Poincaré recurrence

Imagine you have a toy box that has many toys inside. You take one toy out and play with it for a while, but then you put it back in the box. After some time, you take out another toy and play with it, and then put it back in the box. You keep doing this, taking out different toys and playing with them, one by one.

Now, let's say you keep doing this over a very long time, even for years and years. Eventually, you will have played with all the toys in the box at least once. This is because you kept going back to the box to take out and play with a new toy.

A physicist named Poincaré found a similar idea in math. He found that if you have a system that keeps changing over time, like a toy box with toys being taken out and put back in, and you wait long enough, it will eventually return to its starting state. That means, the system will repeat itself exactly like it was in the beginning.

This is called Poincaré recurrence. It tells us that if we wait long enough, a system will repeat itself, at least once. It can happen with things like planets moving in our solar system or molecules bouncing around in a gas. So even if a system seems to be constantly changing, over time it will repeat itself and come back to where it started.