Tuesday, August 24, 2010

A Fifth Tetrahedron

A family of space-filing tetrahedra fill this triangular prism (as well as those next to it). Another vZome by David Koski based on research by Michael Goldberg and others.

This family is in addition to the four space-filling tetrahedra cataloged by D.M.Y. Sommerville in 1923: the Mite, Rite, Bite and 1/4 Rite (using Bucky Fuller's nomenclature).

Dr. John Belt, SUNY, Oswego

Sunday, August 15, 2010

Operation DuckRabbit

:: duckrabbit ::

Calling my project Operation DuckRabbit is somewhat new. I'm alluding to Philosophical Investigations Part 2 especially, which is about the gestalts we associate with meaning. Despite all that "meaning as use" stuff, the importance of showing (not just saying) gets lost in the shuffle if we forget about duckrabbits and other such switcheroos.

My contention has been (and continues to be), that serious-minded philosophers would do well to look at one of the important gestalt switches in 1900s philosophy, what has come down to us in 2010 as Martian Math, at least in my neck of the woods.

The appended link to Notes for Teachers sets the stage: imagine a tribe (sounds like Wittgenstein already), that doesn't consider the Cube to be its model of 3rd powering, uses the Tetrahedron instead (topologically simpler, works well in a ball-packing context).

We get right to the foundations of mathematics with such a consideration, plus we turn the key in what might otherwise be a locked (inaccessible, or perhaps verboten) branch of literature, much of it philosophical and contemporary in nature.

Operation Duckrabbit is about recruiting those schooled in philosophy to apply their understanding of Wittgenstein to this gestalt changing challenge. As the late Dr. Arthur Loeb would remark, crystallographers have something to learn from this alternative more 60-degree-shaped bias. Instead of orienting everything around the cube, other gestalts emerge and hook together -- if one works at it, deliberately fosters the requisite changes in consciousness.

I think we're nearing a time when literacy in Wittgenstein's philosophy will include the concrete example of Martianversus Earthling math, though the narrative may assume a different guise. A lot of fruitful investigations branch out from this tension, this unity-of-opposed-concepts, more than just one or two investigators might handle.

We need more explorers in this "geometry of thinking", seems to me. There are real world implications, as unlocking Fuller's treasure trove (like a pirate stash) is to unleash a cornucopia (the inverse of Pandora's Box). What better way to be a hero then? And if you're already well versed in Wittgenstein, well, you've already got an edge.

Kirby Urner
Oregon Curriculum Network
Portland, Oregon

Notes for Teachers

Background Reading (a previous post to this list):

More about Martian Math c/o BFI blog:

Re: Operation Duckrabbit: