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I think Stephen Wolfram fell in the trap, that any continuous dynamical system can be approximated by a discrete one. His position is a bit like claiming the fu
by yk 11y ago
I think Stephen Wolfram fell in the trap, that any continuous dynamical system can be approximated by a discrete one. His position is a bit like claiming the fundamental theory of the universe is Brainfuck. Proof: I can encode general relativity and quantum field theory in Brainfuck, at least to a arbitrary good approximation. The initial conditions are then just the program to simulate GR and QFT plus the initial conditions in more conventional physics. Thus the fundamental theory of the universe is Brainfuck. ( At least if Turing machines are the most powerful model of computation that can be implemented in our universe.)
- hcarvalhoalves 11y agoWhy would it be a "trap"? The uncertainty principle hints that something discrete may lie at the bottom. It's clear it's deliberate, not something you fall into due to naiveness. Also, Wolfram isn't the only one in this line of thinking, and this is a topic that rears it's head time and time again in the history of physics.
- yk 11y agoIt is a trap in the sense, that nothing he discusses is convincing me that it is any more than a simple application of a general theorem. ( See my example above, obviously we learn nothing about physics, we just shift the missing information from 'theory' to 'initial conditions.') So assuming a discreet space may be fruitful, but by itself is not a step forward.
- euyyn 11y ago> The uncertainty principle hints that something discrete may lie at the bottom. Not necessarily. The uncertainty principle is a direct consequence of some quantities being "the Fourier transform" of each other. You can't play a pure tone unless it extends infinitely in time, and vice versa: You can't play an infinitesimally short sound unless you ring all frequencies. That's all. And actually, if something discrete lies at the bottom of spacetime, the uncertainty principle implies that there's a maximum energy and a maximum momentum. For the same reason that there's a Nyquist frequency when sampling. So, if anything, our intuition that there aren't such maxima makes the uncertainty principle hint that there's nothing discrete underneath.