On Tue, 09 Oct 2007 09:42:58 -0700
Taylor Kingston wrote:

This may be of interest as an intellectual exercise or parlor trick,
but its utility in practical play seems rather limited. I suppose it
might save some calculating time in an unusual endgame where it was
critical to get a knight to a distant square in the fewest moves,

I don't think this is unusual at all. I've played many endgames myself
where doing just this was important. Using a knight to try to stop a
pawn from queening is relatively common. Sure, it doesn't happen in
every endgame, but I think it happens often enough that improving one's
technique would be useful, and certainly more than a "parlour trick".

but in most real-game positions, especially in the middle game, any
moderately experienced player can plot a knight's optimal path with
ease.

Most middlegame knight moves aren't very lengthy, so in general I
agree. But sometimes you do want to get a knight from the queenside
to the kingside (or perhaps to an adjacent square, which can sometimes
take up to four moves), and this method will quickly and reliably tell
you what the minimum number of moves such a path must take. I think
this is also useful... though I suppose some people might be satisfied
with just using a trial and error method.

Does Alexander claim his technique is of much practical use?

Well, here's the blurb from the back of the book. (I don't know if
this was written by Alexander or his publisher)

"Knight moves are the most difficult to visualize on the chess board.
In the endgame it is frequently necessary to determine whether a knight
can reach a certain square to intercept a passed pawn or protect one of
your own pieces or pawns. In the time pressure of many tournament
endgames, it is even more difficult to concentrate and feel confident
that you have correctly calculated the possible path of the knight and
the number of moves necessary in the variation. This often leads a
player to repeat the sequence in the mind a number of times to feel
certain that his projected moves will indeed accomplish the objective.
Mr. Alexander has developed a set of tools which make it very precise
and quick to determine the required number of moves, and whether or not
a sequence of knight moves will achieve a goal. The author has
developed a wonderful set of graphs which visualize the possibilities
of moving a knight to a desired goal. Many players will find this
technique to be invaluable in winning endgames involving the knight, or
even combinations in the course of the middlegame."