1- Panta Rhei
Panta Rhei.
Everything flows.
Everything is movement.
This is the message of Heraclitus,
2500 years ago.
The air around me contains
a large number of molecules
that constantly collide
like billiard balls.
Everything is movement.
Even my rocking chair is carried
by the Earth in its foolish rush!
For years, humans have
observed these movements
and gradually they have tried to predict them.
First astrologers,
then scientists,
and especially mathematicians.
By the way, many mathematicians
have cast horoscopes!
Predicting the movement of the stars
and deducing our future from it
is an old dream.
In the mathematical world around us,
everything is moving as well.
Watch this rolling ball.
Stop!
Can you guess where it will be
in two seconds?
It continues straight on of course, like this!
This prediction was easy!
Here it is a bit harder.
Stop!
The ball is clearly going to hit
the edge of the billiard table.
How will it continue?
The mathematician can calculate
the future position of the ball as a function of time.
This is already a success for Science.
We can even calculate
what happens when two balls collide.
Gradually, the idea of determinism
has imposed itself on Science.
If I know the situation now,
I should "in principle"
be able to determine
the situation a bit later.
Like here for example.
What will be the trajectory of the cue ball?
In the game of billiards,
the player must hit the two balls
with his own ball.
Not bad!
And here, what will happen?
Not bad either!
If I read the paper today,
am I capable "in principle" to foresee
what will happen in the world
a month from now?
Too complicated!
Do not think that this film
will help you predict the future!
Let’s go back to our billiard table,
but now with fifty balls on it.
Imagine a perfect table
on which the balls roll without any friction.
When the cue strikes the cue ball,
the movement is ... complicated.
Can we predict this movement?
Of course we can:
the computer that calculated these images did it.
But it made many calculations.
It's clear that
the balls follow rectilinear trajectories
and they bounce off each other.
There are many bounces,
but if we take enough time,
or we calculate very quickly,
we can predict the trajectory step by step,
collision after collision.
The computer could easily calculate
the position of the cue ball
in one hour, for example,
but this takes so many calculations that
it far exceeds the capabilities of a human being.
Prediction in principle, perhaps ...
but in practice?
Let’s move one of the balls a few centimeters.
Look. .
The two pool tables are almost identical.
Only one ball is slightly out of place.
When we hit the cue ball,
the movement of both sides
starts off the same way
but after a little while, not very long,
the trajectories become completely different.
If I want to predict the future path
of the cue ball,
I can do so,
but I need to know in detail
the positions of all the balls on the table,
and there are many of them!
A small uncertainty about a single ball
will shatter any hope of determining the future.
Here is the classic definition of determinism,
by the mathematician Laplace in 1814.
We must consider the present state of the universe
as the effect of its previous state,
and as the cause for what will follow.
An intelligence which, at a given moment,
would know all the forces by which nature is animated
and the position of every object in the universe
if indeed it was powerful enough
to submit these data to analysis,
would embrace in a single formula the
movements of the greatest bodies of the universe
and those of the lightest atom:
nothing would be uncertain for it,
and the future as the past,
would appear before its eyes. >>
How can we understand
the movements of celestial bodies?
Watch this computer simulation
of a fictional solar system
with two Suns and one planet.
It's somewhat like our billiard table.
The computer can calculate step by step the movement
but can it predict the fate of the system?
Will the small planet
one day collide with one of the Suns?
So...
we could predict the future if ...
we had an infinite intelligence!
But this is not the case ...
unfortunately ...
or maybe ... fortunately.
But then, what can Science do
if it cannot predict?
Well...
if it’s willing to be less ambitious,
and more modest,
it can still make some very useful forecasts.
This requires
a different view on determinism!
We will not try to predict
the future position of a ball
amidst a cloud of other balls,
but rather look for a probability.
The purpose of the forecast is no longer
to determine the temperature
in Paris on a specific day ten years in the future
- this would be pointless -
but rather to try and predict
averages, statistics,
such as the number of hurricanes
that will cross the Atlantic in one season.
Probabilities rather than certainties?
this really is a change in perspective!
There is a whole world
between theory and practice.