In viewtopic.php?p=140972#p140972 Bantari asks whether theory or generalisations vanish if (e.g., as a sufficiently strong player) only analysis in a current position has sufficiently great detail. My answer:

1) There is the kind of theory consisting of mathematically proven truths. It is always correct, regardless of the position to which it is applied. (A weaker form is applicable to a set of positions fitting certain made assumptions.)

2) There is another kind of theory, which is often correct but not always. E.g., a principle can say "Usually, play away from thickness.". The principle must not be applied stubbornly, e.g., because at latest during the endgame good plays near thickness can occur.

3) There is a kind of theory that uses dynamic parameters. Other means, such as reading or positional judgement, must determine the parameter values. Then, with the assumption that the values are determined correctly, the theory can be applied. Greater depth of reading or judgement is possible and increases accuracy of or confidence in the values and so application of the theory.

With increasing depth of analysis, some theory (1) is maintained, other (weak) theory (2) is replaced by better theory or other means (such as reading), yet other theory (3) allows increasingly good application with increasing underlying depth.

Hmm...
If we assume what you say to be true, will the theory 'statements' have to become overburdened with qualifications to the point of being unusable? Or, in case of (1) - complex enough to be more confusing than helpful? Researching theory is well and fine for theory researchers, but for practical players might there be a more efficient way of getting strong - in the long run?

Just like in other directly-competitive disciplines, knowledge of theory and practical achievements do not always (and not even usually) go hand-in-hand? Chess theorists and researchers are usually the best teachers/coaches not best players. Knowing the theory of running does not necessarily make you the fastest runner. And so on...

My point was not that there is no mathematics describing the game at higher levels, or describing the best moves. My point was not that rules cannot be defined by which the best of the best moves can be calculated in any position. I believe that with sufficient knowledge and research that might be possible - Go being just a subset of the universe, which is all probably based on math and nothing more... In the meta-sense I have no problem with all that.

I think my point was that, in practical sense, do we reach a point at which to provide desirable results the theory will have to become complex enough that the same results can be derived with less effort by other means - like expanding pattern database and reading ability. We have had this discussion about intuition some time back, for example, and I still find it intriguing...

So, other than for our own amusement and maybe the applause of the unwashed masses - for practical approach it might be better to put your efforts into other areas than theory if you set your sights on truly advanced play.

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- Bantari
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It depends. E.g., the new semeai formula is applicable to classes of semeais, such as Class 1. It presumes 9 conditions: "exactly two groups are involved [...] there are no kos [...] initially no essential string surrounding a big eye is in atari". Each condition is applicable. However, if you really explore the fundamentals, you find that, at the moment, "essential string" is still undefined. We do not know how easy or complicated it will be to define it. OTOH, for practical purposes, essential string is applicale very well.

The general definition of ko illustrates how applicable top level terms interact with the "quantum theory" of left-parts of strategies and answer-strategies. In practice, it is too time-consuming (and presumably the universe does not offer enough storage space) to actually write down a formally complete strategy. Then, further helping assumptions must be made, such as "Do not fill your own two-eye-formation.". Very easy in practice!

Other theory can become too complex for practical usage. Only a mathematician would ever apply CGT with the precision of a miny and tiny to determine the 100% correct endgame.



Some theory is, on the level of practical application, easy. The new semeai formula is such a theory. Application of the theory is easier than checking the assumptions of whether the theory may be applied. But if you see a simple race without any strange things, you would correctly guess that the assumptions must be fulfilled.

A counter-example of more confusing theory is Müller's semeai classification: some strong eyes are eligible - others not. The distinction is easy for software, but tedious for humans.

Complicated theory (Müller's) can be succeeded by simpler theory (mine): all strong eyes are eligible. One instead of two parameters are used in the formula. Etc.



In the long run, mathematics will beat all players and computers! Ok, you want to know something different, which we have discussed in vain elsewhere;)



What a nice example! :)



At the moment: yes. In future: it will be possible (or at least for every practically relevant position).



Or so one might think, as I do after having just read two books on physics from 1500 to 2001. (Same problem: maths is available, but its calculation needs more time and space than the universe offers.)



Certainly not THE SAME results. At best, ALMOST the same.



Theory shall describe truly advanced play. You know, mathematicians are so lazy that they work extra-hard to find theory, with which then they can be lazy deservedly;)

If we assume that a desired result is finding the best move, what will be the difference?

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- Bantari
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It might or might not be the best move.

Heh...
Ok, so lets define the desired result differently.
Playing at top level pro strength. Will the theory to reach there be far too complex to actually be usable? Or do we even know?

Judging by the other disciplines (of science, for example, where knowledge is the king) - theory becomes too complex pretty fast to be practical. Each scientific field fractured into many more-or-less separated areas pretty early - for human brain to be able to cope with the complexity. In other words - nobody can possibly know it all, not even a significantly meaningful chunk if it 'all'. In science, we can afford it, the competition usually being of a different kind.

In sports-like competition, can we go this path? And will it ever yield practical results of any importance at highest levels?

And can we actually prove it, or do we just hope and believe?

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- Bantari
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No. The limits are rather reading, speed of reading, endgame and speed of reasonably correct endgame calculations. When looking through pro games, I envision that compiling every underlying theory is possible and just a matter of time to write it down. Such involves descriptions of playing style, because different opening strategies cannot always be proven correct, but can explained to be reasonable in terms of exchange and balances.



Sure.



Watch my and others' work during the coming 20 or 30 years, then don't hold your breath and judge whether we will have achieved it!

(In specialised parts, today's theory already exceeds top pro strength.)