Warning: Very geeky post follows. You have been warned!
I know very little about Turing machines.1 In fact, all I know about them can be summed up in this sentence:
OK. I exaggerated. I know one more thing about Turing machines. I know that they can perform only very, very simple computations.
So who cares? Well, I didn't particularly care until I ran across this post from Daniel Lemire. He introduced me to something called the strong Church-Turing thesis, which claims that the universe is a Turing machine.3
OK. That's fairly wierd, but get this. If the strong Church-Turing thesis is correct, and so far no one has produced a counter example, then
I know very little about Turing machines.1 In fact, all I know about them can be summed up in this sentence:
A universal Turing machine is an abstract computational device that can perform any computation that can be performed by any actual or theoretical computational device.2
OK. I exaggerated. I know one more thing about Turing machines. I know that they can perform only very, very simple computations.
So who cares? Well, I didn't particularly care until I ran across this post from Daniel Lemire. He introduced me to something called the strong Church-Turing thesis, which claims that the universe is a Turing machine.3
OK. That's fairly wierd, but get this. If the strong Church-Turing thesis is correct, and so far no one has produced a counter example, then
I'm not quite sure what to make of that, and I'm not sure I like the idea that I'm living in a discrete computer simulation, but it's certainly a thought provoking idea.4
- There is no problem solvable by a human brain that cannot be solved by a machine. In particular, creativity and intuition are computable. Philosophically, we have no soul (not anymore than a PC).
- We all live within a discrete computer simulation. Physics is digital. Continuous functions (such as f(x)=sin(x)) are approximations to the discrete functions governing nature, and not the reverse. We all live in the Matrix.
1I told you this was going to be geeky.
2At least I think I know that. That's off the top of my head, not copied from Wikipedia.
3Where does my geekiness quotient stand now?
4As I said, I know next to nothing about Turing machines (which is why this comment is in a footnote rather than in the main text), but before atheists get all happy about that the strong version of the Church-Turing thesis (svCT, for short) rules out the existence of god, let me throw in a wet blanket. If svCT is correct, it applies only to empirical observations about the universe, i.e., the universe that is accessible to our senses, our instruments, or both. There may be good philosophical reasons to claim that only the empirical universe exists. That would be consistent with at least some versions of the philosophical position known as scientific realism, but scientific realism isn't the only reasonable philosophical attitude towards scientific theories that's out there. Bas van Fraassen, for example, put forward an influential idea known as constructive empiricism, which makes no claim that the entities in scientific theories are "real", only that they are useful. A constructive empiricist could accept svCT and simultaneously accept the existence of god, so long as the god whose existence (s)he accepted played no role in the empirical universe.
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