Stephen Wolfram has written a fascinating book called A New Kind of Science, which describes the universe in terms of cellular automata, which are a long standing interest of his.
First let me say that Wolfram is undoubtedly one of the brightest minds of our generation. Had he lived a couple of centuries earlier he would probably have been one of those people reputed to know all that is known (an impossible standard these days). Having acknowledged that...
...I have one big question about the idea, and it's this: For as far back as we can tell, humans have described the physical world using as a model, essentially, the most complex thing they know at the time. They've also tended to assume, naively, that today's Most Complex Thing will never be surpassed in complexity. Consider:
In pre-history the most complex thing we knew was ourselves, so we explained the universe [earth, or some small corner of it] in terms of malicious gods and capricious spirits who were pretty much like us, except magically powerful. Sadly, many people still do -- but that's a topic for another day. (If you're reading this and you believe in something supernatural, then obviously I'm not talking about your profoundly-held spiritual beliefs. I'm talking about those other people and their irrational, crackpot beliefs in the wrong religion/magic/astrology/pyschics/ghosts/etc.)
When the greeks became mathematicians and, most notably, geometers, the universe [solar system] was understood as a complex problem in geometry. This world model persisted all the way up to Kepler, who believed that the positions of the then-known planets could be explained by nesting Platonic solids -- which makes so much more sense than that Ptolemaic nonsense about concentric crystal spheres!
The scientific revolution that included Newton, Copernicus, and Galileo spawned physical laws based in differential calculus, equations with (theoretically) precise solutions, and a universe described as the most complex piece of clockwork imaginable. The world, like maths and machines, was entirely predictable.
In the 19th century, with the rise of both statistical theory and the industrial revolution, it became fashionable to think of the universe in terms of thermodynamics (in other words, the most complex steam engine imaginable). While the physical laws were still deterministic, the behavior of a complex system (like, say, a universe) was really only understandable in statistically averaged ways. Out of this insight would eventually emerge non-linearity, chaos theory, and sytems that were theoretically predictable yet practically unpredictable. In particular, it became clear that some systems were inherently irreducible: they cannot be simulated by anything simpler than the system itself. (This came as something of a shock to physicists who, as a profession, like to reduce and simplify. These are people who, according to a popular joke, if asked to bet on a horse race would begin "Consider a perfectly spherical, hairless horse...").
In the 20th century we had the digital computer and, surprise, the idea that the universe could best be understood in terms of information theory. In other words, the universe is like the most complex computer imaginable. Or maybe even like a quantum computer, because those are even more complex.
Intriguingly, the history of quantum field theory neatly recapitulates the history above. Quantum mechanics started out as an essentially mechanical theory in which certain quantities needed to be quantized, for reasons then unexplained, to explain well-known experimental results, but not much else about it was particularly weird; it evolved into a theory based in statistical processes and probability and inherent uncertainty; and it is increasingly best understood as a theory about conservation of information rather than a theory about particles and forces. (This latter line of thought is at the root of much of Hawking's work, especially with regard to the physics of black holes, that suggest that the concept of Entropy, so fundamental to the 19th century thermodynamic view, is actually more deeply explained by Information).
And now we have a proposal that suggests that the universe is like cellular automata. The cellular automaton is a wonderful discovery, a construct built from transparently simple rules that can generate behavior so complex and unexpected that it is, for all practical purposes, unpredictable (and some cases, perhaps even formally undecidable). It combines the fundamental certainty of precise laws; the impossibility of predicting the behavior of an arbitrary starting point short of actually running the machine; and fascinating relations to information theory.
So... Maybe Wolfram does have has a unique insight into the how to describe the universe. If anybody is going to, it would probably be a singular mind like his.
Or perhaps Wolfram is merely the latest to model the universe in terms of the most complex thing we know. While it's always nice to understand the universe better, there's a decent possibility that the universe can't be adequately modeled by anything -- or at least, any one thing -- that is, by definition, within the Universe. I think Kurt Godel might have something to say about that...
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