Most reasonably good players on seeing the diagram position will quickly spot the winning sequence known as 'Philidor's Mate': 1. Qe6+ Kh8 (Kf8 allows immediate mate by Qf7) 2. Nf7+ Kg8 3. Nh6+ Kh8 4. Qg8+] Rxg8 5. Nf7 mate. 'Mate in 5,' they say.
'Is there any way to force mate more quickly?' asks the experimenter. The subject then usually stares a little longer and says there is not.
When told that there is a quicker mate, even strong players may deny it. And when asked to justify their conclusions they mention 1. Qc4+, which cannot be so good because Black can at worst delay any mate by interposing the rook on d5, and 1. Qxh7+ which leads to nothing special after 1 . . . Kf8.
Yet there is a mate in four moves with 1. Qe6+ Kh8 2. Nf7+ Kg8 3. Nxd8+] Kh8 4. Qe8 mate.
Why is this so difficult to see? The answer seems to be that we know the Philidor's Mate set-up so well that we become fixated on it. Even though the correct sequence involves a capture with check - just the sort of move one is strongly drawn to in normal analysis - the ritual of Nf7+, Nh6+, Qg8+ and Nf7 mate is so firmly established that once we have started on it our minds cannot tear themselves away.
In Dr Saariluoma's terms, players reduce the vast complexity of the chess board to manageable proportions by unconsciously employing a conceptual selectivity to define very small problem subspaces. But once we have selected the supposedly relevant concepts, it seems hard to go back and swap them for a different conceptual space.
In the above example, there is the excuse that once you have found a mate, there is no point in looking for a shorter one. Fixation, however, can also unbalance one's thoughts in less favourable circumstances.
When Nigel Short missed a string of 'easy' wins in the tenth game against Garry Kasparov, it was because he had discovered that his intended winning plan didn't work. With his mind full of the wrong concepts pulling the pieces in the wrong directions, he could not re-boot his mental processes and think about the position again from first principles.Reuse content