A New Humanism: Part 17

Geometries and the deeper order of things

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.

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.”

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In any case, whether our own inventions or discoveries of universal truths, the important point here is, as Gestalt-related research indicated, all of us expect, find, and apply simple geometry and numbers as we experience our surroundings. They seem to resonate in a human mind and perceiving them becomes a source of pleasure. Their precision and consistency that enable calculations and analysis, and the order of their shapes and grids, have come to feel like a distinctly rational, human mastery over an uncontrolled, disorderly, entropic nature.  And through mathematics we are able – when its useful – to imagine our designs – our habitat – as an integral part of a larger visual, spatial unity – a cosmos of precise measurable relationships.

Forms and Proportions

In Architectural Principles in the Age of Humanism, Rudolph Wittkower spelled out how hierarchies of geometric forms combined with divine or human systems of proportion were thought to be sources of “perfection, beauty, and propriety” in the Renaissance years. The familiar diagrams of a human figure inscribed in a “divine” circle and “secular” square by Vitruvius, Leonardo, and others were used to illustrate the human elements of the idea. And since then the idea of a universal system of proportion, one based on a “perfection” of mathematical relationships in the body of an ideal “well-shaped man,” has been explored again in Le Corbusier’s Modular. But in practice those kinds of systems have foundered on the problem of whose body and which dimensions. Further, Wittkower reviewed the vast, often contradictory literature on proportion written in the 19th and 20th centuries and the fading confidence in finding some “truths” in systems of ratios. He concluded with Ruskin’s words, “it must be left to the inspiration of the artist to invent beautiful proportions.” 

But that simply avoids the issue. For the classical Renaissance humanists, and for my purpose here, the important question still is what deeper order lies behind the “inspiration of the artist?”  Because of the enormous influence of our most thoughtful predecessors, especially the long-lasting imprint of Greece, Rome or medieval France across the globe, it seems to me that we should take seriously the idea of “favored” proportions and combinations of numbers. The pleasures of music may well be based on tones and harmonies heard in human voices, and there may well be parallels in visual harmonies. The evidence is worth more study.

“Regulating lines” applied to Notre Dame Cathedral in Paris by architects and historians – but many different selections of lines and key points have produced splendid, harmonious designs

In addition, while Wittkower does not use the term “regulating lines” – a simplified, coordinated pattern of circles, rectangles, diagonals, or the fish-like vesica pisces, overlaid on admired or chaotic building plans and elevations – the idea of illustrating an organizing geometry in architectural compositions attracted him and continues to attract attention.  In the Modern movement Le Corbusier and a few others have applied them in efforts to update unified systems of geometric traditions. The most persuasive lines have tended to be repeated squares, circles or, more often, diagonals connecting prominent points and corners, their slopes representing a proportion – a ratio of vertical to horizontal – and when they are related, fanned or parallel, many tend to create a settled, rhythmic harmony in a façade. They have proven useful in shaping openings, structural bays, and clusters of related masses and spaces, but in plans, sections or façades, many different selections of the key points to be connected have produced splendid buildings and gardens, and many, naturally, have not. Still, look at the Pantheon, or the bays of the Roman Colosseum repeated around the globe; this idea seems worth more exploration, too.

The Pantheon – Roman geometry engineered into a building for the gods

Further, in the continuing search through history for ideal proportions, the “Golden Ratio,” 1:1.618… has endured. Not only is it a useful number in mathematics and identified occasionally in plants and animals, but in built environments a rectangle having this “divine proportion” is widespread in Western arts and routinely selected as a “most pleasing” shape. Further, the “Fibonacci sequence,” in which each number is the sum of the two preceding it, and “fractals,” repeating “self-similar” shapes at different scales, have been found in nature and the arts as well. Either of these – and others discovered in mathematical studies of the natural world – may well be a promising basis for building firmness-commodity-and-delight. They may, in fact, underly, some of the order we sense, in places, sacred or secular. But, of course, many other proportions and sequences seem to have done that just as well.  Still specific measured, universal relationships may well be inherent in our genetic heritage, and again, it would be useful to find out. 

And we probably can. Today, with the computer’s addition to human capabilities combined with brain research methods, we have an opportunity no one has had before to analyze these hints of some biological/mathematical propensities in ourselves. We are already starting to exploit our new capacity to apply more complex mathematics and geometric forms to physical building structures, materials, and swirling ornament “out there.” An equally valuable study would discover – at a comparable level – how a mind and body are likely to respond, “in-here,” which would, in a parallel way, release a new round of useful, relevant creativity.

Yet in practice we know that’s only a beginning. The objective, orderly “authority” of familiar geometric forms is continually challenged – and not only by mathematicians. In their park and suburban designs the Olmsteads illustrated the equally timeless, humane qualities in more organic forms. And many landscape architects and interior designers have built careers on the idea that architects’ and engineers’ rational, geometric abstractions are threats that need to be “softened” for human use. They merge buildings into the forms of a natural setting or, engaging more senses, add the pleasures of variety, in-formality, light, colors and the fabrics and rounded edges that invite touch.  These impulses are, of course, based on equally primal pleasures.

“Geo-metrics” of human nature and ecology

Following different evolved capabilities and predilections, we are continually applying other geo-metrics in the literal sense of measuring the earth. We “measure” the potential value of, and lay out the human use of land and water guided by many innate propensities that evolved in natural selection – cost and benefit judgments about survival, refuge and prospect, cooperative social patterns, competition and hierarchies. And our own physical structures and capabilities come into play – energy, strength, senses, scale. Further, for millennia our primal emotions – fears and desires – have led us to shape and measure the use of land around sacred visions. And at a more intimate scale, the geometry of human daily life was articulated in Frank Lloyd Wright’s and others’ “organic” architecture. In other words, some human purposes can be expressed in vocabularies of traditional plane and solid geometry and the math is clearly one, but only one form-giving, underlying order; it often seems more of a “tool” we apply. But even more fundamentally, we measure and reshape the “earth” in terms of its own specific resources and functions as they relate to our human nature – to personal survival, prosperity and pleasure. Instead of overlaying an imagined formal, internally logical system of shapes, we evaluate directly sources of food and materials, microclimates, topography, and routes for transportation and trade.  Paralleling our affinity for abstract patterns, we search for and detect the living patterns of people interacting with a natural setting – the ecology of the place.

As our industrializing, urbanizing modern culture has been discovering its limits, we are re-vitalizing that kind of organic understanding of the harmony-of-the-universe. And it’s turned out to be made up of densely interacting, widely distributed, dynamic systems, extensive or intensive, where architecture, landscapes, urban settlements and an array of habitats are shaped by the immediate, physical, deeper order of “god-given” influences of sun and wind, trajectories of temperature and seasons, geological forces and hydrological cycles, energy flows, changing soils, watersheds and topography, orientation, niches, “patches” and corridors, and the growth cycles of plants, animals and ourselves. 

They can be measured by the disciplines of mathematics and geometry, but we’re uncovering, or re-discovering, their internal rules – their own geo-metrics – as a basis for intelligent stewardship. And naturally those rules – and the ecological sciences themselves – are as comprehensive, rigorous, interconnected and rational as, and far more complex than the axioms and corollaries of Euclid’s geometry – or Plato’s. In this sense, a wilderness is more order-driven than LeNotre’s chateau gardens.

This ecological vision – and the idea that whatever is about “me” is about my natural setting –has a long history but it was launched into the mainstream of current professional design practice most effectively by Ian McHarg with his “simple plan for man in nature.” And that’s been followed by the growth of a practical ideology – a survival strategy – we call “sustainability.” We’ve built ourselves into an enormous, complex crisis. Today, defining the challenge and advancing a sustainable response are the most urgent tasks of all of us involved in design and building. And inherent in success is going to be our growing understanding of ecology – of nature and human nature – the sciences of “man in nature.” In that sense, a new humanism – creating an understanding of genetically, biologically based motivations and decision, plus impulses for learning, teamwork, and enthusiasm – is an integral element of building a habitat that may someday be sustainable.

Yet there is still resistance to these perspectives. Both our classical and biblical heritage sharply separated an alien, inferior wild nature from a god-given human destiny to master it – to take over ecological control. As a result we are continually having to adjust familiar romantic, exotic or simply ignorant views of the natural world to new evidence. Even when discussed, “ecology” is still often misinterpreted, even by professionals, to mean processes occurring alongside human action and economics, not recognizing “us” as one of the most disruptive, creative actors in any ecosystem we enter.

And for now, another kind of resistance-to-change also puts the science of ecology alongside and not integral to the arts of landscape, architectural and urban design – just as an equally nonsensical attitude of many good architects for generations put the sciences of “engineering” alongside and subservient to their own “art” and “aesthetics.” 

The rock garden at the Ryoan-ji temple near Kyoto, Japan – aesthetic qualities inherent in the geo-metry of ecology

As often happens, this is a case where the culture of Japan can clarify our vision. In places like the contemplation garden of the Katsura palace, or more compactly Ryoan-ji, in a composition of rocks, moss, and raked sand, there is, in landscape architect Anne Spirn’s words, a place where we can be immersed in “a distillation of those islands’ deep landscape structure: the juxtaposition of mountain and sea, stone and water, with the narrow band of settlement between” – the natural forces at work – and the garden scents and sound of rustling leaves fill in the background. At a larger scale, too, over generations that man-in-nature sensitivity has built working landscapes that draw emotional responses from people from all around the world because of, in a sense, a Japanese-like “cultural lens.”  It is able to humanize the impersonal primal, functional, enduring science and “geometry of ecology” by stirring a fulfilling aesthetic response.

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The next post introduces a new section of the New Humanism ideas called “The Body Responds.” It explores how the experience of architecture originates in the body – drawing on Geoffrey Scott’s classic, The Architecture of Humanism, and Kent Bloomer and Charles Moore’s Body Memory and Architecture to spell out implications for design.

This is the seventeenth in a series of posts that spell out a set of ideas called A New Humanism: in architecture, landscapes, and urban design. They’re about enlarging the way we think about design by applying, in day to day practice, a broader range of insights into the cutting edge sciences of nature and human nature — using them to understand how our evolved mind-and-body actually experience the places we design, and why people respond the ways they do.

Robert Lamb Hart is a practicing architect and planner educated at Harvard GSD and the University of Pennsylvania. He is a founder and a principal in Hart Howerton, a planning, architecture, and landscape design firm with an international practice out of offices in New York, San Francisco, London, Shanghai, Park City, and Boston. He believes that the design professions have been falling behind in their understanding of one of the defining enterprises of the Modern revolution, the application of the maturing, fast-moving sciences of ecology and human behavior — and the compromised results are showing.

Albrecht Pichler, who drew the sketches, is a practicing architect and a principal in Hart Howerton’s New York office.

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