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| Melissa and Doug's Geometric Stackers on my workbench. A piece or two is missing from peg 3, btw. |
I don't recall playing with stacker toys as a kid. Blocks, play-doh, stuff like that, but toys where you stack wood pieces on pegs didn't show up on my radar until I started using them in work on logic.
As part of a larger research problem I'm exploring on the logic of toys, I have some questions about stackers. But first a few observations.
Two obvious big facts about stackers. First, there are lots of brightly colored, variously shaped pieces (they have holes in them that accommodate the pegs they are stacked on). And second, there are those pegs. The pegs force the pieces into some arrangement or other, but the pieces have their various properties independent of their arrangement.
The stackers thus permit a grid system: peg 1, first position--perhaps 1.A, something like that--and on in the obvious way: 1.A, 1.B, 1.C, and so on. The height of the peg and the thickness (height) of each piece, if they are all similar, thus determine how many slots each peg has.
Suppose we create a model as our initial state in which piece a and piece b, both circular, are stacked on peg 1 in the first two positions (1.A and 1.B). Then suppose we create a model to be our final state, in which piece a is still at 1.A, but octagonal piece c is at 2.A and octagonal piece d is at 3.A. (Sorry--next time I'll have more pics. Maybe I'll move this discussion to my Tumblr blog.)
I'll hold off on the list of sentences in the model until Tumblr. For now, let me point out a couple of constraints on the Stackers:
The stackers thus permit a grid system: peg 1, first position--perhaps 1.A, something like that--and on in the obvious way: 1.A, 1.B, 1.C, and so on. The height of the peg and the thickness (height) of each piece, if they are all similar, thus determine how many slots each peg has.
Suppose we create a model as our initial state in which piece a and piece b, both circular, are stacked on peg 1 in the first two positions (1.A and 1.B). Then suppose we create a model to be our final state, in which piece a is still at 1.A, but octagonal piece c is at 2.A and octagonal piece d is at 3.A. (Sorry--next time I'll have more pics. Maybe I'll move this discussion to my Tumblr blog.)
I'll hold off on the list of sentences in the model until Tumblr. For now, let me point out a couple of constraints on the Stackers:
- The universe has pegs, numbered/slotted into a grid system (as I've been suggesting).
- It will help enormously to have functions to make instructions simpler: $remove _top-most_ piece _early-most_$. The $_top-most_$ function is a space function (describing location in space), while the $_early-most_$ function is a time function (describing position in time).
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