How would you answer this thought experiment?

Question

Assume you have a small robot on wheels, and that it has infinite computing capabilities and infinitely fast processing. You program it to move 6 inches in 30 seconds, and then to repeatedly move 1/2 the previous distance in 1/2 the previous time, therefore going
3 inches in 15 seconds
1.5 inches in 7.5 seconds, etc.
Assuming (due to its infinite memory and speed) that it never experienced any computing errors, then it would never slow down, never stop, but never make it to the 1-foot mark.
What would happen?

Answer 1

nothing would happen except it would constantly keep dividing the distance to zero in half - forever. Same as a formula that approches zero but can never reach it, the slope of the curve goes along the axis forever never able to get to zero.

However due to mechcanical limits after a point it would look as if the robot was standing still as motors can not make movements that small.

Answer 2

I might point out that the robot wouldn't get any faster, or slower. It's moving at the same velocity in each of your legs:

6/30=1/5 in/s
3/15=1/5 in/s
1.5/7.75 = 1/5 in/s

So on and so forth. As far as the thought experiments go, since it has a constant velocity of 1/5 in/s it would cover a foot in 12/5 seconds. If you want to get really technical, do the infinite sum, you'll find the same thing. The thing is that you're trying to subdivide a constant interval and then put it back together. The fact of the matter is that no matter how you describe it, I can describe it in a way that it takes a finite amount of time, and both representations are correct, therefore, the result of my representation is probably the same as yours.

You may be referring to Zeno's Paradox which, while is mathematically true, is not *physically* relevant, mainly because we can't discern pointlike movement over a set of measure zero.

Answer 3

To the external observer it woulf trod allong withough problem.
To the computer it would in fact begin to need to make an infinite number of calculations, and then subsequently an greater than infinite number of calculations.

You "just pretent it can do this" then becomes less than trivial to the answer so you get this:

EITHER:

A) It breaks down due to computer error because letrs face it you can't do an infinite number of calcs

Or

B) As you've defined in you problem it is able to do, it actually performs an infinite number of calcs.

Answer 4

I believe it wouldn't move anywhere, you would put it into an infinite loop

Answer 5

It would ultimately reach across every dimension and go beyond time. At that point ---you would invent it.