Here's an interesting argument which I would love to see developed by someone more informed about the relevant fields.
Modeling physical systems on discrete time would require iteratively applying some function which maps a given state of the universe to its successive state. This seems prima facie to make physical systems very difficult to model. To know the state of the universe in n moments, I would need to apply this function to the present state of the universe n times. What a headache!
But what if we learn that, due to Zeno's paradoxes or something, continuous time is metaphysically impossible? That would be most unfortunate. It means that we can figure out a priori that modeling physical systems is going to be nigh impossible.
Hold up. We can model physical systems, though. What's going on here?
Well, one explanation is that God "fudged the numbers." God chose a universe whose evolution across discrete time can still be modeled mathematically at the macroscopic scale, because God wants discoverable laws of nature.
So, to flesh out this argument, we need to show that:
1) Physical systems with discrete time will usually be hard to model (barring something like a God intervening).
2) Our universe operates with discrete time.
3) Our universe is not hard to model.
Discrete systems aren't usually harder to model than continuous systems. If anything they're generally simpler! We have studied difference equations as a discrete version of differential equations, and they require much less computational power to solve. We also actually use discrete time when modelling certain signals and there's a discrete version of the fourier transform for them, which is easier to compute than the continuous version!
ReplyDeleteYou don't need to apply a function n times to get the state of the universe n moments in time from now. Think about it like getting the nth term of the sequence 1,2,3,4,... sure, you could apply the function "add 1" n times, but there's a much simpler general formula: n.