Our attempt to divine why Marcel Duchamp made With Hidden Noise to the measure of 5 inches along each edge of its (ideal) cubic space, may turn out to be a quest never-ending. Intuiting Duchamp's artistic intentions are only of problematical relevance for critical analysis, but we do note here one of the principles long honored by alchemy, both Western and Oriental: that process is every bit as important as product--whether the gold is metaphorical or real. This is one of the secrets of the "Quest," which--as with "Tragedy" in the theater--goes on forever; while Comedy--as with the Pilgrimage--one day returns home again: Odysseus to Ithaca, Dante to Firenze, and the Muslim hajj to his village. In the theater, sometimes production and staging feature presentations in one mode interspersed (as in real life) with those of a complimentary character: comic relief with the serious moment, and burlesque or melodrama with olio. We promise here commedia, naturally, following the weaving paradigm introduced as a "Pretext," in order to play out the game of noughts (knots? holes? wholes?) and crosses.

[See Julia Bolton Holloway, Figure of Pilgrim in Medieval Poetry, unpublished Ph. D. thesis, University of California at Berkeley (1974), brought to our attention by Sue Severin and Walter Barney; also, The Pilgrim and the Book: A Study of Dante, Langland & Chaucer, Peter Lang--American University Studies, (1987). ]

In our search for meaningful relationships in the otherwise big jumbled bag of things five, we may follow the injunction-of-principle to look up every word we use, but this lexical search, initially, provides scant reward. Our word FIVE in the English language comes through the Old English fif from the Germanic fimfe. In turn, that word comes from the much earlier Indo-European root penkwe, the common source also of the Greek pente, and of the Latin quinque, both of which survive as combining forms in English words expressing fiveness.

Some clues about fiveness and five-based systems may be found elsewhere: in Egyptian the word "five" is the same as the word for "hand," a correspondence also found in many other languages. In the Arabic language, the word for five and things related to five have the triliteral root Khaf (kh), Mim (m), Sin (s). From variations of these letters according to conventional paradigms, can be formed (in the way characteristic of Semitic languages) all sorts of words having to do with fiveness. For example, khamees is an army composed of five parts: the van and rear guard, the main body and the two wings; but the graphic image of such an arrangement would appear like a cross. The Arabic word for pentagon, mukhammas, conveys the generic sense of a "magical figure." With the stellated form--the five points disposed around the circumference--we may imagine a superimposed human figure with the apex corresponding to the head and the other star points to the hands and feet. Here we can readily recognize a representation of the idea of mankind prefected: alchemy's real goal, expressed in the Sufi work as al insan al kamil, the Universal Human Archetype.

[Karl Menninger, Number Words and Number Symbols: A Cultural History of Numbers. Translated by Paul Broneer from the revised German edition, M.I.T. Press, Cambridge (1969), p. 149. ]

These associations carry over to the famous drawing of Leonardo Da Vinci in which the circumscribed human figure (by its proportions) stands for the consciousness of man through which are brought into harmony otherwise irreconcilable elements. The ancient problem of "squaring the circle" symbolized this geometrically: given either figure with a known area, one was to construct (with compass and straight-edge) the other figure so as to have an equal area. This contains the problem of relating straight lines--either the square's edges or the circle's diameter--to the curved line of the circumference, and hence to the proverbial ancient mystique about the ratio pi.

[See Ludwig H. Heydenreich, Leonardo Da Vinci, Macmillan, New York (1954). "Sketch showing the Proportions of the Human Figure (after Vitruvius)," Venice, Galleria dell'Accademia, pl. 151. "...drawn with particular care [and] used on a number of occasions as a model for similar diagrammatic presentations of the Vitruvius Canon." ]

The emblematic values of numbers are ever-present, inevitably woven into the expansive fabric of human culture. Mystical traditions naturally accord greater symbolic power to the smaller integers, since they recur most frequently in ordinary experience. There are worlds of things-in-their-fiveness. Conventionally, the five senses are smell, taste, touch, hearing and sight. But such a convention obscures the otherwise obvious truths we experience as many "senses" of perception, such as temperature, balance and kinesis, awareness of electromagnetic fields, and various correlations, for instance, with adrenal, pineal, or pituitary glandular activity. Diane Ackerman, in A Natural History of the Senses, has written a beautiful and lucid account of perceptual awareness in the culturally-sanctioned five, to which she has appended a "Postscript" mitigating the arbitrariness of it all.

[W]e say there are five senses. Yet we know there are more, should we but wish to explore and canonize them....We are as phototropic as plants, smitten with the sun's light, and this should be considered a sense separate from vision, with which it has little to do. Our experience of pain is quite different from other worlds of touch. Many animals have infrared, heat-sensing, electromagnetic, and other sophisticated ways of perceiving. The praying mantis uses ultrasonics to communicate. Both the alligator and the elephant use infrasonics. The duckbill platypus swings its bill back and forth under water, using it as an antenna to pick up electrical signals from the muscles of the crustaceans, frogs, and small fish on which it preys. The vibratory sense, so highly developed in spiders, fish, bees, and other animals, needs to be studied more in human beings. We have a muscular sense that guides us when we pick up objects--we know at once if they are heavy, light, solid, hard, or soft, and we can figure out how much pressure or resistance will be required. We are constantly aware of a sense of gravity, which counsels us about which way is up....When scientists, philosophers and other commentators speak of the real world, they're talking about a myth, a convenient fiction. The world is a construct the brain builds based on the sensory information its given, and the information is only a small part of all that's available.

[Diane Ackerman, A Natural History of the Senses, Random House, New York (1990), pp. 302 ff. ]

In the Tibetan traditions of the Vajrayana, there is a similar organization of the five Sambhogakaya Buddhas (also sometimes called the Dhyana or Dhyani Buddhas), which provide one of the basic schemes for Buddhist art and iconography. These visualizations, together with the convention of the five skandas (or "HEAPs"), corresponding in certain ways to the Western notion of the five senses, are represented by four colors for the cardinal directions: East = blue, South = yellow, West = red, North = green, and the central Buddha = white. These five ways of visualizing the Buddhas, as projections of internal consciousnes, are particularly useful for developing "panoramic awareness" at the fifth bhumi, or "level," of the Bodhisattva Path.

[See, Chögyam Trungpa, Rimpoche, The Myth of Freedom: and the Way of Meditation, edited by John Baker and Marvin Casper [the Clear Light Series], Shambhala, Berkeley (1976), p. 119. ]

Even though the human body, in its basic anatomy and physiology, is one of the great cross-cultural constants, of crucial importance for translating and transmitting information from the most casual level of communication to the most sublime and serious of teachings, there is not even agreement on how many orifices we exhibit. Some say five; but that depends upon counting, for example, the eyes and ears only as apertures of a sort and not as orifices. Then too, each pore of the skin--far more numerous even than the "thousand petals" of the Sahasrara chakra--could be considered an aperture as they can absorb nutrients in many forms, from oils to the light of the Sun itself.

In ancient calendrical systems the year was sometimes partitioned into five seasons; and one of the systems used in Egypt required five intercalated days were as part of a complicated method of helping rectify the calendar with astronomical observation. Among the ancient Irish bards, an alphabet/number system (described by Robert Graves in The White Goddess, which he originally wrote in the space of a few weeks, with no notes, in a an unsolicited state of enlightenment self-described as an analeptic trance) was based on five vowels, with the corresponding calendrical cycle bound to the flowering or fruiting of native trees, honored by true poets as nobility of the plant kingdom.

The connexion of the apple tree with immortality is ancient and widespread in Europe. What does "apple" mean? According to the Oxford English Dictionary its etymology is unknown....Though the apple was the most palatable of wild fruits growing on the trees, why should it have been given such immense mythic importance? The clue is to be found in the legend of Curoi's soul that was hidden in an apple; when the apple was cut across by Cuchulain's sword "night fell upon Curoi." For if an apple is halved cross-wise, each half shows a five pointed star at the center, emblem of immortality, which represents the goddess in her five seasons from birth to death and back to birth again.

[Robert Graves, The White Goddess, pp. 256-258.]


Explicit connections are easier to document among graphic cultural expressions like numerals and letters of the alphabet, than are correspondences with perception, physiology, or phenomena from the natural world. We assume that all writing systems probably had some formal correspondence, between number (which came first) and letters. These systems we call by the generic term Qabala, although other terms are used, including gematria, or in Arabic abjad, a mnemonic term derived from the first letters of the alphabetic sequence: Alif, Ba, Jim, Dal...and so on, adding vowels to render it pronounceable. Often associated with mere silliness and superstition in the West, the numerological associations of abjad and similar systems continue to play an important role in the context of Middle Eastern daily life.

"Qabala," though spelled in different ways and used as a general term, at times may also specifically indicate the medieval Jewish mystical tradition based on the twenty-two Hebrew letters and their numerical values. One customary attempt to overlay systems associates each of these Hebrew letters (and its numerical equivalent) with a card of the Major Arcana of the Tarot deck. In that system, as we have seen, the sixth of the Tarot "trumps" is associated with the letter "v" or "w" called vav in Hebrew and meaning "nail." Confusingly, however, the capital letter "V" corresponds to the glyph for the Roman numeral five, even though here it must equate to the ordinal "sixth," meaning that the card is the sixth of the Major Arcana, after the Essence which is the ordinal first, but which is frequently marked as the cardinal "Zero."

This distinction between cardinal and ordinal should be obvious enough; yet there is such confusion and misunderstanding about the important multi-cultural lore of the Tarot, and having introduced the subject, we owe the thoughtful reader a note of clarification. The order in which the Tarot cards are to be studied requires the Essence (with no cardinal number, or numbered zero) to be "read" or counted (ordinally) first. Then one reads, studies, or counts the fifty-six cards of the Lesser Arcana. Now, in the mystical lore of Persian Sufis, the five-part figure symbolizes nature: the pentagon its static, and the five-pointed star its dynamic form; and the five "elements," as often in the West, are earth, water, air, fire, and the "quintessential" ether. But the correspondences become tricky when we attempt to transpose them to traditions such as the Tarot; for there (following the Essence card) the sequence to be used in study of the pack would be, next the Lesser Arcana with the suits of wands (fire), pentacles (earth), cups (water), swords (air), and only then, the Major Arcana (ether). We mention this to point out that, even in such relatively straightforward schemata, we cannot always assume the correctness of a simple overlay with one-on-one associations.

Upon completion of the Lesser Arcana, the Essence (although it never left) is then "revisited" or tokened again and "re-marked," as it were, by one of the two still-secret cards (both of which are needed for the composition of a "full deck.") Subsequently, one would read the Major Arcana continuing with the card marked by the Roman numeral I and called the Magus or the Magician, followed by the High Priestess (marked II), and so on, in ascending order. If this interpretation is correct, and we are counting the cards in full sequence, the Hierophant might then be reckoned not as the sixth, but--in this technical sense--as the sixty-third of eighty.

In the Tarot tradition, the Hebrew heh, with a numerical VALUE of five and meaning "window," is associated with the card preceeding the Hierophant: the Arcanum marked with the cardinal number IV and illustrating the archetype of the Emperor. The Hebrew heh corresponds to the letter "e"; and correlating the letter-number values we also find that the Arabic letter "ha"= 5, and in Greek the letter epsilon has the value five--just as "e" is fifth letter in our alphabet.


According to associations in the Qabala, 55 indicates the idea of "father and son" which, in the anciently nomadic, patriarchal tribes of the Semites, was the principal channel for transmitting spiritual blessings and material inheritance. In the I Ching, 55 is the number of the hexagram Fêng, translated as "Abundance." Incidentally, the 55-foot statue of Vulcan in Birmingham, Alabama is the largest cast iron such. What does it mean, however, that on the Burmese black market one particular brand of European cigarettes named "555" is particularly prized, above other brands, as a commodity for barter? Then again, as most people know, AT & T's "Information" can be reached by dialing the area code + 555-1212? Also, from L. M. Boyd's syndicated column--in some papers called the "Grab Bag"--we learn that

no private phone number nationwide starts with 555. That's why it's so frequently used as a fictional phone number prefix on TV.

[L. M. Boyd, San Francisco Chronicle, March 27, 1988. ]

Professor Edmund Feldman, in his instructive book Varieties of Visual Experience, compares the Soft Pay-Telephone by Claes Oldenburg (1963) with a photo of what at first appears to be an actual fire-damaged telephone. The burned phone, says the picture's caption, is from an advertisement for Western Electric Phone Company (1968). Oldenburg's canvas and vinyl sculptured telephone has no number; that on the Western Electric exemplar is: (Area code 311) 555-2368. So apparently it wasn't a real phone that had been through a real fire after all, but merely a phone company prop, a faked baked phone--masquerading as Life, then compared and contrasted with "real" Art. But tipped off by the numbers--the mythopoeic qualities of 555--it is now clear that both images must be considered statements of Art. Of course, it is equally valid to claim that both images represent Life.

[See, Edmund Burke Feldman, Varieties of Visual Experience, Second edition, Prentice-Hall, Abrams, New York (1981), p. 346. ]

Some of the secrets told above are old and profound, at one time (and in certain quarters still) closely-guarded intellectual treasures in the inventory of priestly or scientific powers. For knowledge was in antiquity, even as now, among the most important indices of power. Many of the magic questions as well as their answers have been lost, like beads fallen through the woven mesh of ancient traditions and mythologies. We now see the whole fabric of sophisticated awareness about cosmic, ecological and psychological continuity gone somewhat threadbare; and the present generation of children sadly risks losing the sense of an integral cultural frame of reference, altogether.

While knowledge of this kind can be of consuming interest to humanists (including academic poets, inspired historians, and other readers intrigued by cerebral mysteries), such subtly interrelated wisps of wisdom answer questions that, admittedly, almost no one asks anymore. Most people dismiss genuine curiosity about scholarly details of analogs and correspondences as a mere fascination with trivia. However, tracing the fine filigree of relationships does contribute to the most exquisite appreciation of art and literature, philosophy and science, reminding us of the respect that expansive cultural intelli-gence once commanded: whether in the princely courts of Europe, by the Celtic bards and ollaves, and among those formerly in attendance upon the Pharaoh, the Sultan, the Pope, or the Emperor of China.

Not that the Chinese invariably respected learning. Before the rampant destruction in Tibet perpetrated by China since 1959, the monasteries in that high and remote part of the world, among their many other functions, served as libraries with extensive archives documenting psychological studies, records of religious and other ritual practice, customs and tradition collected from widely varied, highly venerable sources. The Lamas made a practice of translating into Tibetan and preserving this documentation, some from peoples long since dispersed or absorbed into other populations, and some from places and cultures vanished or since transformed beyond recognition. Much of this material, along with secret Tantric texts, is written in complex, multi-level cypher. When once a very knowledgeable incarnate Tibetan Lama was asked about the nature of the information thought to deserve such security-conscious encipherment, he said that the very most arcane material was about astronomy and mathematics.

[See, Lama Chime Radha, Rimpoche, (Head of the Tibetan Section, British Library), "Tibet," in Oracles and Divination, edited by Michael Loewe and Carmen Blacker, Shambhala, Boulder (1981).]


As we have noted, etymologies for "temple" in Chinese suggest that the modern character derives from components meaning a place for observing the flight of birds. Many observers in different parts of the world have studied the flight, the calls and the general behavior of birds. Among native peoples of the Pacific Northwest, the crow--or the Raven, its larger cousin--plays an essential role in the mythology of Creation stories, comparable to that of Coyote (alias Hermes, the Trickster) for other Native American peoples. The four-and-twenty "blackbirds" of nursery rhyme are likely related to the sacred crows of Apollo, who took over the earlier number/letter oracles of Hermes. This probably happened around the seventh-century BC, when the Greek alphabet in its archaic 27-letters (where each letter corresponded to one of nine numbers in three registers: units, tens, hundreds--3 x 9 = 27) was modified to a rather more arbitrary system of 24 signs. If the "pie" into which the nursery rhyme blackbirds were "baked" is read as pi, we may have an allusion to the rotation of the earth--regarded as the apparent circuit of the sun around the earth--in 24 hours.

The crow in early European mythology goes back (at least) to a pre-Achaean matriarchal barley cult of around 1500 B.C., in which Kronos was the High Priest or king-consort of the Great Mother-Goddess of grain, or of Her incarnation here on earth as the sacred Queen. This office of kingship was only for a fixed term, after which the consort was castrated and became a human sacrifice. Sometime around 1250 B.C., a more barbaric, warlike branch of Achaeans invaded the Peloponnese and supplanted this religion of the White Goddess with their own patriarchal deity Zeus, who had evolved from being

a herdsmen's oracular hero, connected with the oak-tree cult of Dodona in Epirus, which was presided over by the dove-priestesses of Dine, a woodland Great Goddess, otherwise known as Diana.

[Graves, White Goddess, p. 65. ]

The earthly priest-king consort of this Goddess-incarnation was also originally castrated--as mistletoe euphemistically was lopped off the oak tree bough--and eucharistically eaten. One local survival of this woodland cult at the sacred grove of Diana on the shores of Lake Nemi in the Alban Hills just south of Rome originally inspired Sir James George Frazer to develop the theories for his ground-breaking study of folklore in The Golden Bough. The Neolithic mother-queen-goddess was called by many names, such as Danaë, Demeter, or Ceres; one of Her early important names was Alphito: synonymous with pearl barley and also identified with the star Spica in the constellation Virgo, that was conjunct with the sun at the Vernal Equinox at the beginning of Neolithic grain agriculture, around 12,500 BC. Grains of still wild barley and einkorn wheat were being cultivated in the Nile Valley some four thousand years earlier, back to around 16,000 BC, and

domesticated varieties of both appeared at Jericho by around 8,600 BC.

[See, F. Wendorf, et. al., Science, Volume 205 (1979), p. 1341. ]

In the Greek myth (which is a later form recounting and rationalizing much more archaic traditions) Kronos emasculates his father Uranus and casts his testicles into the okeanos, which could mean either the watery ocean or the "bond" of night sky. Having instituted this terrible patricide, Kronos is warned that his own son will exact from him a like vengeance, whereby he attemps to eat all his children--as illustrated in Goya's memorable painting in the basement of the Prado. He is foiled and fooled in the Dictean cave by Rhea the mother of Zeus, who substitutes for her baby a stone wrapped in swaddling clothes, that Kronos swallows. Other legends associate this stone with the omphalos at Delphi and with similar sacred stones as geodetic markers, with the anointed lingam stones of India, and with the the Philosopher's Stone of medieval alchemy. The Greeks punned the homophones Kronos and Chronos, interchanging kappa and chi.

The Latin Cronos was called Saturn and in his statues he was armed with a pruning knife crooked like a crow's bill: probably a rebus on his name. For though the later Greeks liked to think that the name meant chronos, "time," because any very old man was humorously called "Cronos," the more likely derivation is from the same root cron or corn that gives the Greek and Latin words for crow--corone [or korone] and cornix. The crow was a bird much consulted by augurs and symbolic, in Italy as in Greece, of long life. Thus it is possible that another name for Cronos [Kronos] ...was Bran, the Crow-god. The Cronos myth, at any rate, is ambivalent: it records the supersession and ritual murder, in both oak and barley cults, of the Sacred King at the close of his term of office; and it records the conquest by the Achaean herdsmen of the pre-Achaean husbandmen of Greece. At the Roman Saturnalia in Republican times, a festival corresponding with the old English Yule, all social restraints were temporarily abandoned in memory of the golden reign of Cronos.

I call Bran a Crow-god, but crow, raven, scald-crow and other large black carrion birds are not always differentiated in early times....The crows of Bran, Cronos, Saturn, Aesculapius and Apollo are, equally, ravens.

[Graves, White Goddess, p. 66 f. ]

In Tibet, the significance of crows, especially in the lore of bird-divination, called Bya-rog-kyi-kad-tag-pa, also illustrates typically Tibetan thinking in terms of five-part systems.

While we were escaping from Tibet to India, my companions and I on several occasions appeared to receive warnings of danger from the unusual behaviour of crows. Once, we were on our way up a mountain pass. Many crows were circling around, and their position in relation to us was unfavourable. One flew very close to us and seemed to be trying to make us turn back. As we were confident from the earlier reports of scouts that no enemy troops were in the vicinity, however, we continued on our way. Finally the crow that was most active in its attentions to us actually alighted on the head of my horse and pulled with its beak at the bridle. Immediately afterwards we arrived at the top of the pass and below us we could see two hundred or so Chinese soldiers approaching from the opposite direction. To escape them our party had to split up and scatter, and was reunited only much later. Had we heeded the warning behaviour of the crows, we could have avoided these difficulties and dangers.

There are several texts which deal in a precise way with the meaning of the behaviour of crows. One such is found in the Tanjur itself, the traditional collection of commentaries on the Buddhist scriptures and writings on learned subjects translated into Tibetan from Sanskrit. This demonstrates the importance and antiquity of the regard given to the crow. It is called in Sanskrit Kakajariti ("On the Sounds of the Crow"), and is to be found in the Sutra section of the Tanjur.

[Lama Chime, Oracles, p. 21 f. The text of the Sutra was translated into English, with many philological considerations, by Berthold Laufer as "Bird Divination Among the Tibetans." ]

The original text first describes different types of crows, and the different kinds of tones emitted by them, in relation to the directions and the five-fold division of the hours of daylight when crows are active. Lama Chime, Rimpoche, makes a special point of this five-part organization, and relates it back to the ancient Chinese system of five elements, although details of the colors and their associations do change from one iconographical system to the other.

This precise ordering and identification of the directions of space and the divisions of time is typical of Tibetan divinatory texts. For example, in Daki-Las-Tshog-Rtan-'drel-Mo-Rtsis-Kyi-Skor we find:

From the abyss (nadir) to the highest heaven (zenith), all beings live in the five elements. The causes and conditions are wood, fire, metal, water and earth.

The essence of wood is the Vajra (thunderbolt) dakini [imaginary female personification of divine energy]. She abides in the East and her colour is blue.

The essence of fire is the Ratna (jewel) dakini. She abides in the south and her colour is red.

The essence of metal is the Padma (lotus) dakini. She abides in the west and her colour is white.

The essence of water is the Karma (action) dakini. She abides in the north and her colour is black.

The essence of earth is the Buddha (wisdom) dakini. She abides in all-pervading space and her colour is yellow.

[Lama Chime, Oracles, p. 23 f. ]


All these methods of measuring, although based upon theoretically objective systems of counting, obviously reflect a somewhat arbitrary character, even when the focus of importance is on an aspect of nature itself, such as the apple's five-part internal structure, or in counting orifices. Expanding our methodological net in the scholarly spirit of a new multicultural awareness, we are encouraged to search further--or possibly deeper--for five-part paradigms in cultural domains outside the heretofore usual academic Eurocentric purview. Undoubtedly in China we can see the most significant expression of the number five as a key to the structure and organization of an entire culture's self-awareness. In his discussion of the possible origins of the Chinese system of divination, the I Ching, Joseph Needham cites R. Barde who studied the use of ancient Chinese counting rods.

The symbols would thus have been derived from the procedures involved in the use of an arithmetic to the base 5....(It is noteworthy that the Chinese abacus, which probably goes back to the early centuries of our era, has sliding balls of two values, 1 and 5, separated by a rail.) That arithmetics to the base 5 have existed among primitive peoples is a well-known fact of anthropology. (They would have arisen very naturally from the use of only one hand instead of both.) It may not be without significance that the first five Chinese numerals are, and were, rodlike; while in the Roman numerals there is a clear survival of arithmetic to the base 5, since 6 is 51, 7 is 52, etc.

[Needham, Science and Civilisation, II, p. 342 f. See, R. Barde, "Recherches sur les Origines Arithmtiques du Yi-King {I Ching}," Archives internationales d'Histoire des Sciences, vol. 5, (1952). ]

We notice these Oriental systems have "metal" and "wood" in place of the typically Western "air" and "ether." Moreover, the Western organization is hierarchical, with the fifth point, ether, conceived as the apex of a pyramid, while the Oriental model is heterarchical, conceived as a two-dimensional pentagonal figure. Still, the basic ideas of Oriental and Western alchemy--mystical as well as proto-scientific--are similar in that both involved studying the principles of nature, and learning how to accelerate them in working for the clarification of consciousness and the "perfection" of mankind.

Apparent corollaries between these systems are naturally subject to a critical interpretation that should aspire to articulate distinctions in the spectrum from mere coincidence (easy) to confirmed and documented instances of causal historical transmission (not so easy). Since both systems of Oriental and Western alchemy address the archetypal human consciousness, their respective approaches to meta-cultural phenomena cannot be dismissed out of hand when, for example, they relate to colors, musical tones, stars, anatomy and physiology, and so forth, which, like number, represent basic modes of perception and consciousness that bridge cultures. Indeed, the study of just these themes underscores humanity's essential, global unity--not only of "civilization" (or "civilisation"), but of ALL peoples and geographies--and to a considerable extent through all times, beginning however tentatively with the primordial rituals of paleolithic caves. Such, anyway, ought to be a fair statement of the working basis (in practice and theory) of a meaningful academic multiculturalism, with its load lightened substantially by being separated from sociological special pleading and various attendant political agendas.

Down to the present day, Chinese music is pentatonic, rather than based on the octave and twelve tones as is Western music. For comparison, we can express the intervals mathematically as ratios.

The Chinese gamut consists of the notes

do re fa sol do'

1 9/8 4/3 3/2 16/9 2

and presents serious difficulties to Christian missionaries, it being impossible to adapt the ordinary Western hymn tunes to the musical system of the country.

[H. Gossin, as cited (without source) by Keys, Only Two, p. 86. Needham, Volume IV, Part 4, has a section on the gamut, pp. 169 ff.]

In tracking down the origins of systems such as that of the five-colored Buddhas of Tibet, or of the five intervals in Chinese music, a discovery of major significance is tokened precisely by the recognition of their five-part character. Indeed, the transmutations of the Five Elements--originally derived from a close study of nature--provided a dynamic paradigm by which, as it increased in metaphorical complexity, some of the most complex processes and relationships could be categorized and explained. The "quintessence," literally, provides us with a clue for identifying the roots of Chinese alchemy and one of "The Fundamental Ideas of Chinese Science."

The last phrase in the previous sentence appears in quotation marks because it is the title of a substantial section in the second volume of that remarkable text, Science and Civilisation in China by the Cambridge scholar Joseph Needham. Rather than regarding such data as a kind of product, however, our purposes here are directed toward identifying, and to some extent defining or characterizing, links and connections: between works of art and literature, history and thought, facts and theories of science and nature, or between jokes and ideas. Therefore, we depend greatly upon the judicious choice of material and authors. Professor Needham's enterprise does the same--so does all scholarship; for our model is the construction of the (unfinished) pyramid, as it was for the Founding Fathers of the United States of America: setting letters, and words, and sentences, and ideas into the marked state of written (and printed, then distributed) letters (X-plained) on a plane surface. Clearly, one does not need to do again what has been done already, and better, by others; but the rules of the scholarship game do provide that credit must be given, as a mason lays one course of stone upon another that someone else laid before,and as the continuity of civilization is maintained. Accordingly, we summarize here Professor Needham's main points related to our theme.

[The citations in parentheses after the following paragraphs refer to page numbers in Needham, Science and Civilisation, Volume II. ]

The history of science in China centers on a few basic ideas worked out by philosophical naturalists from earliest times: the Two Fundamental Forces in the Universe (Yin and Yang), the Five Elements (wu hsing), and the proto-scientific elaborate symbolic structure of the Book of Changes, the I Ching. (p. 216)

The real founder of all Chinese scientific thought may have been Tsou Yen (c. 350-270 BPE, i.e. "Before the Present Era"). His school (called the Naturalists), in contrast with the Taoists, "did not shun the life of courts and kings; on the contrary, it would seem they confidently felt themselves to be in possession of certain facts about the universe which rulers could neglect only at their peril. If Tsou Yen had had the 'know-how' of the atomic bomb in his possession he could hardly have faced the rulers of the States with a steadier eye." The doctrine became crystallized around the third century BPE. But by the first century BPE, the Naturalist school "died out as an organized group, all its practical arts had passed over to the Taoists, while its five-elements theories had become common property which the Confucians shared equally with everyone else." (p. 234-235)

All changes in human history could thus be interpreted through the five elements, a theory whose sociological importance was a consequence of its being widely and deeply believed. Yet Needham supposes that Tsou Yen's influence rested upon something more than that, "and there is considerable reason to suspect that their 'arts' included astronomy and calendrical science." (p. 239) In fact, there is much evidence which connects the Naturalists with the beginnings of alchemy. (p. 240) Tsou Yen's school of Naturalists are probably to be identified with the magical technicians of the eastern Chinese coast intimately connected with the lore of "the drug which will prevent death (pu ssu chih yao), attempts to make gold artificially, and the history of chemistry and of magnetism. It is "probable that Chinese alchemy (older.. than that of any other part of the world) began in the School of the Naturalists during the fourth century BPE." (p. 241)

What evolved was a half-scientific, half-political doctrine by which all changes, even to the sequences of political power were to be rationalized. Herein lay one key to the success of the theory, that of the Cyclical Conquest (hsiang sheng), the succession of one of the five by its "enemy" element. This suggests the theory of the Five Elements was not so much one of classifying fundamental matter, but rather one of mapping fundamental processes. "Chinese thought here characteristically avoided substance and clung to relation. (p. 241) But the sequence was not always the same; and the study of different Enumeration Orders came to be a major aspect of the Five Elements theory. We may now recognize in this a principal source of the Tibetan version cited above; for, as Lama Chime Radha, Rimpoche, continues:

To each of these elements, if one is the mother, then a second is the son, a third is the friend, and the fourth is the enemy. If wood is the subject, then water is the mother, fire is the son, earth is the friend, and metal is the enemy. If fire is the subject then wood is the mother, earth is the son, metal is the friend, and water is the enemy. (And so on.) The first, sixth, eleventh, sixteenth, twenty-first, and twenty-sixth days of the month are the Vajra dakini's days. Etc.

[Lama Chime, Oracles, p. 23 f. ]

The other main aspect of the theory considered symbolic corre-lations of the elements with--among many, many categories--astronomy, agriculture, and medicine. The most ancient surviving Chinese medical text (the classic, Pure Questions of the Yellow Emperor; Canon of Internal Medicine, perhaps dating from the third century BPE) con-tained physiological correlations. "There are associations between the elements and the viscera, the parts of the body, the sense organs, and the affective states of mind." (p. 265) The term "element," though customarily used, has never been very satisfactory for hsing which, from its etymological beginnings (based on the diagram of a cross-roads, p. 222, No. 14) carried implications of movement and process as in the "remarkably interesting" association with the five tastes.

Although this is generally considered to be part of that far-reaching system of correlation of the five elements with every- thing in the universe which it was possible to classify in fives, the present correlation cannot quite be written off in this way, since it strongly suggests the chemical interests of the Natural-ists. The association of saltiness with water, while natural indeed to a coastal people, suggests primitive experiments and observation on solution and crystallisation. The association of bitterness with fire, may imply the use of heat in preparing decoctions of medicinal plants, which would be the bitterest substances likely to be known. There would also be a connection of 'hot' and bitter in spices. The association of sourness with wood can readily be explained, since wood, as vegetal, would be connected with all kinds of plant substances which become sour on decomposition. The alkalai in plant ashes would also taste sour. The association of acidity with metal points directly to smelting operations, many of which would give off highly acrid fumes, e.g. sulphur dioxide. Lastly, the association of sweetness with earth would be due to the finding of honey in bees' nests in the earth, and to the general sweet taste of cereals.

[Needham, Science and Civilisation, II, p. 244. ]

However, not all of the associations in the tradition of the Five Elements were so neatly derived from the close observation of nature. Some relationships were natural enough: linking fire and summer and the south seems to come from remote antiquity. The red soils in Szechuan and Yunnan supported this. White was linked with the snows of Tibet and the west, green with the fertile plains and the ocean to the east, and yellow of the center with the loess soils of the Yellow River, the cradle of Chinese civilization. But gradually the system came to be associated with every conceivable category of things five, and the growing complexities contributed to artificiality and arbitrariness. (p. 261) Still, "the origin of the correlation between the elements and the numbers, and between the elements and the musical notes, remains quite obscure." (p. 265) The fascination with systems of number-mysticism from the third century BPE nevertheless retained their interest for Chinese intellectuals through the Sung Dynasty into the thirteenth century, as documented by the Pythagorean quality of the numerological thinking of Tshai Chhen (1167-1230):

If one follows the numbers (shu) (of all things) then one can know their beginnings, if one traces them backwards then one can know how it is that they come to an end. Numbers and Things are not two separate entities, and beginnings and endings are not two separate points. If one knows the numbers, then one knows the things, and if one knows the beginnings then one knows the endings. Numbers and Things continue endlessly--how can one say what is a beginning and what is an ending?

[Needham, Science and Civilisation, II, p. 273. ]