Tuesday, August 28, 2007

Narrative of a higher cognitive level

I hate the term higher cognitive level since it invites to be vague. But right now I don't know a better term so I hope you will bear with it.

Blue Devil has been struggling with this position, lately:

White to move and draw.

I have investigated a similar position about 1.5 year ago here, here and here. Although I have studied the position for days, I made the same mistake initially as Blue Devil by thinking the position above is an easy win for white.

This is a very important point. How can it be that someone studies a simple position with only 4 pieces for about a week and still he doesn't recognize a similar position after 1.5 years? Alright, the position is slightly different, but that doesn't explain this phenomenon. Because if you don't know how to work around this, all your study efforts will be in vain.

The fact is, I never formulated a definite conclusion about the position. I have just investigated it. I never formulated a narrative on a higher level, I got stuck with lower level narratives. I never looked at it from a distance. It are the higher level narratives that connect different positions with the same motif in the brains.

Let me first try to formulate a higher level narrative for this position, in order to reduce the vagueness of the term.

In a position with two pawns and two kings, one of the pawns will fall. Always! No matter what. The reason for this is that one side can put the other in zugzwang. If white starts to run after the black pawn headlessly, he will lose. The reason for this is that the black king is closer to the white pawn than the white king is to the black pawn. Hence black can put white in zugzwang. At move 4 black is already attacking the white pawn, while white can defend it only just in time at move 5.

5.Kf7 Kh6 and white is in zugzwang and loses his pawn.

The fact that the black king is closer to the white pawn is more important than the fact that the white pawn is so far advanced.

So white is going to lose his pawn at all times!
Hence white must find another way to maintain the draw.

The only way to draw is to conquer the keysquare g4 right after the black king captures the white pawn. Since white needs 6 moves to get at g4 and black needs only 5 to capture the pawn, the only reason that white is in time is because he is to move first.

But white can't afford to lose a tempo along the way! So he must prevent that his king is shouldered away by the black king. That is why he has to take such weird route. If black tries to confuse matters by deviating from his ideal path, white can afford to deviate from his ideal path too. Since if black loses a tempo, white is allowed to lose one too.

Of course it are the tricky guys like Grigoriev who put whites king at such a place that there is an only move. If the white king was placed on a2 there would be 3 drawing moves:
1.Kb1, 1.Kb2 and 1.Kb3. But you can find the only move simply by taking the widest arc to g4 at all times.

Summary in order to generalize this narrative:
  • When there are two blocked pawns of opposite color on the board, one of them is going to fall.
  • The king that is closest to the enemy pawn is paramount.
  • The method of conquering the pawn is based on zugzwang.
  • If you are going to lose your pawn anyway, the only way to a draw is when you step on the keysquare right after the opponent captures your pawn.
  • Take always the widest arc possible without losing tempos to the keysquare, to prevent the enemy king from winning a tempo by shouldering you away.

I have tried to formulate the narrative in such way that it describes all positions with the same motif. Now let's wait 1.5 year to see if it works:)

To repeat the main idea of this post:
First you have to formulate the motif of the specific position.
Second you have to generalize the formulation of the motif to all kinds of similar positions.

Without this second step you will find it later to be impossible to recognize the same motif in a different position. Since if you look only at the solution of a specific position, only the low level geometrical patterns are stored and those are different in a similar position.
Focussing on the solution is not enough, you have to generalize the solution. If you do that well it should cut down the need for solving tons of problems. Since there are only very few motif. Say 15 in the middlegame and 15 in the endgame. The difficulty is to recognize them in all different disquises.

It are the higher level narratives that connect different positions with the same motife in the brains.


  1. Great explanation Tempo! I still brake a sweat when I am working tactics and come up against an endgame position. I'm currently going through Alburts' "Just the Facts" to get a better grip on these things. I must say though, that you put it in a way that very few can, that is easily understandable for us patzers.

  2. Each time you explain it, it gets more useful and clear.

    I have found that in my self-explanations of solutions there is a kind of optimal level of abstraction. I am getting to the point now where it sort of "clicks" when I am at the right level for a particular problem. Once I hit that optimal level it makes me more likely to remember the solution to that problem. Just memorizing moves is not enough: that is too concrete (even for mate in one, there are all sorts of features of the position to think about more generally: escape squares, the mating pattern used, etc).

    It isn't that focusing on the solution isn't enough. Rather, a priori it is tricky to know the appropriate level of abstraction at which to explain the solution (or in your language, for the narrative). There is often a kind of cognitive "sweet spot", a level of abstraction that just feels right. But sometimes it takes a really long time to find it, like with this problem.

    Plus, there probably isn't an objectively best level of generality. It depends how much you already know. E.g., I can use the concept of a 'trebuchet' as a basic explanatory device, but two years ago this would have made no sense.

  3. Samurai,
    That's the characteristic of a good narrative. It shows how simple things are in reality.

    I'm convinced that a grandmaster is not so good because he can handle complex situations but because he looks at them as being simple. And everybody knows how to treat a simple position.

  4. Blue,
    while trying to comment on your comment, enough matter for a new post unfolds itself. So I will adress your points in a later post

  5. kggNice explanation. To speak to the invasion subject of last post. The invasion square is often at a crossroads where it interacts with multiple pieces. I wonder if there is value to mapping some of these fields of force. Ct-Art does this as part of their hint section. Do you think there would be any value in doing this?

  6. tempo's series on pawn endgames was quite useful to me a few months ago. It's definitely worth going through if you need help mastering them.

  7. Tak,
    the feedback of you guys helps me to keep the tempo of my posts up. I think I will devote a post to your comment.