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.
Pra del se matematika eshte nje gjuhe shume e fuqishme. Ajo ka gjeneruar njohuri te konsiderueshme ne fizike, ne biologji dhe ekonomi, por jo edhe aq shume ne shkencat humane dhe ne histori. Une mendoj qe njerezit besojne qe eshte e pamundur, qe nuk mund te masesh veprat e njerezimit, qe nuk mundemi te matim historine. Por une nuk mendoj qe kjo eshte e drejte. Dua t`ju paraqes ca shembuj pse.
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.
Bashkepuntori im Erez dhe une ishim duke e konsideruar faktin: qe 2 mbreter te ndare ne shekuj do te flasin nje gjuhe shume te ndryshme. Kjo eshte forca e fuqishme historike. Pra mbreti i Anglise,Alfredi i madh do te perdore nje gramatike dhe fjalor qe eshte shume ndryshe nga ai i mbretit te hip hopit Jay-Z. Qeshje Tash eshte kjo menyre qe eshte. Gjuha ndryshon me kohen, dhe eshte force e fuqishme.
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.
Pra Erez dhe un donim te dinim me shume per kete. Keshtu ne kushtuam vemendje te vecante rregullave te gramatikes, zgjedhimit te foljeve ne te shkuaren. Pra vetem i shton nje mbarese foljes per te krijuar kohen e shkuar. "Sot une eci. Dje une eca." Por disa folje jane te parregullta. "Dje une i 'dhashe' mendjes para mbrapa." Tash ajo qe eshte interesante ketu eshte qe foljet e parregullta qe ndermjet Alfredit dhe Jay-Z jane bere te rregullta. Sikur folja "te martohet" qe e shifni eshte bere e rregullt.
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.
Pra une dhe Erez ndoqem rrugen e me shume 100 foljeve te parregullta gjate 12 shekujve te gjuhes angleze, dhe e kemi pare qe faktikisht eshte nje model shume i thjeshte matematikor qe shpjegon kete kompleks te ndryshimeve historike, domethene, nese nje folje eshte 100 here me e shpeshte se tjetra, ajo behet e rregullt 10 here me ngadale. Kjo eshte nje pjese e historise, por ajo vjen nen nje mbulese matematikore.
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?
Tash ne disa raste matematika mund te ndihmoje edhe te shpjegoje, ose te propozoje shpjegime per forcat historike. Pra ketu Steve Pinker dhe une i dhame rendesi madhesise se lufterave gjate 2 shekujve te fundit. Faktikisht eshte nje rregull i mirenjohur qe numri i lufterave qe jane 100 here me vdekjeprurese eshte 10 here me i vogel. Pra jane 30 luftera qe jane po aq vdekjeprurese si Lufta e 6 diteve por jane vetem 4 luftera qe jane 100 here me vdekjeprurese se Lufta e Pare Boterore. Pra cfare mekanizmi i historise mund te prodhoje ate? Cila eshte origjina e saj?
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.
Pra Steve dhe une, permes analizave matematikore, propozuam qe rrenjet e kesaj jane ne nje fenomen te thjeshte, qe gjendet ne trute tona. Eshte nje tipar i mirenjohur ne te cilin ne perceptojme sasite ne menyra relative sasite si intensiteti i drites ose lartesia e tingullit. Per shembull te vendosesh 10.000 ushtare per betejen e ardhshme, tingellon si shume. Eshte relativisht numer i madh nese ju keni vendosur 1000 ushtare ne betejat e shkuara Por nuk tingellon shume, nuk eshte relativisht mjaftueshem, nuk do te beje ndryshim nqs me perpara ke vendosur 100,000. Pra e shikoni se per shkak te menyres si perceptojme sasite, si lufterat vazhdojne, numri i ushtareve te angazhuar ne te dhe viktimat nuk rriten ne menyre lineare -- si 10,000 , 11,000 , 12,000 por ne fuqi - 10,000 me vone 20,000 me vone 40,000 . Dhe kjo e shpjegon kete model qe ne e kemi pare me pare.
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.
Pra matematika eshte ne gjendje te lidhje nje funksion me mendjen e individit me terme te gjata historike qe shpalos shekujt dhe kontinentet.
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.
Pra keto tipe te shembujve, sot jane vetem disa prej tyre, por une mendoj se ne dekaden e ardhshme do te behen me te zakonshme. Arsyeja e kesaj eshte nje incizim historik eshte duke u bere i digjitalizuar ne ritem shume te shpejte. Pra rreth 130 milione libra jane shkruar qe nga agimi i kohes. Kompanite si Google kane digjitalizuar shume prej tyre me shume se 20 milione. Dhe kur gjerat e historise behen te dixhitalizuara, eshte e mundur qe analizat e matematikes te jene shume te shpejta dhe bindese te analizojne trendet ne historine dhe kulturen tone.
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.
Pra une mendoj ne dekaden e ardhshme, shkencat dhe humaniteti do te jene me te bashkuara te jene ne gjendje t`ju pergjigjen pyetjeve rreth njerzimit. Dhe mendoj qe matematika do te jete nje gjuhe e fuqishme per te bere kete. Do te jete ne gjendje te zbuloje trende te reje ne historine tone, nganjehere ti shpjegoje ato, dhe ndoshta ne te ardhmen te parashikoje se cfare do te ndodhe.
Thank you very much.
Faleminderit shume.
(Applause)
(Duartrokitje)