WEBVTT 00:00:00.000 --> 00:00:03.671 So it turns out that mathematics is a very powerful language. 00:00:03.671 --> 00:00:05.983 It has generated considerable insight in physics, 00:00:05.983 --> 00:00:08.083 in biology and economics, 00:00:08.083 --> 00:00:10.900 but not that much in the humanities and in history. 00:00:10.900 --> 00:00:13.183 I think there's a belief that it's just impossible, 00:00:13.183 --> 00:00:15.829 that you cannot quantify the doings of mankind, 00:00:15.829 --> 00:00:18.348 that you cannot measure history. 00:00:18.348 --> 00:00:19.875 But I don't think that's right. 00:00:19.875 --> 00:00:21.917 I want to show you a couple of examples why. NOTE Paragraph 00:00:21.917 --> 00:00:24.875 So my collaborator Erez and I were considering the following fact: 00:00:24.875 --> 00:00:27.604 that two kings separated by centuries 00:00:27.604 --> 00:00:29.371 will speak a very different language. 00:00:29.371 --> 00:00:31.675 That's a powerful historical force. 00:00:31.675 --> 00:00:33.448 So the king of England, Alfred the Great, 00:00:33.448 --> 00:00:35.088 will use a vocabulary and grammar 00:00:35.088 --> 00:00:38.788 that is quite different from the king of hip hop, Jay-Z. 00:00:38.788 --> 00:00:40.454 (Laughter) 00:00:40.454 --> 00:00:42.625 Now it's just the way it is. 00:00:42.625 --> 00:00:44.917 Language changes over time, and it's a powerful force. NOTE Paragraph 00:00:44.917 --> 00:00:47.204 So Erez and I wanted to know more about that. 00:00:47.204 --> 00:00:50.861 So we paid attention to a particular grammatical rule, past-tense conjugation. 00:00:50.861 --> 00:00:54.125 So you just add "ed" to a verb at the end to signify the past. 00:00:54.125 --> 00:00:56.052 "Today I walk. Yesterday I walked." 00:00:56.052 --> 00:00:57.396 But some verbs are irregular. 00:00:57.396 --> 00:00:58.792 "Yesterday I thought." 00:00:58.792 --> 00:01:00.458 Now what's interesting about that 00:01:00.458 --> 00:01:04.288 is irregular verbs between Alfred and Jay-Z have become more regular. 00:01:04.288 --> 00:01:07.023 Like the verb "to wed" that you see here has become regular. NOTE Paragraph 00:01:07.023 --> 00:01:11.045 So Erez and I followed the fate of over 100 irregular verbs 00:01:11.045 --> 00:01:12.964 through 12 centuries of English language, 00:01:12.964 --> 00:01:15.875 and we saw that there's actually a very simple mathematical pattern 00:01:15.875 --> 00:01:18.417 that captures this complex historical change, 00:01:18.417 --> 00:01:22.077 namely, if a verb is 100 times more frequent than another, 00:01:22.077 --> 00:01:24.742 it regularizes 10 times slower. 00:01:24.742 --> 00:01:28.677 That's a piece of history, but it comes in a mathematical wrapping. NOTE Paragraph 00:01:28.677 --> 00:01:32.331 Now in some cases math can even help explain, 00:01:32.331 --> 00:01:35.210 or propose explanations for, historical forces. 00:01:35.210 --> 00:01:37.042 So here Steve Pinker and I 00:01:37.042 --> 00:01:40.894 were considering the magnitude of wars during the last two centuries. 00:01:40.894 --> 00:01:43.389 There's actually a well-known regularity to them 00:01:43.389 --> 00:01:46.811 where the number of wars that are 100 times deadlier 00:01:46.811 --> 00:01:48.763 is 10 times smaller. 00:01:48.763 --> 00:01:52.107 So there are 30 wars that are about as deadly as the Six Days War, 00:01:52.107 --> 00:01:54.927 but there's only four wars that are 100 times deadlier -- 00:01:54.927 --> 00:01:56.904 like World War I. 00:01:56.904 --> 00:01:59.827 So what kind of historical mechanism can produce that? 00:01:59.827 --> 00:02:01.827 What's the origin of this? NOTE Paragraph 00:02:01.827 --> 00:02:04.092 So Steve and I, through mathematical analysis, 00:02:04.092 --> 00:02:08.333 propose that there's actually a very simple phenomenon at the root of this, 00:02:08.333 --> 00:02:10.023 which lies in our brains. 00:02:10.023 --> 00:02:12.042 This is a very well-known feature 00:02:12.042 --> 00:02:15.017 in which we perceive quantities in relative ways -- 00:02:15.017 --> 00:02:18.733 quantities like the intensity of light or the loudness of a sound. 00:02:18.733 --> 00:02:24.042 For instance, committing 10,000 soldiers to the next battle sounds like a lot. 00:02:24.042 --> 00:02:27.486 It's relatively enormous if you've already committed 1,000 soldiers previously. 00:02:27.486 --> 00:02:29.313 But it doesn't sound so much, 00:02:29.313 --> 00:02:32.333 it's not relatively enough, it won't make a difference 00:02:32.333 --> 00:02:35.285 if you've already committed 100,000 soldiers previously. 00:02:35.285 --> 00:02:38.898 So you see that because of the way we perceive quantities, 00:02:38.898 --> 00:02:40.665 as the war drags on, 00:02:40.665 --> 00:02:43.750 the number of soldiers committed to it and the casualties 00:02:43.750 --> 00:02:45.433 will increase not linearly -- 00:02:45.433 --> 00:02:47.321 like 10,000, 11,000, 12,000 -- 00:02:47.321 --> 00:02:51.596 but exponentially -- 10,000, later 20,000, later 40,000. 00:02:51.596 --> 00:02:54.681 And so that explains this pattern that we've seen before. NOTE Paragraph 00:02:54.681 --> 00:03:00.179 So here mathematics is able to link a well-known feature of the individual mind 00:03:00.179 --> 00:03:03.168 with a long-term historical pattern 00:03:03.168 --> 00:03:06.025 that unfolds over centuries and across continents. NOTE Paragraph 00:03:06.025 --> 00:03:10.042 So these types of examples, today there are just a few of them, 00:03:10.042 --> 00:03:12.731 but I think in the next decade they will become commonplace. 00:03:12.731 --> 00:03:15.123 The reason for that is that the historical record 00:03:15.123 --> 00:03:17.583 is becoming digitized at a very fast pace. 00:03:17.583 --> 00:03:20.193 So there's about 130 million books 00:03:20.193 --> 00:03:22.504 that have been written since the dawn of time. 00:03:22.504 --> 00:03:24.958 Companies like Google have digitized many of them -- 00:03:24.958 --> 00:03:26.542 above 20 million actually. 00:03:26.542 --> 00:03:30.120 And when the stuff of history is available in digital form, 00:03:30.120 --> 00:03:32.500 it makes it possible for a mathematical analysis 00:03:32.500 --> 00:03:34.875 to very quickly and very conveniently 00:03:34.875 --> 00:03:37.600 review trends in our history and our culture. NOTE Paragraph 00:03:37.600 --> 00:03:40.321 So I think in the next decade, 00:03:40.321 --> 00:03:43.071 the sciences and the humanities will come closer together 00:03:43.071 --> 00:03:46.400 to be able to answer deep questions about mankind. 00:03:46.400 --> 00:03:50.521 And I think that mathematics will be a very powerful language to do that. 00:03:50.521 --> 00:03:53.667 It will be able to reveal new trends in our history, 00:03:53.667 --> 00:03:55.417 sometimes to explain them, 00:03:55.417 --> 00:03:58.723 and maybe even in the future to predict what's going to happen. NOTE Paragraph 00:03:58.723 --> 00:04:00.214 Thank you very much. NOTE Paragraph 00:04:00.214 --> 00:04:03.892 (Applause)