04:27
TED2012

Jean-Baptiste Michel: The mathematics of history

Filmed:

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.

- Data researcher
Jean-Baptiste Michel looks at how we can use large volumes of data to better understand our world. Full bio

So it turns out that mathematics is a very powerful language.
00:15
It has generated considerable insight in physics,
00:19
in biology and economics,
00:21
but not that much in the humanities and in history.
00:23
I think there's a belief that it's just impossible,
00:26
that you cannot quantify the doings of mankind,
00:29
that you cannot measure history.
00:31
But I don't think that's right.
00:34
I want to show you a couple of examples why.
00:35
So my collaborator Erez and I were considering the following fact:
00:37
that two kings separated by centuries
00:40
will speak a very different language.
00:43
That's a powerful historical force.
00:45
So the king of England, Alfred the Great,
00:47
will use a vocabulary and grammar
00:49
that is quite different from the king of hip hop, Jay-Z.
00:50
(Laughter)
00:54
Now it's just the way it is.
00:56
Language changes over time, and it's a powerful force.
00:58
So Erez and I wanted to know more about that.
01:00
So we paid attention to a particular grammatical rule, past-tense conjugation.
01:03
So you just add "ed" to a verb at the end to signify the past.
01:06
"Today I walk. Yesterday I walked."
01:10
But some verbs are irregular.
01:11
"Yesterday I thought."
01:13
Now what's interesting about that
01:14
is irregular verbs between Alfred and Jay-Z have become more regular.
01:16
Like the verb "to wed" that you see here has become regular.
01:20
So Erez and I followed the fate of over 100 irregular verbs
01:22
through 12 centuries of English language,
01:26
and we saw that there's actually a very simple mathematical pattern
01:28
that captures this complex historical change,
01:31
namely, if a verb is 100 times more frequent than another,
01:34
it regularizes 10 times slower.
01:37
That's a piece of history, but it comes in a mathematical wrapping.
01:40
Now in some cases math can even help explain,
01:44
or propose explanations for, historical forces.
01:48
So here Steve Pinker and I
01:51
were considering the magnitude of wars during the last two centuries.
01:52
There's actually a well-known regularity to them
01:56
where the number of wars that are 100 times deadlier
01:59
is 10 times smaller.
02:02
So there are 30 wars that are about as deadly as the Six Days War,
02:04
but there's only four wars that are 100 times deadlier --
02:08
like World War I.
02:10
So what kind of historical mechanism can produce that?
02:12
What's the origin of this?
02:15
So Steve and I, through mathematical analysis,
02:17
propose that there's actually a very simple phenomenon at the root of this,
02:19
which lies in our brains.
02:24
This is a very well-known feature
02:25
in which we perceive quantities in relative ways --
02:27
quantities like the intensity of light or the loudness of a sound.
02:30
For instance, committing 10,000 soldiers to the next battle sounds like a lot.
02:34
It's relatively enormous if you've already committed 1,000 soldiers previously.
02:39
But it doesn't sound so much,
02:43
it's not relatively enough, it won't make a difference
02:45
if you've already committed 100,000 soldiers previously.
02:48
So you see that because of the way we perceive quantities,
02:51
as the war drags on,
02:54
the number of soldiers committed to it and the casualties
02:56
will increase not linearly --
02:59
like 10,000, 11,000, 12,000 --
03:01
but exponentially -- 10,000, later 20,000, later 40,000.
03:03
And so that explains this pattern that we've seen before.
03:07
So here mathematics is able to link a well-known feature of the individual mind
03:10
with a long-term historical pattern
03:16
that unfolds over centuries and across continents.
03:19
So these types of examples, today there are just a few of them,
03:21
but I think in the next decade they will become commonplace.
03:25
The reason for that is that the historical record
03:28
is becoming digitized at a very fast pace.
03:31
So there's about 130 million books
03:33
that have been written since the dawn of time.
03:36
Companies like Google have digitized many of them --
03:38
above 20 million actually.
03:40
And when the stuff of history is available in digital form,
03:42
it makes it possible for a mathematical analysis
03:46
to very quickly and very conveniently
03:48
review trends in our history and our culture.
03:50
So I think in the next decade,
03:53
the sciences and the humanities will come closer together
03:56
to be able to answer deep questions about mankind.
03:58
And I think that mathematics will be a very powerful language to do that.
04:02
It will be able to reveal new trends in our history,
04:06
sometimes to explain them,
04:09
and maybe even in the future to predict what's going to happen.
04:11
Thank you very much.
04:14
(Applause)
04:16
Translated by Timothy Covell
Reviewed by Morton Bast

▲Back to top

About the Speaker:

Jean-Baptiste Michel - Data researcher
Jean-Baptiste Michel looks at how we can use large volumes of data to better understand our world.

Why you should listen

Jean-Baptiste Michel holds joint academic appointments at Harvard (FQEB Fellow) and Google (Visiting Faculty). His research focusses on using large volumes of data as tools that help better understand the world around us -- from the way diseases progress in patients over years, to the way cultures change in human societies over centuries. With his colleague Erez Lieberman Aiden, Jean-Baptiste is a Founding Director of Harvard's Cultural Observatory, where their research team pioneers the use of quantitative methods for the study of human culture, language and history. His research was featured on the covers of Science and Nature, on the front pages of the New York Times and the Boston Globe, in The Economist, Wired and many other venues. The online tool he helped create -- ngrams.googlelabs.com -- was used millions of times to browse cultural trends. Jean-Baptiste is an Engineer from Ecole Polytechnique (Paris), and holds an MS in Applied Mathematics and a PhD in Systems Biology from Harvard.

More profile about the speaker
Jean-Baptiste Michel | Speaker | TED.com