# [Retros] Math aspects from Yefim Treger and the 5-th example! 08/23/2004

TregerYefim at aol.com TregerYefim at aol.com
Mon Aug 23 12:21:56 EDT 2004

Thank you, thank you, thank you for catching the following idea: There is a
contradiction between definition of Position in chess rules and Math (which is:
two positions are the same if sets of all games emerging from them are the
same, not paying attention to numbers of moves; also good is graph definition:
if trees are the same then Positions are equal.). And for funny paradox
(pointed out by Michael Mniermannrossi) when we can consider "claiming a draw" as
element of position and to have a contradiction.
HIs words are cited:

> we would consider "claiming a draw" to be a "move" there occurs a

> When there is the same position the third time, the player who has to move

> gets the right to claim a draw. But this right changes the position. So it

> is

> not the same position. But then he can't claim a draw. So it is the same

> position ...

Last idea may be developed in this way: we may consider "claiming a draw in
different moments of the game, that is in different numbers of presumably
repetitions" or even without words "claiming a draw": two positions may be
considered as different always when they take different
Places in sequence-game (one may form a mapping between claiming a draw and
places of positions in a sequence-game). And we have another paradox, something
like: number 5 in sequence 12345 is not the same as number 5 in sequence
11112345.
I think there are several definitions of positions, in some cases you may
pick a concrete one, but if you are referring to Math in your defense of
arguments you have to admit this fact as a reality (it means contradictions,
paradoxes, or maybe Godel conclusions…)
I will develop this topic further, but like the concrete question too.
Does anybody have last-version computer program to tell me about this (my
fifth) example. Here is a game played between humans (choose such option in
computer and type the following game) 1.Nf3 Nf6 2.Rg1 Rg8 3.Rh1 Rh8 4.Ng1 Ng8 5.
Nf3 Nf6. My chess program writes "draw" but it is not true even in chess rules
(position after 1.Nf3 Nf6 has a right to castle but next ones do not). What
does your computer show?
Thanks again, Yefim. 08/23/2004

PS. for Michael: For some reasons I cannot read (type) positions you gave:
4k2r/5p2/3P4/8/8/1q6/8/K7 w k - 0 1 and

> 4k2r/5p2/3P4/8/8/1q6/8/K7 w - - 0 1

> > Or even better:

> 4k1nr/8/8/1p6/1P1P4/KPp5/P1P5/8 w k - 0 1 and

> 4k1nr/8/8/1p6/1P1P4/KPp5/P1P5/8 w - - 0 1

Would you please give them in other way?

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