The mathematics of history
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0:00 - 0:04So it turns out that mathematics is a very powerful language.
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0:04 - 0:06It has generated considerable insight in physics,
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0:06 - 0:08in biology and economics,
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0:08 - 0:11but not that much in the humanities and in history.
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0:11 - 0:13I think there's a belief that it's just impossible,
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0:13 - 0:16that you cannot quantify the doings of mankind,
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0:16 - 0:18that you cannot measure history.
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0:18 - 0:20But I don't think that's right.
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0:20 - 0:22I want to show you a couple of examples why.
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0:22 - 0:25So my collaborator Erez and I were considering the following fact:
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0:25 - 0:28that two kings separated by centuries
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0:28 - 0:29will speak a very different language.
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0:29 - 0:32That's a powerful historical force.
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0:32 - 0:33So the king of England, Alfred the Great,
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0:33 - 0:35will use a vocabulary and grammar
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0:35 - 0:39that is quite different from the king of hip hop, Jay-Z.
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0:39 - 0:40(Laughter)
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0:40 - 0:43Now it's just the way it is.
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0:43 - 0:45Language changes over time, and it's a powerful force.
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0:45 - 0:47So Erez and I wanted to know more about that.
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0:47 - 0:51So we paid attention to a particular grammatical rule, past-tense conjugation.
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0:51 - 0:54So you just add "ed" to a verb at the end to signify the past.
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0:54 - 0:56"Today I walk. Yesterday I walked."
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0:56 - 0:57But some verbs are irregular.
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0:57 - 0:59"Yesterday I thought."
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0:59 - 1:00Now what's interesting about that
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1:00 - 1:04is irregular verbs between Alfred and Jay-Z have become more regular.
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1:04 - 1:07Like the verb "to wed" that you see here has become regular.
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1:07 - 1:11So Erez and I followed the fate of over 100 irregular verbs
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1:11 - 1:13through 12 centuries of English language,
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1:13 - 1:16and we saw that there's actually a very simple mathematical pattern
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1:16 - 1:18that captures this complex historical change,
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1:18 - 1:22namely, if a verb is 100 times more frequent than another,
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1:22 - 1:25it regularizes 10 times slower.
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1:25 - 1:29That's a piece of history, but it comes in a mathematical wrapping.
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1:29 - 1:32Now in some cases math can even help explain,
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1:32 - 1:35or propose explanations for, historical forces.
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1:35 - 1:37So here Steve Pinker and I
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1:37 - 1:41were considering the magnitude of wars during the last two centuries.
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1:41 - 1:43There's actually a well-known regularity to them
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1:43 - 1:47where the number of wars that are 100 times deadlier
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1:47 - 1:49is 10 times smaller.
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1:49 - 1:52So there are 30 wars that are about as deadly as the Six Days War,
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1:52 - 1:55but there's only four wars that are 100 times deadlier --
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1:55 - 1:57like World War I.
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1:57 - 2:00So what kind of historical mechanism can produce that?
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2:00 - 2:02What's the origin of this?
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2:02 - 2:04So Steve and I, through mathematical analysis,
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2:04 - 2:08propose that there's actually a very simple phenomenon at the root of this,
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2:08 - 2:10which lies in our brains.
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2:10 - 2:12This is a very well-known feature
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2:12 - 2:15in which we perceive quantities in relative ways --
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2:15 - 2:19quantities like the intensity of light or the loudness of a sound.
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2:19 - 2:24For instance, committing 10,000 soldiers to the next battle sounds like a lot.
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2:24 - 2:27It's relatively enormous if you've already committed 1,000 soldiers previously.
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2:27 - 2:29But it doesn't sound so much,
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2:29 - 2:32it's not relatively enough, it won't make a difference
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2:32 - 2:35if you've already committed 100,000 soldiers previously.
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2:35 - 2:39So you see that because of the way we perceive quantities,
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2:39 - 2:41as the war drags on,
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2:41 - 2:44the number of soldiers committed to it and the casualties
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2:44 - 2:45will increase not linearly --
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2:45 - 2:47like 10,000, 11,000, 12,000 --
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2:47 - 2:52but exponentially -- 10,000, later 20,000, later 40,000.
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2:52 - 2:55And so that explains this pattern that we've seen before.
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2:55 - 3:00So here mathematics is able to link a well-known feature of the individual mind
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3:00 - 3:03with a long-term historical pattern
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3:03 - 3:06that unfolds over centuries and across continents.
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3:06 - 3:10So these types of examples, today there are just a few of them,
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3:10 - 3:13but I think in the next decade they will become commonplace.
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3:13 - 3:15The reason for that is that the historical record
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3:15 - 3:18is becoming digitized at a very fast pace.
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3:18 - 3:20So there's about 130 million books
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3:20 - 3:23that have been written since the dawn of time.
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3:23 - 3:25Companies like Google have digitized many of them --
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3:25 - 3:27above 20 million actually.
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3:27 - 3:30And when the stuff of history is available in digital form,
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3:30 - 3:32it makes it possible for a mathematical analysis
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3:32 - 3:35to very quickly and very conveniently
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3:35 - 3:38review trends in our history and our culture.
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3:38 - 3:40So I think in the next decade,
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3:40 - 3:43the sciences and the humanities will come closer together
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3:43 - 3:46to be able to answer deep questions about mankind.
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3:46 - 3:51And I think that mathematics will be a very powerful language to do that.
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3:51 - 3:54It will be able to reveal new trends in our history,
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3:54 - 3:55sometimes to explain them,
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3:55 - 3:59and maybe even in the future to predict what's going to happen.
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3:59 - 4:00Thank you very much.
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4:00 - 4:04(Applause)
- Title:
- The mathematics of history
- Speaker:
- Jean-Baptiste Michel
- Description:
-
What can mathematics say about history? According to TED Fellow Jean-Baptiste Michel, quite a lot. From changes to language to the deadliness of wars, he shows how digitized history is just starting to reveal deep underlying patterns.
- Video Language:
- English
- Team:
- closed TED
- Project:
- TEDTalks
- Duration:
- 04:26
Jenny Zurawell edited English subtitles for The mathematics of history | ||
rolf prag edited English subtitles for The mathematics of history | ||
Jenny Zurawell approved English subtitles for The mathematics of history | ||
Jenny Zurawell edited English subtitles for The mathematics of history | ||
Morton Bast accepted English subtitles for The mathematics of history | ||
Morton Bast edited English subtitles for The mathematics of history | ||
Timothy Covell added a translation |