Terence Tao

So Kepler's third law is a little bit like this, except that for the third law, instead of having the thousand data points that Brahe had, Kepler had like six data points.

Like every planet, you knew the length of the orbit and the distance to the sun.

And there was like five or six data points.

And he did what we would now call regression.

You know, he could fit a curve to these six data points, and he got a squared group law, which was amazing.

But actually, he was quite lucky, I mean, that these six data points gave him the right conclusion.

You know, that's not enough data to be really reliable.

There was a later astronomer, Johannes Bode, who took the same data, actually, the distances to the planets, and inspired by Kepler, I think, he had a prediction that the distances to the planets formed basically a shifted geometric progression.

He also fit a curve.

Except there was one point missing.

So there was a big gap between Mars and Jupiter.

his law predicted that there was a missing planet.

So it was a kind of a crank theory, except when Uranus was discovered by Herschel, the distance to Uranus fit exactly this pattern.

And then Ceres was discovered, this asteroid between, I think, in the asteroid belt, and it also fit the pattern.

So people got really excited that Bordeaux had discovered this amazing new law.

of nature but then Neptune was discovered and it was completely like way off and you know and basically it was just a numerical fluke you know there was six data points and

Yeah, so maybe one reason why Kepler didn't highlight his third law as much as the first two laws is that maybe instinctively, even though he didn't have modern statistics, he kind of knew that with six data points, he had to be somewhat tentative with the conclusions.

Right.

So I think AI has basically driven the cost of idea generation down to almost zero.

Yeah.