iceaura, I'm more interested in what you didn't say than what you did. You chose not to engage on your bijection argument. May I take it that you concede my point that you said nothing meaningful when you claimed that bijection preserves computability? And now that I think of it, what has become of your earlier claim that TMs might somehow be construed to compute noncomputable phenomena? You dropped that topic as well. May I assume you concede my point that the definition of computable is whatever a TM can do? I don't pretend to understand the universe or even much physics. But I am justified in pushing back on things I do understand, and these two points got my attention in the extreme. I would like closure on them. ps -- A third missing topic. How can a computation create time in the universe? That claim really puzzles me. Ah, you are confusing physics with metaphysics. When we say that QM says that everything acts as if it were a probability wave, with a nonzero probability of showing up anywhere in the universe; that is a statement of physics. When we make a claim about what that really means, we are doing metaphysics. Bohr - Einstein debates, Copenhagen versus many worlds, etc. You are 100% correct that our current theory of physics says that the world acts like a casino. But you are then making a metaphysical claim about how the world actually works. Can you see this distinction? Billiard balls are observed to do one thing and not another. Why? Can you see that any claim as to why is a metaphysical speculation and not a fact of physics, even a historically contingent one? It's amazing how people accuse others of doing exactly what they do themselves. You think the universe itself is an approximation ... to something. I confess I do not understand the meaning of that statement. Yes I agree with that. The duplication idea is more of a thought experiment. Especially in the context of so much Sci Fi, like the matter transporter of Star Trek. How exactly do they duplicate minds? It's a counterexample to the idea that human made X must work the same as natural X. X being either mind or flight. No no no, that is a metaphysical speculation. If you were to speak accurately, you would say: "It physically APPEARS to be probabilistic." You have no way of knowing if this is how the world works, or if this is only how our theory works. The experts in quantum theory say, "Shut up and calculate." They abstain from interpretation altogether. As, if you don't mind my saying, should you. Chaos is actually an entirely different phenomenon, relating to the inability of practical computations to predict the future even given total knowledge of the state of the universe at some time in the past. I have understood you to be repeatedly claiming the opposite. Could be me, could be your exposition. You have been claiming that the universe is an approximation. Well sure, a game programmer can simulate Newtonian gravity "well enough." But never exactly for all time. And the accumulated errors eventually make the emulation wildly inaccurate. How can you recognize mental illness in machines? And for that matter, how can you recognize it in humans? Surely you are aware that the DSM is as much a political document as a medical one. The premise of this thread is nonsense, which is why I feel justified in ignoring it and focussing on areas where I feel I can correct some misunderstandings of what computations can do.