QUANTUM LOGIC IN CHESS
These problems are taken from the article "Un nouveau type de jumeaux, ou la logique quantique de la composition" in Diagrammes Numero Special 6 (Oct-Dec 1990) by A.Frolkin, S.Komarov & A.Vasilenko. All problems were original to that article, with the exception of {A}.
The article shows through some beautiful chess the amusing and paradoxical effect of an acute attack of amnesia. Related effects are encountered in Consequent Seriesmover problems (where the amnesia may be regarded as chronic). But in these acute problems, each twin has an orthodox stipulation, which heightens the paradox. Quantum Mechanics is a similarly paradoxical subject, hence the title of the paper. [1]
The first two problems brilliantly illustrate the commonplace notion that chess positions have internal variables, not visible from the outside. All problem enthusiasts should see the classic {A} once in their career, although I think it's pretty difficult. {B} is a Circe fairy variant, but structurally resembles {A}.
Then amnesia is introduced in different forms in {C} through {K}. Some weird arithmetic follows: 2-1=2, 2-1=3, 4-1=2, etc. The only equation where the arithmetic works normally is {F}: 3-1=2, but what's going on then? The final twin {K}(b) exploits the A Posteriori convention, to achieve its ludicrous result.
| {A} N.Petrovic 1st Prize, Problem 1960 |
{B} A.Vasilenko & A.Frolkin Diagrammes 1990 |
{C} A.Frolkin & S.Komarov Diagrammes 1990 |
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| (7+12) 8# | (5+10) 4# Circe | (7+12) h#2 b) After the 1st moves of B & W | ||
| {D} S.Komarov & A.Frolkin Diagrammes 1990 |
{E} A.Frolkin & S.Komarov Diagrammes 1990 |
{F} A.Frolkin & S.Komarov Diagrammes 1990 |
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| (7+10) h#2 b) After the 1st moves of B & W: h#3 | (7+12) h#4 b) After the 1st moves of B & W: h#2 | (4+10) h#3 b) After the 1st moves of B & W: h#2 | ||
| {G} A.Vasilenko Diagrammes 1990 |
{H} A.Vasilenko & A.Frolkin Diagrammes 1990 |
{I} A.Vasilenko & A.Frolkin Diagrammes 1990 |
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| (7+5) #2 b) After the 1st moves of W & B c) After the 1st moves of W & B since b | (7+8) #5 b) After the 1st moves of W & B | (14+13) #3 b) After the key and the B defence | ||
| {J} A.Frolkin & A.Vasilenko Diagrammes 1990 |
{K} A.Frolkin Diagrammes 1990 |
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| (13+9) #3 b) After the key and the B defence | (12+8) h#1.5 b) A Posteriori After these 3 moves (!) h#2.5 on the WK |
[1] On reflection, though I love the problems here, I am not convinced by the use of the quantum metaphor. I think the orthodox conventions merit that metaphor much more - and there are already paradoxes aplenty. Under the orthodox conventions for castling and e.p., solutions wander forward in a mixed eigenstate which gradually resolves into a single game state. It is all unbearably complicated and unlikely, but this is the default that has been defined for us! :-) Just like QM in this universe...