II. 1. A DIE







Let us approach Duchamp's piece of sculpture from the outside: as a teaching doctor might approach a cadaver, as Rembrandt depicted Dr. Nicolaas Tulp in Amsterdam, or as in the similarly commemorative portrait by the American painter Thomas Eakins, showing Dr. Gross, in Philadelphia, commencing his didactic anatomy. The mystery is within; for, inside the ball of twine, in the dark space representing the void, is the secreted object, the essential element of the riddle to be solved, the answer guessed, the secret figured out, the enigma untangled, the mystery revealed, the hidden noise bruited--the bean (as it were) to be spilled. We could be, through an effort of our local imagination, once again at that moment in the High Renaissance of the sixteenth century when the great anatomist Andreas Vesalius was beginning the public demonstration and lecture as illusrated in the frontispiece that was published in several editions of both versions of his book, the Fabrica and the Epitome. This illustration

was to prove enormously influential, both as a work of art and as a scientific manifesto. It shows the anatomy of a female....The dissection has just started, with all the fanfare of the public demonstrations....A breathless crowd of students and observers drawn from all classes of society (with what seems to be a fair sprinking of protagonists and antagonists of the new method) has gathered to watch as the master himself, a young man not yet twenty-nine, places his bare right hand with a pointing stylus or tentaculum in the abdominal cavity, while his left hand is raised in a gesture of speech. His handsome face is turned proudly to the beholder, as if to repeat his famous dictum: "Galen never saw a uterus--not even in a dream."

[ Heckscher, Rembrandt, pp. 53-55. Figure 10, Johannes Stephan, van Calcar, "Vesalius Publicly Demonstrating and Lecturing." Woodcut frontispiece, Andreas Vesalius, De humani corporis fabrica, Libri septem. The illustration is from the 1555 edition; the editio princeps was published at Basel, by Johannes Oporinus (1543). ]

We shall apply one of the classic operating procedures of the alchemical schools, summed up by the dictum: "As above, so below." This principle is derived from the Tabula Smaragdina, the Emerald Tablet--in Duchampian green--of Hermes Trismegistos, but here we shall modify it to say: "As without, so within." Let us, then, take the most general external characteristic of the sculpture as a pattern, model, paradigm or die, that is, as a guide for the secret's revelation. Our working rationale is grounded here in associations with the number six, because a cube has six sides; and, as we recall, Marcel Duchamp's piece of sculpture could be contained in an ideal space like a cubical box measuring very nearly five inches along each edge. This image of a cube is "ideal" and not exact, because in the real sculpture the tops of the bolts protrude from one surface, the ends from the other, and so forth--so it isn't really a neat cube. We shall return to the issue of fine and too-fine measurements presently, but for now let us play out some associations with the main idea of sixness, based on this cube of imaginary space implied, anyway, by With Hidden Noise.


In what follows, we present a constellation of examples to illustrate some of the abstract qualities, attributes and associations--first for sixness, and then (counting down) for the other numbers, each of which reveals some aspect of With Hidden Noise. Admittedly, this sculpture has nothing necessarily to do with Hopi Kachinas, bees, or the Seal of Solomon. But we are operating "by the numbers." So, in our scholarly leisure, we naturally ought to be interested in learning something about, or gaining insight into, the properties (whether intrinsic or illustrative) belonging to the numbers we use, especially since the numbers themselves are simply ways to illustrate deeper, simpler, prior, eternal formalities.

Now, this is a sly game from the perspective that everything is related to everything else, anyway. We may expect some surprises when a dangling thread of logic or emblematic association, here or there, is later woven into the texture of our presentation, in some way to complete the figuration. The structure of written text is necessarily linear by its primary mode of transmission: letters following each other in a line of type across the page. But this is not an exclusive paradigm. We propose that the logic models for textual organization may be more fully and accurately represented by retia (or networks), arrays, and feedback (or feed-forward) recursive, self-referential loops (as we are in now!) Accordingly, we may indulge some relaxation of linear logic's usually unchallenged, straight and narrow demands.

This can be seen clearly in the work of the mosaicist. In one magnificent surviving example of Early Christian mosaics in Ravenna, in the Emperor Justinian's sixth-century church of San Vitale, little glass tesserae (cubes!) of intense colors at first appear to be placed almost at random. In detailed illustrations of the mosaics, they seem to have little linear function as agents of depiction and yet, in longer views they are unquestionably coherent visual elements that not only produce an effect of masterful rendering--as if drawn by lines--but also magically enliven and vitalize the total effect.

Mr. Albert Skira has published a superb series of color illustrations which document such a perception. The original dustjacket of the Skira volume, Byzantine Painting, displays a mosaic detail of a patrician lady's graceful hand, with an emerald ring, and a portion of her ceremonial dress in an extravagant burst of hues--with extraordinary, and apparently wholly arbitrary, vermillion cubes of color, like a psychedelic English garden in full heavenly bloom. Tipped into the text pages is another beautiful reproduction of this detail, but the hand appears a bit smaller in scale, and more of the garment is decipherable. Another few pages further along, and we can see a full-length representation of the courtly lady who appears, together with several others, as a member of the Empress Theodora's retinue. All the "stray" vermillion tesserae now are locked into the pattern of flowers on the lady-in-waiting's glorious gown. If we turn back a few pages, we see that the author provides an illustration of the entire panel in the choir of San Vitale (dedicated in 547 A.D.). For the first time we see the Empress herself, with her full group of nine attendants. Still, just to the right of center, but now on a scale where the depiction looks to be elegantly refined and precise, is that same delicate hand with the green cube of glass that is the emerald ring.

[ Byzantine Painting, with a historical and critical study by Andr Grabar, translated by Stuart Gilbert, (The Great Centuries of Painting, collection planned and directed by Albert Skira), Skira, Inc., New York (1953). The sequence of illustrations, following that on the dust jacket, may be found on pages 65, 70, and 63. ]

Theodora had her "open secrets" as well. Together with her two sisters (whose father was a keeper of wild beasts) she excelled in the art of pantomimic dance. Procopius speaks of her intelligence and clever comic portrayals, mentioning her shameless performances of what today we would call a strip-tease. Justinian, who became Emperor in AD 527, fell in love with her; but upon converting to Orthodox Christianity, with her as his Empress,

symbolically at least, the history of the Greek dance had ended.

[ Lillian B. Lawler, Dance in Ancient Greece, Wesleyan University Press, Middletown, CT (1978), p. 143-144. ]


The number six was chosen as the base for the sacred system of counting employed in Mesopotamia at Sumer about 5000 years ago when civilization, displaying all the major features by which we still recognize it, first appeared. The sacred number six (6) was used by priests in ordering all things sacred and celestial, whereas ten (10) was used for counting in the secular world. When these two were

resolved by being taken together, multiplication produced the standard Sumerian soss (6 x 10 = 60). This product times 6 again yielded 360, which remains to this day our numerical referent for the number of degrees in a circle, just as the soss, 60, still accounts for seconds in a minute and minutes in either a degree or an hour. And in America our electricity is also based on a standard of 60-cycles per second.

[ See Joseph Campbell, "Mythic Time," Masks of God: Oriental Mythology, Vol. 2, Viking, New York (1962) pp. 115 ff. ]

Objective experience provides manifold embodiments of sixness directly perceived, even without counting. From his study of experimental aesthetics and the topology of nervous nets, the teacher, physician and pioneer cybernetician Warren S. McCulloch determined:

The numbers from 1 through 6 are perceptibles; others, only countables. Experiments on many beasts have often shown this: 1 through 6 are probably natural terms that we share with the beasts. In this sense they are natural numbers. All larger integers are arrived at by counting or putting pebbles in pots or cutting notches in sticks, each of which is--to use Ockham's phrase--a conventional term, a way of doing things that has grown out of our ways of getting together, our communications, our logos, tricks for setting things into one-to-one correspondence.

[ Warren S. McCulloch, "What Is a Number that a Man May Know It, and a Man that He May Know a Number?" Embodiments of Mind, MIT Press, Cambridge, MA (1970), p. 7. See also "A Heterarchy of Values Determined by the Topology of Nervous Nets," p. 43-44. ]

Water, the proverbial universal solvent, displays a six-part structure in its crystalline state as a snowflake. Geometrically related forms can be observed in many flower blossoms. Refinements of precision in perception and measure in the laboratory sciences eventually revealed the deep six-part structure of the carbon atom, present in all living cells, at least in our corner of the universe; the schematic representation of carbon by a hexagon is therefore objective and not some arbitrary function of aesthetic whimsy. Certain properties of things six in nature have fascinated human beings for millennia, well before the intellectual abstractions of number theory or the rigorous precision essential for mathematical models.


Tight-packing of circles in a plane produces a pattern congruent with hexagonal tesselation--the same principle explaining why the honeybee's comb is hexagonal in section. On a plane surface, a given circle, circular thing, or cylinder touching six surrounding, same-sized circular things, provides a good example of the tight-packing principle. You can't fit seven same-sized things around the circumference; and five things leaves a space. In the warmth of the hive of the honeybee, the malleable wax of the comb structure allows the originally cylindrical elements to become compressed; and the even pressure within the hive produces a strong, efficient layer of tightly-packed hexagonal cells.

Primitive man must have already delighted in the perception of geometrical forms with their stunning regularities, which prefigured their eventual regularization in the useful, powerful, formal terms of a geometry for applied science and technology. Yet the initial appeal of regular forms may have been aesthetic as well as "practical," since they exert a curiously pleasant attraction for most people still today.

Both levels of consciousness have clearly contributed to our higher evolution. Cultures other than our own obsessively categorizing, presumptively world-wide Western one--such as that of the Sufis, flourishing close to the spiritual heart of Islam--have not felt it necessary to erect absolute barriers between science and art. Muslim artists, although discouraged by custom from producing representations of the human figure, richly exploited the expressive qualities of calligraphic curve and geometrical line. Each one of the seventeen different crystallographic symmetry groups, for example, can be discovered in the geometric arts of Islam: fired in tile decoration, cut as openwork screens or inlay, and painted in manuscript illustration. For, as the words of the Blessed Prophet Muhammad (May Peace Be Upon Him) are sung in one of the Suras of the Glorious Qur'an, called Al Nahl, "The Bee":

[ Sura XVI, Nahl or "The Bee," Qur'an, translation with comments by Abdullah Yusuf Ali, Ashraf Press, Lahore, Pakistan (1969). See also Laleh Bakhtiar,Sufi: Expressions of the Mystic Quest. Flare (Avon) Books, New York (1976); Issam El-Said and Ayse Parman, Geometric Concepts in Islamic Art. World of Islam Festival, London (1976) ]

The stars and other signs from nature as well as the lighthouses or beacons and the signposts erected by man--and most especially the carefully crafted, inspired works of the poets, artists, and mathematicians among humankind--express these "symbols for the higher Guidance which God provides for the spirit of man." Yusuf Ali asks:

Whose heart has not been moved by the glorious gradation of colors in the sunset clouds? The gradations are infinite, and it is only the eye of an artist that can express their collective beauty. They are but a type of the infinite variety and gradation of qualities in the spiritual sphere even in the little space of our own globe. The big things that can be measured and defined have been spoken of before. Here we have mention of the subtle nuances in the spiritual world which can only be perceived by men who are so high in spiritual insight that their only reaction is to "celebrate the praises of Allah...."

[ Abdullah Yusuf Ali, commentary, Qur'an, Volume 1, p. 659. ]

While the forms of that which people call God may be infinite, there can be counted ninety-nine names of God according to Islamic Sufi tradition. The devout are encouraged to repeat these, as in the ritual of the Dhikr (or Zhikr) in order to "qualify oneself with the qualities of God." A modern Sufi Sheikh, in a beautiful book with a beautiful name, The Most Beautiful Names, translates and comments upon these traditional names of God:

Compiled from classical Arabic and Turkish texts of Al-Ghazali, Ibn Arabi, Djili, and Abdul Qadir Gilani, among others, these are the divine attributes by which God manifests Himself in the world and by which He completes the spiritual life of man.

[ Sheikh Tosun Bayrak al-Jerrahi al-Helveti, compiler, The Most Beautiful Names, Threshold Books, Putney, Vermont (1985). Back cover. More recently, see Laleh Bakhtiar, God's Will Be Done: The Sufi Enneagram. Volume III, Moral Healing Through the Most Beautiful Names: The Practice of Spiritual Chivalry. Kazi Publications, Chicago (1996). ]

We have all probably heard the saying "You can't tell a book by its cover." So stated, this indicates that while there may be SOME books jacketed with clues of revealing deliberateness, one never can tell. Such details of intentional presentation are not always subject to control by the author--even though many who write about Marcel Duchamp cover their copy with greenness; usually these are decisions (like those of price) made by the publisher. A more correct form of the saying might be: "You can't necessarily tell every book by its cover; some you can."

The front cover of Sheikh al-Jerrahi's book, The Most Beautiful Names, presents a black background; and not coincidentally, black is the color of turban worn by descendants of the Prophet Muhammad. The title and the compiler's name are in white, as is also--on the back cover--the price: the tidy symbolic sum of $9. White may be associated with the white wool, as-Suf from which, so say some, the term Sufi itself derives. And according to Central Asian Sufi lore, the number nine is symbolic of beings of this world: animal, plant and mineral (with each containing three subdivisions) nine elements of the body, and the nine heavens. The body itself is related to the number six, together with the six powers of motion in the six directions: up, down, front, back, left, right. In accordance with the strong Islamic tradition in science and mathematics, six is also called the first "complete" number which is, as we shall see, technically what is meant by the term "perfect" number as used in mathematics.

[ Nader Ardelan and Laleh Bakhtiar, The Sense of Unity: The Sufi Tradition in Persian Architecture {Publications of the Center for Middle Eastern Studies, Number 9}, University of Chicago Press (1973). See especially p. 26 in the chapter "Shape," which begins on page 21 with illustrations of the cubic coordinate system and hexagonal snow-flakes. The Sense of Unity has also been published with a black cover and white lettering, price-marked at $17.95, which we find mystically elusive. The text is the NINTH in the Publications of the Center for Middle Eastern Studies series. Laleh Bakhtiar, God's Will Be Done: The Sufi Enneagram. Three volumes, Kazi Publicatiions, Chicago (1996). See also, Issam El-Said and Aye Parman, Geometric Concepts in Islamic Art, World of Islam Festival Publishing Co., London (1976). ]

Featured most prominently on the front cover of The Most Beautiful Names, is an extraordinary color photograph of a bee's honeycomb looking as if it were made from pure gold, with the form of certain hexagonal elements of the comb naturally filled with beeswax so as to represent the name of God as written in Arabic: "Allah." Elsewhere appears the following explanation of the front cover:

In August 1982 a devout Muslim bee-keeper found this honeycomb in one of his beehives, in the village of Karakoy, Turkey. In the formation of the honeycomb the bees have written in large and clear letters the most beautiful name of the essence of God: Allah.

And Allah says in the holy Qur'an:

And thy Lord revealed to the bee: make your honeycomb in the mountains and in the trees and in the hives which men build, and eat all the flowers and fruits and do in the way of thy Lord submissively. There comes forth from their bellies a liquid of many hues, in which there is healing for men. Therein is surely a sign for men who reflect.

[ From Sura Al Nahl (The Bee), verses 68-69) Sheikh al-Jerrahi al-Helveti, The Most Beautiful Names. This is printed on the back cover of the paperback edition, which may be obtained by writing to Threshold Books, RD 3, Box 1350, Putney, Vermont 05346. ]


Let us, then, reflect on why we include this example of the bee,and why from the lore of Islamic civilization? Our main interest is in illustrating attributes of sixness, and not necessarily in touting entomology and apiculture or promoting the use of honey--although there is much to be said for this. The honeycomb of the bee is an example chosen from the natural world that enjoys a truly global recognition and familiarity. The hexagonal structure of the honeycomb ilustrating sixness is thus widely known from immediate experience; even children--including those too young to read--associate it with sweetness and know what it means, on all continents save Antarctica.

In keeping with the spirit of expanded global awareness we seek in our contemporary approach to education, it is certainly fitting to present a reference to the bee from the Qur'an, the sacred scripture of Islam. Even though this frame of reference may not be familiar to many in America and the rest of the English-reading world, it is perhaps worth noting that approximately one-fifth of the earth's population of homo sapiens count themselves Muslims. Indeed, Islam is reckoned to be the world's fastest growing religion. And it may be instructive for those readers with resolutely anthropomorphic religious views to realize that a holy book such as the Qur'an has Suras (or, chapters) in it named after the Bee and other animal beings, even Ants and Spiders. In fact, the longest Sura in the Qur'an is named "The Cow." Nothing like this appears in the Bible. As Lynn White has pointed out, when the Roman Catholic Church's most extraordinary Saint, Francis of Assissi, preached the Gospel to the birds of the air and the beasts of the field, he technically qualified as a heretic, since those beings are not doctrinally acknowledged as having souls. But, of course, for Taoists, Hindus, or Buddhists--with, for example, their Lotus Sutra--this is no problem.

These bee references also link the orthodox text of sacred scripture with the mystical Sufi tradition within Islam. Some say the Sufi lineage goes back to the Prophet Muhammad himself, may Peace be upon him; others say that while he was a Sufi, too, the tradition is far older. Usually regarded as representatives of the mystical, frequently underground tradition within Islam, Sufis have had a particularly hard time of it in the Middle East during the present century. The radical pro-Western revolution of Kemal Ataturk in Turkey of the 1920s devastated many Sufi schools and other institutions. The puritanical revolt of Ibn Saud and the Wahabbi movement drove Sufis out of what became Saudi Arabia. World Wars and civil wars across North Africa, and the rise of Shiite Fundamentalism in Iran all militated against the continuity of genuine Sufi traditions. Some spiritual refugees found temporary sanctuary in Afghanistan, until that nation was goaded by the superpowers into suicidal violence. And yet, a major portion of historical Islamic art and poetry, the architecture, music, science, philosophy, the esoteric heart of its spirituality and almost all of its humor wells up from the Sufi spring. So it is a matter of great consequence concerning the attitude of receptivity toward gifts borne by the Sufi spirit that must now demonstrated by the people and institutions of the West.

One of the vehicles for transmitting essentially the same message somewhat earlier in this century--when Sufism was already being hounded out of the Middle East--was the fascinating character, George Gurdjieff. In his book, Meetings With Remarkable Men, he tells of seeking out what was rumored to be one of the last surviving authentic Sufi schools, the Sarmoun, or the School of the Bees. His nearly incredible quest took him across the vast wastes of the Gobi Desert, and through the rugged ranges of the Caucasus, the Hindu Kush, and the Pamirs before, finally, he was led (blindfolded) to what then remained at the secret site of the school. Once there, of course, he promptly ran into an old friend! The key to what Gurdjieff was able to bring to the West for transplanting had to do with a very special form of dance, to which both he and his followers have alluded extensively.

It may be just an amusing coincidence to note that in Western scientific literature the dance of the bee has been confirmed as a precise, symbolic language, very practical for transmitting objective information about real sources of pollen and nectar. Naturally, these are favorite metaphors for the Sufis. When one of the Names of God appears in a honeycomb, written in Arabic script, we can understand the excitement. The image is marvelous to behold; but remember that in this example--as with the Skira publication--we are still talking about the COVER of the book. By the same token, with Duchamp's sculpture we are also proceeding from the outside inward. Even so we admit, for the jejune, jaded positivist, this particular illustration may not seem to be very different from discovering the visage of Jesus on the crumply surface of a dry tortilla, or the likeness of Mother Teresa in the folds of a sticky cinnamon bun.


Marcel Duchamp, although not known to have sustained any direct influence from traditions of Islamic mysticism, was plainly intrigued by notions of the fourth dimension and spaces of even higher dimensionality. His notes have the flavor of an authentic autodidactic involvement: they record his own grappling with conceptually rather difficult visualizations and ideas, and provide us with some hints about how he incorporated them into works of art. In order to solve the enigma of With Hidden Noise, to determine a value for the unknown (object), we are working from the outside inward, from the relatively easy but complex toward the hard, simple truth (in the Greek sense of aletheia) that must be unveiled the way Salome danced, or revealed the way one might peel an onion.

Duchamp deserves an admiring technical nod because he did make the conscious, formal gesture of setting forth his assumptions--the esoteric aesthetic postulates upon which he had been working secretly, for years--very much as a mathematician formally allows the axioms upon which his subsequent operations depend. In mathematical procedure the axiomatic basis is introduced conventionally "up front," at the beginning of a theorem; and in Duchamp's procedure, there was a note in The Green Box from 1913-1914--in the early stages of his major stylistic transformation. In a wry twist of Design and Fate, it was only his posthumous piece that bears a title written in this formal mode:

Etant donnés: 1. La chute d'eau,
2. Le gaz d'clairage
(Given: 1. The Waterfall
2. The Illuminating Gas)

[ The title is derived from the 1913 note, later published in The Green Box (1934); Sanouillet, Salt Seller, p. 27 f.]

This posthumous, complex installation piece, Duchamp's "psychodiorama" which still guards some of its secrets, bears instructive comparisons as well as contrasts with the Readymade sculpture of 1916. The key similarity between these two works (or "events," since both must be experienced by an explicit act of participation) is their involvement with secrecy. The notion of secrecy itself is provocatively expressed in both pieces by the articulation and containment of an interior space "where the real action is." In the installation--big and complex--one is invited to view the interior space stereoscopically through two peepholes cut through an old wooden door. There are two holes for two eyes; as with Duchamp's Rectified Readymade Handmade Stereopticon Slide (1918-19), a single lens simply will not do. But sound--not sight--is the secret medium of the interactive experience in With Hidden Noise (assembled between thirty and fifty years earlier), and not even Duchamp himself would peek inside. The artist's formal and profound concepts of space appear in several of the notes. For example, in The White Box Duchamp logs his subtle speculations about spatial multi-dimensionality, setting forth:

Self-evident truths:

In a space, 2 straight lines intersecting determine a plane or 2-dim'l continuum.

In a space, 3 straight lines intersecting at a common point determine a 3-dim'l space.

In a plane, 3 straight lines intersecting do not determine a space. Therefore in a space\4 lines intersecting do not determine a continuum.

[ Sanouillet Salt Seller, p. 94. Originally published as A l'Infinitif or, The White Box, Cordier and Ekstrom, New York (1966). ]

Duchamp's theoretical notes have received extensive discussion elsewhere. He expressed these lofty, intricate ideas by playing them out through reflections of his personality as Rrose Sélavy, his alter ego, and queen of speculative arcana. "Speculation," of course, comes from speculum, a word the Romans used for the ancient magic mirrors they appropriated from the Etruscans. "It's done with mirrors," so some say, "with blue smoke and mirrors."

[ See Henderson, The Fourth Dimension; also, Craig Adcock, Marcel Duchamp's Notes from the Large Glass: An N-Dimensional Analysis, UMI Research Press, Ann Arbor (1983). ]