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Newton’s prisms.

An Essay on Representation

 By Alan Wall.

Five Introductory Reflections.


NEWTON IN HIS room in Cambridge arranges the prism so that white light is rainbowed into the discrete colours it comprises. Then he fixes up an inverted prism, to test that the separated beams suffer no further alteration. Thus does the symmetry of nature demonstrate itself in a single room in Trinity College, Cambridge, in the seventeenth century.

Light arrives as corpuscles, or particles, he reckons; though he allows for the possibility that it has some of the character of a wave. Others insist that light propagates itself entirely as a wave. So in Newton’s representational world light is particulate. We only see light as it arrives in infinitesimal speeding units from the sun. He has a clinching question for those, like Huyghens, who insist that light is a wave: how come it can’t go round corners then, the way sound can?


THE ‘TRUTH’ OF any fact is its demonstrability within a system of representations. No fact is ever singular, or discrete; it is relational. ‘There are no things,’ said the painter Georges Braque, ‘only relations between things.’ Nothing is inherently true or false. It appears in a field of relations out of which truth or falsehood is generated. To stand outside any representational world and describe it is to designate it either as myth, ideology or bad science. And to describe any representational world as any of these is to imply that one is situated, even if partially, in a different representational world, since only this would permit the distance required for such external characterisation.

Newton knows that waves have certain characteristics: they can go round corners, for example. Light does not appear to do this; even when refracting, it always travels in a straight line. So the colours coming out of Newton’s prism in his room in Trinity confirm a world of representation in which light is particulate, made up of individual corpuscles.


IN THE EARLY years of the nineteenth century, Thomas Young conducted (or arranged to be conducted) an experiment which is the prototype of the double-slit experiment. This crude demonstration appeared to show that light forms patterns of diffraction and interference. If it does this then it is exhibiting the behaviour of a wave. There was considerable hostility to Young’s deductions, partly because of the great authority which accrued around Newton’s name and reputation, and partly because of hostilities between the Royal Society and the Royal Institution. The criticisms effectively shut Young up on the subject, but the nineteenth century found more and more evidence to support his notion that light comprised a form of electro-magnetic radiation, and expressed itself in waves. As the century wore on, Young’s wave theory of light seemed to be vindicated.


IN 1900, PLANCK discovered that light arrives in quanta – tiny discrete units of energy. If light is discontinuous, then it cannot be propagating itself as a wave, since one of the defining characteristics of a wave is its seamless continuity. In 1905, Einstein demonstrated that the photo-electric effect is only possible because photons (a term not used in this sense at that time) are granular, and can knock electrons out of a metal sheet, provided they arrive at the right wavelength.

What we now appear to have placed before us are two representational models, in contradiction with each other, both insisting that their terms include the ‘nature of light’. This crisis took nearly a quarter of a century to resolve itself. It did this by abandoning ‘either/or’ and choosing instead ‘both/and’. It is known today as the principle of complementarity. Light is both wave and particle. Ask wave questions and you will receive wave answers; ask particle questions and you will receive particle answers.


‘LIGHT IS PROBABLY the undulation of an elastic medium.’ Thus Thomas Young. This medium was thought to be the ether. Both Newton’s corpuscular theory and Young’s wave theory could be traced back to antiquity. There were proponents on both sides for thousands of years. However, all appeared to be agreed that light could either be a wave or a stream of particles, but it could not be both at the same time. Energy could transmit itself either as wave or as particle, not as both simultaneously. So the crisis that needed to be resolved within this system of representations was an epistemological one: how could one type of energy or matter be both wave and particle at the same time? The ‘resolution’ of this dilemma expressed itself as quantum mechanics, and Niels Bohr coined the word complementarity to permit an approach to the apparent contradiction.

But how much complementarity can any representational world sustain without fissuring? And which types of representations are to be permitted as complementary; which will be simply deemed contradictory? In the space between ‘complementary’ and ‘contradictory’, our intellectual worlds either cohere or disintegrate.

Newton’s corpuscular theory of light can be accepted as valid modern science; his alchemy and his Biblical numerology cannot. They are seen as material from entirely other worlds of representation, worlds which are simply incompatible with the ‘modern scientific world view’. Similarly, Newton’s prism is still with us, but John Dee’s shewglass is not. In that he paid skryers to observe creatures from elsewhere; angels came in the night and spoke the language of Enochian. Such data we cannot include in our modern intellectual world view. We consign it instead to the region of the antiquarian and the occult. When John Dee stared into his crystal he was convinced that he was seeking truths there as valid as any Newton might have observed emitting from his prism. We beg to differ. At this point we say, complementarity must now end, and contradiction begin. Similarly with Newton’s own alchemy. The information we expect to find here is biographical, not scientific. We have no need to ‘save the appearances’ from such a representational world, since we have abandoned it. And we now seem happy to accept that light entered one of Newton’s prisms as particle and exited the other as wave.

Mystical Numbers.

DOES THE TRUTH arrive in words or numbers? Those who are numerate are normally literate too, but there are many highly literate people who close the book on encountering a single equation. For these, according to certain accounts, there can be no precise apprehension of the nature of physical reality; merely a discursive approximation, a fumble of words and phrases, a lexicon of imprecisions. The case of Galileo might seem exemplary here. He argued that God had spoken through the Bible, but that he had also spoken through nature, and the language he spoke there was mathematical and geometrical. Cézanne appears to have been thinking on similar lines when he said: ‘Render Nature by Means of the Cylinder, the Sphere, the Cone, all Placed in Perspective.’ Galileo had specified triangles, squares, circles, spheres, cones and pyramids.

The Bible might tell you how to get to heaven, but it couldn’t tell you how the heavens worked: for that you needed science. Here is an example of complementarity, in this case between scripture, astronomical observation and experiment. Richard Dawkins would say this is a false complementarity. If we interrogate it with sufficient vigour we shall find mere contradiction. So how much intellectual heterogeneity, we ask, is possible under the rubric of complementarity?

The argument can hardly be said to have softened. Is our fate ultimately expressed in numbers? The numbers that calculate whether the universe will die a cold death, dispersing forever into space, or a heat death, contracting backwards through the force of gravity, do of course express ‘our’ ultimate fates, or at least the ultimate fate of our habitat. Roger Penrose and Stephen Hawking also appear to be saying something like this: the calculations which we have applied to work our way back to the Big Bang are the most meaningful forms in which we can talk about creation. From the equations it appears that the universe could have been created ex nihilo, with no matter to start with. We start, in effect, with the equations. Plato’s academy had a sign over its door advising those ignorant of geometry to stay outside. And Pythagoras, it is said, visited many sects and religious leaders in his early life in an attempt to glean any knowledge he could. He was on a quest for the truth of things. Then it was back once more to a serious study of numbers. The most noble pursuit was to understand how nature expressed itself in mathematical form, in uttering itself through the relations inherent in a triangle, or in the intervals discoverable in musical scales. Number was a sacred category. Those ignorant of the knowledge it divulged were doomed to remain outside the brotherhood.

The largest leap is always to get from one to two. Once we have accepted that all is not a singularity of consciousness, in which no laws apply except hunger and desire, a random motion of excitement beyond the trackings of any rationality, but that there is here before us subject and object, and that I cannot include all that exists in the unum mundum of my consciousness, or pre-consciousness, or unconscious, then I have ventured into the perilous realm of plurality. And once I accept that A is not the alphabetic totality, the undifferentiated kingdom of the Alpha King, but that alpha is in a dialectic marriage with beta, then logically this relation between two ones can only be perceived from a third position, even if that triangulation is achieved by apperception. Apperception, after all, is not mere self-communing, but announces a fracture of perception into self-consciousness.

And if there are three, then why not four? A trinity presupposes some sort of quanternion, if only to locate it in space and time, or at least in eternity. If one can look in from outside to see how alpha and beta might link in a copula that issues in gamma, then why cannot the observer of such configurations also be observed?

Even in number mysticism, the trinity can be a form of self-completion, but once we have progressed to quadrilaterals, we have surely entered the multitude of numbers. Once you have counted up to four, you are pointing towards infinity. Infinity (whichever one) can never be specified, because you can always add another digit to the specified figure. Even worse, as Cantor noted with rising mania, some infinities are bigger than others.

Anyone devoted to astrology, in whatever form (and a remarkable number of people are), is ultimately committed to the idea that it is number, in the form of planetary positions and relations, which governs the individual life. And there is a persisting fondness for the idea of mystical numbers with supernatural or magical properties, numbers which could unlock the nature of things.

One number has been obsessing us for thousands of years. At its most banal it is merely π, the number by which you need to multiply the diameter of a circle so as to get the extent of the circumference. It is a transcendental number, which is to say that the line of digits behind the decimal point outcompasses our measurements. Computers have now got into the act: the calculations were last seen at five trillion digits and rising. There is a compelling film by Darren Aronofsky called Pi. In this, Max, a tormented mathematician, believes that numbers control reality, and that even the movements on the stock exchange should be deducible in mathematical form, perhaps as a series of algorithms. A group of Kabbalists is also searching for a number, a number which spells out the secret name of God, and thereby inaugurates the Messianic Era. The number they are looking for consists of 216 digits, and is an application of the Jewish mystical practice known as gematria. Max’s computer Euclid discovers this number and starts to secrete an organic substance, which gives the impression that it could be a form of semen. Max is pursued and harassed by people from the world of finance too: they think he could help them get rich by predicting the daily movements of stocks and shares. Finally, tortured beyond endurance by these numerical and numerological obsessions, Max trepans himself with an electric drill. Only after this neurological DIY does he begin to smile.

The notion of a number which might somehow break open reality, decode it, appears in various forms of religious literature. It is there in the Book of Revelation, which is strewn with examples of the mystical significance of the number seven, as a register of completion, fullness, pleroma; and in the number 666, which was thought to be the number of the beast, the signature in numerological form of the Antichrist. These numerological clues have caused much mischief amongst the inhabitants of this planet. They are still calculated and re-calculated so as to work out when this particular period of history will end, in great tribulation and catastrophe, inaugurating the millennium. When the Great Fire occurred in London in 1666, there was no shortage of pamphleteers explaining that the devil’s hour was at last arriving. The number of the beast was announcing itself through chronology. In an intriguing gloss on this tradition, Arthur C. Clarke wrote a story called ‘The Nine Billion Names of God’, in which a lamasery in Tibet has been working its way through its special alphabet to spell out the nine billion names of the Creator. Once this task is completed the world will end. It would have taken another fifteen thousand years to complete the calculation manually. But the redemptive arrival of computers allows the process to be speeded up. Computer programmers are shipped in from New York, and set to work. At the end of the story, having completed their task, the computer men watch astounded as the stars begin to go out, one by one.

And of course there is Arthur Dent and The Hitchhiker’s Guide to the Galaxy. There the ultimate computer brain is encountered, which finally spews out the answer to life, the universe, and everything: it is, bafflingly, forty-two. (And we have still not fathomed the significance of the magic square in the upper-right corner of Dűrer’s engraving ‘Melencolia I’ in which every line adds up to thirty-four.)

As if to alert us to the danger of mystical numbers, and the decoding of life according to their lights, the earliest papyrus containing a version of the Book of Revelation in Greek was recently discovered. It dates back to the third century. Here the number of the beast is clearly written as 616. So many calculations over two thousand years might have been based upon a misconstrued digit. The number, in any case, appears to have been used to avoid using the name Nero: it is a form of samizdat communication. Those obsessed with applying this number to calculations involving the nature of reality seem to want to find the secret hidden away in the fabric of things, without doing the necessary maths first.

But back to numbers versus words. Niels Bohr was aware of the necessity of both. ‘We are suspended in language,’ he said more than once. On the other hand, in speaking of what quantum mechanics had achieved he wrote: ‘Such an interpretation of the properties of matter appeared as a realisation, even surpassing the dreams of the Pythagoreans, of the ancient ideal of reducing the formulation of the laws of nature to considerations of pure numbers.’ And he is reputed to have said to Heisenberg: ‘When it comes to atoms, language can be used only as in poetry. The poet, too, is not nearly so concerned with describing facts as with creating images.’ This beguiling statement leaves us with a lot to think about regarding the relationship between poetry and ‘fact’. The formulation of the ‘laws of nature’ would undoubtedly appear to be a matter of numbers. And yet poetry and mathematics appear to be portrayed as complementary representational worlds.


WHEN ISAAC NEWTON was not formulating the universal law of gravitation or writing Principia Mathematica, he was engaged in alchemical experiment, or trying to fathom the clues provided by scripture for the duration of history. In all of these activities he was pursuing secrets, and secrets need to be first detected then decoded. The principle of gravitation did not disclose itself readily: it took a long time and a lot of mathematics to arrive at the discovery, and yet the evidence was always there before our eyes, at least in the form of heavenly bodies and their motions. The inverse square law itself follows from Kepler’s Third Law. The word clue takes us back to the labyrinth. What Ariadne gives Theseus is a clue, a clew, a thread, to take him into the darkness and then find his way out again (the original meaning of clew was a ball of thread or yarn). While in there he would kill her half-brother, the minotaur, whose demand for youthful flesh from Athens represented a recurrent terror to the inhabitants of Crete. Ariadne’s reward for this act of sisterly betrayal is to be betrayed in her turn: Theseus dumps her on Naxos. Then, approaching home, he forgets to change the black sail to a white one. His father reads this as an announcement of his son’s death, and throws himself into the sea, thereby giving his name Aegeus to the Aegean. Gaining entry to labyrinths, following the clues, would appear to be a tricky business.

Sigmund Freud certainly thought so. He had a ring made for his close associates: it showed Oedipus answering the Sphinx’s riddle. This for Freud represented the activity of the psychoanalyst, peering into the darkness and bringing light out of it. At the beginning of Oedipus Rex, Oedipus is presented as the saviour of Thebes; he had removed the curse the Sphinx had imposed. He was rewarded with the hand of Jocasta. Here the plot, the machinery of the narrative, conceals a terrible secret. Jocasta’s hand is available only because her husband Laius was killed. As the plot unfolds we have the secret revealed to us: Oedipus kills Laius, his own father, then he marries his own mother and begets children on her. And all of this occurs because the oracle had declared at the boy’s birth that he would grow up to do these things. And so they had him taken up into the hills, to be exposed, so as to die. The real ‘chronological action’ of the play, the fable from which the complications of the plot are constructed, begins with an attempted infanticide. Infanticide in legend always represents the attempted refusal of the future. Unfortunately, the future cannot be refused. It is like the force of a mighty river: dam it up here, and it will find another way through, somewhere else. In a sense, the death of Laius can be seen as time’s revenge upon the attempt to thwart its scheme. You were told that this boy would grow to kill you, and look, he has. All your attempts to escape the oracle’s force have led you to this lethal moment.

Freud’s appropriation of the image of Oedipus seems fraught with danger. After all, the original action being alluded to does not end well. But of course Freud believed he had discovered in the figure of Oedipus a secret so terrible that humanity had collectively agreed to forget it for ever, through the process Freud called repression. It was the end of the nineteenth century and he attended two performances of the play. He asked himself how events so occult and remote in time could have such a profound effect on a modern audience. His conclusion was that it was because a deeply hidden universal truth was being enacted in the form of a literary allegory. All male children want in infancy to kill their fathers so as to possess their mothers entirely. Oedipus actually does it. Immediately after this reading of the play in The Interpretation of Dreams, Freud discusses Hamlet. The main character here, he believes, is implicated in the same sexual labyrinth: he cannot kill Claudius because Claudius has done what he himself secretly wanted to do: kill his father so as to possess his mother. When he does finally kill Claudius, it is as though he were killing his own desires, since he himself dies a few moments later. The action is less explicit than in Oedipus Rex. The forces of repression have grown stronger over two thousand years.

Freud’s reading of Oedipus is possibly the most radical re-reading in history. What he effectively says, and it is a shocking thing to say, is that the whole of modern science knows less than the knowledge secreted in occult form in an ancient play. He is saying that the most important knowledge we can have about ourselves is there to be detected, just as the data regarding the universal law of gravitation was there before our eyes, but it presents itself to us in the form of a secret, and it is a secret because of the dark antagonisms within our own psyches. We cannot own up to our own desires and cravings; civilization imposes its necessary discontents upon us in the form of repression, and repression makes us ill and miserable. Freud’s is in effect a Gnostic creed: the real truth is hidden, and only initiates have the means to discover it.

When John Maynard Keynes read through the writings of Newton concerned with alchemy and Biblical cryptanalysis, he was appalled. Here was the greatest scientist of all time immured in the murkiest intellectual activities. He was looking for secrets in the wrong place. As a scientist he should surely have been dedicated to reputable practice and experiment, but instead he was just as involved in the disreputable practices associated with alchemy and Biblical numerology – not that Newton found them disreputable. The curious thing is that Newton never seems to have drawn any distinction at all between his different forms of activity: they all allowed for a search, an enquiry into the secrets embedded in the fabric of nature or history or scripture. One entrance was as good as another. One representational world as valid as another. His beliefs about many things – his Arianism for example – would have classified him as intellectually disreputable in any case, so he kept quiet.

Narrative and Plot.

IN THE NARRATIVE of attempts to understand why an apple falls from a tree to the ground, Newton’s perceptions and calculations represent the moment of anagnorisis, that point in a story when the information arrives via a messenger; when we realise that Oedipus is the slayer of his father, the husband of his mother, the brother of his own children, the cause of the curse that lies upon the land, rendering it sterile. And in the narrative of attempts to understand why the neurotic becomes ill, Freud’s self-imputed revelation about the nature of Oedipus Rex, and the desires it reveals, if only obliquely, claims to be a moment of anagnorisis in psychology; in our collective understanding of ourselves.

In both these cases something has to be painfully discovered, a secret has to be analysed and decoded. The effort is all in the disentanglement, so that we can proceed to the dénouement, which in French means unknotting: we are back with those clues which were originally clews, threads or ropes, which lead us in and out of the darkness. A lot of energy and ingenuity must go into understanding the clues which nature presents to us. But why should we expend seemingly as much energy in actually creating secrets? Why should we construct plots in plays and novels and stories, whose complexity lets the secret be fully revealed only at the end? Why do we need to create innovative contexts for secrecy, as though there weren’t more than enough of it around already? Should we not be sufficiently exhausted by the attempt to decode the secrets already contained in our world without having to create secondary worlds in which conundrums once more taunt us beguilingly to solve them? Why are we so in love with narratives that we continue to construct them with such an expenditure of effort? What is the nature of our need for secrecy and the divulging of it?

Is it possible that we create our artificial worlds in art and literature, filling them with clues as to the secrets that need uncovering, the riddles that need solving, because we never feel we really can solve them so effectively in life itself? In other words, might our fiction be a way of assuaging our torment in the domain of fact? And if that is so, we then have to ask another question: to what extent does knowledge claiming to decode secrets about nature, what we normally call science, enact (knowingly or not) the manoeuvres which characterise fiction? To what extent does our addiction to narrative shape even scientific thought? This might be one way to describe the work of Nietzsche: when we imagine we are uncontaminated with fiction, it may actually be dominating our thought.

Freud himself believed that the ontogenetic recapitulates the phylogenetic, which is to say that the life of the individual and his psyche mirrors that larger narrative in which we as a race came to have these particular psyches. Thus does the Oedipus complex re-enact the killing of the primal father, to enable the frustrated sons to enjoy the womenfolk whom the primal father had kept for his own pleasure and procreation. These arguments have not withstood much serious historical scrutiny, but it is intriguing how frequently they seem applicable to art, for there one can see a constant rehearsal of our oldest themes, a return to our earliest and most unyielding preoccupations, whether enacted in history or not. In art, said Picasso, one must kill the father.

The etymology of ‘secret’ takes us back through Latin to the notion of separation, setting something aside. Cernere has the sense of distinguishing and secreting. There is an interesting parallel here with the Hebrew word for creation, bara; this also means a cutting, a separation. That which is holy is set aside, where the etymology of ‘profane’ means ‘open to all viewers’ – in other words, not set aside. The sacred, the hallowed, needs to be cut off from the profane, and yet it can only be arrived at (in narrative anyway) through it. It is a great mistake to assume that the secret is in effect secret from the text in which it is embedded; it is instead secreted within it, part of its integral fabric. Only the full understanding of the text, in all its profanity, can lead to the hallowed secret. Another way to put this is to say that we can only arrive at the latent meaning through a scrupulous journey through the manifest one. The sacred element of the text must be discovered as a separation from, a creation set apart from, the profane availability to all which is the published manifest text. Even if the latency (the secret) can only be obtained through the profanity, it still exalts itself above and beyond such profanity, as the narrative completes its journey.

There are other ways of announcing the secret. ‘Riddle’ takes us back to the Old English word for a dark utterance. As for ‘parable’, that takes us to the Greek word for an allegory, analogy or similitude. All three have one thing in common: they devise various means of utterance whose function is to delay or thwart comprehension. They are not straightforward; the meaning is bent into an unfamiliar shape; it is defamiliarized. It is not to be distributed freely to the profane. Or perhaps more subtly, if the profane wish to understand, they will have to set aside a part of their profane minds, dedicating it to the sacred. That will only be possible after the narrative journey. Any narrative involving the sacred and the profane is as much ‘both/and’ as ‘either/or‘.

Art, Model, Toy.

ART ABBREVIATES AND miniaturises. It functions through formal compression. It is like a child’s toy; it gives us the illusion of possessing a larger reality, which is actually beyond our reach. Compressed into art we find what most obsesses us, even when, as in the Oedipus plays or Hamlet, we can’t consciously acknowledge what that obsession might be or how it came into being. In other words, art allows for expression which in another context the psychic censor inside us could negate. It permits the creation of parallels, the inauguration of secondary worlds. It was this facility for bypassing the conventions of expression, for evading the protocol which governed the interior dialectic of disclosure and repression, that made art such a valuable resource for Freud. Here were the clues that led in and out of the labyrinth. They were also to be found in the realm of dream, and Freud spoke of the process of artistic creation as akin to that of daydreaming. When not entirely governed by the conscious ego, the mind lets slip its primeval enchantments and demoniacal possessions. Art facilitates the exposure of the primitive within us, and its entanglement with the discontents of civilization. What we bury deeper and deeper inside ourselves does not thereby get left behind.

One of Freud’s observations of childhood behaviour was watching a little boy engaged in the fort-da game, whereby he threw something away from himself and then pulled it back. This, Freud concluded, was a way of mimicking the ‘control’ of a reality which was in truth beyond his control. His mother went away from him when he didn’t wish her to do so, and the repetitive game was a way of exercising control over things, so that they would seem to come and go at his bidding.

A toy has many similarities with a model in the scientific sense. The child’s little town, in which he can move the figures and animals around, bears a striking resemblance to an orrery, an elaborate model of the solar system, in which, by turning the right handles, the planets actually move around the sun. This is a model, a miniaturization of observable nature so that it can be operated, observed and studied in an abbreviated shape, in a compact form in which all noise, in the cybernetic sense, is excluded; all the data presented is in the form of information.

Is it possible that we take such delight in complex narrative structures whose sequentiality ultimately discloses their secrets because they present us with a kind of model, a microcosm of the process of understanding itself? We see how the evidence, the data, can amass beyond our comprehension; but once the terms of understanding, the agency of translation, has appeared, then all the data is promptly transmuted into information. We are attending to the process of our own understanding; we observe the progress of a specific enlightenment in microcosmic or abbreviated form.

So toys have much in common with both scientific models and works of art as comprehensible abbreviations of reality, or miniaturizations of experience. By so modelling the world we make it manageable for comprehension. We like to read texts that only reveal their secrets after the pleasure of painful scrutiny, after a fastidious negotiation between intellect and the density of material presented for its perusal, because we suspect that this echoes the larger and longer procedures of the history of our understanding. The drama with its occulted aetiology, the novel with its core of revelation that must be lengthily won: these represent a mimesis of our ongoing battle with the data life presents to us.

Why does the apple fall from the tree to the earth rather than flying off towards the moon? This is part of the narrative of human understanding whose secret, when satisfactorily revealed, we call ‘science’. Newton, to make his discovery, had to employ the principle of uniformitarianism, a word he could not have used because it was not yet invented. This principle insists that the same laws apply throughout the universe; that what is valid here is also valid there. The implication of the Ptolemaic system was that universal space was not isotropic; that the universe did not extend homogeneously in all directions, but that nature was centred upon us, our planet, sitting at the centre of a created reality which had in its turn centred itself on humanity. The heavens were immutable, while we lived in the sublunar realm governed by change and decay. Now we assume that we are far from the centre of things, indeed that there is no ‘centre of things’, that the universe is like that legendary circle whose circumference is everywhere, whose centre is nowhere. Space turned out to be isotropic, after all, if not homogeneous; it goes off similarly in all directions but lumpily. The heavens were not the region of perfection; things change as much out there as they do down here.

If we journey back to the 1660s, we find Isaac Newton in his rooms in Trinity experimenting with light and what happens when you pass it first through one prism then through two. The assumption he is working on is what we have just called uniformitarianism. Newton is assuming that light will behave the same way inside his room as it does outside. This is a large assumption, and it is one that can only be endlessly tested rather than proven. It was Galileo’s assumption; it is the assumption of all experimental science. Without that notion we have magic, the notion that universal laws can be suspended by discrete occult operations. Or we have miracles, which presuppose that universal laws can be suspended at the behest of their creator.

What Newton discovers here is that white light contains colours which can be separated by a prism. He has made a fundamental discovery about the nature of light, and he will announce the fact in his Opticks. It is a curiosity worthy of remark that Newton didn’t want an edition of his greatest work Principia Mathematica to be published in English in his lifetime. The book, already formidably difficult, was made a little more difficult by existing only in Latin until the time of his death. This was, so he said, to avoid ‘smatterers’. In other words, he wanted to keep the matter secret, to restrict access to it to those in a position to fully understand, of whom there were remarkably few. He did with Principia what Mark tells us (4:11-12) Jesus did with his teachings about the kingdom: made them a matter of restricted access, lest those not actually chosen for salvation should achieve it anyway. He did not want these hallowed truths made available too readily to the profane.

Two centuries later Freud sat in his consulting rooms at Berggasse 19 in Vienna, having created for himself a space which he believed to be as much a scientific space as Newton’s Trinity rooms, or the laboratory he had built outside. If Newton needed prisms and telescopes, Freud needed his images from antiquity, those sculptures and reliefs and engravings which so cluttered this Viennese space that it often startled his analysands. Yet what this space was proclaiming was another form of  uniformitarianism: that of the psyche. The forces which had driven us in the earliest period of our history are still potent. They might be hidden in the darkest, most repressed depths, but they are still there, as Oedipus and his dreadful secret still lurk murderously inside the male psyche.

Freud surrounded himself with models of the human psyche in operation, shapings of the drives that populate us with their contrarian desires; creatures of heaven and hell, supernatural messengers, gods, goddesses and minor demons. If their first encounter with this anthropological menagerie frequently startled his patients, the objects expressed their own vivid logic: the dark forces configured by the statuary inside his glass cases remained potent agents in the contemporary psyche. The unconscious does not acknowledge time; no drive, no terror or desire, is ever superannuated so long as it lodges in the dark labyrinth of the mind.


WE OFTEN DESCRIBE models of the world as either myth or science; they are frequently combinations of both. Like the minotaur we are hybrid creatures, made half of science, half of myth. We are therianthropic, and it can be hard to distinguish where the two hemispheres actually meet. All too often, when we look back in time, we discover that much of what we thought science turned out to be myth after all. To use the word with something like neutrality, we could say that a myth is a structured world of perception and experience which can be observed externally; it is an inhabited world of meaning, a system of representations, however loosely organized. In which case, we might well be inhabiting a myth ourselves, but because our myth appears to us to be no more than a transparency onto the fabric of reality, we perceive it as science rather than myth. We cannot then see it externally; our structure of thought and the realities it perceives are connected by a transparent filament, invisible to our own eyes. Once such a transparency is superseded, once we can see how seemingly neutral scientific perception was in fact implicated in a set of cultural assumptions, structured if not necessarily contaminated by the fictions of the time, then we can start to make out the lineaments of a myth.

We do not have to travel back far in time to see such operations at work. For example, positivism in the second half of the nineteenth century regarded itself as the least mythic form of thought that had ever existed. Now we can see how its confident scientism, its commitment to a notion of history that was techno-progressive, was about to blow up in its own face in the form of the new century and its quantum mechanics, the Great War, the rise of fascism. Its notion of science was altogether too unproblematical, its notion of history likewise: what appeared to be the transparency of science turned out to involve the motivated operations of fiction, which is to say the non-transparency of the age’s specific configuration of myths. The infinite attenuations of classical physics were about to be broken by the scandal of quantum discontinuity.

Isaac Newton in his laboratory, the fires kept alight day and night, was not attempting to explore the ‘myth of alchemy’; on the contrary, he was engaging in what he believed to be science. It is not time that has rendered Newton’s activity mythic rather than scientific. A hundred years before, Ben Jonson in The Alchemist was already viewing alchemists as creatures of myth in the invidious sense of charlatans committed to untruth, whether wittingly or not. Jonson’s alchemists are the chapmen of wonders, the mountebanks of hermetic lore, but then Keynes came to a not dissimilar conclusion about Newton, having read his secret papers:

Newton was not the first of the age of reason. He was the last of the magicians, the last of the Babylonians and Sumerians, the last great mind which looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance rather less than 10,000 years ago. Isaac Newton, a posthumous child born with no father on Christmas Day, 1642, was the last wonder-child to whom the Magi could do sincere and appropriate homage.

He was looking for the wrong secrets in the wrong place, it would appear, as well as discovering the right secrets in the right places, employing the correct methods.

He was yet another hybrid, a species of intellectual chimera, and he still puzzles us. He inhabits several worlds of representation so radically at odds with one another that we must find him guilty not of intellectual complementarity, but of a pluralism so capacious as to amount to eccentric eclecticism.

Myth and Representation.

REPRESENTATIONS FIND THEIR meaning inside myths, inside the field of mythic discourse, but they find them inside science too. The difficulty as always is disentangling one from the other. We can never do this entirely for ourselves, because it is always too early to judge. By the time a coherent judgment arrives, we shall be dead. We must wait for other generations to do the judging, to work out how much of our science was really a myth so integral to our way of inhabiting the cosmos that it was invisible to us. An image of an auroch on a Palaeolithic cave wall, a chart of the stars in a lab in the astronomy department, a drawing of a proposed new building in the council offices – all of these might have more in common than at first appears. They are all what we might call, with caution, ‘models of reality’, using different technologies to present images which convey information. Which is to say, they are all representations, and like all representations they take their place inside a larger world of meaning which grants them their significance. That significance can change if the representation is extracted from its original position and placed inside a different intellectual context. If the Palaeolithic images had some magical or sacred character, guaranteeing the hunt, or even making reparation for it, then the representation takes on a different function when placed in an analytical context in modernity. Now it is not guaranteeing the hunt but disclosing information about an early society, its beliefs and practices. The image in the council building is printed on paper and uses the current convention of  groundplan and elevation. In two hundred years time its main function could well be as an example of our quaint technology of reproduction, or even the bizarre protocol of our optics; it would have been removed from its original function and significance, just as a medieval altarpiece, placed inside an art gallery, has had its function utterly transformed by its change of context.

In his book Mythologies Roland Barthes argues that a myth is a way of rendering natural that which is in fact historical, cultural or political. It can be a narrative, but does not need to be: it can be a picture, a song, even a gesture, as long as it articulates itself as mythic sign. Another way of putting this could be to say that myth appears to render scientific, as a fact of nature, that which is in fact culturally and historically contingent.

Let us take the moment in the church wedding ceremony when the father of the bride ‘gives her away’. No one gives the groom away. So, if we use Barthes’ categories here, what we see is a ceremonial gesture in which the patriarchal myth expresses itself. A woman is always possessed by a man, father or husband, unless she chooses the identity of spinster, which is to say one who must now provide for herself at her spinning-wheel; one who remains self-sufficient (and childless) at her loom. The bride to be did once have an actual price on her head in the form of a dowry.

Freud believed himself to be a mythographer; we now think of him as being at least as much a mythologist. He created a world of meaning which has never been underpinned, as he had initially dreamt it would be, by the rigorous techniques of science. What is of value in his work is not his discovery of a universal principle in the infant psyche called the Oedipus Complex. The conflicts he might have been observing here were surely far more localised than he ever imagined. What is of value is his elaboration of the nature of narrative. What Freud came to believe about the psychoanalytic space and dynamic was that there was no immediately disclosable truth; that the truth could only tell itself through the procedure of its own self-discovered enunciation. There was no short-cut into this. The narrative would form itself through encounters with occlusions and repressions. The narrative must inevitably encounter these; it cannot evade them. Encountering the repressions, and seeing how they were enacted – this is an integral part of the improvised narrative. The sinuousness of this manoeuvre has of course led to accusations of the whole procedure being unscientific. Psychoanalysis is certainly not scientific, in the sense of obeying the protocol of experimental science as practised since Galileo. It is unable to provide evidences of its own falsifiability, a failure which, according to Popper, made it spurious. Einstein could provide such evidences. He predicted precisely to what extent light from distant stars would bend around the sun in the event of a solar eclipse. A solar eclipse provided the opportunity for the measurements to be made, as they duly were by Arthur Eddington, and they showed Einstein’s theory to be in accordance with scientific observations. Had they not done, his theory would have been shown to be untenable. But if there is any ‘scientific truth’ in Freud then it is in the older sense of scientia, of the accumulated body of knowledge of different sorts. Narratives are more flexible, more freely exploratory, than mathematical proofs.

Not all truths can disclose themselves with the clarity of an equation. Wittgenstein distinguished between truths that could be told and those that could only be shown. The example he gave was the height of Mont Blanc. If I know this, then it is meaningless to say that I cannot tell you what it is. But what of the sound of a clarinet? I might know this very well, but I cannot ‘tell’ you; I can only show it. Language breaks down here. Language cannot convey the sound a clarinet makes.

Let us consider two types of map: the London Underground map devised by Harry Beck, and the ones that preceded it. The earlier ones tended to be topographical, which is to say they situated the railway lines in the actual landscape of London. Beck’s map is topological: it ignores all relationships except those between stations and lines. It is not interested in real distances, or the actual trajectory (topographically speaking) of any of the lines. It is a brilliant map because it presents with great lucidity the interconnecting system of the railway. It maximises signal and minimises noise. The topographical maps, by contrast, retained much of the noise of the actual topography of London to such an extent that it was hard work discerning the searched-for signal: how do I get from here to there by the most economical means on this railway system?

We must always beware, however, in so fine-tuning the signal-to-noise ratio. By effectively excluding so much noise, might we exclude some information which should have been included? By banishing topographic information, Beck’s map might mislead us into imagining that the outlying stations on the longest lines will be reached much more quickly than is actually the case. The map presents the whole railway system as a convenient village of communications. It is no such thing. It takes hours to get from one side of the Underground to the other. The furthest reaches of the London Underground map are not underground; nor are they even in London.

A famous example of the dangers inherent in tuning our signal-to-noise ratio too fiercely is the discovery of the background radiation of the universe. In 1964 in New Jersey, Arno Penzias and Robert Wilson were working on radio waves. They were picking up interference, noise. They tried to get rid of it. They even removed some nesting pigeons, which they assumed had been ‘causing the problem’. Fortunately, something transmuted this noise into a signal; interference suddenly became information. Astrophysicists at Princeton had predicted that the Big Bang must have been accompanied by a mighty radiation blast. Look in the right place, they said, and you would surely find it. Wilson and Penzias had found it, in fact, but they hadn’t been looking, and therefore hadn’t been seeing. Because of the topological map in their minds, they were trying to lose it again. Fortunately the two sources of information joined up and we discovered and measured background radiation. Had we not evolved the theory of the Big Bang, that background radiation would still be noise. We would have had no topological schema in which to situate the data, and find the pattern meaningful.

We know that myth functions like a topological map: it transforms the topography into a specific shape of perception. It appears to have a palpable agenda, but it cannot be analysed merely in terms of its manifest content. Freud understood how psychic significance, investment of energy or cathexis, is frequently in inverse proportion to self-disclosure through manifest content. It is the latent content which must reveal the real significance for the psyche of this particular mythic site. It is often harder to see how science sometimes functions in the same way. We can perhaps see it most clearly when we look at the Ptolemaic system. It seemed not merely natural but proveable that we were situated at the centre of the universe; that everything revolved around us. It was a battle to retrieve enough of the actual topographical information so that this dogmatic topology might be superseded. Science needed to transcend itself, so as to become more scientific. Perhaps we might come to feel that the topological exclusion principle of our times is our metaphysic of things. We talk of electrons and protons and neutrons, but are nouns really the best way to classify these phenomena? Even ascribing nouns to them might betray our hidden topological agenda, as David Bohm has pointed out. Bohm was intrigued by the way that certain Native American languages are verb-based, so that sentences in them can have no nouns at all; instead, they convey an unmediated dynamic process. Underlying all our microcosmic realities are not minute ‘things’, but processes and forces, which cannot properly be specified into objects. And yet the unspoken epistemology of our naming of objects and particles subliminally suggests that all moving things must come to rest at some point, and can then be turned through three hundred and sixty degrees for scrupulous examination. Our nominal assumptions here seem to be radically misrepresenting nature. The word particle itself carries an implication of solidity, of thingness or quiddity. If you treat an electron like an object and try to get it to sit still so as to have its portrait taken, the electron disappears. ‘We are suspended in language,’ said Bohr, and the terms of that suspension can easily mislead.

We might elaborate the distinction between topography and topology a little more extravagantly. Topography, we could say, is realism and metonymy; it represents that horizontal line along which we describe historic occurrence with, we hope, forensic exactitude. Topology by contrast is vertical, connecting discrete intellectual regions, delighting in a riot of categories. So to which realm does the algebraic equation belong? The most famous equation of all time is Einstein’s. It brings together energy, mass, and light in its immaterial speediness. No metaphor ever moved more swiftly than this through heterogenous realms.

While Freud was elaborating his notion of myth, Sir James Frazer was writing The Golden Bough. The fundamental assumption behind that work was that myth was an early and erroneous attempt at science, a primitive and bungled description of reality which science would subsequently supersede. There was not enough reality in myth. Freud’s argument was pretty much the opposite: the reason something becomes mythic is because there is too much reality in it. It cannot be contained in the normal discourse of existence; cannot be held steadily in consciousness; it becomes cathected, which is to say that an investment of energy beyond conscious control exaggerates the dynamic of the mythic representation. Myths are dangerous because they gather such a vortex of psychic energy around them, while never fully disclosing even to themselves the original motivation. Art does something similar, but without any requirement for credal subscription. Aby Warburg believed that art stood midway between the primacy of unmediated perception and the ultimate distancing of conceptual rationality. It inhabited a vortex in which contrary forces could be expressed without either being diminished. There is a similar perception in Lévi-Strauss’s notion of the working of the bricoleur, that poet of the mythic mode: between the perception and the sign, he says, is the image. Art then can function as a representational space in which contradictory forces are momentarily reconciled as complementary. This makes it culturally essential. Art permits a negotiation between forces which must otherwise war upon one another. Contradiction appears under the aspect of complementarity: Newton’s light enters one prism as particle, exits the second as wave. Either/or becomes both/and.

There is one last aspect to our topological formations which Barthes does not explore: it is a species of myth to imagine that culture can always be read back into history; identity into nativity; artistic form into social form. This is an expression of the myth, once scientifically credible, that all of the contingency encountered in life can necessarily be translated into causality. Quantum physics and chaos theory between them should have done away with this particular manoeuvre for ever, but it constantly re-appears. The anti-Stratfordian position regarding Shakespeare’s work is an expression of such a mythology. The great unexpected potency of Shakespeare’s writing, its unprecedented exploratory manoeuvres, its sudden and astounding heuristic autonomy, cannot be accepted. Since the universality of this work can never be explained by the background, education and occupation of William Shakespeare of Stratford, we must choose instead another historical figure, an aristocrat and courtier, who would have been knowledgeable in precisely those areas where Shakespeare was not. The fact is (and here we encounter the mythology with force) Shakespeare’s work cannot be ‘read back’ into the biography of any historical figure at all. It can be historically situated, but not historically explained. It outruns its explanations. That is the source of the intellectual exhilaration it generates. This is work of such richness that it still situates us more than we can situate those plays. Hamlet is still sounding us more thoroughly than we sound him in return

There is always a dissonance between social existence and any serious artistic achievement, whatever consonance there might also be. If it is good enough, it always comes as a surprise. Shakespeare is still surprising us four hundred years on. We find ourselves in a world of representation at least as vivid as our own. No one has ever written anything more intelligent than Hamlet, a fact as shocking in its way as Freud’s belief that Oedipus Rex contained an ancient allegorical truth, of which contemporary science had remained entirely oblivious.

Alan Wall was born in Bradford and studied English at Oxford. He has published six novels and three collections of poetry, including Doctor Placebo. Jacob, a book written in verse and prose, was shortlisted for the Hawthornden Prize. His work has been translated into ten languages. He has published essays and reviews in many different periodicals including the Guardian, Spectator, The Times, Jewish Quarterly, Leonardo, PN Review, London Magazine, The Reader and Agenda. He was Royal Literary Fund Fellow in Writing at Warwick University and Liverpool John Moores and is currently Professor of Writing and Literature at the University of Chester. He lives in North Wales. His poem sequence, Raven, has just been published as a chapbook by Shearsman Books and a collection of his essays is forthcoming from Odd Volumes, The Fortnightly Review‘s publishing imprint.

Note: The publication of ‘Newton’s Prism’ in the Fortnightly today, 22 July 2012, coincides with Pi Approximation Day, more on which here and here.


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