Comments by "kazedcat" (@kazedcat) on "Conway Checkers (proof) - Numberphile" video.

  1. nex The conway result is define for a finite game. They want to extend it to an infinite game where the result migth not apply. You can have a program that does not stop. Now can we have a reverse game that will eventually fill the lower half of the board 5 rows below the starting point using only finitely many instructions? The proof shown does not tell us the answer to this question. You may need infinitely many instructions to fill the board or it migth be that there will always be gaps that even with infinite instructions cannot be filled. But if there is a program to do so what will the program look like.
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  2. Shakal Draconis actually the proof does not show what is possible but only what is not possible. It show you that it is not possible to reach row 5 with finitely many moves but it did not show you that reaching row 5 is possible with infinitely many moves. You know you have just the right amount of fuel to get there but you don't know if the path to get there is blocked. To prove the second you need to show that you can create a program for the reverse game that does not halt.
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