I suppose that the movement of the contestants would be created algorithmically. Eg. let's say that in 1 unit of time the Tortoise (T) moves forward 1 unit of distance while Achilles moves forward 10 units.

Starting at x the sequence of positions of T are given by x (next) = x+1 and the position of A are given by x (next) = x+10.

(OK so far?)

If we give T a head start of 100 units of length then presumably in this case the programme would show A whizzing past T with no problem.

But what if the units of time and distance are defined as fundamental, ie. each unit of time is an 'instant', and each unit of distance is a 'Planck length' (or some equivalent).

In this case the Tortoise couldn't go any slower, since it is racing at one fundamental quanta of space in one fundamental quanta of time.

Under these conditions it seems that the programme can never specify the time or position at which A and T are equal. As a result A passes T

*during*an instant, which seems to be impossible.

Is this a more modern version of what Zeno was trying to say, (that motion cannot be algorithmic), or have I got it wrong somewhere?