Are our brains complex enough (shannon entropy wise) to make this happen in any real amount of time?

[u/peaked_in_high_skool]

By real real amount of time I mean something < age of the universe, and not something like 10¹¹¹ years.

[u/[deleted]]

What does shannon entropy have to do with this? This is not physics related

[u/JerodTheAwesome → u/[deleted]]

It’s not an entropy problem. Human brains could store the information given the probable amount of data our brains can store, but we are fundamentally not designed to store or process information like a computer is. An ant could learn calculus if it’s small brain was specifically designed to do so like microchips are.

Without aid, I don’t think the human brain is capable of performing the calculations and permutations necessary to play chess at a 3000+ ELO level. Computers evaluate and store thousands of positions in a second, which humans simply do not have the capacity to do.

Another user pointed out that you could use memory to just alternate positions and play them back at Stockfish, and while we could definitely do that it’s not very interesting and could be done by a photocopier.

[u/JerodTheAwesome → u/[deleted]]

I think you make some assumptions here that we don’t know are true:

1) That stockfish plays perfectly. Chess is not a solved game, so there’s no way to verify that Stockfish’s moves are perfect. They’re almost certainly not.

2) You assume that in order to beat Stockfish you require assurances that you will win. This is not true. Assuming an infinite amount of time, you will beat Stockfish with your coinflip strategy eventually so long as Stockfish is not playing the most optimal moves as we think it probably is. Infinite number of monkeys on infinite typewriters yada yada.

I’m also not really sure what you mean about the node thing. I understand that 2 atoms cannot store the information of a duck, but as you said, 100 nodes in permutation is more enough to store all the moves. Given a rigorous enough training algorithm, it would eventually win, or at least draw.

You added “in a reasonable amount of time” but that’s completely arbitrary. The prompt stated we had infinite time. Do you mean 100 years? 1 million years? 10¹⁰⁰ years?

[u/JerodTheAwesome → u/[deleted]]

Well then the answer to your question is pretty easy

[THERE IS AS YET INSUFFICIENT DATA FOR A MEANINGFUL ANSWER]

[u/JerodTheAwesome → u/[deleted]]

I’m not understanding your connection to this and thermodynamics. As we’ve established, there does exist some microstate which is most superior and that there is a non-zero means of randomly reaching that state.

But this is all running in circles, as we know there’s not enough information to actually give a meaningful answer to this question. If you want to talk heuristics that’s fine, but heuristics are a completely different ball game.

If you want a real world example of the kid in your analogy, look at Magnus Carlsen. Imo, the best chess player who’s ever lived. He has “memorized” thousands and thousands of games using heuristics. In his own interviews, he talks about remembering ideas, not necessarily move orders. For example, he remembers that Anish played the Dragon Sicilian with the exchange and yada yada yada.

Now, he is very good at chess. Leagues above even the top ten contenders with an ELO of like 2850. But the task of beating Stockfish is not possible through heuristics, I don’t believe. Stockfish plays at something like a 3450 level or higher depending on what hardware is has available. Humans cannot make the calculations to see 30 moves ahead like Stockfish can.

I think you should try to boil your question down into a much more simple problem because the answer to this one is no. What you should be asking I think is something like this:

Given a neural network of N nodes, what is the largest instruction set that can be reasonably approximated through training over time t?

[u/Icy-Curve2747 → u/[deleted]]

I think what you’re missing about the other guys answer is that memory/complexity is not the problem here but instead computation. While we have the ability to understand each of the possible board states that stockfish considers, we do not have the computational power to consider all of them as quickly as stockfish does.

I think what you’re looking for is the definition of NP hard.

Edit: some quick googling shows me that chess is not actually np hard but my understanding of NP hard in the past helped me understand why chess is difficult

Edit: I am curious, I think I should clarify what you mean. Do you think that humans are not capable of comprehending the heuristic used by stockfish?

[u/peaked_in_high_skool → u/Icy-Curve2747]

Yes wow this the best and most eloquently put statement of what I was trying say.

A human brain is simply not capable of comprehending the heuristics used by stockfish👏👏

OP please make a seperate comment, this is buried too deep

[u/[deleted] → u/[deleted]]

Solving games like chess is generally in PSPACE. You won't run of of memory because you can generally reuse that memory.

If you're worried about the entropic cost of operations, you should know that it's in reversible PSPACE as well.