Longest Possible Game/ Discussion

Sub-page of LongestPossibleGame

Anonymous: ilan, perhaps you need to re-consider what a public, open wiki is all about. Deleting legitimate comments by other users is a big no-no. I have no idea about their mathematical validity, but Alex's comments did not seem unreasonable, certainly not vandalism or "harassment".

Alex Weldon: I'm glad someone else brought this up. I consider ilan's attitude to my thoughts incredibly rude and conceited.

First off, there is never a reason to be condescending and dismissive of someone else's thoughts, even if the person is clearly wrong and/or inexperienced in the field in question.

Second, I actually do have a mathematical background; my university degree is in physics. It's insulting to suggest that I don't understand the difference between x^N and N^x.

Third, my tone was never beligerent. On the contrary, I was trying to make a point and was never given a chance.

Fourth, obvious is not the same as trivial.

Fifth, my arguments have some logical justification, and should not be dismissed out of hand. Since he refuses to allow me the chance to discuss it on his page, I'll give it here.

Unless ilan can somehow prove that the actual formula for the longest game on a board of given size (should such a closed solution actually exist) is going to take the form of N to some power, rather than some base to the Nth power, his lower bound is no more or less "trivial" than the upper bound provided by the number of legal board positions.

Furthermore, removing illegal board positions is not an insignificant reduction, nor is it a simple constant factor. As the board size increases, a larger and larger percentage of possible board positions will be illegal. Say you were counting the number of possible N-digit numbers: 10^N. Then say you made one digit illegal, removing all the numbers that contained an 8 (say) anywhere in them. You'd be left with 9^N, a small change for small N, but reducing the base is a huge difference for large N. The mathematics for removing illegal positions in Go is more complicated, but the effect is provably *larger* than just removing a single illegal digit, because larger board positions allow for more possible illegal strings.

Lastly, I think that any attempt to provide an upper bound has to start with counting legal board positions. From there, you can try to formulate theorems about what sorts of board positions are reachable from other board positions. The mathematics involved is way beyond any of us here, though.


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