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Transformations
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 jkarp25-Feb-13, 09:25

Transformations
In my games, I generally remember something in Algebra called Transformations for my game. Sometimes I use Analyze the Board to help me with the transformation. Why? I think about the X and Y axis, and how many units a piece has to shift up, down, left, or right. Like in one of my past games, one rook had to shift down by one unit, while the other had to shift down by about 3 units and to the right by 4 units, in order to deliver mate.
 jkarp25-Feb-13, 09:28

BTW, that game is shown below. gameknot.com
 jkarp25-Feb-13, 09:43

Here is another. I actually won this game against an opponent because I shifted my queen up by 5 units to play a powerful fork between his king and rook. Therefore, I was going to win his rook, so he resigned.
 jkarp25-Feb-13, 09:44

That game is shown below. gameknot.com
 tactical_abyss26-Feb-13, 10:43

I do not use the alg mind formulas that you are using very often,but I do use a form of pattern recognition,more geometric patterns.Although for individual Knight moves,I can see the advantage of Algebraic progressions.If you can place your Knight, ahead in a position,say where it could or would be 12 full moves later and do this in your mind very quickly,then that is more a form of Alg progression,rather than a geometric freeze frame memory recognition pattern.

Its important to also remember where your pieces or your opponents pieces are NOT!
So remembering an empty square on move #9 and what to do with that bare square?Is it a weak square?Should you place your piece on that square,or simply "aim"your Bishop at that open square from a distance?Or should you have patience and "wait"in the shadows for your opponent to move a powerful piece on that open square to potentially initiate an ex-ray attack on that piece with your Rook?

All of this can come alot easier,if you can have a form of geometric pattern recognition from other games played in the past.Its sort of like booting up your own mental past game program from a position you encountered a year ago,but your not using a computer database on that subvariation.

jkarp introduced the notion of algebraic transformations, as they might apply to the chessboard. I infer he is thinking in terms of a transformation of an individual chessman, but I rather think the idea is better applied to positions as a whole. Note, by the way, that mathematics also holds the concept of geometrical transformation. The two are not necessarily mutually exclusive.

A simple example I gave was the endgame position
w
I asked the question here: 'White to move: What result?'
Then I asked what might be the implication if:
1. The whole position was moved one square closer to the Black side of the board?
2. The whole position were moved one square closer to the K-side?
3. It were Black's move?

All these shifts are cognate to algebraic transformations of, say, the graph of a function. Such transformations might or might be significant, depending upon whether they alter the outcome with best play.

The diagram position is a draw, though the thing is by no means elementary. Were White to play
1.Kd5, he would lose to 1...Kb4 (zugzwang!). I'll leave it to the reader for the time being to determine how White might try for the win, and how Black can (just) hold.

Transformation 2 is trivial: nothing material has changed. Transformation 3 isn't quite so trivial: roles are reversed and it is White on the defensive. But Transformation 1 is certainly significant. How is the outcome changed, and in whose favour?

Cheers,
Ion

 tactical_abyss26-Feb-13, 20:09

ion,you and jkarp have one up on me!Its my time to learn,so you guys take the reins!
I have no idea whats being said here!I was an "A"student in HS with Alg,but I cannot relate chess and alg in any way with my brain....atleast not to formulate an equation with a solution.
So go to it,i'll sit back and watch!

I'm having enough problem right now with losing my sound on my computer!I get those "clicks"with page switching,but suddenly for no reason,I cannot listen to UTube video's or get sound from the GK blitz room off the board move/clicks.And yes I have adobe flash and java installed.

Oh well,thats another subject...sorry!