[Retros] Positions illustrating unknowingness of casles! Yefim 10/10/2004

[TregerYefim at aol.com]

   Hello from Yefim. 
 In the previous e-mail I asked a question: 
"From how many positions can we pass (not necessarily directly) to the
Original one?"
  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 
illustrate
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 
and 
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 
interesting positions.
Yefim 10/10/2004
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