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A Two-Body Problem

Philosopher and poet Adam Staley Groves analyses a painting by Joshua Miller in relation to the monolith in Stanley Kubrick's "A Space Odyssey".



A Space Odyssey film still with the monolith

Still from 2001: A Space Odyssey (1968) by Stanley Kubrick.


In respect of the original title given by the artist, Equal Masses, and the meaning of “equal masses” itself, I felt it necessary to imagine a second title, Space Odyssey. 

Before we proceed, it is necessary to affirm that by art one sees with feeling — that’s part of its pleasure. By virtue of feeling a work resists, almost successfully, most concepts. In other words, the critical imagination requires an ethics which means their concept must be thought through. A good critic should first reduce their chosen concept and not, to be clear, the vitality the work in question.


Let’s begin with the spheroids of Equal Masses . They stand on what appears to be bleached wood or marble book shelves, not unlike those of a common household. Shadows cast by the spheroids drape over the edge of the shelves. The shelves subsequently cast shadows of their own. Beyond situating the direction of light in the image, this second set of shadows offers a particle motif. Perhaps this observation is unremarkable? Maybe I am simply noting an abstract rendition of dust? 

However the title Equal Masses does not suggest something so banal. There is an immediate notion at hand. A first test of this notion would be the “two-body problem” — a concept known to classical, mechanical physics used to predict the movement of planetary bodies. By representing planets as object points, the model supposes they affect only each other and for that, are in exclusion to any other force [1]. So how would this apply to the spheroids of Equal Masses ? And what does it mean in terms of shelves, shadows, and particulate dots? It concerns a feeling — a formative relation between the work’s primary subject matter. Let us first address the conceptual then move to the formative.

Joshua Miller - Equal Masses

Joshua Miller, Equal Masses, 2017, Oil, graphite, ink and chalk on canvas. Image courtesy of the artist.

Happily we are able to problematise the two-body problem, that is, defeat — in a way — the concept. Firstly, the concept is restricted to what an unaided eye detects and the subsequent calculations which prove it. Secondly, the concept brackets out of its calculations any additional acting force. The model is not entirely wrong; it simply does not regard the depth of physical reality according to contemporary science. The two-body problem, by virtue of its own limitations, is therefore presupposed by an imaginary force. 

Let’s consider the appearances of the spheroids in relation to such an unseen or concealed force. Despite the fact we assume them to be stable, appearances are inherent ruses. An artist presents this fact by his or her style. When they do, they are able to provoke or rupture popular conceptions. For example, contrary to popular culture, electrons and nuclei are not analogous to solar systems. As for objects in the two-body problem, there is more to the movement than a force-affect exclusive to two spheres. 

This problem is analogous to the famed “uncertainty principle.” [2] Werner Heisenberg’s concept captivates us because his discovery articulates an oft-forgotten bond shared between art and science: demonstrating how that which appears to the intending eye is, in fact, difficult to stabilise. What we find in Equal Masses is, in its own way, congruent. In other words, Equal Masses has an appearance problem, an expression of both physical and imaginative realities.

Our problem is not dissimilar to the image found in an individual’s imagination which often escapes scientific fact. Brains are not minds. Consciousness is not exclusive to neuroscience. Psychoanalysis is tentatively scientific; it tends towards dreams, drives, desire, and meaning. In the fine arts, appearances privilege the use of imagination. They deal in the “unreal”, imagined aspects of a supposed, shared reality. They demonstrate to individual consciousness a poetics of arts and sciences, in other words the relation between form and content. In Equal Masses instability depends on common points of reference: shelves, shadows, spheroids, and dust particles. There is an unreal truth that places these items in relation. 

This relationality (the formative, morphological notion I began with) is held up by the observer. In this relation, there are proliferate meanings and potential identities. For example, one could ask if the black spheroid is a human scalp. They may ask if the beige sphere is a featureless, human head? A rabbit hole awaits. 

If the reader agrees Equal Masses concerns more than orbiting spheres or dust beneath a shelf, they may also feel lingering discomfort. In my attempt to reduce the initial concept, several more have come into play, bringing about uncertainty in terms of a final meaning. Furthermore, Equal Masses does not explicitly conceptualise imperceptible levels of physical reality — substrates at work in inexplicable ways. For that, I’d ask the reader what could? I ask the reader what should, if not themselves? One can only try.

A strong work expresses something exceeding knowledge, demanding concepts that knowledge may build upon. It does so in order to have credibility or merit, but here we are not concerned with canonical matter nor the market. If I refuse to trade the incredible for mere credibility, I am also compelled to consider its elusive fact further — to demonstrate what a work expresses beyond the limits of concepts; to ask what takes place by imagining beyond the initial notion. And finding our thought beyond conceptual limits is, in a way, reducing not the meaning of the work, rather the necessity of putting the form one finds to rest. 

For that I return to the spheroids. One is flat with black texture. Set next to an earth-toned companion, the dimensional differences are obvious. The earthen sphere stands prominent and presses out into two-dimensionality. The black spheroid, by virtue of hair-like qualities, disrupts an otherwise restrictive, one-dimensional flatness. 

This spherical dialogue seems analogous to the synchronous rotation shared between the earth and the moon[3]. The earth-toned sphere is assumed a rotating, planetary form. In proximity to it, as per the moon which is always appearing to face earth, the black sphere appears to not have its own rotation because it is synced with the earth’s. For the black spheroid, waves imply movement, yet these are seemingly internal to itself. If this black sphere is on par with a gravitational lock according to synchronous rotation — as the moon governs earth’s oceanic tides and affects human thought — the affective quality for the black sphere remains to itself. Hence it is not lunar.

If at first compelling, synchronous rotation fails. We have only near misses, and an ever-fleeting, final analysis. Conversely it seems I may be nearer to the centre of an elusive fact. 

Joshua Miller - Equal Masses 2017

Joshua Miller, Equal Masses (detail), 2017, Oil, graphite, ink and chalk on canvas. Image courtesy of the artist.


It seems with Equal Masses we have a “one-body problem” which concerns the imagined title Space Odyssey , an equivocation to the famous monolith found in Stanley Kubrick’s masterpiece 2001: A Space Odyssey . This one-body problem is inherent in the concept of the two-body problem. Yet with our spheroids, the former is once more, not entirely applicable. For both bodies retain distinct movements which are not, so it seems, dependent upon each other. However, they are capable of being proven in exclusion of the other. Thus in the classic concept of the one-body problem, the solution simply creates two, one-body problems which can be reconverted to prove each other’s orbital trajectory as found from the starting point of two bodies in orbit. 

This runs close to a few definitions of “difference” according to the philosophical understanding of the term. In short, difference concerns a relational field generated between two or more entities, in our case spheres, shelves, shadows, and particles. Our primary entities are spheroids and the relational field may well be shadows, which themselves are in difference. The interaction between entities produces the possibility of proliferate meanings.

By imposing an imagined title Space Odyssey , I name the black spheroid. By naming, I make the black object exclusive to the other objects. By naming, I denude the potency of the image and restrict further meaning. In other words, I make an ethical choice which does not come at the expense of the work. Why? Because I have exhausted multiple concepts to arrive at this point; I name the image in mind. For the monolith (a flat, black, rectangular object) is not to be taken lightly. In the film, it represents a superior alien intelligence, perhaps the root of all sentience. HAL 9000, the advanced artificial intelligence (AI) and antagonist of the film, serves to guard humans from the monolith’s existence — to keep it secret [4]. Yet the monolith defies both human reason and the superior capacities of HAL 9000. 

The monolith may be considered to govern the two-body problem. It possesses an ineffable, unnamable force. It is reminiscent to what the great modernist poet, Wallace Stevens calls “the absolute object.” Conversely by naming the black sphere after the monolith, I risk evoking the absolute itself — a one-body problem without the philosophical concept of difference. No difference, no relation: the absolute object. But you cannot have one body; there needs to be two. You cannot have purely one thing, for there is always something else which defines it, hence implied, are two. 

My phantom title demands a thinking internal to the image itself, what is verboten to conventional philosophy [5], that means to shun difference and with arrogance. Whether or not it is impossible, if I assume the absolute, it also means I tend to the surface of the image in mind. It is now possible to say the shadows in question are more than relational phases of the image itself. Shadows do more than simply differentiate within and without one another; I consider how their particulations run off the bottom of the image. I may think the same for the image in mind. Shadows here evade banal or conceptual knowledge. One could say the shadows touch a singular truth. Perhaps that is why they appear twice, first as a substrate of shadows differentiating within themselves, and then as mere shadows on a shelf? Space Odyssey may well show us a thinking internal to itself, not unlike what we suppose artificial intelligence may achieve one day [6].

Impossible as it may seem, overcoming the two-body problem must be shown. Reality demands positive proof. One way is to insist on a second title which was never, in reality, the case for anyone but me. However adventurous it is to solve the impossible, an appearance problem keeps truth inside the object which belongs to time and reality. By attempting a singular, true meaning of Equal Masses , we are always generating another. We shall always return to relational matters which is the apparent barrier to any absolute. The identity of the monolith which infinitely evades identity itself, and in turn creates another, is not ours to own. So too is the nucleus of language, to mirror or imitate (albeit imperfectly) what appears to a self in order to speak to another. Meaning and identity are, in the end, constituted by the relation of image and observer. There is always the matter of relationality, one we attempt to overcome, and one which gives pleasure by the attempt to achieve more. 

Philosophical difference is not lost on the monolith in Kubrick’s masterpiece. In the very first scenes of the film, it provokes lower sentient forms to go to war with one another. The relational field between warring parties is governed by the monolith which possess the nucleus of all difference: friend or foe is never decided entirely by either party.

In the film our eventual human intelligence is inherited from the pre-hominid encounter with the monolith. It is an intelligence we live with and practice today — eventually drafted into the operanda of any AI or why HAL 9000 eventually decides to kill the astronauts of Discovery One. It is this monolith that provokes a war between AI and human beings. It means human life is constituted by, but not capable of overcoming difference. But there is a catch which concerns credibility. A two-body problem indeed. For going beyond difference is precisely the singular privilege of the monolith, a one-body problem humans cannot overcome, yet may still imagine.  

Joshua Miller - Equal Masses 2017

Joshua Miller, Equal Masses (detail), 2017, Oil, graphite, ink and chalk on canvas. Image courtesy of the artist.

Thus Space Odyssey concerns not only artificial intelligence. The intrigue extends beyond the capacities of humans or machines. Whatever it is, it cannot be subordinated. The monolith is the form of the formless: a form because it is clearly presented, yet there is no way conceptualise it in a final, or conclusive way. And in the end, it won’t belong to one artwork; it would belong to them all.

If Equal Masses deserves the title Space Odyssey , it is because it reaches for a status not unlike the floating infant in Kubrick’s film, which places its gaze upon some planet. Art is capable of teaching humans of their own misanthropic tendencies, and of the risk of believing in an absolute knowing, which may well be the consequence of being “artificial by nature”. 

  • 1.

    A well-known two-body problem is the gravitational orbit of satellites, planets and stars. It is possible to predict their behaviour along an elliptical pattern, when modelling each body or object as forces acting on one another.

  • 2.

    Werner Heisenberg depicts his principle this way: “The limitations imposed here on visual representation can be formulated with greater accuracy with the aid of a relationship, called the uncertainty principle, which is based on the quantum theory. It can be expressed in the simplest form as follows: One can never know simultaneously with perfect accuracy both of those two important factors which determine the movement of one of these smallest of particles — its position and its velocity. It is impossible to determine accurately both the position and the direction and speed of a particle at the same instant. If we determine experimentally its exact position at any given moment, its movement is disturbed to such a degree by that very experiment that we shall then be unable to measure exactly the velocity of a particle, the picture of its position becomes totally blurred.” Werner Heisenberg, Nuclear Physics (Philosophical Library/Open Road, 2019).

  • 3.

    Synchronous rotation is why we always see, from earth, the same face of the moon. Its appearance leads one to think that it does not rotate, when in fact it does rotate on its axis approximately every twenty-seven days. However it is locked in phase with the earth, hence synchronised. Therefore it appears, in a way, similar to the black spheroid of the image in question.

  • 4.

    Hal 9000 is not merely an AI, a programme consisting of algorithms capable of solving logical problems. It is something toward AGI or an artificial general intelligence, meaning it possesses the ability to reason by association and make decisions based on consciousness, sentience, or an awareness of its own circumstances.

  • 5.

    Continental philosophy is the legacy of Immanuel Kant’s Third Critique of Judgment. It is impossible to know things in themselves. We only have an appearance of the thing, which is always outside of the thing itself, absolutely.

  • 6.

    I am thinking here of the so-called “singularity” movement, among other dubious interpretations of AI.

Artists and Contributors

Adam Staley Groves

Adam Staley Groves

Adam Staley Groves is an academic teacher, author, and poet, receiving both Master's and PhD in Philosophy, Art, and Critical Thought from the European Graduate School, Saas-Fee, Switzerland. Adam holds a second PhD in Modern Thought, from the University of Aberdeen, Scotland. His research interests are situated in modern poetry and an ethics of the imagination particular to the user of everyday technologies. Translated and published as a poet in France, Adam has worked with noted poet and scholar, Philippe Beck and theorist Judith Balso. In 2013, Adam’s poetry was recognised by the French philosopher, Alain Badiou who situated his work as a “return to the poetry of thought.” Adam has authored two volumes of poetry: “Poetry Vocare” (2011) and “Filial Arcade” (2013). In 2016, Adam’s poem “Etui” and its concept ‘ob-literate’, based on a translation of Walter Benjamin’s “The Destructive Character” was adopted into an experimental musical composition sponsored by Gadaemus Foundation (Muziekweek) in The Netherlands. His monograph “Wallace Stevens and Speculative Poetry”, will be published by Punctum Books, USA. A lifelong musician in the DIY mode, Adam writes and records music with his collaborators in Singapore. He also practices drawing and floristry.