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In 1927 a young German physicist published a paper that would turn the scientific world on its head. Until that time, classical physics had assumed that when a particle’s position and velocity were known, its future trajectory could be calculated. Werner Heisenberg demonstrated that this condition was actually impossible: we cannot know with precision both a particle’s location and its velocity, and the more precisely we know the one, the less we can know the other. Five years later he was awarded the Nobel Prize in Physics for having laid the foundations of quantum physics.

This discovery has all the hallmarks of a modern scientific breakthrough; so it may be surprising to learn that the uncertainty principle was intuited by Heisenberg’s contemporary, the Argentine poet and fiction writer Jorge Luis Borges, and predicted by philosophers centuries and even millenniums before him.

While Borges did not comment on the revolution in physics that was occurring during his lifetime, he was obsessively concerned with paradoxes, and in particular those of the Greek philosopher Zeno. As he wrote in one of his essays: “Let us admit what all the idealists admit: the hallucinatory character of the world. Let us do what no idealist has done: let us look for unrealities that confirm that character. We will find them, I believe, in the antinomies of Kant and in the dialectic of Zeno.”

Kant’s antinomies are paradoxes that are inevitably produced when our reason overreaches the boundaries of what we can learn through our senses and makes pronouncements about the world as it is in itself, independent of how it appears to us. His second antinomy, which deals with the divisibility of space, shows that we can infallibly reason both that the basic components of nature are simple, indivisible substances, and that all substances are infinitely divisible, despite the fact that each of these positions blatantly contradicts the other.

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On the one hand, Kant says, our reason tells us that as we home in on a substance we will eventually come to a unit that cannot be further divided, for if we didn’t, there would be nothing out of which the world and everything in it is composed. On the other hand, our reason also tells us that such a simple substance, if we find it, occupies space; and if it occupies space, that space must be divisible.

In formulating the antinomies, Kant was inspired by Zeno. Zeno’s paradoxes purport to prove the impossibility of motion. To get from Point A to Point B, a traveler must first cross to a Point C halfway between them. Prior to that, though, he or she must cross Point D halfway between A and C, and so on infinitely, such that the traveler never in fact moves.

In both Zeno’s paradoxes and Kant’s antinomies, an act of observation engenders an apparent contradiction in the very knowledge it produces. As it turns out, it is this very same apparent contradiction that we see at work in the uncertainty principle. While any and all observations contain this inherent paradox, it becomes visible only when pushed to the extreme, either of logic or of the physical world.

In a story published in his 1941 collection “Fictions,” Borges created just such an extreme scenario. His character in that story, Funes, has a memory so perfect that he perceives every moment in time as entirely distinct, unrelated to those coming before or after. Consequently, he is incapable of overlooking minor differences in order to connect the impressions of one moment in time to those of the next. He becomes frustrated at our how language generalizes, at how we use the same word, “dog,” to refer to a four-legged creature facing one direction at 3:14 and facing another direction at 3:15.

While Borges may have been inspired by examples of prodigious memory, pushed to such impossible extremes the example of Funes reveals the paradox at the heart of any and all knowledge of the world: namely, that there can be no such thing as a pure observation, one free of the changes imposed by time.

What Funes shows is that, at its most basic level, any observation requires a synthesis of impressions over time. Furthermore, the process by which the synthesis takes place, the media through which it is processed, and the entity doing the synthesizing are all essential aspects of the knowledge being produced. This is, in a nutshell, the first part of Kant’s 1781 opus magnum, “The Critique of Pure Reason.”

Kant had been challenged — awoken from his dogmatic slumber, as he said — by the empiricist David Hume’s assertion that we could never infer any certain knowledge about, for instance, laws of causality, because we are limited to knowing what our senses can learn about the world at any given moment. We may know that the sun is rising now, he famously argued, but cannot infer with any certainty that it will rise again tomorrow.

Kant’s insight was that, in order for the knowledge we get from our senses at any given moment in time to mean anything, our minds must already be distinguishing it and combining it with the information we get in prior and subsequent moments in time. Thus there is no such thing as a pure impression in time — no absolute, frozen moment in which we know the sun is rising now without being able to infer anything from it — because such a pure moment without a before or after would be nothing at all. Funes from Borges’s story could have a concept of “dog” in the first place only if it included the four-legged creature changing positions over time — which is exactly what Borges concludes when he points out that Funes can’t really be said to be thinking at all, because to think means to “forget differences, generalize, make abstractions.” Not only is it entirely possible to infer from our momentary impressions to prior and later events, but we are in fact always doing so.

Related More From The Stone Read previous contributions to this series.

For an observer to perceive an entity, he or she must be capable of distinguishing it from the succession of impressions preceding and following it; in order to grasp those impressions as pertaining to the same entity, however, the same observer must be able to take them as a unity despite the differences that succession implies.

This ineluctable fact of observation underlies the paradoxes of motion, the antinomies, and the uncertainty principle. For in all cases, some minimum of motion, distance or velocity — namely, change over time — is required for any observation to take place, even as the observer posits an unchanged point or particle as being subject to that change.

At the level of normal, physical sensation, the fact that these necessary elements of observation exclude one another passes unnoticed. It is only at the highly focused, granular level of quantum physics or in the extreme situations of philosophical fictions that this mutual exclusivity emerges.

Borges continues the passage I quoted at the outset by writing: “we have dreamt the world. We have dreamt it resistant, mysterious, visible, ubiquitous in space and firm in time; but we have left in its architecture tenuous and eternal interstices of unreason, so that we know it is false.”

It may well be that the uncertainty principle, along with other curious aspects of quantum theory, is another such interstice of unreason, a reminder not that the world we know is false, but that it is always the world as we observe it.



William Egginton is Andrew W. Mellon Professor in the Humanities at the Johns Hopkins University. He is the author of “In Defense of Religious Moderation” and the forthcoming “The Man Who Invented Fiction: Cervantes in the Modern World.”