Category Archives: Uncategorized
Greek mathematics was concerned with understanding underlying rules for numerical relationships and concentrated on geometric proofs. Math became a component of philosophy, a pursuit of the leisure class, and a way of discerning the laws of the gods. Mesopotamian practical applied math could not be disposed of because cities now required it to function, but the philosophical elite would not stoop to learn it.
The Greeks liked geometric proofs because they are tangible, irrefutably a part of the real world. There was a fear that if mathematics diverged from the concrete world it would become fantasy, and that the pursuit of this fantasy math would be a rejection of truth by the learned man.
The fear of deviating from truth meant that there were four important concepts, integral to the way we see the world today, that people were unable to accept in classical times.
1) Algebraic proofs (if you can’t draw it, is it real?)
2) Zero as a number, not just a placeholder (how do you define something that by definition does not exist?)
3) Irrational numbers (why would the gods create puzzles that have no solution?)
4) Negative numbers (again, they don’t exist)
Although mathematically speaking the Greeks had their limits, these obstacles were not germane to Greek philosophy. The point where mathematics moves into abstraction is a point of crisis for any society. There was a Hindu mathematician in the seventh century, Brahmagupta, who proposed using negative numbers for accounting purposes without finding many takers. How can you do accounting without negative numbers? It boggles the mind. Yet it was once hard for people to take numbers, the most irrefutable link to objective truth, into the world of make-believe.
Numerical symbolism was an abstraction the ancients had no problem with, or maybe it was a problem that was resolved in prehistory. Using a word to represent a number is itself a construct, as is all written language, mathematical or otherwise. Numerical symbolism as a predictive device, which was widely used, is complex, difficult and not entirely reliable. It was therefore not difficulty, complexity, or uncertainty that early mathematicians bulked at: it was the idea of consciously embracing something intrinsically unreal (negative numbers) or intrinsically imprecise (irrational numbers).
Note: This is the first of a four part series
I must admit that I approach this subject with trepidation. I’m concerned that some of my readers may be those for whom the keys to the numerical kingdoms have been denied, those who have bumped against that iron door and convinced themselves that beyond lies a sterile uninteresting yet unfathomable realm, filled with errors and yielding nothing of significance. I feel like I should sing a song and do a dance, maybe bring out a colorful Muppet cast for a chorus routine brought to you by the number nine, all to convince you that numbers have something relevant to say, something even you can understand.
Women have long been shut out of mathematical worlds. I can identify nine of these worlds, which should be intersecting but which are in some cases hermetically sealed. These nine worlds are those of arithmetical computation (including accounting and finance), applied mathematics (engineering, statistics, economics, physics), number theory, statistics, music, puzzles or riddles, philosophy, geometry, and symbolism. I do not say that there are only nine worlds; I like the number nine because it is the number for human gestation.
What makes nine the number for human gestation? That comes from a basic division of time based on the moon cycle, which at one time ruled the menstrual cycle. The first mathematicians were women, inventing numerical systems for calculating their menstrual cycles and the course of their pregnancies. Mathematics is, literally, in the blood.
The link to the webinar Mystick Path of the Deer has been corrected. Here it is again:
This webinar promises to answer many of your questions, including why I’m misspelling the word “mystick.”
I believe in general that a symbol, like a word, should have a clear definition, that it should mean something, but X is often the symbol for the unknown. In algebra, for example, it is used as the symbol for the unknown quantity and does not necessarily have a precise definition, which is not the same thing as saying it is undefined. It may be a real number, for instance, or a whole number, or a prime number less than 100. Likewise X in a magical equation can stand for a specific unknown – perhaps a manuscript that is sought whose title is unknown. In detective fiction, X often stands for an unknown person, either the person who commits the crime or some other enactor of an anonymous deed. You would not be using X in your magic to summon a criminal (at least I hope not), but X could stand for an unknown donor or other helper.
The X shaped rune gyfu means “A sign of hospitality and friendship, of joy and celebration.”* It may represent an offering to the gods or some other kind of gift. This interpretation of gyfu relates to another important intimation of the symbol X: as a mark on a map indicating the location of buried treasure. X can mean treasure or it can refer to the place that is sought, be it literal or metaphorical.
*D. Jason Cooper, Using the Runes. (Wellingborough, UK: The Aquarian Press), 1986.
Biblical sacrifice, the idea of which we have become more or less accustomed to, is basically a negative gesture: it deprives us – and we willingly accept this deprivation – of something we reserve for God without his having a need or use for it. In Mesopotamia, on the other hand, sacrifice, offerings to the gods, were positive actions: what was given to them, they needed.
In order to understand the role of food in religious life, it is also necessary to move out of contemporary constructs about food. We think of food as fuel or sustenance, we think of food as sensory enjoyment, we think of certain foods as symbolic, and we think of shared food as a means of social cohesion. For Mesopotamians food was all of these things, but it was something more. Food was imbued with certain powers, particularly the power of life. The various prayers and ceremonies involved in the harvesting, milling, butchering, and preparing of food enhanced these powers and added new ones. Recall that when Inanna is trapped in the underworld unable to save herself, the god Enki sends his representatives down to revive her with the “bread of life” and “water of life.” Recall also from the previous post that Ereshkigal participated in an important ceremony not by being present but by partaking in the food that was served. Throughout Sumerian and Akkadian myth the idea is implied but not specifically spelled out that food is a means of disseminating power.Millers, farmers, herders, and others donated the basic ingredients to meet the voracious appetites of the gods. There were specifications about how animals destined for the temple should be raised and fed. All of the meat was high quality and some of it was exceptional. Special prayers were spoken when butchering temple animals or when milling grain that would be used for temple bread. Though high quality ingredients were used in food preparation, and meals were served on the finest platters and vessels by priests or priestesses dressed in immaculate clothing, the recipes themselves were basic. Meat was grilled or boiled rather than simmered in the elaborate sauces that characterized Mesopotamian cooking from the empire stage onward, at least for people with means. The gods were believed to be traditionalists in their culinary tastes, preferring food as it was prepared in prehistory.What finally became of all that food? The accounting involved in meeting the meal specifications for the gods must have been daunting in itself. In fact, we have learned much about the feeding of the gods by making inferences from temple accounting records, which are extensive. The food could not have been left outside the city once the gods had gorged themselves without creating a huge problem with lions, hyenas, and other scavengers. Nor could this much food have been consumed by the what must have been a large temple staff. Though Mesopotamian cultures in historic times, and even in the archaeological records of prehistory, were highly class stratified, this food would not have been destined for the tables of aristocrats. As mentioned a few posts back, rich men employed an extensive kitchen staff to prepare elaborate meals catering to their sophisticated tastes. They would not have eaten such simple food except when participating in religious rites. Unfortunately the temple accountants did not see a need to document how the food was disbursed once the gods had eaten their share. Probably it was given away.SourceBottero, Jean. The Oldest Cuisine in the World: Cooking in Mesopotamia. Chicago: University of Chicago Press, 2004.
until the end, enjoy your life,spend it in happiness, not despair.Savor your food, make each of your daysa delight, bathe and anoint yourself,wear bright clothes that are sparkling clean,let music and dancing fill your house,love the child who holds you by the hand,and give your wife pleasure in your embrace.That is the best way for a man to live.
The scene sets out starkly the choice humans face of pursuing grand ambitions which may bring frustration and unfulfillment versus the abandonment of dreams for temporal pleasures.SourcesBlack, Jeremy and Anthony Green. Gods, Demons and Symbols of Ancient Mesopotamia. Austin, TX: University of Texas Press, 1992.Bottero, Jean.The Oldest Cuisine in the World: Cooking in Mesopotamia, trans. Teresa Lavender Fagan. Chicago: University of Chicago Press, 2004.Mitchell, Stephen.Gilgamesh: A new English version. New York: Free Press, 2004.