Blind Chess and Working Memory

When I was a kid I liked playing blind chess with my dad and my brother. This is the type of chess when you make moves without looking at the board at all (you just tell your opponent what piece to move and where). I couldn't beat my father (to my defence I couldn't beat him very often in regular chess either), but I could play through end-game with 30 moves or more.

Now I want to compare this skill with my inability to remember a 10-digit phone number after hearing it one time or copy a 9-digit loan number between two computer screens from memory (I need to look at it at least twice). We all know about a span of immediate memory and its limit of seven plus or minus two items (The Magical Number Seven), which (partially) explains my difficulties with numbers. I just don't see how to reconcile it with my ability to play blind chess.

For those who never played blind chess, here is a brief summary of what you need to do. You need to 1) keep the current position in your head (initially 32 pieces on 64 squares), 2) be able to evaluate this position, and 3) consider possible moves and your opponent's responses (for any serious game this analysis needs to be done for several iterations/levels).

One possible explanation is that blind chess has more to do with mental imagery and less with working memory. While imagery is definitely involved here, I don't think this solves the problem. For starters, I don't imagine seeing the board as you'd see it in real life. The board that I see has no texture and no color; even squares are not colored black and white. I can "paint" it any color I want, but this will require some effort and "by default" it's completely feature-less. Much to my own suprise (this is the first time I examine this aspect of my own mental imagery), pieces too have no colors and even no shapes. I just "know" that this square has my pawn and that square has opponent's bishop. As with board colors, I can make them look anything I want, but this doesn't change the fact that by default they don't have any look. It's difficult to explain, but I just know conceptually that this is my piece on this square. Which makes me think that this has less to do with mental image and more with working memory that not only stores all those concepts and their relationships, but is also involved in analysis of the position and future moves.

Another possible explanation is that each of those tasks involves a different type of working memory; alternatively, there may be no separation, but working memory may have different task-specific capacity limits. For example, this article provides seven views on this capacity limit:

  1. There are capacity limits but that they are in line with Miller's 7+2.
  2. Short-term memory is limited by the amount of time that has elapsed rather than by the number of items that can be held simultaneously.
  3. There is no special short-term memory faculty at all; all memory results obey the same rules of mutual interference, distinctiveness, etc.
  4. There may be no capacity limits per se but only constraints such as scheduling conflicts in performance and strategies for dealing with them.
  5. There are multiple, separate capacity limits for different types of material.
  6. There are separate capacity limits for storage versus processing
  7. Capacity limits exist, but they are completely task-specific, with no way to extract a general estimate.

Yet another explanation is that somehow I trained myself to store and process all this information. I don't buy this argument simply because I have been dealing with short sequences of digits for much longer than with blind chess, but without any significant progress.

I think it has something to do with the fact that "chunks" that I'm trying to remember in the first case (digits in a phone/loan number) are not related, while in the second case they are tightly related to each other. Even more importantly, what needs to be captured is a sequence of digits, rather than a group. This may be caused by mutual interference between elements in the sequence; as a result the sequence requires significant effort to maintain itself. If those number can be somehow related to each other (for example, they may be similar to a social security number) it may be much easier to remember by capturing "social security number with some modifications...". I think this also supports the idea of a hierarchical organization of (working) memory as while the chess play requires to maintain significantly larger number of elements, they all seem to be maintained "inside" that concept without much bear on working memory. Yes, you need to focus and pay attention when you play blind chess, but I'd argue that the effort required is probably less than when you need to remember a 9-10 digit sequence for 30 seconds.

Note that this effort doesn't seem to be proportional to the number of pieces to maintain in memory: it's easier to keep the position in memory in the beginning of the game when all 32 pieces are present rather than during end game where only few pieces may be left. This may be related to the fact that the initial position is more constrained (has fewer degrees of freedom) than any end game position, which makes it easier to track.

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I am Paul Kulchenko.
I live in Kirkland, WA with my wife and three kids.
I do consulting as a software developer.
I study robotics and artificial intelligence.
I write books and open-source software.
I teach introductory computer science.
I develop a slick Lua IDE and debugger.