Zero Brane

Blind Chess and Working Memory

Fri, 31 Mar 2006 08:04:16 GMT

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:

There are capacity limits but that they are in line with Miller's 7+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.
There is no special short-term memory faculty at all; all memory results obey the same rules of mutual interference, distinctiveness, etc.
There may be no capacity limits per se but only constraints such as scheduling conflicts in performance and strategies for dealing with them.
There are multiple, separate capacity limits for different types of material.
There are separate capacity limits for storage versus processing
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.

2 Years 3 weeks

Tue, 21 Mar 2006 07:38:42 GMT

I'm watching Andrey who is trying to reach across a small table to grab his toy car. The car is too far and while the table is small he keeps trying even though he can't reach it and it would be very easy for him to go around the table and take the car. Still, he persists in using his (not working) method even after I tell him about the alternative.

This reminded me about what Douglas Hostadter called a difference between physical distance and problem distance (GODEL-ESCHER-BACH, p.612). When a dog wants to get his favorite bone that is just few feet away, but on another side of a fence with a gate not too far away he has two choices: 1) run up to the fence, stand next to it and bark; or 2) get to the open gate and double back to the bone. While the second options seems to be counterintuitive (as it increases the distance to the bone), it actually brings the dog closer to it.

What needs to "click" in dog's brain for this to happen? What's that new level of abstraction that allows to solve this problem? What does this solution in some abstract "problem space" have to do with the real material world, where this problem is being solved in a similar way?

Last time this happened six weeks ago. After brief one-time experience with a real fence Andrey knows how to fetch a toy he wants even though he may need initially to move away from his target. I continue being amazed how quickly he learns even from one-time experiences.

Working Memory: a Black Box?

Mon, 13 Mar 2006 06:01:21 GMT

Chris Chatham posted a brief overview of the classic working memory model and offered a new diagram for that model. There are several interesting points, but I'd like to emphasize two of them: processing and memory are two sides of the same coin and gating functions are likely to be present at every intersection of arrows on the working memory diagram.

Having said that, I side with O'Reilly and his collaborators who proposed a completely different working memory model outlined in their article BANISHING-THE-HOMUNCULUS. The model is based on tripartite architecture, which is composed of the posterior cortex (PC) that performs majority of "automatic" sensory and motor processing, the hippocampus (HC) that is responsible for rapid learning that binds together arbitrary information, and the prefrontal cortex and the basal gandlia (PFC/BG) system that maintains internal contextual information (PFC), which can be dynamically updated by the BG.

In this model working memory is defined as an emergent property of the interactions between these three brain areas. These mechanisms not only support those basic memory functions that are generally associated with working memory, but also those controlled processing functions that are typically associated with a "central executive". The critical difference between this model and the model covered in Chris's post is that all information is viewed to be distributed in a relatively stable configuration throughout the cortext with working memory being represented by the controlled activation of those distributed representations. Authors' view is that working memory and executive function are two sides of the same coin, based on the fact that processing and memory functions are typically distributed within and performed by the same neural substrates.

As a side note, while a framework that separates working and long-term memory may look familiar and computantionally appealing, think about "simple" operation of copying a concept from long-term to working memory. What mechanism would support this copying that (to properly reproduce the concept) would need to include not only sensory and motor information associated with it, but also (potentially) large number of related concepts? How would "activation" of such a copy look like?

The authors also identify six key functional demands underlying working memory and describe how those are addressed in the proposed model:

Rapid updating
Robust maintenance
Multiple, separate working memory representations
Selective updating
Top-down biasing of processing
Learning what and when to gate

There is one more interesting point in the paper that I'll expand on later:

...it is likely that working memory may represent a kind of phylogenetic extension of the same kinds of mechanisms that underlie all forms of complex motor coordination and planning. (emphasis mine)

update 2006/03/20: More on working and long-term memory processes and assessment from Intelligence Testing.

2 years 1 week

Tue, 07 Mar 2006 06:41:44 GMT

Andrey is playing with his older brother, Daniil, who is 10 years old. Daniil is asking him to say words (in russian) -- "say, water; say, pipe; say, boat" -- and Andrey is repeating those words after his older brother. Now it's Andrey's turn: "say, (then after a 3 second delay, mimicking his brother) ...lamp; say, (after looking around) ...room; say, ...car" (much to our surprise as there wasn't any car around him). It looked like he was thinking about what to ask next and was doing search in his memory.

Overall, Andrey appears to be very proficient with words. He can easily say 4-syllable words, 4-5 word sentences, requests like "louder" (when listening to music in a car) and descriptions like "the smallest" (showing a small toy he is playing with).

1 month

Sat, 04 Mar 2006 07:24:11 GMT

Alysa's hand movements look more meaningful. She is not trying to reach for anything yet, but her movements look more purposeful maybe because they are longer, not as random as they used to be, and sometimes follow her eyes (probably just by accident). Her eye-hand coordination has also improved considerably. When she is awake she prefers positions where she can observe what’s happening around her.

4 weeks

Thu, 02 Mar 2006 06:12:16 GMT

Alysa at the rosy age of four weeks

Best Robots Ever

Wed, 01 Mar 2006 06:44:24 GMT

First issue of Wired in 2006 published a list of The 50 Best Robots Ever. Unfortunately, my favorite robot, Johnny-5, was not on the list, even though the list includes many movie robots. I found it on The Ten Best Movie Robots list.

Out of those robots that were on the list, my favorite is Genghis, a six-legged walking robot created by Rodney Brooks and his team and covered with much detail in Brooks's book FLESH-AND-MACHINES. Its unique (for its time) feature was that it was based on the subsumption architecture (described in more detail in HOW-TO-BUILD-COMPLETE-CREATURES), which provides an incremental method for building robot control systems that link perception to action. This control system is implemented as a set of layers, with each layer progressively implementing more and more complex behavior; robot's macro behavior (following people) arises from many independent micro behaviors (moving legs, balance control, steering, and the like). Conflict resolution happens at the motor command level rather than at the sensor or perception level resulting in coherent, smooth, and, as Brooks calls it in his book, "lifelike" behavior. However, contrary to what the Wired article says, the robot doesn't learn; this behavior is "innate" and doesn't change with time.

Those of you who are interested in first hand experience, can start from one of the kits on the Top 10 Robot Christmas Gift Ideas compiled by the robots.net folks.

update 2006/03/20: Not really best robots, but still related to this topic. A brief overview of various military robots from Developing Intelligence