Monday, July 14, 2008

The Blended Mouse

In several of the talks here at GECCO, the issue of complexity has come up. In one talk I just listened to, the speaker discussed three general measures of complexity:

1) Shannon Entropy, or degree of uncertainty
2) Kolmogorov complexity, or the amount of description needed to fully specify something
3) Functional complexity, or how complex its interactions with the environment are

He argued that functional complexity should be kept separate from other measures.

But here's one strange example. Let's say you take a mouse. It has a high degree of regularity in its morphology. It's bilaterally symmetric, hierarchical, and highly modular. Now, if you took that mouse and dropped it in a blender, so that its molecules were distributed randomly in space, by the first two measures above, that blended mouse would be more complex than the intact mouse. However, its functional complexity would be much lower (i.e., a live mouse can run around and do lots of things that a blended mouse can't).

For the things we're interested in either understanding or engineering, I think excluding functional complexity is probably wrong.


Philip said...

I think the mouse would favor the definition of complexity least likely to lead to its placement in a blender.

I'm not sure the blended mouse is more complex based on any of the measures. You don't know where its parts will wind up once blended, but once you do you know they're not going anywhere - not so with a live mouse. And "a mostly static pile of mouse parts" doesn't take long to specify.

Philip said...

Your post reminded me of this video:

Laurie said... why did you have to post a picture of a cute mouse when talking about sticking it in a blender? You could have at least put up a pic of an ugly, potentially-bubonic-plague-infected one so I wouldn't feel so bad.
Poor mouse.

Derek James said...

He is cute, isn't he?

Derek James said...

Philip, you can't define the blended mouse as "a static pile of mouse parts" according to Kolmogorov complexit, any more than you can define a random string of 1s and 0s as just "a random string of 1s and 0s". The description must be sufficient to precisely reproduce the entity.

If the blending distributes all the mouse parts uniformly, that might actually decrease its complexity. But if the parts are distributed randomly, that would increase the complexity, because it would require more description to specify exactly how to reproduce such an entity, and there would be a lot less redundancy and regularity in the randomly blended mouse.

Philip said...

If that's the case, I guess you're right. Seems like a silly metric though. You can apply that to anything - blowing up a house makes it more complex? Plus, it's completely dependent on shared knowledge of the 2 communicating parties. The description length is much shorter if you already know what a mouse is, or hair, a tail, ears, blood, molecules, atoms ... how specific do you have to get?

Kenny Wyland said...

LOL... I was just about to post the same comment that Laurie did...

Was the blended mouse your example or an example brought up at the conference?

Derek James said...

Nah, it was my example. You come up will all sorts of shit while sitting in talks.

Kenny Wyland said...

I love it.