Order vs. Randomness

[Rayaan]

This is simply an argument from incredulity, and thus its conclusion is fallacious.

Then what exactly does the Game of Life explain about the physical universe, aside from being a demonstration of complexity emerging from simple rules?

Just some cellular automatons moving around on a screen with no knowledge, feelings, awareness, nothing ...

In terms of the Kolmogorov-Chaitin concept of information, the measure of information is how tightly you can make the simplest expression which, when uncompressed, yields the original data set.

That sounds correct.

To put it in another way, the Kolmogorov-Chaitin complexity (also called algorithmic information or algorithmic entropy) is the size in bits for the shortest program that would yield the original uncompressed data set (or object) in question. A greater compressibility means that it has a greater simplicity behind it, while a lesser compressibility would mean that it is more complex than simple.

"Sophistication" is not a concept in information that I am familiar with, but since you keep appealing to Chaitin and compressibility, this would seem to be the appropriate guess as to which framework you're using. (If you prefer Shannon and informational entropy, correct my misapprehension.)

"Sophistication," "elegance," "beauty," "subtleness," whatever you call it ... these are all more or less subjective qualities that are often used by mathematicians when they refer to something that maximizes some measure of utility while minimizing the information content. In the same view, computer scientist Jürgen Schmidhuber in the following paper explains how compressibility is a key aspect of beauty and of things like art, music, science, creativity, novelty, jokes, etc., which are all complex.

Driven by Compression Progress: A Simple Principle Explains Essential Aspects of Subjective Beauty, Novelty, Surprise, Interestingness, Attention, Curiosity, Creativity, Art, Science, Music, Jokes

I argue that data becomes temporarily interesting by itself to some self-improving, but computationally limited, subjective observer once he learns to predict or compress the data in a better way, thus making it subjectively simpler and more beautiful. Curiosity is the desire to create or discover more non-random, non-arbitrary, regular data that is novel and surprising not in the traditional sense of Boltzmann and Shannon but in the sense that it allows for compression progress because its regularity was not yet known. This drive maximizes interestingness, the first derivative of subjective beauty or compressibility, that is, the steepness of the learning curve. It motivates exploring infants, pure mathematicians, composers, artists, dancers, comedians, yourself, and (since 1990) artificial systems.

http://arxiv.org/abs/0812.4360

I think that while the rules are certainly an important component of the information in the universe, the number of potential states is also a factor in determining how much total information is present; thus you can't just ignore the size of the universe as a part of what allows for such immense complexity because in doing so, you are simply discarding information content because it is inconvenient to your argument.

I haven't discarded information content nor the size of the universe, but essentially my point was that information - or even an infinite amount of information - without the existence of underlying rules (or programs) to control their future interactions would never be able to produce localized complexity all by themselves. Therefore, the rules are not just an important component of information but they are an indispensable component with regards to how information behaves (or to what is generally known as "computation" or "information processing").

As best I can tell, what you're suggesting is that certain simplicities are themselves possessed of inherent complexity. Beyond the meaning inherent in the Kolmogorov-Chaitin definition of information, this idea seems incoherent.

The Kolmogorov-Chaitin definition of information doesn't actually have an operational definition of what "simplicity" is. It is just a mathematical method of measuring the amount of complexity of a given data set or output which relies on how much it can be compressed (or simplified) in terms of the algorithmic information content. It has more to do with quantity than quality, so the idea that simplicities themselves possess an inherent complexity (in a qualitative/utility sense) is not necessarily in contradiction with such a definition.

Chaitin himself acknowledges that the practical incalculability of a data does not necessarily mean that it is truly random. So the "randomness" of any particular case is actually impossible to prove or disprove. There still may be an underlying order behind such seeming randomness, which would make them sophistacatedly simple.

There are a few other objections to the Kolmogorov-Chaitin concept of information when it comes to defining and measuring simplicity, one of them being that the process of data compression itself is a highly complex process since there are many different ways to do it (see Simplicity in the Philosophy of Science).

Data compression brings about analytic simplicity but only at the expense of being a complex phenomenon itself since it is inherently a manifestation of sophisticated "patterns" in spacetime that make up what we subjectively experience as "thoughts" and "comprehension." And that, once again, shows the paradoxical nature of simplicity.