## Wednesday, July 18, 2007

### Back on track

During a few days I was sidetracked by corresponding squares. I found an interesting article about the book "Opposition and Sister Squares are Reconciled" from Marcel Duchamp and Halberstadt. If I understand it right, they developed a method to cut the board in pieces and to shift them along each other. The effect is that you can find the right move by keeping the heterodox virtual opposition. The result is that calculation isn't needed any longer to find the right king move. You just treat it as the normal virtual opposition, played on a changed board.
Besides this, there seems to be an essay about corresponding squares divided in 11 subsystems from the endgame composer Zinar in Averbakh's book about pawnendings. I haven't read that.

These theoretical approaches are very interesting yet impractical. If you are willing to invest half a year in the method of Duchamp you will become a corresponding square monster which can solve problems whitout calculating within minutes. For tournament play it suffices that you have a bright idea how to apply the concepts in general. It is my take that people differ greatly in how fast the concept of triangulation will appear to them. But that is a different matter about which I hope to post another time.

To study corresponding squares to a certain degree has to be done anyway so I guess now is as good a moment as anytime. But since the tournament is only 6 days away I'm going back to my endgame strategy.

1. Thank you for the interesting article link.

If I'm not mistaken the statement:

"Thus the general formula for heterodox opposition in the principal domains is as follows: without the move, the White King has the heterodox opposition when he occupies, on a right hand adjacent file to the file occupied by the Black King, a square of opposite colour to that occupied by the latter."

is equivalent to what is sometimes called the "knights move opposition." This is seen most clearly with the corresponding squares marked A.

What I find interesting is that if you are willing to shift the board vertically you can see that even the squares marked B, C, D, E, F, and G are (virtually) knights move oppositions also. Also, based on the knights move opposition, I would guess that the unreachable squares a5, b5 and c5 are coded as: a5->D, b5->C, c5->B.