New York architect Steve Bass, long associated with the Institute of Classical Architecture & Art as a teacher of classical theory, recently wrote a book, Beauty Memory Unity, on his favorite subject of architectural proportion. Proportion has long been a dodgy topic for me. I opened his book and skimmed through its pages of diagrams, equations, graphs and charts. Imagine reading passages like this one, taken at random:
[The passage below includes corrections suggested by Steve in the comments section of this post. He also corrects or clarifies some of my assertions made beyond this passage; some of those I have clarified or corrected, others not, so has to accurately reflect my thoughts, however off base they may be. So please read his entire comment.]
The elevation of the house at Stourhead, Wiltshire, 1719, [top illustration], is based on the double square. If the overall width is taken as 2 and the height 1, the basement is Ø[superscript 4], .146, the central tetrastyle is in a square of 2Ø² and each side wing is Ø, thus giving .618 + .764 + .618 = 2.0; a doubling of the 3-4-3 √2 cut. Notice that .764 + .618 = 1.382 and v2 =1.414; about a 2.3% difference, thus either geometrical key could be used to obtain the same pattern. The parapet is Ø[superscript 5] = .090. The midpoint of the overall height sets the spring point of the entry arch. (pp. 295-6)
Try to imagine reading and understanding it, and you (most readers) will imagine my complete befuddlement. The idea that classical architects down through the ages used such formulae to infuse their designs with beauty seems dubious, at least to me. At moments like this I enjoy recalling the warnings of New Urbanist guru Andrés Duany that the great treatises of classical architecture invariably contradicted each other. And yet the very much simplified idea that well-proportioned things are better than ill-proportioned things seems manifestly obvious.
So, in reading Bass’s book (or shall we say treatise), I decided to skip the challenging mathematical portions and read only the textual matter. And although the latter was festooned with enough equations and terminology drawn from classical mythology to stump me entirely, the many passages without such impedimenta turn out to be quite riveting. Here is one that seemed to ratify my own doubts about proportion:
In premodern times many, though not all, aspects of proportional methodology were held in private. Traditionally, artists and architects were not intellectuals. They learned what they knew by actual experience and regular practice in studios, shops or on building sites. In many cases the proportional techniques would have been couched in mythical terms, perhaps presented to the artisan in an initiatic context.
Does that not suggest that the use of proportions and is far from cut and dried, not really the stuff of mathematical precision? Seems so to me. Bass recognizes that he cannot really know what methods of proportion were applied by architects ages ago. And yet I am sorry: this was a poor example. The word initiatic, has, at least to some readers, an indistinct meaning. Does it mean presented to an apprentice on his first day in the studio of his master? Or does it mean presented to a novice as part of an initiation ceremony? Maybe it doesn’t matter. Maybe it does.
Still, as hazy as proportion seems from my perspective, it definitely has a role in making architecture beautiful. Just because I don’t understand it doesn’t mean that proportion’s precise application is anything other than exact and reliable in producing beauty. I can easily imagine classicists of the distant past winging it in their calculation of proportion. But that hardly means that many others – to be sure, more in the past than today – have not learned and internalized the equations set forth herein by Bass and have used them to create beautiful architecture.
Here is Bass’s introduction to his section about Michelangelo:
In looking at the architecture of Michelangelo, geometrical arrangements, particularly pentagonal, have been used. But these are to be considered strictly analytical. They are unlikely to have been the method actually used by Michelangelo, who drew architecture as he would the human body, finding the right place for a division as if playing a fretless musical instrument.
“Strictly analytical”? Hmm. Not sure quite what that means in terms of Michelangelo’s approach to proportion. Something in me wants to suggest that the passage paints Michelangelo as something less than a purist. Maybe the knowledge of proportions was not yet advanced enough to help the great Renaissance man. Or maybe it was.
Was Michelangelo a strict constructionist, as it were, or was his way of using proportion to toy magisterially with the orders really more inspirational? Or are the fundamentals of proportion drawn, as Bass suggests, from divine forces that inspired the rules, and were therefore deployable only by such geniuses as have conscious or unconscious insight into those forces? Now there’s a question that’s above my pay grade!
There are passages in Beauty Memory Unity that, taken out of context, seem to posit any of these theories. It’s sometimes hard to tell while leaping from one equation-free passage to the next, perhaps pages away, whether Bass is expressing his theories or describing the theories of others. Picking my way through a book is surely not the best way to review it, but reading it straight through, struggling with frequent passages that fly over my head, is sure to be equally ineffective – and likely to risk a failure to complete.
All of this should be taken as the admission of a proportion skeptic that the discussion of the origin, history and practical application of proportion is not just educational but a fascinating mystery, a mystery that only heightens in its fascination as chapter follows chapter. It is a great read for the uninitiated devotee of architecture (and doubtless even more so for the initiated).
In proportion as the professional architect of today seeks to climb toward the highest rungs of creative ambition, Beauty Memory Unity will prove useful, indeed inspirational, not just as a path to beauty but as a thing of beauty in and of itself.
(For a far more coherent and constructive assessment of Steve Bass’s brilliant treatise, readers are advised to consult Patrick Webb’s review in the May issue of Traditional Building magazine.)
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David – Thanks for this review – I genuinely appreciate your giving space on your blog to my book. I understand your [and many other’s] reticence on the subject of proportion [the use of number and geometry as design tools]. However, to cite the analysis of Stourhead without also showing the illustration guarantees that the paragraph will be unintelligible – the book contains dozens of pages of preparation on aspects like phi, √2, etc., that allow for such condensed brevity. I also think you may have slightly, and unintentionally, mis-stated some of the paragraph’s technical terms.
Another important point of clarification is that, as stated in the book, I’m not claiming that the methods or analyses given are the ones used by designers in the past. I make no claim to know what people hundreds or thousands of years ago knew or didn’t know. The stated purpose of the book is to assist contemporary designers in their search to create buildings that recapture the sensibility of historical work, that is to say, approach the beautiful. Readers are encouraged to draw the constructions for themselves, in which case the numbers are much more comprehensible, as drawing is a psycho-physical [mind-body] experience. Through drawing one learns with the whole body.
With regard to Michelangelo – the phrase ‘strictly analytical’ refers to my use of the pentagram in analyzing his work. My view of him is that his command of the human figure was so deep and complete that his architectural work inevitably takes on the character of the living body. As our bodies, and those of many other organic life forms, are saturated with phi [the golden section] he needed no technical or numerical guides to achieve these relations; a state that artists and designers might wish to aspire to.
It’s also important to note that the orthodox ‘five orders’ are descriptive not proscriptive. They are the beginning of design not its end. By mastering the conventional orders through study the designer, far from being a ‘prisoner of geometry’ or anything else, is in fact liberated to become a creative inventor; but invention without a baseline of skill and knowledge is just chaotic wandering in the wilderness.
Well, I could go on but in the interest of brevity, thanks again for this review. I take it in the spirit of ongoing conversation which our aesthetic development sorely needs.
Best wishes – be well –
Thank you, Steve, for your gentle corrections and clarifications of my review. I have corrected the errors in the top quoted passage; please let me know if I missed any; I had omitted the postscript numerals as references to notes; I have returned them, to the extent (up to 3) that WordPress permits (unless there is some workaround I’m unaware of).
As noted in a new parenthetical prior to the passage you have corrected, I have not adjusted all of the off-base assertions in this post. My ignorance of this subject is something I regret but am not embarrassed by and cannot, at this point, do much to remove – I try to be honest about my failings of comprehension on many architectural subjects, which are part of the conversation that makes up the architectural discourse.
As you know, my posts are directed not so much at the practicing architect or theorist – some of whom nevertheless peruse my writing, perhaps with a deserved condescension – but at the lay reader, whose technical ignorance is superior even to my own. It is the lay reader whose understanding and support will be required if there is to be a classical revival that eventually restores beauty to its rightful place in the field of architecture. Naturally, I hope that my untutored writing helps the lay reader comprehend what is necessary for them to participate in the accomplishment of that goal.
Thanks for the addition of the illustration of Stourhead – the ‘superscript’ numbers are powers not footnote references – thus Ø or .618 to the 5th power = 0.090.
I agree that there’s no need to apologize for what one knows or doesn’t know – but I would suggest that if someone read the book from the start much of the opacity of the terminology would clear up, as the first two parts of the book are devoted to defining the terms and constructions that are used later in illustrations such as Stourhead.
Thanks again –
I’m sure you are right, Steve, that reading your book through would, from the start, add to the reader’s basic knowledge, bit by bit, page after page, needed to understand your book and its concepts. I’m afraid I’m an old horse unlikely to benefit sufficiently to merit the time. My loss!
It took thousands of years to collect the acquired traits. And dozens of cultures and the periodic acquisition of various technologies to build it. Invention creates new opportunity. For much of it’s history architecture of a given reason was a form of vernacular. Classical took centuries, is divided into numerous enclaves and has perceptions based on cultures the world over. If architecture wasn’t permitted to evolve or if we still hadn’t mingled as human contact with other civilizations, we’d still occupy mud huts. Ancient Greek architecture was the first to introduce a standardized set of architectural rules that went on to influence Roman architecture and, as a result, architecture to this day. The Doric emerged in the7th century BC, the Ionic 150 years later, The corinthian a century after that. It took another millennium for the two new orders to come along. At the start of what is now known as the Classical period of architecture, ancient Greek architecture developed into three distinct orders: the Doric, Ionic, and Corinthian orders. Now imagine if back then a revulsion against the roman, tuscan and composite sprung up with the same set of online critique today.
If an architect today came up with a new “Order” it wouldnt be “classical”, but following the coherent forms………MOST of the architectural styles of the west in the last four centuries were not ‘Classical” they were revival. This day and age they have access to everything in terms of material and shape. Classicism remains but Ideological “orders” are straightjackets to design freedom.
Imagine if I came along and devised a new “Order” I take the column………….and devise a design of my own? How would it be received?Let people formulate and design. Here in this scifi game are you have an extrapolation
but they look similar….you have a modernist interpreation of…
Doric, Tuscan, Ionic and the Corinthian.