Not necessarily fortunately.

The one I brought up above (I just looked it up) is apparently called the "dichotomy paradox", which is apparently a problem with a non-discrete universe.

If the units are discrete, then there is another paradox, which seems actually more intractable to me: the "arrow paradox." Suppose that time takes place in discrete increments. And then you have two arrows, one moving and the other at rest. If you look at any one of those discrete increments, what will look different about the two? If nothing looks different (since it is a moment of time), then how does one know that it should move and the other that it should stay still?

One solution that occurs to me is that there is a projector somewhere, and the projector is mapping the motion onto a screen. The problem is, how does the projector move?

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As above, so below