Modeling

(By Andrew MacKie-Mason)

I'm going to step back from my usual political and legal topics for a moment to talk about a philosophical question that's been bothering me.

Determinism is the idea that the world operates based upon fixed and predictable rules. In other words, everything is predictable, given enough knowledge. Of course, practically, we cannot predict the future. For determinists, however, this is a merely practical problem, not a theoretical one. The system is so complex that we cannot comprehend it at a detailed enough level to predict it accurately.

Laplace's demon is the embodiment of the determinist-predictability idea. The demon is a hypothetical intelligence vast enough to comprehend every single little detail of the universe. It would then be able to predict the flow of events based on deterministic cause-and-effect.

The usually accepted problem with Laplace's demon is that it would have to be larger than the universe and separate from it. This is based upon the idea that you cannot model a system perfectly with a less complex system. Modeling the universe would take something at least encompassing the size of the universe, because if you "compress" the data down, you'll lose some, and then the cause-and-effect calculations will not be infallible.

Laplace's demon would have to also be separate from the system because nothing can fully understand itself. This is based on the same theory as above: it would require your brain (at least) to even fully understand your brain, let alone any other part of your body. Because of this, Laplace's demon is treated as an interesting thought experiment but not actually a possibility.

I would like to propose a possible way that Laplace's demon could exist, within the universe. In fact, the demon could be any one of us.

The arguments against the demon implicitly assume that the universe is a collection of extremely small but discreet particles. "Bits," if you will. If that is true, then it would indeed take one bit to model one bit, three hundred bits to model three hundred bits, and a googol bits to model a googol bits. However, that assumption does not necessarily hold.

Imagine, if you will, that the universe is comprised of matter that can be broken down into infinitesimally small pieces. There are an infinite number of these "pseudo-bits," and each pseudo-bit is infinitely small. Imagine, additionally, that the universe operates like a fractal.

Fractals, for those who don't know, are mathematical images that repeat a patter down to an infinitesimally small level. If you "zoom in" on a fractal, it retains its original pattern. (For a good interactive fractal, see this one.) What does this mean? It means that the fractal contains perfect models of itself that are "smaller" than the fractal itself. There is nothing to differentiate the fractal at a high level of magnification from the fractal at a lesser level of magnification.

If the universe operates as a fractal, then one could comprehend the entire thing (and thus predict the future) by looking to a smaller piece of it, not by trying to understand the universe at the human level.

In the more scientific community, the "universe as a fractal" idea is referred to as fractal cosmology. Just something to think about.

Note: This all assumes determinism. True randomness (or quantum indeterminacy) would change the game.