Thursday, December 13, 2007


There are a number of interesting (to me) opportunities for parallel between the pure abstract world of Mathematics, and the messy, sensual worlds of philosophy, art and thought. Like all parallels, they tend to converge toward infinity. Of course we can't just jump right into this feast of parallax without building up to it with a little digestif. So, by way of a cheese platter (and there may be some olives in there as well):

A Sierpinski Gasket is a type of ternary Cantor set, or self-similar set. It is constructed by taking a triangle, removing a triangle-shaped piece out of the middle, then doing the same for the remaining pieces, and so on and so forth, like so:

Sierpinski Gasket

The result – if an infinite series can be said to have a result – is a pattern of infinite boundary, and zero area. This totally counter-intuitive concept is poetry in itself. To imagine that by recursive Swiss-cheesing, we can arrive at the Infinite, not by adding to the whole, in the gluttonous, possessive fashion of current North American consumerism, but by taking away, after the fashion of Francis of Assisi, Buddha, the Jain Dharmists:

"Trees renounce fruit and keep us alive. The mountains cast away stones and pebbles, which we use for our works and art. One should renounce worldly possessions devotedly within one's power (shaktistyaga)."
Hey. I'm not saying I'm ready to give up my iPod. This is all merely by way of illustrating that the path to enlightenment is multifold. There are many trail heads (We'll talk about Pi next time), and some of these lie outside the province of our personal expertise.

If you're catching what I'm pitching, throw it back in the comments.

2 uninformed opinions:

erin said...

I like this concept. It seems more slippery, though, like Tao.

Not that I'm even close to an expert on any of this, but I've understood nirvana to be something that can be achieved by asceticism. Infinite seems unattainable.

Cool Ranch Luke said...

"Infinity seems unattainable".