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The Rigor of Angels by William Egginton

Leonid Bilmes considers the problems we face if we assume our theories match reality.

Immanuel Kant, Werner Heisenberg, and Jorge Luis Borges walk into a bar. Kant, ever punctual, arrives first. The problem for Kant, though, is that the barman cannot see him as he really is. What the barman at Antinomy Inn sees before him is a short man with keen eyes and an inordinately large head. The barman rubs his eyes: the image of the short man standing at the counter remains, yet somehow, it’s not really there: it’s like he’s surrounded by a cloudy veil. When the man orders a drink, the barman has difficulties understanding exactly what this apparition is asking him, even though he hears the words well enough. All the barman can see and hear of the greatest philosopher ever to have walked the cobblestones of Königsberg, is a mental construct – the product of the barman’s perceptual apparatus. The real Kant, ‘Kant-in-himself’, remains forever veiled from direct sensory apprehension, even by Kant himself.

Next to enter the bar is the youthful and athletic Heisenberg. The barman is again bewildered, as Heisenberg cannot seem to cross the threshold. What the barman perceives is a kind of shimmer: there is Heisenberg just before the threshold, his leg outstretched in mid-stride; and here something is vaguely walking over the threshold, but the barman cannot be sure it’s Heisenberg. The barman can choose to see either the stationary Heisenberg before the threshold, or something crossing the threshold, with some speed. What he cannot see is Heisenberg actually crossing the threshold.

The barman understandably leaves Heisenberg to his undecided state, and looks behind him at the lagging Borges. The blind man, sad to say, never even makes it into the bar. Circumspectly tapping his cane in front of him, he first walks half the distance from the pavement to the entrance of ‘Antinomy Inn’; then half of the remaining distance; then again half… His shuffling steps get smaller and smaller all the while. Soon, Borges’s steps become so small that he hardly seems to be moving at all.

William Egginton’s The Rigor of Angels (2023) tells a riveting story of intellectual adventure involving our three protagonists – an Enlightenment philosopher, a quantum physicist, and an author of labyrinthine fictions – grappling with the kinds of paradoxes that arise the moment we begin, in Egginton’s pithy phrase, ‘to make idols of our tools’. The ‘tools’ Egginton refers to are ideas spanning the breadth of human endeavour, encompassing philosophical concepts, scientific hypotheses, and artistic creations. Such tools have made life as we know it possible – indeed, it would be impossible to understand the world without their mediation. And yet the moment we idolize them – the moment, that we believe that the world coincides with these instruments conceived by human minds – they blind us. A ‘crevice of unreason’ emerges, growing ever wider, due to what seems to be a ‘’radical incompatibility between being and knowledge.” Each of the book’s protagonists deal with this incompatibility in his own way.

Ghost Path
Ghost Path by Paul Gregory, 2024

Real Philosophical Problems

Kant argued that we cannot know the world as it is ‘in-itself’: all we can ever hope to know are what we register of the world through our senses. The inputs through our sense-mechanisms are then interpreted via various innate principles to create our experiences. For instance, in Kant’s view, the pre-programmed notions of universal time and infinite space are two essential categories for experiencing the world. (Einstein proved Kant wrong where the notions of universality and infinity are concerned, but not about the idea that our experiences of the world are necessarily given in terms of time and space.) Heisenberg, in turn, demonstrated that for elementary particles – the warp-and-woof of the physical world’s fabric – we cannot hope to have absolute knowledge of their behaviour. This is because physical reality does not consist of stable threads existing independently of their interactions with observers, but rather, how we measure affects how it manifests.

In his great book, Physics and Philosophy (1958), Heisenberg admonished his fellow physicists not to overlook “a subjective element in the description of atomic events, since the measuring device has been constructed by the observer, and we have to remember that what we observe is not nature in itself but nature exposed to our method of questioning.” Heisenberg’s lasting contribution to the study of quantum mechanics is his uncertainty principle. This principle entails that a physicist studying, say, an electron’s path around an atom, can either determine the electron’s position relative to the measuring instrument or calculate the electron’s momentum (the product of its mass and speed), but he cannot know both things at the same time beyond a certain degree of accuracy. Furthermore, the electron does not independently have these properties. This is because the subatomic world is, it turns out, not a world of continually, stably existent physical objects, but a matrix of probabilities of observations. In Heisenberg’s own words: the world of the elementary particles is “a strange kind of physical reality just in the middle between possibility and actuality” – a statement which tends to leave common sense shaking its head.

‘Just in the middle between possibility and actuality’ is where Borges liked to be in his writing. Throughout his life, Borges was obsessed by the paradoxes inherent in mathematical infinity, the notion of eternity, and the philosophical doctrine of idealism. These include Zeno’s paradoxes of motion, which are well illustrated by the story of Achilles and the tortoise. Achilles, so Zeno’s story goes, challenges the tortoise to a race, giving it a generous head start. Common sense tells us that Achilles must win the race. But here’s the rub, says Zeno: to catch up with the tortoise, Achilles will first have to travel to where the tortoise originally started; but in the meantime, the tortoise will have moved on; and so Achilles has to get to that new place; but by the time he gets there, the tortoise will have moved on still further… and so it goes on indefinitely, meaning that although the distance between Achilles and the tortoise is continually decreasing, Achilles will never quite catch up with the lumbering fellow. In the race of Achilles and the tortoise, the tortoise always wins.

What this paradox demonstrates is not, as Zeno thought, the impossibility of motion, but that the idea of motion becomes contradictory “when we mistake, as we tend to do, real things for the idea of those things,” as Egginton puts it. The idea of space being infinitely divisible, upon which Zeno’s paradoxes rely, is mathematically understandable; but we now know that this idea is not applicable to reality. Space cannot be divided infinitely – such division is limited by Planck’s constant. More to the point, Zeno’s paradoxes illustrate the confusion caused when movement is presumed to equate to the stationary space it covers. As Henri Bergson convincingly argued, although we can parcel up the distance covered in a race into as many intervals as we like, we cannot do the same for movement. When Achilles runs, his movement does not consist of points A, B, C, etc. Rather, his movement is one continuous flow. The immobile points ‘A, B, C…’ thus cannot be an accurate representation of Achilles’ uninterrupted progression through space. They are instead an abstraction of the distance covered.

The spectre of Zeno’s paradoxes lodged in Borges’s imagination. Indeed, he wrote several essays and stories haunted by the echoing abysses of infinity and eternity. One such story (and one of Borges’s greatest literary creations) is ‘Tlön, Uqbar, Orbis Tertius’ (1940).

In this story, Borges recounts, in characteristically convoluted fashion, the lives of the inhabitants of a planet called Tlön, which as we learn in the story’s postscript, was somehow thought into existence by the combined efforts of generations of thinkers, starting with the seventeenth century philosopher George Berkeley, now best remembered for his epithet summing up the tenets of idealism: esse est percipi – ‘To be is to be perceived’. For the idealistic inhabitants of Tlön, it makes no sense to say that a world exists external to their perceptions; instead, they “conceive the universe as a series of mental processes that occur not in space but rather, successively, in time” (trans. Andrew Hurley). No nouns are used in the various dialects of Tlön, because nouns would be inconsistent with this doctrine, inferring as they do the existence of subject-independent objects. In place of nouns, some speakers on Tlön use impersonal verbs designating acts of perception; a description of the moon rising above a river, for example, might be “Upward behind the onstreaming it mooned”. Other speakers on Tlön opt for adjectives: ‘moon’ becomes ‘aerial-bright above dark-round’, or ‘soft-amberish-celestial’. Logically, once things and places are no longer being perceived on Tlön, they cease to exist: “Sometimes,” the narrator tells us, “a few birds, a horse, have saved the ruins of an amphitheatre” from oblivion. “The people of Tlön are taught that the act of counting,” the narrator continues, “modifies the amount counted, turning indefinites into definites.” This weird practice sounds a whole lot like the world of particle physics, where the act of observation also ‘modifies’ the particle being observed, so that ‘indefinites’, like the merely probabilistic position of a particle, become ‘definites’ only in the act of observation.

Across An Abyss

Although Egginton does not single out the above passage, The Rigor of Angels is filled with comparisons of this kind. The aim of the comparisons is to sound a warning: as Egginton puts it in a Kantian manner, “Things are not known according to their natures but according to the nature of the one who is comprehending them.” This is precisely the lesson of the story of Tlön, for it gives voice to our deep desire for the world to conform to ourselves: for nature to be like a game of chess, in which we get to decide what the pieces are. To paraphrase William Blake, the human mind often seeks, and sees, worlds in grains of sand, heavens in wild flowers, infinities held in one’s hand (as in Borges’s cosmos-within-a-marble of The Aleph), or eternities lived in an hour (as in his story The Secret Miracle). Borges’s narrator asks, “How could the world not fall under the sway of Tlön, how could it not yield to the vast and minutely detailed evidence of an ordered planet?” Indeed, falling under the sway of various systems of thought does sound like a fitting description of the intellectual history of our species. Whenever we do uncritically fall under the sway of systems of thought, though, we find ourselves on Tlön, and no longer in the real world.

Egginton points to several instances of the Tlön mindset in modern scientific and philosophical thought, notably in his criticism of those (for instance, Sam Harris) who propound deterministic explanations of human behaviour, as well as in his rejection of the multiverse theory. Advocates of the multiverse, in Egginton’s view, have been misled by math: the mathematical expression of two, three, or even a limitless number of potential outcomes of a given quantum experiment is taken to indicate the actual existence of a corresponding number of universes, wherein each of these outcomes is actualized. “We contort our imagination,” Egginton writes, “and make myths out of math; we brew bubbling Kandinsky multiverses and grow gardens of infinite forking paths. But the intimate rifts, the interstices of unreason that those models seek to obliterate, are indelible. They inhabit us. They make us what we are.”

Egginton’s prose is often lyrical, and not without humour. The alter-ego narrator of Borges’s story ‘The Aleph’, for instance, is described ‘as a snobbish wet blanket of a man’. We also learn about young Borges’s ‘black bile of despair’ occasioned by unrequited love, and young Kant’s hatchet-job review of the writings of the Swedish mystic Emanuel Swedenborg. In Träume eines Geisterseher (Dreams of a Spirit-Seer), first published anonymously in 1766, Kant wrote of Swedenborg: “If a hypochondriacal wind should rage in the guts, what matters is the direction it takes: if downwards, then the result is a fart; if upwards, an apparition or heavenly inspiration.”

In addition to immersing the reader in the lives of Borges, Kant, and Heisenberg, The Rigor of Angels is one of the most lucid and enjoyable introductions to the dizzying world of twentieth century physics, and the assessment of Kant’s philosophy, particularly his rebuttal of deterministic denials of freedom, is equally sharp. But the real hero of the book is Heisenberg, for it is precisely in Heisenberg’s work that the ‘radical incompatibility of being and knowledge’ is most tangibly expressed.

The life and work of Heisenberg has recently featured in two other exceptional books: When We Cease to Understand the World (2020), a novel by Benjamín Labatut that gifts its reader with an awe-inducing glimpse of the quantum secrets perceived by twenty-three year old Heisenberg as he paced the wind-lashed cliffs of Helgoland, a rocky island in the North Sea; and Helgoland: The Strange and Beautiful Story of Quantum Physics (2020), physicist Carlo Rovelli’s exhilarating return in prose to the quantum world. Drawing on Rovelli’s ‘relational’ interpretation of quantum mechanics, Egginton suggests that, like the spectral elementary wave-particles which only really ‘exist’ the moment they are placed in relation with an observer, we, too, are relational beings, entangled as we are in the world’s fabric, which perennially slips through the grasp of even our most refined tools.

© Leonid Bilmes 2024

Leonid Bilmes is a researcher living in Spain. His writing on philosophy and literature has appeared in Los Angeles Review of Books, The Millions, 3:AM Magazine, and others. He is the author of Ekphrasis, Memory and Narrative after Proust (Bloomsbury Academic, 2023).

The Rigor of Angels: Borges, Heisenberg, Kant, and the Ultimate Nature of Reality, William Egginton, Pantheon 2023, $23.45 hb, 368 pages

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