THE PYTHAGOREAN PERSPECTIVE
The Arts and Sociobiology

[Robin Allott. 1994. Journal of Social and Evolutionary Systems., 1 71-90.]

Literature, music, mathematics, art, are constituents of culture and each of them has its separate history. But each of them can also be seen as a manifestation of a human biological drive, a drive towards exploration, experimentation, the analysis of human perception. Culture is not something separate from human evolution but a part of a continuing human evolution, indeed the main form which human evolution has taken over the last few thousand years. It is a familiar idea, but perhaps a wrong one, that human evolution, as a Darwinian process, has ceased and been replaced by something quite new, a more Lamarckian process involving the inheritance of acquired characteristics, more specifically of the changing forms of human culture. On this see for example Dawkins (1986), or Huxley(1926).


Human culture can be seen as an aspect of human behaviour - and changes in behaviour in relation to changes in the environment are a central part of the Darwinian process of evolution for all creatures. What is there then about human cultural development which is not explicable in Darwinian terms? The main problem, which leads to the conclusion that cultural development is not Darwinian, is that the behaviour manifested as culture, the production of music, literature, visual artefacts, mathematical thought, seems to have no special relation to the evolutionary fitness of the individual producers. Many of them, perhaps most of them, like Leonardo, Van Gogh, Newton, Beethoven, had in the now traditional Hamiltonian analysis zero fitness, left no progeny. Even in the case of those who had descendants, it seems impossible to believe that their cultural productions altered in any way, except perhaps negatively, the survival and multiplication of their genes. The beneficiaries of their lives were not their descendants but other members of their human groups, or indeed members of the human race generally. The process of cultural production could thus be seen, in the standard terms, as a universal, undirected manifestation of altruism.

This conclusion that for humans the process of evolution has ended and been replaced by something totally new no doubt is flattering to human beings and allows them to mark themselves off from the rest of animate beings but it leaves a rather unsatisfactory incoherence in evolutionary theory - how can the non-purposive, inescapable processes of genetic evolution, which in effect value all form and behaviour in terms of the relative survival of differing physical genetic patterns (see Dawkins (1989) again) give rise to a form of development for one species totally disconnected from previous evolutionary history? Does this mean that evolutionary theory is only a partial theory of life?

There are several lines one can explore in attempting to resolve this paradox. A first approach is to observe that the problem can be reduced to a more familiar one, the level of selection, the gene, the individual, the group, the population, the species. A second approach is to look not at the products of culture, the Shakespearean play, the Mona Lisa, the Eroica, the Principia of Newton, but at the process of production of the cultural object - the emotional, perceptual, symbolic, and ultimately neural matrix out of which the cultural product emerged, the brain-organisation of Leonardo, Shakespeare or Beethoven. The third approach, not distinct from the two preceding approaches, is to consider what it is that different forms of culture share, what there is in common between literature, art, music, mathematics, how far there are underlying structural relationships between these different cultural manifestations.

It is this approach which is the occasion for the title of this paper, `The Pythagorean Perspective' since, however mythical Pythagoras or his achievements may have been, he is remembered and renowned as the protagonist of a novel unitary view of human existence and the world, where number generated not only mathematics but also astronomy, the organisation of the cosmos, music, and the ethical standards within human society. In modern terms the Pythagorean Perspective is that there are not Two Cultures (or many cultures) but One Culture, of which the different arts and sciences are partial expressions.

The fourth line of approach, again more a necessary consequence of the others than something separate, is to look at the individual arts, at the different forms of literature, of music, of visual arts, and indeed of mathematics (which is an art as well as the foundation of physical science) to attempt some more biological, physiological or neurological account of their functioning and of their `evolution'; one might attempt to indicate precursor behaviours in other animals which have some structural resemblance to the elaborated forms of the human arts: the numerical and pattern-forming abilities of many animals, the `aesthetic' of peacocks, bowerbirds etc., the `architectural' capabilities of beavers, bees, termites, birds, the `music appreciation' of gibbons, wolves, whales, and so on. And of course one must come again to the apparent Rubicon between animal and human, the evolution of language and so the possibility of literature.

This is a huge prospectus. What it expresses is that it may be profitable in considering the sociobiology of the arts to look at the totality, before diving into the multiple manifestations of the individual arts, and to consider the unity of the origin of all the cultural manifestations in the indubitable products of classic Darwinian evolutionary processes, the human brain and human sensory mechanisms.

PYTHAGORAS

" Over the origins of Greek philosophy and science lies the shadow of a great traditional name". (Burkert, 1972: 1)

Radical scepticism as to the reliability of the sources shown by some modern scholars has on the whole been abandoned in recent research. It now seems possible to extract bits of reliable evidence from a wide range of ancient authors.

Pythagoras of Samos settled in Croton in southern Italy about 525 B.C. He held that reality, including music and astronomy, is at its deepest level mathematical in nature: number is the ultimate reality. The contribution of Pythagoreanism to Western culture has been significant for social and moral thought as well as for mathematical and scientific: the belief in the kinship of all beings; the principles of the brotherhood - loyalty, modesty, self-discipline, piety and abstinence; a higher view of womanhood, community of property, the parallel between the macrocosm and the microcosm ; the cosmos as an organism; the brain as the locus of the soul. To many humanists, Pythagoras was the father of the exact sciences. Copernicus considered his system to be essentially Pythagorean. Galileo was called a Pythagorean. Leibniz felt himself to be in the Pythagorean tradition.

The chief ancient source is Diogenes Laertius who quotes Empedocles` description of Pythagoras as a man of superhuman knowledge, with the greatest wealth of wisdom. Pythagoras was initiated into all the mysteries and rites of Greece and Egypt (learnt the Egyptian language), journeyed among the Chaldeans and the Magi. Examples of his ethical guidance: he told his disciples on returning to their house to ask themselves: Where did I go wrong? What did I achieve? What that I should have done did I not do? To think nothing is one's own. To make enemies into friends. To strive against lawlessness. To injure no cultivated tree, to harm no animals that do not harm man. If angry, to say and do nothing. Do not pray for yourselves because we do not know what will help us. The greatest thing in human life is whether the soul [the individual self] is persuaded to pursue good or evil. Those who acquire a good soul are happy; a bad soul can never rest or be stable.

Not less than six hundred people went to hear his evening lectures. On finding that in a right-angled triangle the square on the hypotenuse is equal to the squares on the sides containing the right angle, he offered a sacrifice of oxen. He was the first to say that the Evening Star and the Morning Star are the same; that the earth itself is spherical and inhabited all around; that there are antipodes with their `down' being our `up'; that the moon draws its light from the sun; that living things are born by seed and there is no such thing as spontaneous generation.

Windelband (1956) comments that in the Pythagorean society mathematical investigations were pursued for the first time quite independently, and were brought to a high degree of perfection. Detailed views were developed concerning the number system, concerning the series, of odd and even numbers, of prime numbers, of squares, etc. The regular revolution of the stars - of which they made careful observations - made the world order appear to the Pythagoreans to be numerically determined. In their theory of the formation of the world, the Pythagoreans placed fire as the original condition of things, as the self-determining One and impelling force. Fire drew around itself chaos (i.e. empty space) - and formed it in ever-growing dimensions. The most brilliant achievement of the Pythagoreans was their astronomy far in advance of their contemporaries; the world-all was globular, the single stars luminous globes; the earth a globe moving around the central fire; the distance of the spheres from the central fire depended on simple number relationships.

MUSIC

To attempt an evolutionary account of any one of the arts, the first step is to see what points of contact the particular art has with biology, what are the physiological and neurological foundations of the art, both in production and reception. What are the biological prerequisites, components, or effects? What relevant clinical or scientific evidence is there?

In the case of music, there is a good deal. This section draws on material from a variety of sources of which the most important have been the papers assembled by MacDonald Critchley (an eminent neurologist) in his Music and the Brain (1977) and Terence McLaughlin`a Music and Communication (1970).

McLaughlin points out that music conveys the subjective experience of composers - but in what way? Herbert Spencer tried to trace a development of music from speech gestures. Darwin suggested that music preceded and gave rise to speech. But there has been no consensus. "Wherever we turn, the origins of music remain mysterious". One proposal has been the that music should be thought of as `audible arithmetic`. Leibniz wrote that music is "a hidden arithmetical exercise for the soul". The Pythagoreans observed that the ratios of the lengths of strings, or other vibrating materials, followed simple mathematical relationships with the sounds they produced. Tests by experimental psychologists have shown that the order of preference for chords in most people follows the lines predicted from Pythagorean theory. The relation of music to what might be called `neural mathematics` is a topic to which I shall return in a later section.

More specific information is available on other physiological aspects of music:

Synaesthesia

The most common musical synaesthetic experience is seeing colours or patterns when music is heard or composed. `Colour hearing' has been reported as far back as the time of Ptolemy. The British composer, Arthur Bliss, experienced a constant play of colour sensations while he was composing; Rimsky- Korsakov and Scriabin associated different musical keys with different colours. Timbre especially has close colour affinities, see the descriptive use of `tone-colour' - `Klangfarbe`. An analogy (even a homoeomorphism) has been seen between the seven colours of the spectrum, with their steadily increasing electromagnetic frequency from red at one end of the spectrum to blue or violet at the other, and the seven notes of the diatonic scale, with their increasing audio-frequency. Newton pointed out the resemblance between the colour scale and the musical scale. Colour-sound synaesthesia can be seen as a demonstration of sympathy between the various sense modes (which we take for granted in the form of metaphor and symbol). Many other types of synaesthesia associated with music have been recorded. Body schema, tactile and kinaesthetic synaesthesias and hallucinations linked to music seem fairly common.(Critchley)

Temporal (rhythmic) effects

Apart from the rhythm of breathing, the other dominant rhythmic sound in our lives is the heartbeat. The rhythms of the heart, lungs, brain and body - the swing of the arms and legs in walking, account for most of the small units of pattern to which we have become accustomed. All give us some sense of the `natural' tempo: moderate neutral M.M. [metronome mark] 50 to M.M. 95 is felt as `comfortable'. The duration of 0.75 second seems to be a psychic constant corresponding to the duration of the complete process of perception. The connection of this natural tempo with walking pace and heartbeat is not a coincidence; the brain is controlling all our muscular processes, and it seems natural and economical that for the rhythmic ones, it should select a tempo that is already in use. The other important human reaction to time is to break it up into units or unit patterns, the origin of our sense of rhythm.(McLaughlin)

Motor effects

Music has a direct relation to the nervous organisation of postures and movements. These postures and movements are complex combinations and recombinations of the simplest fixations and movements of individual joints brought about by a few muscles acting at each joint. The whole listening group responds by motor responses, rarely - in public - overt motor activity but rather sensations of movement, a succession of postural adjustments or even foot tapping. Composition, performance and listening imply wide involvement of the cerebral motor cortex, subcortical motor and sensory nuclei and the limbic system (Critchley)

Muscular response differs between cranial muscles and those of the extremities. At rest only minor differences occur between muscular activity in the forehead region and in the legs. While the subject listens to a record of dance music the effect of the music goes, so to speak, `into the legs'; muscle action potentials increase sharply in the legs and relatively slightly in the frontalis muscles.

Other bodily response

Perceptual and emotional musical experiences lead to changes in blood pressure, pulse rate, respiration, the psycho-galvanic reflex and other autonomic functions. These autonomic changes represent the vegetative reflections of psychological processes. During the act of conducting, the highest pulse frequencies are not reached at moments of greatest physical effort but occur at passages producing the greatest emotional response, passages which the conductor [Karajan] singled out as being the ones he found most profoundly touching. At these moments the pulse rate increased for a short while to twice the level of the initial value.

It is sometimes possible to `drive' the pulse rate by dynamic changes in volume such as the crescendo and decrescendo of a rolling drum beat. The same phenomenon can be obtained by a change in rhythm acceleration deceleration. sometimes synchronously with the respiratory rhythm. Recordings of respiratory movements during the playing of music are very informative. During performance of a Brandenburg concerto, oscillations of the pulse rate occurred synchronously with the respiration. At the end of the performance the respiratory rate fell to levels which were less than half those at the peak. When a subject is asked to squeeze an ergometer, an instrument which measures the strength of the handgrasp at regular intervals and with equal effort he will be unable to carry out the test properly while music is being played. Lullabies invariably decrease and march songs increase muscular strength.(Harrer) The elements of musical language could also be analysed to see how far their emotional associations correspond to their physical effects. Other bodily reactions [besides pulse, blood pressure, respiration] such as the digestive system, the pelvic reflexes, the skin, and so on, would well repay attention.(McLaughlin)

Neural patterning

There are strong analogies or structural similarities between music and the fundamental operations of the nervous system. The characteristics of nerve impulses - timing, intensity, synchronicity, frequency-contrasts, patterning generally - can be set in parallel with many aspects of musical construction. The fibre tracts of the auditory system are arranged tonotopically so that the frequency organisation of the cochlea is maintained at all levels from the auditory nerve to the cortex. How auditory information is processed centrally is far from clear. A feature of any periodic wave, however, complex it may be, is that it can be analysed according to what is known as Fourier's Law into its component pure tones the frequencies of which bear to one another the ratios 1 2 3 4 5 and so o n. it is a remarkable feature of the ear that it carries out just such an analysis [how] remains a matter of speculation the basilar membrane appears to be performing a mechanical form of frequency analysis (Hood) From the auditory cortex the patterns are passed to the data-processing regions in the lower (temporal) lobes of the brain, and to the emotional regions in the upper (frontal) lobes, for analysis.(McLaughlin)

As with the operation of the neural network generally, nerve impulses must all be the same and are not affected by differences in the source of the external stimulus. A quiet noise produces only a few pulses per second, a loud one several hundred per second. The pulses are identical, whatever the intensity of the stimulus, in every nerve. whether from the ear, the eye, a chemical receptor in the nose, a Pacinian corpuscle (responding to pressure on the skin) or a touch or cold receptor. The same code is used not only for signals going towards the brain, but for signals coming from it to the muscles and glands, producing behavioural responses. The only indication of their message is the organ from or to which they travel and the route which they take. The only way we know that a particular pattern of impulses is `hearing,' in fact, the only meaningful definition of hearing, is that these patterns are travelling from the ear to the auditory cortex. As a vivid illustration, Grey Walter has said that if the tongue was connected to the auditory cortex and vinegar placed on it, `You would taste nothing. You would hear a very loud and startling noise'(McLaughlin 1970:59).

The implications for the perception of music of this identity of nerve impulses and patterning are discussed by McLaughlin. When the incoming signal, as in the case of music, is a pattern which has no immediate function as a useful sense impression, equivalent patterns from other sense modes will be activated. The selection and succession of the musical notes may in themselves have no significance for us but the electrical patterns into which they are translated can be compared and identified with patterns from other sources.

In the brain, the patterns of tension and resolution implicit in music are translated into an electrical code of pulses, used in common for all the senses, including hearing and bodily sensations. The basic patterns of musical experience can be analysed into patterns of tensions and resolutions melodic, harmonic, rhythmic and dynamic. If the patterns of tension and resolution in the music are similar to those usually connected with body movement, touch, sight, taste or any other sense impressions, we will have a sense of association between the two or more sets of impressions amounting, to a greater or less degree, to identification. While musical patterns are strictly speaking meaningless in themselves, the fact that they are translated in the brain into the general lingua franca of all other patterns - mental patterns such as grief, expectation, fear, desire, and so forth, and bodily patterns such as hunger, pain, retention, sexual excitement, any of the tensions associated with a raising of the adrenalin level in the blood - and the corresponding resolutions - allows us to see the similarities between the musical patterns and these more personal ones. Susanne Langer (1953) makes the same point, that the tonal structures we call music bear a close logical similarity to the forms of human feeling.

Emotions

If the function of music were only to simulate the effects of simple emotions, it would not be a very important art The actual effects of great art are far more complex and constitute a synthesis of many emotions and feelings to make up a whole that is greater than the sum of its parts. We are made aware. at one and the same time, of intellectual, emotional and bodily patterns. We find ourselves experiencing a synthesis or fusing of many events, many memories. (McLaughlin)

Paul Valéry, the poet of mind and consciousness (see Sewell 1952), pondered (1974: 951 ff.) upon the "puissance illégitime" of music. Effective music, he thought, "s'adresse directement au système nerveux qu'il travaille. La musique est un massage. excitation directe et externe de toutes les fonctions qui généralement sont excitées de l'intérieur. Il ne serait pas impossible de faire une table de traductions, un dictionnaire: Musique - Mécanique neuropsychique-musculaire - Il servira à illustrer la système nerveux".

But, it may be said, most of the evidence in this section relates to the effects of music on the hearer, on the performer or the conductor and very little to the composer, the process of music production, the neurological and physiological precursors or prerequisites for the creation of music. The short answer is that the composer`s neural system, the physiological bases of his emotions and perceptions, are the same as those of the performer, the conductor or the responsive listener. The composer draws the structure and the power of his composition from the same structures as determine the impact of his work. In the same way as bird-song and the response to bird-song have been shown to use directly related neural structures (Nottebohm et al. 1990) and as there are direct neural links between speech production and speech perception (Liberman and Mattingly 1985), so music-production and music-perception are two faces of the same neural complex. The structure of the composed music, the emotive and other effects the melody and harmony have, are, on this view, derived from the neural patterning associated with the composer`s non-musical experience, the neural record of his own life, his own emotions and perceptual organisation, and bodily feelings of all kinds.

VISUAL ARTS

What evidence parallel to that for music is there for the visual arts? Not much that I have come across. The most comprehensive recent survey has been Kemp`s The Science of Art (1990) from which much of the material in this section is drawn. Prominent artists, modern and older, have written about their approach to painting; though interesting and important as indications of how they see their aims and the process of producing art, little is in any way scientific. No one apparently recently has thought it worthwhile to attempt to parallel the psychophysical observations made in relation to music, changes in pulse-rate etc. on exposure to individual paintings or classes of paintings, sculpture etc. There is little sign of any motor or other bodily reactions to great art. The field of thought about and investigation of the visual arts in modern times seems to be limited and confused. There is of course a long history of aesthetics, the philosophy of beauty and so on but beauty is far from being accepted as the criterion in the visual arts today - what is thought to matter is impact, the stimulation of interest, often a conceptual response rather than an aesthetic one.

Unlike the case of music, the traditional visual arts have been radically challenged by new visual technologies, photography, film, and currently computer graphics. Representation, subtlety of form and colour, highly skilled technique, were seen to be not sufficient justification for the eminence of the artist. Again one might appropriately quote Valéry writing in 1929: Les crises artistiques [in the past] ne mettaient en question que les manières de peindre, d'écrire, de voir. Depuis ce qui est mis en question c'est la peinture, la littérature même.(Valéry 1974: 914) The Cubists, Picasso, Duchamp and the surrealists, Klee, Miro, and later Rothko etc. posed so far unanswered questions about the justification, value and aim of visual art.

Though the material is limited, some general ideas from artists and others seem relevant, for example, about the relation of colour and music, creativity and the inner content of art, about art and science, and about the condition of contemporary visual art.

Colour and music

There is a long history of theory about the relation between colour and music from the side of the artists (parallel to that from the side of the musicians described in the previous section). As Kemp points out, the musical analogy had been suggested by Aristotle himself, and was progressively taken up during the course of the Renaissance. The musical theorist perhaps most concerned to draw parallels between the Pythagorean system underlying Renaissance harmonics and the visual beauty of colours was Gioseffe Zarlino. In Le Institutioni harmoniche of 1558 he writes: "The reaction of the ear to the combination of sounds is analogous to the reaction of the eye to the combination of colours." (Kemp, 1990: 273) The formulation of such parallels into a more precise colour theory was accomplished by the extraordinary Milanese painter Giuseppe Arcimboldo. During his period as court artist and general maestro of visual effects for the Habsburg Emperors in Prague (1562-1587), Arcimboldo discovered that all musical tones are consonant with the colours, and are precisely equivalent to that same art of harmonic proportions discovered by Pythagoras. A table of precise equivalences for notes and colours. was constructed by Kircher in 1650. Stimulated by his contacts with the composer Rameau, in 1748 Castel`s similar system reflected a conviction that colour and music are entirely analogous phenomena, physically and aesthetically. Colour and music also have emotional links. Seurat increasingly regarded colours as having specific emotional connotations which artists could exploit. More recently, Paul Klee, a talented musician as well as an original artist, a visual poet, held a similar view. In his notebooks recently published he devotes fifty pages to thinking in colour and the relation of colour to music. A number of his works have musical themes: for example, Fugue in Red. Music, he thought, was well ahead of the visual arts in structural complexity and power.

Creativity and the artist

In modern times some eminent artists have recorded reflections on their art. So Cezanne: "strong experience of nature is the necessary basis for all conception of art". And Rouault: "Art I aspire to, will be the most profound, the most complete, the most moving expression of what man feels when he finds himself face to face with himself and with humanity. Art should be a disinterested, passionate confession, the translation of the inner life, as it used to be"(quoted by Ford 1993: 79). Paul Klee, one of the most thoughtful of modern artists, was concerned with the mysterious sources of creativity. He sought to place visual art on an intellectual level equal with mathematics and science. In his continual search for the principles of creative behaviour, he wrote: "Nothing can be rushed. Things must grow, they must grow upward, and if time should come for the great work, so much the better. We still lack the ultimate strength, for there is no culture to sustain us." In his last diary, published with other notebooks as `The Thinking Eye`, he wrote "Wishing to render things that can be verified I limit myself to my inner life"(extracts from Hyatt 1993: 106-108). Similarly, a contemporary artist, Adrian Berg, writes "The sole purpose of painting is to reveal what has not been seen"(Lynton 1993: 94), an approach summed up by the child`s remark: `I draw my think`.

Science and art

Kemp`s book Science of Art is the most comprehensive recent survey. Richard Gregory, as a perceptual psychologist, in the foreword says that the book is for those with sore eyes and brains tired of woolly generalisations on art and pictures. Kemp draws a parallel between the desire, in the physical sciences, to construct a visual model of the world as it appears to a rational, objective observer and the aims of naturalistic painting, the continued quest for a wholeness of perception of man in the world. He gives an account of the form this quest has taken, for example, in the approaches of Runge (and Goethe) in the 18th century and of Charles Henry in the 19th century.

In reaction to Newton`s optics, including ideas on the relation of colours and musical notes, with a desire to move beyond the limited technology of perspective which had for long ignored any more profound questions about the nature of visual representation, Runge and Goethe saw the objective as the forging of a union between scientific analysis and poetic insight. Runge`s ultimate aim was the Gesammkunstwerk, consisting of a great fusion of musical, visual and literary aesthetics into a spiritual whole. As he wrote to Goethe in 1809, `I am thinking more and more how I could bring about the union of various arts, and that can only happen if they aid each other in their scientific knowledge, when scientific knowledge could really blossom". (Kemp 1990: 287)

In the 1880s, Charles Henry, a remarkable `neo-Renaissance' man of science and art, attempted to build an all-embracing scientific aesthetic on the foundations of psychophysics, the then new science of the mind. For him every aspect of aesthetic reaction could be subjected to systematic analysis in terms of the perceptual dynamics of the human senses and brain. These techniques would extend to the age-old mysteries of Pythagorean harmonics, to the expressive music of colour, to the orchestration of visual rhythms, and, indeed, to every effective and affecting aspect of a work of art. The foundation of his analysis was a mathematical system of proportional harmonics of considerable sophistication and complexity.

Contemporary visual art

An abstract painting judged by seven experts to `display a certain quality of colour balance, composition and technical skill` and selected for the Manchester Academy of Fine Arts annual show, turned out to be, in her own words, `just a little pattern` by Carly John, aged 4. Professor Antony O`Hear has commented: "Anything goes. The absence of discrimination and judgment tends to diminish the worthwhile work: the infantility of pop, wheelbarrow-fulls of justificatory verbiage in inverse proportion to intrinsic interest. Celebrities and sensation-mongers are placed on a level with true artists. The language of criticism is debased by those who defend the indefensible, and the obvious becomes unsayable" (O`Hear 1993: 100-101).

In the light of the above, what progress can be made in considering the evolutionary history of the visual arts? Unlike music, the evidence of the development of the visual arts goes back many thousands of years. The human impulse to present some enduring record of aspects of the environment, of individual life, has been around a long time. Changes over the centuries can be seen in the content, in the objectives, in the techniques of visual art. The objectives of externalisation, and of communication, the individual and the social, in visual art have intertwined, coupled with the fundamental drive to make what is transient enduring. But what can be said about the biological bases for visual art, the physiological and neurological processes and requirements for successful visual art? There is obviously an important motor element - visual art is also skilled action. Also visual art depends on perceptual mechanisms in the appreciation of colour, shape and structure generally. The art products in a sense are demonstrations of human perception, though in modern times the perception may have been as much or more of inner perception rather than of external perception (bringing the nature of the art closer to that of music or of poetry). For major artists, their art often has been the product of a particular way of seeing. The evolutionary basis of the visual arts then leads back to research into the neural and physiological bases for visual perception - the mechanisms of perception of colours and shapes, of depth and perspective as well as the technical (increasingly scientific) issues of the nature of art materials. Why the visual arts exist, why artists paint and sculptors sculpt, is to be considered along with why composers compose, poets write, mathematicians pursue their theorems and where their creations, their innovations come from. It is in the psychology of the visual and other arts that we may find the real biological foundations and how the existence of the arts can be reconciled with sociobiology.

POETRY

What is poetry as an art and how did it come about in human evolution>? On the first question one can quote Shakespeare:

"The poet's eye, in a fine frenzy rolling, Doth glance from heaven to earth, from earth to heaven; And, as imagination bodies forth The forms of things unknown, the poet's pen Turns them to shapes, and gives to airy nothing A local habitation and a name." (Midsummer Night`s Dream V.i.7)

The second question is less easily answered. It may seem bizarre to contemplate an evolutionary or sociobiological account of poetry. Writing is relatively recent, the poetry we have available is the product of historical times. But this attitude depends upon too narrow a view of poetry. How poetry should be defined, characterised, has been the subject of debate over centuries - but at least we can say that poetry is the use of powerful or specially effective words, where the individual words and the order in which they are placed matters; in the ordinary use of language, the individual words and the order in which they are placed does not matter - we extract the meaning and rapidly forget how it was phrased or expressed. If we think of poetry as the use of especially powerful words, then there may be reason to suppose that poetry was more important in the prehistoric, preliterate past than it is today - in song, in ritual, in myth - with the structure and choice of words compensating for the impossibility of any written record. Some have even suggested that in the beginning was poetry - in the evolution of language each new word was a poem, the outward expression of a new inward perception.

However that may be, we have the present fact of poetry as one of the arts, to be accounted for along with music and the visual arts. Poets and others have attempted to describe what poetry is for them, what the process is by which poems are produced. Some examples:

Or est poème ce qui ne se peut résumer. On ne résume pas une mélodie. La puissance des vers tient à une harmonie indéfinissable entre ce qu'ils disent et ce qu'ils sont.

The labyrinthine communings of words. Above everything else, poetry is words, and words, above everything else, are, in poetry, sounds. In poetry,the word seems to operate as a unity of all its powers.

Poetry is both perception and the thing perceived. Poetic form far from being a mere public convention is the personal and organic made objective and accessible: giving form to the living stuff of the imagination. Poetry like science is the process of discovering. We write in order to understand, not in order to be understood: the poet's relentless compulsion to know himself. The structure of poetry is an exact presentation of the nature of human perception.

There can be no doubt that poetry is powerful and that the power of poems comes from the power of the words which form the poems - but what can be said about the source of the power of poetic words? There is the general power of words in poetry or otherwise. Words crystallise our thoughts, Make our thoughts recoverable, Make the thought of others recoverable; but in poetry the particular words chosen matter much more than they do in the case of words for simple communication. Poetry calls upon the full content, the total complex, of each word.

A poem is a structure of words which persists. The poem operates by creating a sound-structure which preserves the actual words. Rhyme locks the words of a poem together, as do repetition and rhythmic patterning or assonance and alliteration. The network of words which forms the poem preserves in it the `iceberg' words, the words which go deep into the conceptual and emotional structure of the individual.

The poet, as much as or more than the musician or the artist, is concerned with externalising his inner world (to use Paul Klee`s phrase) - an inner world formed by his experience of and reaction to the ordinary physical and social world. The source of the effective poem, as of the effective musical composition or painting, is within the neural structuring of the poet. The basis of poetry is as much neural and physiological as the basis of music or painting; the sources of the poetry are in the emotions, in the life-experience, the bodily sensations, the perception of the poet, just as much as the case for the musician or artist. The mystery, as for music, is how the internal, neural, structure, recording the experience, programming the emotions, is converted, transduced, into words; how words, those apparently arbitrary, social constructs, can be effective in conveying to the poet himself and to others responsive to poetry such intangible, invisible, ineffable things.

Beyond poetry then there is the greater mystery of the functioning of language. An evolutionary account of language is possible and is a prerequisite, no doubt, for an evolutionary account of poetry. This is not the place to discuss this larger issue. I have suggested elsewhere (Allott 1988) that the complexities of language derived from, were modelled on and integrated with the neural motor control system (speech is skilled motor action) and that all the structures of language, syntax, lexicon, phonology, can be traced back to the already elaborated complexities of the motor system. If this is so, then poetry also must be a product of the intersection between motor control and perception, the concrete neural set of connections between the motor and perceptual systems in the brain. If, as I believe (Allott 1991), emotions also are essentially motor-based - emotion in some sense is motion - than one begins to understand the power of poetry. What is powerful for the producer of the poetry can be powerful for the receiver of poetry, the person responsive to poetry, because he has similar neural structuring to that from which the poem originates,

The particular word, on the motor theory of language origin and function, was not an arbitrary formation, with an arbitrary relation to its meaning but a structure derived from and parallel to the elements forming the structure of the percept or the action. The word is a specific pattern of neural organisation directly related to neural organisation involved in perceiving some specific object or performing some specific act. The effectiveness of language results from the transmission via articulated sound of a pattern of neural organisation from the speaker to the hearer, who reproduces in his own neural organisation an order, a structure, homoeomorphic with the pattern in the speaker.

A poem is formed of carefully selected words and is thus a representation of a particular pattern of brain organisation. The words are not simply a linear string but a multi-dimensional structure where all the words forming the poem interact. A poem resembles in this way patterns in music, the combination of melody and harmony. Recall the poet's phrase quoted earlier: `the labyrinthine communings of words'. Because the poetic form preserves the selected words, the success of the poem flows from the power of the individual words, the power of the `iceberg' words.One gains the impression that though the external form is different, the process in the production of poetry is close to that in the production of music or the visual arts.

Poetry is exploration of the individual and of the world and as St. John Perse suggests very similar in this to science:

De ce nuit originelle où tâtonnent deux aveugles-nés, l'un équipé de l'outillage scientifique, l'autre assisté des seules fulgurations de l'intuition... Le mystère est commun. Aussi loin que la science recule ses frontières, et sur tout l'arc étendu de ces frontières, on entendra courir encore la meute chasseresse du poéte. C'est d'une même étreinte [que la poésie]... embrasse au présent tout le passé et l'avenir, l'humain avec le surhumain, et tout l'espace planétaire avec l'espace universel. L'obscurité qu'on lui reproche ne tient pas à sa nature propre, qui est d'éclairer, mais à la nuit même qu'elle explore et qu'elle doit d'explorer : celle de l'âme elle-même et du mystère où baigne l'être humain."(Saint-John Perse 1970: 241 ff.)

In this speech accepting the Nobel prize, the modern French poet echoes Shakespeare`s description of the poet with which this section began.

MATHEMATICS

Is mathematics an art? Can it reasonably be treated along with music, poetry and the visual arts? Can anything be said about its evolution?

To answer these questions we perhaps need to have some clearer idea of what mathematics currently is, as a body of knowledge and as an activity. Mathematics can be defined, its content described and the way mathematicians approach their work examined. The objects with which mathematics deals can be stated, the emphasis on proof as characteristic of the mathematical process considered and then larger questions dealt with about the foundations and evolution of mathematics.

A contemporary definition is that mathematics is the science of pattern and deductive structure (replacing an older definition of mathematics as the science of quantity and space). The extent of mathematics is indicated by Davis and Hersh`s estimates that mathematics is contained in 100,000 volumes; that a skilled mathematician might know 10%, that there are 3000 categories of mathematical writing and that some 200,000 theorems are published every year. Mathematics is generally thought to place major emphasis on proof and to be concerned with a variety of mathematical objects such as circles, polyhedrons etc. Some professional mathematicians think the emphasis on strict proof is a mystification. G.H. Hardy, one of the most eminent pure mathematicians, commented: "There is strictly no such thing as mathematical proof; proofs are what Littlewood and I call gas, rhetorical flourishes, devices to stimulate the imaginations of pupils". How mathematicians see their activity is often equally surprising. Quoting G.H. Hardy again: "I have never done anything useful. The highest aspiration in mathematics is to achieve a lasting work of art". Poincaré also emphasised the aesthetic rather than the logical aspect of mathematics. Davis and Hersh (from whom the Hardy quotations are drawn 1983: 29, 85, 173). suggest that mathematics is a great art form distinguished from other humanities only by its science-like quality, its conclusions not subject to permanent disagreement like ideas of literary criticism. The meaning of mathematics is to be found in the shared understanding of human beings, not in any external nonhuman reality. The object of mathematics is to extract structure and invariance from apparent disorder. A mathematician, like a painter or a poet, is "a master of pattern" (Hardy). In their creative work, mathematicians rely, not on language or logic but on a semi-conscious stream of analogic thought, visual, or sometimes even musical (Hadamard). Views about the nature and foundations of mathematics are in process of change. Since the Greeks, mathematics has been seen as the `Queen of the Sciences', the only sure source of truth. Recent books such as those of Davis and Hersh, Lakatos,and Ormell contend that formalistic accounts of the nature of mathematics have had their day. Instead, mathematics is to be thought of as human-made, connected with the rest of knowledge, and just as much a cultural product as literature and music. With this change it starts to make sense to consider the evolution of mathematics in parallel with the evolution of other aspects of culture such as music, the visual arts and poetry.

There have long been speculations, both in philosophy and psychology, about the origin of mathematical knowledge and numerical concepts. The evolutionary view is that mathematics began with the study of real things, and was a product of the evolution of the brain, along with language and other aspects of culture. Mathematics is a form of perception which draws its unique power from the narrowness of the range of phenomena with which it is concerned, number, shape, pattern. At first sight, one might ask, with Davis and Hersh: How can man impose his mathematical will on the great cosmic processes? This is parallel to the problem considered by Lorenz how Kant`s categories could relate to the real world, to which he answered that our cognitive apparatus evolved over time precisely in such a way as to make its operations valid, effective in relation to the real world. Mathematics has evolved as a symbolic counterpart of the universe. Certain mathematical concepts and procedures have survived and others have been abandoned, survival of the fittest symbols, models, processes, constructs.

Mathematics began when the perception of three apples was freed from apples and became the integer three. There seems something specially natural about arithmetic. There are no preliminary axioms; arithmetic furnishes us with experimentally verifiable facts about the world. Quite young children can learn or discover basic arithmetic and even animals have some awareness, as experiments have shown with rats, canaries, parrots, raccoons, pigeons, and chimpanzees. Infants as young as 2.5 months old showed elementary addition abilities (1 + 1 = 2) as did rats and chimpanzees. Infants were able to recognise a group of three objects as such without counting. Wynn (1992), from whom the material in this paragraph is drawn, concludes that such abilities in a wide range of species and at a very early age in human infancy suggest that the knowledge is innate. This fits rather neatly with the long-disputed ideas of Brouwer on intuition as the foundation of mathematics. Brouwer's position was that the natural numbers are given to us by a fundamental intuition which is the starting point for all mathematics. Wynn comments moderately that it seems reasonable that our initial numerical knowledge somehow serves as a basis for the development of mathematics. For Kant, the truths of geometry and arithmetic are forced on us by the way our minds work but, following Lorenz, the way our minds work is the product of evolution of our cognitive structures to match the real structures of the environment in which our ancestors had to survive. Mathematical perception is a specialised segment of perception, which, along with other forms of perception, evolved in the service of survival. Davis and Hersh quote (1993: 319) Rene Thom: "I don't see why we should have any less confidence in this kind of perception, i.e. in mathematical intuition, than in sense perception"; both may represent an aspect of objective reality.

In summary, one can understand The Unreasonable Effectiveness of Mathematics in the Natural Sciences (title of an article by Wigner) if one accepts that there must be a structure in the universe and this structure is what is studied by every science, including mathematics, and determines the shape of mathematics. (Ormell) And one can add that mathematics as a specialised form of perception can legitimately be considered alongside music, the visual arts and poetry which are forms of representation of the contents of perception of rather more complicated, many-factored, aspects of the world and of the individual human being`s existence. Mathematics is another form, besides these other arts, which exploration of human presence in the universe can take. Like other arts, the prerequisites for mathematical exploration are to be found in the structure of the brain.

BIOLOGICAL LINKS BETWEEN THE ARTS

All the arts can be seen as a manifestation of one and the same impulse. The drive to the arts must surely have had a biological origin. But why do these types of behaviour exist? Why should Beethoven choose the massive labour of composition rather than eating, drinking, a family life? Maybe there was the desire to create a `ktema es aei` (a possession for ever), in the awareness of death to survive somehow, but this does not indicate why his activity took this specifically artistic form.

The basic biological drive, impelling composers to compose, artists to paint, poets to write and even scientists to do their science is towards exploration of the perceived world (the outer world and the inner world) and the attempt to replicate it in some durable form. In a sense artists and musicians are engaged in exploration of the properties of the eye and exploration of the properties of the ear.

We are perceiving creatures set in a multi-sensory world who have acquired an awareness of our perception and even perception of our awareness of our perception. We have a drive to the externalisation of our perception, of our awareness. Externalisation is transduction - transfer from one (neurological, physiological, cerebral) system to another - conversion of simultaneous patterning into time-patterning or extended experience into immediate unextended structure. The ability to transduce in this way must depend on cross-modal connectivity in the brain. On this view the production of art is a process of cross-modal transfer, for example, from neural emotional patterning to music, painting, the words of a poem.

The artist is creating equivalent structure - moving from the perceived world to central neural patterning to externally presented form. As sensory read-in from different sources or through different channels goes to modify a central (neurally uniform) network, so read-out from the central uniform network may go to different outputs or through different channels. If this is so, there can be a kind of homoeomorphism between the various forms of artistic expression. The artistic process thus can be seen as part of, derived from an evolutionarily valuable capacity to model the world, to model oneself, and to model oneself in the world, a capacity which evolved because it served to increase the ability of the individual or the species to act more effectively and extensively in the world. There is the analogy - or parallel case, or directly-related case - of language as an instrument for modelling the world, converting internal patterning into articulatory action-patterns, sound patterns. Beyond art, one can see a similar process at work, a similar drive functioning, in science, the attempt to transduce the structure of the physical world, to externalise the scientist`s understanding of the world. And it appears that scientists may even use much of the perceptual and creative methods of the artist: "Tous les hommes de science ont dû prendre conscience de ce que leur réflexion, au niveau profond, n'est pas verbale: c'est une experience imaginaire, simulée à l'aide de formes, de forces, d'interactions qui ne composent qu'à peine une `image' au sens visuel du terme. Je me suis moi-même surpris... à m'identifier à une molecule de protéine".(Monod 1970: 170)

Mathematics is no exception. It is not exceptional in the reliability of the information it provides about the world - visual and other forms of perception also produce reliable forms of information (verified by action). Mathematics is exceptional only in the narrowness of the category of information with which it deals. The mathematician's art materials are number and shape and the interrelation of number and shape. In the case of other forms of art, other forms of perception, the information is many-faceted, dependent upon the point-of-view, not susceptible to instrumental measurement. Between artistic and scientific perception there is no essential difference. As Hayek (1952: 165) suggests: "The apparatus by means of which we learn about the external world is itself the product of a kind of experience. We cannot regard the phenomenal world in any sense as `more real' than the constructions of science" - or, I would add, any less real.

CONCLUSION: EVOLUTIONARY ISSUES

The process of art production as a biological reality, presents problems for a number of aspects of evolutionary theory (e.g. fitness, altruism, gene determination of behaviour, group selection) which may best be solved by refining or amending the theories rather than by ejecting the art process from the realm of biology. If the arts are correctly treated as biological in origin and in the processes of artistic creation, the issue that matters, on the analysis in the preceding section, is not the mode of transmission of cultural patterns (via hypothetical memes, culturgens, etc.) but the origination of the cultural patterns, artistic or cultural `creation.'

Evolution is dependent on imprecise adaptation, adaptation with a margin of uncertainty to allow for the imprecision of future environments. The greatest example of imprecise adaptation comes from growth in the size and complexity of the brain, in the potential for the formation of new neural connections (in embryonic development and later). The complex brain, moulded into uniqueness by manifold epigenetic factors, in interaction with a complex environment, variable in time and space, can produce an unlimited range of behaviours - in the same way as language can generate an unlimited number of utterances. Inevitably then there can be no close gene-control over patterns of behaviour - the brain is an organ with multiple degrees of freedom. The arts, along with many other aspects of human behaviour, are the product of the impossibility of any close adaptation of the brain to actual or potential environments, the inevitable margin of error or flexibility in evolution once brains reached a sufficient size and degree of internal complexity. Perception is behaviour as well as neurologically programmed - and the transduction of perception into external art forms is possible in a multitude of ways. The evolutionary question is the manner in which the cross-modal connectivity which makes this transduction possible came about.

This of course assumes that human cultural development is continuous with, and a part of, human evolution generally, that the processes of evolution have not been suspended or diverted. There are sharply differing views on this. At one extreme there is the view that cultural `evolution' is not really evolution at all, that humans are unique and genes irrelevant to the determination of modern human behaviour:

"For an understanding of the evolution of modern man, we must begin by throwing out the gene as the sole basis of our ideas on evolution. Once this new evolution begins, it will in no necessary sense be subservient to the old" - it is not altogether clear how this is reconciled with Dawkins` remark elsewhere: "What on earth do you think you are, if not a robot?)" (Dawkins 1989: 191, 193, 270). At the other extreme, Jan Wind (1980) has suggested that all religious and cultural phenomena, music, poetry and many other cultural aspects can be compatible with the selfish gene theory. Dogma about group selection may also need to be reconsidered to account for human cultural evolution.The scale of human social organisation is hard to explain without group selection, cultural not biological. (Boyd and Richerson, 1985)

Maynard Smith (1986) has identified as by far the major unsolved problems of biology, the topics of behaviour and development and Dawkins has said what a very complicated business it is to demonstrate the effects of behaviour on long-term survival. Not one gene has been identified to correspond to any behavioural `trait'. There is no experimental evidence for the genetic inheritance of altruistic behaviour though this is hardly surprising, since little work has been done on the genetics of any behaviour(Dawkins 1989: 4, 60). There is thus a gap in evolutionary theory on the subject of behaviour and there seems no reason so far to conclude that the behaviour categorised as "the arts" should be treated as non-evolutionary and non-biological.

If creative and aesthetic behaviour is to be excluded, one wonders how theory should account for what might be called the bower-birds` "installations" (the term used by avant-garde artists). Bower-birds build towers as much as nine feet high, with internal chambers, in the middle of circular lawns. These they embellish with flowers, which they replace as soon as they are withered. They may dye the walls with the juice of berries, or decorate the bower with snail shells, bits of glass or spider silk. One bower contained nearly a thousand pebbles, more than a thousand sticks and more than a thousand strands of grass. Rather more interesting than some of the exhibits at London`s Tate Gallery!

REFERENCES

Allott, Robin. 1988. The Motor Theory of Language Origin and Function. In Language Origin: A Multidisciplinary Approach. NATO Advanced Study Institute Series Vol. 61 ed. by Jan Wind et al., pp. 105-119. Dordrecht: Kluwer Academic Publishers.
Allott, Robin. 1991. Objective Morality. Journal of Social and Biological Structures 14: 455-471.
Boyd, Robert and Peter J. Richerson. 1985. Culture and the Evolutionary Process. Chicago: Chicago University Press.
Burkert, Walter. 1972. Lore and Science in Ancient Pythagoreanism. Trans. by Edwin L. Minar. Cambridge, Mass.: Harvard University Press.
Cavalli-Sforza, L.L. and M.W. Feldman. 1981. Cultural Transmission and Evolution: A Quantitative Approach. Princeton N.J.: Princeton University Press.
Cooke, Deryck. 1962. The Language of Music. London: Oxford University Press.
Critchley, Macdonald and R.A. Henson eds. 1977. Music and the Brain. London: Heinemann.
Davis, Philip J. and Reuben Hersh. 1983. The Mathematical Experience. Harmondsworth: Penguin.
Dawkins, Richard. 1986. The blind watchmaker. Harlow, Essex : Longman.
Dawkins, Richard. 1989. The selfish gene.(2nd edition). London: Oxford University Press.
Diogenes Laertius. 1972. Lives of eminent philosophers. Trans. R.D. Hicks. London: Heinemann.
Ford, Boris. 1993. Words - Words - Words. Modern Painters 6(2): 78-79.
Hadamard, Jacques. 1945. The Psychology of Invention in the Mathematical Field. New Jersey: Princeton University Press.
Hamilton, W.D. 1964. The Genetical Evolution of Social Behaviour. I and II. Journal of Theoretical Biology 7: 1-52.
Harrer, G. and H. Harrer. 1977. Music, Emotion and Autonomic Function. In Music and the Brain ed. by MacDonald Critchley et al., Chapter 12.
Hayek, F.A. 1952. The Sensory Order. London: Routledge and Kegan Paul.
Hood, J.D. 1977. Psychological and Physiological Aspects of Hearing. In Music and the Brain ed. by MacDonald Critchley et al., Chapter 3.
Huxley, Julian. 1926. Essays of a biologist. London: Chatto and Windus.
Hyatt, Derek. 1993. I draw my think. Modern Painters 6(2): 106-108.
Kemp, Martin. 1990. The Science of Art: Optical themes in western art from Brunelleschi to Seurat. New Haven and London: Yale University Press.
Klee, Paul. 1991. Notebooks. ed. by Jurg Spiller. London: Lund Humphries.
Lakatos, Imre. 1976. Proofs and Refutations: The Logic of Mathematical Discovery. ed. by John Worrall and Elie Zahar. Cambridge: Cambridge University Press.
Langer, Susanne. 1953. Form and Feeling. London: Routledge.
Liberman, A.M. and I.G. Mattingly. 1985. The motor theory of speech perception revised. Cognition 21: 1- 36.
Lorenz, Konrad. 1977. Behind the Mirror. London: Methuen.
Lumsden, Charles J. and Edward O. Wilson. 1981. Genes, Mind and Culture: The Coevolutionary Process. Cambridge, MA: Harvard University Press.
Lynton, Norbert. 1993. Adrian Berg. Modern Painters 6(2): 93-94.
Maynard Smith, John. 1986. The Problems of Biology. Oxford: Oxford University Press.
McLaughlin, Terence. 1970. Music and Communication. London: Faber and Faber.
Monod, Jacques. 1970. Le Hasard et la NÚcessitÚ. Paris: Editions du Seuil.
Nottebohm, R. et al. 1990. Song learning in birds: the relation between perception and production. Phil. Trans. R. Soc. Lond. B 329: 115-126.
O`Hear, Antony. 1993. The Sixties and after. Modern Painters 6(2): 100- 101.
Ormell, Christopher ed. 1992. New thinking about the nature of mathematics. Norwich: MAG-EDU University of East Anglia.
Saint-John Perse. 1970. PoÚsie: Allocution au banquet Nobel. In Amers. Paris: Gallimard.
Sewell, E. 1952. Paul ValÚry: The Mind in the Mirror. Cambridge: Bowes and Bowes.
ValÚry, Paul. 1974. Cahiers. Volume II. Paris: Gallimard.
Vernon, M.D. 1930. Synaesthesia in Music. Psyche 10:
Wilson, Edward O. 1978. On Human Nature. Cambridge, MA: Harvard University Press.
Wind, Jan. 1980. Man's selfish genes, social behavior and ethics. Journal of Social and Biological Structures 3: 33-41.
Windelband, W. 1956. History of Ancient Philosophy. Trans. H.E. Cushman. New York: Dover.
Wynn, Karen. 1992. Evidence against empiricist accounts of the origins of mathematical knowledge. Mind and Language 7: 315-332.