So it turns out that mathematics is a very powerful language. It has generated considerable insight in physics, in biology and economics, but not that much in the humanities and in history. I think there's a belief that it's just impossible, that you cannot quantify the doings of mankind, that you cannot measure history. But I don't think that's right. I want to show you a couple of examples why.
Ispada da je matematika veoma moćan jezik. Ona ima značajno uporište u fizici, biologiji i ekonomiji, ali ne tako veliko u društvenim naukama i istoriji. Mislim da postoji verovanje da je upravo nemoguće, da se ne može izmeriti količina ljudskih dela, niti izmeriti istorija. Ali ne mislim da je to tačno. Hoću da vam pokažem par primera zašto.
So my collaborator Erez and I were considering the following fact: that two kings separated by centuries will speak a very different language. That's a powerful historical force. So the king of England, Alfred the Great, will use a vocabulary and grammar that is quite different from the king of hip hop, Jay-Z. (Laughter) Now it's just the way it is. Language changes over time, and it's a powerful force.
Moj saradnik Erez i ja smo razmatrali sledeću činjenicu: dva kralja razdvojena vekovima će govoriti veoma različitim jezikom. To je veoma snažna istorijska sila. Tako će kralj Engleske, Alfred Veliki, korisititi rečnik i gramatiku koji su vrlo različiti od kralja hip hopa, Džej Zija. (Smeh) To je tako. Jezik se menja u vremenu i to je snažna sila.
So Erez and I wanted to know more about that. So we paid attention to a particular grammatical rule, past-tense conjugation. So you just add "ed" to a verb at the end to signify the past. "Today I walk. Yesterday I walked." But some verbs are irregular. "Yesterday I thought." Now what's interesting about that is irregular verbs between Alfred and Jay-Z have become more regular. Like the verb "to wed" that you see here has become regular.
Tako da smo Erez i ja hteli da saznamo više o tome. Tako da smo obratili pažnju na posebno gramatičko pravilo, promenu glagola u prošlom vremenu (engleski jezik). Tako dodajemo "ed" glagolu da označimo prošlost. "Danas hodam (walk). Juče sam hodao (walked)." Ali neki glagoli su nepravilni. "Juče sam mislio. (thought)" Sad, ono što je interesantno povodom toga je da su nepravilni glagoli između Alfreda i Džej Zija postali pravilniji. Kao glagol "venčati se" ("to wed") koji vidite ovde je postao pravilan.
So Erez and I followed the fate of over 100 irregular verbs through 12 centuries of English language, and we saw that there's actually a very simple mathematical pattern that captures this complex historical change, namely, if a verb is 100 times more frequent than another, it regularizes 10 times slower. That's a piece of history, but it comes in a mathematical wrapping.
Tako da smo Erez i ja posmatrali sudbinu preko 100 nepravilnih glagola kroz 12 vekova engleskog jezika, i uočili smo da ustvari postoji veoma jednostavno matematičko pravilo koje obuhvata ovu složenu istorijsku promenu, naime, ako je glagol 100 puta češći nego drugi, on postaje pravilan 10 puta sporije. To je deo istorije, ali ima matematički opis.
Now in some cases math can even help explain, or propose explanations for, historical forces. So here Steve Pinker and I were considering the magnitude of wars during the last two centuries. There's actually a well-known regularity to them where the number of wars that are 100 times deadlier is 10 times smaller. So there are 30 wars that are about as deadly as the Six Days War, but there's only four wars that are 100 times deadlier -- like World War I. So what kind of historical mechanism can produce that? What's the origin of this?
Sada, u nekim slučajevima matematika čak može pomoći da se opiše ili predloži objašnjenje za istorijske sile. Ovde smo Stiv Pinker i ja razmatrali veličine ratova za vreme dva poslednja veka. Tu postoji u stvari dobro poznato pravilo gde je broj ratova koji su 100 puta smrtonosniji 10 puta manji. Tako da ima 30 ratova koji su u stvari smrtonosni kao šestodnevni rat (rat Arapi-Izrael 1967), ali ima samo četiri rata koji su 100 puta smrtonosniji -- kao Prvi svetski rat. Pa kakav istorijski mehanizam to može prouzrokovati? Šta je poreklo ovoga?
So Steve and I, through mathematical analysis, propose that there's actually a very simple phenomenon at the root of this, which lies in our brains. This is a very well-known feature in which we perceive quantities in relative ways -- quantities like the intensity of light or the loudness of a sound. For instance, committing 10,000 soldiers to the next battle sounds like a lot. It's relatively enormous if you've already committed 1,000 soldiers previously. But it doesn't sound so much, it's not relatively enough, it won't make a difference if you've already committed 100,000 soldiers previously. So you see that because of the way we perceive quantities, as the war drags on, the number of soldiers committed to it and the casualties will increase not linearly -- like 10,000, 11,000, 12,000 -- but exponentially -- 10,000, later 20,000, later 40,000. And so that explains this pattern that we've seen before.
Tako Stiv i ja, kroz matematičku analizu predlažemo da postoji veoma jednostavan fenomen u korenu ovoga, koji leži u našem umu. To je veoma dobro poznata osobina gde mi doživljavamo količine na relativan način -- količine kao intenzitet svetla ili jačinu zvuka. Npr, angažovanje 10 000 vojnika u sledećoj bici, zvuči kao mnogo. To je relativno veliki broj, ako ste već angažovali 1 000. Ali to ne izgleda tako mnogo, nije relativno dovoljno, neće praviti razliku ako ste ranije već angažovali 100 000 vojnika. Tako da vidite zbog načina na koji mi doživljavamo količine, kako se ratovi nastavljaju, broj vojnika koji su uključeni u njih i žrtve se neće povećavati linearno -- kao 10 000, 11 000, 12 000 -- već eksponencionalno -- 10 000, pa 20 000, pa 40 000. I to objašnjava pravilo koje smo videli ranije.
So here mathematics is able to link a well-known feature of the individual mind with a long-term historical pattern that unfolds over centuries and across continents.
Tako da ovde matematika može da poveže dobro poznatu osobinu pojedinačnog mišljenja sa dugotrajnim istorijskim uzorkom koji se otrkiva kroz vekove i kontinente.
So these types of examples, today there are just a few of them, but I think in the next decade they will become commonplace. The reason for that is that the historical record is becoming digitized at a very fast pace. So there's about 130 million books that have been written since the dawn of time. Companies like Google have digitized many of them -- above 20 million actually. And when the stuff of history is available in digital form, it makes it possible for a mathematical analysis to very quickly and very conveniently review trends in our history and our culture.
Mislim da će ovakve vrste primera, kojih danas ima samo nekolicina, u sledećoj deceniji postati uobičajene. Razlog za ovo je to što se istorjski zapisi veoma brzim tempom digitalizuju. Ima oko 130 miliona knjiga koje su napisane od rađanja vremena. Kompanije kao Google su digitalizovale mnoge od njih ustvari preko 20 miliona. I kad su istorijske stvari dostupne u digitalnoj formi, to omogućava da se matematičkom analizom, veoma brzo i vrlo povoljno pregledaju trendovi u našoj istoriji i kulturi.
So I think in the next decade, the sciences and the humanities will come closer together to be able to answer deep questions about mankind. And I think that mathematics will be a very powerful language to do that. It will be able to reveal new trends in our history, sometimes to explain them, and maybe even in the future to predict what's going to happen.
Tako da mislim da će u sledećoj deceniji, prirodne i društvene nauke postati bliskije i da će moći da odgovore na suštinska pitanja o ljudskoj vrsti. I mislim da će jezik matematike biti veoma snažan jezik da to uradi. Moći će da otkrije nove trendove u našoj istoriji, ponekad da ih objasni i možda čak da predvidi šta će se dogoditi.
Thank you very much.
Hvala mnogo.
(Applause)
(Aplauz)