The Open File - Chaos, Chess, and the Weather
Submitted by
NM Zug on Tue, 02/10/2009 at 8:39am.
The Open File
by Life Master Mike Petersen (Zug)
Chaos, Chess, and the Weather
In 1960, an MIT meteorologist by the name of Edward Lorenz was using his computer to simulate a simple weather pattern in the earth's atmosphere. He was admittedly using a small number of initial variables because of the limitations of computer hardware at the time. He decided to repeat one "simulation run" in order to check some details. He plugged in the starting numbers from the previous run, but rounded them off to three decimal places
instead of the six he used initially in order to save time. He cranked up the computer and went out for a cup of coffee. When he came back he received quite a shock. Instead of an approximation of his previous weather forecast, it was totally different! The small three decimal place difference had been grossly magnified by the iterations of the computer in solving the equations. He later said he knew immediately that if real weather behaved like his model, then long-range forecasting would be impossible. So, it seems that in complicated systems small changes in initial values can cause huge changes in final results. Of course weather is a complex system with an almost infinite number of initial conditions to take into account, so it is natural to conclude that long-term weather forecasting is going to be next to impossible. If you ask me, even short-term forecasting is impossible if you judge by our local weather forecasters! But what has this got to do with chess?
Well, chess is a complex system with a large number of initial values to consider. Many people who are not familiar with chess ask me if I play the same moves all the time. I try to explain that there are various systems with which one can start the game, but very quickly the astronomical number of possible moves cause the game to branch into unknown waters, with the resulting positions never having been played before. This doesn't seem to sink in, though. They seem to think that chess is a game, though complex, that will yield itself to a set of concrete rules. Not so, of course. The incredible variety of moves obliterates any notion of predictability. The total number of chess positions has been calculated to be more than the total number of atoms in the observable Universe (reference my other column "Is Chess Infinite?"). If you had a computer equal in size to the known universe, with each atom capable of performing a calculation of one move every second, even the amount of time since the big bang wouldn't be enough to put a dent in the number of positions possible. Next to this kind of immense complexity, weather seems like a parlor game.
Look, another way to go at this is to consider the following: I have played the same opening for black against e2-e4 for over 30 years - a certain variation of the Sicilian. I have kept all my games. No two have been even remotely alike. Oh, sure they start out looking the same. You can recognize the pawn structure, the ideas, etc. But before long, one player will vary, if only slightly, from a previous game. This is now analagous to Lorenz feeding in his rounded off numbers. We don't get an approximation of a previous game, but a completely different game. If we did, then chess would rapidly die off as a serious game, because then it really would yield itself to a set of concrete rules.
Here is another fascinating thing to think about. Edward Lorenz, by accident, had stumbled on to a new branch of mathematics called Chaos Theory. One of the more amusing observations resulting from this was that "a butterfly beating its wings in Tokyo can cause a thunderstorm in New York City." Just another way of saying that small initial changes cause big differences in results, but the analogy is apt. Is it possible that chess might be looked at under the microscope of Chaos Theory? Who knows? But at least now it gives you the opportunity to have another excuse for losing. You can now say that your loss was caused by a butterfly in Tokyo beating his wings too hard.
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Click here for links to Mike's other work on Chess.com
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