D SPERRY FINLAYSON

• Beauty cannot be imagined or retained. We must find it or make it. • Fractal images as “beautiful,” “a new art form”? No. • What is Beauty? • The “science” of Aesthetics and its history. • A universal standard of beauty? The Greeks and Romans, the Renaissance. • The power and danger of beauty • Medieval theory. Masonic mastery and “the mystery.” • The Golden Ratio in music and architecture, and in the patterns of the Cosmos. • Le Corbusier and the Modulor.

…for the eye is always in search of beauty.

[Vitruvius (27 BC- 46 AD), Book III chapter III, 13 p 86]

Over and over again, the world displays a regular irregularity.

[James Gleick, Chaos: Making a New Science, p 98]

How to keep—is there any any,

is there none such, nowhere known

some, bow or brooch or braid or

brace, lace, latch or catch or key to keep

Back beauty, keep it, beauty, beauty,

beauty, …from vanishing away?

[Gerard Manley Hopkins, The Leaden Echo and the Golden Echo, 1880, quoted in Leonard Bernstein, The Unanswered Question, p 212]

Beauty cannot be imagined: we must find it or make it. It can be remembered as having existed, but to bring it to mind from memory or imagination is impossible. It cannot be definitively identified. It is a quality found only in the actual, and when so found, intensely real. Though we know of it and can talk about it, it is only in the moment of now that we find it—sometimes in the seeming-reality of a dream. Beauty always carries a sense of the transcendent. At the same time, at some moment in our lives it begins to be accompanied by a stab of poignancy; we have arrived at the tragic knowledge that it can never be grasped, never retained. The great masterworks of art are those which can fairly reliably, again and again, provide us with the experience of beauty.

In order to think about beauty let us imagine or remember an instance of it, as fully as is possible, so that we consider an actuality rather than a concept. Perhaps, in order to consider it at all meaningfully, we should first read a poem or listen to a piece of music in which we find beauty, or go for a walk and look at clouds or stars or reflections in clear water, so that our subject may be vivid in our minds.

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I once visited a science museum exhibition of fractal images produced by endlessly generated computer iterations of simple mathematical equations (which are, let us remember, only statements of human logic made in the form of symbols). [1] The images played continuously and repeatedly on computer screens, expanding and contracting in colorful complexity. Accompanying texts described these images as “beautiful,” and proposed that here perhaps was a new art form.[2]

Certainly the patterns were brightly colored, and rhythmic and harmonious in an obvious way; clearly the story provided with them, of a visual world generated by mathematics and directly relevant to the “real” world, had fascinating implications. The images were attractive at first—but not, to me, beautiful. Why not, I wondered? Their relentlessness, their endless iteration of exactly the same shapes, in large and small versions, ad infinitum, quite soon seemed horrible, like a self-generating wallpaper pattern—growing and shrinking, repeating itself forever, exactly the same in every instance. Are unpredictability or finiteness necessary for the experience of beauty? What is beauty, really? It turns out that there are fog banks of confusion and disagreement and even of political emotion obscuring the subject.

Let us look first at a paragraph on beauty taken from a dictionary of philosophy:

Since the 18th century the term [beauty] has virtually been displaced in favour of the concepts of art and creativity. For contemporary purposes, there are two principal difficulties with the concept of beauty: first, it is ambiguous between the idea of a universal standard of aesthetic merit and the idea of a particular quality standing in specifiable relation to, for example, elegance; second, while classical works of art may strike us as beautiful, the term seems wholly inapplicable to modern works such as Picasso's Guernica.

[Antony Flew, A Dictionary of Philosophy, p 39]

Anyone who has thought about beauty will recognize these “difficulties” with the concept. Is there some sort of universal standard of aesthetic merit, so that paintings and musical compositions, landscapes and people and butterflies, are considered more or less beautiful in comparison to that imagined standard? Or, instead, is something beautiful to the degree to which it possesses certain qualities, such as elegance: beauty as celebrated in the realms of fashion, glamour, décor, and so on? The latter choice, as the quotation above reminds us, raises the problem that although works of art from past eras may be seen as beautiful, many people do not find “beauty”—as presumably meaning pleasant subject matter, attractive colors, lyrical phrasing, pleasing harmonies, “elegance”—in much of 20th century art. This second difficulty is the inevitable product of the first, that is, of a confusion as to what might constitute a standard of “aesthetic merit,” of “beauty.”

The word “aesthetic” itself has had a problematic existence in the language since it came into general use in the mid-19th century; one cannot say precisely what it means today. Certainly Picasso’s Guernica could be described as concinnitous, if we could still use that word and hope to be understood. At the same time, Guernica could be said to be symmetrical in the occult sense, and thus to exhibit the beauty resulting from the right relationship among its parts, in a complex order which, though clearly experienced, can be explained only in hopelessly simplistic and therefore unsatisfactory ways. Such a work is intuitively made, through a back-and-forth play between intellect and heart, or between a (limited) conscious and a (vast) subconscious mind, using the mysterious human capacity for insight, as we will see in a later chapter. And it is intuitively experienced, since it is a system of relationships far and away too complex and nuanced to be analyzed by any cause/effect account, no matter how informed, expert, systematic and careful.

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Possible reasons for the difficulties and confusions which now burden our Western conceptions of both beauty and aesthetics can be found by following the evolution of these conceptions over many centuries. The examples in this chapter generally come from the field of architecture: in buildings the fundamental need for strength and stability dictated by gravity, and the requirements of various climates, set limits on what is feasible there. Comparisons and contrasts are therefore easier to see.

A search for the foundations of Western understanding of beauty and its relation to the arts can reasonably begin with the ancient Greeks. We are told that they did not have a word for “art” in anything like its current lofty and mysterious meaning, but that art, in the sense of humankind’s natural making of things (arte), held a recognized place in their view of the world.[3] “Beauty” was thought to be an important quality present in (or absent from) aestheteke, i.e. that which is consciously perceived by the senses. Thus the logical opposite of “aesthetic” would be “anaesthetic.” The Greeks believed that beauty, though undefinable, could be found in order and harmonious proportion. They searched for fundamental proportional relationships in Nature which could provide a basis for their own production of beautiful form.

In the fifth century BCE Pythagoras and his followers saw the “real” in terms of numbers and forms. Beginning with discoveries of proportional relationships in the tuning of musical instruments, they recognized the unity or harmonia of the whole world, of all that is. [4] At the highest level, this included what they called the “music of the spheres,” in which the heavenly bodies emitted vibrations or tones as they swung in orbit. Every object “sang” or gave out its own force.

[That which] was well adjusted or well-proportioned or harmonious…was the ideal. It was also the most “real.” It followed that whatever form or image a man himself created, that which had the most perfect proportions was the truest. In sculpture an ideal human shape carved in marble was “truer”—that is, more universal and relevant to the nature of man—than a representation that dwelt on the individuality of some one man….In architecture a temple was most “true” (and this also in the literal, builder's sense of the word) when it stood in a just balance between vertical and horizontal, between thrust and support, between lift and weight, mass and interval. True proportion led to grace and beauty: indeed, the whole basis of beauty lay in proportion. This was a thought many creative Greeks had been entertaining well before Pythagoras’ time….

[William Harlan Hale, The Horizon Book of Ancient Greece, p 201]

Greek prescriptions for the achievement of beauty through harmonious proportion, derived from nature, have been relied upon in Western culture ever since, undoubtedly because they succeed in practice, in the real world. In fact, given the chance, most of us will choose them instinctively. In what is known as the “golden” ratio, parts—or dimensions like length and width—are related to one another in a ratio that is an irrational number and therefore impossible to represent precisely, but is approximately 5 : 8, or 0.615 to one. It is found as an essential organizing principle in cultural artifacts of all times and all places—for example in American Northwest Indian blankets, ancient Egyptian monumental sculpture, the placement of the great rocks at Stonehenge, the massive Buddhist stupa at Borobudur in Java, harmonic relationships in music, and the proportions of the Boeing 747—as well as everywhere in Nature.[5]

The mathematical proportional relationships used by the Greeks were re-stated by the Roman architect Vitruvius, in his Ten Books on Architecture, dedicated to the Emperor Caesar Augustus. Vitruvius gratefully acknowledged his sources in earlier Greek texts, all now lost. His is the only treatise on architecture surviving from classical times, and it was the principal text of the great architects of the Renaissance. Leon Battista Alberti tells us: “It grieved me that so many great and noble instructions of the ancient Authors shou’d be lost by the injury of Time, so that scarce any but Vitruvius has escaped this general Wreck: a Writer indeed of universal knowledge…”[6]

Vitruvius’s small book is still recommended reading for students of architecture. He wrote:

Order gives due measure to the members of a work considered separately, and symmetrical agreement to the proportions of the whole…Symmetry is a proper agreement between the members of the work itself, and relation between the different parts and the whole general scheme, in accordance with a selected part taken as standard….Thus in the human body there is a kind of symmetrical harmony between forearm, foot, palm, finger, and other small parts [as the Athenian sculptor Polycleitus had noted]: and so it is with perfect buildings.

[Vitruvius, The Ten Books on Architecture, pp 13-14]

Note that by “symmetry” Vitruvius means not bilateral symmetry, but a relationship among parts used by the Greeks and earlier civilizations; it can be expressed mathematically, using one part as a standard for measurement of the others. Vitruvius observes further that

[I]n the human body the central point is naturally the navel. For if a man be placed flat on his back, with his hands and feet extended, and a pair of compasses centered at his navel, the fingers and toes of his two hands and feet will touch the circumference of a circle described therefrom. And just as the human body yields a circular outline, so too a square figure may be found from it. For if we measure from the soles of the feet to the top of the head, and then apply that measure to the outstretched arms, the breadth will be found to be the same as the height, as in the case of plane surfaces that are perfectly square."[7]

[Ibid. p 73]

The ancient Greeks were well aware of beauty’s power to cause disruption and strife, but they valued it highly, and pursued it avidly. Plato declares their general conclusions in the Philebus: “[M]easure and proportion manifest themselves in all areas as beauty and virtue,” and “Therefore if we are unable to net the good in a single concept, we must use three to capture it, namely beauty, proportion, and truth.”[8]

The classical period ended when Rome fell. In Medieval works of art, in sculpture, painting, and architecture, irregularity and asymmetry are common.[9] But Jonathan Hale, in his courageous and profound book, The Old Way of Seeing, points out that the eccentricities of Gothic design are grounded in the ancient proportional systems—systems so powerful, consistent, and meaningful that such irregularities do not disturb the overall harmony; rather they serve to enliven it. The notably dissimilar bell towers of Chartres Cathedral somehow work together in the whole building, though the south spire is 351 feet high and was built in the 12th century and the north, 377 feet high, wasn’t completed until the 16th.[10] Standing as they do on either side of the bilaterally symmetrical main façade of the cathedral, the two towers are so different that at first one is taken aback by such an obvious and fundamental anomaly. Yet this may in fact be one of the reasons why the cathedral is so widely loved; its eccentric silhouette rising over the wheat fields as you drive toward the town from the north is one of the great sights of France.

The Gothics, intentionally following the Greeks, used musical intervals to determine architectural forms.[[11]] They also understood the human body, and they put those patterns into buildings.… Pattern was taught, architecture as music was taught, and every place came alive.…

It [was] understood that there was something magical about proportion. An air of secrecy and initiation has always attached to proportioning systems. The sign of the Pythagoreans, for example, was the pentagram [the five-pointed star]; they were forbidden to reveal that it was an extremely rich expression of phi [i.e. Golden Ratio] proportions. Proportioning systems connect to the nonverbal side of our minds, the “magic” side. The words “magic,” “secret,” “mystery” still tend to crop up in literature about architectural proportions….[[12]

[Jonathan Hale, The Old Way of Seeing, p 73]

Gothic cathedrals, Mr. Hale tells us, are like “numerical prayers,” since for Gothic cosmologists, every number had meaning derived from ancient systems. Ratios and proportions expressing definite spiritual qualities were built into the material reality of the great churches of the time, he says.

We do not believe as purely as the cathedral builders in the powers of number and shape. But if a building no longer can create heaven on earth, it can still evoke what is heavenly and earthly in us. The reason a cathedral still “works,” still inspires, excites, attracts, is that its patterns [of proportion and shape, of solid form and space] resonate with the shapes of our own bodies and the shapes of the plants and animals around us.[[13]]

[Ibid. p 81]

A young visitor wrote of the experience still available in such a building:

Notre Dame is as white as it once was black—beautiful—and inside, under the arching, soaring beams—it draws the heart out of your body, it is so holy, so miraculous—it is purely good to be there.

[Lesley Finlayson, in a letter, November, 1999]

The masons who built the great Gothic cathedrals in the Ile de France at the turn of the 12th century did not follow builders’ treatises or manuals, nor had they all studied at the same school:

They were linked by a shared culture, their perambulatory practice, their masons’ lodges, and a close interest in each others’ work. They shared a precise sense of what was right and wrong, fueled by their faith and their brotherhood.…

From Vitruvius onward, architects have been fascinated by the idea that there could or should be a kind of organic unity between the whole and its parts.…Medieval masons were required to demonstrate their mastery of the “mystery” by setting out and carving a pinnacle.[[14]] All the geometry and skill required to design a cathedral would be tested by this construction of a detail.…And modern architects have retained the obsession with the telling detail.

[Tim Benton, “When Is It Right To Be Wrong?” Harvard Design Magazine, Fall 2000, p 69]

Let us remember here that throughout history there have been those who fear that the beauties of nature and of the arts may distract us from love of God and desire for virtue. Thinkers such as the influential 9th century theologian Johannes Scotus Eriugena believed that if works of art, even those depicting sacred subjects, were too beautiful, they would lead the faithful in the direction of the seen rather than the unseen world—to a spiritual focus on God’s works, rather than on God.[15] I have read somewhere that centuries later, Michelangelo wrote that the fascination with the world of everyday objects found in Flemish paintings bordered on heresy.[16] Even today some fear that attention to beauty in art “may distract us from the world’s injustices.”[17]

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As we have seen, Vitruvius was the essential authority studied by Renaissance architects; his precepts were generally accepted as final.[18] Eventually Mannerists like Michelangelo took liberties with the classical rules of proportion and relationship. Later still, Andrea Palladio, the renowned 16th century architect (who, like Alberti, trained himself by measuring surviving ruins of great Roman buildings), also relaxed Vitruvian rules in his late works, as he saw fit—his judgement perhaps influenced by the frisky eccentricities of Mannerism.[19] The Greeks themselves had finessed their own rules, for instance in the buildings of the Acropolis, as we saw earlier. A period of strict order is necessarily followed and relieved by the disturbance of that order, to a greater or lesser degree, and in a range from the playful to the chaotic, through historical time or within the same work.

In the 18th century, Palladio’s The Four Books of Architecture became the textbook for neoclassical architecture in both Britain and the United States.[20] Much of the celebrated beauty of New England towns is provided by the classical proportions of their 18th century houses and meetinghouses derived from Palladio, who restated the ancient principles:

Beauty will result from the form and correspondence of the whole, with respect to the several parts, of the parts with regard to each other, and of these again to the whole; that the structure may appear an entire and complete body, wherein each member agrees with the other, and all necessary to compose what you intend to form.[[21]]

[Andrea Palladio, The Four Books of Architecture, Book 1, Chapter 1]

Here is the Third Earl of Shaftesbury (in 1709) ecstatically describing the classical image of the cosmos itself: the complex but at the same time fundamentally simple relations between the parts of the Creation and the sublime entirety of it, the “immensity and magnificence of nature:”43

…[S]o many worlds hanging above one another, and sliding round their axles in such an amazing pomp and solemnity…. Nothing surely is more strongly imprinted on our minds, or more closely interwoven with our Souls, than the Idea or Sense of Order and Proportion. Hence all the Force of Numbers, and those powerful Arts founded in their Management and Use….

[Anthony Ashley Cooper, quoted in Nikolaus Pevsner, The Genesis of the Picturesque, p140]

In the mid-twentieth century, the French modernist architect Le Corbusier restated yet again the classical recommendations for the use in architecture of proportional relationships found in the human body. He drew the abstracted figure of a man, divided into parts based on a grid of dimensions in phi (that is, Golden Ratio) relation to one another, in a proportioning system he called the “Modulor.”

Le Corbusier developed…the Modulor, to order “the dimensions of that which contains and that which is contained.” He saw the measuring tools of the Greeks, Egyptians, and other high civilizations as being “infinitely rich and subtle because they formed part of the mathematics of the human body, gracious, elegant, and firm, the source of that harmony which moves us, beauty.” He therefore based his measuring tool, the Modulor, on both mathematics (the aesthetic dimensions of the Golden Section and the Fibonacci Series) and the proportions of the human body (functional dimensions).

[Francis D.K. Ching, Architecture: Form, Space and Order, p 318]

Le Corbusier claimed that without the Modulor he could not have designed his brilliantly original chapel at Ronchamp, but he emphasized that he had ignored or modified the system’s dictates as it suited him. The chapel, a work of daring and genius— and of occult symmetry—is an example of a rigorous order enlivened by something else, that something else being brought to it by the intuition, the spirit of the artist-architect at play.[22] The chapel is an unambiguous instance of < >´ in architecture. Jonathan Hale calls it “Modernism at its most Heroic and Original.”[23] Le Corbusier wrote:

I demand of art the role of the challenger…of play and interplay, play being the very manifestation of the spirit….I still reserve the right at any time to doubt the solutions furnished by the Modulor, keeping intact my freedom which must depend solely on my feelings rather than on my reason.

[Le Corbusier, The Modulor, pp 220, 63]

This is clear testimony to the fundamental necessity of a dynamic balance between order and freedom (that is, of < >´) in the act of creation, a paradox noted again and again by working artists and by the more enlightened critics and historians. An example of the latter:

Throughout the successive periods of Hellenic, Hellenistic, and Roman domination (roughly the millennium spanning the five centuries before and after Christ), and despite the social evolution from city-state and kingdom to world empire, this balance between the extremes of naturalistic uniqueness and stylized convention was maintained [by the Greeks]. Though the scales could tip at any time in one direction or the other, the precarious balance between democratic individualism and aristocratic traditionalism, the actual and the ideal, the changing world of appearances and the permanent reign of abiding principles, spontaneity and self-restraint, emotional and intellectual elements somehow was maintained. Classical art was never wholly one or the other, but in the work of various generations, geographical centres, and schools of artists, now one aspect was predominant, now another.

The declared principle of Greek aesthetics was the imitation, or representation, of nature. Taken at face value this would be a straightforward naturalism, and to some extent it was; Myron’s bronze “Heifer” on the Acropolis at Athens, for example, was so lifelike that cows were said to low at it as they passed by.[[24]] But the desire to idealize, to perfect, to create types, to work out canons of proportion and rational concepts of order invariably asserted itself.

[Encyclopedia Britannica Vol 2, p 491]

“[T]he precarious balance…somehow was maintained.” This is where beauty (and life) in art (and in life) can be found, achieved and maintained “somehow.”

Again, Jonathan Hale, writing of the interior of British architect Sir John Soane’s 1811 Dulwich Picture Gallery in South London, the oldest public art gallery in England:

At Dulwich, Soane takes big chances. The arches are too wide, they come too close to the break between wall and ceiling, and the break is not defined by the expected molding. The little arches in the sloped ceiling are too small, and the monitor windows cantilever too far in, making the structure look unstable. And it all works, the whole room dances. Soane’s rooms play at the edge of discord and disintegration.

[Jonathan Hale, The Old Way of Seeing, p 145]

Yes. That’s where it happens.

[1] Briggs, John and Peat, David F., Turbulent Mirror, 1989. Benoit Mandelbrot coined the term fractal in 1975. In mathematics, a fractal is “a geometric figure built up from a simple shape by generating the same or similar changes on successively smaller scales; it shows self-similarity on all scales.” [http://en.wiktionary.org/wiki/fractal. Sept 7, 2010]

[2] In 2009, the Italian promoter Odifreddi filled every seat in Rome’s 1960 Olympic Stadium, the largest auditorium in the city, for three days—for a Festival of Mathematics. The New York Review of Books [8/13/09, p 17] reported that “the presiding geniuses were the late artist Maurice Escher and the mathematician Benoit Mandelbrot, with their followers displaying new works of art created by humans and computers.…also a performing juggler, who also happens to be a professor of mathematics.” Interesting things to look at, made by machines? Possibly. True works of art made by machines? I doubt it.

[3] Encyclopedia Britannica Volume 1 p 224

[4] For a history of Western tuning of musical instruments see Stuart Isacoff, Temperament: How Music Became a Battleground for the Great Minds of Western Civilization.

[5] For a thorough disquisition on this subject, with geometric illustration, see Gyorgy Doczi, The Power of Limits.

[6] Leon Battista Alberti, in Elizabeth G. Holt, ed.: A Documentary History of Art, Volume I, p 227.

[7] This is of course the “Vitruvian Man” drawn by Leonardo da Vinci. Statements such as Protagoras’ often-quoted “man is the measure of all things,” taken to mean that man is all-important, may simply be saying that men cannot, or often do not, measure things except in relation to their bodily size or to their opinions. “Huge” means very big in relation to me, not to the nearby mountain. “Good’ often means “good for me,” or “advantageous to my nation or political or social group or corporation.”

[8] http://www.cacioppe.com/writings/plato-artistotle-beauty-01

[9] Encyclopedia Britannica Volume 2, p 493

[10] Ibid. Volume 5, p 339

[11] For an interesting account of this see Stuart Isacoff’s book: Temperament: How Music became a Battleground for the Great Minds of Western Civilization.

[12] The simple mathematical relationships between musical notes are believed to have been discovered by Pythagoras. He found that strings which, when plucked, sound an octave apart, (i.e. the same tone but 12 tones higher or lower in the scale) are in the proportion 2:1 to each other in length, the lower-sounding string being twice as long as the upper. The string sounding the fifth is half way between the two, and so on. This discovery—of a simple mathematical relationship between the musical sounds instinctively preferred by human beings, and the physical world—was the beginning of Greek understanding of the apparently mathematical foundations of reality.

[13] “[The] cathedral still ‘works’”: This is an interesting usage, employed regularly by artists and teachers of the arts and often encountered. (See for example, the first epigraph in chapter 3, Life and Death.) It means that < >´ has been approached or produced thereby, but we have now no way of saying this. To say that it “works” is to say that it does what it is intended to, fulfills its purpose in our lives, its reason for being—which is to manifest < >´, to express what could reasonably be called “the mind of God” in the world.

[14] The “gift” of the artist is in knowing where to put what—in setting up the proportional relationships of part to part and of part to whole. The presence or absence of this gift could be detected in the carving of one small part of the projected whole, and this is as true of musicians, essayists and choreographers as it is of sculptors and painters.

[15] Encyclopedia Britannica, Volume 2, p 493.

[16] I can’t find the source of this, but I remember my delight when I did come across the “fact.”

[17] Harvard Magazine, Sept/Oct 1999 p 46

[18] Encyclopedia Britannica Vol. 23, p 90

[19] Ibid. Vol. 17, p 180. The “Palladian” windows added to so many developer-pastiche houses built in the United States today are in part a tribute to the persistent “high class” connotations of Palladian classicism.

[20] Palladio’s treatise was translated into English, at Edmund Burke’s behest, by the same Italian expatriate who had translated Alberti’s earlier work.

[21] Francis D.K. Ching writes, in Architecture: Form, Space and Order (p 314), that Palladio’s statement can serve as a definition of classicism, “whether it be in Frank Lloyd Wright or Le Corbusier or Inigo Jones or the Greek, or other much-loved architects.”

[22] But what is intuition? Non-verbal modes of thought—such as insight and intuition—occurring in the right, “mute,” hemisphere of the brain, are now commonly confused with, or identified as, emotion. Emotion (especially love) is important as impetus and energy for art but it is different from non-verbal thought. The role of emotion in art-making is often insisted upon now, in part because the importance (and even the existence) of non-verbal thought is not generally recognized.

[23] Jonathan Hale. The Old Way of Seeing, p 143

[24] The connection between “lifelikeness,” or liveliness, and the dictates of order is implicit here.