(I’d like to present some more of my answers to philisophical questions, mainly because it saves me the trouble of coming up with a new idea. This week: Zeno’s Paradoxes, suggested by alert reader Djcian and lifted unashamedly from this Wikipedia article.)
1. Suppose Homer wants to catch a stationary bus. Before he can get there, he must get halfway there. Before he can get halfway there, he must get a quarter of the way there. Before traveling a quarter, he must travel one-eighth; before an eighth, one-sixteenth; and so on. This description requires one to complete an infinite number of tasks, which Zeno maintains is an impossibility.
The explanation for this one seems fairly simple. I’ve ridden on quite a few buses in my time, and passengers always seem to regard them with a sort of blank contempt. Trash is left everywhere, exchanges of witticisms questioning the opponents maternal figure are engraved on the backs of seats alongside contact information of a dubious nature, small piles of debris gather in corners and eventually support local crops, and an astonishingly large number of farm animals earn front-row seats. Eventually the amount of dirt increases to the point where it becomes integrated into the buses molecular structure, whereupon a sort of exoskeleton develops that usually manifests itself as vandalised movie advertisements. Obviously the buses of the world eventually became so filthy that it became physically impossible to become dirtier, and the laws of physics accordingly restructured themselves so it became impossible for anybody to board a bus.
The obvious way around this paradox would simply be to never leave the bus. I’m going to be conducting a few experiments involving a novelty giant slingshot, but I’m pretty sure this thing is ironclad: there is no way to reach a bus under any circumstances. Therefore, if you do manage to get on a bus, I advise you to stay on it: the resulting fracture to the space-time continuum will probably propel the bus at least a few feet. If the glowing lights outside your window stop and you see a British man in an oddly-placed telephone booth, you’re probably safe.
2. In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 metres, for example. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 metres, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 metres. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise.
Now this one is obviously false. The hare beat the tortoise in that one children’s story, after all. Yes, I know you were probably taught the “Slow and steady wins the race version”, but that’s pure propaganda. The hare actually won the race in question quite handily, because, y’know, tortoise. He went on to what would have been a successful career in the athletics and breakfast cereal mascot industries. Unfortunately, the tortoise didn’t fare so well. His mind simply couldn’t take the humiliation, and he murdered the hare in cold blood. The “tortoise wins” story was just a fabrication made up to appease him long enough for the authorities to place him in a mental institution. I still have no idea why we teach this story to children.
So why isn’t Achilles passing the tortoise? Simple. Achilles isn’t an idiot.
3. For motion to occur, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one (durationless) instant of time, the arrow is neither moving to where it is, nor to where it is not. If everything is motionless at every instant, and time is entirely composed of instants, then motion is impossible.
This requires a complete rethinking of our current understanding of both time and arrows. Specifically, I propose that time is made out of arrows. Think about it. Time goes somewhere. Arrows usually go somewhere. Therefore, time is usually arrows. Ergo, the arrow isn’t moving because it’s lazy and its cousin Time doesn’t have enough of a spine to tell it to get a job.
Even if this isn’t true, I say we shoot an arrow at a bus and see what happens.