00100		I think  you  are  mistaken  in  supposing  that  the  second
00200	representation of the swap-knights problem is simpler only because of
00300	the  human  visual  system.    Suppose   I   describe   the   allowed
00400	transformations by saying that a piece can be moved from p[i] to p[j]
00500	if and only if j≡i+1 mod 8 or j≡i-1 mod 8, by  saying  that  p[i]  is
00600	given by the table
00700	
00800		i	1 2 3 4 5 6 7 8
00900		p[i]	1 8 3 4 9 2 7 6
01000	
01100	In this case, the problem is  still  easy  to  solve  even  though  a
01200	geometric  representation has not been given.  From the point of view
01300	of a problem solving program, the problem has been made even  easier,
01400	because  the move operation has been identified with the operation of
01500	adding  or  subtracting  1  mod  8  which  has  lots  of  well  known
01600	properties.   My  point is that the changed representation is simpler
01700	for elementary logical reasons, and the complex and poorly understood
01800	properties of the human visual apparatus need not be invoked.