[bill_from_tampa]

> If numbers are finite and limited in their precision, then nature itself is inherently imprecise, and thus unpredictable.

Is this not what Planck's constant implies? We can only know position and/or motion to a certain degree, and not exactly? Does not quantum mechanics already include this idea?

[Koshkin]

How does discreetness imply imprecision and randomness? If anything, it should indicate some degree of certainty.

[akira2501]

I'm an amateur, but I like to think about this:

If spacetime is quantized, then the speed of light would be 1 planck length / 1 planck time. Assuming spacetime is actually quantized to that metric, we can then ask: How does something move at 2/3c? Or two discrete planck lenghts in 3 discrete planck times?

In one instance it could be:

t=0,x=0, t=1,x=0, t=2,x=1, t=3,x=2

It could also do:

t=0,x=0, t=1,x=1, t=2,x=1, t=3,x=2.

It implies a hidden variable, or at the very least a hidden phase of some sort. All sorts of oddness abounds when you consider all velocities are then quantized fractional values of c.

[Ono-Sendai]

If you can have real numbers at each spacetime point (as opposed to boolean values) then you can easily get a speed less than c. This is similar to simulating the wave equation on a grid on a computer.

[tines]

But then your 2/3c is an average, it's not the real speed of the object at any actual instant.

[hinoki]

It depends on your rules for rounding I think.

[viklove]

You're thinking of the Heisenberg Uncertainty Principle