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The Language of Calculation

The Language of Calculation

Jun 26, 2010, 12:46 PM 1

When you look at a chess position and calculate the various possible move sequences, what type of symbols represent the situation for you in your head? Do you simply visualize the move sequences themselves without words--purely spatial/temporal? Do you describe the position in words to yourself and formulate plans verbally: "We are castled on opposite sides. My best idea is to throw my pawns at his king?"

What is the language of your thought?

Computers can calculate so fast and so far into the future that it boggles the mind. But have they yet reached the stage where they can think about the position? Is the pattern recognition they experience the same as ours? Is it meaningful, or does it simply return nonsense? "Last time I saw a knight next to a pawn, I lost that pawn, therefore a knight should never be anywhere near a pawn."

Chess demands thought--simple formulas and easy bake recipes cannot be substitued. The calculation of a computer is a kind of thought, and it is certainly successful. This binary logic is a type of language, but it is limited. Surely it could never replace the language of analogy, judgement, or poetry. In fact, according to philosopher and author Hubert Dryfus, artifical intelligence, once thought capable of reaching this type of thought, has entered the realm of what he calls degenerative research, and has failed to reproduce the understanding of the average four year old. However, the latest research may indicate a resurgence of the pursuit of symbolic reasoning. In the meantime, according to the programming of Larry Atkin and David Slate, the chess programs of today have been successful precisely because they do not try to mimic human thought. While this might seem to indicate that humans should mimic the purely abstract calculation of the successful computer, I would argue that it indicates just the opposite. Let computers be computers, and let humans strive to do what humans do that even the most sophisticated cannot do--use the imagination. Because, as Garry Kasparov pointed out, the computer is only able to surpass human chess analysis because "quantity became quality."

I have studied with many gifted chess teachers. Some would explain the positions and concepts to me using strictly the move sequence that would result from certain move choices. They might even tell me things like "The knight will be very powerful on this square." or "Your king is not safe here." One teacher set up difficult positions and had me calculate out loud without moving the pieces. When I would reach "the white cloud" and give up he would remind me where all the pieces were in their new imaginary position and urge me to visualize one more move. From those exercizes I knew that I could calculate much further than I felt like doing, and saw my rating increase 200 points in about a months time.

Some coaches spoke of the positions in visual images I could grab onto with humor and a vivid imagination. This is not a quality unique to a creative type, (which I am) but according to Isreali American psychologist and Nobel lauriete Daniel Kahneman, it is universal. 

Look at the following position. How do you think about it? 









With black to move in this position, there isn't much to calculate in the way of "if this then that", because there are no immediate tactics. So how do you think about formulating a plan. Do you say to yourself that the knight looks rather silly on h6? What about the pawn on d5? Do you think it looks like a developing move with no meaning? White has played 1. f4, also known as "The Bird," (because it was popularized by a man with that last name.) What are your thoughts about that move? Perhaps you have a whole system prepared against The Bird, or maybe you are a beginner who says, "I thought you weren't supposed to move your "f-pawn."

Do you notice that the knight would have, if it moved to f5, what is called an artifical outpost? This means that it doesn't technically fall under the definition of an outpost. An outpost is a knight where no pawns exist on either file that can move to kick the knight. This knight qualifies temporarily as an outpost because of the pawn on d5, which stops e4. And as far as g4, the fact that pushing g4 has a weakening and very commital nature makes it something black shouldn't fear. Knowing this information would give the pawn on d5 a whole new meaning and suddenly the knight on h6 isn't completely ridiculous, in fact there is method in the madness.

But now consider that this sequence of moves by black actually has a name. It is called "The Horsefly." The knight is like an annoying horsefly which cannot be gotten rid of, is large, and buzzes around your face. The image is suddenly vivid. Unforgettable even.

It changes the language of thought not to another system but to the Heideggarian "house of being." In other words, it becomes not only mnemonic, but surrounds itself with associations from non-abstract daily life. The annoyance of a horsefly. 

Consider the bishops in this position.









The white bishop on d3, and the black bishop on d6, these are both "good bishops" but when you think about it, what connection does the description "good bishops" really have in terms of your imagination. Chess coach Brian Wall calls these bishops "show time Bishops." The pawns near them are  "stagelights." They surround the bishop on opposite colored squares, allowing completely unhampered mobility for those bishops. In his essay, "From Socrates to Expert Systems: The Limits and Dangers of Calculative Rationality"  Professor Dreyfus describes this as a shift in perspective, which differs from the rule-following, or number-crunching utilized for artificial intelligence research and applicaton. "Seeing an event in one way rather than some other almost-as-reasonable way, can lead to seeing a subsequent event in a way quite different from how that event would have been interpreted had the second perspective been chosen."

Consider following two perspectives. In the position below the king is having the difficulty of guarding pawns that are too far apart.








You could say this was a situation where the king is unable to guard both pawns, and that certainly has some meaning. But think about this position like this a farmer guarding pigs. Immediately pops up the image of a farmer with pigs running different directions, and it goes from being a dry and unpleasant, losing chess position to a funny and chaotic situation to be avoided at all costs. It helps prepare for these kinds of positions, or to avoid them, seeing always the image of the farmer chasing after those squealing pigs, (one of the many teaching stories from Brianwallchess by Brian Wall, co-author of "How To Play Chess Like An Animal". ) adds visual imagery to the language of chess thought, linking vivid experiences to the patterns on the board. Or visualize, and then remember not to "run from ghosts," as he described in Jeremy Silman's book "The Amateur's Mind." This becomes part of the language of calculation. It is not exactly a different language, but in a way it is, because it is the language of being. Heideggar says "Language is the house of being." This is something that computers can't do. They can't associate chess patterns with life experiences, they can't laugh at funny situations, and they can't plan based on "intuitive" instincts from memories such as visualizing the pawns literally being thrown across the board at the enemy king. All they can do is the pure calculation of "if this then that".

I have a coach friend who always says he will "fritz" the position to find out what the "right" move is--meaning he will run it through a computer program known as "Fritz" to find the correct move. He may indeed find the correct move, as computers can out calculate humans, and the pure number crunching of binary logic will outperform us making us shrink to a kind of humiliated obedience. And in many ways it does teach players to be comfortable in uncomfortable positions, as the computer has no emotion about them. But I don't think it is the best way to produce creative genius on the chess board.

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