Sebastian Hayes

These thoughts were triggered by a conversation I recently had with a friend of mine Graham T. He is a trained scientist who is also an author (he is currently writing his autobiography) whilst I am an author who has occasionally written on scientific topics (I once reviewed a book of his which is how we originally got to meet). Over lunch we discussed whether wine was a help or a hindrance to writing. I said that when writing poetry, even worse when translating poetry, which I usually did in the evening, I found I needed to be half cut —  and for that reason, having been given a warning by my doctor, it was a good thing that I’d decided to shift over to the science side of the great divide in my declining years. For science and mathematics you need to be cold sober and to get started early in the morning.

My friend agreed. I added that the probable reason was that alcohol facilitates the ‘associative’ capacities of the brain and this is what you need especially when writing poetry which thrives on surprising  but apt correspondences between very disparate domains, whereas scientific thinking works by analysis, splitting things up and narrowing things down. “So there is something in the two cultures idea, then?” my friend asked. I said that I thought there was.

However, supposing there is only one reality and science undoubtedly has a firm handle on it, this split is a bit puzzling. On reflection I decided that, when you get to the bottom of things, both science and mathematics and art (religion also) are responses to the human condition, in particular its unsatisfactory aspects. Science, and more particularly mathematics, concentrates on what is constant and relatively unchanging whereas art, secular art at any rate,  is typically concerned, not to say obsessed, with what is ephemeral. Put more crudely, the aim of higher mathematics is to escape from biological reality, whereas the aim of art, painting and poetry in particular, is precisely to revel in it and celebrate it (see Note at the end concerning a recent New Scientist article). This is why flowers are such frequent sources of delight in painting and in lyrical poetry since flowers are, by definition, lovely but short-lived and, incidentally, are supreme manifestations of biological (rather than physical or mathematical) reality since they are, quite literally, sexual organs.

Pythagoras, who was a sort of holy man and early scientist rolled into one, is credited with being the first thinker to recommend the study of mathematics along with music (which, in Pythagoras’ eyes had a strictly numerical basis) as the best means of transcending the hopeless imperfections and indignities of everyday existence. Numbers have no direct connection with human beings at all, which is precisely why they are at once deeply satisfying and repellent. For the Pythagoreans, not only could one detect, if one looked hard enough, numerical ratios underlying natural phenomena such as the production of different sounds, but the universe itself at bottom was ‘ratio’. This idea found its way into Plato’s philosophy  although by Plato’s time Geometry, rather than Number Theory, had become the most important branch of mathematics. In many ways Geometry was even better as a panacea for world-weariness, since the subjects of geometry, circles and triangles and polygons, could actually be visualized, even drawn — or at any rate imperfect human copies of these transcendent Forms could be described.  The sage absolutely had to study geometry — “Let no man enter here who does not know geometry” was carved on the portal of Plato’s Academy — and only someone trained in mathematics and philosophy had any hope of penetrating to the heart of things. Only he could glimpse the daylight outside the darkened cave where the miserable rest of humanity lived, chained together like prisoners, staring stupidly at delusive shapes on the wall in front of them and mistaking these flickering shadows for reality (the image is taken directly from Plato’s Republic ).

Moreover, the truths of mathematics were in some sense intemporal, absolute : they were exempt from the ravages of time and age.  I myself remember, when I first, somewhat belatedly, started studying Euclidian geometry, that I came across a little book which included beautiful shaded drawings of spheres and polyhedra with tinted shadows. I stared at them in a trance, like a religious adept staring at the portrait of the Madonna or the Buddha. In the ancient world, which was at once more horrifying — and occasionally  more enchanting than ours — such geometric shapes would have had even stronger appeal. The streets of cities in the ancient world were thronged with beggars and helpless invalids (as we know from the Gospels); even the temples had traces of dried blood on the stone floors and must have stank of animal sacrifices that the ever-present incense never entirely dispelled. This was biological reality ‘red in tooth and claw’ indeed.

I have imagined the tremendous effect the discovery of geometry might well have had on an impressionable young man of the Hellenistic era in my poem The Initiates which is part of my collection The Portrait Gallery (Brimstone Press, 2008).

“…We met always by night: a household slave brought in
A tray of sand, giving each visitor a cane,
With joy we gathered round; the latest theorem
Imported from North Africa was scrutinised,
The argument abridged, occasional points of style
Touched up…Then silence fell, a sense of ultimate peace
Came over us; these lines and circles that we traced
Were clearly images of a superior world,
Indifferent to man, exempt from frailties,
War, death, disease, could not affect them and their truth
Did not depend on trial or experiment,
Each step self-evident, demonstrable and sure.
‘Diana!’  ‘Tammuz!’  ‘Attis!’ Cybele!’ — these cries
Brought to us by the breeze seemed cries of agony;
For in those fleeting moments we had thrown off flesh
And merged our being with those cold majestic Forms,
Perfect embodiments of abstract principles,
Containing in themselves the laws of Harmony,
While all around us raged the sea of ignorance.”

(The cries “Diana!” “Tammuz!” come from a fertility festival going on in the streets outside, a celebration in which the young man in question does not participate, esteeming he has better things to do.)

Actual factories, mines and workshops have been, for most of human history, hellish places where impoverished workers, in the ancient world criminals, prisoners of war and slaves, toiled in appalling conditions at the mercy of brutish foremen and taskmasters. And yet, by entirely abstracting from real-life conditions and concentrating only on the movements of coordinated pieces of polished metal, Newton and his successors were able to provide us  with a second  Wonderland, mechanical this time. Newtonian science  is  a science of ideal machines “where motion is transmitted without collision or friction between parts” (Prigogine) since the pulleys are frictionless and the cords made of the finest silk. As for the heavenly bodies, they followed elegant elliptical or hyperbolic paths already described by the later Greek geometers in their studies of conic sections. All these complicated movements, whether terrestrial or celestial,  were orderly, and so they should be since the rules governing their behaviour had been laid down from all eternity by the supreme Mathematician, Architect and Industrial Designer, God. It is astonishing how deeply the notion of ‘laws of Nature’ has permeated Western thinking, given that theoretical science has long since dispensed with a cosmic lawgiver. Of course, to some, such as the Romantics, the inherent orderliness supposedly underlying the splendid confusion of Nature appeared detestable, as indeed it does to many of us today, but people who had just emerged from the throes of Civil War in England saw things differently, and it was precisely during the Restoration period that the ‘new science’ of Mechanics took off.

What is staggering about Newton is his temerity and air of authority :

“Objects attract each other with a force that  varies directly as the product of their masses and inversely as the square of the distances between them”.

“How the hell does he know?” one might be tempted to retort (and many continental scientists at the time did so retort), especially since this statement applies to every particle of matter in the entire universe. There is something at once objectionable and consoling in the enunciation of such sweeping ‘natural laws’ : objectionable because they are unprovable in their entirety and in practice subject to all sorts of qualifications, consoling because it is pleasing  to imagine that there is at least something that is certain and permanent in a world of change. It is no accident that the hey-day of Newtonian Mechanics  coincided with the era  of absolute government, many of whose practitioners, such as Frederick the Great of Prussia and Catherine the Great of Russia, were enthusiastic converts to the ‘new ideas’ and patrons of rational thinkers like Voltaire and leading mathematicians like Euler.

Generally speaking, change was an unwanted guest in the physical and mathematical world and still is : until very recently (the nineteen-thirties) astronomers blithely assumed that the universe had been more or less the same size from the beginning of time (inasmuch as there was a beginning). Biologists, prior to Darwin, assumed that current species had always existed more or less as they were at present. Even today, theoretical physicists have the greatest reluctance in imagining that the important constants in Nature, such as G, the gravitational constant, might have changed over time, nor do biologists exactly embrace the notion that the procedures of evolution may themselves have ‘evolved’ — though, surprisingly, even Dawkins concedes such a possibility (Climbing Mount Improbable pp. 204-5).

Broadly speaking, people with an ‘artistic temperament’ are not attracted to what is fixed and unchanging : on the contrary, it is precisely the perpetual play of light and colour which appeals to painters (certainly to myself) and the fixed geometric forms of Euclid generally repel rather than attract even in architecture, the only art form where they have ever made a passing appearance (in the functionalism of the Thirties). I have often counted it an inestimable blessing that Mother Nature was not a trained mathematician.

Conversely, it is the acute sensation that ‘life’ is excruciatingly fragile and ephemeral that provides poets from all eras with an unvarying theme to which they return again and again and again :

“The Bird of Time has but a little way
To fly — and Lo! The Bird is on the Wing.”

(Omàr Khayyam)

Human life is gone almost as soon as it has started, and the human machine is, compared to man’s own formidable artefacts in stone and metal, alarmingly vulnerable. “L’homme n’est qu’un roseau, le plus faible de la nature… Une vapeur, une goutte d’eau suffit pour le tuer” wrote Pascal, who ended his brief days as a chronic invalid (“Man is nothing but a reed, the weakest thing in Nature… a vapour or a drop of water is enough to kill him”).

But has physical science nothing to say about all this?  As a matter of fact, yes, quite a lot, though only during the last one hundred and fifty years. Newtonian Mechanics rarely if ever mentions decay and breakdown : rust doth not corrupt and God can always be relied upon to intervene, in the last resort, to stop serious disasters happening in the sky above, such as stars getting too close to one another. But all this changed in the first half of the nineteenth century.

The theory of thermo-dynamics, which was developed piecemeal ‘on the ground’ by practical people such as Joule, Carnot and Clausius appears, in retrospect, like a sort of Iron Curtain suddenly let down onto the world of physics. All the laws have a restrictive character : they are a warning to would-be inventors and industrialists. It has become fashionable to present the 1^st Law in a positive manner, i.e. as a statement of the ‘conservation’  of energy, but  in practical terms what it meant to the people who first enunciated it was that there was a fixed upper  limit to the amount of work that could, even in ideal conditions, be got out of a mechanical system. The 2^nd Law states that a fair amount of the energy locked up in a mechanical system is inevitably going to be wasted anyway — usually by the production of unwanted heat and sound. Putting the first two laws together, we get the very important negative conclusion that “A perpetual motion machine is impossible”. (This had previously been considered a distinct possibility and indeed it is quite possible to have ‘perpetual motion’ such as the movement of electrons in an electronic circuit just so long as no attempt is made to get them to do useful work such as activating a light bulb.) The 3^rd Law sets a definite lower limit to all heat extraction (Absolute Zero on the Kelvin scale) and, combining this with the 2nd Law, Lord Kelvin himself drew the melancholy conclusion that the universe itself would die of ‘heat death’— by which he did not mean that it would get too hot but that temperatures would eventually get so averaged out that no part of the universe would be warm enough to support life.

As for biology, no scientist prior to the mid twentieth century had the faintest idea what a performance was necessary just to maintain  the human body alive : it is no exaggeration to speak of a perpetual state of war going on in all parts of our bodies practically all of the time. Moreover, in this  ‘battle’ the individual always loses, and must lose. As von Bertalanffy (a practising biologist) put it, “To define life in terms of death would scarcely be going too far”.

All this, of course, was hardly new to the poets : though they did not know anything about entropy and the 2^nd Law of Thermo-dynamics, they sensed what was going on acutely enough. Catullus, the Roman poet, quite properly  contrasts the repeatability of astronomical phenomena with the unrepeatability of biological life:

“Suns set and  rise again,
But we, when our brief light is spent,
In one everlasting sleep are lain.”

The typical lover, such as Catullus, does not, moreover, seek ‘love’ for the sake of procreation but in the hope of attaining some temporary release from the quasi-permanent state of anxiety with which he is afflicted : few poets have found much  consolation in the promise held out by Dawkins and his ilk that the ‘gene’ will persist even if the individual dies. (Actually, it is not even the ‘gene’ itself which persists but only the ‘genotype’, the ‘type’ of gene, and who cares about that?)

The 2nd Law of Thermo-dynamics has become, if anything, more of an unassailable dogma than ever today, although it is currently interpreted more in the computing sense of a ‘loss of information’ rather than a ‘loss of activity’. All this flies in the face of the staggering complexity and variety of life-forms that exist or have existed and the vastly increased, indeed excessive, complexity and diversity of modern society.  We are nonetheless assured that all that we see and hear is only a passing counter-ripple and that the ‘Big Picture’ is always an inevitable movement from order to disorder rather than the reverse.

But what if ‘life’ is on the contrary, something to be expected ?  Rather few thinkers have taken such a position. Prigogine emphasizes that life, by definition, exists permanently in a “far from equilibrium” state and that, given this precarious situation, “new self-organizational processes arise… In this way biological organization begins to appear as a natural process” (Prigogine, Order Out of Chaos p. 84).  What we consider key features of life, for example consciousness and hierarchical organizing principles, may simply be emergent given a certain level of complexity and, if Wolfram is to be believed, quite simple systems can readily give rise to very great complexity. So maybe, after all, life, even ‘human life’, is not an “event whose singularity we have to recognize” (Monod), but something in the order of things.

It is surprising, and perverse, that so many thinking people, whether from the scientific or the ‘artistic’ side, seem unable to commit themselves to the ongoing life process itself, but oscillate perpetually between fantasies of a fixed, unchanging Neverneverland and gloomy predictions of the inevitable decline and disappearance not only of ‘civilisation’ but of humanity and ‘life’ itself. Fortunately, species are rather more hardy and resilient than intellectuals : maybe in some semi-intuitive manner, the former have a faith in ‘evolution’ that evolutionists themselves lack.

Taoism, alone of all religions and philosophies, views ‘salvation’ — to use the theological term — not as some sort  of an escape or abstraction from the ongoing process, but, on the contrary, as a deliberate ‘blind’ commitment to it without any looking back. This is the famous ‘Way’ (Tao), which is not a ‘way’ leading to anywhere or anything in particular, but simply a ‘way’ to live, the best known to its practitioners and, seemingly, that employed by Nature herself.

Note :   Since first writing this post, I came across a very interesting article in the New Scientist (March 27 p. 12) entitled Slow thinking may nurture creativity.     The article, written by Linda Geddes, reports on work done by Rex Jung from the University of New Mexico. Geddes writes, “Several recent studies have suggested that white matter of high integrity in the cortex, which is associated with higher mental function, means increased intelligence.” While not disputing this, Jung found that “the most creative people had lower white-matter integrity in a region connecting the prefrontal cortex to a deeper structure called the thalamus, compared with their less creative peers.” He even suggests that slower communication between some areas may actually make people more creative.
This entirely corroborates my experience over a lifetime. Typically, ‘new ideas’ come to me in a realaxed, slow-motion brooding state — I actually lie down on the floor or, even better, soak in a bath for hours if I want to ‘think things over’ and get a new take on some problem. But if I want to do Sudoku or do a mathematical puzzle I make sure I’m alert  : speedy information transport is crucial here. Of course, it’s quite possible  — though  very rare — to have the two going full tilt : this is what makes, or can make, a mathematician or scientist who is right out of the ordinary. Ramanujan, the Hindu mathematical prodigy, had precisely the brooding, moody temperament of an artist, the same taste for solitude, indifference to public acclaim  and the same world-weariness (he tried to commit suicide by throwing himself onto the tube line), but he was also a very rapid calculator, as was Gauss.  Einstein was a deep rather than a brilliant thinker and was a lazy and mediocre university student — amusingly he found Minkowski’s lectures dull.  But he was addicted throughout his life to mathematical puzzles of the newspaper variety, which somewhat bemused his colleagues.

Sebastian Hayes