Back when I was a math undergrad, another of the math students showed me and some others what he said was known as “gestalt counting”. He took 10 (give or take a few) pencils, laid them down on a table, arranged them a certain way and said that represented the number one. He rearranged a few and said that was two, and so on up until around 10, I think (I have no idea how long it could have been extended). Certain arrangements he would call “symmetric”, like “that’s a symmetric four” (not sure what that meant, but my WAG is that it meant the pencils still represented four if you viewed them upside down). He did it a few times, running from 1 through 10 or so; each time it was somewhat different–different representations for the same number, and I never caught on to what the key was to the representations. He only did it for a few minutes, and I never saw it again.
I know that’s really vague, and unfortunately I don’t remember any specific arrangements; but I thought maybe this little trick may be somewhat widely known by that name. Does anybody know what I’m talking about?
The term “gestalt” refers to patterns where the unified whole adds up to more than the sum of the separate elements. Gestalt psychology refers to the character of perception as a unity - for example, a square is more than 4 straight lines enclosing 4 right angles, but is the perception of the totality of the square as a whole, or a melody is a totality of a series of tones, not the sum of the separate tones.
Yeah, I figured that “gestalt” refers in some way to the interpretations of the pencil arrangements. Unfortunately, I can’t remember anything specific about the arrangements, and it’d be impossible to answer this question without being familiar with it. Oh well, just one of those things that recur to me from time to time, and I wondered if anyone here had ever seen it before, as well, but it doesn’t look that way.
Apparently you don’t know of any purpose in what your fellow student did with the pencils. Where a given configuration was associated with a number, was that number the number of pencils used in the configuration?
Ray (Maybe he wasn’t clear on the concept of a pencil.)
It was just some pattern recognition thing, but it definitely wasn’t the number of pencils used, that stayed constant. It would start off (this will not be accurate, just a generalization) with all the pencils, say, side by side, which would be “1”, then he’d move a few, slide some up or down, rotate some, or whatever, and that would be “2”. There’s actually no point in me trying to describe the actual arrangememts, because I don’t remember it well enough.