We all enjoy a good paradox, right? Well, I thought I’d do a blog post on one particular philosophical paradox that I personally find to be quite – if you’ll forgive the term – cool. It’s the “arrow paradox”, first invented by Zeno (one of those clever Greek fellows) in an attempt to prove that movement is logically impossible – an idea that was the controversial brain child of Parmenides (another Greek). It’s a surprisingly persuasive argument, if you can get past the inherent counter-intuitiveness of it.
First, let’s imagine that we have two points; a point A and a point B.
Now, imagine an object moving from A to B. Traditionally, the example of an arrow fired from a bow is used – an archer fires the arrow from point A, aiming at a bullseye at point B. So far so good. However, basic logic dictates that before the arrow can reach point B, it must pass through a midpoint, M, halfway between A and B.
This is where things start to get a little tricky. You see, applying the exact same indisputable logic, we find that before the arrow can each this midpoint, it must first reach the midpoint between M and A. However, before it can reach that point it has to reach another midpoint, between this new halfway point and the archer, and before it reaches that point it has to reach yet another midpoint, and so on and so forth. It is possible to conceive of an infinite amount of points and midpoints separating A and B, and the arrow has to reach each point before it can advance to the next, which is impossible since the amount of points is infinite.
Therefore, it is logically impossible for the arrow to even start moving towards B. This same concept can be applied to any motion, like your hand moving from your hip to your face, or your finger scratching your butt. Thus, movement is logically impossible. Of course, that’s not the end of the story. It’s said that when Zeno first presented this paradox, Diogenes the Cynic simply stood up and moved, thus disproving the argument’s conclusion. Naturally, he didn’t actually disprove the argument properly by doing this, though I think his response corresponds quite closely to how most people react to the paradox. It is, as said, deeply counter-intuitive. But that doesn’t necessarily mean it’s false.
There are, however, more thorough ways to disprove the paradox. For instance, one might argue that there is a fundamental difference between an object that is in stasis and one that is in motion. The argument being, it makes sense to think of a stationary object as occupying a particular point in space, but an object in motion is moving between points, rather than moving through them. This doesn’t feel entirely convincing, but it is apparently also possible to disprove the paradox using maths. Unfortunately, I promised myself that I’d avoid maths as much as possible after finishing my exams, so if you want to find that particular solution, you’ll have to go elsewhere.
There is one funny thing about the paradox. If it worked, it would prove that time doesn’t move either. This is because you get the same problem popping up when you consider a measure of time, such as an hour (before you can have an hour you have to have half an hour, before that a quarter of an hour, etc. etc.). As Zeno’s paradoxes were designed to help prove Parmenides’ concept of Eternalism – the idea that nothing in the universe ever changes and that past, present and future are all essentially the same thing – this isn’t surprising. Anyway, while the paradox may be disputed, I’ve heard that most modern quantum physicists are firm adherents of Eternalism, for various complex reasons I don’t yet fully understand. So maybe there is some truth to it after all. It seems clear, either way, that the universe is a far stranger and more complicated place than we might think.
- Hay Festival 2012: Unlocking the secrets of the Universe (mytechnologyworld9.blogspot.com)
- Top 10 Pre-Socratic Philosophers (listverse.com)