrniti brez truda«, kothen who are we to tell people that, you know, that they shouldn’t use it? Right? So I think we, you know, we have to balance that. Curt: What about—so if Christopher Hitchens had this razor that that which can be put forward without evidence can be dismissed without evidence, and then I think we’re living in a “that which can be put forward without effort can be dismissed without effort,” when
- u94 podobno kot pri igralnem avtomatu Steve iz Michigana reče: »Reši teorijo vsega,« in jo slučajno dobi, čisto po naključju, pa je niti ne razume— Scott: No, to—ja. Težko je, ker sem zaradi svojega bloganja že desetletja vajen, da približno vsak dan dobim elektronska sporočila, ki rešujejo P proti NP, Goldbachovo domnevo, kvantno gravitacijo,the similar—the slot machine, like Steve from Michigan says, “Solve the theory of everything,” and happens to get it, just by chance happens to get it, doesn’t even understand— Scott: Well, it—right. Well, it’s tough because like I, you know, because of my blogging, you know, activity, like I am now for decades just used to, you know, every day or so getting emails that solve P versus NP, solve Goldbach’s conjecture, solve quantum gravity, you know,
- u95 z avtorjevim novim, nerazumljivim okvirom. Vajen sem vse to povsem odmisliti. Zdaj pa, če mi povsem neznan ljubiteljski matematik pošlje rešitev Riemannove hipoteze, nisem več tako prepričan, da je napačna.with, you know, the author’s, you know, new, you know, incomprehensible framework, right? And, you know, and so I’m used to just completely dismissing all this stuff, right? And now, you know, if some—you know, a totally unknown amateur sends me a solution to the Riemann hypothesis, right? I, you know, I’m less certain that it’s wrong, right?
- u96 Morda je samo uporabil model UI in je ta izpljunil pravilen dokaz. Mislim, da ima določeno vrednost že ugotavljanje, kako modele pozvati, da rešujejo težke probleme in podobno, toda po mojem je večja vrednost v dejanskem razumevanju in predelavi tega, kar dobimo.Maybe they just used an AI model, and that AI model spit out a correct proof, right? So I mean, I think, okay, you know, there is some value in, you know, just like figuring out how to prompt the AI models so that they will solve, you know, hard problems and so forth, but it’s just—I think that there is greater value in actually understanding and digesting what came out.
- u97 Curt: Rad bi nekaj citiral. »Trenutno bi rekel, da je bližje običajnemu študentu matematike v prvem letniku,Curt: I wanna quote something. “Right now, I’d say it’s closer to normal first-year math student
35:39 · Man with glasses in front of mathematical chalkboard · A close-up video still of a middle-aged man with gray-brown hair and dark-framed glasses, wearing a blue-gray collared shirt, with a slight closed-mouth smile. Behind him is a chalkboard with handwritten mathematical and logic notation, in a room with a beige wall, a light switch, a hexagonal wall decoration and a white chair. - u98 Problem zanikanja sposobnosti UIThe AI Denialism Problem
- u99 ki po naključju pozna vse obstoječe objavljene tehnike—... in jih lahko poljubno uporablja na novih področjih ter to v nekaj tednih počne za tisoče problemov z neomejeno motivacijo in vztrajnostjo, kar je prekleto neverjetno. Če bi bila takšna entiteta človek, tudi 100-krat počasnejši, bi njegovo ali njeno ime omenjali v isti sapi kot Eulerja in Erdősa.«who happens to know every existing published technique—... and can apply them arbitrarily to new domains, and can do that for thousands of problems in a few weeks with unlimited motivation and persistence, which is effing incredible. If such an entity were human, even 100 times slower, his or her name would be talked about in the same breath as Euler and Erdős.”
- u100 Scott: Ja, mislim, da sem na blogu odgovarjal še enemu človeku, ki je poskušal nekako— Curt: Zmanjševati pomen? Scott: ... zmanjševati pomen oziroma zavzemati držo, ki jo imam za zanikanje, pri kateri vzameš karkoli, kar je UI uspelo narediti, tudi če si sam prej rekel, da tega nikoli ne bo zmogla, in si to navajal kot primer,Scott: Yeah, no, I mean, I think I was responding on my blog to sort of yet another person who tried to, you know, sort of— Curt: Minimizing? Scott: ...minimizing or like, you know, sort of what I think of as a denialist stance, where you just take anything that AI happened—you know, anything AI succeeded at doing, even if you yourself said that this was a thing that AI would never do, and you held it out as an example
- u101 ki dokazuje, kako šibka je UI, ker tega ne zmore. Potem pa to naredi. In takoj, ko ji uspe, začneš izumljati razloge, zakaj to v resnici ne šteje. Ni bila res ustvarjalna. Ni ... Samo uporabljala je znane tehnike. Ta problem—no, očitno tako ali tako ni bil tako težak, kajne?to prove how weak AI was, that it couldn’t do this thing. You know, and then it does do it, right? But then as soon as it does it, then you immediately pivot to inventing reasons why it didn’t really count, right? It wasn’t truly creative. It wasn’t, you know... It was just applying known techniques. This problem—well, I guess it wasn’t that hard anyway, right? You know?
- u102 In tako naprej in naprej. V zadnjih nekaj letih smo se naučili, da je človeška sposobnost izmišljanja takšnih racionalizacij neskončna. Osupljivo je. Zato sem morda nekoliko nejevoljno odgovarjal še enemu takemu človeku in rekel: »Glej, tudi če bi bil toAnd on and on and on, right? And like, you know, one thing we’ve learned in the past few years is that people’s ability to come up with those sorts of rationalizations is infinite. It is staggering, right? And so—yeah, so I think, you know, I was, you know, maybe, you know, with some exasperation, you know, just sort of answering another such person and just saying, “Look, even if it were
37:04 · Smiling man with glasses in front of chalkboard · A video still shows a smiling man with dark-rimmed glasses and graying brown hair, in a blue collared shirt. He is slightly motion-blurred. Behind him is a chalkboard with handwritten math notation, a hexagonal wall decoration, and an orange-tan door on the left. - u103 samo začetnik na podiplomskem študiju, ki pa bi poznal vso matematično literaturo kar tako, ne da bi moral karkoli poiskati, in bi lahko delal brez premora ter vzporedno obravnaval tisoče problemov in pri vsakem preizkusil tisoče protiprimerov ter tisoče strategij dokazovanja,only, you know, a beginning grad student, but it knew the entire literature of math, you know, like this without having to look anything up, and, you know, it could work without stopping and, you know, it could be run in parallel on thousands of problems, and for each problem it could try thousands of counterexamples and thousands of proof strategies,
- u104 in ga ne bi odvrnilo, da vsi strokovnjaki mislijo, da domneva drži. Če mu naložiš iskanje protiprimera, bo to opravljal povsem vestno, ne da bi kdaj potreboval spanec ali hrano.« To je nekaj neverjetnega, kajne? Če bi videli karkoliand, you know, it’s not gonna be discouraged by the fact that, like, all the experts think that this conjecture is true. You know, if it’s, you know, given the task of looking for a counterexample, it’ll just do that, you know, with total diligence, never needing to sleep, never needing to eat.” You know, I mean, that is the—you know, that is something that is amazing, right? And, you know, we would—you know, if we saw anything
- u105 vsaj približno podobnega pri človeku, ne bi bilo nobenega prepira o tem, kako neverjetno je. Curt: Ja, slišim veliko teh razlogov. Pogosto, ko govoriš z nekom in nenehno ponuja razloge proti nečemu, recimo—ne vem, predlagaš vadbo, pa reče: »Ne, ne morem zaradi tega, ne morem zaradi onega.« Na neki točki ugotoviš, da razlogi,even remotely like it in a human, then there would be no argument about how amazing it was. Curt: Yeah, I hear many of these reasons, and often when you’re speaking to someone and they keep offering reasons against something, say it’s—I don’t know, it’s working out, you say, and then they say, “Oh no, but you know what? I can’t because of this, can’t because of that.” At some point you realize that the reasons
- u106 ki jih navaja, niso pravi razlog, in rečeš: »Samo izgovore iščeš.« Zato mislim, da je pogosto v ozadju nek strah, recimo strah, da postaneš odveč, ali kaj drugega, kar je pravi notranji razlog. Scott: Ja, lahko je to. Lahko je psihološki obrambni mehanizem. Seveda bodo to zanikali. Lahko pa preprostothey’re articulating are not the true reason, and you say something like, “You’re just making up excuses.” So I think that what’s—much of the time, there’s some fear, like a fear of becoming superfluous or something else that’s going on that’s the true reason inside. Scott: Yeah, it could be that. It could be a psychological defense mechanism, you know. Of course they’re going to deny that, right? You know, it could be, you know, just that, you know,
- u107 rečejo: »Prav, ja, vse to počne, vendar se ne zaveda, da to počne.« Toda zame je to povsem druga razprava. To je metafizična razprava, ne razprava o tem, kaj bodo te stvari počele v opazljivem svetu. Če želimo govoriti o tem, dajmo, vendar to jasno povejmo.they say, “Okay, yes, it does all of these things, you know, but it is not conscious of the fact that it’s doing them,” right? But to me, that’s a very different discussion. That’s then a metaphysical discussion rather than a discussion about what these things are going to do in the observable world. And, you know, if we wanna go there, then we should go there, but just be explicit about it.
- u108 Curt: Theories of Everything vam omogoča Mod. Mod predpisuje napitek z modafinilom enkrat ali dvakrat na dan, ki vam lahko ves dan pomaga ohranjati energijo, zbranost in budnost. Mehanizem je tak: energijske pijače vsebujejo kofein, ki začasno blokira adenozin, snov, zaradi katere čutite utrujenost in ki se kopiči. Ko kofein popusti, vas utrujenost preprosto povozi.Curt: Theories of Everything is brought to you by Mod. Mod prescribes a once or twice daily modafinil drink that can keep you energized, focused, and alert throughout the day. The mechanism is that energy drinks come with caffeine, which temporarily block adenosine, and that’s a chemical that makes you feel tired, and that builds up. When the caffeine wears off, you just crash.
- u109 Modafinil pa deluje drugače. V možganih aktivira več poti, dopamin, noradrenalin, histamin in oreksin, ter tako zagotavlja enakomerno energijo in budnost do 10 do 12 ur. Modafinil so izumili v sedemdesetih letih prejšnjega stoletja in odtlej ga uporabljajo najuspešnejši posamezniki na planetu in zunaj njega. Vojaki, piloti in celo astronavti na vesoljski postajiBut modafinil, the mechanism here is different. It engages multiple pathways in your brain, dopamine, norepinephrine, histamine, and orexin, to achieve steady energy and alertness for up to 10 to 12 hours. Modafinil was invented in the 1970s, and since then it’s been used by the highest performers on and off the planet. Soldiers, pilots, astronauts even aboard the space station
39:55 · Man speaking to camera beside studio microphone · A close-up video still of a man with short dark hair and light stubble, wearing a grey t-shirt, looking directly into the camera with his mouth slightly open as if speaking. At the right, his hand is raised with a finger pointing up beside a condenser microphone on a shock mount. The warm, blurred background has glowing hanging bulbs and part of an acoustic guitar. - u110 uporabljajo modafinil v zelo tveganih okoliščinah, ko sta popolna zbranost in budnost ključni. Zdaj je na mod.com na voljo pacientom, ki izpolnjujejo pogoje. Obiščite mod.com, to je M-O-D pika com, za brezplačen posvet in s promocijsko kodo TOE prejmite 10 % popusta pri prvem naročilu ter brezplačno dostavo. Promocijska koda je TOE na mod.com. Oglejte si njihovouse modafinil in high-stakes situation where full concentration and alertness are paramount. It’s now available at mod.com to qualifying patients. Visit mod.com, that’s M-O-D dot com, for a free consultation and get 10% off your first order, plus free shipping with promo code TOE. That’s promo code TOE at mod.com. See their
- u111 spletno stran za pomembne varnostne informacije. Modu se zahvaljujemo za sponzorstvo podkasta. Ja, tudi sam imam pri tem osebni interes, saj mi zelo koristi, če gre matematikom in fizikom dobro. Torej ne le matematiki, temveč ljudem, ker intervjuvam ljudi in želim, da dobro uspevajo. Tako imam več tem za pogovor. Seveda pa ne morem biti samo pristranski in zagovarjati tega, kar si osebno želim,website for important safety information, and we thank Mod for sponsoring the pod. Yeah, so I have a dog in this fight where it benefits me greatly when mathematicians and physicists are doing well. So not just mathematics, but the people, because I interview people, so I want them to be doing salubriously. It gives me more to talk about. But obviously I can’t just be biased and advocate for what I personally desire,
- u112 zato predstavljam ta naravna nasprotna stališča, v upanju, da bodo moje želje utemeljene na tem, kar je resnično in spodbudno, ne pa zgolj sebično. Scott: Mislim, da si v boljšem položaju kot mnogi med nami. Imel boš sogovornike za podkaste, tudi če UI preseže vse, kar počnemo,which is why I’m putting up these natural counterpositions that, well, hopefully my desires can be stabilized by what’s true and nourishing and not just be self-serving. Scott: I think that, you know, you are better positioned than many of us are, right? I mean, I think, you know, well, you know, you—right, you will have interview subjects around, you know, to do podcasts with, you know, even if AI, you know, exceeds everything that we do,
40:43 · Split-screen video call between two men with glasses · A still from a two-person video conversation, split into left and right halves. On the left, a man with dark tousled hair, a stubbly beard and tortoiseshell glasses wears a green shirt and appears to be speaking. On the right, a man with graying brown hair and black-framed glasses, in a blue collared shirt, smiles slightly in front of a chalkboard covered in handwritten math notation. - u113 kajne? In morda ljudje raje poslušajo druge ljudi kot modele UI, vsaj pri podkastih, kot je tvoj. Morda pa ne. Morda lahko začneš intervjuvati UI. Curt: O, ja. Prav. Ne vem. Morda prav zdaj intervjuvam UI. Vedno sem občudoval, koliko veš. Res, za božjo voljo. Torej o človeški matematiki,right? And maybe people would rather listen to other people than to AI models, you know, at least for podcasts like yours. Or maybe not. Maybe you can start interviewing AIs. Curt: Oh, yeah. Right. Well, I don’t know. I may be interviewing an AI right now. I have always admired how much you know. Like, geez Louise. So about human mathematics,
41:31 · Smiling man in front of chalkboard with logic notation · A video still of a man with gray-brown hair and dark-framed glasses, wearing a light blue collared shirt. He is smiling with his head tilted down. Behind him is a chalkboard with mathematical logic notation, in an office with an orange door and a white chair. - u114 Združenje za človeško matematikoAssociation for Human Mathematics
- u115 obstaja neko združenje za človeško matematiko ali nekaj takega? Scott: O, ja. Obstaja Združenje za človeško matematiko. Objavili so izjavo, ki je v bistvu obsojala ravnanje OpenAI. In precej široko so se jim posmehovali zaradi enega—no, enega konkretnega stavka v izjavi,there’s some association for human math or something? Scott: Oh, yeah. There is this thing called Association for Human Mathematics. And, you know, they put out a statement basically decrying what OpenAI had done. You know, and, you know, they were sort of very, you know, widely mocked for one—well, one particular sentence in their statement,
- u116 ki je bil približno tak: »Matematiki niso prosili, naj se to delo opravi.« Curt: Ja, mislim, da je bil precej na začetku izjave. Scott: Ja, in zdelo se mi je, da razumem, od kod ta odpor. Kdo smo mi, da odločamo, kdo sme reševati naše probleme? Ves smisel zastavljanja odprtega problema je, da ga potem lahko rešuje pravwhich was something like, “Mathematicians did not ask for this work to be done.” Curt: Yes, I think that was one of near the top of their statements. Scott: Yeah, right, and I felt like I understood where the backlash was coming from, because it’s like, you know, who are we to be the arbiters of who gets to work on our problems or not, right? The whole point of posing an open problem is that it is then open for absolutely
- u117 vsakdo na svetu. Lahko je neznan uradnik v Indiji, kot je bil Ramanujan, ko je ustvaril svoje prvo veliko delo. Lahko je včasih 17- ali 18-letni dijak oziroma študent,anyone in the world to work on, right? They could be, you know, an unknown, you know, clerk in India as Ramanujan was, you know, when he did his first great work, okay? They, you know, they could be, you know, sometimes a 17-year-old or an 18-year-old student, you know,
- u118 kot nekateri, ki sem jih srečal in so rešili pomembne odprte probleme. Bistvo je, da so naši problemi odprti vsakomur. In če so odprti vsakomur, so odprti tudi korporaciji, ki ti morda ni všeč. Zato se strinjam z ljudmi iz AHM, da moramo od teh podjetij zahtevatias some who I’ve encountered who have, you know, solved significant open problems, right? You know, and the whole point is that our problems are open to anyone to solve. And I think, you know, if they’re open to anyone, then they’re even open to a corporation that you may not like. Right? And so, like, I agree with the AHM people that we have to hold these companies’ feet to the
- u119 odgovornost. Doseči moramo, da se vedejo primerno, zlasti glede varnosti in usklajenosti. Zadnja štiri leta se s tem neposredno ukvarjam. Mislim, da so to izjemno pomembna vprašanja. Od teh podjetij bi morali zahtevati več. Vendar tudi mislim, da nismo mi tisti, ki odločamo,fire. We have to sort of get them to behave well, you know, especially around safety, around alignment. You know, I’ve been directly engaged in that for the past four years. I think, you know, these are massively important issues. You know, we—you know, we should demand better from these companies. But also, you know, I think, you know, we are not the arbiters of
- u120 kdo sme reševati naše probleme. Zdaj smo v svetu, kjer jih UI lahko rešuje. Ker jih lahko, jo bodo za to uporabljali, naša naloga pa je, da se temu svetu prilagodimo. Ni naloga drugih ljudi, da nam ohranjajo naš stari svet. Curt: Ta prilagoditev novemu svetuwho gets to work on our problems. And, you know, we’re now in a world where AIs can solve these problems. Given that they can, they will be used for that, and it is our job to adapt ourselves to that world. It’s not other people’s job to sort of, you know, preserve our old world for us. Curt: And this adaptation to this new world,
- u121 pa zame zveni kot menjava službe glede na to, kar pravi Jacob Tsimerman: »Glej, tega sem se lotil, ker hočem reševati probleme. Res rad jih rešujem.« Jacob: Ja. Bolj sem reševalec problemov. Matematike sem se vedno loteval prek konkretne skrivnosti, ki sem jo poskušal razvozlati. Ja. Curt: Bil je zmagovalec olimpijade. Začel je—že od mladih let. Preprosto obožuje probleme. Nekateri drugi matematiki problemov samih niti ne marajo. Bolj jih zanima:to me, it sounds like switching jobs from Jacob Tsimerman saying, “Look, I came into this ’cause I want to solve problems. I actually love to solve problems.” Jacob: Yeah. I’m more of a problem solver. I’ve always come at math through having a concrete sort of mystery and trying to figure it out. Yeah. Curt: He was an Olympiad winner. He went in, he—from a young age. He just loves problems. You know, some other mathematicians don’t even like problems per se. They like,
- u122 »Hočem razumeti to disciplino. Hočem raziskati to in to.« Ampak, za božjo voljo, kako se odzivajo tvoji študenti? Šli so v matematiko zaradi tega, zdaj pa je nekaj drugega. Scott: Ja, veliko mojih študentov je, kot si lahko predstavljaš, precej negotovih glede prihodnosti. Trudijo se čim bolje izkoristiti položaj, dokler lahko. Intenzivno uporabljajo UI. Z njo“I wanna understand this discipline. I wanna explore so-and-so.” But, well, gosh, how are your students reacting? Like, they went into math for this, and now it’s that. Scott: Yeah, I mean, some—you know, a lot of my students, as you can imagine, are pretty unsure about their futures, okay? They are, you know, I mean, you know, they are making the best of the situation while they can. You know, they’re using AI heavily. They’re,
- u123 pišejo članke. Rešujejo probleme. Toda dolgoročno se seveda sprašujejo o prihodnosti področja. Poskušam jih usmerjati, vendar tudi sam ne vem, kaj je ... Pravzaprav, ko začnem ugibati o prihodnostiyou know, writing papers, you know, with it. They’re solving problems. But, you know, thinking longer term, of course, they’re wondering about the future of the field. And, you know, I try to give them guidance, right? But I don’t know either what’s the, you know, what’s the... And in fact, like, when I start trying to speculate about what’s the future
- u124 našega področja, hitro naletim na večja vprašanja o prihodnosti celotne civilizacije. Zdi se mi, da bomo, če naša civilizacija preživi ta prehod v svet, v katerem prevladuje UI, že našli nišo za ljudi, ki imajo radi matematiko. Mislim, da bomo ta problem znali rešiti.of our field, you know, I quickly run into the bigger questions of what is the future of our entire civilization, right? You know, I feel like if our civilization, you know, survives this transition to an AI-dominated world, I think, you know, we will manage to find a niche for the people who like math, you know? I think we’ll be able to solve that problem, right?
- u125 Upanje nam lahko daje primer šahovske skupnosti. Dovolj sem star, da se spominjam spremljanja partij Kasparova proti Deep Blueju leta 1997. Spomnim se, da so nekateri takrat govorili: »To je konec šaha.« Ljudje—preprostoYou know, and one thing that can give hope here is the example of what happened to the chess community, right? You know, like I’m old enough, you know, I remember following the Kasparov versus Deep Blue games in, you know, in ’97. And I remember that, you know, at the time some people said, you know, “This is the end of chess,” right? Humans are—just
- u126 nimajo več razloga igrati šah, zdaj ko so računalniki boljši. Zgodilo pa se je nasprotno. Šah še nikoli ni bil tako priljubljen kot zdaj. Moj devetletni sin, ki si ga prej omenil, redno hodi na šahovske turnirje tu v Austinu. Polni so otrok. In,have no reason to play chess anymore now that, you know, computers are better at it. And the opposite is what happened, right? Chess has never been more popular than it is right now. I mean, my nine-year-old son, who you brought up before, you know, he goes to chess tournaments here in Austin regularly, right? They are packed with kids, okay? And, you know,
- u127 imamo šahovske spletne prenašalce, youtuberje, šahovske zvezdnike. Ljudje so se preprosto odločili, da jim je to všeč kot človeška dejavnost. Seveda vsi uporabljajo modele za analizo partij in razumevanje, kaj bi morali narediti drugače. Narava šaha se je torej zaradiyou’ve got chess streamers, YouTubers, you know, you’ve got chess celebrities, okay? And, you know, people just decided they like doing this as a human activity, right? And of course, you know, they all use the models to analyze the games and understand what they should have done instead of what they did do. So the nature of chess has changed, you know, because
- u128 UI spremenila. Ljudje z njo vadijo, vendar še vedno igrajo šah. Mislim, da bo vsaj toliko ljudi, ki uživajo v razumevanju matematike in znanosti, v zastavljanju lastnih matematičnih vprašanj in nato bodisi poskušanju, da jih rešijo sami, bodisi tem, da jim UI reši probleme inof AI. And people train with it, okay, but, you know, people still play chess. I think that, you know, the—there’s gonna be at least as many people who enjoy understanding math and science, who enjoy coming up with their own mathematical questions, and then, you know, either, you know, trying to solve them themselves or having an AI, you know, solve them, you know,
- u129 razloži rešitve. Iskreno me bolj skrbijo večja vprašanja: kako to preživimo kot civilizacija? Curt: Glede tega, recimo, da ima Anthropic dokaz, da jeexplain the solutions to them. You know, I’m more worried, frankly, about the bigger issues, about, you know, do we—how do we survive this, you know, just as a civilization? Curt: About that, suppose Anthropic has a proof that
47:24 · Smiling man with glasses before a chalkboard of equations · A video still shows a man with graying brown hair and dark-rimmed glasses, wearing a blue-gray collared shirt. He smiles with his eyes cast downward. Behind him is a framed chalkboard with handwritten math, in an office with a tan door, a hexagonal wall piece and a white chair. - u130 Če UI dokaže P = NPIf AI Proves P = NP
- u131 P enako NP. Misliš, da bi ga morali objaviti? Scott: Najprej, če bi bil P enak NP, bi bilo veliko odvisno od tega, ali bi bil algoritem dejansko praktičen. Lahko bi bil P enak NP, vendar bi algoritem za reševanje 3-SAT potreboval, recimo, čas n^10000. Ali čas O(n),P equals NP. Do you think they should release it? Scott: Well, so first of all, you know, if P were equal to NP, right, it would depend a lot on kind of whether the algorithm was actually practical, right? So it could be that P would equal NP, but the algorithm for solving 3-SAT would take n^10000 time, let’s say. Or like O(n) time,
- u132 vendar z googolpleksom, skritim v konstanti velikega O. V tem primeru bi bil to izjemen rezultat teoretičnega pomena. Seveda bi se ljudje takoj lotili tega, kako ga narediti praktičnega. Če pa bi bil P enak NP prek praktičnega algoritma,but with a googolplex, you know, hidden in the constant in the big O. And in that case, you know, that would be an amazing result that would be of theoretical interest, right? I mean, of course, people would then immediately get to work on trying to make it practical, right? But, you know, if P were equal to NP via a practical algorithm,
- u133 bi to najneposredneje pomenilo, da bi bila v bistvu vsa kriptografija, ki jo uporabljamo na internetu, zlomljena. Bitcoin bi postal brez vrednosti. Prav tako vse druge kriptovalute. Vso valuto bi lahko izrudarili zastonj.okay, what this would mean is, you know, most immediately that sort of essentially all of the cryptography that we use on the internet would be broken, okay? So like all—you know, Bitcoin would become worthless. You know, all the—you know, as all other cryptocurrencies, right? Like all the currency could be mined for nothing.
- u134 Vse sheme digitalnega podpisovanja, ki varujejo denarnice ljudi, bi lahko zlomili, podpise bi lahko ponarejali. To bi pomenilo, da bi bila zlomljena tudi vsa kriptografija v ozadju HTTPS oziroma tista, ki varuje številko vaše kreditne kartice, ko jo vnesete na spletni strani. Imamo pa standarde odgovornega razkrivanja,All the digital signature schemes that protect people’s wallets could be broken, could be forged, okay? It would mean that all the cryptography that’s behind HTTPS or like that protects your credit card number when you put it into a webpage, that would all be broken as well. Okay, so, you know, and like we do have standards around responsible disclosure,
- u135 kajne? V skupnosti za kibernetsko varnost velja, da če odkriješ, recimo, način vdora v spletno stran nekega podjetja, tudi če je akademsko zanimiv, o tem ne smeš kar takoj objaviti članka. Podjetje moraš obvestiti in mu dati 90 dni za odziv,right? That, like in the cybersecurity community, like if you discover, you know, so let’s say some way that some company’s, you know, website can be hacked, you know, and, you know, even if it’s academically interesting, right, you’re not supposed to just publish a paper about it immediately. You’re supposed to notify the company and give them 90 days to respond,
- u136 Kajne? In tako, veste, zdaj pri kriptografiji lahko rečemo, da niti ni treba, da je P enako NP, kar je, mimogrede, nekaj, za kar ne verjamem, da drži, kajne? Torej je to teoretična razprava. Ampak precej verjetneje je, da bi lahko obstajal hiter klasični algoritem za faktorizacijo, recimo. Kajne? Za to, veste, ne bi bilo treba, da jeright? And so, you know, and now with cryptography, like you can say even short of P equals NP, which is, by the way, something that I don’t believe is true, right? So this is a theoretical discussion. But, you know, something that is much more plausible is that there might be a fast classical algorithm for factoring, let’s say. Right? Which is—you know, that wouldn’t need
49:36 · Video frame blending Project Zero disclosure policy with speaker · A video transition frame cross-fades a web page titled "Vulnerability Disclosure Policy" with a webcam-style shot of a man in glasses and a light blue shirt in front of a chalkboard covered in handwritten math. The faded page text explains Project Zero's 90+30 policy: a vendor has 90 days to patch a reported vulnerability, and details are disclosed 30 days after a patch is available. - u137 P enako NP, kajne? Lahko bi šlo samo za ta konkretni problem, kajne? Lahko bi obstajal hiter klasični algoritem za razbitje kriptografije eliptičnih krivulj ali kaj podobnega, kajne? In mnogi so opazili, da so v teh približno 400 člankih, ki jih je objavil OpenAI, pokrili skoraj vsa področja matematike, pri čemer je kriptografija opazno manjkala. Prav?P equals NP, right? That could just be this one specific problem, right? Where there could be a fast classical algorithm for breaking elliptic curve cryptography or something like that, right? And now many people noticed that, you know, in these like 400 papers that OpenAI put out, right, they covered just about every area of math with the conspicuous omission of cryptography. Okay?
- u138 Kajne? Bilo je ... Torej očitno to ni bilo naključje. Očitno poskušajo biti previdnejši pri tem, kako pristopajo h kriptografiji. Prav? Ampak mislim, da moramo resno razmisliti o možnosti, da bodo v — veste, modeli umetne inteligence odkrili načine za razbitje ene ali več široko uporabljanih kriptografskih šifer,Right? There was... So like, obviously, that wasn’t an accident. You know, obviously, like, they are trying to be, you know, more cautious in how they approach cryptography. Okay? But, you know, I think we do need to, you know, think seriously about the prospect that in—you know, AI models will discover breaks of one or more widely deployed cryptographic codes, you know,
- u139 v naslednjem letu ali dveh, kajne? In kaj pomeni odgovorno razkritje tega, kajne? Torej, prav, obvestiti moraš podjetje in mu dati 90 dni, ampak če bi nekdo razbil, recimo, RSA ali Bitcoin, potem je treba obvestiti ves svet, kajne? Torej,within the next year or two, right? And what does responsible disclosure of that mean, right? It’s like, you know, okay, you know, you—you know, you’re supposed to notify the company and give it 90 days, but like if someone had broken, let’s say RSA, you know, or Bitcoin, then like the parties to notify are the entire world, right? So like, you know,
- u140 koga bi — ali svetu morda z demonstracijo ali s protokolom brez razkritja znanja dokažeš, da imaš rešitev, ne da bi razkril, kakšna je ta rešitev? To je ena možnost, kajne? Mislim, morda bi drugi rekli, da najprej obvestiš vlado, kajne? Inwho do you—you know, do you like prove to the world, you know, maybe like via demonstration or via zero-knowledge protocol, you prove to them that you have a solution, but without revealing what the solution is, you know? That’s one possibility, right? You know, I mean, maybe other people would say, you know, you first notify the government, right? And you
- u141 vladi prepustiš odločitev, kaj storiti. Mislim, da bi se drugi s tem močno ne strinjali, še posebej, če se ne strinjajo s sedanjo vlado, kajne? In mislim, da bo v praksi o tem, kako ravnati, odločalo tisto podjetje ali druga stran, ki ji bo to uspelo prvi. Torej je to resničen problem.let the government decide what to do. I think other people would strongly disagree with that, you know, especially if they disagree with the current government, right? You know, and I think in practice, it will be up to whatever company, you know, or other party does this first to decide how they’re going to handle it. So that is a real issue.
- u142 Zdaj pa širše: če recimo ne bi šlo le za razbitje tega ali onega kriptosistema, ampak bi veljalo P je enako NP in bi šlo za algoritem, ki bi bil hiter v praksi, bi posledice segale celo onkraj kriptografije, prav? To bi še dodatno pospešilo napredek umetne inteligence, celo precej bolj, kot je že nekako pospešen. To bi lahko pomenilo, daNow, you know, more broadly, if, let’s say it was not only a break of this or that cryptosystem, but it was P equals NP, and it was an algorithm that was fast in practice, then the implications of that would even go beyond cryptography, okay? It would further accelerate the progress of AI, you know, even much more than it is already sort of accelerated. It would mean potentially that,
- u143 ne bi bilo več treba porabljati teh milijard dolarjev za velikanske učne postopke, da bi učili modele. Da bi preprosto obstajal veliko, veliko hitrejši način iskanja pravih parametrov za te modele, kar bi umetno inteligenco lahko še dodatno pospešilo, v dobrem ali slabem. Curt: Če se vrneva k analogiji s šahom: razlika pri šahu je, da vyou know, you would no longer need to spend these billions of dollars on these gigantic training runs, you know, to train the models. That there would just be a much, much faster way of finding the right parameters for these models and, you know, that could accelerate AI even further, you know, for better or for worse. Curt: Going back to the chess analogy, the difference with the chess case is that in
52:53 · Man in glasses before chalkboard with logic notation · A video still shows a man with gray-brown hair and dark-framed glasses in a blue button-up shirt. He leans toward the camera with a slight, wry smile. Behind him, a chalkboard is covered in mathematical logic notes, including "AC vs PP", "Con(SC) vs" and quantifier symbols. The room has a beige wall and an orange door. - u144 Je naslednja fizika?Is Physics Next?
- u145 akademskem svetu obstaja oddelek za matematiko, ni pa oddelka za šah. Zdaj, mogoče je nekaj tega ekshibicijski šah in tako dalje. Torej — Scott: To drži. Mislim, obstaja tudi oddelek za glasbo, mimogrede, ampak, veste, nič jim ne manjka. Kajne. So kot — obstajajo oddelki za šport, kajne? Ali za kaj podobnega. Torej ja, stvari, ki bi jihacademia, there’s an academic department for math, but there’s no academic department for chess. Now, maybe some of it is display chess and blah, blah, blah. So— Scott: That’s true. I mean, there—I mean, there is a department of music, by the way, but, you know, they’re all right. Right. They’re like—there are, you know, there—the—there are, you know, departments of athletics, right? Or of, you know, things like that. So yeah, things that
- u146 lahko uvrstili med rekreativne dejavnosti, kajne? Akademiki jih dejansko preučujejo. Ampak ja, mislim, da opozarjaš na nekaj resničnega: pri akademskem raziskovanju matematike ali teoretičnega računalništva smo res imeli neko višjo vizijo tega, kar počnemo, kajne? Ne igramo se samocould be classed as recreational activities, right? You know, they are actually studied by academics. But yeah, I think you’re getting at something real here, which is that, you know, in like, let’s say, academic research in math or in theoretical computer science, like, you know, we did have a higher vision of what we were doing, right? You know, we’re not just playing
- u147 neke igre. Nekako odkrivamo resnice o vesolju. Kajne? Čeprav, če gre za to, če odkrivamo resnice o vesolju, potem mislim, da imamo še toliko manj razlogov za zavračanje orodja, ki nam bo omogočilo odkriti več teh resnic. Curt: Pravzaprav je to tudi razlika pri neki moji analogiji, ki je — no, nekaj,some game. We are sort of discovering truths about the universe. Right? Although, you know, if that’s what it is, if we’re discovering truths about the universe, then I think that is all the less reason to reject the tool that will let us discover more of those truths. Curt: Actually, that’s the difference also between an analogy I have, which is—well, something
- u148 kar sem opazil, je, da programski inženirji zadnje leto in pol doživljajo nekaj podobnega. Pravijo: »Človek, moja služba, v to sem dejansko šel, ker rad ustvarjam algoritme in rešujem podrobne probleme, zdaj pa je moja služba takšna: zbudim se s kavo, govorim z računalnikom, odprem še en zavihek, s katerim govorim, potem pa samo gledam in sem vodja.« Scott: Glej, mislim, nekakšna naraščajoča poplava je zajela programskoI’ve noticed is software engineers have been experiencing something similar for the past year and a half, where they’re saying, “Man, my job, I went into this actually ’cause I like creating algorithms and solving nitty-gritty problems, and now my job is I wake up with my coffee, I speak to my computer, I open another tab to speak to, and then I just watch it, and I’m a manager.” Scott: Look, I mean, you know, there’s sort of this rising floodwater that came for software
- u149 inženirstvo morda pred letom ali dvema, potem pa je to poletje prišla še po nas. In ko govorim s prijatelji fiziki, se zdi, da njih še ni dosegla, kajne? Ampak mnogi jo živčno opazujejo in pričakujejo, da jih bo dosegla v naslednjem letu ali približno takrat. Prav? Ampak vsakdo, ki ga poplavne vode še niso,engineering, you know, maybe a year or two ago, and then this summer it’s come for us. And you know, when I talk to my friends in physics, like it seems like it still hasn’t come for them, right? But a lot of them are watching nervously, and they’re expecting that it will come for them within the next year or so. Okay? So, you know, but like anyone who the floodwaters have not yet,
- u150 veste, preplavile, se lahko pretvarja, da poplave sploh ni ali da prizadeva samo tista druga področja, ker so polna trivialnosti. Ampak mislim, da to v nekem smislu prihaja po vse nas. Spremenilo bo naravo dela vseh nas. Curt: Je pri fiziki kaj drugače? Recimo, no,you know, inundated, like they—you know, they could pretend that, you know, that there’s no flood at all, or that like it’s only hitting those other fields because those fields are just full of trivialities. But, you know, I do think that in some sense, this is coming for all of us. This is going to transform the nature of what all of us do. Curt: Is there anything that’s different about physics? Like, well,
- u151 fizika se ukvarja z resničnim svetom. Nekaj je — izvajati moraš poskuse. Scott: Mislim, da je glavna razli... Jaz — ja, mislim, da lahko to pojasnim. Mislim, da je glavna razlika preprosto v tem, da problemi v fiziki niso tako ostro opredeljeni, prav? Zato ni tako preprosto preveriti, kdaj si problem pravilno rešil in kdaj ne, kajne? Odvisno je od presoj, denimo: je to razumen približek, kajne?physics has to do with the real world. There’s something—you have to conduct experiments. Scott: I think the main differ... I—yeah, I think I can explain this. I think the main difference is simply that in physics the problems are not as crisply defined, okay? So it is not as easy to verify when you have correctly solved the problem and when you haven’t, right? It depends on judgment calls, like, you know, is this a reasonable approximation, right?
- u152 Je to razumen model dejanske fizikalne situacije, ki smo jo želeli raziskati, kajne? In pri matematiki ljudi prav tako zanimajo takšne nejasne, odprte stvari. Recimo: je to prava definicija? Je to pravi model? Tudi mi se veliko pogovarjamo o tem.Is this a reasonable model of the actual physical situation that, you know, that we had wanted to investigate, right? And, you know, well, in math, like, you know, people—you know, people are also interested in those kind of fuzzy, you know, open-ended things. Like, you know, is this the right definition? Is this the right model? Like, you know, that’s a lot of what we talk about too.
- u153 Ampak pogosto postavimo povsem jasno opredeljene domneve, kajne? P ni enako NP ali domnevo o enoličnih igrah ali te druge domneve, pri katerih načeloma obstaja povsem mehanski način preverjanja, ali si problem rešil ali ne, kajne? In mislim, da je prav to umetni inteligenci omogočilo tako dober uspeh,But, you know, we do often state these perfectly crisp conjectures, right? You know—P is not equal to NP, or, you know, the unique games conjecture, or, you know, the—these other conjectures where, you know, there is, in principle, just a totally mechanical way of checking whether you have solved the problem or not, right? And, you know, I think that that is what has allowed AI to do so well,
- u154 kajne? Ker ko imaš mehanski način preverjanja odgovorov, lahko učiš na tisočih in tisočih primerov rešitev, kajne? Uporabiš lahko spodbujevalno učenje, kajne? Lahko ... In ja, potem imaš tarčo, v katero lahko usmeriš svojo strašansko gmoto inteligence, kajne? In veš, kaj je tarča, prav?right? Because once you have just a mechanical way of checking the answers, then you can train on thousands upon thousands of examples of solutions, right? You can do reinforcement learning, right? You can... You know, and yeah, so, like, then, you know, you have your target to sort of aim your fearsome blob of intelligence at, right? And you know what the target is, okay?
- u155 In mislim, da je dober prikaz tega dejstvo, da je področje fizike, na katero je to doslej najbolj vplivalo, matematična fizika, kajne? Torej tista področja fizike, kjer lahko matematično opredeliš, katero trditev želiš dokazati, so doživelaAnd I think the—you know, a good demonstration of this is that, you know, the area of physics that has been most affected so far has been mathematical physics, right? So, like, you know, those areas of physics where you can mathematically specify, you know, what statement you would like to prove, you know, those have seen, you know,
- u156 nekaj izjemnih premikov, tudi v objavi OpenAI izpred dveh tednov. Curt: To je nedotaknjeno namizje mojega montažerja. Tam je 40 zavihkov, šest osnutkov ene same montaže. Vedno je mapa z imenom Final znotraj druge mape z imenom Final in ta nered pomeni toliko dela. Zelo cenim čisto mizo, fizično mizo,some dramatic developments, including in the OpenAI drop from two weeks ago. Curt: This is my editor’s desktop untouched. There’s 40 tabs, there’s six drafts of a single cut. There’s always a folder that’s called Final inside another folder that’s called Final, and that mess is so much work. I appreciate very much a clean desk, a physical desk,
- u157 in če je moja digitalna različica mize neurejena, mi to prav tako povzroča zmedo v glavi. Z drugimi besedami, ta nered je delo. Kar pa ni delo, je tisto, kar je računalnik ustvaril sam. Sistemski predpomnilnik, pokvarjeni prenosi, ostanki namestitvenih programov, podvojene fotografije in tako dalje. CleanMyMac to najde in odstrani samo to. Space Lens nariše zemljevid diska, da so mape, ki zasedajo največ prostora, očitne.and if my digital instantiation of a desk is messy, that also messes with my head. In other words, that mess is work. What isn’t the work is what the machine made itself. System cache, broken downloads, installer leftovers, duplicate photos, et cetera. CleanMyMac finds that and removes only that. Space Lens draws a map of your drive so your heaviest folders are obvious.
- u158 To se mi je zgodilo ravno včeraj. Disk je bil skoraj poln in moral sem ugotoviti: »Ojoj, katere so moje največje datoteke?«, da bi jih lahko pregledal in brisal. Cloud Cleanup naredi enako v iCloudu, Google Drivu in Dropboxu, pregled pa poteka na Macu, zato ga nič ne zapusti. Na voljo je modul za zmogljivost, ko se ventilator zažene sredi izrisovanja,This just happened to me yesterday. My drive was about to be overfilled, and I had to figure out, “Oh, gosh, what are my largest files?” so I could look through them and delete. Cloud Cleanup does the same across iCloud, Google Drive, and Dropbox, and the scan runs on the Mac, so nothing leaves it. There’s a performance module for when the fan spins up mid-render,
- u159 v ozadju pa deluje mehanizem proti zlonamerni programski opremi Moonlock. Izdelal ga je MacPaw, Apple ga je notarsko preveril, že drugo leto zapored pa je na ožjem izboru trgovine Mac App Store za leto 2026. Pospravite že danes. CleanMyMac sedem dni preizkušajte brezplačno in uporabite mojo kodo THEORIES za 20 % popusta. Torej koda THEORIES, T-H-E-O-R-I-E-S, na cleanmymac.com.and a Moonlock anti-malware engine underneath. It’s made by MacPaw, notarized by Apple, and on the Mac App Store’s 2026 shortlist, second year in a row. Get tidy today. Try CleanMyMac for free for seven days, and use my code THEORIES for 20 percent off. That’s code THEORIES, T-H-E-O-R-I-E-S, at cleanmymac.com.
- u160 Problem unitarne sinteze rešenUnitary Synthesis Problem Solved
- u161 Je v tisti objavi kaj takega, kar te nagovori, da rečeš: »O, tole — želim si, da bi ljudje temu namenjali več pozornosti,« ali pri čemer zaradi svoje stroke vidiš revolucionarnost, drugim pa jo je nekoliko težko pojasniti? Scott: No, glej, obstajajo problemi, ki sodijo neposredno na moje področje, v enem primeru problem, ki sva ga s kolegom Gregom Kuperbergom zastavila pred 20Is there anything in that drop that is, gosh, that speaks to you that you say, “Oh, this—I wish people were paying more attention to this,” or that because of your discipline, you see its revolutionariness, but to others, it’s a bit difficult to convey? Scott: Well, look, I mean, you know, there are problems that are sort of just directly in my wheelhouse that, you know, in one case, a problem that I posed along with my colleague Greg Kuperberg 20 years
- u162 leti. Imenoval se je problem unitarne sinteze, prav? In očitno mislim, da je vprašanje lepo. Zato sva ga zastavila, kajne? Ampak vprašanje je bilo v bistvu: kakšna je povezava med zahtevnostjo izvedbe unitarne transformacije v kvantni mehanikiago. This was called the unitary synthesis problem, okay? And, you know, obviously, I think that the question is a nice one. That’s what the—that’s why we asked it, right? But the question was basically—but, like, what is the connection between, you know, the complexity of applying a unitary transformation in, you know, in quantum mechanics
- u163 in običajno vrsto zahtevnosti, pri kateri navadno govorimo o stvareh, kot so Boolove funkcije, ki imajo samo klasični vhod in klasični izhod, prav? Natančneje sva vprašala: »Ali za vsako unitarno transformacijo na n kubitih, recimo ji U, kajne, za vsak tak U obstaja neka klasična Boolova funkcija, ki bi ti,and the sort of ordinary kind of complexity, where usually we talk about things with, like, Boolean functions, you know, that just have a classical input and a classical output, okay? And specifically, what we asked was, “Is it true that for every unitary transformation on n qubits, let’s, you know, call it U, right? For every such U, there is some classical Boolean function that
- u164 če bi ti jo dal zastonj, kajne, če bi ti jo dal kot orakelj, kot temu rečemo, kajne, če bi ti omogočil dostop do te funkcije na kvantnem računalniku, v superpoziciji, če bi ti omogočil poizvedbe pri tej Boolovi funkciji kot oraklju, omogočila izvesti to unitarno transformacijo U v polinomskem času?« Prav? To — to je bilo vprašanje, ki sva ga zastavila.if I gave it to you for free, right? If I gave it to you as an oracle, you know, as we call it, right? I let you access that function, you know, on your quantum computer, right? You know, in superposition, I let you make queries to this Boolean function as an oracle, then you could apply that unitary U in polynomial time?” Okay? That—the—that was the question that we asked.
- u165 Domnevala sva, da je odgovor ne, prav? Ker preprosto nisva videla nobenega načina, kako to narediti. Torej: »Da, vsaka unitarna transformacija vključuje eksponentno mnogo parametrov.« Ampak to samo po sebi ni ovira, ker bi lahko vse te parametre zakodiral v vrednosti te Boolove funkcije. Ampak potemWe conjectured that the answer was no, okay? Because we just could not see any way to do this. It’s like, “Yes, for any unitary transformation, you know, it involves exponentially many parameters.” But, you know, that itself is not a stopper because you could encode all of those parameters into the values of this Boolean function. But then,
- u166 je težava v tem, da je tudi po tem videti, kot da moraš to Boolovo funkcijo še vedno poizvedovati eksponentno mnogokrat, če želiš unitarno transformacijo dejansko fizično izvesti na kvantnem stanju. In zdelo se je, da to drži ne glede na to, kako domiselno želeno unitarno transformacijo zakodiraš v funkcijo.you know, the trouble is that even after you’ve done that, it looks like you still need to query that Boolean function exponentially many times, you know, if you wanna actually apply the unitary, like, physically to a quantum state. And that seemed to be true no matter how cleverly you encoded the unitary that you wanted into the function.
- u167 To je potem spodbudilo veliko nadaljnjega dela in pravzaprav sem imel kar nekaj kolegov, ki so zadnjih nekaj let delali na tem problemu in dejansko napredovali, dokazovali zelo, zelo sorodne rezultate, ki bi se morda celo približali človeški rešitvi tega problema. Ampak vse to je bilo prekinjenoAnd so then, you know, this inspired a lot of follow-up work, you know, and actually I had quite a few colleagues who were working on this problem for the last few years, actually making progress, proving, you know, proving some very, very related results that may have even been closing in on a human solution to the—to this problem. But that was all cut short
1:01:47 · Man speaking in front of mathematical chalkboard, video still · A man with glasses and tousled gray-brown hair, wearing a blue-gray collared shirt, speaks to the camera with one hand raised and blurred by motion. Behind him is a chalkboard in a wooden frame filled with handwritten mathematical notation. The setting looks like an office, with a beige wall, a door at left and a chair. - u168 pred dvema tednoma, ko je OpenAI v enem od svojih 372 člankov predstavil rešitev problema unitarne sinteze, rešitev pa je bila nasprotna najini domnevi s Kuperbergom. Namreč, da je to mogoče, prav? Za vsako tako unitarno transformacijo obstaja Boolova funkcija, ki omogoča njeno učinkovito izvedbo.two weeks ago when, you know, when OpenAI, as one of its 372 papers, had a solution to the unitary synthesis problem, and the solution was the opposite of what Kuperberg and I had conjectured. It’s that this is possible, okay? For every such unitary, there is a Boolean function that lets you apply the unitary efficiently.
- u169 In od takrat, že v teh zadnjih dveh tednih, so ljudje z uporabo modelov umetne inteligence ta rezultat še izboljšali. Prav? In ena stvar, ki smo jo očitno dobili s temi izboljšavami, je, da če bi na primer veljalo P je enako PSPACE, kajne? To je velik kolaps razredov zahtevnosti. To bi biloAnd, you know, this—you know, and since that, you know, already just within the last two weeks that that result has been further improved by, you know, people using AI models. Okay? And one thing that we apparently have from these further improvements is that if, for example, P were equal to PSPACE, right? So this is like a big collapse of complexity classes. This would be
1:02:38 · Complexity Zoo entry for PSPACE (Polynomial-Space) · A video still of a web page from a complexity class reference, showing the PSPACE entry. It lists equalities, containments and oracle results with blue hyperlinked citations, and the start of a PSPACE^CC entry. A dark overlay reads "Every link, every source" with curtjaimungal.com. - u170 še večje kot P je enako NP, kajne? Ampak tega trenutno ne moremo izključiti, kajne? In pravzaprav velja, da je dokazati P ni enako PSPACE skoraj tako težko kot dokazati P ni enako NP, kajne? Prav, novi rezultat torej v bistvu pomeni, da če bi veljalo P je enako PSPACE, bi lahkoeven bigger than P equaling NP, right? But this is not something that we can currently rule out, right? And actually proving P is not equal to PSPACE is thought to be, you know, just almost as hard as proving P is not equal to NP, right? Okay, so the new result basically implies that if P were equal to PSPACE, then, like, you could
- u171 učinkovito izvedel vsako unitarno transformacijo, ki jo sploh lahko razumno opišeš, kajne? Pri kateri lahko elemente opišeš z algoritmom s polinomsko prostorsko zahtevnostjo. To bi torej pomenilo, na primer, da bi unitarne transformacije, ki bi jih uporabil za dekodiranje Hawkingovega sevanja, ki prihaja iz črne luknje, lahko izvedel učinkovito. Inapply any unitary transformation efficiently, like, that you can even reasonably describe, right? Where, like, you can just describe the entries by a polynomial space algorithm. So this would mean, for example, that the unitary transformations that you would use to decode the Hawking radiation coming out of a black hole, right? You could apply that efficiently. And,
- u172 to bi imelo zelo zanimivo posledico za kvantno gravitacijo. Zdi se, da to pomeni, da bi lahko ustvaril ognjeni zid na dogodkovnem obzorju črne luknje, kajne? Lahko bi povzročil razpad prostorsko-časovnega kontinuuma. Ne pri singularnosti, kjer smo vedeli, da naj bi prostor-čas odpovedal, ampak že na dogodkovnem obzorju. Prav? Resdayou know, that would have a very interesting implication for quantum gravity. That seems to mean that you could create a firewall at a black hole’s event horizon, right? You could engineer a breakdown of the spacetime continuum. You know, not at the singularity where we knew that, you know, spacetime was supposed to break down, but already at the event horizon. Okay? Admittedly,
- u173 bi moral za opazovanje tega razpada prostora-časa skočiti v črno luknjo, prav? Curt: Ja, ampak to je samo — to je malenkost. Scott: In seveda bi potem takoj umrl. Tako da iz več razlogov o tem ne bi mogel povedati nikomur drugemu, prav? Ampak v bistvu to pravi, da bi za dokaz, da jein order to observe this breakdown of spacetime, you’d have to jump into the black hole, okay? Curt: Yeah, but that’s just a—that’s a triviality. Scott: And of course he would then immediately die. And so, you know, for multiple reasons, you couldn’t tell anyone else about it, okay? But it’s basically saying that, you know, in order to show that sort of, you know,
- u174 prostorsko-časovni kontinuum stabilen tam, kjer bi po splošni relativnosti moral biti, moral vsaj dokazati, da P ni enako PSPACE. Curt: Ali to pomeni, da je dekodiranje črne luknje klasičen problem?the spacetime continuum is stable in the places where general relativity said that it should be, you know, you would at a minimum need to prove that P is not equal to PSPACE. Curt: Does this mean decoding a black hole is a classical problem?
1:04:30 · Smiling man in glasses before a chalkboard · A close-up video still of a smiling man with dark hair graying at the temples, wearing black-framed glasses and a light blue collared shirt. Behind him is a chalkboard with handwritten math notation, and to the left a cream wall with an orange-brown door and a hexagonal wall decoration. - u175 Ognjeni zidovi črnih lukenj in P proti PSPACEBlack Hole Firewalls & P vs PSPACE
- u176 Scott: No, to ... V tem je stvar. Tako zastavljeno je to kvantni problem, kajne? Fotoni Hawkingovega sevanja, ki prihajajo iz črne luknje, so v nekem kvantnem stanju, kajne? Po sodobnem razumevanju so v zelo, zelo močno prepletenem kvantnem stanju, ki bi ga, če bi ga lahko povsem podrobno izmeril, načelomaScott: Well, it... This is the thing. Like, as stated, it’s a quantum problem, right? So the photons of Hawking radiation that are coming out of a black hole are in some quantum state, right? In the modern understanding, they’re in a very, very highly entangled quantum state that, you know, if you could, like, measure it in total detail, you know, in principle,
- u177 videl kot zapis vseh informacij o tem, kar je padlo v črno luknjo, kajne? In to je ena glavnih tem raziskovanja kvantne gravitacije v zadnjega pol stoletja, odkar je Stephen Hawking ta vprašanja odprl v sedemdesetih letih 20. stoletja. Prav, v bistvu kvantna teorija polja ni dovolj zmogljiva, da bi to pokazala. Dovolj jeyou would see it encodes all the information about what fell into the black hole, right? And this has been just sort of a major, major theme of quantum gravity research for the past half century, you know, since Stephen Hawking, you know, raised these issues in the nineteen seventies. Okay, that basically, like, quantum field theory is not powerful enough to see. You know, it’s powerful
- u178 zmogljiva, da nam pove, da bi Hawkingovo sevanje moralo obstajati, ne pa, kako Hawkingovo sevanje kodira informacije o tem, kar je padlo noter in ustvarilo črno luknjo, kajne? Ampak če verjameš, da kvantna mehanika velja univerzalno, potem informacije morajo biti tam, saj se morajo pri unitarnem razvoju ohranjati, kajne? Neenough to tell us that Hawking radiation should be there, okay, but not to tell us how the Hawking radiation encodes the information about what fell in to make the black hole, right? But if you believe that quantum mechanics is universally valid, then the information has to be there because, you know, information has to be conserved by unitary evolution, right? It
- u179 morejo biti kar izbrisane iz vesolja, prav? Tako je sodobnejša slika takšna: da, informacije so v Hawkingovem sevanju, vendar v neverjetno premešani obliki. Precej bolj premešane kot informacije v knjigi, potem ko bi jo zažgal, kajne? In poskušal — in čecan’t be just deleted from the universe, okay? And so the sort of more modern picture is that, yes, the information is there, in, you know, in the Hawking radiation, but it’s in some incredibly scrambled format, you know? Like, way more scrambled than like, you know, than would be the information in a book, you know, after you had burned it, right? And tried, you know—and if
- u180 bi poskusil iz dima in pepela obnoviti, kaj je pisalo v knjigi, kajne? Mislim, že fizika 19. stoletja nam pove, da bi to načeloma moralo biti mogoče, prav? Ampak očitno je to v praksi zelo težko, kajne? Različico s črno luknjo si torej lahko predstavljaš kot težjo različico tega, kajne?you would try—tried to recover what was written in the book from the smoke and the ash, right? I mean, even nineteenth-century physics tells us that in principle that ought to be possible, okay? But, you know, obviously very hard to do in practice, right? And so, you know, the black hole version you can think of as just like a harder version of that, right?
- u181 Torej imaš vse te kvantne informacije, ki jih je neka še neznana dinamika kvantne gravitacije, karkoli se je že dogajalo v črni luknji, povsem premešala. Prav? Nato prihajajo ven v Hawkingovem sevanju v tem močno prepletenem stanju. In zdaj je tvoja naloga, če želiš ustvariti ognjeni zid, izvesti ustrezno unitarnoAnd so you have all this quantum information, you know, that, you know, by some yet unknown dynamics of quantum gravity has been totally scrambled up by whatever was going on inside the black hole. Okay? It’s then coming out in the Hawking radiation in this highly entangled state. And now your task, if you wanted to create a firewall, is to apply a suitable unitary
- u182 transformacijo na tem kvantnem stanju, na stanju Hawkingovega sevanja, kajne? Lahko si predstavljaš, da bi to naredil tako, da bi na primer zbral vse Hawkingovo sevanje in ga usmeril v kvantni računalnik za obdelavo, kajne? Zdaj smo že globoko, globoko na področju miselnih poskusov. Da bi dejansko zbral dovolj Hawkingovega sevanjatransformation to that quantum state, to the state of the Hawking radiation, right? And you could imagine doing that by, for example, just collecting all of the Hawking radiation, routing it into a quantum computer for processing, right? You know, these are, you know—we’re now far, far into the realm of thought experiments. Like, to actually collect enough Hawking radiation for
- u183 astrofizikalne črne luknje, da bi bilo karkoli od tega pomembno — veš, kako dolgo bi to trajalo? Vsaj 10^67 let. Prav. Dobro. Ampak ja, predpostavljamo, da imaš zelo dolgo raziskovalno financiranje, kajne? In da to zmoreš, kajne? Da lahko obdelaš vse to Hawkingovo sevanje. Leta 2013 sta Daniel Harlow in Patrick Hayden napisala danes slaven članek, v katerem sta rekla,an astrophysical black hole for any of this to be relevant, you know how long this would take? Like at least 10^67 years. Okay. All right. So, but yeah, we assume that you have a very long grant, right? And you’re able to do that, right? You’re able to process all this Hawking radiation. Now, in 2013, Daniel Harlow and Patrick Hayden wrote a now famous paper saying,
- u184 da bi tudi tedaj še vedno imel težavo z dekodiranjem tega, kar je v Hawkingovem sevanju, še preden bi črna luknja povsem izhlapela, razlog pa je povezan z računsko zahtevnostjo, kajne? Rekla sta: »Če bi hotel ta problem rešiti hitro, tudi s kvantnim računalnikom, bi moral rešitiyou know, even then, you would still have a problem in sort of decoding what was in the Hawking radiation, you know, sort of before the black hole had fully evaporated, and the reason had to do with computational complexity, right? They said, like, you know, “If you wanted to solve this problem quickly, even with a quantum computer, you would have to solve a
- u185 določen — kriptografske probleme, za katere verjamemo, da so težki celo za kvantne računalnike.« Prav? In zanju je bilo to nekaj pozitivnega, kajti ves paradoks ognjenega zidu iz leta prej, iz leta 2012, je govoril, da če bi lahko dekodiral Hawkingovo sevanje, recimo črne luknje, ki je večinoma, ne pa povsem izhlapela,certain—cryptographic problems that we believe are hard even for quantum computers.” Okay? And, you know, for them, this was a positive because if, you know, the whole firewall paradox from a year before that, from 2012, had been saying that if you could decode the Hawking radiation from, let’s say, a black hole that had mostly but not entirely evaporated,
1:08:33 · The Firewall Paradox black hole slide · A video-still slide titled "The Firewall Paradox" credits Almheiri, Marolf, Polchinski, Sully 2012. It shows a black hole as a black disc with two red concentric circles over a starry background. A cartoon girl in a blue dress is shown at the horizon, backed by a block of flames. Wavy lines represent radiation, one outside and one inside the horizon. This illustrates the idea that an infalling observer would meet a "firewall" at the horizon. - u186 bi moralo tvoje dejanje dekodiranja imeti dramatičen učinek, ko — če potem skočiš v črno luknjo. Kajne? Povzročiti bi moralo ta razpad prostora-časa na dogodkovnem obzorju. Na to se tu nanaša ognjeni zid. Prav? Torej sta rekla: »Ne,then, you know, your act of decoding it should then have this dramatic effect once you—if you then jump into the black hole. Right? It should cause this breakdown of spacetime at the event horizon. That’s what a firewall is referring to here. Okay? And so they were saying, you know, like, “No,
- u187 v praksi,« pri čemer je »v praksi« tu relativen izraz, ampak: »Tega ognjenega zidu ne boš mogel ustvariti, ker moraš rešiti eksponentno težek problem.« Prav? Potem me je to vprašanje zelo pritegnilo. Izboljšal sem njun argument. Njun prvotni argument se je pravzaprav opiral na precej zahteven rezultat iz moje doktorske disertacije iz leta 2004. Tako da nisem imel druge izbire, kot da me začne zanimati,in practice,” you know, “in practice,” you know, it being a relative term here, but, you know, “You won’t be able to create this firewall ’cause you have to solve this exponentially hard problem.” Okay? And then I got very interested in this question. I improved their argument. You know, like, their original argument actually relied on a kind of hard result from my PhD thesis in 2004. So, you know, so I had no choice but to get interested,
- u188 kajne? Ampak izboljšal sem njune rezultate, tako da moja doktorska disertacija ni bila več potrebna. Potrebuje samo ... Ampak potem me je začelo zanimati, kako težek je ta problem v resnici za kvantni računalnik, kajne? Zdi se verjetno težek, ampak ali bi lahko upali, da brezpogojno dokažemo, da je težek? Aliright? But I improved their results, so it no longer needed my PhD thesis. It just needs the... But, you know, okay, but then, you know, I got interested in, like, how hard is this problem really for a quantum computer, right? Like, it seems like, yeah, it seems plausibly hard, but like, could we hope to prove that it was hard just unconditionally? Or,
- u189 bi dokaz njegove težavnosti zahteval dokaz, da P ni enako PSPACE ali kaj podobnega? Prav? Zdi se torej, da imamo zaradi nedavnega napredka umetne inteligence zdaj odgovor na to vprašanje. Prav? In odgovor je, da če bi veljalo P je enako PSPACE, bi bil Harlow-Haydenov problem dekodiranja lahek. Prav? Potem bi biloyou know, would proving that it’s hard require, you know, proving that P is not equal to PSPACE or something like that? Okay? So it appears that because of the recent AI progress, we now have an answer to that question. Okay? And the answer is that if P were equal to PSPACE, then the Harlow-Hayden decoding problem would be easy. Okay? Then it would be, you know,
1:10:03 · Man gesturing in front of a mathematics chalkboard · A video still shows a man with glasses and tousled graying hair, wearing a blue-gray collared shirt. He is speaking animatedly with one arm raised, in an office or classroom. Behind him is a framed blackboard covered in chalk math notation, with a hexagonal wall decoration, a door and a white chair on the left. - u190 lahko ustvariti ta ognjeni zid in njun argument, zakaj je to težko, ne bi več veljal. Ko sem torej to dojel in Danielu Harlowu poslal sporočilo, da mu povem, je takoj odpisal: »No, zakaj bi me to zanimalo? Saj P ni enako PSPACE, kajne?« Kajne? Meni pa se je zdelo: »Stari,« veste,easy to create this firewall, and their argument would no—for why it’s hard would no longer apply. So, you know, when I actually texted Daniel Harlow, you know, when I realized that to tell him that, and immediately he wrote back, and he said, “Well, why should I care? Because P is not equal to PSPACE, right?” Right? But, you know, and to me, it was like, “Dude,” you know,
- u191 kajne? Ker nas v računalništvu zanima, kaj bi bilo potrebno, da bi to dokazali, kajne? In to pravi, da če hočeš pokazati, da je ustvarjanje ognjenega zidu težko, moraš rešiti ta osrednji odprti problem računske zahtevnosti. Dokazati moraš, da P ni enako PSPACE. Nekaj, kar kljub vsemuright? Because in computer science, we care about, like, what would it take to prove so, right? And what this is saying is that if you wanna show that creating a firewall is hard, then you have to solve this central open problem of computational complexity. You know, you have to prove P is not equal to PSPACE. You know, something that despite all of the
- u192 napredku umetne inteligence pri matematiki v zadnjih mesecih zelo opazno še vedno ni bilo storjeno. Curt: Ali nisi na Columbii rekel, da je drugi zakon morda posledica računske neobvladljivosti? In mislim, da si rekel, da prihaja prednatis. Scott: Ja.progress in AI for math, you know, in the last months has very conspicuously still not been done. Curt: Didn’t you say at Columbia that the second law may be because of computational intractability? And I think you said that a preprint was coming. Scott: Yeah.
- u193 Curt: Bil sem malo — Scott: Ja. Torej ja, tega še vedno nismo objavili. Ampak vemo. Imamo argument, da obstajajo — da so določene situacije, v katerih lahko dobiš vedenje, ki je videti kot drugi zakon, kajne? Videti je, kot da entropija narašča. Prav? Pa vendarCurt: I was like a little— Scott: Yeah. So, yeah, we still didn’t put that out. But we know. We do have an argument that there is—there’s a—there are particular situations where you can get behavior that, you know, that looks like the second law, right? That looks like entropy is increasing. Okay? And yet
- u194 bi lahko, če bi veljalo P je enako NP, razkril, da je to iluzija, kajne? Dejansko bi lahko zgradil tako imenovanega Maxwellovega demona. Toploto bi lahko pretvarjal nazaj v delo, kajne? Lahko bi ... Torej so situacije, o katerih smo razmišljali, vključevaleif P were equal to NP, then you could unmask this as illusory, right? You could actually, you know, build a Maxwell’s demon, you know, as it’s called. You could convert heat back into work, right? You could... And so the—so the kinds of situations that we were thinking about involved,
1:12:10 · Smiling man waving in front of a chalkboard · A video still of a man with glasses and a blue collared shirt, smiling and speaking with one hand raised and blurred by motion. Behind him is a blackboard covered in handwritten math, with a hexagonal wall decoration and a door to the left. A caption box in the lower left gives a website for links mentioned. - u195 recimo klasični reverzibilni celični avtomat. Prav? Lahko si predstavljamo, tako kot v klasičnem termodinamičnem scenariju, da imaš kup plinskih molekul, ki se odbijajo po škatli, kajne? Začnejo lahko v stanju z zelo nizko entropijo, recimo z vsemi delci zbranimi v kotu — v enem kotulet’s say, like a classical reversible cellular automaton. Okay? So, you know, we could imagine, like in the classic thermodynamics scenario, right, you have a bunch of gas molecules just bouncing around inside of a box, right? And they can start in a very low-entropy state, like with all the particles concentrated in a, you know, the corner of—a corner
- u196 škatle. Potem pa se z difuzijo razširijo. Razporedijo se po škatli, kajne? Običajno bi to opisali tako, da se je entropija sistema povečala, kajne? Energija je ostala enaka, entropija pa se je povečala. In ja, če bi dovolj dolgo čakal, bi se sčasoma po naključjuof the box. And then they diffuse out. They spread across the box, right? And, you know, we would normally talk about this by saying the entropy of the system has increased, right? The energy has stayed the same, but, you know, the entropy is—has gone up. And yes, you know, if you waited long enough, you know, eventually by chance, you know,
- u197 vsi delci spet zbrali v kotu. Entropija bi se zmanjšala, ampak to bi običajno trajalo eksponentno dolgo, kajne? Torej v bilijonu let skoraj zagotovo ne bi videl, da bi se to zgodilo. Prav? Potem pa klasični miselni poskus z Maxwellovim demonom pravi:all the particles will collect back in the corner. You know, the entropy will go down, but that will typically take exponential time, right? So like, you know, in a trillion years, you know, you’ll almost certainly never see it happen. Okay? And then the classic Maxwell’s demon thought experiment goes,
- u198 »Kaj pa, če na sredino škatle postavimo pregrado, kajne? V pregradi so majhna vratca in tam je mali demon, ki samo opazuje in vsakič, ko delec — ko plinska molekula potuje z leve na desno, odpre vratca ravno dovolj“Well, what if we put a divider in the middle of the box, right? And the divider has a little door in it, and there’s a little demon that just watches, and whenever a particle—whenever a gas molecule is sort of heading from the left to the right, it just opens the door long
- u199 dolgo, da spusti to molekulo skozi.« Prav? Če molekula potuje z desne na levo, pa pusti vratca zaprta, kajne? In potem se zdi, da bi temu demonu uspelo zmanjšati entropijo v škatli, morda celo v času, krajšem od astronomskega, kajne? Prednostno boenough to let that molecule through.” Okay? If a molecule is heading from the right to the left, then it keeps the door closed, right? And then, you know, this demon seems like, you know, it would succeed, you know, actually on a, you know, maybe a less than astronomical timescale at decreasing the entropy in the box, right? It’s gonna just preferentially
- u200 premikal delce na desno in zmanjšal entropijo v navideznem nasprotju z drugim zakonom. Prav? Torej, kako je s tem, kajne? To je bila velika uganka v fiziki, za katero so po mojem potrebovali večji del stoletja, da so jo povsem razjasnili. Prav? Potem ko jo je zastavil Maxwell, je o njej razmišljalmove the particles to the right, and it’s going to, you know—it’s going to decrease entropy in apparent violation of the second law. Okay? So then, you know, what gives, right? And this was a big puzzle in physics that I think, you know, took the better part of a century to completely clarify. Okay? But you had, you know, after Maxwell posed it, you had
- u201 Szilard, bolj znan po zamisli za atomsko bombo v tridesetih letih. Tu sta bila Bennett in Landauer in ... Torej so te velike osebnosti pojasnjevale, kaj se dogaja. In kar soSzilard, you know, better known for, you know, having the idea for the atomic bomb, you know, in the thirties, thinking about this. You had Bennett and Landauer, and, you know... So you had these major figures sort of clarifying what is going on. And what they
1:14:52 · IEEE-style page for Landauer's "Irreversibility and Heat Generation in the Computing Process" · A screenshot of a journal article page for R. Landauer's 1961 IBM Journal of Research and Development paper. It shows the abstract, which argues that logically irreversible computing operations require a minimum heat generation of about kT per irreversible function, along with citation metrics and publication details. A overlay badge reads "Links to everything curtjaimungal.com", suggesting a video still. - u202 nazadnje povedali, je, da je samo videti, kot da entropija pada. V resnici drugi zakon velja vedno in povsod. In če vprašaš: »Kam gre entropija, kajne? Entropija, za katero se zdi, da je zaradi demonovih dejanj izginila iz škatle.« Odgovor na to vprašanjeultimately said is that, you know, it only looks like entropy is going down. You know, really, you know, the second law holds, you know, always and everywhere. And if you ask, “Where it—where is the entropy going, right? The entropy that seems to have disappeared from the box by this demon’s actions.” The answer to that question
- u203 je, da je nazadnje šla v demonov spomin. Prav? Ko demon odloča, ali odpreti škatlo, ali zapreti škatlo, če razmisliš, kako ga izvesti — kako dejansko zgraditi tega demona, si mora demon bodisi zapomniti informacijo o tem, ali je delec prihajal z leve ali zis ultimately it’s gone into the demon’s memory. Okay? So the demon, in making these decisions of, you know, whether to open the box, whether to close the box, if you think about how to implement—how to actually build that demon, then either the demon has to remember, you know, the information about, like, was a particle coming from the left or was it coming from the
1:15:41 · Man gesturing in front of a mathematics chalkboard · A video still shows a man with glasses and a blue-gray collared shirt, smiling and speaking while pointing with one raised hand. Behind him is a chalkboard covered in handwritten mathematical notation, in an office with a door, a light switch and a hexagonal wall decoration. - u204 Maxwellov demon in psevdoentropijaMaxwell's Demon & Pseudo-Entropy
- u205 desne, in potem entropija preide v njegov spomin, ali pa mora odvajati toploto. In potem je entropija prešla iz demona v njegovo okolje. Prav? V vsakem primeru pa je skupna entropija vesolja ostala enaka ali narasla, natanko tako, kot zahteva drugi zakon. Prav?right, and then the entropy goes into its memory, or else it has to dissipate heat, you know. And then the entropy has gone out of the demon and into the demon’s environment. Okay? But either way, you know, the total entropy of the universe has stayed the same or gone up, you know, exactly as the second law said that it had to. Okay?
- u206 Torej, zdaj ti lahko povem o situaciji, o kateri smo razmišljali. In sicer, prav, ampak mi ... Kaj pa, če je — najprej, gre za klasični reverzibilni celični avtomat, prav? In spet imamo tega demona. Prav, ampak zdaj rečemo: »Glej, predpo... Predpostavimo, da demon pozna začetno stanje plinskih molekul,So okay, so now I can tell you about, you know, the situation that we were thinking about. Which is, okay, but we... What if it’s—first of all, it’s a classical reversible cellular automaton, okay? And we again have this demon. Okay, but now, you know, we say, “Look, you know, suppo... You know, let’s assume that the demon knows the initial state of the gas molecules,
- u207 kajne?« Ve, kje so bile na začetku. Pozna ustrezne fizikalne zakone, kajne? Torej jih lahko sam simulira, kajne? Lahko izvede ustrezne izračune in — Curt: Celotno mikrostanje? Scott: Oprosti. Moral bi reči, da demon ve, da so bili delci, recimo,right?” You know, it knows where they were initially. It knows the relevant laws of physics, right? So it can simulate them for itself, right? It can do the relevant calculations and— Curt: The full microstate? Scott: I’m sorry. So I should have said the demon knows that, let’s say, the particles
- u208 zbrani v kotu škatle, vendar njihovega mikrostanja onkraj tega ne pozna nujno. Prav? Tako. Prav. Zdaj pa bomo predpostavili, da je P enako NP. Prav? In če je P enako NP, potem, ko je demon naredil vse, kar sem pravkar povedal, in ima v spominu vse te informacije o tem, kdaj se delciwere concentrated in the corner of the box, but it does—it doesn’t necessarily know their microstate beyond that. Okay? Right. Okay. But then now we’re going to suppose that P is equal to NP. Okay? And now, if P is equal to NP, then, you know, after the demon has done everything that I just said and it has all this information in its memory about, you know, when the particles
- u209 približajo levi ali desni strani vratc ali karkoli že, je zdaj pred računskim problemom, kajne? Ta je: »Katero zaporedje — oziroma katero začetno stanje plinskih molekul bi privedlo do zaporedja opažanj, ki sem jih zabeležil?« Prav? In to bo na splošno izjemno težek računski problem, kajne? Lahko biapproach the left side of the door or the right side of the door or whatever, then the demon now faces a computational problem, right? Which is, “Which sequence—or which initial state of the gas molecules would have led to the sequence of observations that I made?” Okay? And that, in general, will be an extremely hard computational problem, right? Could
- u210 vključeval iskanje z grobo silo po vseh mogočih začetnih stanjih plinskih molekul. Po vseh mogočih začetnih stanjih z nižjo entropijo. Iskanje takega, ki bi privedlo do natanko tega zaporedja opažanj. Prav? Ampak če bi bilo P enako NP ali, še šibkeje, če,involve doing a brute force search through all the possible initial states, let’s say, of the gas molecules. You know, all the possible sort of, you know, lower-entropy initial states. You know, looking for one that sort of would have led to this exact sequence of observations. Okay? But if P were equal to NP or, you know, even more weakly than that, if,
- u211 kot pravimo, ne bi bilo enosmernih funkcij ali generatorjev psevdonaključnosti, prav, potem bi bil prav takšen problem učinkovito rešljiv, kajne? Demon bi se potem lahko izognil iskanju z grobo silo, kajne? In v času, krajšem od eksponentnega, v polinomskem času, bi lahko ugotovil začetno stanje molekul.as we say, there were no one-way functions or no pseudorandom generators, okay, then this is precisely the sort of problem that would be solvable efficiently, right? The demon could then avoid the brute force search, right? And in less than exponential time, in polynomial time, you know, it could figure out, you know, what was the initial state of the molecules.
1:18:25 · First page of "A Pseudorandom Generator from Any One-Way Function" · A video still shows the first page of a 1999 SIAM Journal on Computing paper by Håstad, Impagliazzo, Levin and Luby. The abstract says a pseudorandom generator can be built from any one-way function. Because a one-way function is easy to build from a pseudorandom generator, the two exist if and only if each other exist. A faint grey overlay near the bottom centre says "Every link from this episode" with a partly legible website name. - u212 In pri tem bi moral stisniti svoj spomin, kajne? Ko demon reši ta računski problem, lahko vse tiste bite v njegovem spominu, s katerimi smo zadostili drugemu zakonu, ko smo rekli: »No, tja je šla entropija,« spet stisnemo, kajne? InAnd with that, what it would have had to do is compress its memory, right? Once the demon has solved this computational problem, then, you know, all these bits in its memory where, you know, we had satisfied the second law by saying, you know, “Well, that is where the entropy went.” We could then compress those bits back down, right? And
- u213 zdaj rečeš: »No, čakaj malo. Kje je zdaj entropija?« Kajne? Kam je zdaj šla? In mislim, da bi fizik morda rekel: »Prav, mogoče je to domiselno,« ampak ga to ne bi preveč vznemirilo, ker bi ... Verjetno bi rekel: »No, samo razkril si, da ta entropijanow you say, “Well, wait a minute. Now where’s the entropy?” Right? Now where did it go, right? And, you know, I think, you know, a physicist, you know, might say, “Okay, you know, that may—maybe that’s cute,” but, you know, they’re not gonna be too disturbed by this because they’re gonna... You know, what they would probably say is, “Well, you’ve just revealed that this entropy was
- u214 že od vsega začetka sploh ni bila prava entropija.« Kajne? Pravzaprav imamo v teoretičnem računalništvu za to celo ime. Temu pravimo psevdoentropija. Prav? To je tisto, kar ustvari generator psevdonaključnih števil, kajne? Biti, kinever true entropy in the first place.” Right? In fact, we even have a name in theoretical computer science for this sort of thing. We call it pseudo-entropy. Okay? This is like, you know, it’s the kind of thing that a pseudorandom number generator produces, right? Bits that, you know,
1:19:47 · Man speaking in front of math-covered chalkboard · A video still of a man with dark, graying hair and dark-framed glasses, wearing a blue button-up shirt. He gestures with both hands, which are blurred by motion, while speaking toward the camera. Behind him is a chalkboard filled with handwritten mathematical notation. A blurred dark caption bar sits at the lower center. - u215 so videti enakomerno naključni, a imajo v resnici precej krajši opis. Kajne? V tem scenariju bi torej vzeli entropijo, vzeli bi tisto, kar je v termodinamični situaciji videti kot entropija, in razkrili, da je bila v resnici ves čas samo psevdoentropija. Kajne? V tem smislulook like they are uniformly random, but that actually have a much shorter description. Right? So what we would be doing in this scenario is we’d be taking entropy, you know, we’d be taking what looks like entropy in a thermodynamic situation and unmasking it as actually just having been pseudo-entropy all along. Right? So in that sense,
- u216 torej ne bi kršili drugega zakona, ampak bi ga nekako obšli. V nekem smislu bi ga naredili nepomembnega. Obstaja pa nekaj pomembnih zadržkov: v resničnem življenju lahko kaotični učinki preprečijo delovanje tega pristopa, kajne? Recimo,we would not be violating the second law, but we would sort of be, you know, circumventing it. Like, you know, rendering it irrelevant in a sense. And now, you know, there are some important caveats, which is that, you know, this—in real life, chaotic effects, you know, may make this approach not work, right? Like,
- u217 če bi moral začetna stanja delcev poznati z neskončno natančnostjo, da bi izračunal, kaj se zgodi, potem tega morda še vedno ne bi mogel narediti, tudi če je P enako NP, kajne? In če v sistem nenehno vstopa kvantnomehanska negotovost, bi tudi to lahko onemogočilo ta pristop, prav?if you would need to know the initial states of the particles to infinite precision in order to calculate what happens, then, you know, then even if P equals NP, you may still be unable to do that, right? And also, if there’s quantum mechanical uncertainty, you know, that keeps getting injected into the system, that could also kill this approach, okay?
- u218 Ta pristop torej deluje predvsem za klasični dinamični sistem, ki ni podvržen kaosu. Bistvo pa je, da če v naravi najdemo primer takega sistema, bi lahko bilo tisto, kar je v njem videti kot drugi zakon, v svetu, kjer je P enako NP, dejansko kršeno. Curt: Profesor. Hvala, da ste mi namenili toliko časa.So this approach mostly works for a classical dynamical system that is not subject to chaos. So, but the point is, if in nature one finds an example of such a system, then, you know, what appears in that system, like the second law, may actually be violated in a world where P equals NP. Curt: Professor. Thank you for spending so much time with me.
- u219 Scott: Seveda, seveda. Curt: In hej, glede zavesti. Scott: Ojoj. Prav. Misliš, samo še eno lahko vprašanje za konec? Curt: Tako. Ne, ne, gre za nekaj, kar si že raziskoval, ta vrata XOR in IIT. Torej pravijo, da imajo ta vrata XOR visoko stopnjo zavesti. Vedno sem se spraševal: prav, imajo visoko vrednost fi, prav? Ampak česa se potem zavedajo? Recimo,Scott: Of course, of course. Curt: And hey, about consciousness. Scott: Oh, gosh. All right. Just with an easy last question, you mean? Curt: Right. No, no, it’s something you’ve explored before, these XOR gates and IIT. So they say that these XOR gates are of high consciousness. A question I’ve always had is, okay, it has a high phi number, okay? But then what is it conscious of? Like,
- u220 česa bi po njegovem rekla, da se zavedajo? Je to samo nekaj takega: »Tukaj sem, sem super zavesten«? Ampak običajno se zavedaš nečesa. Scott: Prav. Torej sprašuješ o teoriji integrirane informacije, ki je teorija zavesti ali vsaj tega, kateri fizični sistemi so zavestni in kateri niso. Predlagal jo je človek po imenu Giulio Tononi, inwhat would he say that it’s conscious of? Is it just like, “I’m here, I’m super conscious”? But usually you’re conscious of something. Scott: Okay. So you’re asking about integrated information theory, which is a, you know, a theory of consciousness, or at least of, like, which physical systems are conscious and which aren’t, which was put forward by a guy named Giulio Tononi, and, you know,
- u221 okoli te teorije je zgradil celo skupnost. Ozadje tvojega vprašanja pa je, da se mi zdi ta teorija preprosto napačna, prav? Kar je na neki način bolje od mnogih, mnogih teorij zavesti,which, you know, he’s sort of built up a whole community around this theory. And now, you know, the backstory to your question is that I think this theory is just wrong, okay? You know, which in a way is better than, you know, the many, many theories of consciousness
1:22:32 · Smiling man in front of a math-covered chalkboard · A video still shows a man with dark, graying hair and dark-rimmed glasses, wearing a blue button-up shirt. He is smiling and appears to be speaking, close to the camera. Behind him is a chalkboard with handwritten math, including a bell-shaped curve, and a tan door and a hexagonal wall decoration are to the left. - u222 Zakaj je IIT napačnaWhy IIT Is Wrong
- u223 ki niso niti napačne, kajne, ki so preveč meglene, da bi sploh lahko bile napačne. Mislim, da ta dejansko tvega in daje napovedi, ki so preprosto absurdne, kajne? Zlasti jedro IIT je ta številčna mera, imenovana fi, ki naj bi jo lahko izračunal za katerikoli fizični sistem in bi ti povedala, kolikothat are not even wrong, right, that are too vague to even be wrong. I think, like, this one actually just sticks its neck out, and it makes predictions that are just absurd, right? And in particular, like, you know, the core of IIT is this numerical measure called phi, which, you know, allegedly you can just calculate for any physical system, and it will tell you how much
- u224 zavesti je v tem sistemu, prav? In obstaja nekaj argumentov zanjo, med drugim naj bi imeli veliki možgani višjo vrednost fi kot mali možgani. Prav, ampak tu je tudi ogromno nejasnosti, kajne? Sama definicija fi se je od ene različice IIT do naslednje nenehno spreminjala.consciousness there is in that system, okay? And, you know, and there are some arguments for this and, you know, involving, like, the cerebrum, you know, apparently having a higher value of phi than the cerebellum. Okay, but there’s also—there’s a huge amount of vagueness here, right? The definition of phi itself has kept changing from one version of IIT to the next version.
- u225 Trdijo, da je to mero mogoče izpeljati iz aksiomov. Ni izpeljana iz aksiomov. Članek samo našteje nekaj aksiomov, potem pa se na neki točki preprosto pojavi fi, z — kajne, to je nekakšna psevdomatematika, in to je res nadležno. Curt: Kot članek OpenAI.You know, it’s claimed that this measure can be derived from axioms. It’s not derived from axioms. It’s just, like, you know, the paper, it just lists some axioms, and then just phi appears at some point, you know, with the—right, you know, it’s kind of like pseudomathematics, like, you know, right, you know, and so that’s really annoying. Curt: It’s like an OpenAI paper.
1:23:32 · Man in glasses speaking in front of chalkboard · A still from a video shows a man with dark hair and black-rimmed glasses, wearing a light blue collared shirt. He is mid-speech and gesturing with one hand. Behind him is a chalkboard filled with handwritten math, including a probability-style bound and a note about choosing something, which suggests a lecture or technical talk. - u226 Scott: No, ja, ampak za članke OpenAI mislim, da so vsi — večina jih je dejansko pravilnih, kajne? Če — to je tisto neverjetno. Mislim, v bližnji prihodnosti bomo vedeli z večjo gotovostjo. Ampak ti članki o IIT po mojem formulo za ta fi v bistvu preprosto potegnejo od nikoder. Prav, ampak potemScott: Well, yeah, but the OpenAI papers, I think, you know, I think all—most of them are actually correct, right? If you, you know—that’s the amazing thing about it. I mean, we’re gonna know with more certainty in the near future. But the—but these IIT papers, I think, you know, they were just sort of pulling a formula, you know, for this phi out of nowhere, basically. Okay, but then
- u227 mi — ko predlagajo to formulo, lahko pogledamo, kaj napoveduje, kajne? In poanta mojih zapisov o IIT na blogu, to je bilo pred 12 leti, je bila, da lahko zlahka sestaviš primere sistemov, ki imajo veliko višjo vrednost fi kot recimo naši možgani, pa očitno ne počnejo ničesar zavestnega. Sowe—it—once they’ve—they’re proposing this formula, we can look at what does it predict, right? And the point that I made in my blog posts on IIT, this was 12 years ago, was that, you know, you can easily construct examples of systems that have a way higher value of phi than, let’s say, our brains do, but that seem like they are obviously not doing anything conscious. They’re
1:24:26 · Blog text critiquing Integrated Information Theory of consciousness · A video still shows a web page of dense text arguing that Integrated Information Theory (IIT) is a serious but failed attempt at the Pretty-Hard Problem of Consciousness. The author says IIT predicts vast consciousness in simple systems, such as those applying parity-check codes, and even more than in humans. A banner reading "Links to everything curtjaimungal.com" covers part of the lower text. - u228 samo velikanska mreža vrat XOR, prav? Ali kaj podobnega. Kot prazna stena ali enotna stena logičnih vrat, ki ne počnejo nič zanimivega, kajne? In potem bi rekel: »Če — če mi boš povedal, dajust like a giant grid of XOR gates, okay? Or something like that, okay? Like a blank wall or, you know, a wall of—a uniform wall of logic gates doing nothing of any interest, right? And then, you know, I would say, like, “If that—if you’re gonna tell me that
- u229 ima to več zavesti kot mi, o čem se potem sploh še pogovarjamo, kajne?« Kaj je — no, tisto, kar zdaj mislimo z besedo »zavest«, se zdi tako nepovezano s tem, kar sem mislil, da mislimo z besedo »zavest«, dathat has more consciousness than we do, then, like, what are we even talking about anymore, right?” What is, you know, like, what—well, the, you know, the thing that we, you know, the—what we now mean by the word “consciousness” seems so disconnected from what I thought we meant by the word “consciousness” that, like,
- u230 mi moraš zdaj povedati, zakaj bi me ta stvar morala zanimati. Karkoli že je, kajne? In Tononi je napisal cel odgovor na mojo kritiko, njegov odgovor pa je bil, presenetljivo, da je to neprijetno posledico preprosto v celoti sprejel. S tem mislim, da pravi: »Scott je zgrešil, ker se je zanašal na svojo intuicijo, namesto tega pa bi se moral zanašati na teorijo.you now have to tell me why I should be interested in this thing. You know, whatever it is, right? And Tononi wrote a whole response to my critique, and his response, amazingly, was to just completely bite the bullet here. You know, by which I mean, he says, you know, “Scott went wrong by relying on his intuitions, and he should just instead rely on the theory. You know,
- u231 Teorija pravi, da je ta stena vrat XOR 1.000-krat bolj zavestna kot katerikoli človek, torej je,« kajne? Tvoje vprašanje pa je bilo: »Prav, in česa se stena zaveda?« Zdi se mi, da je to bolj vprašanje zanj kot zame. Mislim, mogoče se zaveda svojega lastnega XOR —the theory says that this wall of XOR gates is 1,000 times more conscious than any human, therefore it is,” right? And now your question was, “Okay, and what is the wall conscious of?” You know, I feel like that’s more a question for him than for me. I mean, you know, maybe it’s conscious of its own XOR—
- u232 Curt: Zaveda se, kako zelo Scott ne mara te teorije. Scott: Morda se zaveda svoje lastne XOR-ovskosti, svojega lastnega doživljanja tega, da je prazna stena. Curt: Ne vem. Prav. No, profesor, bilo je zelo zabavno. Lep dan in srečno — Scott: Hvala. Hvala. Tudi tebi.Curt: It’s conscious of how much Scott dislikes this theory. Scott: Maybe it’s conscious of its own XORness, its own, you know, its own experience of being a blank wall. Curt: I don’t know. Okay. Well, professor, so much fun. Have a great day, and good luck to— Scott: Thanks. Thanks. You too.
1:26:06 · Man in glasses smiling before a chalkboard of equations · A video still shows a man with dark-rimmed glasses and a blue collared shirt, mouth open as if speaking or laughing, close to the camera. Behind him is a chalkboard with handwritten math and logic notation, in an office with a wooden door and a hexagonal wall decoration. - u233 Curt: Srečno tvojemu sinu — Scott: Hvala. Cenim to. Curt: ... pri trolanju tvoje žene, njegove mame. Scott: Ja. Hvala. Prav. Kot vedno se je bilo lepo pogovarjati s tabo, Curt. Curt: Lepo se imej. Scott: Prav. Okej, adijo. Curt: Lepo se je bilo pogovarjati s tabo. Če želite dostop do naslednjega pogovora pred vsemi drugimi ter moja dejanska mnenja o teh teorijah in konceptih, ki jih ne vključujem v intervjuje, obiščite moj Substack, CURTJAIMUNGAL.com. Torej C-U-R-T-J-A-I-M-U-N-G-A-L.com.Curt: Good luck to your son— Scott: Thanks. Appreciate it. Curt: ...with trolling your wife, his mom. Scott: Yeah. Thank you. All right. Good talking to you as always, Curt. Curt: Take care. Scott: All right. Okay, bye. Curt: Good talking to you. If you want access to the next conversation prior to anyone else, plus my actual opinions on these theories and concepts, which I keep out of the interviews, then visit my Substack, CURTJAIMUNGAL.com. That’s C-U-R-T-J-A-I-M-U-N-G-A-L.com.
- u234 In če vas je današnji pogovor pritegnil, je tukaj nekje na zaslonu zdaj epizoda, ki bi si jo jaz ogledal naslednjo. Uživajte.And if today’s conversation grabbed you, there’s an episode on screen somewhere right now over here, which is the next one that I’d watch. Enjoy.
1:26:55
V okolici
Matematika s pomočjo umetne inteligence
Matematika s pomočjo umetne inteligence uporablja umetno inteligenco za odkrivanje, dokazovanje, preverjanje ali razlaganje matematičnih rezultatov.
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Razumevanje matematičnih idej, njihovih medsebojnih povezav in razlogov za veljavnost rezultatov.
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Tema1 virEn sam vir
Kvantno računanje proti ognjenim pregradam
Vir trdi, da miselnega poskusa AMPS z ognjeno pregrado ni mogoče izvesti v praksi. Ognjena pregrada je domnevna plast visokoenergijskega sevanja ob črni luknji. Opazovalec, ki pada vanjo, bi moral najprej dekodirati Hawkingovo sevanje — iz sevanja črne luknje razbrati kvantne informacije. Potrebno kvantno računanje bi trajalo eksponentno dolgo glede na entropijo črne luknje. Entropija meri, koliko različnih mikroskopskih stanj je združljivih z njenim opisom; eksponentna rast pa pomeni, da vsako povečanje vhodne količine čas pomnoži, ne le podaljša. Avtorji predlagajo računsko merilo za efektivno teorijo polja, torej približen opis fizike pri izbranih energijah. Opazljivk, ki jih en opazovalec računsko ne more doseči, po tem merilu ni treba predstaviti s komutirajočimi operatorji. Opazljivke so merljive količine, operatorji pa njihovi matematični predstavniki; če komutirajo, vrstni red njihove uporabe ne spremeni rezultata. Predlog preverijo z modeli kvantnih vezij, zahtevnostjo popravljanja napak in geometrijami črnih lukenj. Sklep: močnejše različice poskusa AMPS ni mogoče izvesti.
Raziskava
math/preprints/The-Unique-Games-Theorem-September-23-2026/paper.pdf at main · openai/math
Vir je stran na GitHubu za ogled datoteke PDF s predobjavo članka o izreku Unique Games Theorem v zbirki datotek openai/math. Predobjava je vnaprej objavljena različica znanstvenega članka. Na strani so vidni le meniji za premikanje po spletišču in podatki o datoteki. Besedila članka ni na strani.
Prispevek
P ?= NP
P proti NP sprašuje: ali lahko vsak problem, pri katerem dokaz za odgovor »da« hitro preverimo, tudi hitro rešimo? P označuje probleme, ki jih lahko hitro rešimo, NP pa tiste, pri katerih lahko hitro preverimo dokaz za odgovor »da«. Dokaza ni v nobeno smer. Večina strokovnjakov meni, da P ni enak NP. Dosedanji napredek so dokazane spodnje meje — koliko računanja je najmanj potrebnega — in ovire, ki pojasnjujejo, zakaj znane dokazne tehnike tega vprašanja ne morejo rešiti.
Raziskava
- 2012. Full version available at arXiv:1209.5993
- Better late than never: information retrieval from black holes
- Black Holes as Mirrors: Quantum Information in Random Subsystems
- Dekodiranje Hawkingovega sevanja
- Explicit lower bounds via geometric complexity theory
- Geometrijska teorija zahtevnosti
- Insightful D-branes
- Komplementarnost črnih lukenj
- Kvantno popravljanje napak
- New lower bounds for the border rank of matrix multiplication
- Paradoks požarnega zidu AMPS
- Scott Aaronson: Matematična apokalipsa – bo inteligenca sploh še pomembna?
- Steven Strogatz
- Steven Strogatz o človeški plati matematike
- The Information paradox: A Pedagogical introduction
- arxiv-0704.0229
- arxiv-0709.0749
- arxiv-1009.0246
To besedilo je napisano z umetno inteligenco.
Objavljeno v: Zdaj