Author: Stephen A. Boak
Date: 00:08:40 05/15/01
Go up one level in this thread
>On May 15, 2001 at 01:00:00, Uri Blass wrote: <snip> >If you find by evaluation that the king is not close enough to capture the pawns >and that there are no stalemate chances then it is a win without doubt. > >It is only one example and there are a lot of positions that can be evaluated as >a win without doubt. > >You can define rules that it is illegal to go to these positions so you get less >positions. <snip> >Uri Oh, Uri! Nothing personal, please excuse my humor, but...Mr. Mathematician, you are being hoisted by your own petard. :) Please excuse my ramblings, in advance, but don't simply believe me, a priori. I lack the background to formally criticize--because I am merely a Mathematician wannabe. :) Let me illustrate some points, if you please. 1A. Give me: 1) A lever long enough, and 2) A place to stand, and 3) I will move the world! I know you know this conundrum / paradigm / whatever you call it. Sound familiar? I'm not talking about the author of the original quote, I'm talking about who makes this claim today. Okay, if you convince me that you have obtained 1), and 2), I may begin to discuss whether you have proven 3). 1B. (CLAIM) Give me: 1) Enough positions that I can toss out, and 2) A way to evaluate them easily to show that they are definitely losing positions, and 3) I can reduce the solution tree and reduce the numbers of calculations significantly enough to *solve chess*!!! MY SKEPTICAL POINT OF VIEW: I say, show me the lever, prove to me how long it is, and how strong it is; then show me where you intend to stand, how you will get there with that giant lever, and how solid is that ground. Then we can talk about logic and try to calculate whether you *can* move the world as you claim. DISCUSSION OF THE PREMISES: 1) PREMISE #1: Enough positions that I can toss out Okay, to start you off with a fair advantage, not more of course, I grant you this premise: These positions exist. That is, there are enough positions that you can toss out, that if you did toss them out, you would have a practically managable amount of positions left allowing you to *solve chess*. There, wasn't that one easy? Aren't I a nice guy? :) I agree that the lever exists, and you can have it; well...if you can first find it. I know it is there if you look hard enough for them--this is called a 'search', for the uninitiated. The sticking point (a small one, I'm sure you will agree) is that you need to show me you have a search that can find these positions in exponential time. 2) PREMISE #2: A way to evaluate them easily to show that they are definitely losing positions Whoa! (This means STOP right there!) I can't hand you a second gift (premise) for free! I never promised you a rose garden. TANSTAAFL--"There ain't no such thing as a free lunch", pardner. You will have to work a bit to convince me you can find these positions: a) By a way to evaluate them easily, and b) Enough of them. The good news is that if you solve this well enough, you may have a method for finding the lever (those 'enough positions' to be tossed out). The bad news is that if you have a simple way of knowing they are 'skippable' or 'tossable' you may not be saving the orders of magnitude you need for your idea to bear fruit. You need something that beats exponential growth, and a simple gate (test) may not produce such an explosion of positions to be tossed out. For some positions that are 'obviously losing', perhaps the determining test is a calculation of 10^(umpteen) positions, the ultimate chess tree (longest one, etc). It may have many branches (for moves that are 'not obviously losing'), and may be very, very deep. Horrendously deep! If you miss just one of those, and prune it accidentally, you may not get to the truth of chess. You may think you have solved it, and never have come close. You may try to solve it, thinking the solution is a short time away, and never come close in real time to solve it. How will you ever know a priori (in advance) if you have such deviously complicated and long lines that need to be resolved, how long they will take to resolve, or whether you can avoid all such lines? You can't. We don't have the math to handle all complexity, all exponential growth, in real time. We don't know the true complexity, and depth, of a chess solution, simply by our feeble estimates and insights about a trivial amount of position types (and quantities of those types of positions) that can be 'skipped' or 'tossed out'. We don't know the complexity and depth of the positions that will remain, after those others are 'tossed out'. The estimates of how many such positions 'could' (and that remains to be determined) be 'tossed out' require exponential calcuations of prohibitive complexity. We can't know, in advance, how complex and how deep the longest lines in chess are--without doing the nearly impossible, iterating and evaluating all such possible positions and trees. It's just too complicated. If you can toss out all easily determined 'obviously losing' positions, but not those critical positions, you will not have solved the exponential growth problem, even if you toss out zillions of positions in a short time period (relatively speaking). Likely the 'easily determined' obviously losing positions will be a small proportion of the total possible positions. After all, there are mates known that are 200+ moves deep (IIRC). I'd like to see the simple rule that avoids all such positions (so they don't have to be calculated at the root, through all 200+ moves). It may take you a while to produce one! :) We have tablebases for endings with a few pieces (2-5, and some 6-piece endings). Some of these are known to be losses "without a doubt". There are probably more possible (middlegame!) chess positions in which the game ends (mate!) before a known (calculated) endgame tablebase is reached. Okay, I'm guessing this without calculation. What do you think? The creation (solution) of n-piece tablebase endings is exponentially difficult to do, based on today's best algorithm (exhaustive iteration, with pointers between possible successor and successor positions, or whatever is the exact methodology, you get the picture). I don't have the figures handy, but just note the quantity of unique positions to go from 2-piece, to 3-piece, to 4-piece, to 5-piece, to 6-piece, to ... n-piece exhaustive tablebase endings. Bob Hyatt will know the figures, I'm sure (close approximation is fine, thanks). c) What you contemplate (I give you credit for an idea that *may* bear fruit, conceptually) is tossing out positions i) Easily enough, and ii) Fast enough, so that you can iii) Significantly reduce the chess tree and number of calculated positions enough to solve chess. You have shown none of these (i, ii, iii). You merely assume them. d) What you don't show (and I'll wager cannot show) is that you have any algorithm or methodology or technique to toss out positions: i) Easily enough ii) Fast enough (at a great enough rate) iii) Significantly enough to reduce the chess tree and calculations to a total solvable in practice in the next 100 years or so (I'll give you 10,000 years, if you can use the extra time!). Sorry, but you don't have a place to stand, or if it exists, you don't have a way to get there. If we can't create endgame tablebases other than by exponentially difficult (slow) algorithms--not fast enough to solve chess, how can you create what I will call 'middlegame tablebases' any faster? Won't the calculation of them be at least as slow (exponentially) as calculating endgame tablebases? Don't forget, you have to create these positions to be 'skipped' by a method that is faster than the general problem--the exponential generation of possible chess trees and positions--otherwise the exponential explosion of possible chess positions will render your generation of 'middlegame tablebases' insignificant. Not nearly enough, nor fast enough, to make a perceptible dent in the list of all positions and trees possible in the game of chess. GRANT OF PREMISE #1 AND PREMISE #2 Okay, okay, I've been too hard on you. You don't deserve it. After all, you are a mathematician. Let's say I grant you BOTH PREMISE #1 and PREMISE #2. Whoa! You say that the CONCLUSION is now a given? No sir. Didn't I say that I would then examine your logic and begin to see if 1+2 leads to 3? You need to PROVE that all the positions you skipped (tossed out, without calculating them exhaustively) by some fabulous (as yet undiscovered) algorithm, are in fact losing positions, as you believe the are. You can't simply wave your hands and have us believe that all the positions you are feverishly tossing out by super-exponential (supernatural?) means are indeed those exact ones, with the characteristics you claim they have, without some sort of formal proof. Or is that what you want, the grant of a 3rd major (but hidden, undeclared) premise? You realize that I can't grant you everything you want, or you will have it all. That wouldn't be fair, now would it? Don't forget, you must show the connection between the remaining moves in your calculations and those you have tossed out. Otherwise you may (I say *may*) prove that chess is a draw or a win (granting you virtually all that you ask for), but not have the full tree(s) to prove your result. Let's say that the 'obviously losing' positions you wish to toss out exist on the order of 100 times more often than the 'drawable' positions that remain in your calculations. Does that mean that tossing out 99% or 99.999% of all possible branches or moves will reduce the general 10^(umpteen) total positions to a managable number? Can you prove that you can toss out an exponentially greater number of positions than will remain thereafter? If not, my mathematician friend, you will not have devised much more than a bare concept (worth something, as all ideas are), void of practical meaning. If you do not sharpen up your ideas, exponentially speaking, you will never get there from here. Take care, thanks for the ideas and keep thinking about the subject. You may make or stimulate a breakthrough. I just don't see it yet. --Steve (Mathematician 'wannabe')
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