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…

Experiencing a sense of community – belonging to a successful network of human alliances – is one of the great pleasures of the places we build.  And at village or at city scales we dedicate an enormous share of our resources to accommodate and symbolize the group’s protection, effectiveness, and cohesion.  Facing the propensity for destruction and violence that’s inherent in person-to-person competition, we strengthen bonds and loyalties with places to meet, act out our agreements and shared stories, resolve the inevitable conflicts and plant symbols of our “social contract” – the places to eat together, judge, worship, trade, play, and celebrate with shared movements, ideas, voices. and action – and finally in the burial grounds that record the continuity of the shared gene pools.

“The Greek theater where a city saw and heard itself being a community – sharing its myths, passions and history”

Civil society’s most honored monuments are the places where a community can read the stories of individual competitors surviving and prospering together – stories of victories, resolved conflicts, bonds of loyalty, generosity and philanthropy, and the favor of a deity. It’s seen in the bold, arrogant commercial and town hall towers of medieval Europe’s newly independent cities – with their symbolism of wealth and power that’s inherent in penetrating a skyline. Today we do the same. We announce our stability and pedigree in the neo-classical languages of power – in finance, universities, and governments – or the engineering of grand transportation infrastructure and waterfronts that tell stories of still larger geographical alliances. And the most moving are the places where citizens see – and hear – themselves being a community, sharing the passions stirred by their myths, arts, and on-going history – the Greeks in their intimate theaters or today’s crowds in museums or performing arts venues. And it can happen in parks, plazas, and arenas where spectacles, music, or sports – at small and large scales – evoke feelings of solidarity, working or fighting side-by-side as a team or as a gang, making connections just as binding – at least for the moment – as genetic kinship. These places where we reinforce and celebrate – respond to – our prospering alliances are the settings where we experience what we call “sense-of-place” and “authentic” communities.

Alienation

In any mix of diverse and mobile populations, under any social structure, the built environments, the public faces of places financed and occupied, naturally express the victories, values, religion or status of the winners. When, for better or worse, they also become symbols of exclusion and oppression, they become physical targets for the outsiders – called, naturally, barbarians, rebels or terrorists. They have been throughout history. And in our globalizing, urbanizing settlements we can expect continued destructive responses to the places we build.  The alienation is just as deeply felt as “belonging,” and the winners are responding as they always have, with hardened perimeters and surveillance – refuge and prospect.

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