Math and Chess?

I see that my reply in the previous Math and Chess related topic has already been quoted, but because the subject is coming up again I’d thought I’d try to give a long version of my insight (being both a mathematician and a chess player) about the subject.

First I’d like to address the concept of calculation. The secret to this is doing good book holding.

1) When people speak of calculation in chess they often mean this: They look at the current situation and see a candidate move, and then they try to visualize the situation after this move has been played. This procedure then repeats for the candidate moves of his opponent, and so on. So if you are strong in visualizing these new situations, you are doing good book holding.

2) When people speak of calculation in math I guess I can illustrate with an examples:

Lets multiply 15 by 17 and assume the answer is not known, we will calculate it, by doing good book holding.

15 * 17 = 10 * 10 + 5 * 10 + 7 * 10 + 5 * 7

Multiplication before addition, so working this out gives:

100 + 50 + 70 + 35

And this adds up to 255

So what did we just do? We divided this problem in to several smaller problems. We solved the smaller problems and therefore solved the main problem! Now this is relatively small and straightforward, but any math problem can generally be divided into tiny sub-problems.

Then there’s pattern recognition. I guess we can imagine this in chess, varying from simple forks to complicated and subtle plans and tactics. Why do we recognize these patterns?

Chess has laws (ie: mate the king and you win) and the patterns we remember apply to the rules we derived from these laws. Now, how does this work in math?

People might not see this, as in simple examples this is so straightforward that you do not realize it, but I think it’s the same thing. A very simple example of the quantity field of mathematics:

3+4

Now anybody will see that this simply equals 7, but how do we know that and what steps did we take?

First off let’s look at what we see: We recognize 3 and 4 as natural numbers, and we see a sign of addition.

The laws for natural numbers say that we can think of these numbers as a line from 0 to infinity and the magnitude of the number is the distance to the begin of the line at 0. Knowing this law we learned the pattern that we can solve the addition by adding up their magnitude, since this means that we added up the distance to 0, giving the correct result.

We can do this so quickly that we don’t think about it, but in more complicated examples one could really see that these patterns are everywhere. Just think about other fields of mathematics such as change (calculus and differential equations), space (geometry, goniometry), logic and set theory, discrete mathematics and so on.

PS I’m not trying to say chess=math, just trying to clear up on terms as calculation and pattern recognition. Also sorry for a lengthy post.

Yes, they are not equal!