“Nothing annihilates like the nothing,” as Heidegger reportedly said, and I’m pretty sure some of my brain cells have been annihilated by Aristotle’s examination of the non-existence of the nothing, AKA “void.” All morning I was dreaming about an enclosed spherical universe, and it was about as close to being a bad dream as I can remember from my adult life. When my brain resumed functioning more or less normally I thought I had an answer to why the math and science seminar has been so much more mind-bending than the other classes I’ve had here.
The thing about Aristotle’s Physics is that he’s living in an alternate reality wherein elements are continuous rather than atomic, have a natural motion residing in themselves and a natural place they’re trying to get to rather than a center of gravity, and an enclosed, spherical limit with planets and stars moving in bands around the outer edges. In that universe void is impossible. So when he says void and I immediately start thinking about the spaces between the parts of an atom or between molecules or in outer space, and then he says that this is impossible and then gives reasons for this impossibility it hurts my brain, because I’m so used to the way we imagine the world to be, and so unused to the way A imagines it. Perhaps that’s the point of our class: ways in which the universe can and can’t be supposed to exist based upon logic and observation.
Time in A’s universe is much like time in ours: confusing, but in a familiar way. If I remember correctly time for A is not a separate thing, as though it had being in itself, but is rather an attribute of motion, and is measured in relation to motions, as of the Sun and moon, and is itself the measure of motions, as fast or slow, taking up such an amount of time, and so on. He likens the moment, the “now” as it’s usually translated, to a point on a line; the point itself has no substance — no part, as Euclid says — and so a continuous line is not simply a great many points, as though it had been drawn by an ink jet printer, but something else, and time is not simply a collection of “nows,” but is rather continuous, and continuity is difficult to make an account of, since the human mind tends to want to number things and divide them into discrete units. Indeed, for A without that ability to divide and number time as he means it would not exist, but only motion. That, however, was a very sloppy account, so don’t take my word for it.
In Euclid we are to Prop 13, and can now make right angles. Hooray! As it happens it’s possible to know that you have right angles with nothing but straight lines and circles, without any units of measurement. It’s all about proving various lines and angles equal to each other.