Wednesday, December 1, 2010

Philosophy and Mathematics

Logan Fletcher asks his philospher friends whether this video can prove the Pythagorean Theorem, and whether knowledge can exist in perception. Or something like that. Actually he asks:
When you watch this video, is this a case of *seeing that* the Pythagorean Theorem is true? And if so, does that mean that we can apprehend mathematical truths within perceptual judgments? I'd appreciate any thoughts people have to offer about this.

I start to write him a response:

No. The video presumes unreasonable skill with scissors and paper squares, so it's just one more removal from any actual faith in tangible mathematical proof or provability.

On the other hand, dogs and cats can tell when you feed them less or more, so there is clearly a mathematical element to perception. Great apes can add and subtract and can be taught to show it on touch screens. Even poetry majors can be taught to express opinions of the philosophy of mathematics. So there's hope, but not in animation.

Watching any cartoon is an exercise in the suspension not only of disbelief, but of consciousness. Americans have studied each other's brain activity during various typical activities. The electrical activity while we watch tv is equivalent to that while we sleep. The language of cartoons is a language of cliches of impossibility.

Anvils fall from clear blue skies and only ever land on characters' heads, temporarily crushing them. People and personified rabbits continue walking off cliffs until we notice we have left the ground behind and then decide to fall. In watching animation we turn off our brains and sleepily watch a series of impossible events that vaguely approximate the foolish ideas that get us through our days without questioning the difference between ourselves and a terrarium full of caffeinated yeast.

This cartoon may show that mathematics is simple and beautiful and capable of explaining everything we ever need to know about unobtainable mathematical abstracts such as "right triangles," but most cartoons we watch from before the time we can understand words or count our own thoughts just teach us that life is meaningless nonsense where injuries are inevitable and hilarious. Perhaps if we were ancient greeks watching this cartoon, we could understand some math but not us, not today, not as Americans.

And the Ancient Greeks would be too busy wondering where all the strings were, and how the pictures moved. In the end they'd probably just take your laptop and sacrifice you to Athena.


Then I decide I've been writing in Don Delillo's voice, and I should find my own, so I skip posting it. Life is complicated enough without the requrement that it be unique. At this point I'd settle for a day of focus on anything, whether or not it's happened already.