Wednesday, March 26, 2008

Gnu Math Chatter

Per my Chicago Pycon talk, an early bridge twixt lexical math type expressions and graphical sphere packing ala the IVM (CCP, FCC) are the figurate and polyhedral number sequences, developed minus any foreground coordinate system apparatus, although you need something under the hood in support of the ray tracer (a mechanical device).

This focus on geometric growth (gnomon studies) is prominent in late 20th century geometry: The Book of Numbers by Conway and Guy, Encyclopedia of Integer Sequences by Sloane et al (AT&T), Gnomon by Midhat Gazale, and of course Cuisenaire bricks ala Caleb Gattegno (more about linear color coded distances and the various time serialized entrainings thereof).

Coxeter was leading this charge in many dimensions with polyhedral numbers -- made sense Bucky would see the connection twixt his own deliberately remote vocab and this soon to be mainstream stuff.

Pascal's Triangle and Tetrahedron form a Grand Central here, where these many threads converge / diverge. Python insinuates some generators at this point, syntax that has already spread to the latest JavaScript, along with list comprehensions, in turn credited to Haskell no? The languages all swap DNA with wild abandon -- actually in tightly controlled fashion, but still not predictably.

Pascal's Triangle and Fibonacci Numbers are part of what go out preloaded on XOs, those "little green monsters" (Shrek colored) showing up in places like Peru, Uruguay... Alabama, any number of privileged homes in North America. The application is called Pippy and provides early exposure to Python.