Fun with representations III – Hidden in plain sight

A while back, as part of a series of fascinating studies of perception in chess, Simon and Chase showed a chessboard to people with several degrees of chess expertise, for very brief moments, and asked them to reproduce the position of the pieces in the board they saw, using a second board and set of pieces.

For half of their runs, they used reasonable mid-game positions, such as the following:

For these cases, expert chess players were able to reproduce the position faster and more accurately than novice players, and they needed fewer ‘peeks’ at the original board too.

Now, for the second half, they used positions with about the same number of pieces than the first, but the pieces were placed at random cells of the board. Here’s an example of my own:

If you don’t know chess, this image will be just as cryptic as the previous one. You would probably take as much time to reproduce it, and make as many mistakes too.

If you’re competent at chess, however, the second image will feel ‘wrong’. It will make no sense to you. If you’re an expert, it may even look like an abomination. And if you were to try to reproduce the position, you’ll lose your advantage over novices -you’ll perform just as slowly and inaccurately as them, perhaps even worse.

That’s what Simon and Chase discovered. Furthermore, they found that experts tended to add clusters of pieces at once. They conjectured that, when looking at a game position, a chess master does not see the same things mere mortals see. Somehow, after years of training, they get used to identify structural patterns and interactions between pieces. And they learn to exploit their ever-expanding knowledge base at will, almost unconsciously, so that when shown a ‘reasonable’ position they grasp it effortlessly, but when shown something that doesn’t make sense, their elaborate mental model is useless to understand it. In my previous example, for instance, I (with a merely competent chess knowledge) can identify these clusters:

Meanwhile, a novice does not have access to this wealth of information. They don’t see the clusters and structures experts see, and so they have to work out the position piece by piece, no matter the structure’s degree of normalcy.

This phenomenon happens all around us, in any domain where expertise plays a role. For example, I’ve always been confused when doctors point to abnormalities in radiographies that I simply do not see. On the other hand, expressions such as, say, a simple quadratic function, are instantly recognizable for me -I have a visual image that goes hand-in-hand with the expression, and I’ve seen and applied it enough that it probably means to me more than what it means to someone with a high school level math education.

Once a community of experts starts to discuss their domain, they will inevitably create words, or assign new meanings to old words, to refer to concepts they use commonly and for which their natural language falls short. This development of terminology is a sign that the domain is becoming mature and well explored. To stick with chess, for example, players will talk about controlling the centre, forking, and open columns naturally. Game discussions frequently use these loaded terms, so representations that use them are economically convenient. However, this practice raises the entry barriers for newcomers (as anyone who has listened to doctors discuss would agree).

Incidentally, it is sometimes also the case that a novice sees things that an expert will not. The expert assumes things that, in strange cases, may not be true. For example, consider the following chess retro-puzzle from Raymond Smullyan:

Black has made the last move. What was it, and what was White’s previous move?

The puzzle, as it stands, has two possible answers. Try to figure them out. I discuss them in the next two paragraphs, so skip them if you just don’t care!

For both answers, it should be obvious that Black’s last move was with the king -no other piece available- and from the cell below of where it currently is (it cannot come from the right because that would imply an impossible check from the white king). This means it escaped from a bishop check. But how did the bishop get to that seemingly unreachable position in the first place? The first answer is that the check was revealed by another piece -but it would have to be a piece no longer on the board. The only possibility, then, is for a white knight to jump (from b6) to the board’s corner, uncovering the check. The black king then escaped the check by capturing the knight, leading to the current position.

The second answer depends on realizing that, perhaps, we’re not looking at the board from the perspective of White, but of Black. If that’s the case, we can explain the bishop’s placement as a promoted pawn! A white pawn moves to the bottom row, gets promoted to a bishop, checks, and the Black king escapes to the corner of the board.

Some people have a hard time seeing the second answer. It runs against two standard assumptions of chess -that White’s side is displayed on the bottom, and that when we promote a pawn we promote it to a piece of greater power than a bishop. However, if you’re not familiar with these conventions, but know enough of chess to understand how pieces move, you may even outperform an expert chess player (being, in Dan Berry‘s terms, a “smart ignoramus“, a person whose ignorance of a domain, paired with a sharp intelligence, leads him or her to ask valuable questions that experts would not think of asking.

I think I’ve abused of chess long enough. In the end, what I want to do is remind us that people see, literally, different things in the same representation. Their understanding of it, and their potential with it, will depend on their domain and language expertise. Meaning is in the mind of the beholder. And so representations are not just useful or not -they are useful for a particular person, or type of person, to accomplish a particular task.

Next in the series: How to search for books in a library that has no index, and Borges’ Library of Babel.

ADDENDUM, April 2016: I created the chess images above and I release them with a CC0 license to the public domain. Feel free to use them!