[kolbe]

I don’t think anyone on Earth has obsessed over Rule 30 as much as Stephen Wolfram. And I think there are maybe single-digit number of people who are more intelligent than he is. So, if he can’t answer some Rule 30 related problem, I seriously doubt anyone else can.

[concreteblock]

The problem seems to have the same flavor as the Collatz conjecture. Simple dynamical system - very difficult to tell what happens in the long run.

Perhaps these things are too hard for (human) mathematics. I wonder if anyone has proved any theorems that make this precise. E.g. "Most cellular automata rules cannot be analyzed efficiently".

I don't know enough complexity theory/set theory to formulate this precisely.

[schoen]

> Perhaps these things are too hard for (human) mathematics.

I'm guessing this thought is partly inspired by Erdős's remark about the Collatz conjecture?

https://hsm.stackexchange.com/questions/6389/paul-erdos-quot...

[schoen]

Though, to be fair, Wolfram did run a previous prize contest about a conjecture that he had thought about but not solved, and someone else successfully solved it:

https://www.wolframscience.com/prizes/tm23/

[sblom]

And that was all about proving that Rule 110 was capable of universal computation. (They first found a way to map Rule 110 to the tag system put forth in that prize.)

This zoo of 3-predecessor cellular automata is an impressive lot.

[0-_-0]

Intelligence is not the only relevant factor. You probably know a lot of things that the most intelligent person on the planet doesn't. Some of those things might help you solve a problem that nobody can.

[lifthrasiir]

It's probably the other way around: Wolfram wants to make more people obsessed over Rule 30.

[sblom]

It's not really about Rule 30 specifically. It's more about Rule 30 being a particularly simple example, probably, of Wolfram's Principle of Computational Irreducibility.

From what I can tell, he'd love to drop that "probably", or move on from Rule 30 to the next simplest system that could possibly work.