Blog #3: Foundations of modern civilization - Sumer?

Initial development of agriculture in the Fertile Crescent area of the Middle East is often quoted as the roots of our modern day culture. We are also taught in school that the earliest forms of writings ever employed by humans come from the cuneiform system of Sumer who lived in the area. What we are not necessarily exposed to is that the ancient Sumerians invented many other present day cultural concepts that are still seen in modern day Western world, such as schools, libraries, legal writings and importantly philosophy and our worldview Kramer (1956). To properly understand our present day culture and worldview, it is critical to recognize the Sumerian culture as the unique creative and innovating impulse that laid the foundations for our modern day culture.

Cuneiform tablet showing the glyph “An” for sky or heaven in the upper left hand corner.

The Sumerians were a settled, non-nomadic people who survived on agriculture and lived in temple-centered city-states on the banks of the Tigris and Euphrates Rivers. The culture exhibited strong links between social and religious responsibilities. It is likely that the culture existed at least 5,000 years BCE – over 7,000 years ago (http://en.wikipedia.org/wiki/Sumer).

While the Sumerians are often perceived as just one of several influential middle-eastern cultures that make up our cultural evolutionary line along with the later Akkadians and the better-known Babylonians, they deserve our special attention as creative innovators who initiated the cultural evolution that continues today in our present day western world.

Identifying Sumer’s real influence on our modern Western culture is somewhat difficult due to the implementations and modifications of their creations by the intervening subsequent cultures of Akkadian and Babylonian.

There existed strong cultural interactions between the Sumer and Akkad cultures. Over the period of the late 3rd and early 2nd millennium BCE, the Sumerian culture both coexisted and was conquered by the Akkadians. There is evidence for bilingualism in the Sumer and Akkad societies (http://en.wikipedia.org/wiki/Sumerian_language). While the Akkadian spoken language generally became dominant into the 2nd millennium, the Sumerian persisted as a sacred, ceremonial, literal and scientific spoken language into the 1st millennium (http://en.wikipedia.org/wiki/Sumer#language_and_writing).

Already mentioned is the cuneiform writing system that was first developed by the Sumerians. The later Akkadians and Babylonians employed the same cuneiform method of writing.

The same myths and cultural stories are evidenced in all three cultures Sumer, Akkad and Babylon. Although the story of the struggles and successes of the hero in the Epic of Gilgamesh is best known in a single comprehensive Babylonian writing, it originated much earlier in the literature of Sumer in several stories such as “Gilgamesh and the Bull of Heaven” and “Gilgamesh and Humbaba”: http://etcsl.orinst.ox.ac.uk/cgi-bin/etcsl.cgi?text=c.1.8.1*#

While we trace law codes back to the well-known Babylonian Hammurabi’s Code, they truly originated with the Sumerians. Few of us can name the Sumerian king Urukagina for which there is evidence of his legal code of 600 years before the Babylonian work.

While the extensive interactions between Sumer, Akkad and Babylon tempt one to mash the Sumerian culture into a single cultural concept covering 3,500 years of Middle East history from the peak of Sumerian culture through the Akkadians and Babylonians of the 2nd millennium BCE, it is important to recognize the large differences amongst the three. Sumer pre-dates the Akkadians by at least 1,000 years and the Babylonians by at least 2,000 years. Sumerians were agriculturalists who lived primarily through farming. The Semitic cultures of the region such as Akkadian and Babylonian were primarily nomadic peoples who survived by moving around with their herds of sheep and goats. The difference in languages between Sumer and Akkad required bilingualism in their interactions. Mitchell (2004) highlights the extent of their language differences by stating that  “Sumerian is a non-Semitic language unrelated to any other that we know, and is as distant from Akkadian as Chinese is from English.”

It is fortunate for us that original Sumerian writings recorded on preserved clay tablets allow us to explore their culture in great detail. Clay tablets with cuneiform writing have been dated to circa 3,300 BCE (http://etcsl.orinst.ox.ac.uk/edition2/cuneiformwriting.php). The oldest snippets of Sumerian writing appear as word lists intended for study and practice circa 3,000 BCE (Kramer 1956, page 3). Full historical and literature writings start circa 2,600 BCE.

The Electronic Text Corpus of Sumerian Literature (http://etcsl.orinst.ox.ac.uk) provides transcriptions for the various Sumerian literary texts. The site deals with over 400 compositions from the late 3rd and early 2nd millennium BCE. Within the texts provided, there are many themes that modern day readers will find familiar.  The original World creation theme from the Sumerian culture is captured in the story “Gilgamesh, Enkidu, and the Netherworld” (http://etcsl.orinst.ox.ac.uk/cgi-bin/etcsl.cgi?text=t.1.8.1.4#). Here we see the first recording of the separation of the heavens from the earth from the netherworld.  In regards to the netherworld, the Sumerians represent it an existence parallel to our regular existence into which beings can journey (“Inanna’s Descent to the Netherworld” - http://etcsl.orinst.ox.ac.uk/cgi-bin/etcsl.cgi?text=t.1.4.1). The travel and/or existence of beings in the netherworld is similar to what is encountered in the Egyptian concept of the Duat and has some similarities with the much later Christian concept of Hell. The story of the great flood, including the ultimate saving of humans, is captured in “The Flood Story” (http://etcsl.orinst.ox.ac.uk/cgi-bin/etcsl.cgi?text=t.1.7.4#).

Kramer (1956) presents at least 39 cultural aspects of civilization that were originated by the Sumerians and can still be found in our present day Western society:

• Education
• Schooldays
• Juvenile Delinquency
• International Affairs
• Bicameral Congress
• Civil War historian
• Social Reform
• Law Codes
• Justice and Legal Precedent
• Pharmacopoeia
• Farmer’s Almanac
• Horticulture
• Man’s first cosmogony and cosmology
• Moral ideals
• “Job”
• Proverbs
• Aesopica – animal fables
• Literary debates
• “Paradise”
• “The Flood”
• Resurrection
• Dragon slaying
• Literary borrowing
• Epic literature
• Love Song
• Library catalogue
• “Golden Age”
• “Sick” Society
• Liturgical Laments
• “Ideal King” – Messiah
• Long-distance champion
• Poetry
• Sex Symbolism
• Weeping Goddesses – Mater Dolorosa
• Lullaby
• Ideal Mother
• Funeral Chants
• Labor’s first victory
• Aquarium. 

Although separated by 6000 years, the links between our modern world and the developments of Sumer are easy to see and should be given more attention by those interested in our cultural evolution.

 References:

Black, J.A., Cunningham, G., Ebeling, J., Flückiger-Hawker, E., Robson, E., Taylor, J., and Zólyomi, G., The Electronic Text Corpus of Sumerian Literature (http://etcsl.orinst.ox.ac.uk/) Oxford 1998–2006.

Kramer, S.N., 1956. History Begins at Sumer: Thirty-Nine Firsts in Man's Recorded History. University of Pennsylvania Press.

Mitchell, S. 2004. Gilgamesh: A New English Version. New York: Free Press.

Blog #2: WHAT DO YOU KNOW ABOUT EGYPTIAN MATHEMATICS? THEY WERE DIFFERENT, MAYBE THEY'RE BETTER?

Old Kingdom Egyptian mathematics was quite different from our present day view of mathematics (https://en.wikipedia.org/wiki/Ancient_Egyptian_mathematics). They used only positive numbers and used only unit fractions (e.g. 1/n). Egyptians pre-1740 BCE, like the later per-Hellenistic Greeks and Romans, had no “zero” character (https://en.wikipedia.org/wiki/Egyptian_numerals#Zero_and_negative_numbers). For these, and other reasons, the Egyptian system of numbers is often seen as inferior to our own. Yet, the Egyptians were able to construct some of the largest and most pleasing architectural structures known to man. We need to better understand and appreciate their system, both for its complexity and for its philosophical basis.

The Egyptians, and later Greeks and Romans, used characters to represent values in decimal systems:

The Roman system addresses the task of tallying, i.e. counting. It uses numerals made up of simple lines and strokes (http://youtu.be/Ik4yloCszYo). In contrast, the Egyptians used a much more complex system of numerals, particularly for characters higher than 100. Their use of a water lily for 1,000, a bent finger for 10,000, a tadpole for 100,000 and a kneeling man with both hands raised (perhaps the neter Heh) for 1 million are much more complex than the simple lines and curves of the Romans. Both the high values and the complexity of the characters of the Egyptian system seem beyond the requirements for simple tallying from which our system is said to have evolved. To even have a character for 1,000,000 is amazing! How long would it take a person to tally a million?  At one count per second, it would take 277 straight hours. Why would the Egyptian need such a number?

In regards to the use of a numeral for zero, the Egyptians did use a character for zero in accounting after 1740 BCE: nfr - 

The Ancient Greeks avoided the use of a character to represent “nothing”. Early Greek studies in mathematics, prior to the works of Euclid circa 300 BCE, involved both philosophical and mystical beliefs (https://en.wikipedia.org/wiki/Arithmetic). It seems that the Ancient Egyptians, and the Greeks who followed, couldn’t see a role for zero or “nothing” in their number system which probably reflects the strong linkage between their use of a number system and its necessary representation of their philosophy and world view. It wasn’t until the time of Ptolemy circa 70 CE that the Greeks began using zero as true numeral in their astronomy:  (https://en.wikipedia.org/wiki/Greek_numerals#Zero).

For characters to represent number values the Greeks simply used their alphabet employing equivalence between letters and characters up to the value of 9,000. Our system shows many similarities to the Greek system that provides many numerals for efficient use in arithmetic calculations.

Modern day Western culture uses a base-10 system of numbers for calculations. As a result we use and need to memorize multiplication tables for the numbers 2 through 9. The Egyptians used a methodology based on the doubling of numbers to complete multiplication and division (https://en.wikipedia.org/wiki/Ancient_Egyptian_mathematics#Multiplication_and_division). A system based on doublings is a powerful and relatively easy system to use as it requires only the 2-times table for all multiplication and division. It has been suggested that a similar system was used for multiplication of Roman Numerals millennia later. Egyptologist R.A. Schwaller de Lubicz was the first to explore the power of this system in addressing a number of complex algebraic equations with his French publication “Le Temple de l'homme” (Paris: Caractères, 1957) that is now available in English under the title “The Temple of Man (Schwaller de Lubicz. 1998). A system of doubling is reflected in our present day use of the binary system in computer technology.

Geometrically, architecturally and artistically, the Egyptians recognized the importance of using a triangle with sides measuring 3:4:5 to generate 90-degree right angles. Tied to this knowledge of the 3:4:5 ratios, the Egyptians essentially solved quadratic equations (https://en.wikipedia.org/wiki/Ancient_Egyptian_mathematics#Quadratic_equations).

 Representations of irrational functions are found throughout Egyptian architecture and art. There are numerous examples of the use of the both Pi (π ) and Phi (Φ )in Ancient Egypt (https://en.wikipedia.org/wiki/Golden_ratio). Whereas Pi is taught to all school-age children for the practical calculation of the dimensions of a circle, the lesser-known ratio of Phi, also known as the Golden Section, is not so well recognized in Western culture. This ratio is found in many natural phenomena from biological structures to atomic-scale crystals (https://en.wikipedia.org/wiki/Golden_ratio#Nature). Phi is related to the fibonacci series that is often found in nature: http://vimeo.com/9953368.

Human endeavors by many artists, musicians, historians, architects, psychologists, and mystics have explored the use of Phi in their works.

The Golden Section is the ratio built on two quantities “a” and “b” such that the ratio of the smaller (a) to the larger (b) equals the ratio of the larger (b) to their sum (a+b).

Mathematically, the ratio is irrational with a continuing non-repeating series of numbers to the right of the decimal point: 1.68033 . . .  It is thus difficult to deal with arithmetically. Geometrically it is easily dealt with; represented as the ratios of lines, squares and volumes (Lawlor, R.  1982).

As an irrational number, Phi is tied to the concept of creation and generation in Ancient Egypt (Schwaller de Lubicz 1998).  Schwaller de Lubicz (1998 page 125) states, “Phi is a function and not a number.” This is an important distinction between the Ancient Egyptian and our present day modern Western systems, where we are interested in calculating particular values, whereas the Egyptian system seems more intent on capturing the nature of the broader functioning of the world around us.

Both the 3:4:5 and Phi functions in Egyptian structures and art were used throughout the 3-millenium duration of the culture starting at least 2,000 years before the work attributed to the Greeks such as Pythagoras that began only circa 600 BCE (Lawlor, R.  1982).

It is hard to believe that the Ancient Egyptians didn’t have an appropriately sophisticated system of math, geometry and algebra when seeing the size, precision and beauty of their constructions. We customarily regard what is early as likely to be primitive and inferior. It is difficult to avoid a pre-judgment of their different, earlier system as being somehow inferior to our later “development”. Thus we highly value our present use of numbers as concrete tools for calculating in an “objective” world. The Egyptian’s developed and maintained a number system for thousands of years that seems to contain subtler and broader meaning for numbers. For example, at one level in their use of Phi that is so wildly seen in the natural living biological world, we can see their attempts to capture a mysterious distinction between the existence of physical matter and the creation of the life-force with its new emergent properties (Schwaller de Lubicz 1998).

As with mysticism, there are suggestions that the Egyptians influenced the later development of the Greek mathematics that are so highly valued by the present-day Western World (https://en.wikipedia.org/wiki/Greek_mathematics#cite_note-LH-2). Thus, Greek mathematics are said to have begun with Thales, who was trained by an Egyptian priest!

In conclusion, it is not a question of whether any one mathematical system is inferior or superior to any other. It is rather a question of recognizing the seeming distance between our calculation orientation and the efforts of the Egyptians to connect with the natural and spiritual world that they considered important.  Schwaller de Lubicz (1998) makes the case that in spite of their building prowess, the Ancient Egyptians were not primarily interested in engineering and the concrete physical world.  Rather, their aim seems to indicate a desire to capture in their numerical system the broader nature of the creative and enlivening forces that make up us and our world.  It is difficult not to agree with him.

 References:

Lawlor, R.  1982. Sacred Geometry: Philosophy and Practice. Thames and Hudson.

Schwaller de Lubicz, R.A., 2011.  Le Temple de l'homme.

Schwaller de Lubicz, R.A., 1998.  The Temple of Man. Inner Traditions.

Schwaller de Lubicz, R.A., 1957.  Le Temple de l'Homme, (3 vol. en coffret) Édition Caractère, Paris, 1957. Réédition Dervy Livres.

Schwaller de Lubicz, R.A., 1998.  Sacred Science: The King of Pharaonic Theocracy. Inner Traditions.