Friday, March 27, 2009

Monsters and Mandelbrots -and The Wrath of Kahn

Yesterday I attended a Mathematics and Theology seminar at Wheaton College, merely to watch a film on Benoit Mandelbrot's discovery of fractal geometry and how it mathematically describes very complex shapes we see in nature. Benoit Mandelbrot is an older man, a Lithuanian Jew who, as a boy in World War II, evaded the Nazis in occupied France for four years.

He was a remarkable and imaginative thinker who did not "fit in" says the film. He was grabbed by an aggressive IBM in its early years to solve certain problems. One was that they were having signal noise whenever they transmitted data over phone lines. While the film did not explain how or if IBM was able to fix the problem - we must assume they did - this signal noise formed a strange pattern that was recognized by Mandelbrot the mathematician.

They were called "monsters".

Let's say you take a line: ____________ (this is 12 underscores long, BTW) and then take out one-third of it: ____ ____ . Then you do this again, and again to the remaining sections: _ _ _ _ and . . . . - you end up creating little "Space Invader" -type images, i.e. "monsters".

____ ____
_ _ _ _
. . . .

You get the idea.

This iteration, creating a feedback again and again towards infinity seems a useless exercise in futility. You can always divide something ONE MORE TIME in mathematics.

But a strange thing occurred. Mandelbrot saw that this infinite complexity based on a simple pattern was PRECISELY how nature worked her [formerly] incomprehensible magic, making mountains, waves, etc. In fact, the first CGI world ever created for film was seen in Star Trek II: The Wrath of Kahn.

Every fanboy remembers the "Genesis Effect" demonstration video Kirk, Spock and McCoy saw when Dr. Marcus did her presentation, right?

Mandelbrot was directly responsible for that. That's how incredible this discovery was for understanding nature's geometry.

As the film by NOVA explained, it showed how this way of looking at fractal geometry made it possible to measure the very irregular shapes - like the coastline of England - with the strange effect that by going smaller in our measurements - getting more and more precise - actually seemed to enlarge the coastline! When you measure the coastline in smaller and smaller increments - counter-intuitively - it makes the coastline larger and larger by default. You see, this creates a maze of ins and outs, and if you measure every last section - with an infinite amount of reduction - you end up spiraling into infinity as you dig deeper and deeper.

So a finite coastline can have an infinite shore. You have to decide where to stop, how "deep" you want to go.

And since this WAS a theology meets mathematics conference, a thought came to me: this is how God works in nature, in the spirit, in the incarnation, in everything.

No wonder Jesus put so much emphasis on guarding your heart and watching how you view other people: "If the light within you is darkness, how GREAT is that darkness!"

We are creatures of infinite imagination; I do not mean infinite creativity. We all hit dry spells and brick walls and all that. But we cannot stop working problems or people over in our minds. It is fantastically hard to do so.

We calculate - and "are calculating". We worry and reason and fear and fight and love - we only get to decide WHICH direction we will aim. We cannot stay still. As one man said "Living things grow. Only dead things stay the same."

Frighteningly, we can spiral inward - an emotional/spiritual Mandelbrot set. When you see a homeless guy repeating himself on the street corner, I think that is what you have run into.

When you see a woman crying over the loss of her child to something good - say little Suzy got married - you are witnessing the same thing. Her mother loop has been disabled. She is grieving and happy at the same time.

I have only experienced one Person who could change my re-iterations so I could begin again: Jesus.

And would it not be funny to discover that an infinite God became a finite Man by some method of spiritual geometry? To undo our runaway fractals?

It can happen in mathematics. We are told it happened in history - created by nature's very God.

I think that amazing.

Maybe you will too when you think about it.


No comments:

Post a Comment