Rules of Proportion in Architecture. Patrick Suppes

8/13/2019 Rules of Proportion in Architecture. Patrick Suppes

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MIDWEST STUDIES IN PHILOSOPHY, XVI 1991)

Rules of Proportion in ArchitecturePATWICK SUPPES

T h e ancient Roman architect Vitruvius begins the second chapter of the firstbook of his The Ten Books o Architecture with the statement that architecturedepends on order, arrangement, eurythmy, symmetry, propriety, and economy.Although the other works on architecture from the ancient world are mostlylost, there is every reason to believe that Vitruvius was stating a commonlyand widely accepted view in his emphasis on order, eurythmy, which we maythink of as proportion, and symmetry. In the first chapter of Book 3, he alsomakes the familiar classical assertion that the principles of proportion andsymmetry used in architecture are in fact derived from thesymmetry to befound in the shape of the human body. He even states his conclusion this way:Therefore, since nature has designed the human body so that its members are

duly proportioned to the frame as a whole, it appears that the ancients had goodreason for their rule, that in perfect buildings, the different members must bein exact symmetrical relations to the whole general scheme [Dover edition,196Q p. 731.f

In Chapter III of Book 6 Vitruvius gives specific rules for the proportionsprincipal rooms; I cite three typical cases.In width and length, atriums are designed according to three classes. Thefirst is laid out by dividing the length into five parts and giving three parts tothe width; the second, by dividing it into three parts and assigning two partsto the width; the third, by using the width to describe a square figure withequal sides, drawing a diagonal line in this square, and giving the atrium thelength of this diagonal line. 1771Peristyles, yingathwart,shouldbeone hird onger han heyaredeep,and their columns as high as the colonnades are wide. Intercolumniationsof peristylesshouldbenot ess han hreenormore hanfour imes hethickness of the columns. 11791Dining rooms ought to be twice s long as they are wide. The height sf alloblong rooms should be calculated by adding together their measured length

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sixteenth ent tu^ Italian architect, Andrea Palladio, much of whose work isstill preserved and who wrote one s the most influential works in theof architecture, The Four Books of Architecture published in 1570. Iwonderful 1737 English translation by Isaa e, which Ras been reprintedby Dover. Wmtin in a vein that sounds v ose to that of Vitruvius,


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354 PATRICK SUPPESis what Palladio has to say about the proportion of rooms in Chapter XXI ofBook I. The most beautiful and proportionable manners of rooms, and whichsucceed best, are seven, because they are either made round ( Q but seldom)or square, or their length will be the diagonal line of the square, or the squareand a third, or of one square and a half, or of one square and two-thirds, orof two squares [p. 271. Palladio also gives a detailed discussion in ChapterXXIII of the same book of the height of a room given its length and width. Hedistinguishes whether he ceilings are vaultedor flat. His three alternative rulesfor vaulted ceilings use just the arithmetic, geometric, and harmonic meansrespectively-all familiar to the Greeks since the time of Pythagoras. One isthat the height should be equal to half the sum of the width w and the lengthof the room, which is the rule derived from the arithmetic means. In modemnotation, but in terms of proportionl - h = h - w (arithmeticean)

The second geometric rule is thatas he ength of heroom shouldstand in proportion to the height, the height of the vault stands in proportionto the width. This means that the height of the vault will be the square root ofthe product of the width times the length, i.e.,

l hThe harmonic rule for the height is slightly more complicated. It may berepresented by the following equation

x = r (geometricean)

l - hht; WW (harmonic mem)which can easily be solved to find h and which Palladio gives n example of.Palladio ends his discussion y saying There arealso other heights for vaults,whichdonotcomeunderanyrule,andare herefore eftfor hearchitectto make use of as necessity requires, and according to his own judgment.Palladio has a number of other rules of proportion for the dimensions of doorsand windows, and principles for the location of doors and windows. However,it will be enough for the purposes of the discussion here to restrict ourselvesto the rules and remarks cited from Vitruvius and Palladio.There are twoobviouspoints o be madeabout herulescitedfromVitruvius and Palladio, and similar ones that they give. The first is that no realjustification of the rules is made. There is no extended argument in Vitruviusand Palladio as to why these particular rules are the ones that should be takenseriously, andwhy they have the special status theyre given by the authors. Itmay be reasonably argued that it was precisely their immersion in the classicaltradition that made no argument necessary. The theory of proportion was centralto this tradition. The second comment is already to be anticipated by remarksby the architects themselves. Namely, the rules re not rules that re to befollowed with precision and with algorithmic dedication. They are rules thatre adjusted to particular sites and situations.By the middle of the eighteenth century a sea change in philosophical

attitudes toward beauty had taken place. Not uniformly but widespread was the


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~~r~ ~res~nta t~on~f a definite conceptre ~ a ~ ~ ~ r ~ i n go which alone it is possi-

ent of the critic which

ality being closely connected with the nature of beauty:All stiffregularity such as appmximates omathematicalregularity)has

to taste; for our ~ n t e ~ a i ~ m ~ ~ tn the contem


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356 PATRICK SUPPESof it lasts for o length of time, but it rather, in so far as it has not expressiyin view cognition or a definitepracticalpurpose,producesweariness.Onthe other hand, that with which maginationcanplay in anunstudiedandpurposive manner is always new to us, and one does not get tired of lookingat it. (p. 80)

The strongly subjectivistic view of beauty that received detailed statementin the eighteenth century has continued to be part of the talk about architectureboth by architects and critics alike. Unfortunately, i t has encouraged a rhetoricthat is naive and primitive in conceptual formulation. With some notable ex-ceptions th is is as true of what Frank Lloyd Wright has to say about organicarchitecture as it is about Robert Venturis admonitions about complexity andcontradiction in modem architecture. Fortunately, in both their cases, but espe-cially in Wrights, their architectural practice has in its underlying design muchcloser affinity o the classical theory of proportion and symmetry than wouidap-pear from their own descriptions of their work. Many of Wrights most famousworks, for example the Johnson Administration Building in Racine, Wisconsin,exhibit a relentless pursuit of symmetry in the sense of Vitruvius that no doubtis one of the main reasons for the impressive quality of the building.

It is certainly true that we do not necessarily expect from modem archi-tects a clear and explicit statement of how they think about the proportionsof the structures they design. This is, as has already been noted, in contrastwith earlier traditions. Palladio wrote about architecture in very explicit termsand also was active as an architect himself. It is disappointing that what pro-nouncementswe do have from the great modern architects, such as FrankLloyd Wright, le Corbusier, Walter Gropius, and Mies van der Rohe, are mad-deningly vague and general in nature instead of interesting and detailed abouthow particular problems are solved.Of course, most of us tend to be intellectually put off by the bald state-ments about proportions to be found in classical architects, like the examplesfrom Vitruvius or Palladio cited earlier. What they are saying is not entirelywrong or mistaken, it is just put in far too simple way. The rules are statedcategorically. Even if reservations are expressed elsewhere, there is norealdefense of why these particular rules should be adopted. There is no detailedattempt to give either more fundamental principies from which they may bederived or a rich account of past experience on which they are based.

But classical or modern architects are o worse in these matters than thephilosophers cited. Hume and Kant work in that great tradition of philosophicallegislation without empirical representation and without concern for legislativedetaii. The psychologically subtle question of why proportion does appeal andhas appealed so strongly in our architectural evaluations of buildings is notaddressed in any serious way at ail by Hume or Kant, or more generally, thephilosophical traditions in which they are working.

Visual illusions Perhaps the most disappointing aspect of developmentssince the time of Palladio is the absence of a rich theory of architectural


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phenomena that re subject to thorough scientific studyehere s in the older psychological Iiterature in this century experimentalstudy of preferencesforrectangles, triangles of a certainshape, etc. aimedat understanding in a


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358 PATRICK SUPPESclassical theory of proportion. But this approach has not been systematicallyextended, so far as I know, in thepast several decades. In studies of thiskind or in the Greek computations of entasis we should beable ocometo an understanding of the contributions of proportion and symmetry to ourperception of beauty, and also to understand the role of illusion as well. It willnot do, with Hume and the British empiricists, to think of the mind as a t bulr s fixing individually on its own conception of beauty without any attentionto innate capacities of perception and how theyelate to the physical world. amnot suggesting for a moment that a deepened and more sophisticated theory ofproportion will encompass all that is interesting about the perception of beautyin architectural structures, but I do believe that a more thoroughly developedmodern theory would be able to provide on many occasions systematic reasonswhy we find some buildings more pleasing to the eye than others.What we expect of a theory of proportion as a guide to the constructionof beautiful structures is in many ways not much different from what we expectof a physical theory in the design of buildings. Proper use of physical theoryeliminates unsound structures and also suggests new possibilities, but physicaltheory does not categorically dictate how the parts should be arranged. Andso it is with the theory of proportion in organizing the elements of a strut-ture aesthetically. The aesthetic elements of a building cannot be reduced tosimple formulas, and neither can the physical elements of the mechanical strut-ture and function. Yet a building, constructed without proper engineering andunderstanding of the strengths and weaknesses of the technology used, is un-acceptable. So should it also be with the way the elements are proportionatelyarranged.

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Rules of Proportion in Architecture. Patrick Suppes