For millennia we have applied our innate capability for reasoning in mathematics to understand and master the environments we face. Whether “god-given” or laboriously evolved, structures built into a brain are prepared to organize sensations of space into complex orderly relationships and, in built environments, simple geometries.  Once they have been identified and put to work, generations of designers and their patrons have come to believe in the divinity, magic or purity of circles, squares, triangles, pentagons, trinities, and pairs, as well as wholes and proportions – like Palladio’s simple whole-number ratios or a double-cube room or musical rations – as if they may somehow be inherent in an underlying cosmic order – a harmony of the universe.

Their unfolding recognition may have been an experience of what we call “formal beauty.” Plato, who thought deeply about it, found Greek geometry “eternally and absolutely beautiful” and whether it is or not, its systematic use in skillful hands has produced extraordinarily pleasing, coherent harmonious design. For uncounted people it has felt deeply “right” and the forms have pervaded the patterns of both secular and sacred monuments from ancient classical design to Hindu mandalas to French rose windows and ornament around the globe. Their practical survival value has been put to work, too, in enormous investments in geometry – in points and lines that seem to decipher the sun and moon’s movements at Stonehenge and stone structures across the British countryside. And our ancestors embodied the divine itself in geometric forms, placing Poseidon as an architectural presence in the temple where his wild, open Aegean Sea begins at Cape Sunion.

The Greek god Poseidon embodied in the geometry of a temple where his wild,  open sea begins at Cape Sunion.

But there’s another plausible hypothesis that our readiness to “see” geometric principles and the simpler numbers we use in built environments can be found within ourselves – that, again in Plato’s words, “the mathematical structure of nature and the beauty of pure mathematics” is natural selection at work. They are representations of the complex realities “out-there” that have been created by evolving mental structures “in-here” – structures enabling logic and reasoning – as our ancient ancestors learned to master a natural setting through spontaneous, everyday visual, tactile, muscular experience. We ourselves live inside forms that have clear, coherent boundaries, bi-lateral symmetry, the insistent perpendicular pull of gravity, cycles of full circle rotation, straight lines of sight, and parallel, angled, jointed limbs, plus a propensity in our minds to see lines and shapes implied by points. In interactions with our surroundings we observe celestial geometry, and we discover crystalline forms, smooth, curved arcs of trajectories, our own flows of movement, the efficiency of straight-line paths and the stable horizon line. From all those and related sensory experiences, one might trace a direct path, through our capacity for abstraction and logic – and the pervasive human dream of perfectibility – to the simplified, cohesive, lucid, predictable, idealized relationships that have seemed so obvious in Euclidean geometry. In other words, the working geometries of places we have been building may well have developed out of human interaction with nature as the relevant “deeper order.” Read more…