My favorite part of Lucretius’ theoretical apparatus in De rerum natura (but something I’ve had a hard time getting students interested in) is his theory of time. Notoriously, Lucretius is a realist about the present time but not about the past and the future; he considers any historical statement to be about eventa, configurations of atoms which have passed away and no longer exist even though the atomic substrate on which they were formed is, of course, eternal. This is cool, but the really puzzling thing about Lucretian time-theory is that he represents the passage of time as a falling-downward in space. Everything that exists has been “falling down” forever, through an infinite void, and the various “presents” that have existed are conjunctions of atoms at particular points in this downward course.
The only way to parse this meaningfully, I think, is to understand Lucretius as identifying time, not with an independent fourth dimension, but which the dimension of verticality: his universe is three-, not four-dimensional. I used to spend a lot of time worrying about how this would work. Was it really a thinkable thought to treat time as identical with one of the three dimensions of space? Mathematically, the conversion was possible – but only if one or more of the spatial dimensions were taken to be “granular,” which is to say discontinuous and measured on a number-line that had a cardinality no greater than aleph-0. I’ll write out the argument someday, when I’ve figured out how to put mathy stuff into wordpress.
In any case, I couldn’t find any evidence in the DRN that Lucretius holds such a position. He does of course hold something like it for material objects, of which the atoms are discrete chunks, but everything in the poem suggests he considers the void (or space) to be continuous. Having just read an interesting article by D. L. Dusenbury (“New Light on Time,” forthcoming in Studia Patristica) which argues for a certain granularity in Augustine’s notion of time, in part on the basis of Lucretian parallels, and which shows that Augustine treated time in a spatial way, I wonder if I wasn’t onto something before. If I was, though, then I think the relevant granularity has to inhere, not in Lucretian physics, but in the Latin language itself.
I posted here a few days ago about the absence of a specialized depth-dimension in some basic fields of Latin vocabulary. If we suppose that the world does inescapably contain verticality, this raises a phenomenological question: how would a Latin-speaker have experienced this verticality without a fully-articulated three-dimensional language in which to think or express it? One conceptual possibility, suggested by elementary phenomena like the sky and multi-story buildings (which go far back in Roman history if Livy is to be believed), is that they might have thought of the world as a layered stack of two-dimensional planes. Latin does, after all, have plenty of words for height-ranking; perhaps these could have done duty in place of words for depth.
If that’s true, then the vertical dimension is exactly the one that’s discontinuous, and Lucretius’ transposition of time onto this dimension becomes thinkable (although not standard for Romans, who seem to have conceptualized time as a line on which the speaker stands, facing the past). Moreover, my hypothesis can be falsified by looking at actual Latin texts – a project to which I’ll be returning here from time to time.