0:00:00.000,0:00:03.671 So it turns out that mathematics is a very powerful language. 0:00:03.671,0:00:05.983 It has generated considerable insight in physics, 0:00:05.983,0:00:08.083 in biology and economics, 0:00:08.083,0:00:10.900 but not that much in the humanities and in history. 0:00:10.900,0:00:13.183 I think there's a belief that it's just impossible, 0:00:13.183,0:00:15.829 that you cannot quantify the doings of mankind, 0:00:15.829,0:00:18.348 that you cannot measure history. 0:00:18.348,0:00:19.875 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: 0:00:24.875,0:00:27.604 that two kings separated by centuries 0:00:27.604,0:00:29.371 will speak a very different language. 0:00:29.371,0:00:31.675 That's a powerful historical force. 0:00:31.675,0:00:33.448 So the king of England, Alfred the Great, 0:00:33.448,0:00:35.088 will use a vocabulary and grammar 0:00:35.088,0:00:38.788 that is quite different from the king of hip hop, Jay-Z. 0:00:38.788,0:00:40.454 (Laughter) 0:00:40.454,0:00:42.625 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. 0:00:44.917,0:00:47.204 So Erez and I wanted to know more about that. 0:00:47.204,0:00:50.861 So we paid attention to a particular grammatical rule, past-tense conjugation. 0:00:50.861,0:00:54.125 So you just add "ed" to a verb at the end to signify the past. 0:00:54.125,0:00:56.052 "Today I walk. Yesterday I walked." 0:00:56.052,0:00:57.396 But some verbs are irregular. 0:00:57.396,0:00:58.792 "Yesterday I thought." 0:00:58.792,0:01:00.458 Now what's interesting about that 0:01:00.458,0:01:04.288 is irregular verbs between Alfred and Jay-Z have become more regular. 0:01:04.288,0:01:07.023 Like the verb "to wed" that you see here has become regular. 0:01:07.023,0:01:11.045 So Erez and I followed the fate of over 100 irregular verbs 0:01:11.045,0:01:12.964 through 12 centuries of English language, 0:01:12.964,0:01:15.875 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, 0:01:18.417,0:01:22.077 namely, if a verb is 100 times more frequent than another, 0:01:22.077,0:01:24.742 it regularizes 10 times slower. 0:01:24.742,0:01:28.677 That's a piece of history, but it comes in a mathematical wrapping. 0:01:28.677,0:01:32.331 Now in some cases math can even help explain, 0:01:32.331,0:01:35.210 or propose explanations for, historical forces. 0:01:35.210,0:01:37.042 So here Steve Pinker and I 0:01:37.042,0:01:40.894 were considering the magnitude of wars during the last two centuries. 0:01:40.894,0:01:43.389 There's actually a well-known regularity to them 0:01:43.389,0:01:46.811 where the number of wars that are 100 times deadlier 0:01:46.811,0:01:48.763 is 10 times smaller. 0:01:48.763,0:01:52.107 So there are 30 wars that are about as deadly as the Six Days War, 0:01:52.107,0:01:54.927 but there's only four wars that are 100 times deadlier -- 0:01:54.927,0:01:56.904 like World War I. 0:01:56.904,0:01:59.827 So what kind of historical mechanism can produce that? 0:01:59.827,0:02:01.827 What's the origin of this? 0:02:01.827,0:02:04.092 So Steve and I, through mathematical analysis, 0:02:04.092,0:02:08.333 propose that there's actually a very simple phenomenon at the root of this, 0:02:08.333,0:02:10.023 which lies in our brains. 0:02:10.023,0:02:12.042 This is a very well-known feature 0:02:12.042,0:02:15.017 in which we perceive quantities in relative ways -- 0:02:15.017,0:02:18.733 quantities like the intensity of light or the loudness of a sound. 0:02:18.733,0:02:24.042 For instance, committing 10,000 soldiers to the next battle sounds like a lot. 0:02:24.042,0:02:27.486 It's relatively enormous if you've already committed 1,000 soldiers previously. 0:02:27.486,0:02:29.313 But it doesn't sound so much, 0:02:29.313,0:02:32.333 it's not relatively enough, it won't make a difference 0:02:32.333,0:02:35.285 if you've already committed 100,000 soldiers previously. 0:02:35.285,0:02:38.898 So you see that because of the way we perceive quantities, 0:02:38.898,0:02:40.665 as the war drags on, 0:02:40.665,0:02:43.750 the number of soldiers committed to it and the casualties 0:02:43.750,0:02:45.433 will increase not linearly -- 0:02:45.433,0:02:47.321 like 10,000, 11,000, 12,000 -- 0:02:47.321,0:02:51.596 but exponentially -- 10,000, later 20,000, later 40,000. 0:02:51.596,0:02:54.681 And so that explains this pattern that we've seen before. 0:02:54.681,0:03:00.179 So here mathematics is able to link a well-known feature of the individual mind 0:03:00.179,0:03:03.168 with a long-term historical pattern 0:03:03.168,0:03:06.025 that unfolds over centuries and across continents. 0:03:06.025,0:03:10.042 So these types of examples, today there are just a few of them, 0:03:10.042,0:03:12.731 but I think in the next decade they will become commonplace. 0:03:12.731,0:03:15.123 The reason for that is that the historical record 0:03:15.123,0:03:17.583 is becoming digitized at a very fast pace. 0:03:17.583,0:03:20.193 So there's about 130 million books 0:03:20.193,0:03:22.504 that have been written since the dawn of time. 0:03:22.504,0:03:24.958 Companies like Google have digitized many of them -- 0:03:24.958,0:03:26.542 above 20 million actually. 0:03:26.542,0:03:30.120 And when the stuff of history is available in digital form, 0:03:30.120,0:03:32.500 it makes it possible for a mathematical analysis 0:03:32.500,0:03:34.875 to very quickly and very conveniently 0:03:34.875,0:03:37.600 review trends in our history and our culture. 0:03:37.600,0:03:40.321 So I think in the next decade, 0:03:40.321,0:03:43.071 the sciences and the humanities will come closer together 0:03:43.071,0:03:46.400 to be able to answer deep questions about mankind. 0:03:46.400,0:03:50.521 And I think that mathematics will be a very powerful language to do that. 0:03:50.521,0:03:53.667 It will be able to reveal new trends in our history, 0:03:53.667,0:03:55.417 sometimes to explain them, 0:03:55.417,0:03:58.723 and maybe even in the future to predict what's going to happen. 0:03:58.723,0:04:00.214 Thank you very much. 0:04:00.214,0:04:03.892 (Applause)