The Complete Amnesiac
Andrew Buchanan
6 Jan 2002 v0.1
28 Jan 2007 v0.2
(Comments welcome)

There are elements in a chess game which are not visible in the diagram. These are collectively called "state". The most important such elements are (a) castling rights (b) en passant status & (c) who has the move. Diagram + State = Position. [1] Many retro chess problems are about state.

Wherever possible the solver should be able to reason about the diagram and answer any necessary questions about state that are not addressed in the stipulation. Conventions have also been established to determine state in cases where ambiguity still remains.

The goal of this article is to classify problems where during the course of solving the problem, we deliberately forget about state. We call these cases of amnesia. Most of these involve castling and en passant state only: the problems normally keep rigorous track of who has the move, even if this does not alternate in the regular way.

The initial position in a chess composition is like the first scene in a novel or a movie, or like waking up in the morning. For a moment, we don't know exactly where we are: we don't know our state. Let's call this state waking amnesia. The metaphor is not exact: as we watch a movie, or as we wake up, more information floods through to us about the state. We find out that the protagonist is Prince of Denmark and has a ghostly father, or we remember our own name and that we are in a hotel that we checked into the night before, etc. In a chess problem, there is no more information about the past, but for example, as soon as the first move is played there can be no more mystery about en passant.

The Quantum Logic problems of Frolkin et al. are examples of acute amnesia. After a move or two, the position is deliberately plunged into waking amnesia again, by restarting the composition, in one phase. We forget about the history of the position, and the state, and as a result have to reapply the conventions once to tell us what is legal.

The disease is more severe in the case of Consequent Series Movers. Here we suffer from chronic amnesia; after every move, the same person is newly to play again, and we have no idea about the history of the position, except knowing that it must be legal. But it could be worse: note that in a consequent series help mate, after the final Black move, we do not lose state before the initial White move.[2][3]

In complete amnesia it is worse. In a complete amnesia problem, after every move we lose track of state, whether or not there is a change as to the player. A composition may still have the players correctly alternating in move. There is still the requirement that each position be legal.

All orthodox chess problems may be regarded as suffering from chronic amnesia, which never cuts in because the alternation of players is strictly adhered to, so there can never be any bout of waking amnesia. However, this does give us the chance to create some generalized genres, which subsume both orthodox problems and consequent series movers under the rubric of chronic amnesia.

The first of these is the marseillais. Here the solver is given a sequence for the moves, for example Black moves twice then White moves twice to mate. In the example here, Amnesia would happen here (and the conventions apply) before every move except White's first (since that follows correctly after a Black move).

The second of these is the niçois. This is like the marseillais, except the solver is just told, e.g. "four single moves" but not which player should take each move. However, waking amnesia would happen after any move followed by the same player to move. It is still a requirement that for a player to move, it must be legal for that player to move. In a sense, this is still not fairy chess! At every point we are hopping from one legal position to another - it's just we aren't taking the regular route.

It would be possible to create complete amnesiac versions of both these genres.

And it would be possible to go further still, to forget how many moves have taken place, what the stipulation is, where the pieces are on the diagram, or even that one is engaged in solving a chess problem. But this way madness lies…

[1] Occasionally other elements are relevant: for draw by repetition or the 50 move rule. But these are excluded from the definition of position (or otherwise a position could never be repeated).
[2] Note that the Retro Corner definition of Consequent Series Movers is in error, in implying that CSM is complete, not chronic amnesia.
[3] This is not the same as "regular" non-consequent series movers. This is a fairy genre where we do not concern ourselves whether the intermediate positions are legal at all, and therefore no retrograde analysis is possible. This genre is not discussed further in this article.

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