There is a great story about the Renaissance painter Giotto di Bondone (1267-1337) who is said to have won a Vatican contract from Pope Benedictus XII by submitting nothing more than a perfectly executed hand-drawn circle. The circle became famously known as the “O of Giotto”, and remains to this day part of artistic lore. But it is not famous for its realism; realism, as an aesthetic pursuit, was not yet a virtue in Giotto’s time, even if Giotto did much to usher that virtue in. It is famous, rather, for its symbolism: the idea of perfection. The perfect circle, we know, has had a long history of expressing the perfect, the ideal, and thus the divine. Giotto’s O becomes emblematic of a Renaissance obsession with symmetry, with the aesthetics of geometry, with the unity of the whole, and with the spiritual features of the circle. And we can see this worked out in the many Roman arches and halos that Giotto painted for churches and ecclesiastical patrons. But it was more. It also became emblematic of the human aspiration to master an ideally integrated world, one in which the divine imprint on the created order not only could be perceived with the eye and the mind, but also – and this the Renaissance championed most expressly – could be replicated by an aesthetic gesture. This gesture, perfectly rendered, is what so obviously endeared Giotto to the Pope, and allowed Giotto his celebrated career. His O was an immaculate sign of a higher order – indeed, the highest.

But of course, this side of the Enlightenment, and with all our scientific advance, we have become more skeptical. We are first compelled to ask whether there is ever such a thing as a perfect circle in the natural world. And even if we admit the possibility, we preclude the chance it was made by a human hand, at least one unaided by instrument. But we go further, and ask can any symbolism be pushed beyond the platitudinous use we still find, say, within a wedding ceremony, or with such phrases as “the winner’s circle”. The question is quickly dismissed if we try to extend it to more ideal, or heavenly, spheres. For us moderns, the symbolic ideal of a perfect circle has become antiquarian, and we see it for what it always was: a doctrinal construct, a theological hope, a philosophical dream, or some form of a utopian wish. In the pre-modern West, the perfect circle found its representational power within a large schema of unity and oneness. In such a schema, which went by the name of a cosmology, the circle was a pure symbol of the one true divine perfection, not only reflected in the heavens and their movements, but also resident as the ultimate Sovereign in those heavens. So that by drawing freely his circle, Giotto proved not only his technical prowess but his theological acumen. But with the coming of modernity, we lost that ruling sense of one, or the One. It fell victim to irreparable division. It is not just that, in the Renaissance, the perfect circle was applied to humanity, as in da Vinci’s famous Vitruvian drawings. Nor was it simply that the Catholic Church lost its catholicity in the upheavals of the Reformation, and in the bloody wars that swept across Europe in their consequence. It was also that the true and perfect circle was finally seen for what it was: a spiritualized aesthetic.

The development of modern science had much to do with this shift in perspective. In the 17th century, Johannes Kepler, for example, a man who was not without a deep sense of the spiritual, wrote with great implications for the future understanding of circular movement, and any attendant symbolism:

For if it was only a question of the beauty of the circle, the spirit would decide with good reason for it, and the circle would be suitable for all bodies, principally for celestial bodies, since bodies participate in quantity, and the circle is the most beautiful form of quantity. But since it was necessary to rely not only on the spirit but also on natural and animal faculties to create motion, these faculties followed their own inclination, and they were not accomplished according to the dictates of spirit, which they did not perceive, but through material necessity. It is therefore not astonishing that these faculties, mixed together, did not fully reach perfection.*

Kepler, of course, figured for us this “material necessity” in the form of the ellipse. And to arrive at the ellipse we must distort the circle. The etymology of Greek ellipsis already shows us the radical consequence: a “coming up short”, most egregiously of perfection itself. Only a spiritualised circle can remain purely whole, as a visionary reality. As a factual reality, the phenomenal circle remains bound to “quantity”. That is, it goes beyond the singular, the unity, the idea of ultimate oneness. As Kepler says, with ramifications he probably did not intend, spirit and nature divide, and therefore so does the symbol, as the sign is rent from any divine signified. In modernity, the circle can no longer point to the One, or the One is no longer at its centre. “The centre cannot hold”, wrote Yeats in this oft-repeated quote from his “The Second Coming” poem.

In an earlier blog I had written about the slow but inexorable encroachment of the concept of nothing into our modern sensibility. I can now say that the coming of this nothing is not without its own symbols. Yet ironically, its most prevalent and persistent symbol is one that it has appropriated from its ostensible opposite: the circle that had come to represent the divine perfection in its wholeness, unity and oneness, virtues that so impressed Benedictus XII in the O of Giotto. The “O” becomes hollowed out by modernity, we might say, and in that hollowing arises the nothing that is “zero”. It is not that the symbol of “zero” entered our thinking by means of some modern form of numerology. (The symbolic notation of zero has a very different history, as we’ll see in my next blog.) It was rather that the circle had lost its symbolic sense of unity and wholeness, even in the very sphere where it once held sovereignty, the heavens. The appearances – deviation from circular perfection – no longer needed to be saved, because now science could account for them efficaciously and comprehensively. But the knock-on effects back down on earth, the material necessities that rendered the divine ideal lost to the centrifugal pull of a space emptied of cosmological unity, led to a breaking apart of the wholeness on every level. Division entered our world to a degree not seen in a millennium. And it continues to reside in our present world as a commonplace. Today we have many circles, many centres, many Os. Like Kepler’s ellipse, the O is no longer one, no longer truth with a single and perfect centre, no longer One. Its spirit has absconded, chased away by the material purpose of scientific or instrumental rationality. We must do our calculations, and we must do them now with a zero that is both functionally and conceptually necessary. We can still marvel at Giotto’s O in our museums and churches. But we marvel at a bygone theology, as much as a bygone aesthetic. The question for us now is how, in the many Os we might draw, and in the many circles we form on a daily basis, we negotiate our way across the empty spaces and the deep chasms they inevitably bring into our view. Yet Giotto’s legacy is not all lost: he at least tells us that something, even if that something is a “nothing”, remains there for our creation.

* Johannes Kepler, Gesammelte Werke, eds. W. Von Dyck, M. Caspar, et al. (Munich: Beck, 1938 et seq.), Vol.7, p. 330, as translated by Fernand Hallyn in The Poetic Structure of the World: Copernicus and Kepler (New York: Zone Books, 1990), p.213.