Anti-ray. Everything flows, everything moves. This is the message of Heraclitus 2,500 years ago.

The air around us contains a large number of molecules that constantly collide like billiard balls.

Everything moves. Even my rocking chair is carried by the Earth in its race around the Sun.

For years, humans have observed these movements and gradually have tried to predict them. First astrologers, then scientists, and especially mathematicians. By the way, many mathematicians have cast horoscopes.

Using the motion of the stars to predict our future is an old dream.

In the mathematical world about us as well, everything is in motion.

Look at the cue ball. Stop! Can you guess where it will be in two seconds? Of course, it continues straight on, like so.

That prediction was easy. This time, things are a bit harder. Stop!

Obviously, the ball will hit the edge of the billiard table. Where will it go next? Mathematicians can calculate the future position of the ball as a function of time. This is already a success for science.

They 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, then, in principle, I should be able to determine the situation a bit later. Here, for example, what will be the path of the cue ball?

In the game of billiards, the player must hit the two balls with the cue ball.

Not bad either.

If I read the paper today, can I predict, in principle, what will happen in the world a month from now? Of course not. You must not think that this film will help you predict the future.

Let's go back to the billiard table, but now with 50 balls on it.

Imagine a perfect table, where the balls roll without friction. After the cue strikes the cue ball, the movement is... complicated. Can we predict this movement?

Of course we can. After all, our computer made these images. But it made many, many calculations. It's clear that the balls follow rectilinear trajectories as they bounce off of each other. There are many collisions, but if we take enough time, or we calculate very quickly,

we can predict their trajectories step by step, collision after collision. The computer can easily calculate the position of the cue ball in one hour, for example. But this takes so many calculations that it far exceeds the abilities of a human being.

Prediction in principle, perhaps. But in practice, let's move one of the balls a few centimeters. The two pool tables are almost identical.

Only one ball is slightly out of place. When we hit the cue ball, the movement on both tables starts off the same way.

But after a little while, not too long, the trajectories become completely different.

If we want to predict the future of the cue ball, we can do so. But we need to know in detail the positions of all the balls on the table. And there are so many of them. A small uncertainty about a single ball shatters any hope of determining the future path of the cue ball.

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 of 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 this 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 just one planet.

It's a bit 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 infinite intelligence? This is not the case, unfortunately, or perhaps fortunately.

So, what can science do if it cannot predict the future? Well, if we are willing to be less ambitious and more modest, we 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, amongst 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 10 years in the future, for that is impossible, but rather to try and predict averages, statistics, for example the number of hurricanes crossing the Atlantic in one season, probabilities rather than certainties, that is a big change in perspective.

There is a whole world between theory and practice.