[Retros] Positions illustrating unknowingness of casles! Yefim 10/10/2004
TregerYefim at aol.com
TregerYefim at aol.com
Sun Oct 10 22:19:58 EDT 2004
Hello from Yefim.
In the previous e-mail I asked a question:
"From how many positions can we pass (not necessarily directly) to the
I received an answer from Francois: 280367, which is absolutely true!
I do not know what "chess engine he has", but somehow he did it in several
hours but I was counting several days. :) (: Good job!!!
And more important that Francois has found two surprising positions which
the topic of castling e.g. unknowingness of castle (one of the beautiful
topic in retro)!
Explanations: we have two "mirror" positions.
r1bqkbNr/pppppppp/7N/5n2/6n1/8/PPPPPPPP/R1BQKB1R b KQkq
r1bqkb1r/pppppppp/8/6N1/5N2/7n/PPPPPPPP/R1BQKBnR b KQkq
I have conditionally given the first position with 4 castles, that is not
true, read below.
Properties of those:
1. The first position cannot be obtained from the Original one and from the
second one we cannot pass to the Original (unless some castles are lost).
2. The first one may be obtained if we assume that one of the two White
castles is lost. Then the last White move was either Rb1-a1 or Rg1-h1. And we have
the famous wonderful conclusion:
We know that some castle is lost, but do not know which one!
3. For the first position it concerns Past of position. But for the second
position it concerns its Future. Black may save its castle but only one of two
and we may formally say that one castle will be definitely lost, but we do not
know which one!
4. These two positions illustrate mirror notions between Space, Color, and
Time, between knowledge and unknowingness. And all of this due to castle rule!
(human mind takes it into account, but computer does not).
5. At last, these positions illustrate conflict between REAL and UNREAL (to
be or not to be!) e.g. between legality and illegality: the first position is
illegal - at least one letter in KQ expression should be omitted (what
computer does not understand!).
Personally to Francois (and others): It is interesting to know that a
structure with f3 pawn (and 4 castles) contains almost 15000 positions more than
Original structure (concerning the same question). This structure also has some
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