Author: KarinsDad
Date: 12:30:31 03/29/00
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On March 29, 2000 at 12:59:18, José de Jesús García Ruvalcaba wrote: [snip] >>And in fact, computers have solved many >>problems that were beyond human mathematical capability just a few short decades >>ago. > >I am not aware of any relevant mathematical problem solved by a computer. Putting the question of relevance aside, I do not have any off the top of my head. But it is obvious that there has to be complex problems such as real time missile flight detection (or the recent bullet deflection systems) which could not be solved before the advent of computers. Whether you consider problem solving time to be a function of mathematics or not does not make the problems irrelevant to solve. Also, there are problems so complex that people could spend lifetimes working on them and not solve them, but a computer could solve within a day. An example of this type of problem could be the location of all planets and moons within our solar system 1000 years from today. Whether this is a relevant problem to solve is irrelevant. > >>For example, EGTBs. > >They are mathematically irrelevant. I disagree. What is the main purpose of mathematics? It is a series of equations which are used to model or emulate some portion of the real world or some real world problem (usually) in order to achieve a result or an answer. Endgames are a problem which are relevant to chess. Some people can do real well at them, most people cannot. So, they can be represented with a series of complex mathematical equations and solved. However, these equations are SO complex that the vast majority of people could not even define them. In fact, they are so complex that I believe that nobody has even attempted to solve them for endgames with more than 3 pieces (with a few specific exceptions). But, a computer can be used with relatively simple equations to exhaustively create EGTBs for various number and types of pieces. Hence, the problem can be solved. Just because it was solved (for 3, 4, and 5 piece endings) using an exhaustive approach as opposed to a complex mathematical approach does not mean that endings are mathematically irrelevant. In fact, the exact opposite is true. This is a real world model which is extremely hard to represent with mathematics without a computer, even if you had a decade to solve it for 5 piece endings. It is even more difficult to resolve in real time (i.e. without setting up all of the answers in a database ahead of time). But a realtime without a large database solution probably can be done with a computer. It just hasn't been done yet due to complexity. Hence, I propose to you that without the use of a computer, you could not create a set of "tables", "charts", and/or "equations" that could be handed out to people and could answer all 3, 4, and 5 men endgames. Therefore, you could not solve this problem mathematically without a computer in any reasonable timeframe (say, the next 50 years), if at all. KarinsDad :)
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