I am eight and in the third grade. At night I lie awake, feeling bad. I even imagine sneaking silently into the kitchen so I can stab myself with the butcher knife. The reason? because I cannot understand arithmetic. Yet I'm supposed to be smart --- smart is the one thing I have going for myself.
My father uses numbers to work in the steel factory, to measure the dimensions of its products. In the little dresser drawer near his bed, three sets of calipers lie in their soft bed of blue velveteen inside a stiff black pouch, which folds close around them like the covers of a black and holy book. My craftsman father is very proud and careful of his calipers. I am not to play with them, and though I break this admonition in all other instances, I respect my father's calipers, only using them under his instruction, to draw circles.
My father's narrations incorporate number in detail. A pistol is never just a pistol. A gun is not just a rifle. No --- it is named in detail, with numbers: a 45-caliber semiautomatic Smith and Wesson with a seven-shot magazine, a quarter-inch bore, a double barrel, a nine millimeter shell, a ten-inch barrel, a split-second action, a $639 price tag, a 1940 year of manufacture, a World War I history, and "a kick that will take both yer arms off."
I notice as I grow older that if I don't have numbers and names right, the men will stop talking, snort at me, and then continue without me. Precision of number as well as name is how they keep [p. 153]
track of who is paying attention, who is "smart" enough to stay in the conversation game with them. Number tells us how much to believe a story.
My mother, who hates guns, withdraws from the dialogue and then the room while these conversations go on. In her little kitchen there is almost no measurement. Nearly everything she cooks comes from a can or is prepackaged and presliced. Her sewing basket, equipped with two spools of thread, a package of needles and a thimble, is used only for darning socks: "That's all I know of sewing." Often no one believes my mother's stories, she stumbles over details and dates, can't recall addresses, loses track of weeks, and months. Without number, she can't find her place in stories.
In earlier times, when my mother retreated to the kitchen, she would have joined in an ongoing discussion between women regarding the size of pickle barrels, weight of the herring fillets, age of the children, teaspoons of vinegar. Cups of flour would have mixed with the number of stitches in the quilt, number of colors in the rug, yardage of the bolts of cloth, timing of the plantings, number of seeds, and dispositions of the harvest and the number of days until the baby's birthday. Her meagre sewing basket would have held more than socks. She would have participated in the rich traditions of women's sewing, knitting, crocheting, quiltmaking, netmaking, macrame, weaving, plaiting, basketry, and pottery --- with their geometry, mathematics, color sense, and storytelling, splendid ceremonial occasions. Still further back in the women's tradition were astronomical divination, card and palm reading, the Tarot, the architecture of houses and farm buildings, and before that, the temples. Any part of this once would have been my mother's inheritance, but in her life, none of it was. In her understanding, men had created the world, and its numbers. She had inherited the industrial revolution, which scooped up all of her arts and treasures and carried them into factories outside the home and outside of her charge [p. 154]
What is the story of number? According to Alexander Marshack, who decoded the earliest known human markings on bones and stones as notations of lunar months, people approached number with a sense of groupings, rather than with any linear sense of sequence. As I imagine it, the original number must have been what we now call a month, a unit synchronized to menstruation. Within this unit, other units began to take shape: a set of three units meaning "dark moon," a set of fifteen units meaning "half moon," and so on. From long before the earliest known numerical notation, people must have been thinking in terms of groups of numbers, using number as story --- plot, character, and relationship
As first, the menstruant, whenever she secluded during the dark of the moon and emerged at the new moon, was the calendar. She marked a definitive, externally visible, unit of time, the month (moonth) as synchronized within the human body:
Chinese women established a lunar calendar 3000 years ago, dividing the celestial sphere into 28 stellar "mansions" through which the moon passed. Among the Maya of central America, every woman knew "the great Maya calendar had first been based on her menstrual cycles." Romans called the calculation of time mensuration, i.e., knowledge of the menses; menstrua is a grammatical form of menstruus, monthly; mensura is measurement. Gaelic words for "menstruation" and "calendar" are the same: miosach and miosachan. The new-moon sabbaths of ancient Latium were kalends, possibly related to the Aryan name of Kali.
The Hindu goddess was the goddess of the dark of the moon. She was connected to blood of all kinds and was often portrayed with dreadful face painted red, an uncontrollable deadly force, though her religion is extremely complex and she is also Mother Kali, Kali Ma, Sara Kali. However, she is crone and dark moon more than most goddesses, and she is a trinity, so the number three --- the number of the dark moon --- belongs to her. [p. 155]
The ancestress cloistered herself in her hut, gathering the paraphernalia of her r'tu around her: her blood-drawing flint, her scratching stick, her little white, red, or black marking stones, her bird bone straw. Sooner or later she would scratch the units of her correspondence with the moon into written form. Such calendric markings have been found in the south of France, on two hollow eagle bones dating from the Upper Paleolithic period of 12 to 15,000 B.C.E. One of these bones investigated by Marshack, long, hollow, and three-sided, was also grooved to be a whistle. Without the groove, it could have been a straw, as perhaps the second bone was. Remembering that hollow eagle-bone straws were used in menstrual rite to "separate the waters," it makes sense that a lunar calendar was kept on eagle bones. The eagle surely was at times imagined as the moon itself, as other large birds have been, or as a cloud and therefore a bringer of rain, the menstruation of the sky. The eagle shows a striking white moon shape on its tail in flight, and is a predator associated with blood. It is also the supreme spirit bird for many peoples of the North American continent.
One of the eagle wing bones examined by Marshack contained a six-month lunar calendar on two of its sides. Through careful microscopic examination of the strokes, Marshack deduced patterns marking the lunar phases: quarter, half, crescent, dark, crescent again. The marks on one bone were in distinct groups of 7 and 15, then 29, then 25 plus 4, suggesting direct observation of the moon's changes. Calendar markings from a similar age have been found on stone disks, breast- and vulva-shaped stones, and other objects signifying the feminine.
The question of which gender made which specific Paleolithic markings or drawings is largely unanswerable and probably irrelevant, since both genders have had to practice these arts in order to learn time's dimensions. Through parallel menstrual rites of the hunt and of animal and human sacrifice, men were coordinated to the lunar cycle. They went out hunting the eagle and brought its bones back to the village. They, too, sat in seclusion in lonely places with bones and stones, a flint knife, pondering the shape-shifting [p. 156]
light above their heads. But the menstruant, having the most direct connection with the lunar cycle, would surely have been the first to know; she had motive, method, and opportunity to be the originator of lunar notation.
Menstrual seclusion rites enact and make sacred specific numbers, and it is this specificity of attention to groups of numbers connected to lunar events that makes the science of numbers so much larger than simple sequential counting could ever have been. The group of numbers used in a tribe's particular seclusion rites varied, even among tribes living in the same areas. But whether the number of days of menarche was 3, 4, 5, 6, 7, 8, or 100, whether it stood for one month or seven years, its significance was defined by the central physical rite. Not only was the menstruant secluded, she was secluded for a particular number of days and nights. And whatever number was specified for menarche, the same number was sacred in other tribal rites and was recognized by the tribe as their "sacred number." Thus people studied number as if it were name, a group of letters adding up to a sacred, creative word: Three, Five, Seven.
I'm suggesting --- keeping in mind Marshack's expression "time-factored thought" --- that our ancestors may have learned to think numerically through their recognition of relationships between groups of numbers that were also units of time measured through menstrual rite. Perhaps this explains the fact that although many tribes described in the nineteenth-century accounts did not seem to have words for very high numbers --- no idea of "thousand," for instance --- they nevertheless had complex numerology in their social customs, dances, and crafts, paying strict attention to ritual numbers and "proper" timing. It seems likely that ancestral people began by using number ceremonially, as ratio, as relationship --- not as quantity, not even as sequence.
Menstrual rite measured durations of time that were witnessed [p. 157]
by the people as a whole, beginning of course with the menstruant's relation to the presence and absence of light. Logically, the original sacred number would have been one menstrual cycle, which was commonly counted as twenty-eight days --- twenty-five of the moon's light and three of the moon's dark --- or thirty days.
It is not important that the actual number of days in the menstrual cycle may have been slightly more or that the moon is by modern calculations completely dark for only one day, not three. Early humans, just beginning to express their consciousness of time, were not so much observing the sky in the interest of precise counting as they were closely connecting its patterns to their bodies, spirits, and stories. Three days for the moon's menstruation is a closer entrainment to women's bleeding than is one day. Three is worldwide the number associated with death, with completion, and with birth, all of which are also equated with the moon's disappearance and reappearance. Three days for the dark of the moon remained the convention over much of the world as late as the founding of the Jewish calendar, which retains it.
Even today, long after the practice of a three-day seclusion, number lingers in menstrual lore: "Whenever they had their very first period, my mom sat with each of her daughters for about ten minutes on the third stair, so that they would always have regular periods. She was born in 1939, and this was in Bulacan Province, in the Philippines."
Although I have no explicit evidence, I believe the earliest notation of number must have been on the human face; where men, especially, could see it. Perhaps, like Snake, numerical cosmetikos represents "Female Instructing Principle." The connection of three to menstrual cosmetikos was most dramatic and artful in the practice of chin tattooing, the widespread use of three vertical lines to mark the passage of a woman through menarche into adulthood. As we [p. 158]
have seen, the highly visible, emblematic chin tattoo served to protect the vulnerable mouth.
But the lip bar with three evenly spaced "dribble" lines running from it may also have imprinted the sacred number three on the whole tribe --- the unit of time of the moon's disappearance as related to the female vulva. Turned up on its right side this mark is a squared-off version of how we write the number three today.
Cosmetikos, as I have said, begins with an embedding of the significant mark or shape in the flesh itself, then later the same mark is painted on the skin, and later still, painted or indented on another surface --- cloth, bread, or a pot --- that is metaformic of human flesh. Over the course of time and cultural additions, cosmetikos migrated out from the flesh onto other surfaces. Thus, while in 1936, an Aleutian woman would have cut the tri-bar line into her daughter's chin with flint or a thorn, a Moroccan bride would have her chin marked with three lines of charcoal, and in Central Asia, a smith might have worked the number three into a design of silver and gems to be worn as a delicate veil over the married woman's mouth whenever she went outside.
The work of Marija Gimbutas, an archaeologist specializing in woman-centered cultures of prehistoric Europe, seems to confirm the significance of the number three. One of the female figures she describes, from Mycenae 1300 B.C.E., has a serpent head. Its mouth consists of a bar with three lines coming down the chin. Patterns of three lines are also found on woman-shaped pots and figurines from the Upper Paleolithic. Since the pots are goddess figures --- in my view, representations of the collective menstruant --- at one time these marks may have been chin tattoos incised on the faces of real women on the European continent. Gimbutas considers these tri-lines and similar numerical lines on clay and stone to have been the early basis of writing. If so, the notation of significant numbers --- particularly in the Northern Hemisphere, the number three --- could have begun as incisions on the face representing the achievement of menstrual status.[p. 159]
Gimbutas also points out the significance of the large number of V's or chevrons identified as vulva marks. The V was painted and incised on early goddess figures as the vulva, possibly also as an early method of drawing the crescent moon or representing one lunar day. Some of the pot marks seem to be an entire statement of time. In one instance the chevrons can be seen as the waning and waxing moon, with the space between being menstruation, the dark, chaos, nothing: < >. In another example, the waning and waxing crescents surround three vertical lines: <|||>. Perhaps the three-line chin tattoos are merely a remnant of a great complexity of numerical incisions worn by people in the distant past.
The menstruant kept time with her seclusions, and women kept number on their bodies. They taught us what time it is, and how to think proportionately; they taught us how to connect events together, to add them up. They taught us the power of the essential metaphor implicit in the connective word "and." They also taught us where in the world we are.
The word "orientation" comes from Latin and means "east." It is related to both oriri, "to rise," and rivus, "stream." The word "cardinal," meaning primary, and applied both to the four directions and to elemental numbers, also means a woman's hooded cloak, formerly made of scarlet material. In the derivations of these words, I am reminded that in many menarchal rites, the menstruant emerged from her seclusion at dawn. This act faced her toward the east. It must have been part of r'tu from the earliest division of light from dark --- mythologically speaking, the second "world" or level of consciousness after the ancestress noticed that predators were attracted to her blood. Since in so many seclusion rites her emergence, as an act of world formation, was at dawn, she can be said to have "created" east.
Later the seclusion hut itself would have been built so that its opening faced east for her emergence. She had become a ritual [p. 160]
compass. The hut and her emergence from it established the original cardinal direction and the basis for orientation. Her reappearance from the hut with the reappearance of light was public, with her family and perhaps her entire village present for the feast. This meant that everyone would observe her orientation, her "eastness." That orientation would have passed over into other rites as they developed, and people would have learned direction by imitating the menstrual emergence toward the east at dawn. The keeping and display of direction became one of the central organizing principles for all human ritual and was integrated into tribal and village life to a degree modern minds can scarcely imagine. Thus, in some menarchal rites, the menstruant was required to dance all night long, facing east, often shaking a rattle. Women companions stood on each side to hold her when she was tired, for she must not stop. Other menarches included a race, in imitation of the sun or moon. The emergent menstruant led the race --- she was the light --- running in its course from east to west, and then returning. She could not look back. In Kinaaldá, the elaborate menarchal ceremony of the Navajo, she runs at dawn and at noon toward the east in a clockwise direction, around a tree or other significant plant, and then runs back to the hogan. Her companions give chase, careful to let her win. She embodies east and west and the path, or course (rita), that light follows. West was reinforced in many mourning rites. For example, the relatives or the healer would leave a sick person's hut by the "back door," that is, toward the west, the direction of death for many peoples. Special holes were torn in the west walls to remove a corpse from a house. Since east represented renewal, birth, revelation, and source of light, in many origin stories west became the place of death, disappearance of light, and onset of dark.
The circle, arc, straight line, triangle, cone, square, and rectangle are used in the mathematical method of reasoning called "geome [p. 161]
try" (from geo, "earth," and metron, "measure") because eventually combination of these shapes with number led to the ability to measure the surface of the earth, the circumference of the equator, the distance from equator to pole, the distance between the earth and the moon and sun, and the circumference of both. The shapes used for these calculations were worn on the menstruant's body as cosmetikos. They ordered the cosmos by imitating its sky shapes and protected the sacred vulva by honoring its pubic triangle. For millennia, such forms as parallel lines, the circle, triangle, and crescent had been carved, painted, and inserted into the skin, arched into eyebrows, woven in string designs, baskets, and garments, constructed in sacred huts and lodges, and drawn on the walls of caves and cowsheds in coordination with menstrual r'tu. Somewhere back in the millions of years that the ancestress sat shedding her apehood in her seclusions, her mother cut her lip and inserted a piece of round shell to protect her from harm. In expressing the correspondence between menstruation and significant shapes, the menstrual mind gathered the fundamentals of what would become geometry. When sacred shape and sacred number migrated away from cosmetikos and were applied to movement, architecture, landscape, and story, we had the beginnings of the sciences of surveying, engineering, navigating, and "pure" geometry. But as with number, the primary shapes of geometry were metaformic. They were held sacred and learned through r'tu.
Almost everywhere, people perform rites after first forming themselves into a circle. This is not a "natural" pattern; few animals make circular formations. Here on earth there was nothing to draw people to the circular shape. The circle was in the sky, the light that came and went, the light whose habits and whose shapes the menstruant imitated. Early peoples devised ingenious methods of studying the circle: rouge spots were painted on cheeks; dots, circles, and round shapes were engraved on the body; round lip pegs and disks were fitted. The people ate from round plates and bowls, used round mats, round baskets. Plazas and other places of public ceremony were laid out in a circle, as were many villages. [p. 162]
Plains Indian women arranged the tribe's tipis in a circle of wholeness. Dwellings themselves articulated the circle --- round houses, huts, tents. Hoop games, games played in a ring, circle dances, and the making of round drums- --- whose shape imitates the moon and whose beats make use of rhythmic timings --- all reinforced the image. And everywhere on earth people now make the circle --- in games and dances, around campfires, in churches, and in hundreds of other ways.
The moon, as we've seen, is the source of a number of sacred shapes. Fullness, the circle, became the philosophical idea of wholeness because the moon goes through its cycle of less whole, vanished, and then increasingly whole to the point of completion again. Crescent forms dominated the adornment of tribal people all over the world, especially horns, tusks, nails, and claws. These shapes were worn all over the body. Tusks and even slender horns were used as nose ornaments. Horns were a prominent feature of the costumes of holy people, shamans, and of mediums impersonating deities --- from the West African goddess Oyá, whose horns are those of the buffalo, to the single- and double-horned gods of the Pueblo peoples and the buffalo spirits of the Plains tribes. In the West, the crescent is singled out on the female body when polish is applied to every part of the fingernail except the little lighter colored area near the cuticle, an area known as the "moon." And croissants, French crescent rolls, are still sometimes called "the moon's teeth."
The gathering of metaforms that imitated the shapes of the moon's changes led people to subdivide the unit "month" into halves, thirds, and the measure we use so often in the West, "quarters." The specific designations might vary, for they did not need to be based in an exact number of days, but rather on the appearance of the crescent, the half, and the full moon. Nevertheless, recognition of a semicircle as the shape of a moon halfway through its cycle represents the idea of the fraction: half, the even division of parts. Quarter is a further extension of this important geometric (originally lunametric) perception. [p. 163]
Dividing the lunar cycle into quarters enabled people to quarter the entire visible sky as well. The fact that both moon and sun follow a similar east-west course, so that the path of light appears to "cut" the sky in half, would have expressed further the idea of proportional division. For some peoples, the fundamental directions east-west were sufficient, but most others quartered the sky and established four directions. The Tibetans coordinated the moon's phases with the directions: east was crescent, west was full moon; south, the half moon, and north, the dark of the moon.
Once this scheme of measurement was in place, it could be transferred to the earth. Mythology from many places insists that measurement began in the sky and then fell or otherwise came to live on earth. Imperial China used the sacred number nine --- the sum of the four directions in the sky, the four directions on earth, and the emperor in the center, representing all human society. Many other peoples took three as the sky's number and four as the earth's, in a sacred number that combined them: seven.
The idea of dividing the sky or the moon into parts was practiced by the ritual cutting of the lunar pie or cake by the emergent menstruant or by a parallel menstruant, such as a priest. Round cakes in many religious services are carefully cut by quartering or are decorated in cross marks, especially on those occasions associated with sun/moon coordinations.
In the sixth grade, the veil that has hidden numbers from me suddenly lifts with geometry. The relationship of number to shape, of ratio to proportion, of proportion to balance and esthetic ---this I understand well and get great pleasure from. I don't excel at solving problems, but I comprehend the principles. Then with algebra, the curtain falls again. The relationship of number to itself baffles me completely.
I know only one girl who "gets" higher mathematics --- my best friend, Francine, whose Arab ancestors discovered and developed [p. 164]
algebra and whose mother as well as father is a technician in rocket engineering at White Sands Proving Grounds. Mathematics is not an abstraction to her, and trigonometry is a delight. Her parents give her the patterns of mathematics as my own give me the patterns of poetry.
I want measurement through number, orientation, and shape to be my own. Simple addition and subtraction become my mother's when at forty-two she goes to work outside the home, as a photographer's assistant. She uses her salary to pay the gas, water, and light bills, and sometimes for food and rent too. She gets great and obvious satisfaction from paying these bills, partly because of the security of having household money in her own control, for my father is periodically likely to drink up and gamble away his own salary.
I also believe she gets satisfaction simply from using number in her daily life, from writing down amounts, adding and subtracting the slender figures on paper, and then again in her head when doling out money for me to go to the store. "Three peaches, the smallest container of baking soda, and a quart of milk," she says, her eyes rolling to the ceiling as she mentally calculates the probable cost before fishing a bill and change and wrapping my small fist around them. "Don't forget to add it up when the checker does," she says. "Sometimes they make a mistake." I consider the chore a success if I am accurate within five cents of the checker's conclusion.
In the absence of a strong feminine tradition, and without much access to the male tradition, my mother's mind drifts away from us, at times completely. I am afraid this will happen to me as well. But, like her, having lost number in the sudden abstraction of algebra, I find it again when I go to work. Almost all my first jobs require using a cash register, making change, and immediately addition and subtraction are back in my life. Long before turning me out into the world at seventeen, my mother carefully teaches me how to manage a bank account, to fill out the checks and keep track of the amounts. [p. 165]
I am proud of this skill that my mother did not have until half way through her long life, and that my grandmother did not have at all. My mother stresses that the difference between having money of one's own --- however small the amount --- and having none was the difference between survival and hell.
When at twenty-one I spend a year training as a medical laboratory technician, I am thrilled with the amount of measurement and math required. Chemical substances are not only named but given numeric value, valence, based in their molecular structure. Once again, what has been a veil of secrecy lifts as I take the calibrated tubes (glass straws!) and vessels in my hands, and mix exact amounts of human blood and chemical toward a particular end --- the proportion in millimeters of white cells to red indicating the difference between leukemia and not leukemia for the very real man sitting in the examining room. Stopwatch in hand, pipette in mouth, sharp smell of sulphuric acid in nose, charts and graphs fixing my eye, I revel in the measurements of my occupation despite my dislike for the more mechanistic, fragmented, and unjust aspects of Western medicine. At least, I feel, I have a piece of numerical mind.
The geometric forms based, not in circles, but in straight and parallel lines --- the cross, the square, and the triangle- --- cannot be based in the moon's shapes or motions. Yet mythology and art history tell us that straight-line forms such as triangles are very much related to menstruation and women's arts. Where did they come from?
We don't have to go far to find a method by which women in the most distant past could have been drawing complex parallel line figures without using any materials other than a bit of vine and their two hands. Cat's cradle is a game played by looping a continuous cord over the fingers of both hands held apart with palms facing, making patterns in the cord by changing the relationship [p. 166]
of the loops. Girls in my culture still play cat's cradle. (I didn't, of course --- that was "girl stuff.") People worldwide play string games --- in the South Pacific, whole families do --- and in nineteenth-century Africa, it was a test of intelligence.
Women of the Yirrkalla people of Australia tell how the two creation sisters, the Wawilak Sisters, originated cat's cradle and the use of string. As the two sisters looked at each other's menstrual blood, each made a loop of the other's blood and put it around her neck. They had become blood sisters in the most fundamental sense of that expression. In the myth, the Snake of synchroneity appeared when the younger sister saw the blood of birth on the elder's vulva and started her own period --- and she was making a cat's cradle design at the same time. A Yirrkalla cat's cradle figure is titled "Menstrual blood of three women." The loops are made around the thumb, forefinger, and little finger of each hand, forming three interconnected "streams." The figure as a whole contains triangles and a central diamond shape, and of course, it calls attention to synchrony between menstruation and the number three. (It is not surprising, then, that the triangle figure is associated with the vulva.) In Yirrkalla society only the women do cat's cradle. The men must walk past a woman looping the string with their eyes averted. Women of the aboriginal tribes are said to "own the string."
In the mythology of geometry, two sisters comprehended the synchrony of their blood flows as "Snake" and also saw that the strings of blood and the navel string and strings of vine were all the same. They expressed the correspondence by creating figures from a hand-held net of string --- the cat's cradle --- understood metaformically as "strings of blood." When the string formations of cat's cradle are imitated in chalk or carving, they are drawings, ways of attracting and capturing spirits toward specific purposes. (Art critics in modern times describe art's spirit-catching attributes in terms of proportion, balance, form, and energy.)
The string held taut in the hands taught us to use forms based in straight lines, parallel and intersecting: triangles, trapezoids, rec- [p. 167]
tangles. These forms were transferred from string to other human "drawings." In all the crafts and ornaments of humankind, geometric designs served as protection against the disintegrative power of menstrual consciousness of disaster. Women painted and tattooed the figures on their own and also on the men's bodies, as they do still today along the Amazon River and other places. Their scratching sticks and combs were decorated with significant lines and triangles. Once they learned to weave cloth, they dyed the geometric figures in it, giving the cloth of Africa and South America, as prime examples, its exquisite artfulness. The geometric pottery painting and beadwork of American Indians gave their societies their distinctive esthetic. In Scandinavian and other folk cultures, linear formality of design was the rule. In old African cultures, triangular and circular forms, usually painted by the women, dominated the external ornamentation and design of villages and buildings.
The sun, or light, is also related to the cat's cradle game, which for its original users was far more than a recreation. The string figure was a method of affecting the external world. The Eskimo of Iglulik used cat's cradle figures to slow the sun's disappearance during the fall months, "to catch him in the meshes of the string," while farmers used string figures to influence their crops.
When sacred number and sacred form were combined, the science of formal measurement resulted, and the relationships, sizes, and distances between the bodies in the sky and the earth began to be determined. The sacred rope (the umbilical Snake), with a peg or rod to center it, could be used to draw a perfect circle on the ground, of which the rope was the radius. The circle could be halved by any two opposed points on its circumference, and the line of splitting was Tiamat, diameter. When the sacred number three was applied to the circular form and to its rope diameter, a "magic" formula emerged that operated for any circle of any size: [p. 168]
three multiplied times the diameter equals the circumference. Stated mythically, application of the dark of the moon (three) to the half moon (diameter) produces the full moon (circumference). This formula could have used units that consisted of ropes of equal lengths; it did not require number units. In folk medicine, an act must often be repeated three times, and that symbolic equation might be stated thus: perform a metaformic action (diameter) three times (dark moon) to achieve healing (wholeness, full moon).
A second formula can be pulled from a similar combination of elements: the sum of the radius multiplied times itself times the sacred number three equals the area within the circle. The elements of the formulas --- the full moon shape, divided into light/dark or aboveworld/belowworld by the rope diameter, which is multiplied by the dark moon three --- lead again to the fullness of the circle with its circumference and area. The application of sacred number to sacred form enabled early thinkers to capture the measure of light and dark in a new rope web, just as they had been "capturing light" for millennia in cat's cradle figures and witches knots.
Formulas based in three applied to the circle were used by temple, ziggurat, and pyramid builders in China, Mesopotamia, and Egypt. More recently, the sacred number three became refined to a decimal value, by convention now, 3.14 or 3 1/7. Greeks called this number pi; they learned its formula thousands of years after the earlier architects of Stonehenge, Babylon, and Egypt had incorporated it into their temples and pyramids. In China, the Pi-dragon retained the formula's association with the (vaginal) serpent. I find I remember it better if I also think of my mother's cherry pie.
The most prominent numbers of cosmetikos --- measuring the separations of menstrual creation (five), the days of lunar death (three), and the directions of the oriented earth (four) --- when applied as a ratio, a relationship, make a triangle with a very special quality: one of its angles is 90 degrees. With this formula, walls and floors can be perfectly squared; the relationship of the horizontal to the vertical can be perfectly squared. Babylonian architects [p. 169]
used a knotted rope divided into 3-4-5 proportions to align their buildings. And in Egypt, not only did the royal builders and master architects use it, but even ordinary Egyptian farmers used 3-4-5 knots to mark out their fields and reestablish boundaries after the annual Nile flood.
The Greek mathematician Pythagoras, who studied in Egypt, separated the proportionate structure of the old 3-4-5 triangle from its knotted umbilical rope and from its practical uses, teaching its proportions as a purely mental and spiritual exercise to his Students. Pythagoreans and Platonists believed the triangle to be the fundamental building block of the cosmos. Since Pythagoras was the first to bring the form to Western consciousness; he was long believed to have "created" it.
How long ago our ancestors first set a pole upright from the ground and used the angle it made to measure the sun's shadow, and from this, to begin to calculate the dimensions of the earth, moon, and sun, and their relative distances from each other, is probably unknowable. But clearly, peoples long before the Greek mathematicians possessed the fundamental elements of this kind of measurement. Mythology credits both genders, as it should. Egyptian hieroglyphs portray the goddesses Isis and Nepthys as measurers; they often hold a rope between them. A graphic description of the right triangle is particularly apt: the two short sides are formed by the body of a long thin serpent; the hypothenuse is the leaning body of an Egyptian King, his erect penis centered. The glyph thus credits the sacred 3-4-5 triangle to the female tradition of Snake, coupled with the royal male. In the Book of the Dead, a hooded serpent is consistently part of the glyph for the many goddesses named in the text.
Sacred numbers remained attached to the deities as they developed in the Greek pantheon, and also the pantheon of the Macumba religion in West Africa. Hera's number was nine; to goddesses connected to the underworld and death- --- Hecate and Kali, for example --- belonged the sacred number three. Number is narrative, for number establishes relationship in space and time. Num- [p. 170]
ber thus gave us a capacity to tell sequential stories --- stories with a specific past or future, with relationships between significant characters, or "names," units of sacred meaning. Our capacity to repeat in fixed numbers enabled us to find significance in other fixed repetitions, as when the cock crows three times. The metaforms of number, orientation, and shape have given us certain key elements of our stories: when, where, who, how many, how long? The lunar--menstrual ratios of number and shape gave us ideas of partialness and wholeness. In short, the connective capacity of metaform gave us story itself, the connective word "and." The moon is secluded and so is the menstruant. [p. 171]