D SPERRY FINLAYSON

We are inclined to think of mystery as woolly or amorphous, yet Mozart, working in the light, openly, is all coherence…. His sounds and rhythms correspond to states of feeling which we have all somehow learned to interpret…. In it we hear; through it is expressed our sense of the radical mystery of our being.

[Saul Bellow, in Boston University Magazine, 1980s]

…[T]he Poet’s blood,

That ever beats in sympathy with Nature’s ebb and flow…

[Percy Bysshe Shelley, “Alastar; or the Spirit of Solitude”]

In a discussion of the harmonious order which must be present to some degree if an organism or a work of art is to have life, there are two words in our language which could be useful—but in fact they are not. One of them, “symmetry,” has lost its most fundamental meaning. The other, “concinnity,” is virtually never used.

Symmetry

The first meaning of symmetry given by the dictionary is: “right proportion of parts, beauty resulting from it, congruity, harmony.”[1] That use of the word is now almost entirely obsolete, although it is the most important. The second meaning given is: “divisibility into two or more parts each of the same shape and size as the other(s) & similarly placed with regard to the dividing point(s) or line(s), repetition of exactly similar parts in contrary or equally divergent directions” and so on—that is, bilateral symmetry. Since the 18th century the second meaning has swallowed up the first; the word “symmetry” is now used as if bilateral symmetry were its only meaning. It may be that the ever-increasing pervasiveness of machine-made objects in our lives has resulted in this loss of understanding. A friend who lived for several years in a remote African village told me that when the local children studied “symmetry” as a concept in school, they would be sent to her to look at her machine-made tea mug, since nothing in their hand-made environment qualified as being perfectly bilaterally symmetrical. Yet bilateral symmetry is only one kind of symmetry —the simplest and most obvious kind.

Bilateral symmetry (which can be extended to repeat in multiple radii from a central point in two or three or more dimensions) is much easier to produce. . . than what?[2] The temptation is to say much easier than a-symmetrical symmetry. An author remarked on what he called the dyssymetric complementarity of men and women.[3] This seems to say that the two genders are not identical, but that together they form a harmonious whole.[4] Such a unity is not entirely bilaterally symmetrical —it tends toward symmetry in its other, lost sense, and nowadays we have no word for it.

Bilateral symmetry is easy to identify. We can readily see that one side is the mirror image of the other, or that all parts are balanced in pairs on opposite sides of a dividing point. John F. Kennedy’s speech, “Ask not what your country can do for you, ask what you can do for your country,” and so on, achieved a somewhat monotonous rhythmic balance with bilaterally symmetrical language. On the other hand, the harmonious whole which is the Gettysburg Address cannot be broken down into obviously balanced parts in an attempt to explain its power; we experience its “symmetry” in the first sense.

Many living animals and plants appear to be bilaterally symmetrical, but none of them is completely so. Snowflakes, and other “inorganic” crystals, are multi-laterally symmetrical, and each one is unique—there seems to be an infinity of possible patterns:

One of the most beautiful examples of this principle [unity in diversity] in nature is the snowflake: every one is different, yet all are united by their basic hexagonal pattern. Each snowflake is restricted to one pattern, repeated and reflected twelve times.… Such uniformity is characteristic of all inorganic, crystalline patterns, which have more order and uniformity than living patterns.

[Gyorgy Doczi, The Power of Limits, p 79]

Living things—our own faces and bodies, the two sides of a leaf, the two halves of a mussel shell—are none of them exactly the same on both sides of the center. If a photograph of a human face is cut in half, and one side is reproduced in reverse and then lined up to make a fully bilaterally symmetrical image, the result is unnerving, unconvincing as being a real person. No one ever looks like that. Nevertheless, studies in the mid-1990s indicated that animals (including humans) and even insects are attracted to potential mates to the degree to which the candidate is bilaterally symmetrical. The researchers concluded that too radical a variation from bilateral symmetry is instinctively felt to indicate disease or damage, no doubt because it often does.[5] A general bilateral symmetry is the normal condition of most living creatures, but that order is never entirely “perfect.” In being alive, a creature is in a condition of < >´. We feel intuitively that if the order of the parts is overly disturbed an unhealthy condition exists, yet in living things some degree of irregularity is always present.

Bilaterally symmetrical wallpaper patterns, carpet patterns, building façades or garden designs are soothing and stabilizing. We can easily see how the design system works, and the obvious balance and predictable order allow us to rest, or to occupy our minds with other things, secure in an orderly environment. Such patterns make good backgrounds for human activity. Charlotte Perkins Gilman’s well-known 19th century novella The Yellow Wallpaper uses the heroine’s irritated attempts, and failure, to discover any fully logical repeating pattern in the wallpaper of the room where she is imprisoned, as the metaphoric starting point and propellant for her descent into madness. [6] It is “a constant irritant to a normal mind.”

In the Blue Mosque in Istanbul, where the walls and ceilings are covered with hand-painted ceramic tiles, the design painted on each tile is bilaterally symmetrical, or constitutes a piece of a larger bilaterally or quadrilaterally symmetrical pattern, and then of course the tiles are set in that most stable of visual frameworks, the grid. But this relatively easily-achieved symmetry is never exactly perfect: the glossy tiles are skillfully painted, but hand-painted and hand set; they sit in the mortar at subtly different angles and reflect the light differently. There is underlying order, and there is subtle disturbance of that order; the overall effect is of a dazzling liveliness and beauty. Today, factory-made wall tiles are sold in groups attached to squares of webbed backing for easy installation. But premium prices are paid for handmade, hand glazed small tiles, affected by different glazes and firing times and temperatures, arranged in intuitively randomized groups in small specialty plants. Such arrangement cannot possibly be accomplished by machine, and the human ability to make the pattern harmonious though varied (that is, “natural”) is both rare and highly valued.[7] Such order is “symmetrical” by the first definition quoted above.

But what about that fundamental symmetry, that is, “right proportion of parts, beauty resulting from it, congruity, harmony”—a symmetry which is not bilaterally symmetrical? Do we any longer know what this means? It is sensed, experienced, but its cause and origin are hidden. Historically, it has been called “occult symmetry.” The word “occult” means mysterious, magical, hidden away; in the 17th century certain of the early sciences, believed to involve secret and mysterious knowledge, (alchemy, for instance) were described as “occult.” By the late 19th century the word was capitalized as “The Occult,” indicating a world beyond the physical which some believed could be contacted through sensitives and mediums, allowing living people to talk to ghosts, tables to thump out messages, and so on. The word “occult” now carries all that baggage, and it is difficult for us to hear it as meaning only “of unknown origin.” In fact, the universe and we ourselves are ultimately “occult,” though we have our stories.

Why did we discard the concept of an inexplicable symmetry or balance? It may be that, with the Enlightenment, the idea of something which empirical science could not investigate, and yet which had no apparent function in religion, was seen as a concept to be dispensed with, falling into a sort of Cartesian divide somewhere between that which is of this world and that which is of God. Perhaps it was dismissed as being a superstition of earlier times, when people had believed in a great harmonious cosmic order, and “the music of the spheres.”

Look how the floor of heaven

Is thick inlaid with patines of bright gold.

There’s not the smallest orb that thou beholdest

But in his motion like an angel sings,

Still quiring to the bright-eyed cherubins.

Such harmony is in immortal souls;

But whilst this muddy vesture of decay

Doth grossly close it in, we cannot hear it.

[William Shakespeare, The Merchant of Venice]

The façade of Chartres Cathedral, Handel’s Ode for Saint Cecilia’s Day, Picasso’s Guernica, Beckett’s Waiting for Godot—none of these works is bilaterally symmetrical, although Godot is so to a notable degree. Nevertheless, all are examples of a “right proportion of parts, beauty resulting from it, congruity, harmony,” and therefore by the primary definition “symmetrical.” Indeed, Architecture, that great potential source of dignity, serenity, and reassurance, is the only “high” art form (as contrasted to “craft”) where bilateral symmetry is commonly found in any obvious way. In painting, sculpture, music, poetry, dance, and theatre, the “symmetry” is seldom noted; it is hidden, mysterious, “occult.” Nowadays we rarely speak of it, and most of us have forgotten that it exists. It is impossible to speak of it except by analogy, because we no longer have the word for it.

In the symbol < >´, the figure representing symmetry, both in its obsolete (occult) and in its current (bilateral) sense is < > . This is not entirely satisfactory, since when machine-made, as here, it is in fact bilaterally symmetrical along two axes, and so must function, in part, at a remove from its meaning. When quickly hand-written it loses this bilateral symmetricality: the hand puts irregularity and thus life into it. Although in print form it graphically represents only a simplistic bilateral symmetry, it should be “read” as both bilateral and occult symmetry. In representing both, it functions as does the Chinese ideogram 人, which means man, but also can mean woman, depending on the context—as can our word “man,” women are often assured. In fact the Sanskrit symbol for OM, ॐ, a human sound chosen to represent the true sound of the manifestation of the highest psychic energy, the “sound” of the universe’s ongoing creation[8] would do beautifully, and it is likely that it bears some affinity with that which I am intending to express with

< >´. The Korean ideogram for nothing, emptiness, resembles to some degree the one which I propose, in that it is bilaterally symmetrical—almost.[9]

空

It may be that Western culture, increasingly exposed both to Eastern understandings and to the discoveries of twentieth century science, will grow into a need for such a symbol.

+

The gardens of many civilizations have been laid out in generally bilaterally symmetrical patterns; in Europe before the eighteenth century they were the rule. English gardens of the early 1600s were designed much as were European and Islamic gardens, in easily comprehensible and easily laid out Euclidean squares and circles, triangles and rectangles. However, seventeenth century missionaries and traders returning to England from China soon brought news of very different qualities found in gardens there. In 1685, in an essay on garden design, Sir William Temple wrote of lessons which might be learned from the “irregularities” of Chinese gardens:

What I have said of the best forms of gardens, is meant only of such as are in some sort regular; for there may be other forms wholly irregular, that may, for aught I know, have more beauty than any of the others; but they must owe it to some extraordinary dispositions of nature…or some great race of fancy or judgement in the contrivance, which may produce many disagreeing parts into a figure, which shall yet upon the whole be very agreeable. Something of this I have seen in some places, but have heard more of it from others, who have lived much among the Chinese.… Among us the beauty of building and planting is placed chiefly in some certain proportions, symmetries, or uniformities…. [T]he Chinese scorn this way of planting, and say a boy that can tell an hundred may plant walks of trees in straight lines…but their greatest reach of imagination, is employed in contriving figures where the beauty shall be great, and strike the eye, but without any order or disposition of parts, that shall be commonly or easily observed.… And whoever observes the work upon the best Indian gowns, or the painting upon their best screens or porcelains, will find their beauty is all of this kind (that is) without order. But I should hardly advise any of these attempts in the figure of gardens among us; they are adventures too hard of achievement for any common hands; and though there may be more honour if they succeed well, there is yet more dishonour if they fail, and ‘tis twenty to one they will; whereas in regular figures, tis hard to make any great and remarkable faults.

[Sir William. Temple, quoted in Nikolaus Pevsner, “The Genesis of the Picturesque,” Architectural Review 96, Nov. 1944]

For Sir William, “without order” means without any obvious order. This idea—that there is an “agreeable” arrangement of parts other than the visual security of an easily apparent order—has not been part of our general Western cultural awareness for hundreds of years, despite the fact that most of us try to achieve such orders in our arrangement of objects, and even though such “occult” orders are the foundation of most of that which we call “art.” Certainly many eighteenth century garden makers were undaunted by Sir William’s warnings of probable difficulties in such adventures, with some unfortunate results. A claim that there are situations where “the beauty shall be great, and strike the eye, but without any order or disposition of parts, that shall be commonly or easily observed…” would be as little understood today as it was in Sir William’s time. And yet, at the same time, we do necessarily refer to it, even if obliquely:

…the “inaccessible order” and “inexplicable reason” toward which artists from Jean Arp to John Cage have been drawn.

[Roger Lipsey, An Art of Our Own: The Spiritual in Twentieth Century Art, p 127]

Every note is like a diamond—if one is missing or different, you know it.

[Violinist Fran Peder Zimmerman, speaking of Mozart: 11/94, WCRB, Boston]

As we have seen, the ancient Chinese took the ability to give life to a work of art to be the most important attribute of the artist. In the West, though we speak often of a harmony among parts, we generally avoid any discussion of what that order may be, no doubt because to say that something is “inexplicable” is clearly not scientific, and is therefore suspect. Harmonious order in both the arts and the natural world has sometimes been identified as being fundamentally geometric, based on the powerful and geometrically achievable golden proportion and on mathematically obvious proportional relationships. We are told that major Renaissance artists like Mantegna and Masaccio and Piero de la Francesca relied heavily on geometry in the composition of their paintings. The great Renaissance theorist and architect Leon Battista Alberti wrote, in his treatise on painting, that a knowledge of geometry is essential to the artist. But such geometries are only a first step in one possible approach to the hidden goal of a total lively harmony among parts; that goal can only be fully achieved by also using “irrational” methods like intuition, insight, and luck. Claims that a harmonious order is the goal of the arts are now commonly dismissed as belonging to the errors and enthusiasms of Renaissance and Classical times, left behind in our more enlightened and scientific age.

Concinnity

I first chanced upon the word “concinnity” in its original Latin form, in a Dover edition of Alberti’s great treatise on architecture, De rei aedifactoria, which he presented to Pope Nicholas V in 1452. Alberti’s Latin was provided opposite the English translation (made by Giacomo Leoni in 1726), and in that translation Alberti’s word concinnitus was given as “beauty” in the English.

Webster’s dictionary tells us that the English word “concinnity” (from the Latin concinnitas, from concinnus, skillfully put together) means: “harmony or fitness in the adaptation of parts to a whole or to each other…” which is almost identical to the first meaning given for “symmetry” in the same dictionary.[10] Did Leoni consider “concinnity” too arcane a word in English, and choose “beauty” as being closest to its meaning? Or was a definition of beauty as the harmonious adaptation of part to whole already seen as old-fashioned and unscientific? Did Leoni believe that concinnity and beauty mean the same or a similar thing? Do they, in fact?[11] After all, the Latin word for “beautiful” in our contemporary sense was the adjective pulchritudo; the noun which indicated “beauty” was forma,-ae: form, or shape. In those days long past, before the machine age, beauty and fully realized form were apparently synonymous.

Alberti’s majestic achievements in architecture, and his evident generosity of spirit and skill in describing what he has learned, are such that we should give respect to what he says. In 1486 he wrote the following (given in the 1726 translation).

There may be some hidden cause why one shou’d please you more than the other, into which I will now pretend to enquire. But the judgement that you make that a thing is beautiful, does not proceed from mere opinion, but from a secret argument and discourse implanted in the mind itself….Whence this sensation of the mind arises, and how it is formed, wou’d be a question too subtle for this place….It is my opinion that beauty, majesty, gracefulness and the like charms, consist in those particulars which if you alter or take away, the whole would be made homely and disagreeable….[T]here are three things principally in which the whole of what we are looking into consists: the Number, and that which I have called the Finishing, and the Collation. But there is still something else besides, which arises from the conjunction and connection of these other parts, and gives the beauty and grace to the whole: which we call Congruity, which we may consider as the original, of all that is graceful or handsome. The business and office of congruity is to put together members differing from each other in their natures, in such a manner, that they may conspire to form a beautiful Whole: so that wherever such a composition offers itself to the mind either by the conveyance of the sight, hearing, or any of the other senses, we immediately perceive this congruity….[N]or does this Congruity arise so much from the body in which it is found…as from itself and from Nature, so that its true Seat is in the mind and in reason: and accordingly it has a very large field to exercise itself and flourish in, and runs thro’ every part and action of Man’s life, and every production of Nature herself….Congruity, that is to say, the principal Law of Nature….This is what Architecture chiefly aims at, and by this she obtains her beauty, dignity, and value….[emphasis mine]

[Treatise De re Aedifactoria, 1486. (1726 translation), in ed. Elizabeth G. Holt, Documentary History of Art, pp 235-237]

At this point it is helpful to compare some word definitions in order to note the strong connections and resemblances among them. (I offer only those definitions which relate to my purpose here.) In the last chapter I remarked the fact that when looking in a dictionary for words that refer to the most fundamental subjects, we find that their meanings go in circles, in which one word is essential for the definition of another. [12] Ancient insights, now lost, can be found encoded in the language.

symmetry : right proportion of parts, beauty resulting from it, congruity, harmony

concinnity : harmony or fitness in the adaptation of parts to a whole or to each other

congruity : inner harmony: agreement or accordance of the parts of a whole

beautiful : 2a: attractive or impressive through expressing or suggesting fitness, order, regularity, rhythm, cogency or perfection of structure. (“this most beautiful system of the sun, planets, and comets” - Isaac Newton)

harmony : combination or adaptation of parts, elements, or related things so as to form a consistent and orderly whole: agreement, congruity

structure : 3. The mutual relation of the constituent parts or elements of a whole as determining its peculiar nature or character. [emphasis mine] 1. An organized body or combination of mutually connected and dependent parts or elements. Chiefly in Biology applied to component parts of an animal or vegetable organism.

coherent : 2. logically consistent and ordered

incoherent : lacking orderly continuity or relevance

We can see that all these words are more or less closely related to one another in their meaning, and that they all bear on the experience and quality that Alberti called “Congruity.”

Once again then, symmetry is “the mutual relationship of parts (as in size, arrangements, or measurements,[13] due or balanced proportions, beauty of form or arrangement arising from balanced proportions.” Concinnity is “harmony or fitness in the adaptation of parts to a whole or [I would say “and”] to each other.”

I believe that our discourse would be clarified and therefore improved if we revived these words, especially since the word “beauty” has been so corrupted. Concinnity has a certain appealing briskness and precision; to use symmetry in its primary meaning would revive a long-dormant understanding, and would remind us that balance is at the essential heart of nature, life, and art. Neither word, however, includes the understanding of Life, of what Dylan Thomas called “the force that through the green fuse drives the flower,” and of which Stephen Hawking writes:

Even if there is one possible unified theory, it is just a set of rules and equations [i.e. a satisfactorily orderly system]. What is it that breathes fire into the equations and makes a universe for them to describe?

[Stephen W. Hawking, A Brief History of Time, bantam Books, 1988]

Let us note that both concinnity and the two kinds of symmetry—bilateral and occult—can be indicated by the symbol < >. Great art, however, exists in a condition of dynamic equilibrium, of < >´ —at the “shimmering edge” between order and chaos, where Life is also found.

Beauty can occur either as < > or as < >´. It is only when it is fully < >´ that we experience it as transcendent.

[1] Webster’s Third New International Dictionary

[2] Twentieth century geometer Donald Coxeter explored bilateral symmetries in n dimensions. In a jacket blurb for Siobhan Roberts’ fascinating book, King of Infinite Space: Donald Coxeter, the Man Who Saved Geometry, James Gleick describes Coxeter’s field as being “a whole universe—our universe—of kaleidoscopes and crystals, groups and symmetry, bicycles and snowflakes, music and movement.”

[3] Utne Reader, Jan/Feb 1995 p 94

[4] Gyorgi Doczi demonstrates with measured diagrams that all corresponding longitudinal dimensions of tall, average and small women, and tall, average and small men tend to fall upon coaxial circles. The diagrams show that “[t]he trend towards unity of these wave patterns is so marked that they are almost identical, appearing to be stroboscopic images of one and the same moving pattern.” [Gyorgi Doczi, The Power of Limits, p 100.]

[5] reported in the New York Times and Discovery magazines.

[6] Charlotte Perkins Gilman, 1892.

[7] I learned this on a tour of a small artisanal tile factory in New Hampshire.

[8] Rammurti Mishra, The Fundamentals of Yoga, p 246 etc.

[9] http://en.wiktionary.org/wiki/空. In various oriental languages it can mean empty air, and also pure energy; it is associated with power, creativity, spontaneity, and inventiveness.

[10] Quoted on page 29: “right proportion of parts, beauty resulting from it, congruity, harmony.”

[11] In a recent translation, the word “beauty” and the Latin concinnitas are given together, as in “The eyes are

by their nature greedy for beauty and concinnitas.” [Leon Battista Alberti, On the art of building in ten books.

Joseph Rykwert, Neil Leach, Robert Tavernor trans. p 312]

[12] in this instance, Webster’s Third New International Dictionary, G. & C. Merriam Co. 1966

[13] Importantly, in the arts, “parts” must include sound, color, tone, size, shape, intensity, pitch, speed, rhythm, sonority, clarity, movement, angle, volume, etc. etc. etc., in all their infinite and complex possible relationships with one another.