The Rigor of Angels: Borges, Heisenberg, Kant, and the Ultimate Nature of Reality

by William Egginton

To deprive a human being, any human being, of the opportunity to cultivate his or her own mind was to undermine the free use of reason that Kant believed an essential part of being human.

It wasn’t merely that the physicist isn’t able to see a particle’s position and momentum at the same time; astoundingly, the particle doesn’t have a momentum and a position in any meaningful sense until the physicist decides to measure one or the other.

A few weeks later he wrote a summary for nonspecialists in which he explained that quantum phenomena required us to put aside Newtonian mechanics. When it comes to quanta he wrote, “the more precisely we determine the position, the more imprecise is the determination of velocity.”[15]

The uncertainty principle, as it came to be known, showed with inescapable, mathematical precision that such full knowledge of the present moment wasn’t just hard to pin down; it was actually impossible.

For the rest of his long and vibrant career, Borges would remain haunted by the flow of an afternoon in life, an afternoon when his beloved’s gaze turned elsewhere, and he lost faith in the persistence of his own being in space and time. Over decades, Borges would obsessively conjure characters whose special abilities and most urgent desires reveal for them a paradoxical disconnect between knowledge and the world.

According to Hume, absolutely everything we know about the world comes from our senses. Not only does this mean we can easily be wrong about what we think we know; even worse, we have no basis to suppose that such “certainties” as Isaac Newton’s laws of motion are anything other than habits we’ve acquired through repeated exposure to similar impressions.

But our perceptions, Kant realized, aren’t things in the world; rather, they are versions of those things that we construct in our minds by shaping them in space and time. When we imagine the world as being identical to our conception of it—when we assume, specifically, that space and time are fundamentally real—our reason becomes faulty, and science responds with paradox.

On a walk together in 1926, a venerated older scientist pressed the younger Heisenberg on the weakness he saw disqualifying his approach—that he was jettisoning our long-held belief in the independence of reality from our observations of it. Heisenberg pushed back. Had not the renowned professor himself come up with his own epochal discovery by overturning our most basic assumptions about time and space? “Possibly I did,” Albert Einstein grudgingly conceded, “but it is nonsense all the same.”[23]

Knowledge is man-made, our own way of making sense of a reality whose ultimate nature may not conform to our conceptions of it. Is the saturated red of a Vermeer part of that ultimate reality? The soft fuzz of a peach’s skin? The exalted crescendo of a Beethoven symphony? If we can grasp that such powerful experiences require the active engagement of observers and listeners, is it not possible, likely even, that the other phenomena we encounter have a similar origin? When we do the opposite, we forget the role we have in creating our own reality.

In their lives, struggles, and obsessions, Borges, Heisenberg, and Kant pushed far enough against the limits of imagination, observation, and thought to unearth the antinomies engendered by that forgetting. This book is divided into four sections, each of which revolves around one of those antinomies: Are space and time infinitely divisible, or are they composed of indivisible chunks? Is there something like a supreme and unconditional being, or is everything in existence conditioned and affected by something else? Is there a spatial or temporal edge to the universe, or does it extend infinitely with no beginning or border? Are we free to choose our path in life, or is our every choice determined by the physical world we live in?[26]

But if there is a completely new viewer for every frame, with no relation at all to the prior or subsequent frame, then all that remains is an absolute unity. But such a unity, which is exactly what Funes and Shereshevsky and Hume claimed they could experience, utterly negates perceiving anything at all, since all perception requires bridging impressions over time. In other words, it requires exactly what a truly perfect memory, a truly perfect perception, or a truly perfect observation absolutely denies: overlooking minor differences enough to be a self, a unity spanning distinct moments in time.

Like Kant before him, he also discovered that the conceit of slowing time down to a single frame, honing the moment of an observation to a pure present, destroys the observation itself. The closer we look, the more the present vanishes from our grasp. Which was precisely the insight that hit Werner Heisenberg in Copenhagen as he walked in Faelled Park on that cold winter evening.

In Heisenberg’s words, “The ability of human beings to understand is without limit. About the ultimate things we cannot speak.”[45] Or to put it inversely, by presuming we know the ultimate nature of reality, we limit our ability to understand.

That stain is what we might call the paradox of the moment of change: the instantaneous sliver of time when something, some particle, must be both perfectly identical to itself in space and time, so as to be the thing that changes, and somehow different, so as to have changed at all.

If we assume time is infinitely divisible, we can neither age nor move; and if we assume there’s a minimal chunk, an atom or pixel of time something occupies, then again no thing moves, no thing changes, because continuity is broken, and its new manifestation is just that, something entirely new. Each sliver of being is imprisoned in a minuscule eternity of space-time. Or, to put it slightly differently, we can focus on a particle, or we can focus on its movement, but if we want to see both simultaneously, we can’t.

So more than a century later, when Heisenberg explained to Pauli that the path a thing takes through space-time “only comes into existence through this, that we observe it,” this was another way of saying that things in space and time are, by definition, always in relation to other things and that someone, an observer, needs to put them in that relation.

A new math for a different kind of space and time, where no baseline continuity could be assumed, but rather rupture and discontinuity.

In simple terms, Heisenberg decided to invert the relationship between particles and movement: movement is not something that happens to particles; particles are something we derive from observations about movement.

Just as Einstein had shown that the seeming consistency of space and time crumbles as one approaches one limit, the speed of light, Heisenberg had revealed that the seeming solidity of location and movement dissolved as humans approached another limit, this one hidden deeper in the crevices of space and time than anyone had ever delved. Until now.

What is an observation? At its very minimum, any observation entails something connecting two disparate moments in time and space. As for Kant and Borges’s character Funes, a being who was truly, exclusively saturated in a present moment wouldn’t be able to observe anything at all. Observation, any observation, installs a minimal distance from what it observes, for the simple reason that for any observation to take place, one here and now must be related to another here and now, and that relation needs to be registered by some trace or connector between the two. Crucially, this aspect of observing doesn’t assume a conscious or otherwise human agent. It also doesn’t mean, as the popular misunderstanding of Heisenberg’s discovery would have it, that the tools we use to observe something always affect what we observe, although that, too, is true. Far more fundamentally, the blur of the instant of change that is a logical prerequisite for stitching together any two moments in space-time inextricably inheres in the very reality being observed. This, in a nutshell, is the uncertainty principle: you can know a particle’s position or its momentum, but you can’t know both.

In a fascinating and parallel way, the two constants that form the backbone of modern physics, Einstein’s c and Planck’s h, turn out to be fundamental limits built into the fabric of our observed reality: on the one hand, a speed limit at which time comes to a standstill; on the other, a size limit on how closely we can focus on the warp and weft of space-time.

Primary among these was the fact that uncertainty arises not only from the fundamental discontinuity of reality at the quantum level—that no matter how closely one looked at a particle’s movement there was no way to close the gaps and find a smooth path—but from the fact that the observer always decides in advance whether to look for a wave or a particle, and that decision determines the reality one will find.

Whatever the tools we use, as we focus on reality at the quantum level, we must make certain choices. We can zoom in on an electron’s position or on its momentum. We can further define the energy of an event or its time. But in each case, the more we focus on one factor, the greater the uncertainty of the other. And the value lodged in the pivot between one side and the other of his equation was nothing other than our old friend Planck’s constant.

Hence complementarity: we can see different aspects of reality, depending on what we choose to observe; and those aspects complement each other; but we can never grasp the entirety of that reality.

And there was the rub. In observing one particle, the researcher would instantaneously know the position or momentum of the other particle, no matter how far the distance between them; even worse, by observing the one, the scientist would also instantaneously determine the outcome of any observation of the second. As Einstein had asked Rosenfeld at his lecture, “How can the final state of the second particle be influenced by a measurement performed on the first?”[30] Einstein had driven a stake through the heart of what he called spooky action at a distance in 1915 when he redefined gravity as the curvature of space-time. Now here it was poking its head up again. Einstein just knew it couldn’t be right.

if Schrödinger and Einstein were right, and this entanglement represents a kind of hidden state that is only revealed by measurement and not produced by it—that is, if reality at the subatomic level could be said to exist on its own, independent of observations—or if Heisenberg’s theory that observations determine the underlying reality would ultimately prevail. Unfortunately for reality, their experiment proved Heisenberg right.

Quantum entities remain indeterminate until they are measured, and measuring them seems to be able to change their entangled pairs even across distances, in apparent violation of relativity. It was like a kind of magic trick, as one commentator pointed out. It was as if twins always managed to order a different drink no matter what bar they were in and how far apart the bars were. “If one says, ‘Beer,’ the other instantaneously says, ‘Whiskey.’ ”[39] And to make matters even more mysterious, you could change one twin’s order in the act of ordering and, lo and behold, the other twin’s order would change as well.

“The ‘paradox’ is only a conflict between reality and your feeling of what reality ‘ought to be.’ ”[42]

What we are really trying to understand, he now saw, is our picture of the world. And our natural tendency to think we are speaking about the world is what must be subjected to critique. Thus would be born a new “age of critique” that would initiate the downfall of humanity’s submission to the age-old idols of its own creation. This would be called Enlightenment.[27]

One presupposes a self-contained cosmos that one can never fully know, one presupposes a perfect moral law that one can never fully embody, precisely to derive the standards of what one can know and ought to do.

It was this something that Borges glimpsed as he paged through his worn copy of Plotinus. To be human, Borges saw, is to straddle the impossible border between ephemerality and eternity, loss and permanence. From the vantage of a sifting, vanishing time we project an eternity hopelessly out of reach. Like the exile who, “with a melting heart,” recalls “expectations of happiness,” we “gather up all the delights of a given past in a single image.”[11] Eternity is nostalgia, the inextinguishable desire for what we’ve lost.[12]

For Kant that object of desire was both the motor of science and what reason needs to guard against, lest we ever believe we’ve found it. For Borges that object is the motor of literature, indeed of life, and yet, in story after story, he always sounds a note of caution. For as Borges would learn, to find that object, to enter that ultimate reality, is something no temporal being could ever survive.

The questioner, the observer, brings something unique, namely, a finite self, to each and every perception in time and space; this very observer produces bad infinities the moment he or she tries to step into the shoes of the god of very large things by transforming the limited connecting of moments and places necessary for any perception into the unlimited realm of everything at all times.

the creation begins not in time but with time.

Like Kant sparked to hope by Hume’s despair, Borges saw that the very memory needed to see a recurrence as a recurrence would of necessity be an alien element. The order thus discovered, that underlying rigor, is one of chess masters, not angels. But it is a rigor nonetheless. Like Dante’s cosmos, the universe that others call the Library is contained by its center; unlike Dante’s, that center isn’t God. It is, instead, the very observer whose absorption into the whirling, buffeting, random chance generator of temporal and spatial existence requires a minimum of abstraction, an iota of order, an atom of rigor just to feel lost and absorbed in the first place. It is, indeed, that very observer for whom the conditions of possibility of knowing anything at all also require that universe turn itself inside out, become a hypersphere whose central point envelops all existence.

No matter where we train our gaze on the starry skies above, we look inward toward the very origin of space and time. Thus freeing our minds from our senses, we find that the universe is, indeed, turned inside out.

This architecture derives from the very principle that Einstein’s relativity theories salvaged, the principle that there could be no privileged place in the universe from which to adjudicate different measurements. That no motion whatsoever, even that of the water in Newton’s bucket, is motion in an absolute sense, but is always motion in respect to some other point of reference. That the universe is not located anywhere, but rather has no other where than here—not in the mind of God, but in the very minimum conditions that permit anything to be observed in the first place. For this extraordinary truth—that when gazing out into space, we are also gazing in toward the origin of all space and time—is not merely an interesting quirk of cosmology. It is what enables there to be cosmos in the first place.

Like Dante’s center, the infinitesimal point at the origin of space and time envelops all of creation; it is the horizon that we gaze out upon, only to realize we have been gazing inward all along.

As we have learned by now, the inescapable law of the macrocosm is the maximum amount of space that can be traversed by information relative to an observer in a given amount of time. Likewise, the law of the microcosm is nothing other than Heisenberg’s uncertainty principle, which states that for an observer to reduce the uncertainty of the position of a particle to zero, its momentum becomes infinitely unknown, and vice versa, and for an observer to reduce the uncertainty of the time of an event to zero, its energy becomes infinitely unknown. Since conceiving of the origin of the universe by definition means focusing on a moment when time was nothing, uncertainty requires that the energy at that moment be literally anything. Uncertainty awaits us at the dawn of creation.[43]

Heisenberg was willing to face the consequences of his realization that our science is always an exploration of the world as it is revealed to us, in space and time. Indeed, the uncertainty principle tells us with enormous precision what the limits on that knowledge are in the world of the very small, just as relativity tells us with enormous precision that what we can know here and now about the larger universe around us is fundamentally limited by the speed of light. Those limits are baked into reality, yes, because our knowledge is also baked in. For what does “position” mean, what does “momentum” mean, outside a measurer, a knower who seeks to determine them? Likewise, what could the shape of the cosmos in space and time possibly mean independent of someone positioned in time and space, for whom the cosmos can assume a shape in the first place?

The philosophical problem that emerged from the realization that our very existence as sentient beings owes a great deal to chance has led some scientists to what they call the anthropic principle. This principle takes two forms: a “weak” one that scientists often accept as likely true but not particularly mind-blowing as revelations go; and a “strong” one that comes across to most scientists like a lot of hocus-pocus. The strong anthropic principle also goes by the name of “design”—as in, to explain how something as wildly improbable as intelligent life emerged from such a potentially inhospitable set of possibilities requires us to presume that a being of vast power and intelligence planned it that way. The weak anthropic principle, in contrast, simply concedes that, as improbable as it may seem that the universe emerged to support intelligent life, it would be more improbable for life to find itself living in a universe that didn’t support it.

In the first Critique, Kant had shown that the condition of the possibility of our perceiving anything at all was our innate ability to translate an otherwise bewildering chaos of sensory input into ordered events in space and time whose causal relations could be objectively established. Such objectivity in turn required the presumption of a total unity of the physical world, a mechanistic chain of causality from past to future, just as our ability to stitch disparate moments in time together depended on the presumption of a unified seat of consciousness. Crucially, Kant realized that we must presuppose such unity even though we can never verify it in our experience—never see the universe as a coherent object in space and time; never see the self on its own, apart from the flow of experiences it sutures together. Similarly, Kant now realized, whenever we connect two or more specific claims as being examples of a more general truth, of an idea that contains them both, the very coherence of our judgments requires us to assume a web of connections that links each specific instance to the whole of creation, even though that whole can never itself be an object of our experience. Here, Kant said, lay the harmony that the ancients had identified as the source of beauty. For when we perceive the chaos of data we receive about the world to be connected by an underlying unifying idea, we find that amalgam to be beautiful, harmonious, complete on its own. Our desire to explain furthe...

But whereas in nature we are attracted by the sense of a guiding hand even when there is none, in art the analogy is reversed: we are attracted to products of a guiding hand where the hand itself has become invisible. For a work of art whose artistry is too evident loses its ability to cause wonder; it becomes staid and predictable. In both art and nature, we see beauty in signs of purposiveness without purpose, natural artistry—but with an important difference. Whereas in nature we supply the artist, in art we supply the sense of its naturalness, that it was produced without evident artifice.

Purposiveness without purpose is thus a model for making claims about the aesthetic value of works of art, since we find art beautiful if it exhibits a harmony as if it had arisen there naturally.

The irony of such subjectivism is that while it sounds coherent enough (how indeed can I trump someone’s argument that, hey, this is beautiful because I find it beautiful?), no one in practice seems to believe it.

The sublime, like the beautiful, does not reside in things in the world, whether natural or made; it emerges as a reaction of our judgment to the representations we make of the world. For our representations to cohere, we must assume a greater order to them that ultimately outstrips our ability to verify it. As we verify such order locally, our judgment gratifies us with a feeling of beauty, of the parts fitting an ideal of the whole, a center that seems to contain the astonishing variety of existence and give it sense or purpose. In contrast, whenever we engage phenomena that threaten to overwhelm our ability to grasp them with our senses, reason stretches in a vain attempt to comprehend the very edges of totality itself, the border conditions of the universe, small and large, and we are taken simultaneously by our inadequacy to the challenge and by the awesome power of reason that permits us to conceptualize that very impossibility in the first place. The capillaries of coherence flowing from species to genus, from the particular to the universal, are the necessary presupposition that permits us to encounter and differentiate particulars in the first place. As we uncover those patterns of coherence, we experience their necessity and feel pleasure. Contemplating such purposiveness, we are lulled by its harmony, but we simultaneously strive toward a totality whose very incomprehensibility stokes that desire like an ever-present dissonance we desperately wish to resolve. St...

We can make sense of the antinomy only when we understand and accept that our cognition has two modes of ordering the world as we encounter it and that both have their place. One pertains to explaining local and discrete changes in space-time; the other kicks in whenever we explore the edges of our knowledge, whenever we ask the big questions of where it all came from, what should I do, and am I making this choice freely or am I constrained. When we use the one in the domain of the other, when we think mechanistically about our obligations or the whole of creation, or when we apply teleological thinking as we drill down into the phenomena of nature, we fall into error.

God can know every move and every decision I will ever make, and yet still I can choose freely. In other words, that we can imagine a being who isn’t constrained by having to live from one moment to the next is utterly irrelevant to what in fact happens in time. Some things happen purely by necessity; some things result from different degrees of choice. Whether we presume that all our decisions from now to our deaths are determined because God sees all of existence, all that happened, is happening, and will happen, in one eternal instant, or whether we presume that all our decisions from now to our deaths are determined because they stem from physical processes subject to the laws of mechanical causality, amounts to the same thing. But here’s the crucial point: because they implicitly avoid the limitations of time, neither presumption undermines free choice.

Far from grasping the universe as a transparent whole, we are blind, groping seekers adrift in time and space. As such, free will isn’t a metaphysical implant or delusion of grandeur but an admission of our fallibility in the face of an unknowable future.

Both sides of the antinomy imagine an ideal, ultimate cause, outside space and time, as a precondition for either assigning or denying responsibility. In an analogous way, those favoring either of the anthropic answers to the question of the initial settings of the universe imagine an ideal, ultimate cause, outside space and time. One version imagines a conscious intent to that cause in the form of God’s design, the other an infinite store of real universes so as to deny design. In both anthropic principles, the otherworldly scenarios are invoked to avoid the embarrassment of accounting for the existential fact that we find ourselves in this universe and these are the values that we derive from our measurements. Likewise, otherworldly scenarios to implant a free soul into a mechanistic world or to deny all responsibility to human agents fall on the same strategy. They create an uncaused cause outside space and time and then pretend it has real purchase on the here and now. They also do so for the same reason—to avoid the embarrassment of accounting for an existential fact. We are physical beings whose every move occurs in the mechanistic flow of space-time, and we are rational agents who can visualize options and choose which one to take.