# [Retros] How many times could a Diagram be repeated during aproofgame?

Rol, Guus G.A.Rol at umcutrecht.nl
Mon Feb 9 03:47:35 EST 2009

Jonathan is right about "Or does this way lie madness?". The situation
is equivalent to the ancient logical "barber-paradox" - the barber who
shaves everyone in the village who doesn't shave himself; does he shave
himself?". If we do make the assumption that a position 47 moves into a
50M series is "irreversibly" different from one 46 (and 45, 44 ... 1)
moves into the series, then clearly these positions are all just the
first species in their private 50M series. But if they are all number 1
in their own 50M space and they are all "reversible" into one another
then they must all be considered "isomorph" in respect to the 50M
convention! Indeed, if the barber shaves himself then he doesn't shave
himself and vice versa. The same is (even more) true for the repetition
convention.

As in every paradox the solution lies in preventing self reference. The
postions are part of the "game layer" and the counting of occurrences is
part of the "evaluation layer". Entities in the evaluation layer should
not be made properties of the game layer and then recycled into the
evaluation process. This is an important principle which also affects
formal definitions in other areas like AP-logic.

Guus Rol.

-----Oorspronkelijk bericht-----
Van: retros-bounces at janko.at [mailto:retros-bounces at janko.at] Namens
andrew buchanan
Verzonden: maandag 9 februari 2009 1:25
Aan: The Retrograde Analysis Mailing List
CC: Jonathan Mestel
Onderwerp: Re: [Retros] How many times could a Diagram be repeated
during aproofgame?

Hi Jonathan,

This is a reply to an old mail of yours. I found it in my draft Folder.

> As I understand it, we're defining a position as "different" if

> different moves are available to each side...

(1) We don't get to define what is a position. That is defined for us in
the Laws in the section 9.something on Draw by Repetition of Position.

> ...even though logically in a game

> having the extra option to castle shouldn't prevent one side from

> claiming a draw if it wants to.

(2) I like your idea that if the current position dominates a previous
position, then it should be treated equivalently for Repetition
purposes.

So for example, if a position occurs 3 times (White to Play) with WKa1,
except the first time there was also BQb1 present on the board, then
does White have the moral right to claim a draw? After all, he now has
all the moves and more that were at his disposal the first time round.

domination the wrong way round: White can only lose castling rights not
gain them, and its less convincing an argument for a draw if White has
less moves available than the first time the diagram occurred. Surely
Black could claim that he is making slow but steady progress by
whittling away White's castling rights. (Indeed there is a famous
problem by somebody where White spends the first 4 double moves
eliminating Black's castling rights, returning twice to the original
diagram.)

Of course if only White has lost castling rights, then Black may be
considered to have the right to claim a draw. (Ignoring the mechanical
arguments one sometimes gets about whether Black has to write his last
move and not actually make it, yawn. By "mechanical", I mean
"characteristic of the Laws pertaining to the mechanics of playing the
physical game", e.g. touch move, clock management, recording the moves,
disqualification for cheating, etc.)

> Yet, unless I've missed something, we are defining two positions as

> the same even if one is winning but the second is not because of the

> 50 moves rule!

>

> We could argue that a position with 50 moves left is different from

> one with 47 moves left is different from one with 2 moves left...

(3) The notion of "position" *only* exists in the Laws to define draw by
repetition thereof. I suggest that you might use the word "game"
instead. Two *games* do map on to the same position even if one game is
winning but the second is not because of the 50 moves rule.

> Or does this way lie madness?

(4) Madness lies all about on this crazy planet where I seem to find
myself. But I think here we just have a definitional question.

Cheers,
Andy

--- A J Mestel <A.J.Mestel at damtp.cam.ac.uk> wrote:

> As I understand it, we're defining a position as "different" if

> different moves are available to each side, even though logically in a

> game having the extra option to castle shouldn't prevent one side from

> claiming a draw if it wants to.

>

> Yet, unless I've missed something, we are defining two positions as

> the same even if one is winning but the second is not because of the

> 50 moves rule!

>

> We could argue that a position with 50 moves left is different from

> one with 47 moves left is different from one with 2 moves left...

>

> Or does this way lie madness?

>

> Jonathan

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