Lucretian Physics

 I've been reading On the Nature of Things this week, and it must be said that Lucretius is hit-or-miss in the extent to which his physical theories have stood the test of time. Some aspects of his physics have not aged well. For instance, he seems to contemplate that the sun may have to be reignited each morning at dawn, in order to complete its heavenly journey before vanishing in the sea (even though other passages refer to the "antipodes," showing that Lucretius was no flat-earther). 

More plausibly, though no more correctly, he believes that sound is produced by emitting particles from the vocal cords that must reach the ears of strangers, in order to be heard, rather than being transmitted by means of a wave. And he seems to entertain, in at least one passage, that darkness may not be merely the absence of light—but the presence of a kind of murky haze or smoke. Something like the "black air" that figures in the theories of Flann O'Brien's fictional crank scientist De Selby. 

But there are other respects in which Lucretius reads to us now as remarkably prescient. Not only is the atomic theory that he helped to systematize and popularize still the basis for many of our physical models of the universe today; he also seems to have foreseen the principle of the conservation of matter. He knows—more than a millennium before Galileo—that lighter and heavier objects would fall at the same rate in a vacuum, presaging the concept of air resistance. 

Furthermore, in his recently-popularized concept of "the swerve," he makes the case for the idea of a contingent rather than a purely deterministic universe, anticipating (if we are willing to stretch a point) the theory of quantum mechanics. 

Finally, there is one domain of physics in which the current scientific consensus holds him to be wrong—but in which I still think, in my infidel heart, he's right. This is on the question of the extent of the universe. 

In a recent post on this blog, I quoted from a speculative passage in Xavier de Maistre's Nocturnal Expedition Around My Room, in which he makes a seemingly irrefutable logical argument that the universe cannot have an end, but rather must be infinite. This is so, because any outer boundary or "wall" to the universe could only be identified by marking out the "inside" of the universe from something "outside" it—yet, there can be nothing outside the universe, by definition, because the universe is the sum of everything that is. And so, if we were to travel to the furthest reaches of the universe, we could never find an end of it. 

From my reading this week, I have learned that Lucretius makes a similar argument—and maybe Lucretius even influenced the passage in de Maistre. Lucretius argues, along the same lines, that there can be no limit or outer boundary to the universe. Space, therefore, must spread out infinitely in all directions.

This is, of course, at odds with the modern scientific consensus. Our current models of the universe posit that spacetime itself was at one point coiled into an infinitely hot, infinitely dense singularity, and has been spiraling out ever since in a vast cosmic expansion. What was once confined in so small a space and is now expanding cannot be infinite. It must have an outer boundary, then, no matter how far removed. 

Yet, Lucretius—like de Maistre—offers an argument against such a theory that is hard to contradict. He asks us where and how we might identify such a limit or wall to the universe. Suppose we were to travel to the outermost edge of the universe, and lob a spear toward that edge. Would the spear keep traveling past it? If so, then we are not truly standing at the edge of the universe. In the alternative, would it halt and ricochet back to us? But, in that case, what is intercepting it? The notion of there being a "wall" at the edge of space itself seems absurd, not to mention self-contradictory, in exactly the way de Maistre found it. 

And so, Lucretius finds, there must be one exception to his general principle—repeated several times in the treatise—that all things must have a limit and their own intrinsic "boundary stone." (Ferguson Smith trans.) The universe does not. The universe—the sum of all possible space—has no boundary. It must be infinite, by definition. 

Now, attempts have of course been made to refute Lucretius, and resolve the paradox he points to in favor of our modern physical theories of a limited and expanding universe. Wikipedia addresses the controversy in its article on the "Javelin argument" (apparently Lucretius's argument about the spear is famous enough to merit its own entry), and the online encyclopedia finds that Lucretius has been refuted on this score. The article complacently declares: "The argument fails in the case that the universe might be shaped like the surface of a hypersphere[.]" And what is a hypersphere? It is defined in turn as a sphere existing in n-dimensions. 

And here is where I feel that modern physical theories are not so much resolving the paradox as restating it. For, the only way they have found to refute Lucretius's argument is to gesture to something that exists in dimensions that the human brain cannot perceive or even conceive. And since Lucretius's whole case is an argument from conceivability, this response effectively concedes the main point. The notion of a limited, bounded universe is indeed inconceivable, just as Lucretius said. And what is philosophy but an attempt to define the limits of the conceivable? 

Let us clear up at once a common misconception on this score. Philosophy does not say that we are forbidden from invoking inconceivable notions because of some sort of arbitrary law or dogma of its own devising. It says that we are not allowed to appeal to the inconceivable because any such appeal must fail on its own terms. It must fail to articulate a cognizable thought. And so, it is not really saying anything at all. It is not so much a false statement as a non-statement. It is, in the terms of the logical positivists, nonsense. 

But then, as I've also argued at length elsewhere, there are a number of domains in which we appear to be forced to conceive the inconceivable anyways, despite its apparent impermissibility. Maybe the notion of the "hypersphere" enclosing the bounded universe is another one of them. But we shouldn't then pretend that this is all easy, or that we've solved the underlying paradox. All we've really managed to do is to push it back a step. 

We can perhaps concede that the universe may exist in a form impossible for the human mind to conceive, after all: but then the paradox just becomes: how are we able to talk about it? What do we mean by a "hypersphere," when its alleged traits transcend the limits of our categories of perception? 

Perhaps we can borrow from Wittgenstein his concept of the "bounded whole." We can say that the universe—for us—must be infinite, in the sense of containing everything, just as life, for us, must be endless, since we cannot conceive of our own non-existence. Yet, at the same time, the universe may have an end, just as our lives have an end. 

In order to render this paradox somewhat more conceivable Wittgenstein offers—in the Tractatus—an analogy to the field of vision. We cannot see the "boundary" of our field of vision. There is no way to perceive the edge, for in order to see the edge, we would have to see something beyond it: thus, it would not really be an edge. Perhaps the universe is something like this: a whole, a totality—for us—and yet not the whole, not the entirety, of everything. Perhaps both life and the universe are "bounded wholes." 

But once again—have we solved the paradox? Or merely postponed it? For what is a "bounded whole" but a contradiction in terms? What have we achieved other than to prove that, once again—in even the most elementary matters of space and time and cognition—we are forced very quickly to accept that we don't know what we're talking about. We are forced to explain even the tenets of our own perceived reality by recourse to self-contradictory and inconceivable ideas—to nonsense, in short. 

And so we find, yet again, that philosophy does not so much enlighten us to the truth of the universe as teach us intellectual humility. It reminds us, as Hume put it, of the "whimsical condition" of humankind, in which we "must act and reason and believe," and yet we "are not able, by [the] most diligent enquiry, to satisfy [ourselves] concerning the foundation of these operations, or to remove the objections, which may be raised against them."