The mathematics of history JeanBaptiste Michel

so it turns out that mathematics is a

very powerful language it has generated

considerable insight in physics in

biology and in economics but not that

much in the humanities and in history I

think there’s the belief that is just

impossible that you cannot quantify the

doings of mankind but you cannot measure

history but I don’t think that’s right I

want to show you a couple of examples

why so my collaborator Aires and I were

considering the flow in fact the two

kings separated by centuries will speak

a very different language that’s a

powerful historical force so the king of

England after the great will use the

vocabulary and grammar that is quite

different from the king of hip-hop

jay-z now it’s just the way it is

language changes over time and it’s a

powerful force

so Aries and I wanted to know more about

that so we paid attention to a

particular grammatical rule past tense

conjugation so you just add eg to a verb

at the end to signify the past today I

walk yesterday I walked but some verbs

are irregular yesterday I thought well

now what’s interesting about that is

irregular verbs between Alfred and JZ

have become more regular like the verb

to Wed that you see here has become

regular so everything I followed the

fate of over 100 irregular verbs through

12 centuries of English language and we

saw that there’s actually a very simple

mathematical pattern that captures this

complex historical change namely if a

verb is a hundred times more frequent

than another it regularizes ten times

slower that’s a piece of history but it

comes in a mathematical wrapping now in

some cases math can even help explain or

proposed explanations for historical

forces

so here’s chief tinker and I were

considering the magnitude of Wars during

the last two centuries there’s actually

a well known regularity to them where

the number of wars that are hundred

times deadlier is ten times smaller so

there are thirty wars that are about as

deadly as the six days war there’s only

four wars that are 100 times deadlier

like world war 1 so what kind of

historical mechanism can produce that

what’s the region of this so Steve and I

through mathematical analysis proposed

that there’s actually a very simple

phenomena at the root of this which

which lies in our brains this is a

well-known feature which we perceive

quantities in relative ways the

quantities like the intensity of light

or the loudness of a sound for instance

committing 10,000 soldiers to the next

battle sounds like a lot it’s relatively

enormous if you’ve already committed

1,000 soldiers previously but it doesn’t

sound so much it’s not relatively enough

it won’t make a difference if you’ve

already committed a hundred thousand

soldiers previously so you see that

because of the way we perceive

quantities as the war drags on the

number of soldiers committed to it and

the casualties will increase not

linearly like 10,000 11,000 12,000 but

exponentially 10,000 later 20,000 Native

40,000 and so that explains this pattern

that we’ve seen before

so here mathematics is able to link the

well-known feature of the individual

mind with a long-term pattern a

historical pattern that unfolds over

centuries and across continents so this

type of examples today they’re just few

of them but I think that in the next

decade they will become commonplace the

reason for that is that the historical

record is becoming digitized at very

fast pace so there’s about 130 million

books that have been written since the

dawn of time companies like Google have

which as many of them above 20 million

actually and when the stuff of history

is available in digital form it makes it

possible for mathematical analysis to

very quickly and very conveniently

reveal trends in our history in our

culture so I think as in the next decade

in the sciences and the humanities will

come closer together to be able to

answer deep questions about mankind and

I think that mathematics will be a very

powerful language to do that it will be

able to reveal new trends in our history

sometimes to explain them and maybe even

in the future to predict what’s going to

happen thank you very much