Thursday, February 18, 2010

Kite Sighting

I found clever placement of Ben Franklin's kite in this post to a math list. OK, I put it there, so hardly geocaching on my part. I buried the treasure.

The context is explaining how variables work in Python. They're names for objects, more like strings to balloons. I drew this on Chairman Steve's tablet PC at Chicago / Pycon, not that he was any stranger to the concept.

However, I'm also suggesting that multiple names for the same object might not be a good idea (or design pattern). In Ben Franklin's case, however, one string went from the kite to the key in the jar, the other to his hand in the barn (staying out of the storm). Thanks to only one string being conducting, he wasn't shocked when the lightning hit.

This is the kind of mnemonic I'm suggesting around the NCTM conference, with kites a motif. You might have seen where Alexander Graham Bell (AGB) was into Kites.

These were later considered early prototypes of the octet truss, considered de rigueur for awhile by NASA, for any space station design, and still a good conservative choice. You'll find these things all over the place in architecture.

And at the microscopic level, you'll find the CCP and/or FCC lattice amounts to the same thing. Fuller chimed in with "isotropic vector matrix" or iso-matrix, but people mostly shouted him down. Maybe this sounded too Keanu Reeves or something, like in those movies?

I've likened the IVM to a "holodeck" like on Star Trek, a kind of "empty stage" (until the action happens) but more 60-degree coordinated than 90-degree coordinated. More like Flatworms by M.C. Escher.

Sir Roger Penrose has a kite (a tile, complements his dart). Bucky Fuller has a kite (actually two kites, a kat and a kate -- two ways for his Sytes to combine into space-filling pentahedra).

With so many meanings of Kite, most of them mathematical, you can see why NCTM might have picked them (NCTM = National Council of Teachers of Mathematics).

The corresponding council in the UK was founded by Caleb Gattegno right? He did a lot with those algebra bricks, wanting to color code and consistently teach all four operations in a way that would groom kids to read algebraic expressions.

Seemed like a good idea, not sure why the UK threw it out, if that's what happened.

Not sure why establishmentarians in the USA had no room for AGB either, though they made a mint off his Bell System. No room for his kites in everyday math class. Not until recently anyway.

One standard way to draw a kite is as a rhombus, a diamond shape. Crease the diamond along either its short or long diagonal and make that a trough, a concavity, with a correspond outside convexity. The tips are now closer together, so add a sixth edge. There's your tetrahedron.

NCTM must have really put on its thinking cap to come up with this stuff!

In the meantime, we're pawing through textbook series to see what to salvage for cyber-spatial access. Shipping hardcovers by sea or plane just doesn't make any sense given how the UN has to scrabble for coins.

MIT puts everything on-line. So do prestigious schools in India.

If we really think education is an asset, and that a world mired in poverty could really use this asset, then it's immoral, unconscionable, ugly and unethical to deprive said mired world of free access, at least to this basic K-12 pre-college material.

Yes, it's great to have real teachers in the picture, to make learning that much easier, and the way those real teachers will bone up, is through these various portals, though they'd often prefer live teachers too.

We don't require that every math textbook be conversant with 21st Century spatial geometry. We know that most aren't and it's too late to rewrite them. We mix old and new, rely on a variety of sources, encourage faculty to mix and match.

We do not trivialize the importance of teacher creativity, are counting on creativity to keep the ball rolling.

Keep a lookout for more kites!