Inclining to the View
A talk given at the symposium Seeing From Above, Wellcome Trust, London, 6 February 2010. [pdf]
On high. ‘From height’ would make much more sense. With the sky unavailable to them, human beings have usually envisaged the aerial view as a kind of territorial advantage, typically to be achieved, not by the eye in the sky, but by the occupant of higher ground. Google Earth has given us all access to the noon view, tunnelling directly or perpendicularly down on things, but the actual embodied experience of this direct perpendicularity is still rare, because it means looking down between your feet, or, since even this could not be directly perpendicular, hanging upside down with your feet above your head, in which case your eyes are at the wrong angle for looking directly down. The closest experience I have had to this view is from the top of the St Louis arch, which has a strip of glass which allows you to look straight down at the ground below. ‘On high’ seems right, because we have never found it easy to imagine being high without nevertheless still being on something, an eminence, a peak, a ledge. And this means that, unless you are a transparent being, your view will always be at some kind of diagonal. This is why the eye of noon is a pure eye, unprovided by any corporeal setting. And this in turn is to say that it has always been a supplemented eye, an eye separated from a body, whether that makes it the eye of God or of a satellite. The view from above is the fantasy of an Anschauung, a world-picture from which you yourself could be entirely absent, into which you could not on principle enter, since by doing so, you would introduce complication, muddle, approximation, departure from the true. Inclination.
The direct gaze from sky to ground is met and answered by the gaze upwards. But even this is harder to achieve than might be thought. I’ve always been intrigued by the difficulty of assigning rights to airspace. In theory, the owner of a patch of ground also has jurisdiction over the space above that territory, in a column of air that rises directly upwards. But if rights were really extended upwards in parallel columns, gaps, like infinitesimally thin slices of brie, would eventually start to appear between the columns as they were extrapolated into space, so that the airspace owned by number 35 Haystack Road would eventually find itself light years away from that owned by no 33. Either my airspace ascends upwards for ever like a chimney, of exactly the width of my houseplot, or my airspace must be imagined as a cone rather than a column, widening as it goes to take up the spare space opening up between it and neighbouring plots.
Direct. Michel Serres is fond of reminding us that there is a squint even in this word, which derives from the word for right. In English, we tell people to go ‘right ahead’, just as the French say ‘tout droit’. So going straight means veering off, walking with a rightward slant. Serres reminds us that lateralisation and partiality are everywhere in nature – not just in animals, but also in molecules. The myth of beginning that Lucretius gives suggests the necessity of some inaugurating swerve or deviation in things. Lucretius asks us to imagine a world in which atoms simply rained down through empty space. In such a condition of what we now call laminar flow, in which separate streams of atoms flow in non-interfering parallel lines, there would be no collisions, no yet collusions, no alterations of any kind. There would be no time, but simply a relation of equality: A=A=A=A. Adopting the equals sign in his Whetstone of Witte in 1557, Robert Recorde explained that he had chosen two parallel lines ‘bicause noe .2. thynges, can be moare equalle’ (Recorde 1557 sig. Ff1r). In order for there to have been anything at all, there would have to be at least one atom that swerved from its course, ‘tantum quod momen mutatum dicere possis’ ‘just so much that you can call it a change of direction’ – the clinamen (Lucretius 1994, 2.220, 43). Without this swerve, there is only necessity, endlessly repeating itself. This absolutely non-necessary waver, this minimal departure from self-identity, is necessary for everything in our universe to be. Everything comes from this inaugurating fissure, this chink of incipience, this ‘atom of angle’ (Serres 2000, 11). But by now, in our world, that is the arborescent integral of millions of deviations, it is the laminar that is the unheard of exotic, not the deviant.
For Michel Serres, the body is not a vertical, but a diagonal:
if the body plays the part of a statue, with its weight, toward the bottom, it sculpts a second one, through its lateralization, to the right or the left. It rests on its feet, but drawn to one side. It would be necessary to trace a composing oblique line that would give the true vertical line of the living being who is unceasingly attracted by this diagonal, and which would form the angle of its own fall with the normal line. Everything leans and is exposed on the side where it will fall. (Serres 1997, 24)
The diagonal is a vector, for it is never in place. It is approximate, which means that we can only ever approach it. Equilibrium convokes a shimmering of diagonals, as they approach and depart from the true north of verticality:
We do not find the center, and we are inclined to abandon it. We lean to the right, to the left, to get away from it. Are we afraid of it? We neither know how to nor can we inhabit this fault line, this axis or this vortex: who would build his house in the middle of a current? No institution, no system, no science, no language, no gesture or thought is founded on this mobile place – which is the ultimate foundation and founds nothing.
We can only head toward it, but at the very moment of reaching it, we abandon it, compelled by the arrows that depart from it. We spend only an infinitesimal moment there. Time and site of extreme attentiveness. (Serres 1997, 27)
If there is agon – striving, straining – in this diagonality, there is also the beauty of rhythm. For the diagonal is time and speed and desire (‘inclination’). Descartes’s grid will suffice to determine the position of any point in space, through the combination of verticals and diagonals, but if we are to model the movement from one position to another we will have to have recourse to diagonals, that mediate the x and y axes. There is an excitement and incitement in a slope that there is not in a wall or a floor, precisely because we can be carried away with a slope, which can get us ahead of ourselves (the problem with slippery slope arguments, I once heard somebody innocently say in a radio interview, is that you never know where they are going to lead).
One sees nothing at noon, in its bleak incandescence. There is only blinding glare. If God’s eye were to pulse back to itself without residue, without loss, it must surely consume itself. There must be delay, phasing, diagonality. Edwin Abbot and other early reflectors on n-dimensional spaces realised that to inhabit a further dimension of space would mean that it would be possible to look in on us unobserved, just as a creature of three dimensions can overlook and look in on the roofless enclosures of the inhabitants of two-dimensional space. But to look directly down on something is to reduce its three dimensions to two, scouring away every hint and intimation about its height and volume. It is to reduce things to their diagrams, their outlines. It is to make oneself monocular, blind. The view from directly above, favoured by bombs, smart and dumb, is already a devastation, a razing. At the imaginary centre of things, I too vanish from view, my profile shaved down into pure, vertical equivalence – the gnomon I. As I lean sideways, or the sun to tilt away from me, I start to cast a shadow, and come back into view. Two eyes are necessary for parallax. You can be where you are or you can see where you are, but not both, for if you can see where you are, then you are no longer quite in place, you have minimally departed from yourself, in the way you always must to know exactly where you are.
If there is always cruel decisiveness in the view from directly above, there is often pathos and compassion in the diagonal. The crucifix gives an image of the intersection, exactly at right angles, of the divine and the human. Painters of the crucifixion know that much depends on the angle of its elevation, such that we must lift up our eyes to it – or, in Dali’s version, look down on it, in heightened shame, shame abased in its elevation, from a position just to the side of the vertical. A carpenter knows that there is no strength in perpendicular relations, or cross joints, if they are not braced at the corners, by diagonals. The diagonals of the dovetail holds joints tightly together, while the many forms of the wedge, driven in to secure wonky joints of all kinds, is the subject of admiring analysis in Richard Coyne’s The Tuning of Place (2010).
The slanting view includes its own shortfall, it indicates what it does not reveal. In the diagonal view, there is always a ratio between the revealed and the concealed. Paradox: the diagonal view puts us in the picture by displaying in it the evidence of our relation to it, projecting the conditions and dispositions of our seeing into the scene. We are both more and less than what we see – more because we see that we do not see everything. It puts and shows us in our place. But it does this by displacing us, by making it necessary to see that we are both at the centre of our own point of view, and also not at the centre of what is seen. And yet we see everything, including the fact that we do not have the best seat in the house. I am there by anamorphism, diagonally laid out across the lines.
For Sartre, being can only ever be being-there, and being-there always means being at a particular angle to the world, such that ‘[f]or me this glass is to the left of the decanter and a little behind it; for Pierre, it is to the right and a little in front. It is not even conceivable that a consciousness could survey the world in such a way that the glass should be simultaneously given to it at the right and at the left of the decanter, in front of and behind it’ (Sartre 1984, 306). The fact that being means orientation creates a kind of mixture of necessity and contingency: ‘while it is necessary that I be engaged in this or that point of view, it is contingent that it should be precisely in this view to the exclusion of all others’ (Sartre 1984, 308). My obliquity to things is not just my contingency: it is the absolute necessity of that contingency.
Diagonals fix us in our place by slightly unseating us. We see that we are where we are not, that we are not in what we see, even if we are in the end nothing more than this finitude, this always particular angle of divergence from being able to see everything. To get a fix on something, you do not stare at intently, you move our head slightly from side to side. We determine positions by triangulation. The astronomical enthusiast I was as a young boy was taught that, to see the dimmest stars. you should look just to the side of them, for then the light falls on a part of the retina that is more sensitive to faint light than the middle.
The diagonal is the noise, the aberration, the shimmer of cross-purpose, that fixes and finitises form and position, like the random scribbles at all angles that yield up the lineaments of a brass rubbing. The discipline of crystallography is founded upon X-rays, which enable us to see the structure of matter – making possible, for instance, the remarkable photographs of the tobacco mosaic virus by Rosalind Franklin which helped Watson and Crick see for the first time the helical structure of DNA. But nothing could have been achieved by simply staring into or through the heart of things. Crystallography depends upon the technique of X-ray diffractometry, in which a beam of X-rays is fired at a crystalline arrangement and diffracts into many specific directions, the angles and intensities of these diagonals then making it possible to infer with great exactitude the structure of the crystal. Newton’s experimentum crucis, which showed that a prism scattered the different colours in white light, rather than adulterating the white light with colour, depended upon the refraction of refraction, and far from taking place at one Eureka point in time, was itself arrayed across a series of different operations over a substantial period of time.
The diagonal has always been enigmatic and rather suspicious (the shifty look, the bend sinister of illegitimacy). It is the vehicle and dimension of the incalculable, the infinitesimal, the asymptotic. As such, it also has magical power. At the beginning of the Meno, Plato shows a slave that it is possible to solve the surprisingly difficult problem of how to construct a square b with precisely twice the area of a square a by drawing the second square on the diagonal of the first. The Pythagoran Hippasos of Metapontum is said to have been drowned for revealing the demoralising truth that the ratio of a square’s diagonal to its side is √2, which is neither a whole number nor a fraction. The episode is cheerfully evoked by Beckett, the great ethicist of the geometrical:
‘betray me’, said Neary, ‘and you go the way of Hippasos.’
‘The Akousmatic, I presume,’ said Wylie. ‘His retribution slips my mind.’
‘Drowned in a puddle,’ said Neary, ‘for having divulged the incommensurability of side and diagonal.’
‘So perish all babblers’ said Wylie. (Beckett 1957, 47-8)
The death of Hippasos, as described by Iamblichus in the 3rd century, was more generally given as expulsion or being drowned at sea. Though there has been some doubt about this myth of the Pythagoreans and their terror of the irrational (Hodgkin 2005, 45-6), versions of this story have often been used to explain the disinclination among the Greeks, so brilliant in their apprehension of geometric relations and proportions, and in the exercise of deduction, to measure and calculate. And yet, Michel Serres has suggested, the observation of the ecliptic, the fact that the path of the sun over the year is at an angle to the celestial equator, opens up a gap in the middle of this rational scheme: ‘At the very heart of the formal project of cleaving only to the efficacy of Ideas or mathematical Forms, in the very dream of universal deduction, the powerful and hollow dream which meant that the Greeks could never arrive at modern science, inclination returns, introducing noise into the redundancy of the Same, to open the story of the beginnings of the world’ (Serres 2006, 154). The incommensurability of the side and the diagonal may be taken to be the concentrated image of the incommensurability of abstract or theoretical mathematics and the behaviour of things in the physical world. The rational and the irrational are not, perhaps, opposed, since this is a perpendicular notion, but are, rather, slightly, and all the time ever so slightly less, yet still eternally divergent. However close they may approach to each other, in embodied time, this incommensurability will never entirely close. ‘Physics’, as Michel Serres has said, ‘is indeed an affair of angles’ (Serres 2000, 10).
Beckett’s Quad seems to be a dramatisation of this structure formed from departures or deviations. Four figures enter a square in succession, pace in regular patterns along one side of it, then turn into the middle to cross along the diagonal to the opposite corner, each time swerving around the centre. It is a kind of geometrical cosmogony. The combination of their movements of avoidance creates a vortex, as many departures from the vertical may. And we view it, not from directly above, though this is how Beckett diagrams the piece, but from above and at an angle of about 20°. We not only see the piece, we are in the midst of our seeing, in the angle which subtends all life
Let us say that the relations between the parallel and the perpendicular on the one hand, and the relation between the line and the diagonal on the other, figure the relations between the abstraction of mathematical laws and the infuriating, beautiful aberrancy of actual natural facts, which only ever approximate to those laws. Physical laws and their fields of application can neither be separated from each other, nor ever coincide exactly. The nuptials of reason and the real are never celebrated. No one has ever seen a mathematical law, any more than anyone has ever seen their own seeing. In fact the relation of a law to its field of operation is homologous to the relation between an act of seeing and the scene on which it operates. Both are deductions. A law gradually begins to reveal itself through the averages of natural forms and actions, which approximate ever closer to laws without ever quite coinciding with them. The more times you toss a coin, the closer the average proportion of heads to tails will approach to 50:50 – until, that is, having got as close as it ever will, it begins to oscillate back and forth around this ratio, or begins to register the effect of slight imperfections in the coin’s manufacture, or some other form of systematic bias in the environment. The law will be apparent in this movement towards convergence of reason and reality. Similarly, the fact and condition of our own seeing is apparent in the ways in which we see everything, even as that act of seeing will never itself fully enter the field of vision. In both cases, there is a minimal divergence, meaning that the law and the occasion can neither be distinguished nor identified. There can be no law, no government of the eye, without this irreducible astigmatism in it and of it. The noncoincidence of the rational and the real is their angle of incidence.
Where the language of metaphysics touches in the language of geometry it discloses the importance of angular thinking. Where the axioms of geometry deal with essential and necessary truths, the work of the tangent results in which we call contingency, or the occasional or the incidental. Existence is not opposed to essence, it is at a very acute angle to it.
The angle arises between the divine and the mundane. The view from above that we can entertain is not that of the eye of God, for we are all binocular. The closest we can come is that view entertained by those in the shadow or at the shoulder of God the Father, the chips off the old block, who prism his light into rainbow glory, the iridescence of the all-but – those companion entities we know as angels, but of whom we might better say, inverting Pope Gregory’s mot, non angeli sed angli. ‘I am vertical’, says Sylvia Plath, ‘but would rather be horizontal’ (Plath 1981, 162). Human life comes into being in the radiant arc between these two inhuman possibilities: we fall exquisitely short, to the side, of being homo erectus, in the subtending tilt of homo diagonalis.
Beckett, Samuel (1957). Murphy. New York: Grove Press.
Coyne, Richard (2010). The Tuning of Place: Sociable Spaces and Pervasive Digital Media (2009). Cambridge, Mass.: MIT Press.
Hodgkin, Luke Howard (2005). A History of Mathematics: From Mesopotamia to Modernity. Oxford: Oxford University Press.
Lucretius (Titus Lucretius Carus) (1994). On the Nature of the Universe. Trans. R.E. Latham. Ed. John Godwin. London: Penguin.
Recorde, Robert (1557). The Whetstone of Witte Whiche is the Seconde Parte of Arithmetike… London: John Kyngston.
Plath, Sylvia (1981). Collected Poems. Ed. Ted Hughes. New York: Harper and Row.
Sartre, Jean-Paul (1984). Being and Nothingness: An Essay on Phenomenological Ontology. Trans. Hazel E. Barnes. London: Methuen.
Serres, Michel (1997). The Troubadour of Knowledge. Trans. Sheila Faria Glaser and William Paulson. Ann Arbor: University of Michigan Press.
—————– (2000). The Birth of Physics. Trans. Jack Hawkes. Manchester: Clinamen Press.
—————– (2006). Récits d’humanisme. Paris: Le Pommier.