When we are offered a new tool for interpreting
and assisting design, how do we evaluate and judge it? Somehow, we need
to try it on, test it with our own experience, and see what value it has
Rachel Fletcher's "Geometer's Tour of the Pantheon" in the Fall issue of Design Spirit, for example, gave an evocative view of the value of looking at the geometry of the architectural past for insight and inspiration. It left me, however, with more questions and doubts than inspiration, and it felt like more dialog was needed before I could accept the inspiration she offered.
Here are some of the comments and questions her article raised for me:
On a gut level, I still find little inspiration from either current or ancient buildings which depended upon simple geometric analysis as the basis justification in their design. Even after studying Rachel's analysis, her underlying enthusiasm for the building didn't change what has always been my gut reaction towards the Pantheon - a somewhat ugly, ponderous and somber building, whose value lay in its tremendous structural achievement in spanning space rather than as an architectural or spiritual whole.
I've always wondered, if a building as innovative as this one did have any significant architectural or spiritual power, why the Romans didn't replicate it? Part of the reason has seemed to me that the structural enthusiasm resulted in a building that didn't fit its use - the Gods were relegated to marginal niches around the edge, while the main space was given to the worshipers.
To the degree that the builders imposed a Euclidian geometry onto the shape and composition of a domed building such as this, it showed a glaring ignorance of structural properties of domes. Underneath that pure and sacred geometry is a frightened, corseted lady, crying to get out. Bound together by hoops of timber and steel, with a waistline weighted down by bulging layers of concrete to keep the dome from cracking open, is a reality that has nothing to do with the surface geometries. Shouldn't geometry have a stronger fit to its application?
Fletcher makes an analytical analogy to architecture as "frozen music". But how universal is the musical system she refers to? Does a voice or trombone, for example, just create sounds at certain musical intervals? Does the music of other cultures use the same tonal ratios? And which parts of the building are notes? Looking at her drawing, I see a lot of other possible "significant" notes that might not come out to the simple ratios she is enthusiastic about.
There is an underlying assertion in most geometric analysis that the builders used the postulated system in their design process, and that it was an important part of that process. Where is the proof here, or some concrete clues that this might be so? I've seen it in original drawings for Indian, Japanese and other buildings, but did the builders of the Pantheon use
geometric analysis in their design? If so, was it a matter of significance or convenience? And even if they did use esoteric geometric in their design, why should we copy it? Should we also copy their religion, slavery and limitations of structural knowledge?
There is a danger in reading intentions into other people's actions as justification for the universality of our own beliefs. Solar advocates in the early 1970's used the Anasazi cliff dwellings at Mesa Verde as an example of sophisticated solar design. Architectural registration exams ask you to say that Gothic architecture is a better learning source about the role of structure in architecture than Islamic architecture. Japanese architecture is frequently pointed to as an example of the evocative power of modular design and ornament-free structure. And the "sacred circle" of tipis, kivas, and yurts, is repeatedly been used to assert that rectangular buildings have no soul.
In reality, the vast majority of Mesa Verde's cliff dwellings face east or west, not south, because that is where the cliff alcoves occurred in the mostly north-south canyons. Almost all accessible alcoves had cliff-dwellings, not just the south facing ones. Their builders sought the vital water source from the springs which formed the alcoves, and possibly protection. Solar design, when it happened, appears incidental.
A close look at the actual development of vaulting and construction in gothic cathedrals shows it to have been a spiritually-based esthetic rather than structural development. The entire "flying buttress" system of construction used in gothic cathedrals was only a cumbersome byproduct of failure to understand the structural forces in vaulting, of which Islamic builders were masters. Instead of using circular or spherical arcs for their arches and vaulting, they used what we now call catenary curves, keeping the support material of the vault in line with the increasing forces of the weight of the vault as it moves closer to its supports. Observation, not preconception. What we glorify by calling the "scientific method", but rarely use ourselves.
What we see of structure in the wonderful Japanese temple roofs it turns out is not structure, but actually ornament - a false roof hiding the real structure inside. Similarly, Japanese architecture employs not one but several "modular" systems - each with problems and limitations and elaborate means of disguising and covering their warts and pimples.
The power or absence of power in tipis and hogans and kivas and yurts, and mini-and mega-geodesic domes.doesn't come from the geometry - some have it, some don't. And it would be real hard to say that Japanese teahouses that fit none of the rules of circular geometry have less spiritual power than that supposedly given only by the circle.
If we are going to study the past for inspiration, we need to study it with care. Otherwise, we create false gods, we diminish ourselves, we fail to see or learn to see real achievement, and we fail to know things deeply enough ourselves to accomplish anything of significance. When we later discover that what we imagined into the past wasn't there, we infer that there was nothing else of value to be learned, and no way to make places that avoid the spiritual emptiness of our buildings.
Whenever we see drawings of geometry imposed over buildings, I think we have to look beyond a pretty diagram and ask some questions. What significant design elements don't fit into the geometry, or only come close to fitting? How many symbolically more vital analyses had to be discarded because they didn't fit? If you throw enough lines at a building, you're bound to hit something sometime. LeCorbusier's geometric design system, for example, had so many options that anything would fit it with a little juggling, and the design didn't look a bit different from one not using his geometric analysis.
In the Pantheon, recessed coffers were used to lighten, stiffen, and reduce the cost of the dome. With it only making sense to use whole coffers, it is inevitable that geometers would come up with some sacred significance for whatever number was used, even if it originally occurred merely from the size of forms the builders had. It seems that there has to be some greater justification as well as proven value before assigning significance to the geometry used in construction.
Geometric analysis seems to assume greater vitalness of certain geometric relations as opposed to others. What are they? Why are they vital? How does this building, in contrast to others, embody them powerfully?
Rachel Fletcher quotes Aristotle and Plato, "The circle is of all lines most unified.....Can there be...any greater good than the bond of unity?" But compare for a moment the incredibly powerful expression of that unity in Islamic faceted vaulting and ornament, where that unity and bond remain untouched, and only gains power, through the dazzling manifestation of complexity, richness, and variety which arises from it. Some might say that a circle doesn't have to be round to be a circle, and that some of the most wonderful unities and encirclements have bumps and bulges and rough spots which in no way blemish the wonder and power of their oneness.
What conclusions are we supposed to draw from
geometric analysis? Are their rules or guidelines that should be used? What
parts of the building are significant enough that they ought to fit into
a geometric analysis? Is the use of geometric analysis in design supposed
to give power to the design? If so, what power, and do people really sense
* * *
With one exception, I have never found that the employment of a geometrical system - whether Palladian, symmetrical, asymmetrical, golden mean or other - has been a major factor in the power of places I have visited in any part of the world.
That exception was in the Kailasanath Temple at Ellora, India, where.the time/space geometric system used in the yantric sculpture made it jump off the wall and burrow into my mind. That experience, along with the work of Anne Tyng and Dan Winter on the geometric linkage of the ordering of energy and consciousness, suggests that there can be a powerful experiential effect of geometry in the making of space, but I have yet to experience its effective use except at that one ancient rock-cut temple.
There are several ways in which I do find geometry to be of value in the design process, none of which deal directly with spatial organization. The geometry which I find does have the greatest value in the making of place is topology. Topology is a qualitative rather than quantitative geometry - one that cares about relationships, not exact size and shapes. In feeling the way towards a design that fits well with the purpose of a place, it helps resolve first the essential questions - "Does this belong within or apart from this other?" "Do these things coincide, or should one encompass these other things as well?" I find that when these questions are answered well, the circumstantial geometry of adapting to the particular details of site, budget, program, etc. resolve themselves without imposition. And the fitness that the topological study generates results in a quiet power of rightness irrelevant of the final design geometry.
Geometry may also prove of value as a process of establishing relationships between a designer and the forces of nature in a place. Look, for example, at traditional practices for determining north/south orientation. One common method was to mark the rising point and setting point of the sun, moon, or stars, connect those points with a line, which gave an east/west direction. Drawing a perpendicular to that line creates another line pointing north/south. The process requires you to be on the site for some time, at different and significant times of day. It causes you to acknowledge cycles of the forces in our environment and how they are connected. Locating north by the Polar star at night, or south by the shadow length and direction at mid-day does the same. They establish an inner orientation and connectedness, out of which a design grows which is cognizant of those forces.
That brings us back to the basis question we all are asking:
From what does the spirit of a place arise?
Where does a place or an object or a person get the magic that penetrates our own spirits, causes our hearts to pound, and forges an unbreakable bond between us?
Where does power come from?
Many writers speak of "sacred geometries". or "sacred places" because of the power those individuals feel in them. Yet when we find places which violate every rule of sacred geometry, and every criteria of "sacred places", but which have equal or greater power, we need to inquire further where the power originates. What appears to me more important than the physical or energetic or historical characteristics of a place is simply the fact that someone has chosen to hold a place sacred.
Those human acts acknowledge the finding of something in a place which makes us aware of certain relationships and their value to us. They forge and strengthen bonds between us and the universe in which we believe. They empower us by affirming the wholeness of the universe we see revealed about us, and by reflecting our chosen place and role in that universe. They marshall our inner resources and bind us to our beliefs. Our act of "holding sacred" is root, not where we choose to carry out that act.
WE give places power to affect our lives.
The surroundings we create, like all our acts, truly reflect every nuance of our beings. They expose to the world, in concrete and steel, all our loves, our blindnesses, our passions, our fears, and our greed. They don't lie! If we don't like what we feel through them, perhaps it's more important to look in the mirror than for some magic geometry which will give them the appearance of some imposed meaning.
* * *
Hindu tradition in the design of temples talks frequently of temples being created in a single night. Whether or not this was true of actual construction, it certainly was true of the design process, where each attribute of the deity in question was meditated upon and empathized and identified with, until the designer "became one with the deity, at which point the (design of the) temple burst forth in full and complete detail."
That deep touching, exploring, feeling, and mingling - searching for, trying on, and suddenly finding the spirit that is sought, before even considering such things as geometry, is vital. It creates a powerful and essential touchstone which guides, and against which is tested, every major and minor decision in the process of actual design and construction. It IS the temple or the place. The visible designing and construction which follows is merely the recording, clarification, and embodiment of that deep inner sense - even taste - of the place. Without it, things go awry, and the spirit and power of one thing does not build upon that of others. With it, you know immediately that this detail or that color or opening is or is not right, and each adds to the others like voices in harmony to create a powerful and pure creation.
Many cultures have had strong, rich, and deeply held symbol systems which guided and directed how they related to the natural world, the shaping of their homes and communities and gave them rich and deep meaning in their lives. Doors or alters oriented to the rising sun, the sacred fire or center post, a certain use of geometry, sculpture, arrangement of things, use of materials, or ritual in making and use. Our culture has lost the commonality of such shared symbol systems, and lost their power - for they do have power. Their absence leaves a powerful void. Yet the nature of our culture contains something of equivalent power.
The certainty of a common symbol system ensures a level of cohesion, power and meaning in our surroundings. It's limit, however, is that a deep and living understanding of things cannot be just passed on from one generation to another. It has to be created, recreated, forged and transformed anew inside each of us. Our culture does not give the assurances of tradition. Instead, it in theory gives the incentives and abilities for each of us to make that search ourselves. That fire of fresh creation (true, deep, loving and connected) is the power we feel so strongly in great places, and whose absence we equally feel in our everyday lives and surroundings. It is that which exists in the spirit of a place in harmony with its universe, its surroundings, its culture and itself.
The first steps towards any new understanding of things are tentative and fragile, and those who are searching are understandably hard pressed to come up with powerful and all-compassing explanations. We need to recognize this, and nurture them gently. But refusal to dig deeper, to question, to look for explanation of inconsistencies, to search harder to find explanations that do work ultimately only leads to failure.
Rachel's article was beautifully done, and it was wonderful of her to share how she finds value in geometry and the past so that others can learn from it and grow through it. She has raised some important questions that we all together need to answer.
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