For this to work, I think the person has to consciously halve the distances and not be running. If he runs, his running force will surely overcome the tiny atomic repulsion forces. (Just like my fingers do as I strike these keys.)
But if a person consciously halves the distances, he should be quickly institutionalized. (But will he ever make it to the asylum?)

My brain just hurt.

The first time I heard this example is was given with a wheel (or maybe 2 wheels) and that made it work well as wheel progress across distance pretty constantly.

ie. you don't make progressively smaller steps while walking, but roll a bit less each time.

but yes. a scientist needs to explain to me how this problem gets overcome before I can ever feel comfortable again.

We assume space is continuous. But if it's discrete then we can't continue the process forever. At some point, the atoms "jump" from a point close to the wall, directly to the wall.

How about pushing a beer "pi" centimetres away from the edge of the bar. First move it 3cm. Then 1mm. Then .4mm. Pi is a non-terminating decimal, so this process will never finish.

Anyhow, the first problem gets overcome by running into a wall. Feel the pain.

the anwer is, that you will reach the wall. when you keep halving the distance there will be a point where the distance is unmeasurable in human scale.

There seems to be two points that you (or the author of the book) are conflating. The 1st is whether an infinite summation can be finite. The second is whether you can ever be zero distance away from something. For the first, the answer is yes. The sum of 1/x where you let x go from 2 to infinity is 1. It's simple to show: http://en.wikipedia.org/wiki/Geometric_progression. So while it will take you infinite time to reach the wall if you take steps of 1/x, you won't so it won't. For the second the answer depends on your definition of "something". If you are talking on the quantum scale then a distance between you and something is meaningless, since quantum things have no edge. If you are talking on the macro scale then of course you can be zero distance from the wall. That's when you're touching it.

Correction: 1/(2x) from 1 to infinity.

All of these scientific arguments are fine, but I think there is a bigger problem.

"As you run, you halve the distance to the wall, then halve it again, and so on."

Just because the distance is half of what it was doesn't mean that you were consciously halving it. You were probably just running, and the halving was just a natural effect. It would be like thinking that a cake that takes an hour to bake would never finish because the time keeps halving and can never reach zero.

It's about causality. At least that's my ignorant opinion.

In my humble opinion, it is scientifically provable that the paradox isn't really a paradox, and Master P has proven it above.

Algebra is a funny thing. If you make it the starting point, everything makes sense. However if you start at the opposite point of it, suddenly everything seems like a paradox.

it's like measuring the arc of a jizz shot