Elegance, harmony, and logic seem to be in our very bones. In the arts, it is true – and this was especially so in the twentieth century – we no longer share a common aesthetic. Modern “brutalist” architecture, hideous childish daubs on modern-art gallery walls, “inaccessible” literature, and music which, to a classically inclined ear, sounds like industrial noise or cats in agony, are characteristic examples. Besides these home-grown examples, the indigenous high art of other cultures may seem bizarre or incomprehensible to a Westerner. Musical quarter-tones, for instance, while not always appreciated by Westerners, have a subtle beauty for a Chinese ear; while statues or pictures which a Westerner might find menacing can have a beauty or a rare magic power for a non-European. But aesthetics always makes sense to the culture that expresses it in its own indigenous art. Indeed, one might even suggest that twentieth-century Western nihilism and revolt against the classical and Judeo-Christian cultural tradition have created a cult of the ugly which must – presumably – make some kind of logical sense to its own cognoscenti. For we all respond to beauty, irrespective of how we see it.
Things are more straightforward in science, however; for while different people’s brains – be it that of the Roman poet Virgil or that of a modern-day recipient of a British Arts Council grant – process aesthetic data differently, there is less room for diversity of expression in science. If a scientific theory is wrong, it will not predict measurable phenomena.
And while the Greeks were by no means the first people to invent “beauty”, they were the first to subject it to analysis. Plato and Aristotle both discussed aesthetics as an aspect of human understanding, yet it was the Greek geometers, from Thales (c. 625 BC) onwards, who were perhaps the first to be bedazzled by pure form, shape, and number in the abstract. We are told in Greek literature, for instance, of geometers sacrificing an animal as a “thank you” to their heavenly powers for revealing to them the exquisite truth of a new geometrical proof. A pure intellectual symmetry, indeed, and quite independent of any physical shape existing in the material world.
If the Greeks invented “science”, as opposed to record-keeping, counting, and fabricating, they did so because of their emerging grasp of the power of number – or mathematics. A domain unlike art or poetry, quite independent of human emotion or opinion. Poets might argue about the perfection of a verse, yet no one could argue about a geometrical theorem, for it either worked or it did not! I would argue, moreover, that this was not only one of the great intellectual “revelations” in human cultural development, but it is no less valid today than it was in 500 BC. Why do we need a thing to be “geometrically elegant” to be beautiful, be it a Bach fugue, an African vase, or Einstein’s theory of general relativity?
And why do we instinctively demand that for a thing to be true, it must also be beautiful? Not necessarily visually, of course; but making sense and bestowing an intellectual comfort or satisfaction. One might suggest that a true work of art is one that endures or becomes a “classic” because it feeds a deep need for order in human beings, be their culture Western, African, or Asian. And likewise in science.
Greek medicine in the tradition of Hippocrates – and with cultural parallels in indigenous Chinese and Arabic medicine – saw health as a state of balance, when the “humours” of the body were each in their proper place. Illness occurred when one or more “humours” usurped another’s place, to result in the patient becoming too hot, dry, moist, or cold. And the doctor’s art lay in diagnosing which humour was misbehaving, and restoring the body to its correct balance. We still speak of being “out of balance” when we are unwell, and a person who is mentally ill or behaves obsessively is often described in popular parlance as “mentally unbalanced”.
It was the classical Greek philosophical geometers who not only linked the body to geometry, but even related our musical tastes to both the world and the cosmos. One later Greek philosopher tells us how Pythagoras was watching a brass worker in his forge, and noticed that when he struck the hot metal with a hammer of a particular weight, it always made a “clang” of a particular tone. Be it a heavy bang or a light tap, the musical pitch emitted by a blow from the same hammer was always the same. And hammers of different sizes produced different pitches in a consistent and unvarying manner. Could it be that musical sounds were the product of different weights and blows, and that they were mathematically related?
Of course, elaborate musical instruments had been around for millennia by Pythagoras’s time in the sixth century BC. The trumpet, harp, and other instruments are mentioned in the Jewish Old Testament, while Egyptian artists routinely depicted a variety of instruments being played in their paintings. But the ingenious Greeks took it all much further, for they realized that the relationship between pitch and weight (or length) did not just apply to hammers, but also to blown pipes and plucked strings. And what other cultures had taken for granted in their pursuit of musical pleasure, the Greeks analysed mathematically. And sounds, in their tones, semitones, and octaves, were found to possess a mathematical unity that was no less exact than the component steps of a geometrical proof.
And then, when they observed the heavens, and timed what were believed to be the periods in which the planets and stars rotated around the earth, the Greeks noticed that the planets not only travelled at different speeds, but they described increasingly large circular orbits around the earth: the moon’s orbit being the smallest and Saturn’s (the outermost known planet until 1781) the greatest. And beyond Saturn came the largest sphere of all, which carried the fixed stars and zodiac constellations. And could one not think of the planetary orbits as rather similar to gigantic rings in space? Hit a small metal ring with a hammer and it emits a high-pitched sound; hit a big ring, and it emits a deeper tone – in much the same way that a shorter or longer tube emits a higher or lower pitch when you blow air into it or a string when you pluck it. And it would be the late classical Christian and medieval scholars – especially in Paris and Chartres – who would develop this “music of the spheres” idea, to link astronomy, musical aesthetics, logic, mathematics, the mind of man and the mind of God into one beautiful congruent whole.
Now as the moon went around the earth in twenty-eight days, whereas Saturn needed twenty-nine and a half years, it stood to reason that Saturn’s orbit was bigger – and its track much longer – than the moon’s. So Saturn’s orbit must represent a deeper musical pitch than that of the moon. And this was the logic that lay at the heart of the Greek idea of “the music of the spheres”. Not that the planets were necessarily singing as they rotated (though some later Greek and medieval philosophers suggested that there might be an angelic or heavenly “symphony”), so much as that there was a clear logical parallel between the mathematics of musical pitch and the number and motions of the planets: seven planets – the moon, Mercury, Venus, sun, Mars, Jupiter, Saturn – with the sphere of the stars making up the celestial octave as the eighth sphere.
And what more stunning example of the divine Logos could you hope for, when the sounds which delighted the human ear, and soul, had clear parallels in the mathematical proportions of hammers, vibrating strings, pipes, and planetary orbits? Medieval Christian philosophers, with their association of the Logos with God the creator and saviour, included music in the university curriculum by 1220. Not music as a performing art, so much as a study of the divine harmony of ear and intellect, God and man, heaven and earth. And as late as 1596, indeed, the German astronomer, mathematician, and theologian, Johannes Kepler, in his Mysterium Cosmographicum (“Cosmic Mystery”), would try to relate the planetary orbital spheres to the “regular solids” – cube, tetrahedron, and such – of three-dimensional geometry, and both of these to the mind of God, as discerned through human reason. And it would be in his Harmonices Mundi (“Harmony of the World” [or “Universe”]) of 1619 that Kepler would announce his three laws of planetary motion, which sixty years later would provide Sir Isaac Newton with the principal clue for his theory of gravitation.
So not only do we relate to the beautiful, but the Greeks tried to work out why we do so: namely, because of geometry, harmony, and balance – a balance that links art, science, medicine, reason, and God. And while we now know that there are more than seven planets, and that curing illness is rather more complex than rectifying the balances in the body, the intellectual and spiritual goals of the ancient Greeks still form the bedrock of our aesthetic values and ideas today. Just as a beautiful human face requires symmetry and balance, so does a satisfying body of sound, and an adequate explanation of how a complex drug acts upon the human body or how we might evaluate a scientific theory. And all of this involves what might be considered in the widest sense a series of spiritual criteria, to remind us once again how religious values have always fed and sustained scientific aspiration and understanding at their deepest level.
Indeed, the whole of Greek science, from cosmology to medicine, was rooted in these concepts, Logos and geometry, and to deny science’s debt to them is to rubber-stamp atheist ideology in the teeth of historical evidence.