## Monday, January 12, 2009

### Proposal Re: Dimension

So there was a time, let's call it the one room schoolhouse era, when the teacher could just hold up a box and say "height, width and breadth" have the children recite, go through that a few times, and we're done: "space is 3D" (we don't really bother with proofs at that age).

Given philosophy for children is still a new idea in some circles (Montclair a champ, my sis has a degree in that), you don't get any real debate at this level. Kids don't sound like Cantor saying "hey, if the box atoms are discrete, we can address them serially, like computer memory bricks, so don't give us any of that 'because it takes three coordinates' phony baloney". Yes, Cantor made the criticism, but patches were applied, at a very high level though, not worth yakking about in K-8 (too over their heads).

Part of this is self interest, because with "Claymation Station" we go with Karl Menger's idea of "a geometry of lumps", distinguishing points, lines and planes in terms of relative shape, not dimension. "Everything is an arrowhead" in this geometry, meaning a simplex. If you wanna call that "4D" because of the strongly evident 4ness, go right ahead, free country, Medal of Freedom winner Bucky did, made perfect sense. XYZ 3D still a contender, not saying it's either/or.

Then came "fractional dimensions" ala Mandelbrot, in some ways resurrecting Cantor's objections in terms of mapping a plane to a line. Discrete math has come a long way, in terms of authority, given quantum physics and our use of "voxels" (named after "pixels") to map cellular automata ala Wolfram etc. People think more like computer scientists these days. Once "continuity" goes out the door, there's less need for "dimension" in the old fashioned sense.

But this gets to be very technical, not a one room school house yak. Save it for high school, when we do the complex plane anyway (fractals as Python objects, old hat at Saturday Academy (advertisement)).

A caveat to the above is I have no problem whatsoever with the less metaphysically tortuous meaning of the word, i.e. a unit of measure "in some dimension" be that time, weight, location, energy level or whatever. Metrology (attention to empirical accuracy) remains a number one focus of K-8. Being able to work with tools and get good results is way more important than mouthing off about "dimension" in ways that'd get you a math degree 100 years ago, but sounds pretentious that early. Again, we can get to it later, when their voices deepen a bit.

Any feedback? I've been looking over the shoulder of UK math wars thanks to connections through Stanford, have had remarks to this effect published, albeit in abbreviated form.