I am thinking that the explanation will be sufficiently complex that it will be about meaningless to humans. We get some fads from AlphaGo like the early 3-3 invasion, etc., which may give us new ideas, but we're far from understanding the real rationale. If we have a go program that plays perfectly, I imagine the situation will be pretty similar.

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be immersed

Worse than that. Because you'll know the reason why the perfect program played a move : because all the possible following plays lead to victory

And that's absolutely useless for humans.

This is exactly why I wrote:

In other words: if (and to the extent of) the correct moves of a game can only be reasoned by minimaxing, that game is worthless, or rather, not a game at all. And this is not just because of some limitation of the human skill, but because of the lack of the high level aspects that make a game interesting and worthwhile for an intelligent being. (A "game" is basically a simplified practice for efficient (!) real world problem solving.)

Consider prime factoring, for example. Would that make a decent game? Yes, but only to the extent there are potential algorithms for more efficient solutions than brute forcing. There are humans enthusiastically playing that game - researching such algorithms. But how about cryptography, where a certain encoding is proved to be completely secure (so only brute force attacks remain)? IMO the moment such proof exists the "game" part disappears (except the interest in the proof itself, as that may be useful in other "games" as well).

But with AG the situation doesn't seem that bad. I think about half of it's unusual moves do have understandable meanings. Go is not completely random at least.

There are lots of theorems not (or not only) using minmax. Since those include those for the very late endgame, opening and middle game also do not only reduce to boring minmax.

Hi,
What's the largest goban size for which perfect play is known (from an empty board) ? Is there a record of the perfect game, with the final score ?
If this size is even, is there a record of the perfect play on the largest odd goban size ?

See forum/viewtopic.php?f=18&t=11608&hilit=li+zhe+solved

It seems 5x5 and 5x6, though human pro Li Zhe claims to have a very weak solve of 7x7.

One trouble, from comments I have heard, with the top neural network programs is that they are trained on specific conditions, a specific board size and specific komi. Presumably a good bit of what they have learned will apply to other conditions, but the question is, how well?

I imagine that AlphaZero, if trained on a 7x7 board with different values of integer komi, could produce perfect play on an empty board with each value of komi within a day or two.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

I'm ignorant about these things, but curious. If the ultimate test is to play everything out by computer, why do we need a mathematical proof? I can see that a proof might be intellectually interesting and have implications for cases that computers cannot handle yet, but it seems easiest just to wait for faster hardware, especially given the rate of progress so far.

And if there is a good reason for being able to write down a proof, would it have any value outside of go?

Playing everything out by computer would be one form of proof, if it meant iterating all combinations of play. It’ll be a long time before that’s feasible for large board sizes.

_________________
be immersed

You need to apply mathematical methods in order to reduce the number of possibilities (its not about aesthetics). The number of board positions is of the order of 3^361 ~= 1.7*10^172 which is a pretty huge number. If your computer works at a speed of 10^12 operations per second and with each operation you check one position you'll still need about 5.5*10^152 years to sort it all out. Even with parallelization and an enormous increase of speed and using hypothetical, fancy new technology this task may never be achieved.

That means you need to use (applied) mathematics to reduce the number of possibilities by many, many orders of magnitude. There are already methods of tree-pruning available but lot more methods are needed. I have no idea whether such methods are within reach but it would be pretty cool, even for a 9x9 board.

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Couch Potato - I'm just watchin'!

Here is a logical theorem. A and B are propositions.

(A is true only if B is true) if and only if (B is false only if A is false).

Most people are not used to saying "only if", but once you get over that unfamiliarity, this theorem is fairly obvious. You can verify it by the use of truth tables, showing that it is true for every truth value of A and B, which is akin to playing everything out by computer. But, OC, once this theorem is proven, we can use it in other proofs, without having to write down every truth table.

Of what value is it to know best play on the 7x7 board? Of limited value, certainly, as the corners interact in ways that the corners of larger boards do not. The best initial play on the 7x7 is surely tengen, which may not be true of the 9x9. But the 7x7 still offers lessons in tesuji and principles that apply generally, as do most small boards. The 3x3, for example, has a lesson about eye vs. no eye.

_________________
The Adkins Principle:
At some point, doesn't thinking have to go on?
— Winona Adkins

Visualize whirled peas.

Everything with love. Stay safe.

Computers cannot play everything out because the game space (including all legal sequences of positions) is orders of magnitude larger than the number of atoms in the universe and the operation time is orders of magnitude larger than could be executed during a duration equalling the age of existence of the human species. Mathematics is required to prune calculation space and time. Faster hardware cannot provide sufficient acceleration combined with management of more space than atoms in the universe, unless and until maybe in the far future a sort of super-quantum computer can use enough Boltzmann or quantum states for storage whilst not suffering from the uncertainty principle.

Since computers that do not apply mathematical theorems need to sample, their output can be correct or incorrect. By just looking at the output without using other interpretation means, we do not know which.

Mathematical theorems, where applicable according to their presuppositions, do tell us the truth provided the theorems are proven by mathematical proofs. Yes, they are also intellectually interesting if one appreciates effort and skill or simply the facts of having proven truths.

Proofs can have value outside go theory research if the proof techniques are new and useful. The basic proof techniques are universal to mathematics so only more sophisticated proof structures can qualify. Of course, more likely theorems can have value outside go theory research because they might be applied or modified to achieve that. I have recognised possibilities for that but it would require quite some additional research time to write down such carefully. Think in terms of years rather than days of extra time investment. It takes seconds to point out something (e.g. hypothetical-strategy) whose transcription could be useful but maybe years (in easy cases, several weeks) to work it out carefully for a different or generalised domain.