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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:

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

1. 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).
2. 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.

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