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So it turns out that mathematics is a very powerful language.

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It has generated considerable insight in physics,

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in biology and economics,

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but not that much in the humanities and in history.

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I think there's a belief that it's just impossible,

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that you cannot quantify the doings of mankind,

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that you cannot measure history.

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But I don't think that's right.

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I want to show you a couple of examples why.

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So my collaborator Erez and I were considering the following fact:

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that two kings separated by centuries

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will speak a very different language.

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That's a powerful historical force.

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So the king of England, Alfred the Great,

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will use a vocabulary and grammar

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that is quite different from the king of hip hop, Jay-Z.

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(Laughter)

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Now it's just the way it is.

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Language changes over time, and it's a powerful force.

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So Erez and I wanted to know more about that.

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So we paid attention to a particular grammatical rule, past-tense conjugation.

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So you just add "ed" to a verb at the end to signify the past.

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"Today I walk. Yesterday I walked."

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But some verbs are irregular.

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"Yesterday I thought."

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Now what's interesting about that

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is irregular verbs between Alfred and Jay-Z have become more regular.

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Like the verb "to wed" that you see here has become regular.

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So Erez and I followed the fate of over 100 irregular verbs

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through 12 centuries of English language,

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and we saw that there's actually a very simple mathematical pattern

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that captures this complex historical change,

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namely, if a verb is 100 times more frequent than another,

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it regularizes 10 times slower.

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That's a piece of history, but it comes in a mathematical wrapping.

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Now in some cases math can even help explain,

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or propose explanations for, historical forces.

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So here Steve Pinker and I

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were considering the magnitude of wars during the last two centuries.

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There's actually a well-known regularity to them

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where the number of wars that are 100 times deadlier

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is 10 times smaller.

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So there are 30 wars that are about as deadly as the Six Days War,

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but there's only four wars that are 100 times deadlier --

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like World War I.

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So what kind of historical mechanism can produce that?

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What's the origin of this?

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So Steve and I, through mathematical analysis,

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propose that there's actually a very simple phenomenon at the root of this,

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which lies in our brains.

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This is a very well-known feature

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in which we perceive quantities in relative ways --

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quantities like the intensity of light or the loudness of a sound.

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For instance, committing 10,000 soldiers to the next battle sounds like a lot.

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It's relatively enormous if you've already committed 1,000 soldiers previously.

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But it doesn't sound so much,

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it's not relatively enough, it won't make a difference

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if you've already committed 100,000 soldiers previously.

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So you see that because of the way we perceive quantities,

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as the war drags on,

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the number of soldiers committed to it and the casualties

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will increase not linearly --

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like 10,000, 11,000, 12,000 --

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but exponentially -- 10,000, later 20,000, later 40,000.

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And so that explains this pattern that we've seen before.

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So here mathematics is able to link a well-known feature of the individual mind

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with a long-term historical pattern

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that unfolds over centuries and across continents.

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So these types of examples, today there are just a few of them,

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but I think in the next decade they will become commonplace.

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The reason for that is that the historical record

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is becoming digitized at a very fast pace.

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So there's about 130 million books

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that have been written since the dawn of time.

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Companies like Google have digitized many of them --

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above 20 million actually.

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And when the stuff of history is available in digital form,

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it makes it possible for a mathematical analysis

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to very quickly and very conveniently

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review trends in our history and our culture.

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So I think in the next decade,

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the sciences and the humanities will come closer together

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to be able to answer deep questions about mankind.

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And I think that mathematics will be a very powerful language to do that.

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It will be able to reveal new trends in our history,

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sometimes to explain them,

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and maybe even in the future to predict what's going to happen.

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Thank you very much.

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(Applause)