Terence Tao

Again, a spherical cow type model of hailstones where hail forms because a little ice crystal forms in the clouds.

Sometimes currents bring it up where it's colder and then more ice forms.

and then it goes down a little bit and maybe it melts.

And the, the, the hell stone bounces up and down in the cloud, but eventually it lands to earth.

All the hell stones eventually hit the ground.

And the bigger insurance claims for your car.

In principle, there could be some really...

unusually lucky hailstone that somehow always hit the currents that go up and don't hit the ones that go down and just keep bouncing up and up forever.

I mean, occasionally you could sort of defy the statistical laws of physics.

And so in principle, there could be this very lucky number that just sort of always keeps hitting the odd numbers and going up rather than hitting the even numbers to go down.

It would be like someone who's consistently winning at a casino, at a game that's rigged.

It's theoretically possible, but we don't know if you can actually do it with an actual number.

And that's the collapse conjecture.

So it's part of a general phenomenon called chaos.

So you can have very simple operations like halving a number if it's even or 3 and adding 1 if it's

As you say, if you just do it once or twice, it's a very easy operation.

A kid in third grade can implement it.

But when you iterate,

even very simple operations over and over again, you can get vast amounts of complexity.

And so sometimes you don't, sometimes you get like these universal laws, like these bell curves and things settle down.