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