So, my friend Josh and I were at our coffee-shop talking over Stumptown-filled mugs. Those conversations are workshops for us, and in this one we ended up talking about, after making another interesting arc through psychoanalysis, Zeno’s Paradox of Achilles and the Tortoise. Josh offered a “solution.”
For those who don’t know it, in this story Achilles and a tortoise get in a race. The tortoise requests a bit of a head-start, as Achilles is surely faster than he is. However, Achilles realizes that (or the tortoise comes around to explain that) if he gives the tortoise a head-start, to catch up to him he will have to traverse half the distance already between him and the tortoise. What’s more is that this problem is built into every (half-) point conceivable in the whole situation– Achilles would have to go half of half of half of half ad infinitum. In the end, Achilles concedes the race to the tortoise before even attempting it.
The paradoxical point is that movement is impossible, in theory. Josh had thought of a solution a while ago, long before even I was interested in (Lacanian) psychoanalysis, which is to make one’s aim an infinitesimal point just beyond where you’re “really” going. Seeing this as an opportunity to make an explanatory point with an example given to me, I jumped nearly out of my seat and said, “that’s it right there– that’s the objet petit a!” This is not a solution, in the sense that it rids us of Zeno’s paradox, but that it allows us to displace the problem in a way that makes it conventionally not the same problem, if a problem at all.
I had figured that Zizek, if not other Lacanians before him, already made this connection. I looked back in my copy of Looking Awry: An Introduction to Lacan through Popular Culture, and sure enough Zizek opens the book with a strikingly similar analysis. Zizek’s point in Looking Awry is that the tortoise is this impossible object that, by the logic of the drive, we constantly encircle but never actually achieve. I’d like to make a different point though.
What we get from the paradox as Zeno gave it to us is that movement is suppose to be impossible. The impossible quality is in movement itself. I immediately recognized in my friend’s “solution” that what he was doing, and I explained this to him, was moving the impossibility out of movement itself and into an object. The tortoise could be this object, which is Zizek’s position, but for a different reason. As I see it, this solution explains the logic of the impossible kernel of the Real as the condition of the possibility of “reality.” In this sense, Zeno is quite literally correct when he seeks to imply that movement is an illusion. This illusion is what Lacan would call fantasy.
What we should also get from Zeno, then, aside from classical and otherwise interpretations, is that it prompts us to give a solution that is (or allows us to better grasp) precisely the logic of fantasy itself. It is not simply that the tortoise is an object with which it is impossible to meet, but that Achilles really can match and exceed the tortoise insofar as he is aiming beyond it and, presumably, the finish line too. If the aim is the tortoise, as Zizek explains it, then of course Achilles will never attain it lest all he attains is its always-already lost status and it just disappears.
This taken qua the logic of fantasy means that “reality” as we know it requires an impossible kernel of the Real in order to exist. This is why I don’t think Zizek’s interpretation really goes the distance, so to speak, because we can grasp an even more elementary principle if we take the position that movement or reality– i.e. Symbolic contrivance– is possible only insofar as we displace its Real impossibility into an impossible object that, by definition, exceeds our conventional, conscious aim.
We should be cautious of the naive realist’s interpretation of this logic though, for whom it would seem that this logic is supposed to be a conscious one we employ in a pragmatic fashion. The logic of fantasy is not conscious, except for the few of us who have traversed it.