The first class of the new semester began Monday (I’ve posted the reading list here); we discussed Euclid’s definitions and postulates and the first half of Lucretius’ On the Nature of Things. Some classmates have expressed how glad they are to begin with something as logical as Euclid as opposed to last semester plunging in with the Republic. While I’m hopeful about the forthcoming semester, I can’t say I share their enthusiasm. I enjoyed reading Lucretius, especially the first two sections, better than discussing him. The reason is that the thing I really enjoy about Lucretius is the juxtaposition of scientific earnestness with the sensibilities of a Latin poet. The in-class discussion gave an affect rather like if a class were to read A Wrinkle in Time, and then proceed to talk quite seriously about how the popular understanding of string theory affects people’s belief in the existence of God. My favorite quote so far:
Since the difference between the forms is finite, it is necessary that those forms which are similar be infinite in number, or the sum total of matter will be finite, which I have proved not to be the case, showing in my verses that the tiny bodies of matter from the infinite continue to hold together the totality of things by a continuous harness-team of blows from all sides. For whereas you see that certain animals are rather rare, and perceive that there is in them a less fertile nature, still in another region and place, and in remote lands, there may be many of this kind that replenish the number. So we see this especially among the four footed beasts in the case of snake-handed elephants. India is protected by an ivory wall of many thousands of these, so that it can never be deeply penetrated by an attack, so great is the supply of those beasts of which we see so few examples. (525-540)
Thus it is proved that there is an infinite number of each configuration of atom in the universe!
Proposition 1 of Euclid is how to draw an equilateral triangle beginning with a line segment. I wonder if computer programmers tend to like Euclid. It seems like they would, because between an action that involves measuring and moving something, and an action that involves perfect circles magically drawing themselves around points, he would prefer the latter every time (though I hear there’s one proposition where he resorts to flipping a triangle, that is no doubt an action of last resort). Having learned most of my geometry from crafts involving physical objects, such as making quilts, this is counter-intuitive. The easiest way to approximate an equilateral triangle would seem to be to replicate the line segment twice and then physically construct a triangle. Not being sloppy like myself, however, Euclid uses the line segment as the radius of two overlapping circles, and puts the top of the triangle where these circles touch. Since I imagine geometry as though I were trying to construct a physical object with as little difficulty as possible, I would avoid circles — indeed, all curves — unless I actually wanted a circle, because I immediately imagine trying to find a compass, draw a perfect circle, and then try to keep the edge of the curve (probably in the form of fabric) from distorting as I conducted the rest of the steps of Euclid’s proposition. In Socrates’ ideal city I would totally be a peasant.