0:00:00.000,0:00:02.625 So it turns out that mathematics is a very powerful language. 0:00:02.625,0:00:05.875 it has generated considerable insight in physics, 0:00:05.875,0:00:08.083 in biology and economics, 0:00:08.083,0:00:10.792 but not that much in the humanities and in history. 0:00:10.792,0:00:12.875 I think there's a belief that it's just impossible, 0:00:12.875,0:00:15.583 that you cannot quantify the doings of mankind, 0:00:15.583,0:00:17.333 that you cannot measure history. 0:00:17.333,0:00:19.875 But I don't think that's right. 0:00:19.875,0:00:21.917 I want to show you a couple of examples why. 0:00:21.917,0:00:24.875 So my collaborator Erez and I were considering the following fact: 0:00:24.875,0:00:27.250 that two kings separated by centuries 0:00:27.250,0:00:28.125 will speak a very different language. 0:00:28.125,0:00:29.875 That's a powerful historical force. 0:00:29.875,0:00:33.417 So the king of England, Alfred the Great, 0:00:33.417,0:00:35.042 will use a vocabulary and grammar 0:00:35.042,0:00:37.542 that is quite different from the king of hip hop, Jay-Z. 0:00:37.542,0:00:40.792 (Laughter) 0:00:40.792,0:00:42.625 Now it's just the way it is. 0:00:42.625,0:00:44.917 Language changes over time, and it's a powerful force. 0:00:44.917,0:00:46.542 So Erez and I wanted to know more about that. 0:00:46.542,0:00:50.292 So we paid attention to a particular grammatical rule, past-tense conjugation. 0:00:50.292,0:00:54.125 So you just ad "ed" to a verb at the end to signify the past. 0:00:54.125,0:00:55.667 "Today I walk, yesterday I walked." 0:00:55.667,0:00:57.042 But some verbs are irregular. 0:00:57.042,0:00:58.792 "Yesterday I thought." 0:00:58.792,0:01:00.458 Now what's interesting about that 0:01:00.458,0:01:04.042 is irregular verbs between Alfred and Jay-Z have become more regular. 0:01:04.042,0:01:05.792 Like the verb "to wed" that you see here has become regular. 0:01:05.792,0:01:10.583 So Erez and I followed the fate of over a hundred irregular verbs 0:01:10.583,0:01:12.333 through 12 centuries of English language, 0:01:12.333,0:01:15.875 and we saw that there's actually a very simple mathematical pattern 0:01:15.875,0:01:18.417 that captures this complex historical change, 0:01:18.417,0:01:21.708 namely, if a verb is a hundred times more frequent than another, 0:01:21.708,0:01:24.250 it regularized 10 times slower. 0:01:24.250,0:01:28.000 That's a piece of history, but it comes in a mathematical wrapping. 0:01:28.000,0:01:31.500 Now in some cases math can even help explain, 0:01:31.500,0:01:34.625 or propose explanations, for historical forces. 0:01:34.625,0:01:37.042 So here Steve Pinker and I 0:01:37.042,0:01:40.125 were considering the magnitude of wars during the last two centuries. 0:01:40.125,0:01:42.958 There's actually a well-known regularity to them 0:01:42.958,0:01:46.042 where the number of wars that are a hundred times deadlier 0:01:46.042,0:01:47.917 is 10 times smaller. 0:01:47.917,0:01:51.292 So there are 30 wars that are about as deadly as the Six Days War, 0:01:51.292,0:01:54.542 but there's only four wars that are a hundred times deadlier -- 0:01:54.542,0:01:56.458 like World War I. 0:01:56.458,0:01:59.458 So what kind of historical mechanism can produce that? 0:01:59.458,0:02:01.458 What's the origin of this? 0:02:01.458,0:02:03.292 So Steve and I, through mathematical analysis, 0:02:03.292,0:02:08.333 propose that there's a very simple phenomenon at the root of this, 0:02:08.333,0:02:09.208 which lies in our brains. 0:02:09.208,0:02:12.042 This is a very well-known feature 0:02:12.042,0:02:14.125 in which we perceive quantities in relative ways -- 0:02:14.125,0:02:17.625 quantities like the intensity of light or the loudness of a sound. 0:02:17.625,0:02:24.042 For instance, committing 10,000 soldiers to the next battle sounds like a lot. 0:02:24.042,0:02:26.917 It's relatively enormous if you've already committed 1,000 soldiers previously. 0:02:26.917,0:02:28.667 But it doesn't sound so much, 0:02:28.667,0:02:32.333 it isn't relatively enough, it won't make a difference 0:02:32.333,0:02:34.500 if you've already committed 100,000 soldiers previously. 0:02:34.500,0:02:38.667 So you see that because of the way we perceive quantities, 0:02:38.667,0:02:39.542 as the war drags on, 0:02:39.542,0:02:43.750 the number of soldiers committed to it and the casualties 0:02:43.750,0:02:45.125 will increase, not linearly -- 0:02:45.125,0:02:46.875 like 10,000, 11,000, 12,000 -- 0:02:46.875,0:02:51.042 but exponentially -- 10,000, later 20,000, later 40,000. 0:02:51.042,0:02:54.250 And so that explains this pattern that we've seen before. 0:02:54.250,0:02:59.625 So here mathematics is able to link a well-known feature of the individual mind 0:02:59.625,0:03:03.583 with a long-term historical pattern 0:03:03.583,0:03:05.333 that unfolds over centuries and across continents. 0:03:05.333,0:03:10.042 So this type of example, today there is just a few of them, 0:03:10.042,0:03:12.500 but I think in the next decade they will become commonplace. 0:03:12.500,0:03:14.292 The reason for that is the historical record 0:03:14.292,0:03:17.583 is becoming digitized at a very fast pace. 0:03:17.583,0:03:19.208 So there's about 130 million books 0:03:19.208,0:03:21.750 that have been written since the dawn of time. 0:03:21.750,0:03:24.958 Companies like Google have digitized many of them -- 0:03:24.958,0:03:26.542 above 20 million actually. 0:03:26.542,0:03:29.458 And when the stuff of history is available in digital form, 0:03:29.458,0:03:32.500 it makes it possible for a mathematical analysis 0:03:32.500,0:03:34.875 to very quickly and very conveniently 0:03:34.875,0:03:37.292 review out trends in our history and our culture. 0:03:37.292,0:03:39.875 So I think in the next decade 0:03:39.875,0:03:41.625 the sciences and the humanities will come closer together 0:03:41.625,0:03:45.708 to be able to answer deep questions about mankind. 0:03:45.708,0:03:49.583 And I think that mathematics will be a very powerful language to do that. 0:03:49.583,0:03:53.667 It will be able to reveal new trends in our history, 0:03:53.667,0:03:55.417 sometimes to explain them, 0:03:55.417,0:03:58.200 and maybe even in the future to predict what's going to happen. 0:03:58.200,0:03:59.583 Thank you very much. 0:03:59.583,0:04:03.892 (Applause)