Monday, October 25, 2010

From scratch: algorithmic complexity

I feel like reiterating a point from my last post. The code that describes a human being has very little impact on the actual complexity of a mature human being. Here's a math example for you:

Circumference divided by diameter.

Those four words encode the infinite number of digits of pi (perhaps you've seen videos of a 10th grader reciting it out to 10 thousand digits). Four words precisely and uniquely defines an object of infinite length, which has an infinite amount of data in it. The length of that description is called Kolmogorov complexity, or algorithmic complexity.

You can write a finite length computer program (less than 100 lines of code) that will calculate pi out to arbitrary length. It will run on its own without any additional input, and spit out millions and millions of digits. Human beings, while inside the womb, develop the same way! That genetic code of the baby will unfold itself and generate something far more complex: bones, muscles, organs, integrated nervous system, brain, blood vessels, all of it.

(Heck, we're all probably described in the digits of Pi somewhere. Infinity is a funny thing.)

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