Wednesday, January 23, 2008

3 layers of invisibility

After doing lots of visualisation exercises I came to the following reasoning:

If you can't solve a problem while looking at the board and moving the pieces around with your hand, you certainly aren't going to solve it with with your eyes closed before your mind's eye only. So the best you can hope for as result of visualisation exercises is that it is as if you are looking at the board with your eyes open. But it doesn't shift your boundaries as problemsolver.

There is more to it though.
Yesterday I introcuded the 3 layers of chess vision:
  • 1. The squares covered by my present pieces (part of the present cage)
  • 2. The squares covered by a piece of me in the future (part of the future cage)
  • 3. The squares covered by the enemy (limits the places where I can put my pieces hence my ability to create the future cage)
Here I have a diagram that perfectly demonstrates these features.

White to move

This is a problem of masterlevel. You can't say that it is a very difficult problem though. The goal is this: mate the king. And every move is a check.
The tree of analysis isn't very big at all.

The problem is purely caused by the visualisation of the squares and the volatility of the memory. I now see a flaw in the reasoning that working on visualization can only have very limited results: even if you allow yourself to move the pieces by hand, you still have to visualize the cage. Otherwise you are going nowhere. Moving the pieces by hand relieves your problem to see the future cage, but you still have the visualise the current cage.

So the question is, again, how can we ease the task of the short term memory which is overloaded by coping with all those invisible squares?
I know the theoretical answer on this: make chunks and store them in your long term memory.

But the question is: how to make that practical? Or in other words: solve the diagram above and ask yourself "what must I learn to relieve this task and how must I train it?"


  1. Be practical in situations like this. what makes it more or less difficult to calculate the variations in this position? first the ply depth of some variations, secondly de number of alternatives.
    But when you are practical you can get to the answer in a straightforward way.
    the forcing move is 1 Rxe7+. Allthough Kg8 and Kg6 both allow mate in 3 I even dont have to consider them to realise that they are no argument against Rxe7 since the move leave me with initiatieve and an material advantage. So 1 ..., Kxe7 is the move only move you really have to calculate. Then 2 Qxb7 suggests itself. No need to look at king going to the e8 rank since this drops two rooks (allthough again white could also choose to calculate and find the mate (which is a relatively long variation though. So 2 ... Kd6 is the only move to calculate. Now 3 Qc7 jumps into the eye. this move leaves only Kd5. If you dont see the mate immediately (I didnt, then you could pause and make a clear picture of the position. Hy the king cant go to the e file. c4 is mate! Oh no, Qxc4, what about other checks. I bet you would see Qxc5 in a minute or so. As wel solving this problem as in a otb game.

    Only calculate the variations that are neccesary for decisionmaking. youre not Kasparov, and dont need to be him to cope with situations like this.

  2. Anon,
    I think it is a good idea to sign your comments with your initials or so, since now it's not possible to see if there is a relation with previous Anons.

    Of course this is no problemsolving contest. Can you adress the subject as raised in the post otherwise than "we are not Kasparov"?

  3. Hi tempo,

    No offense intended, I just wanted to make clear with my "youre no Kasparov" remark that one can calculate situations like this, even when you dont have gm calculating power. To speak for myself, i dont calculate very well, but i am able to find my way in these situations by eliminating all unnessecary calculations.

    keep up the good work you do on this blog!


  4. Adrian,
    no offense taken. It is good that you point out that material considerations can help to prune branches of the tree of analysis. In doing so the example becomes worthless though, which forces me to find another example where such pruning doesn't work. In stead of that I ask you to be flexible and find all the mates.

    If I say "I will never be a Kasparov" and somebody asks me "Why not?" ,I'm standing with my mouth full of teeth. This post intends to find out what makes the difference:)

  5. must be the most awesome chess player ever!

  6. "So the question is, again, how can we ease the task of the short term memory which is overloaded by coping with all those invisible squares?"

    to me, THIS right here is the issue. when i calculate, by the third move, i've forgotten where everything is. other than patterns and chunking, is there a way to increase visual retainability, knowing where everything is going to be and all that?

  7. oh, and i just want to thank you for writing this blog and all the work that goes into it. i learn stuff when i read your blog, you help make me a better chessplayer. thank you.

  8. I stared at the position for a couple minutes, lost in a sea of variations.

    Adrian, excellent analysis. You broke down a complicated-looking position and made it seem quite simple!

    'If I say "I will never be a Kasparov" and somebody asks me "Why not?" ,I'm standing with my mouth full of teeth.'

    I will answer, I began playing chess in my 20s, and it's a hobby! :)

    But seriously, in previous articles didn't you argue that being able to quickly see the truth of a position -- like Adrian did here, you've done in many tactical positions, and I've done in some endgames -- is more important than deep visualization?

    Is it perhaps even sufficient to become a national master?

  9. Some chess pundit said that thinking in squares was the highest steps in chess development. As we develop we think first in terms of pieces, then pawns then squares. Reading your post reminded me of this.

    I am playing through a averbakh-kotov position on my blog. I am hoping to narrate it. I think that a benefit of narration is in defining a problem and once the problem is accurately defined it is well on the way to being solved.