“For this reason they (the Celts) measure periods of time not by days but by nights; and in celebrating birthdays, the first of the month, and new year’s day, they go on the principle that the day begins at night.” — Julius Caesar, The Gallic Wars (58 BC–49 BC), Book VI, Chapter 18
The pioneering Ice Age proto-science was astronomy. As early as 33,000 BC a reindeer antler from Abri Blanchard in France was inscribed with notations which Alexander Marshack[1] (1972) has described as tracing the 29 1/2-day lunation cycle.
In time, seasonal variations in temperature and other weather changes, animal migrations and moultings, and the flowering or ripening of plant life were correlated with the star patterns along the path through which the sun passed annually and the moon passed each month. Onto this starry path were projected earthly images from everyday life—the springtime flow of water and its fish life (Aquarius and Pisces), the autumnal harvest (Virgo) and the weighing out of barley (Libra), and various symbolic animals such as the bull (Taurus, originally signifying the springtime full moon sign), the lion (Leo, signifying the sun at its solstice in the heat of summer, and hence appropriately a “southern” animal), and the eagle (subsequently represented as Scorpio). The result was an annual calendar of constellations that evolved into the zodiac through which the sun moved during its 365 1/4-day year.
A great problem was posed by the fact that the moon’s phases and 354-day lunar year could not be reconciled with the solar year. At the inception of the Bronze Age, lunar calendars were replaced by solar (or at least lunisolar) ones, whose months dropped their relationship to specific lunar phases.
This transition became the source of much mythology. The Lion-Bull conflict depicted the solar animal—the lion, associated with the heat of summer—fighting the lunar animal—the bull, whose 28 ribs[2] corresponded to the 28 days of lunar visibility. The 11-day solar-lunar gap between the 354 and 365 1/4-day year (or in Egypt between the 360 and 365 1/4-day year) became a time of Saturnalia in which usual behavior was inverted, culminating in a re-creation of order. The New Year festival provided an occasion to cleanse all disorder, imbalances and sins, debts, and other social blockages so as to begin the New Year with a properly reordered earthly kosmos.
The word “calendar” derives from the Latin word “calendarium,” which means a banker’s account book.
Why the Paleolithic Lunar-Female Kosmos Had to Be Replaced
The earliest documented artifacts with decipherable cognitive meaning date back into the Ice Age as early as 35,000 BC (Marshack 1972[3]: pp. 32ff.). They have lunar markings, pointing to the lunation cycle as mankind’s first perceived example of regularity. The moon’s paramount calendrical role survived well into the neolithic and has characterized most tribal communities throughout history. In antiquity the lunar calendar survived in its most pronounced form in Rome, and via Semitic culture it has been elaborated to an extreme degree by modern Islam.
In its role as civilization’s first measurer, the moon provided a major impetus to counting. Most Indo-European words for measurement derive from the word for moon (“mensis,” “mental,” “mensuration,” “menstruation”), hence the term “lunar-menstrual cycle.”
Much primitive counting seems to have been developed to mark the 28 days of lunar visibility in the typical 29/30-day cycle. Omitting the dark period when the moon is eclipsed by the earth’s shadow, some societies in New Guinea and Indonesia retain systems of body-counting which extend from 1 through 28 (Biersack 1982[4] and Ifrah 1987[5]). This number seems to have been a widespread archaic count, and typically has been divided in half (14 + 14) to represent the waxing and waning periods separating the new and full moons. A further division into quarters is responsible for our seven-day week, and probably for much of the lore centered around the number seven. Yet the moon is an elusively variable measurer: Instead of tracing out round numbers, the lunation cycle lasts slightly over 29 1/2 days, and varies somewhat as a result of gravitational perturbations. It must be timed by actual empirical observation, not by abstract or “automatic” calendar-making.
This fact that lunation cycles vary in length meant that rations could be allocated regularly only by making a transition to uniform solar months. For although counting systems can be based on the 28- or even 29/30-day lunar cycle, no known weights and physical measures are lunar in character, and hardly could be. The first documented weights and measures appear only with the Bronze Age transition to solar calendars and their schematized 30-day administrative months. And as a result of the central economic role played by Sumer’s temples and palaces, solar-deities and iconographies first became most prominent in Mesopotamia and spread throughout the region’s general commercial and culture area.
The earliest observers no doubt began to count simply in terms of ordinal sequences, such as Monday, Tuesday, Wednesday… Sunday, or A, B, C… Z, without quantitative arithmetic notions. But at least by the late neolithic, numbers were perceived to have interesting cumulative and quantitative characteristics. It happens that the sum of 1 + 2 + 3 + 4 + 5 + 6 + 7 equals 28. This sevenfold measure was correlated with the lunation cycle and the seven heavenly bodies taken together: the sun, moon, and the five visible planets—Mercury, Venus, Mars, Jupiter, and Saturn. Gradually, a predictive astronomy was built up on the basis of their respective orbiting times as seen from the earth. These computations required a higher mathematics and geometry, whose basis moved away from all reference to the lunation cycle as it adopted the decimal system and the “solar” numbers 360, 60, and 30.
The Medium for Counting Was the Human Body
The results still leave considerable room for speculation about how measures and numbering first developed. Commonsense approaches derive counting from the fingers (and perhaps the toes), and measures of length also from the body—originally the hand, armspan, foot, or pace of the ruler. More esoteric theories derive weights and even lengths from the measurement of water by weight and volume (Böckh[6] 1838, elaborated by Warren[7] 1899 and Petrie[8] 1911). Geographically there is an equally broad range of attempts to trace modern measures back to Mesopotamia (an early example is Brandis[9] 1866), Egypt (Petrie[10] 1911 and Irwin[11] 1962), and even western Europe (the megalithic yard).
Numbers and counting did not begin as the general abstractions they later became. Abstraction comes only at the end of an intellectual process, achieving a synthesis of what hitherto was perceived to be disparate functions. For archaic cultures the numerological synthesis was woven tightly together with calendrical cosmology into a single system of nature and worldly social policy/structuring.
“In the beginning,” different numerical systems and counting-words existed for different categories of things. We still refer to a gaggle of geese, a herd of cattle, a flock of sheep, a pride of lions, etc.
Out of these counting systems two numerical bases emerged above all others: the decimal base 10 (sometimes in its multiple, 20), used to count whole integers, and a base 12 or its multiples (above all 60, also significantly a multiple of 20) for computing fractions. The latter tended most often to be calendrical. The means of counting were, for 10, the fingers, and for 12 or 60, the calendar.
The preceding chapter has traced how the earliest number systems and their associated weights and measures were designed to reflect the calendar, specifically a solarized calendar composed of standardized 30-day months in Mesopotamia and Egypt. (In the less centralized peripheral societies of classical antiquity, Greece borrowed Egypt’s non-calendrical decimalized system of fractional arithmetic, weights, and measures. The Romans used a fractional “troy ounce” system based on 12ths.)
But there was one other important mode of counting, also based numerically on parts of the body. That number was 28, a clearly lunar number.
In a sense, mankind may have learned to divide before it could multiply, subtract, or even perhaps add. But once you know how many digits you have, it becomes less interesting to count them over and over again. (If people had begun to count on their toes, the foot-rulers would have 10 inches, not 12.) Fingers and toes are used to teach children how to count, but the first people to count seriously no doubt were adults—probably individuals with a shamanistic bent of how their world was put together.
There are many ways to count the parts of the human body. Astrology, for instance, divides it into two parts, from the head, ruled by Aries, to the feet, ruled by Pisces. Each part of the body thus corresponds to one of the 12 zodiacal-calendrical signs—that is, to a constellation which ruled one month of the year.Missing IllustrationHelp us track down an image/images that there was a note here to insert: Cosmological Body (and possibly Zodiacal Man).OpenSee All Queries
It is awkward to count on full parts of the body. For such purposes the digits are preferable. But even here, there are many ways to count digits. The count follows not the number of fingers or parts of the body, but what is being counted.Missing IllustrationHelp us track down an image that there was a note here to insert: Zodiacal Man.OpenSee All Queries
If days of the month were the most important archaic things being counted, the vehicle for counting was the human body. The human body was divided up into counters—fingers and toes, parts of the upper body, and so forth. There is an ethnographic account of the first anthropologically inclined visitors to New Guinea, who asked the natives to count. They began with their fingers. But instead of stopping with the little finger, they kept on counting by touching the parts of their body, up the arm and across the face, then down the other arm—finally ending up with a clap of the hands, exclaiming “pongo” (Biersack[12] and Ifrah[13]).Fact CheckMore validation that this story is true is needed, and a check that it is appropriate and up to date. Can you help?OpenSee All Queries
The things (counters) are manipulated to symbolize the whole.
Indeed, when we refer to counting one’s fingers it should not be overlooked that these in turn may be subdivided into the knuckle digits. If the two knuckles that divide fingers into thirds are included, we get 12 per hand (if counting only the fingers and not the thumbs). Multiplying the 12 knuckle-digits on the right hand by the fingers on the left produces a 60-count.
Actually, there are 14 digits on each hand: 3 knuckles on each finger (for 12) and 2 on the thumb. (14 x 2 = 28) x 10 = 280, the number of days it takes for pregnancy, 40 weeks (40 x 7).
It thus would be erroneous to imagine that the number 10 is inherent in the human hand. As with most things in life, people have been able to find in the hand whatever they are seeking.
We will first explore how the important archaic numbers, weights, and measures were based on the calendar (Neugebauer[14] 1969Verify CitationCan you help us verify that the cited work was the text meant?OpenSee All Queries: p. 20). There are some obvious reasons why time was important to count. The first reason is abstractly intellectual and had to do with calendrical cosmology: To find and count out order in the universe, especially in developing the mathematical foundations for astronomy. In time the Sumerians had to greatly elaborate their mathematical abilities in order to disburse rations regularly. But this worldly activity likewise was based on the calendar, for most economic phenomena—the distribution of rations, the payment of interest, taxes, and contributions.
Counters Distinguished From the Things Being Counted
The gamut of numbers was first developed in the neolithic to mark calendrical time, apparently beginning with the number of days in the lunar month. Alexander Marshack has shown that even before the quantitative idea of numbers, the lunar days and phases were being marked. An intellectual leap occurred when the repertory of signs to notate the days of the month sequentially took on actual quantitative functions. But before they could be abstracted as numbers, these moon-counting measures had to be generalized to count things other than time—animals, bones, stones, and so forth.
At first the counting of objects such as bones or stones (Latin “calculi”) would have appeared to the archaic mind as an analogy: “There are as many joints in my hand as there are days in the first half of the month,” that is, 14 (three joints on each finger, two on the thumb). Henceforth, various categories of things or phenomena could be counted in terms of sevens or 14s, that is, “gamuts” of the lunar quarters. Later they could be counted in terms of 12s (the number of joints on the fingers excluding the thumb), 10s (the number of fingers), 20s (the number of fingers and toes together), or 28s.
Early counting systems were based on the single most important thing being measured—calendrical time—not on the “counters” (e.g., fingers). The earliest measurement systems likewise were calendrical. They were first developed in Mesopotamia and Egypt to feed consumers with rations distributed on the basis of the 30-day months described in the preceding chapter. Similarly, when we find measures divisible into 12ths, as in the Roman “troy ounce” system and that of feet and inches, there is good reason to suspect a calendrical analog to the 12 months in the year. Mycenaean Greek measures were divisible into quarters, perhaps for weekly consumption each month. Irwin[15] (1962: p. 32) pointed out that in medieval England measures divisible by four or eight had a convenient calendrical function: “A peck of peas would last four weeks, since the peck was equal to eight measure-fulls and [the wife] would be using two measure-fulls each week.”Verify CitationCan someone with access to this text verify that the text in the quotation is accurate to the original source?OpenSee All Queries This worked out to 12 pecks a year. Early volume units typically were based on human consumption needs (barley in Sumer, peas porridge in England). Only with the metric system were measures subordinated to decimalized arithmetic. This decimalization began in ancient Egypt, and spread via Crete to classical Greece, much as it did from revolutionary France in modern times.
For a time, numbers probably served as sets of analogies. The number of stars in the Pleiades or Ursa Major or Minor (seven) was the same number as the days from the new moon to the quarter-moon, that is, the seven-day week. Over time an intellectual bridge developed for such analogies. A means of counting or “set of counters” shared a numerical common denominator with the things being counted.
The most convenient such common denominator historically has been supplied by various selected parts of the human body. The body is portable and has the same number of “counters” or “counting spots” for most people. From this fact developed the phenomenon of body-counting, that is, counting on parts of the body as “stations.” Ultimately, the human hand was isolated as containing in its own fingers and joints all the counters needed for computations in systems based on the numbers 10, 12, 14, or even 60.
The modern world is familiar with counting on one’s fingers to 10. But fingers were not the first things to be counted. Everyone knows how many fingers they have, and few adults find it very interesting to count their fingers. After one has done it the first few times, the excitement wears off. The number remains constant, so that there is neither a surprise nor a reason to be interested in counting one’s fingers. What is worth counting are things that change in magnitude. To count, it helps to have a number system or gamut fixed in magnitude, e.g., the number of fingers or digits, against which to enumerate the things being counted.
Historians of mathematics infer that archaic populations must have counted on their toes as well as their fingers from the widespread systems of 20-based counting (see Menninger[16] 1969).Missing Page NumberCan you help to find page numbers specific to this citation?OpenSee All Queries The French break their count at 20, and the Aztec number system was based on 20. Evidently the idea was to coordinate the counters (the digits) with the things being counted, beginning with the days of the 20-day Aztec month.
Most mathematical historians have explained the fact that the Aztec word for “20” was the same as for “man” by the fact that a human has 10 fingers and 10 toes.Citation NeededCitation needed.OpenSee All Queries But a comparison with Mesopotamian usage suggests another explanation. The Sumerian term for 60 (and for 1), “gesh,” also means “man.” The idea seems to be “man” is synonymous with “whole unit.” It stands for a monthly measure.
In any case, the Mesopotamians could count to 30 (and hence, 60) on their fingers, using the knuckles: Twelve on the right hand, times any of the five digits on the left hand.
In discussing the evolution of counting systems it is helpful to distinguish between the counters being used for convenience—such as one’s fingers or perhaps groups of stones (Latin “calculi”) as analogs—and the actual things being counted—days of the month, barley rations, and so forth. If fingers and other parts of the body were the first referential counters, it was first in reference to calendrical time. The human body probably was “counted on” as a calendrical vehicle even before numerical digits were developed. After all, the hand is as amenable to counting to 12 or 30 (using the joints of the fingers) as to counting to 10 by whole fingers.
No one would consider these 28 body points a “natural” base for counting. But by the same token we should beware of assuming too quickly that the number 10 is inherent in the number of fingers. The four fingers beyond the thumb each have three joints, making it just as easy to think of them in terms of 12s, or 60s, one hand for 12, while the fingers of the other hand multiply these 12s as a “place” notation.
The inception of urban civilization and its large public institutions in the Bronze Age Near East made it necessary to replace lunar calendars and order-goddesses with more regular and standardized administrative calendars. The problem was that the lunar year cannot serve as a foundation for the solar year, for the 354-day period of 12 lunations is more than 11 days short of the 365 1/4-day solar year. Attempts to start each new year with the moon invariably miss a corresponding alignment at the solstice, equinox, or following new year.
For the centralized Bronze Age states, the problem with lunar months and years was not just the aesthetic one of their incommensurability with the solar year. After all, Greece, Rome, and many other first-millennium BC societies found little difficulty in maintaining an approximate correlation with the solar cycle by adding an extra intercalary month to fill out every third year or so. But a serious administrative problem remained for economies which required forward-planning: Lunar months vary irregularly in length, making them difficult to forecast with any uniformity. Each new moon could be timed only by direct observation. This meant that lunar calendars could not provide a basis for Bronze Age temples and palaces scheduling a large-scale division of labor which received rations on a regular basis. Such planning calls for a standardized monthly regimen, and hence a regular annual calendar.
The focus of kosmos-building accordingly shifted from nature’s spontaneous fertility land hunting/gathering cycles to the more complex regimens of standardized man-made administrative equity. And as this shift occurred, “female” ordering principles associated with water (as in the monthly lunar-tidal cycles ruling oceans as well as menstruation) gave way to annual principles associated with gods of sunlight and fire (Table 2.1). Emanating from Mesopotamia and Egypt, whose cities were ruled by palaces and temple priesthoods who associated themselves with sun-gods of justice, aspects of this great transition may be found in every chapter of The Creation of Order. A brief summary is therefore in order.
Table 2.1
Consolidation of the Bronze Age Solar-PatriarchalKosmos
Lunar Attributes
Solar Attributes
Night (dark and cold), ruled by the moon.
Day (light, fire), ruled by the sun.
Nocturnal wetness (dew), and above all the ocean (including tidal movements).
Dryness and land, the mountains over which the sun rises on the solstices and equinoxes.
Women as icons of order and the 40-week birth cycle.
The 365-day year (360 + a 5-day New Year festival, or 354 + an 11-day festival, perhaps 12 days on a leap year.
The lunar-menstrual symbolism was epitomized by the cow or bull, both of which have 28 ribs.[2] The bull’s great circular horns were depicted as holding the moon or evoking an image of the lunar crescent. The latter happened to resemble a boat, specifically of the Egyptian variety used on the Nile (but not well suited for rougher waters). The new crescent moon accordingly came to be depicted as a boat carrying the lunar-goddess across the nighttime sky.
The sun was associated with the numbers 30 and 12, reflecting the 360 days in the solar administrative year divided into 12 30-day months. (It was recognized, as noted earlier, that the true solar year has 365 or 365 1/4 days, but these were inconvenient numbers to deal with.) The typical solar animal was the horse, drawing the sun-god in his chariot across the sky. Significantly, the horse has 36 ribs, a number which factors into 360 by the decimal number 10. This makes 10 and 36 also “solar” numbers.
The problems involved in trying to reconcile lunar and solar periodicities inspired myths of conflict in which the solar-lion, the sun-god or his representative such as the Babylonian Marduk (himself a late version of Sumerian Enlil) subdued the old lunar kosmos represented by the female chaos-dragon Tiamat. The dragon was basically a water-dragon, and the lunar zodiac was symbolized as a Flood or dark watery chaos out of which the earth and its calendrical cycles were shaped. Marduk, like his analogs outside of Babylonia, symbolized the order-giving sun/light/fire principle which inaugurated the Bronze Age order by replacing the old nocturnal lunar attributes.
Early in the 20th century AD the British anthropologist G. Elliot Smith[17] (1919: p. 206) noted that the lunation cycle inspired the first calendar-making, and hence an astrological belief in “fate.” It accordingly was quite natural for lunar-order–goddesses to evolve into justice-goddesses, for their lawfulness—indeed, the rule of law itself—was associated with the predictive calendrical cycles of the starry heavens. These calendrical cycles were inexorable, and from this idea developed that of inevitable (and just) consequences, a balancing-out of one’s deeds. The Egyptian Book of the Dead, for instance, depicts Thoth, a deity with many surviving lunar characteristics, using the balance to weigh out the souls of mortals (originally of rulers) to determine their fate after death.
Native deities traditionally have been incorporated as patrons or mascots of newer pantheons, e.g., in Tibetan Buddhism with its BonpoFact CheckShould this just be “Bon”?OpenSee All Queries survivals. The neolithic lunar-goddesses were no different. As the justice-goddesses were assigned the patronage mainly of the poor and needy, their personalities came to be portrayed as more vindictive than was the sun-god’s more positive discretionary assertion of authority. Instead of initiating policies, the justice-goddesses protected the new order which had been set up by the Bronze Age solar-oriented regimes. In particular they became patrons of fair dealing with accurate weights and measures (as decreed by solar-deities, to be sure).
This imagery survives most vividly in the form of Libra holding the scales of justice. Her constellation immediately follows that of Virgo, the grain-goddess. The allusion seems to represent the Sumerian harvest, which was followed by the weighing out of grain to pay the cultivator’s debts, sharecropping rent, and, where applicable, various public fees or taxes. “Big-man” officials, creditors, and wealthy merchants maneuvered to reduce sharecroppers and debtors to poverty and servitude, often by using false measures. Patronage of fair weights and measures by Sumerian Nanshe/Inanna and other justice-goddesses protected these weaker individuals from the arrogance of wealth.
This egoistic grandiosity, which the Greeks called “hubris,” was primarily a male psychological problem, given the patriarchal character of antiquity. The goddess Nemesis became a patron of the oppressed and cheated. In this role she maintained the distinctly submissive feminine personality familiar from classical antiquity.
The shift to solar cosmologies entailed a warlike iconography. Horses replaced cattle, and the Iron Age of Zeus replaced the Bronze Age of Saturn. Especially outside of Mesopotamia and Egypt, the storm-god, representing a dangerous and disturbing element of the weather-cycle, replaced the more regular calendrical aspects of water as the prime indicator of the seasonal cycles of nature.
Ordering Principle: Make Artificially Tempered Administrative Months
The 360-day year was composed of 12 equal 30-day months. This required separating the month from the lunation cycle. It also required an extra “out-of-year” 5 1/4 days. This meant usually five extra days, sometimes a leap year of six days every four years—and a special adjustment once a century (decimalized count).
This solution to the problem became paradigmatic. It became the occasion for renewing the cosmos in general.
One way of reconciling matters was simply to not try to interpret them, but to have two disparate calendrical cycles, solar and lunar.
After all, archaic societies had numerous crop years, each depending on the planting and harvesting seasons for particular crops.
Students of astronomy have not found it easy to recognize in the zodiacal constellations an objective basis for their names or shapes. Aries, Pisces, and the other constellations really do not look like their names at all to the average observer. The two most recognizable constellations are the Big and Small Dippers, and their “official” names are of course not dippers at all, but bears (Ursa Major and Minor, the former including the Pole Star). What is “bearish” about them is mainly their northern latitude. It is an area populated distinctively with bears. In short, it is obvious that early correspondences for parts of the year (with the zodiac) or their place in the heavens (the polar constellations) are the key, not any pattern found in the stars themselves.
By dividing the ecliptic into a zodiacal path, archaic astronomers used animals as emblems of the seasons (with a few related seasonal activities such as the Virgo harvest month and Libra weighing out the harvest and payment of barley obligations).
There of course can be no such thing as an “original” zodiac, for the simple reason that each region’s seasonal characteristics were different. Each had its own times of the year associated with the rising of the waters, the spawning of fish, the harvesting of crops, the migrations of animals, and so forth, from one latitude to another. The ultimate creation of the modern zodiac seems to be a Hellenistic phenomenon, found only from about the time of Alexander the Great.
The rising and setting sun demarcated the earth’s east and west directions, sunrise and sunset, respectively. The movement of the sun between the solstices as, looking eastward, it moved from the far south in summer to the north in winter, demarcated the earth’s north–south axis. Thus, it was from the solar movements that the four directions were traced. The Four Quarters of the World corresponded directly to the year’s four seasons, and indeed, no doubt in turn reinforced the idea of “fourness” of the seasons, in contrast to possibly three seasons found in some societies.
So, our earthly directions are basically solar. And of course, because of the earth’s direction and axis of rotation, all the other stars share the rotation of the sun, moon, and planets.
The Symbolism of Star-Groupings and Constellations
In the Ice Age, the idea of a zodiac was to correlate earthly behavior with the star-groupings (literally “constellations,” from the Latin root “stella,” “stars”; also called “stellium” by astrologists).
The earthly activity concerned mainly the behavior of animals (migrating, molting, and giving birth), fish (spawning, changing their features), and plant life (sprouting and flowering in the spring, losing their leaves in the autumn).
The other mundane corollary with the seasons was much less animate: the weather. To archaic minds, more comprehensive (less category-segregating) than our modern habits, this included the behavior of physical nature in general: not only changes in the temperature, but the rains. The English word “weather” derives originally from German “Wetter,” meaning “storm”—see also “wet,” which is what one gets in a storm.
In addition to the rainstorms, there was one other key aspect of water which was important, especially in the neolithic when the planting of crops developed. This was the rising of the rivers, swollen with the melting mountain snows. It was the melting snows of the Taurus, Zagros, and other ranges that swelled the Tigris and Euphrates, and the mountains of southern Egypt (modern Sudan) that provided the waters for the Nile.
In this respect the zodiac had to do both with animals and with water. And the traditional water figure is the prototype for modern Aquarius, the water-bringer with his two jars of water—Enki to the Sumerians, Ea to the Babylonians, Thoth to the Egyptians, and so forth.
There was one other aspect of “water”: That was not annual but monthly. It was the monthly expectation of menstrual blood. This is what associated females—specifically their presumed menstrual cycle—with order. I believe that it is part of what made order-goddesses who they were. It certainly was what associated women with the moon—hence leaving the other half of the duality, the male, to be paired with the sun.[19]
The other monthly association of water of course concerns the moon’s effect on the tides. Here too we find a reason for associating women with water—with the tidal movements as well as the menstruation cycle.
In Aquarius we may recognize one of the four “original” or “seasonal” fixed signs of the modern zodiac. The others are Taurus (springtime), Leo (summer), and Scorpio (autumn, originally also signified by an eagle).
In explaining the modern zodiac it is both its lunar predecessor—the 28 mansions—and the four-seasonal “squared” zodiac that we must refer to.
What has been for about 2,500 years the solar zodiac (composed of 12 houses of 30 degrees each) began as a series of 28 lunar constellations/houses. (We know this especially from India.) These lunar star-groupings usually are called “mansions,” to distinguish them from the solar constellations/houses.
This lunar zodiac probably started with the bull, by virtue of its 28 ribs.[2] This evolved into the solar constellation Taurus.
This is not because the stars “looked” like a bull. Given the star dots, playing the “connect the dot” game does not immediately bring a bull to mind. But archaic zodiac-makers grouped these stars into the bull because of the latter animal’s particularly lunar characteristics.
It was solarized probably in 4000 BC–2000 BC, when Taurus was the sign rising on the horizon with the sun in spring.
This indicates an original attempt to reconcile the solar and lunar zodiac, when the lunar month still was ascendant or the lunisolar year still referred most communal festivals to the moon as “measurer.”
There was always a balance between the main two celestial bodies, the sun and moon. The sun for its part dominates earthly life most visibly in summertime, through its heat and light (the long day).
Speaking of the long day, note that all the Mesopotamian and Egyptian approximations were wrong. But there is always method in error, and the method here is to try to believe that there is a particular “natural” ratio between the shifting lengths of the days and nights, e.g., between a 3:2 ratio (that is, from 8 hours of night and 16 hours of daylight in the summer, to 16 hours of night and 8 hours of daylight in the winter).
Here again we find a space/time correlation: The distance from the earth’s equator (equating not only north and south, but the length of the days of the year). This space-time correlation will be a common theme.
If the moon ruled two signs—Aquarius and Taurus—the sun ruled the other two. Leo is clear: the summer sun. The sun also ruled Scorpio/the eagle, flying in the sky like an eagle. (The Egyptians found the appropriate bird to be the falcon.) Later, the image of the sun moving across the heavens depicted the sun-god “Sol” or his analogs as being driven in a chariot by a horse.
Why a horse?
First of all, he pulls a chariot. Second, we all know that around this time the horse became increasingly important as the military innovation of the Bronze Age. But the fact is that horses were quite familiar and important already in the Ice Age. In fact, there is suggestive evidence that the earliest domesticated animals were horses.
Skeletons of Ice Age horses have been found whose teeth show definite signs of chewing, apparently bridles. Furthermore, Ice Age paintings appear to show bridled horses.Missing IllustrationCan you help us find an illustration/illustrations of this?OpenSee All Queries
What is not clear is the point at which the horse’s ribs began to be counted. The human rib cage has 24 ribs, the bull has its “lunar” 28-count,[2] and the horse has 36 ribs, 18 to a side.
Certainly by the neolithic this was done, for once counting was developed, neolithic shamans seem to have “gone wild” in hoping that the new counting would open a world of correlations that somehow would “explain” the world.
The horse appears in just one sign of the zodiac, and that is a composite one: Sagittarius (which currently rules November 22–December 21) (approximately from Thanksgiving to the winter solstice).
The signs on each side of the fixed signs seem to form a complex. We have Virgo/Libra together. They probably go with Leo, for the solar New Year (linked to the crop cycle). And therefore, Scorpio/Sagittarius/Capricorn.
It may be significant that the two most “solar” fixed signs, Leo and Scorpio/eagle, are in opposition to the two “lunar” fixed signs, Aquarius and Taurus, respectively. This gives us the two contrasting hemispheres, lunar and solar (180 degrees each), and the two corresponding sexual polarities, female and male.
Jupiter: 12-year cycle—that is, cyclical return to its “original” zodiacal point
Water (Aquarius/Pisces)
Fire (Leo, also Sagittarius)
The Temporal Demarcation of Space
The first concepts of space were based on ideas of how to measure and demarcate time, above all the year. And before civilization measured earthly space, it projected spatial divisions onto the heavens. It was from the heavens that space was projected on earth.
This is why we still divide the circle into 360 degrees. The first such measurement obviously was done in the process of dividing the solar administrative year into 360 days. Each day the sun traversed 1 degree of the zodiac, each 30 days one of the 12 constellations. The 360-degree ecliptic thus was divided into 12 parts, whose stars were grouped into constellations.
What is important to recognize in analyzing spatial measurements is that the same periodicity of time applies to measures. A new foot begins every 12 inches, just as a new year begins every 12 months. Our yard of 36 inches carries forth on earth the 36(0) principle of the solar administrative year. Only later did it decay into the fathom or cubit, based on the bodily proportions of individual rulers. As this was done, the actual measurements shifted, although the conceptual standard of measurement and periodicity remained constant.
The measurement of space on earth is of course an exercise in geometry. What is important to recognize is that the measurement system of this geometry derives directly from the heavens, and specifically from measuring the calendrical movements traced out by the sun. This is why the circle has 360 degrees, and probably also why the Roman foot has 12 inches (not “10” toe-inches).
For thousands of years the main use of trigonometry was to navigate by the stars.
The second thing to recognize about the evolution of worldly geometry is that when space did begin to be measured on earth, it was not everyday mundane space “at large,” but specifically sacred space. When archaic rulers are depicted measuring and surveying, it is in “stretching the cord” to measure out the temple area. (Note that the ziggurat’s red cord-lines are still visible to excavators. See Childe[20].)
Note here also the idea of orientation. Here, the spatial idea is purely associated with the sun’s daily rising.
The major orientation is apparently facing north, so that the sun rises in the east on one’s right. The key here seems to be one of rectitude. (Left, the sunset, is associated with night and hence its analog death, hence sinister forces—the literal meaning of “left”/“sinestre.” It is with the sun that such ideas are associated at least in northern culture.)
The officiating priest, in Episcopal churches, is still called the “rector.” This may come from “righteous” (or a model of “rectitude”), appropriately a distinctive adjective of sun-gods of justice and the rulers loyal to their principles.
Another parallel showing the extent to which the conceptualization of space followed that of time is found in the practice of measuring from midpoints. The midpoint of the lunar month was the full moon—the Roman ides. Sumerians measured sacred space not to the brick wall (either their outside or inside dimensions), but to the middle of the brick. (Also, note the importance of midpoints of the year: the solstices were the midpoints of the half-year; the long-dayed summer solstice was the midpoint of the year “born” on the winter solstice.)
The word “measure” comes from the root proto-Indo-European word “mes,” “mens” for moon, from which our modern word “menstruation” also derives. It shows our paleohistory of the moon as a standard measure.
This probably was a great catalyst inspiring emphasis on the solar year’s midpoint—the summer solstice, being the longest day of the year—and also the midpoints between the two solstices, namely, the equinoxes, where days and nights are equal, on March 20 and September 23, demarcating spring and autumn respectively.
But there also is another root: and that is the idea of midpoint. This is a byproduct of measure. And it also is most visible above all in lunar measures of time (measures of moon-time). If the moon is “born” as a new moon, it reaches its peak growth and midpoint at midmonth—the full moon. Thereafter it wanes, in exactly the same length of time that it took to wax (from German “wachsen,” to grow).
By the time we find the myth of Enki in the Sumerian Bronze Age, the key to calendrical wisdom and measure had passed from the lunar to solar periodicities. The “median” from the full moon shifted to the fixed sign Aquarius.
If the year was “born” or conceived in the dead of winter, the real renewal came in springtime with the melting of the northern mountain snows which swelled the rivers.
It is above all with the movements of water that archaic calendars were concerned—and mainly the springtime thaw and rising of the rivers. Thus on Marshack’s Magdalenian bone, one of the seasonal markers is the spawning (salmon) swimming upstream.
By the time the image can be picked up on the verge of historical times in Mesopotamia and related to mythology, the chief “intellectual” of the Sumerian pantheon, Enki (“Lord or en of the earth, ki”), appears cast in the guise of Aquarius the water-bringer. On cylinder seals he is depicted as “the god with two streams.”Missing IllustrationCan you help us find the illustration/illustrations that belong here?OpenSee All Queries He typically is shown holding a vase of water, out of which two streams flow. Often fish are swimming upward (upstream).
This iconography and its associated mythology suggest that the fixed sign of Aquarius is associated with spring, and subsequently was subdivided into two signs, Aquarius and Pisces. This left Aquarius, usually designated an “air” sign, leaving Pisces as the “water” sign which closes the zodiacal year. It is usually believed that a knowledge of water and the calendar belongs to the “airy” realm of intellect and mentation. This certainly picks up the association of Enki with magic, along with his related intellectual achievements.
Significantly, the Creation myth was read at the New Year which fell in spring (the first day of the first month, Nisan, in Mesopotamia).
The inundation thus literally was the time of a new beginning. In this we see the iconography of the Flood. The year is ended and begun with a flood, the renewing flood of water. The inundation “originally” (if that word can be used with regard to cosmology) signified an inundation. Obviously, this was more important in some regions than others: in Egypt (the Nile, at the heliacal rising of Sirius), and in Mesopotamia, where it inaugurated the planting season. Later, the Flood became an icon for new beginnings and rebirth, or the repetition of a cycle.
It seems that most archaic societies incorporated directional colors into their cosmologies, but of course what cannot be done is to find “the” colors corresponding to particular directions—an Ur-cosmology is impossible, unless we believe that only a single society made a cosmos. Instead, it seems that every region made its own cosmology, that is, its own coordination of phenomena, time, and measures.
Often the south was “hot,” hence red, but might also be white. And of course, with summer (the “hot” link to the south) came greenery. The north might be blue, or dark, perhaps black. Or perhaps there were migrations of birds and animals from the north, bearing distinctive colors.
The east also was bright, for that is where the sun rose. And the west, the land of the sunset, accordingly was grouped with the north as being a land of relative darkness.
This is seen most clearly in the “original” paradigm for NSEW directionality—the zodiac. Leo in the south (summer, African), fish migrating in the spring (Aquarius: the rivers rising, with Pisces following. See Enki, the god with two streams, usually depicted with fish swimming up them.).FragmentCan you help us turn this fragment into a complete sentence?OpenSee All Queries These are on the eastern horizon of modern horoscopes (to the left, therefore facing south, just the opposite of earthly maps).
Numbers and the Zodiac
When people began to count, the zodiac took on a much more regularized character.
The transition between the lunar and solar trains of associations would seem to be Saturn. The outermost planet, it was associated with the heaviest metal, lead. Heavy was associated with slow-moving.
Saturn shared with the innermost planet the number 28—actually, the variation from 28 to 30. The lunation cycle—the days of visibility of the lunar phases—lasted 28 days. The Saturn return lasted 28 years, that is, the synodic year of Saturn, the length of time it took to pass through the zodiac and return to its original position on the 360-degree zodiacal grid.
Now the number 28 is a remarkable number, and was recognized as being such in antiquity (See Plutarch[21]).Verify CitationCan you help us check that Isis and Osiris is the right Plutarch text to cite?OpenSee All Queries On the one hand it is the sum of 1 + 2 + 3 + 4 + 5 + 6 + 7. On the other hand was factorial 7 (represented by mathematicians as 7!), representing 1 x 2 x 3 x 4 x 5 x 6 x 7 = 5,040. When this number is divided by 28 the result is 180. This is equal to half a 360-day year. And the number 18 represents half the number of ribs of a horse. In this way the number 7 is “solarized,” that is, transformed from a 28-base “lunar” number to a 360-based “solar” number.
Table 2.3
Synodic Rotations of the Planets
Moon
28 days (then, it must go farther, to catch up with where the sun has traveled during the intervening month, i.e., through one more sign, lasting another 2 days)
Mercury
116 days
Venus
584 days
Mars
780 days
Jupiter
399 days
Saturn
378 days
Why Have Regular Order in a Calendar?
The key lies in what it is that the calendar regulates.
Distribution of rations. If these are to be regularized—in daily proportions, handed out at monthly intervals—then the monthly intervals also need to be regularized. This created the great impetus for going beyond variable lunar months to solar ones. It also is the source of mythology concerning the sun-god of justice.
Calendar for amphictyonic meeting places: Each tribal faction is supposed to govern for a precisely equal period of time.
The unique “gap” provided an interval for periodically restoring order and its inner symmetries and equalities.
The predictive astronomy needed to accurately forecast the planets as omens or “indicators of destiny” formed the foundation for new solar cosmologies from Mesopotamia to Egypt and their commercial spheres.
These innovations marked the transition from neolithic to Bronze Age calendar-making, and specifically from pre-numeric calendar-counting to the world of numbers. It was in fact the calendar that provided the first great inspiration for counting and the development of archaic arithmetic and its associated geometry, and hence possibly too for the alphabet as an early calendrical-numeric notation.
Of course, the solar year also had problems requiring solutions. The number 365 1/4 does not lend itself to convenient division into equal monthly units. Even the number of days in the year must be added to once every four years, on leap year. The first transition thus was not directly to our modern calendar, but to an intermediate one composed of a “regular” 360-day year and a Saturnalia-type residual. What had been an 11-day gap in Mesopotamia was made most clearly a 5 1/4-day gap in Egypt, probably supplemented to 6 1/4 days on leap year.
What made this great transition to a solar-year calendar necessary was the public sector’s need to rationalize the calendrical distribution of rations to public-sector dependents. The Bronze Age Mesopotamians and Egyptians achieved a regularized order by replacing lunar months of variable length with standardized administrative ones of 30 days each, creating a 360-day year. This was closer to the true solar year than the 354-day lunar year, but it was still artificially off the actual solar return by 5 1/4 days. Like the lunar year, the difference had to be reconciled by special “out-of-year” time which became the occasion for periodic cosmological creation and reordering festivals.
Irregularities were set aside in the intellectual realm of Saturnalia, which became the raw material, the maelstrom of Plutonian re-creation. For the remarkable thing about earthly calendrical periodicities is that they are not precise and “clean.” They have irregularities which must be removed to distill a regular cosmos that can be administered equitably and in which rations and other periodic distributions can be made fairly. Quantification of the requisite adjustments called for the development of a sophisticated fractional mathematics. We have covered in this chapter why this quantitative numerical cosmology and its guiding principle of regularity were first developed in Mesopotamia, and how they spread to that region’s commercial periphery.
In order to measure, one must first count. And counting began with a perception of sequential patterns, especially those of the lunar month and year. Earlier we showed that the earliest time-keeping was pre-numeric. But there was an awareness of pattern, and above all of sequence—probably the zodiacal star-groupings through which the moon, sun, and planets move. The result was a pre-arithmetic order.
The word “order” derives from Latin “ordo,” meaning a line (originally of men), hence the idea of sequence, as in numerical or alphabetic order. Long before numbers were developed as quantitative abstractions, and much longer before alphabetic writing and its familiar order of letters were developed, the first regular sequence to be perceived was the calendrical ordering of the days and months. It was from this sequential numerical order that the idea of numbers as quantities seems to have evolved.
Some philologists (e.g., Shipley[22] 1984: pp. 16ff.) derive the Latin term “ordos” from Greek “arthron,” meaning “joint” (whence the word “arthritis”), the same root as for “art,” “arrangement,” “articulate,” and “arithmetic.” This idea of joining or fitting is related to that of “ligature” (“connection”) and “religion” (from Latin “ligare,” “to bind”) in that both have the meaning “to connect.”
In time the idea of sequential order came to be associated with that of social rank (literally as in the rings or rungs of a ladder), and hence of subordination: A superior gives orders in a chain of command. The resulting “law and order” produces a properly aligned society, divided vertically into hierarchies based on status or wealth (especially with regard to supporting one’s military rank) and horizontally into tribes or related demographic fractions. Calendar-making, social ranking, public measures, and laws thus form part of a broad archaic complex.
Sumerian Enki, like his Egyptian counterpart Thoth, is called “the measurer.” We might translate it, the “director,” because he makes things straight, that is, “direct.” The word “direct” in turn derives from right, alignment along the “correct” course.
In these respects calendrical time was “spatialized,” culminating in mandala-type figures. The directionality of time was translated not only into spatial relations but to moral functions as well as the paired duality right and left, evolved into that of right and wrong. The latter is ultimately a problem of orientation to the sun.
The Autonomous Development of Mathematics and Arithmetic
If it was the calendar that inspired the earliest development of numbers, the flowering of numerical thought in its own right, abstracted from its original calendrical matrix, became in turn a tool to further astronomical and calendrical knowledge. Indeed, mathematics had to develop autonomously before correlations could be found among the calendrical cycles of the sun, moon, and planets, e.g., Saturn’s “lunar” 28- to 30-year cycle and Jupiter’s “solar” 12-year cycle. To quantify these numerical resemblances thus took on a life of their own.
While astronomy was shaping these numerical gamuts, the idea of numerical regularity in turn shaped the conceptualization of time and its major periodicities. By the Bronze Age the calendar was itself modified to conform to the regularity of number and measure. This is why months were standardized into 30-day units. Numeration, originally the intellectual offspring of calendar-keeping, ended up becoming its master by creating the artificial 360-day administrative year. This innovation went hand in hand with the transition from lunar to solar administrative calendars, and associated the new solar-deities inextricably with the principle of regularity.
The reason for 360 rather than 365 1/4 ultimately had to do with the development of arithmetic measures, originally by the public sector to distribute rations to its dependent workforce. The convenient fractional divisibility of the number 360 was only one aspect of this remarkable number’s inherent numerology.
So revolutionary was this great calendrical transition and its cosmological associations that it was elaborated into a cosmology highlighted by sun-gods of justice.
And as an extension was made what originally was a calendrical numerical base, the solar-deities vanquishing the calendrical chaos of lunar periodicities, elaborated into a full-fledged sun-gods of justice.
As solar months replaced lunar ones, the idea of order was associated with male rulers, not with female rhythms. Sun-gods of order and justice sponsored standardized months, vanquishing the calendrical chaos of lunar periodicities. The new solar-deities were given the character of sponsors of equity and order reflecting the calendrical regularity which solar calendars introduced.
The preceding chapter has described how lunisolar years of varying length were replaced in Mesopotamia, Egypt, and their culture areas by administrative calendars that rounded off the year to 360 days. This latter number was conveniently divisible into 12 equal 30-day months, a precondition for distributing on a regular basis standardized rations within the temple and palace estates. In fact, 360 was the original round number, representing the origin of the 360-degree circle.
The number 360 was not only round (as in a 360-degree circle) but dodecahedral. The dodecahedron was a remarkable geometric shape, which seems originally to have been called a “12-faced sphere.” Each of its 12 faces was a pentagon. (And significantly, 12 x 5 = 60.) It had 20 vertices, and 360 lines (12 x 30). It thus was the archaic “calendrical solid” par excellence, a physical analog to the 360-day administrative year which displaced the lunisolar festival calendar throughout the Bronze Age Near East.
In time the “first order” took on the connotation of “best” (Greek “aristos”), and also “arete,” “virtue,” preserving the essential idea of order. The line is usually straight (Latin and Greek “ortho”), hence the ideal of straight rather than crooked order and judgments.
Central to the archaic idea of preserving social order, and also deriving from Greek “arthron” (by dropping the initial a) are “rituals” (“rites”). These rituals periodically restored order once it got out of balance as obligations accumulated and various forms of economic inequality emerged as wedges threatening to polarize society.
And the most important thing being counted was time. To the extent that lengths, weights, and measures were elaborated, they reflected calendrical proportions—i.e., to compute astronomical space (the stars and the path of the planets), interest (at key calendrical times), and even temple distances and measures which reflected the calendrical kosmos on earth. This explains why there are 36 inches in a yard—not because of actual finger/fathom ratios of particular English rulers, but because 36 (x 10 = 360) is a solar measure.
Numbers as a Key to the Organization of Knowledge
The preceding text has described how calendrically based measures and weights were needed to facilitate the regular monthly distribution of rations and the administration of bulk commodity flows. Beyond this pragmatic virtue, archaic scribes discovered that the number 360 is remarkable in its own right. It is found in the “highest” natural solid, the dodecahedron with its 12 faces and 30 vertices. Such cosmological geometry and numerical convenience also played a major role in Egypt and Greece even though their weights and measures were decimalized. But it was primarily in Mesopotamia that they did so in such a way as to establish common denominators between the calendar, weights and measures, music and geometry, omen-taking, and even prices and interest rates. The result was an elaboration of arithmetic proportions into what might be called cosmological numerology, out of which the Kabbalah was a late development as numbers took on an autonomous life of their own.
Long Developments: Increasing Abstraction and Generality of Number; Declining Specificity
The classical Greeks (especially the Pythagoreans), like the Hebrew Kabbalists and early Christian Gnostics, correlated all things with reference to number. A natural connection was suspected to exist among phenomena having the same common denominator or gamut (composed of 28s, 14s or 7s, or 12s or 10s).
What today would be dismissed as numerological coincidence seemed to archaic cosmos-builders to contain a message reflecting natural order. For instance, the shift from lunar months of approximately 28 days of visibility to a 360-day year composed of regular 30-day months was a seemingly natural progression that could be comprehended in a fortuitous numerological coincidence: The first seven digits—1 + 2 + 3 + 4 + 5 + 6 + 7—happen to add up to 28. This inspired ideas of an inherent relationship between 7 and 28 in lunar-based cultures, no doubt playing a role in determining the seven-day week rather than the four-, five-, or six-day weeks as found throughout the world in communities that did not develop the mathematical system found in the archaic Near East.
What must have struck the archaic cosmological mind seeking numerical correspondences as a hint to the likely essence of nature—and above all to the naturalness of the 360-day year—was the fact that the sum of the first eight digits—that is, the above-cited 28 + 8—is 36. Lacking a zero, archaic mathematicians viewed this number 36 as a species of 360. If 9 is added, the sum increases to 45, which happens to be 1/8 of the 360-day year.
The number 36 is a remarkable number for other reasons. As the square of 6 it is the product of (1 + 2 + 3) times (1 x 2 x 3). The factorial product of 6—or as mathematicians write it, 6!, signifying 6 x 5 x 4 x 3 x 2 x 1—is 720, which happens to be the number of days and nights in the 360-day administrative year.
To a kosmos-builder eager to find some hint in nature as to how to fashion life on earth, these numerological correspondences made the 360-day year seem natural and divinely dictated.
The Dodecahedron and Its Four Related ‘Regular Solids’
Proceeding beyond the calendrical world into that of pure geometry stands a central image for The Creation of Order, integrating calendrical numbers and cosmological geometry into what became a major social template: the dodecahedron. While the 360-degree year might be somewhat artificial as a calendrical principle, the dodecahedron actually was found in nature as one of the five so-called Platonic solids.
The dodecahedron goes together with the icosahedron as a strikingly calendrical solid.Missing ChartOriginally, there was an author’s note here to “explain in chart from GEOMETRY paperback”—can you help?OpenSee All Queries
But to discover the remarkable numerical characteristics and calendrical parallels, counting was necessary. Indeed, many phenomena had to be correlated, to group together objects or constructs that shared similar counts. Discovery of the dodecahedron seemed to link the archaic calendrical, numerical, and geometrical kosmoi together.
The development of standardized measures of volume, length, and weight of course required numerical computation, above all the division of the basic units into fractional units on a calendrical basis, e.g., the 60ths used by Mesopotamia and Egypt, and the 12ths used by the Romans. Only the decimalized 10ths used by later Egypt and classical Greece broke from the calendar to become more abstractly numerical concepts, culminating in our modern decimal notation.
It seems that the first number systems were developed to count the days of the month, and subsequently to forecast lunar, solar, and other astronomical periodicities. The objective was to schedule festivals, and also no doubt to forecast the seasons and their weather. Popular expectations were infused with astrological associations to bolster the idea that the ruler was in accordance with heavenly law. In these prognostications the outermost planet, Saturn/Nabu, the “planet of justice,”Fact CheckCan you help us check that this is still the current research?OpenSee All Queries was of great importance. Its period of revolution around the sun took 29 to 30 years—the same number in years that it took the moon to revolve around the earth in days each month.[23] To find such parallelisms, counting was necessary. And numbers in their turn began to take on a life of their own. Geometry likewise was calendrical. The 360-degree circle derives from the Bronze Age administrative calendar and zodiac.
Measures presuppose counting, and this seems to have been inspired in the first instance by measuring time—first the lunation cycle, and then the year. The gamut of numbers—that is, whether they were based on 10s, 12s, 28s, or 60s—depended on just what was being counted. Our modern decimal system was by no means obvious as a numerical base, for there are not many calendrical periodicities or groups of things that “naturally” group themselves into 10s.
No doubt the most important such class comprised one’s fingers and toes—but in this case they served as counters, not as the things being counted. And the hand also could be used to count by 12s (the 12 knuckles on the four fingers), 14s (including the knuckles on the thumbs), or even 60s (counting to 12 on the right hand, multiplying it by the five fingers on the left hand).
For that matter, there was no reason to limit counting only to the hands, or even to the hands and toes, prior to the decision to create a decimal system. Biersack[24] (1982) and Ifrah[25] (1987) described the body counting familiar to anthropologists for tribes from New Guinea and its neighboring islands based on lunar counts of 28.
Solar Time: 360 and 12 as Key Numbers; Annual Numbers Are Solar; the Lunation Numeration System Was Changed From a 28-Base to a 30-Base
Having discussed the role played by the human body as a medium for counting, I will elaborate the pursuit of numerical relations in and of themselves by various cosmological figures/shapes “Pythagorean” triangles (going back to the late neolithic or chalcolithic) and the five regular or “Platonic” solids such as the pyramid, cube, and dodecahedron, found a millennium before Plato lived—culminating in Kabbalistic relations.
Counting initially was based on the lunar month. Tribes in Oceania still have counting systems based on the lunar number 28. The Romans developed a duodecimal (12-based) system, reflecting the number of months in the average year. From this derived the modern/Roman troy ounce containing 12 ounces, and also the Roman rate of interest—one 12th (8 1/3 percent) per annum. The Egyptians and Greeks adopted a less calendrically grounded decimal system.
The Sumerian sexagesimal (60-based) system emerged above all others throughout the Near East, thanks to the fact that the number 60 could be divided conveniently into 30, 20, 15, 12, 10, 6, 5, 4, 3, and 2. To be sure, a calendar based on these numbers had to be somewhat artificial, for neither the 354-day lunar year nor the 365 1/4-day solar year was divisible by 30, 12, or any other number. The choice of the 360-day administrative year was thus a compromise—and one which could be rounded out by being supplemented by an extra 5- or 6-day New Year interregnum.
Numerical series generated higher sums by cumulative addition of all their subordinates. For instance, the numbers 1 + 2 + 3 + 4 + 5 + 6 + 7 added up to 28—the number of days in the lunar month. This linkage between 7 and 28 bolstered the lunar month’s division into four weeks (plus, it seems, an out-of-time day on the new moon). Addition of the next number in this series, 8, made 36, one 10th of the 360-day year; and 9 made 45, or one eighth of 360.
In all these applications 360 served as the original round number, representing the origin of our modern 360-degree circle. It also came to be viewed as a dodecahedral number, referring to the dodecahedron. An early name for this remarkable geometric shape was a “12-faced sphere,” referring to its 12 pentagonal faces. Its 20 vertices and 360 lines made it a natural analog to the 360-day administrative calendar. It thus may be thought of as the archaic calendrical shape par excellence.
Quite apart from the fact that lunar months vary in length from 28 to 30 days, the problem with generalizing lunar-based measures of 7s and 14s into a higher arithmetic is that 7 a prime number, that is, not divisible; 14 is divisible only by 2 and 7. Also awkward for forming the basis of fractional weights and measures is the number 10, for it is not divisible by 3, 4, or 6.
For such purposes the number 12 is much more convenient. It happens also to be an astronomical number, representing the usual number of months in a year. It could be used to count the days of the month in a 360-day calendar if the year were divided into 15 24-day months, presumably composed of four six-day weeks. But this is not what the Sumerians did. They divided their year into 12 30-day months. What was needed in any system of regular fractional computations was a large “even” number: 12 or 24, 30, or 60, or perhaps even 18 or 36. The numbers 24, 36, and 60 have the advantage of being divisible by 12, while the number 60 is also divisible by 5 and 10, thereby incorporating the decimal system.
This factor of arithmetic convenience probably was responsible for the Sumerians adopting the sexagesimal system. They recast the calendar into an artificial 360-day year divided into standardized months whose length was chosen primarily for reasons of arithmetic convenience. The number system, originally developed as a byproduct of calendar-keeping, thus ended up becoming the master of calendrical time.
The 360-day administrative year was reconciled with the 365 1/4-day astronomical year by adding five (occasionally six) extra days as an interregnum. But the 30-day months (like the Aztec 20-day months)Citation NeededCitation needed.OpenSee All Queries lost their traditional connection with the 29 1/2-day lunation cycle. This is what made the new public administrative calendars of Mesopotamia and Egypt solar rather than lunar.
Our decimal system based on the numbers 10, 100, or their multiples is not well-suited to perform found divisions by 12s, 6s, or other such calendrical fractions. To multiply (or divide) by 60, the Sumerians needed merely to add (or subtract) their equivalent of a zero, namely, the “place position” if not yet a formal decimal point. Division by 30 could be done by the equivalent of shifting the place notation to the left and doubling the result.
Sumer’s sexagesimal system was further simplified by setting the value of a bushel (gur) of barley at 1 shekel of silver. This enabled accounts to be kept interchangeably in either silver or barley. Prices for the major commodities likewise were set in round multiples of silver and barley. This enabled bulk multiplication and division to be done with relative ease, so that the rations needed to support a number of workers for a month in digging a given length of canal, building a dike, making bricks, or weaving textiles could be computed without involving awkward fractions or irrational numbers such as the infinite 0.33333 for a third, or 0.1666…7 for a sixth as in the decimal notation.
Archaic words for festivals reflected the fact that calendars were above all schedules of feasts, involving the entire community in the rhythms of nature and social renewal. These festive gatherings were conceived as being analogous to other forms of coming together, namely the roots “syn” and “sym.” Gernet[26] (1981: p. 46 citing Gruppe[27] 1906: pp. 163, 457) found a bundle of meanings associated with Greek synodes, ranging from solar conjunctions with the moon to marriages and assemblies. “From very early on, the representations of the celestial world were associated with this fundamental notion” of sacred union. The new moon occurs when the moon aligns with the sun and thus has its dark side to the earth. It was at these times that archaic communities typically convened, as being a symbolically propitious time for all types of coming together, from group meetings to marriages, and intergroup compacts.
It is in the Bronze Age that we find for the first time male deities overshadowing the goddesses, who were subordinated and even diabolized. Most of these goddesses were linked to the old lunar calendars, and hence retained an association with disorder. Their future task often was to negate disorder, in their manifestation as punishers of crookedness and irregularity. Shedding the traces of the chaos-dragon Tiamat, they became the guardians of equitable worldly order. Tiamat became the dragon subdued by the sun-god Marduk, signifying the solar calendar which replaced the lunar disorder. But once she had been suitably vanquished, she could be rehabilitated within the new solarized order.
What happened to the old lunar-deities? They were diabolized by the post-astral religions of personal gods and national power, first by Judaism and then by Christianity. Cyrus Gordon[28] (1988: p. 293)Verify CitationCan you help us double-check the publication in the footnote is the correct one?OpenSee All Queries has traced how the Old Testament devil—“the Satan” (always with the definite article, not his actual name)—seems to have been a celestial-deity as late as the mid-third millennium BC. Tablets excavated in the north Syrian site of Ebla dating from c. 2400 BC describe an astral-deity HabhabySpelling of TermCan you help us verify (and check the spelling of) both versions of the name (Habhaby and Haby)?OpenSee All Queries as having “the horns of the moon and the tail(s) of the sun.” A millennium later in Late Bronze Ugarit (on the northern Phoenician shore) this same deity, now rendered as Haby,Spelling of TermCan you help us verify/spelling check both versions of the name (Habhaby and Haby)?OpenSee All Queries is described as having “‘horns and a tail,’ anticipating the familiar iconography of Satan.” By the time of the Old Testament, Isaiah (xxvi 20) admonishes the Israelites to “take cover behind locked doors until the menace of Haby passes.” Habakkuk iii.4 refers to him as Hebyon, identified by his horns which connote both light and strength. (These references are lost in the usual English translations of the Bible, which reads as if the Lord himself comes as Haby.)
Evidently the idea was to discourage worship of all gods save Jehovah, whose major rivals were the old celestial sky-gods, who were diabolized. In any case these are the only two biblical passages in which the devil was cited by name. Gordon concluded that “What may have happened is that his name was so feared that it was avoided. haśśātān ‘The Satan’ and o diabolos ‘The Devil’ both have the definite article, strongly suggesting that ‘The Satan’ and ‘The Devil’ are epithets of Habhaby/Haby, that gained currency to avoid the real and terrifying name of the demon.”[29]
What is important for the discussion at hand is the devil’s originally astral character. By the first millennium BC the idea of divinity had become predominantly theocratic, dropping its calendrical and related cosmological characteristics. Whether male as in the case of Haby, or female as in Tiamat and the host of lunar-goddesses, these celestial-deities—originally of a lunar character—were transformed into devils, first by the solarized Mesopotamian Bronze Age order and then by the civil and imperial religions of the first millennium.[30]
Key Concepts
This glossary of key concepts will help readers who are new to the subject of archaic human history.
Keywords: Our words “mental” and “measure” derive from the root-word for moon, civilization’s first measurer. But after the shift to solar calendars the words “lunatic” and “moonstruck” are more characteristic, reflecting the irregularity of lunar months.Key Concept Missing in Chapter BodyThis Key Concept is not discussed in this chapter’s body. Can you help us add it?OpenSee All Queries
Key image: The zodiac, composed of animals and other phenomena that characterize each season, correlates seasonal earthly behavior with the stars rising over the eastern horizon in the corresponding season.
Lunar symbol: The calend (new moon), whose observation marked the birth of each month. The days of the month were counted by the dragon-zodiac of lunar mansions, probably starting with the bull (Taurus), a lunar symbol by virtue of its 28 ribs.[2]
Solar symbols: The lion (Leo) of summer vanquishing the lunar bull in the lion-bull combat. The eagle flying across the sky like the sun (opposite Taurus in the zodiac), and ultimately the sun-god of justice driving across the sky in his horse-drawn chariot. The horse was a solar symbol by virtue of its 36 ribs.
Principle of regularity: The hitherto lunar zodiac composed of 28 mansions was “solarized” into 12 houses dividing the 360-day year into standardized 30-day months.
Periodic renewal ceremony: Calendars were regularized and the cosmos renewed at the New Year festival, at the solar solstice, or at a major harvest when payment of debts, contributions, etc., were due.
Integration with other dimensions of the archaic kosmos: Weights and measures were developed to distribute rations on a regular calendrical basis every 30 days, hence Mesopotamia’s sexagesimal (60-based) arithmetic. Tribal divisions rotated administration of the amphictyonic or ritual center on a regular calendrical basis. The solar calendar’s regularities became a metaphor for the equitable principles of administrative justice in general.
Public character: Rulers, and in time a specialized priesthood, became calendar-keepers scheduling public festivals and other social activities. In ancient civilizations astronomy and astrology typically were a confidential royal monopoly inasmuch as “private” persons might use them to foretell government policy.
Ultimate dissolution: At the end of the Roman Republic, Julius Caesar began the year with a new moon, trying to reconcile the irreconcilable lunar and solar calendars. This delayed January 1 10 days behind the December 21 winter solstice.Fact CheckIs the year actually begun 11 days late, not 10 days late?OpenSee All Queries (Later, Islam’s retrogression to a lunar cycle abandoned all solar moorings.)Key Concept Missing in Chapter BodyThis Key Concept is insufficiently discussed in this chapter’s body. Can you help us add it?OpenSee All Queries
Charles Warren, Palestine Exploration Fund Quarterly (April, June, October 1899).
↑Alexander Marshack, The Roots of Civilization (New York: 1972).
↑ 2.02.12.22.32.42.52.6Observatory Editor’s Note: “Bull” or “cow” in The Creation of Order generally refers to bison, which have 28 ribs. (Modern-day cows in the U.S. have 26 ribs.)
↑Alexander Marshack, The Roots of Civilization (New York: 1972), pp. 32ff.
↑Alexander Marshack, The Roots of Civilization (New York: 1972).
↑Not all these elements and aspects and pairings and associations are found in any single zodiac. There is some degree of synthesis in my exposition here. But it exemplifies the underlying spirit of archaic kosmos-building.
↑Gordon noted (1988, pp. 293–294) that “It is a common feature in the history of religions that the deities of the older system are debased into demons in the new system.” Thus I-li-lu, “the Father of the Gods”’ in the Ebla tablets, sunk to a minor rank in Ugarit and ended up meaning in Hebrew “a non-god, lifeless idol… (’elîl, plural ’elîlîm).”
