In the end, the simple rules yielding a complex output do not create complexity out of nothing, they channel complexity extracted from an external system
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Simple rules can generate great complexity. But that complexity only arises when you execute the rules. To do so, you need a physical computer -- a CPU, a brain -- of great complexity. No free lunch.
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Maybe this is sophistic, but it's a fun hypothesis when applied to the universe: however simple the laws of physics may turn out to be, whatever system is executing them (bringing the universe into existence) must have greater complexity than the output universe
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It's interesting to consider exceptions. Spin glass systems can have enormous complexity in their ground (and other low-temperature) states. One still needs dynamics to thermalize, but it can be quite generic.
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A (related) example is the emergence of fractionally-charged quasiparticles in fractional quantum Hall systems: https://en.wikipedia.org/wiki/Fractional_quantum_Hall_effect … It feels very much like something out of nothing.
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That was part of my point. But thermalization is a remarkably generic process; it's like almost any computer running almost any program will do.
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It's still got something of a free lunch feeling. Generically interact with a generic low-temp bath, voila, you can be in a remarkably complex low-temperature state.
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From a bayesian point of view, those exact same computations are a strikingly expensive lunch without strong simplifying assumptions. You're coarsing over a lot of complexity with language to make your point.
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I disagree: the Mandelbrot-set is extremely complex but arises from a single very simple rule and does not need any complex system which drives it. It is just a complex object existing on its own.
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Common type error. Mandelbrot set comp is undecidable even though there're small program to generate approximations of it. Leaving that aside,you can need arbitrarily large numbers to encode displacement and zoom of a section of the image. To compute it, powerful computer needed
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For complex patterns to emerge there is no need for a CPU or brain; only to perceive it. Locally updating cells are sufficient e g cellular automata. Indeed we could argue the opp-CPU/brain limits the complexity it can compute or and so increasing complexity implies lack of a CPU
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