Zeno sequences and discrete space-time

I heard a paper today defending discrete space-time. I'm not totally clear on the issue, but the guy mentioned some fun puzzles to think about. I'm sure there are other ways out of these, but one way the guy suggested was to just think that space and time (or space-time) are discrete, meaning there are smallest units of space and time.

Impenetrable walls:

Imagine you have a bomb in your hand, and want to throw it. Unfortunately, there is a sequence of walls in front of you. At 50 feet in front of you, there is an impenetrable wall that is 5 ft. thick. At 25 feet in front of you, there is another impenetrable wall that is 2.5 ft thick. At 12.5 feet in front of you...you get the idea. So, these walls come right up to the tip of your nose, but do not touch it. So, if you throw the bomb, it looks like it's going to bounce off and come back to you. But, it doesn't bounce off any wall. This is because for any wall you pick, there's one between the tip of your nose and it that it would bounce off of first.

Ninjas:

Imagine there is an infinitely large group of ninjas who always succeed in killing their target. But, each ninja is reluctant to be responsible for the target's death. So, the first ninja says "If he isn't dead at 1pm, I'm going to kill him." The next ninja says "If he isn't dead at 12:30pm, I'm going to kill him." The third ninja says "If he isn't dead at 12:15pm, I'm going to kill him." And so on. So, at 12 noon, the target is alive. But, for any arbitrarily short time after that, he is dead. The problem is that no ninja killed him. This is because for any ninja you pick, there is always a ninja that would have killed the target before that ninja got the chance.


Thinking that space and time are discrete is supposed to help with this. If space is discrete, then there really is a smallest distance from your nose, and the wall at that position will be the one that stops the tennis ball. If time is discrete, there really is a smallest amount of time past 12 noon, and the ninja scheduled to kill the target at that time is the one who kills him.

Anyway, that's the idea.