This is Part 3 in the Ancient Mathematics series. (To read earlier parts: Part 1: Prehistoric Origins of Mathematics, Part 2: The Mathematics of Uruk and Susa).
This article explores what the people of Mesopotamia wrote about, counted and produced in the last part of the fourth millenium BCE. It does so by examining the frequency of signs in the proto-cuneiform tablets from the period c.3500-3000 BCE. For those wishing to build up experiential understanding of life in the Neolithic and early Bronze Age near east, this article provides suitable references as well as practical explorations of the economic and productive activities of the people: rope-making from grass, basket-weaving from reads, baking, weaving of cloth from linen, breaking ground, sowing, reaping, making flour, etc.
The first part of the article look closely at the collection of artifacts in each period that are associated with the evolution of writing and mathematics in ancient Mesopotamia, examining noteworthy individual artifacts that showcase a key development.
The study uses the CDLI database of cuneiform documents, and software I’ve written that parse the files in the CDLI database, extracting counts, parsing signs, generating frequency distributions of signs, creating a proto-cuneiform glossary, and assisting in the quantitative analysis of artifacts and semi-automated translation (see CDLI parser software library written in Ruby).
The earliest written documents
Writing began c.3500 BCE in Uruk in southern Mesopotamia (Iraq) as the culmination of a series of innovations for better economic control. These innovations simplified and extended a pre-existing quantitative tradition that appears to reach back as far as 8500 BCE (5 millenia prior).
What led to this pre-existing ancient quantitative tradition? The impetus was the management (generation, collection, and redistribution, trade) of the surpluses produced following the transition to sedentary life. Over time [Charvat/2002], early Mesopotamian settled civilization increased agricultural yields through better tools and practices, leading to bigger harvests (barley, wheat, grain), the growth of livestock herds (sheep, goats, cows, pigs, birds) the extraction of animal products (milk, cheese, meat, eggs, wool, leather) and the rise of specialized craftsmen (brewers, carpenters, sculptors, potters, and weavers) manufacturing from grain, wood, stone, clay, flax (plant-based), wool and leather (animal-based).
The innovations that led to writing and mathematics was initially concentrated in the city of Uruk with its early temple economy whose administrators needed to account for transactions (archaic book-keeping) as the contributing population grew expanding beyond what could be managed through trust relationships and collective memory. The success of Uruk and its centrally managed economy led to growing power, influence, trade, and the spread of this new technique. An early rival, Susa in Elam, shows a similar arc in written and mathematical artifacts around the same period, followed by the spread of this new mathematical and literate technology wider afield through the various city-states of southern Mesopotamia and western Khuzistan.
Cultural Exploration: Ways of Life and Thought
Daily Life
[Chavrat/2002] describes ways of life during the Neolithic through to the Early Bronze Age (c.3500) when writing began.
The Sumerian Precedence Debates (Disputation Literature) provide first-hand insight (stylized) into the ways of life of the Sumerians. They were composed in the mid- to late third millenium BCE (c.2500-2000), once writing had evolved beyond its original book-keeping/accounting function.
- Debate between Sheep and Grain
- Debate between Winter and Summer,
- Debate between Hoe and Plough,
- Dumuzid and Enkimdu (Herdsman and Farmer) (or Innana Chooses Farmer)
- Debate between Bird and Fish, (the fate of the marshes in s. iraq)
- The Home of the Fish, (the importance of fishing to the ancient ways)
- Debate between Tree and Reed,
- Debate between Silver and Copper,
- Song of the Hoe,
- Date Palm and the Tamarisk
Sumerian Heroic Literature
- Sumerian King List from the Weld-Blundell Prism
- The Tummal Inscription
- Epic of Atrahasis (aka Noah, Utnapishtim, Zinsuddu)
- Enmerkar cycle, 4 narrative poems about Enmerkar of Uruk and his commander Lugalbanda.
- Gilgamesh cycle: 5 poems about Gilgamesh of Uruk and Aga of Kish, son of Enmenbaragesi
- Epic of Gilgamesh: Gilgamesh & Humbaba (Huwawa) (Version A, Version B),
- Gilgamesh and the Bull of Heaven,
- Gilgamesh and Aga (of Kish I),
- Gilgamesh, Enkidu, and the nether world,
- The death of Gilgamesh
Sumerian Wisdom Literature
Was a favourite item for scribes to copy. Circulated throughout Near East and was studied and copied to the end of Cuneiform.
- Proverbs Collection;
- Instructions of Shurrupak (apparently to Zinsudda, aka Utnapishtim, Atrahasis, Noah, before the flood), first existent copy from c.2500 BCE (which would have been soon after writing was expanded to capture the spoken word and therefore literature).
- Advice of a Senior to a Junior Scribe
- Farmer’s Instructions,
- A man and his god
- The Heron and the Turtle
Reference:
[Cohen, Wassermann, 2018] – Mesopotamian Wisdom Literature, Ch.8
Before Writing – Pre-Uruk V stage (8500-3500 BCE)
Vital Stats:
- 217 pre-Uruk V artifacts are recorded in the CDLI database.
- 136 artifacts have images
- see raw CDLI data file (text) of all 217 artifacts.
Of the 217 artifacts:
- 167 (77%) of these are bulla (clay envelopes)
- 41 (19%) are loose tokens
- 6 (2.7%) are economic seals
- with the remainder a tag (1), a disc (1), and one artifact from Umma and is currently in the Yale Babylonian Collection that is listed as a tablet (1, P291023, from Umma) but which not been examined.
Of the 167 bulla,
- 59 bulla have numerical information associated, either through tokens, surface markings, or both.
- see CDLI transliteration file (text) with added translations and classifications
Of the bullae there are four kinds with provenance from three sites, Uruk, Susa, and Umma (Tell Jokha):
- unopened with seals intact, tokens clearly contained inside, but no ideographs on the bulla itself and no access to the tokens.
- Example: P274842.
- opened with tokens extracted but no ideographs on bulla itself
- Example #1: P274843 showing 7x N01 cylinders.
- Example #2: P285630 showing 5x N64 prism and 2x N39 concave disc.
- Example #3: P285646 showing 3x N65 large prism, 2x N66 medium prism, 4x N64 small prism, 2x N45 large ball, 4x N14 small ball.
- Example #4 P411582 containing 3 tokens. Hard to identify token type from the picture.
- Example #5: P254184 showing 2x N34 large cones. Unclear from the picture if also 2x N45 large balls.
- Example #6: P235737 showing 1x N45 large ball, 2x N01 cylinder, 2x N41 crescent with 2 slashes, 4x N64 small prism. Transliteration appears to mis-identify N64 as N14 small ball.
- Example #7: P235738 with tokens 1x N45 large ball, 5x N34 large cone, 7x N14 small ball, 3x N01 cylinder (16 tokens in total)
- unopened, with tokens clearly inside and surface indentations suggesting contents.
- Example #1 P254193 with indentations of 8x N14 small balls. Need to know whether the surface notations match the tokens inside.
- Example #2 with x-ray contents P274833 showing 2x N45 large balls, 2x N14 small balls, 2x N39 concave discs. Hard to definitively identify the tokens in the scan. No picture of the surface of the bulla.
- with tokens extracted AND ideographs on bulla itself.
- Example #1 P285645 with tokens 3x N01 cylinder, 3x N39 concave disc. Clear match between surface indentations and tokens inside.
- Example #2 P274841 with physical tokens 1x N34 large cone, 3x N01 cylinder, 3x N39 concave disc. Bulla surface has token impressions show 1x N48 large punched cone, 3x N14 small balls, 3x N39 concave disc. Indentations appear to have been made by pressing in the point of the cones, creating the mismatch between physical token and sign indentification. The N48 is the result of impressing the large cone N34 both lengthwise and pointwise, leading to the large punched cone N48 sign. Shows clearly the intent to record the type of token in the surface of the envelope. Ambiguities in sign identification are unavoidable based on how the token was pressed.
- Example #3 P254191 showing tokens 4x N14 small balls. Clear match between surface indentations and token contents.
- Example #4 P281696 with tokens 2x N67 biconic, 2x N39 concave disc, 1x N34 large cone, 2x N01 cylinder. Hard to distinguish N39 from N34 or to match the indentations.
- tokens only.
What happened? Before writing began, the precursors of writing went through several stages:
- use of small clay tokens for accounting, different shapes/sizes denoting different quantities and/or commodities
- enclosing the clay tokens in clay envelopes (bullae) to indicate individual transactions
- using a seal on the outside of the envelope to identify owners
- impressing the tokens on the surface of the envelopes to avoid having to open them / break the seal to check the quantities contained within
What do we know?:
- Various types of tokens were in use.
- In some cases these correspond with indentations into the surface of the clay envelopes (bulla).
- Later reproduction of the same shapes into tablets with a stylus made them notation signs.
- Still later decipherment associated these signs with values that depend on which metrological system they were used within which depended on what commodity they were quantifying.
sign, shape, system(s),
N01, cylinder, SEG/SZE, dis
N34, large cone, SEG/SZE, ges
N48, large cone punched with small ball, SEG/SZE
N14, small ball, SEG/SZE
N45, large ball, SEG/SZE
N39, concave disc, SZE only,
- From later decipherment of the numerical signs as impressed on tablets, we see tokens representing two main metrological systems: SEG (sexagesimal, for discrete counting) and SZE (meaning grain, for grain accounting by weight or volume)
- sexagesimal (SEG) system
N1 < N14 < N34 < N48 < N45
1 < 10 < 60 < 600 < 3600
10x < 6x < 10x < 6x < 10x
dis < u < ges < gesu < sar
For number names see [Powell/1971] - grain (SZE) system
N39 < N1 < N14 < N45 < N34 < N48
1 < 5 < 30 < 300 < 900 < 9000
5x < 6x < 10x < 3x < 10x
- sexagesimal (SEG) system
- Instead of tokens values being in 1-1 correspondence with the quantity being counted, it appears that the different token shapes corresponded already to different standard values.
- Some tokens never made it to numerical signs, e.g. N64 (small prism), N65 (medium prism), N66 (large prism) from Susa did not appear in later period texts. N67 – also did not appear again.
- Fractional system possibly appears once in pre-Uruk V, but the single bulla surface sign 1(N28)? (1/4) does not show well in the image (P285644)
What might have led to such uses and systems?
- The rise of settled life and the generation of material surpluses (grain, harvests, flocks, wool) led to needs for recording:
- Shepherds in the region are documented to use pebbles to keep count of their flocks, also tally sticks (see Sumerian literature)
- Counting and storage of economic surpluses (grain, harvests, wool)
- Temple contributions, redistribution tax, tribute
- Trade between communities
- If indeed tokens were used in this way to represent various quantities, then the mathematical thinking involved is akin to money (example UK pre-decimal monetary system that was in use for almost 900 years, from William the conqueror in 1066 to decimalization on Feb 15th, 1971). The efficient representation of number uses the fewest possible tokens, for which there is always a unique solution (starting always with the largest units). All other ways to represent the number require using more tokens. This is essentially a “change-making problem” (e.g. modern UK money: 1p=100, 2p=50, 5p=20, 10p=10, 20p=5, 50p=2, £1=1).
- There was clearly a canonical representation of number using the fewest number of numerical signs, i.e. using bundling rules, but there are a few instances in which this is not the case. In pre-Uruk V times this could be explained if the document recorded a physical transaction/collection of separate tokens gathered, rather than the scribe reformulating the number using the canonical representation (i.e. bundling into the next higher metrological unit).
- What might have motivated the specific metrological systems?
- No step between units was larger than ten, allowing all calculations to be able to be made with counters (tokens) and fingers.
- By constructing the factors judiciously to match conventional quantity bundles, one encoded common mathematical operations to allow correct reasoning without having to do the math.
- Example from pre-decimal Britain. 12 pence to a shilling makes it easy to price dozens, e.g. if an egg is 4 pence, then a dozen eggs is 4 shillings.
- Made-up example to motivate SZE system: a bowl of grain (N39, SILA3) is wage for one day’s labor. a typical gang of workman has 5 laborers (ERIM). 5 N39 sila to an N01, so 1x N01 is a day’s wages for a gang of laborers. 6 days working for a week. 6 N01 to an N14, so 1x N14 is a week’s wages for a gang of laborers. Now it is easy to calculate grain requirements for wages. 3 weeks work by a single work-gangs is will cost 3x N14. 3 weeks work by two work-gangs is 6x N14.
Pre-Uruk V (before 3500 BCE)
CDLI (searched 11th Jan 2020) had 217 Pre-Uruk V artifacts, 77% (167) bullae (clay envelopes), 19% (41) loose tokens, 4% other (6 Seals
1 Tablet, 1 Disk, 1 Tag).
The bullae have enclosed tokens. Impressed on some of their surfaces are economic seals or token signs. Ex: MDP 43, 539. The loose tokens are plain (undecorated) or complex (decorated with markings or signs). Plain ex: MS 3126. Decorated ex: MS 3131. Only the plain ones have been found in bullae.
Ancient accounting (book-keeping) was the driving reason for literacy.
The notation for number was undergoing evolution.
Experimentation with notations for area and geometry also appear to have occurred around this time:
Toward the end of this period, non-numerical writing first appears:
32 ideographs appear, first ideographs to appear
The next steps of the transition were critical and occurred in quick success over a period of 150 years as the new technique was explored and expanded:
- impressing the tokens on flat clay tablets, i.e. doing away with the enclosing envelopes altogether
- inscribing numerical ideographs with a reed stylus on the tablet
- initially numbers were ungrouped, example: Sialk 1631 and Fs Kraus 012-025, no 6.
- then numbers were grouped and ordered i.e. systematically using a counting system and gathering excessive tokens into the next larger signifying token, e.g. 10 N1s (ones sign) replaced with 1 N14 (tens sign), example: MS 3147/1 and Fs Kraus 012-025, no 4
- experimental notations for calculating area using perhaps shaped tablets (triangular, round) or laying out numbers suggestively
- numero-ideographic tablets combining number signs with ideographs describing the commodity being quantified, one commodity and one transaction per tablet (simple tablets)
- combining multiple transactions of different commodities on a single (complex) tablet then required broadening the sign repertoire for commodities
- multiple ideographs further describing attributes of a commodity or participants in the transaction
Uruk V (3500-3350 BCE), a period of 150 years
Vital Stats:
- 416 Uruk V artifacts are recorded in CDLI
- 4 (1%) are clay envelopes (bulla), a tiny percentage in comparison to pre-Uruk V period (77%)
- 412 (99%) are tablets, showing that the new technology of documenting transactions on tablets replaced almost entirely the previous practice of enclosing tokens in clay envelopes (bulla). By comparision, in pre-Uruk V period only 1 tablet (<0.5%) was listed, and even this has no database details allowing verification (the item is apparently in the Yale Babylonian Collection unpublished).
- raw CDLI data file (text) of all 416 artifacts.
Of the 412 tablets:
- 380 (91%) are numerical only tablets
- 32 (8%) numero-ideographic tablets
- 342 have transliteration data recorded, see CDLI transliteration file (text) with added translations and classifications
Of the numero-ideographic tablets:
- there are 63 attestations of non-numerical signs
- with 32 distinct signs, see Uruk V sign frequency & glossary (text output file from CDLI parser software)
Of the tablets, there are X kinds, of which known provenances are variously in the south Uruk Warka (many!), Umma (Tell Jokha), Jemdet Nasr, in the north Ninevah, Habuba Kabira, Jebel Aruda, Mari (Tell Hadidi), in the east Susa Shush (many!), Choga Mish, Tepe Sialk, Godin Tepe, Nagar (Tell Brak), Tutub, and many more with uncertain provenances (see Appendix 6 for map of sites):
Uruk V concepts
The following were likely the most important economic produce during the Uruk V period given that these were the first non-numerical signs developed:
DUG: 4 (1) n. pot, tt. liquid capacity vessel (reading=dug), DUG_b for semi-liquids (dairy fats), DUG_a for liquids (beer), [Englund 1998, pp.159-169] UDU: 4 n. sheep, small cattle (reading=udu) SUHUR: 4 n. fish (carp?) (reading=suhur) SIG2: 4 n. wool (reading=siki) SZE: 3 n. barley; tt. weight measure = 1/180 shekel (reading=sze) TUG2: 2 n. cloth, garnment (reading=tug2) NE: 2 v. to burn, to roast (reading=bil), n. fire (reading=gum3, izi), heat (reading=kum2), adj. burning (reading=bar7), hot (reading=kum2) LAGAB: 2 (2) n. total (reading=kilib, nigin2) [early periods] n. block of wood, slab of stone, trunk of tree (reading=lagab) [later literary periods] ZATU753: 2 (1) -- no match -- ZATU697: 2 -- no match -- ZATU659: 2 -- no match -- MASZ: 1 n. goat, interest (reading=masz) AB2: 1 n. cow (reading=ab2) DUR: 1 n. rope (reading=dur) UKKIN: 1 n. vessel of special type (from sign) MA2: 1 boat, barge (reading=ma2) GADA: 1 n. flax, linen (reading=gada) ME: 1 (2) n. priest (reading=iszib), n. existence (reading=me, Dasein) BAHAR2: 1 n. potter (reading=bahar2) NUN: 1 gn. Eridu (reading=eridu), n. prince; v. to rise up; adj. princely (reading=nun) NIM: 1 adj. high (reading=nim), place name Elam (reading=elam) AN: 1 n. sky, heaven; deity name An (reading=an), deity (reading=dingir) SZU2: 1 (1) n. cover, to cover (reading=szu2) PU2: 1 n. well, cistern (reading=pu2) BU: 1 v. to tear out (reading=bu), snake (from where?) ZATU644: 1 (1) -- no match -- ZATU758: 1 -- no match -- ZATU700: 1 -- no match --
We will look at these in turn and, in each case, consider what this might have meant for Sumerian daily life, and indeed, what fundamental skills we can learn that are useful today from investigating these ancient economic and productive activities.
- Agricultural production DUG_b (vessels of dairy fat) in 4 tablets, UKKIN (special pot) in 1 tablet
- Example #1: P009448 recording 33 DUG_b (vessels of dairy fats), c. 264 litres (8L each DUG_b)
- Example #2: P000842 recording 25 DUG_b (vessels of dairy fats), c. 200 litres
- Example #3: P342536 recording 3 UKKIN (special pots)
The proto-cuneiform signs for pots are shown below, indicating quite a variety. Uruk V texts only show DUG_b and UKKIN_d (a slightly different variation). Uruk IV texts add KISIM. By contrast, metal vessels (not shown, also appearing in Uruk IV) were SZEN, URI, MUD3, GAN. Also not shown are GI (reed) GA2 (baskets) the insides of which may have been coated with naturally occurring bitumen (pitch) to provide a container for milking (GA) or carrying water or other liquid.
A key point to note is the mouth of the vessel. Semi-liquids (dairy fats, cream, cheese, oils) are shown in jars with no spout. Liquids (beer, water, wine) are shown in jars with a spout.
What was stored in them? In the Uruk V texts this is not detailed, but later texts and the sign lists identify likely contents as being NI (oil, dairy fats), GA (milk), GA’AR (cheese), GADA3 (cream), SZE (barley), NAGA (a soap from alkaline plant, or potash), KASZ (beer), DIN (grape, or wine), KUR (plant related to grapevine, grown in mountains), SUHUR and KU6 (both types of fish), SZAH2 (pork)
How big were they? A standardized bowl (SILA3) is thought to have held a capacity of ca. 0.8 liters [Englund 1998, p.161], so a DUG_b (vessel) is estimated to have a capacity of 8 liters based on text W21682 that shows 1 DUG (vessel) SI (filled) with 5 SILA (4L = 0.8 x 5) EACH of GARA2 (cream) and GA (milk), i.e. 4L+4L, a measurement estimate that is in line with other dairy texts and vessel capacity texts.
How heavy? An 8L DUG_a of A (water) would have 8kg net weight excluding the weight of the clay vessel itsef (density of water is 1kg/L). Beer and milk would be heavier with densities of 1.01kg/L and 1.03kg/L respectively. A DUG_b of NI (oil) would be lighter at approx 6.4kg (density of oil is ca. 800g/L).
Liquids and semi-liquids had their own metrological system.
A drinking song – ode to the jars
Agriculture is hard work. It is hypothesized that the reason for agriculture was to create beer.
- Beer/bread vs. Dairy/Meat. (cf. the debate between shepherds/herdsmen and farmers, above)
- How Beer has made history – 10 facts through the ages
- Natufians, early beer, feasting, and complex social politics
Baskets
How to make a basket from reeds and sticks? Weaving a cat-tail mat with wood frame, base of basket. - Tablets showing grain accounting (barley SZE)
Cultivating crops
- Seeds germinate in water or in a moist paper towel. Dried peas take about a week to germinate (planted 5/2, germinated 5/9 and moved to soil). Popcorn seeds take about two weeks.
- Once the seeds germinate, plant them in soil, in a starter pot, with the root down and shoot up above the soil. Water daily and sometimes twice daily.
- Leaves curl when the plant is short of water, and stems lose their rigidity. Plants will recover if watered, but it is not good to stress them out in this way frequently.
- Be careful of starter pot soil drying out quickly in sunshine
- Growing peas. Dried peas grow quickly, and need a trellis for the tendrils to wrap around. Try using guttering as the base. Harvest is ready 3 months after growth. Planning Guide, Growing Guide
- Example #1: P411630: supplies, trade, or wages for a BAHAR2 (potter), who receives DUR (rope) and SZE (barley grain). Translation: 5 DUR (ropes) [from/to] BAHAR2 (potter). 10 [SILA3 standard size bowls, 8L] of SZE (barley) [note the SZE system is used, where 1x N01 = 5x N39 SILA3]. The approx capacity of a SILA3 standard bowl is 0.8L (see Englund 1998, p.169).
Why might a potter need rope? To create the cordage around the neck for easy handling of the vessel, and potentially the strap or net for carrying it.
Interpretation This could be the receipt for central provision of supplies of rope and grain by the temple to the potter to obtain later his finished vessels. Or it could be the purchase of rope for grain (grain payments were standard). Regardless the 10 SILA (standard 0.8L bowls) of barley would be 2 days of standard wages in grain-payment per rope. It may indeed be the two days to fashion a finished vessel including the straps from finished ropes. If this interpretation is true, it suggests that the temples controlled the central payment and consolidation of many intermediate products required to manufacture useful finished articles, coordinating grain payments between artisans of different types. This is an early precursor to the bala taxation system in place during Ur III empire (c. 2000 BCE). BALA first appears in Uruk IV signs (1 instance, tablet P001399, records exactly such a transaction) then increases in Uruk III sign frequency (24 instances). This would later give way to a silver-based economy in the Ur III empire times (1 shekel of silver = 300 sila (L) of barley grain). (Englund 2012, p.427)
How was DUR (rope) made? From natural plant material to create cordage: examples GI (reed), GADA (flax) or fibres from GISZIMMAR (date palm). Example videos showing how to make twisted fiber rope from natural fibres using two-strand (from reed-like grass, Matt Alderson) and three-strand (from die-back leaves of the iris, a shore-based reed, JD Lenzen) techniques. A fistful of dead iris leaves can make 30 feet (~9m) of a strong 1/8″ (4cm) diameter natural fibre rope. These can be braided together to make thicker stronger ropes as needed. Making rope from dried grass (2 minute clip starting at 3:35 to 5:28). History of string and rope-making (dating from c.26,000 BCE).
Ancient uses of DUR (rope) For creating carrying nets for jars and baskets (GA2), leads or restraints for herded animals, wraps for the necks of jars for better grip, use to climb trees, use to secure baggage to pack animals (donkeys), use as a belt for clothing, used as a line for catching fish, hanging fish, drying fish, used as a line for generally hanging anything.
Making a thick rope for climbing
(May 5th) I have made a 2.4m long, 4cm diameter grass rope that can carry the weight of my 8yo daughter when slung over a branch! Took 90 minutes to weave this rope.
Essential knots for rope craft Fundamental to using rope are knots. There are a few essential knots which are worth learning for easy of use and to master ancient rope craft. The clove hitch is the easiest way to secure (permanently) a rope to a spar.
- Example #1: P000852: showing 74 UDU and 9 UDU on reverse in SEG counting system
- Example #2: P342569: showing 61 UDU and 50 (sign too faint to identify)
- Example #3: P200044: 1 SIG2 (wool), 5 ?, 3 UDU (sheep), 7 ?, 16 ? … 44 SIG2 SIG2 (wool-wool, or lots of wool) [for] ME priest. Remarks: the sheep may have been part of the temple flock, or the wool added to the temple stores.
- Example #4: P200051: 1 SIG2 (wool), 7 TUG2 (clothes), then numbers with no sign: 4, 5, 12, 2, 1. The reverse surface has damage, but inspection shows 22, with possibility of 32 due to N14 positioned where the damage is. If so, then the reverse would hold the sum of items on the obverse.
Role of UDU (sheep) Sheep were one of the earliest domesticated animals, beginning from c.9000 BCE. The keeping of flocks led to nomadic movement of animals and people following grazing pastures, and moving between the alluvial plain the summers and the mountains in the winters [Charvat/2002] Wild sheep had hair not wool. After domestication, sheep were selectively bred for wool. Sheep provided milk, cheese, wool, and when slaughtered, meat, oils and fats, and skins.
How were sheep sheared for SIG2 (wool)? For some breeds, when the wool is “ripe” (ready) it will naturally start to shed (roo) its wool. Hand rooing (plucking) can accelerate this. By medieval England at the height of the wool trade (c.1400 CE, or 6,000 years after tablet P200044), the entire sheep-to-wool value chain was well developed with custom inventions for every step of the process path.
Why the cross-in-circle sign for UDU (sheep)?
Most animal signs in proto-cuneiform resemble the animal, except sheep and goat. Why are sheep (UDU) a cross within a circle, and goat (MASZ) a cross (no circle)? Imagine looking at a sheep head on. Plump wooly head (circle), with the vertical axis defined by broad nose ridge and horizontal axis defined by the extended ears. With goats, no wool but same distinctive cross axes for the face (cross-without circle). With fat-tailed sheep (GUKKAL, a distinct type of sheep, 25% of world sheep population), the fat tail (up to 16% of sheep’s weight, concentrated in the tail and therefore easy to harvest as a source of cooking fat/tallow) is pinned to the back of the symbol. GUKKAL sign first apppeared in the Uruk IV period.
The proto-cuneiform signs for UDU (sheep), SIG2 (wool), and TUG2 (clothes)
All three are circle signs, UDU is cross in circle, SIG2 is several parallel lines in circle, and TUG2 is two parallel lines in circle. Speculating, the parallel lines may relate to the fiber strands and to weaving, the processes of passing the weft strand up and down over the warp (parallel) strands to create the pattern of the weave.
How was SIG2 (wool) turned into TUG2 (clothes)? Making clothes from wool passes through 7-8 (modern) steps: shearing the sheep (or rooing/plucking if done by hand), scouring the wool (degreasing and cleansing), carding to smooth the strands, combining to separate and stretch the wool fibers into strands, spinning into yarn, weaving into cloth either by hand or with a loom, and finally finishing (washing, shrinking, restretching). Dying is an optional step that can be done at any point after carding. History and process. Modern manufacturing process. Ancient process and clothes.
What TUG2 were worn? Artistic evidence from seals depicting humans, and from statuettes show that clothing for both men and women consistented of skirts and shawls, both made from rectangular fabric (wool or linen) that could be wrapped or draped and secured with belt or pin. Ancient clothes.
When did GADA (flax/linen) begin to be made/worn? From proto-cuneiform signs, GADA (flax/linen) came in the Uruk IV period following SIG2 (wool), i.e. 150-300 years later. Flax production may have originated in Iran/Zagros, and indeed the single possible attestation of GADA in Uruk V is an economic text from Susa P235750. The transformation of flax into linen cloth is intensive. Here’s a pictoral description of the process from flax seeds to linen (Susie Gillespie, handweaver). Linen is mentioned in connection with Dilmun [Reade/Potts, 1993] Interestingly, there is evidence of basic clothmaking with flax recorded as far back as 36,000 BCE.
From flax seeds to linen in 12 steps
- Example #1: P342512: 3 SUHUR, 5 SUHUR, 2 SUHUR BA (rations) [note: the CDLI transliteration indicates ME (priest), but to me the sign is much closer to BA].
How might ancient humans have fished? There are a few ways of fishing: (1) active by hand: catching with a trident or spear (video 30s), using a hand-basket (video 45s from Cambodia) or hand-net; (2) by hook and line, with live bait on the end of the hook (video 1:20s from Sri Lanka); (3) using a trap or broad area net, and luring fish into the trap (building a trap basket from bamboo and cordage, catching the fish (20s); (4) digging for mud-fish or noodling catfish in their hole.
We’ve already seen how natural fibres (grass, leaves, etc.) can be used to make thin, flexible, but strong cord. A hook can be made from a naturally growing thorn. This video shows how to use secure a thorn-hook in the end of a two-strand cord end (1:30).
Mudfish digging Mudfish and lungfish can survive up to 3.5 years under the dirt in areas formerly underwater. The fish secrete mucus to form a cocoon to keep themselves from drying up, surviving through respiration through the skin, and awaiting renewed rainfall. This video of mudfish digging in Ghana is astounding.
Uruk V (3500 – 3350 BCE)
CDLI (searched 11th Jan 2020) had 415 Uruk V artifacts, 98% (407) tablets, 2% others (3 seals, 3 bullae/tokens, 2 tags). Of the tablets,
* 88% (358) are purely numerical, Plain W6245,d2 and Ex MW 0188/037, Ex w/ seal MDP 43, 520 and CahDAFI 3, 103 04
Within these, we can discern two stages, with numbers ungrouped and with numbers grouped i.e. systematically using a counting system and gathering excessive tokens into the next larger signifying token, e.g. 10 N1s (ones sign) replaced with 1 N14 (tens sign). Ungrouped ex: Sialk 1631 and Fs Kraus 012-025, no 6. Grouped ex: MS 3147/1 and Fs Kraus 012-025, no 4
* 4% are numerical on shaped tablets (13 triangular, 3 round), Ex circle MW 0188/112
* 2% (6) are numerical with area calculations: Ex MDP 17, 264 and MDP 17, 362
* 8% (27) are numero-ideographic describing a single commodity transaction (simple tablets with on non-numerical proto-cuneiform sign) or a multi-commodity transaction (complex tablets). Simple tablet ex W6782,a w/ DUG (jar) and MS 3147,2 w/ SZE (barley). Complex tablet ex MW 0188/034 but see barbeque at Eridu for further discussion of this tablet.
The earliest non-numerical ideographs to appear in Uruk V period tablets are:
Commodities:
DUG (jug, x5 standalone)
SZE (barley, x3)
UDU (sheep x3)
GADA (flax/linen, x2 badly attested)
DUR (rope x2)
BAHAR (pot, x1 of barley SZE)
MASZ (goat, x1)
AB2 (cow, x1, roasted NE)
TUG (clothes, x2, incl. 1 SIG night),
MA2 (boat x1, hollow? BU)
Places:
NIM (Elam, high, x1)
NUN (god Enki, Eridu, x1),
SZU2 (cover, x1)
IB (corner)
Participants:
PU2, NIR (prince)
ME (priest)
UKKIN (assembly)
Other:
PAP (check or verify)
LAGAB (total?),
LA?
A barbeque at Eridu? (Uruk V, 3500-3350 BCE) This one MW 0188/034 is the only complex numero-ideographic tablet currently assigned in the CDLI catalog to Uruk V. There are no other examples of this level of written complexity in Uruk V, and because in addition this tablet belongs to a collection of unprovenanced finds that have not yet been published, my working assumption is that this may be an incorrect assignment. Nevertheless, what is recorded is fascinating:
“50 goat (MASZ), 2 cow (AB2) for roasting? (NE)” and on the reverse: “1 cover (SZU2), 14 at/for Eridu (NUN)”.
There is no archaeological context as to what it was recording or why, but the fact that such records were being kept, using the new technology of writing, with the additional invention of ideographic signs describing the transaction, is remarkable, as it shows the evolution of the writing/sign invention process from pure numeric only having quantity information (presumably commodity was obvious to the record-keeper and user, from context) to simple numero-ideographic that also add commodity information, and finally to complex records with quantity, commodity, and intention recorded.
A plausible scenario is provision for a feast. How many people might be fed from this provision list? A male cow of average 1000 lbs weight will have ~40% consumable meat (~400lbs) due to live weight contribution from blood, hide, head, hooves, lungs, viscera, bone, fat. (high est., low est.), which would feed approx 800-1600 people depending assuming 1/4 lb (110g) – 1/2 lb (220g) portion size. An average goat of 100lbs weight may have ~40lbs of consumable meat and feed 80-160 people (1 cow = 10x goats) assuming similar meat to carcass ratio for goats. This suggests this provision list would have been enough to feed 5,600-11,200 people. Given the sign for Eridu, which had the earliest temples and was viewed as the holy city of Sumeria, this may have been provision for a large festival. Estimates are that ancient Eridu had at least 4,000 inhabitants during the period before this (Ubaid, 4500-3800 BCE), which may have increased and been supplemented by festival visitors from nearby settlements (Ur was 12km away).
Grinding flour and baking
Mar 9th, 2020
In March of 2020, seeing the impending COVID-19 crisis, and having been studying the mathematics of the ancient Sumerians, and their late Neolithic survival technologies, I bought a home grain milling machine (£72.90, Amazon UK).
Stocked up subsequently on dried rations as they keep longer than cans or fresh food. Quite varied stuff: barley grains, red kidney beans, dried lentils, popcorn kernels, brown rice, almonds. All of these grind up into fine flour in 60 seconds or lesss.
Since then have been having a blast baking very simple nutritious biscuits for my family (2 young children and me).
Recipes so far (watch this space for more!)
- barley-almond cookies combining almond and barley flours (Sun Mar 8th)
- corn, kidney bean, and barley cookies (Mon Mar 9th)
- coconut and barley macaroons (Sun Mar 15th)
- chicky-choco-oaty-boaties, combining equal parts chick-pea flour (gram flour) and oatmeal, with cocoa and orange essence for (Fri Mar 20th)
- spelt and oat (Fri Apr 10th)
- atta (wholemeal wheat) and oat (Sat Apr 11th)
- atta, oat, and cocoa (Sat Apr 18th)
- sweet atta (Mon Apr 27th) – 1/2 cup of sugar (same
- cinammon atta (Fri May 1st) – 3 cups of flour, 1/3 cup of sugar, 3 eggs, 1 cup of milk, 1/2 cup of corn oil, plenty of cinammon (3-4 tablespoons) This forms a dough that can be rolled and cookies cut out and put on baking tray: 15 min at 170 deg.
- chocolate atta (Wed May 6th) – note, 1/6th cup of cocoa requires an extra 1/4 cup of sugar to offset the inherent bitterness of cocoa
- coconut macaroon filling (Sun May 3rd) – coconut flour, 1 egg, sugar, milk. Mix well. Leave it in the fridge for 2 days. Forms a delicious macaroon filling.
- oatmeal, cinammon, raisin atta (Thu May 21st)
- atta pizza base (Fri May 22nd)
- cocoa ginger snaps (Fri May 29th)
Basic cookie recipe has just 5 natural ingredients:
2.5 cups of flour (mix whatever kinds you like, I typically use 2 cups of a basic grain, and 0.5 cup of exotic stuff)
0.25 to 0.5 cups of sugar (I use less where the flours are basic and more with the exotics which have a stronger less child friendly taste)
2-3 eggs (more eggs, yummier)
0.5 cups of oil (I use sunflower or corn oil)
0.5 cups of milk (I use soya as it has a thicker texture)
0.2 cups of baking cocoa (unsweetened) optional
1-2 tablespoons of extract (e.g. orange, almond, lemon, etc.) optional, I use this only with high exotic blends like 50% chickpea flour due to mask their strong taste and make the results more appealing for little palattes
Mix the dry goods first in a mixing bowl. Add the wet stuff. Mix with a fork into a batter. Adjust ingredients to get the texture to a scoop-and-blob consistency, and blob onto baking tray with baking paper. Over pre-heated to 170*C. Bake for 10-15 minutes depending on how crispy vs. soft you like the insides.
Bakes about 60 small and nutritious cookies, which in my family, then last 4-5 days, as they become part of breakfast and snack times.
The grinder is easy to set up, a snap to use, and easy to clean with the brush (I have not felt the need to clean it with water).
Uruk IV (3350-3200 BCE)
The next 150 years see an explosion in innovation as comfort is built with the new writing system
- proliferation of signs for numerical notations – in Uruk IV, all the known numerical signs appear
CDLI (11th Jan 2020 search) attests 1861 Uruk IV tablets, 98% (1833) tablets and <1% (14) tags. There is a marked explosion in finds and signs, commodity, non-commodity, and complex records, including lists, multi-sign descriptions. Communication through writing has taken off. I have written Tablet Parser software (v1, Jan 18, 2020, download available here) in the Ruby language to parse signs from the CDLI transliteration download file and form a sign frequency table. See this article for discussion of the Tablet Parser software design. Using Tablet Parser, there are 7827 simple sign attestations in the 1861 Uruk IV tablets, with 390 unique simple signs. The top 12 simple signs are:
EN (high priest, x248, 3%)
NUN (Eridu, x175)
DUG (clay pot, x149)
BA (portion, ration, to divide, x130)
AN (sky, heaven, the god An, x125)
SANGA (temple administrator, x123)
UDU (sheep, x96)
KASZ (beer, x94)
AB2 (cow, x89)
SZU2 (cover, x88)
U4 (day, sun, x87)
UNUG (Uruk, x86)
Other frequent signs:
BUR (stone bowl, x4)
NAM2 (ruler, x78)
NIMGIR (herald, x27)
BARA2 (throne, x23)
GISZIMMAR (date palm, x10)
NI (cereal product?, )
IR (perfume, )
BIR (kidneys )
DA
BU
AN (god, sky, )
HI
EN (chief administrator, )
A (water, )
Uruk III/Jemdet Nasr (3200-3000 BCE)
CDLI (11th Jan 2020 search) attests 4922 Ur III/Jemdet Nasr tablets. Now tablets are highly structured with individual cells containing information, and document wide organization, showing break-out of categories and rollups of counts to higher level summaries.
Cuneiform Tablets & Related Artifacts
5000 Years of Artifacts & Tablets (periods from 8500 through 3000 BCE, Ur III)Period | Dates | # of Artifacts | Breakdown | Remarks | CDLI queries |
---|---|---|---|---|---|
Pre-Uruk V | Before 3500 BCE | 217 | * 77% (167) Bullae (clay envelopes) * 19% (41) loose tokens, * 4% other (6 Seals 1 Tablet, 1 Disk, 1 Tag) | Bullae have enclosed tokens. Impressed on some surfaces are economic seals or token signs. Ex: MDP 43, 539 Loose tokens Ex: MS 3126 | Pre-Uruk V artifacts |
Uruk V | 3500-3350 BCE | 415 | * 98% tablets (407) * 2% other (3 seals, 3 bullae/tokens, 2 tags). Of tablets, * 88% (358) are purely numerical, * 4% are numerical on shaped tablets (13 triangular, 3 round), * 2% (6) are numerical with area calculations. * 8% (27) are numero-ideographic describing a single transaction (simple tablets), | (1) purely numerical, Plain W6245,d2 and Ex MW 0188/037, Ex w/ seal MDP 43, 520 and CahDAFI 3, 103 04 (2) Numbers ungrouped Sialk 1631 and Fs Kraus 012-025, no 6 (3) Ex numbers grouped MS 3147/1 and Fs Kraus 012-025, no 4 (4) Shaped numerical tablets, Ex circle MW 0188/112 (5) Geometric/area calculations, Ex MDP 17, 264 and MDP 17, 362 (6) Simple numero-ideographic, recording one transaction, of typically one commodity (proto-cuneiform sign). Ex W6782,a w/ DUG (jar) and MS 3147,2 w/ SZE (barley) The earliest non-numerical ideograph appear, with commodity and non-commodity signs: Commodities: DUG (jug, x5 standalone) SZE (barley, x3) UDU (sheep x3) GADA (flax/linen, x2 badly attested) DUR (rope x2) BAHAR (pot, x1 of barley SZE) MASZ (goat, x1) AB2 (cow, x1, roasted NE) TUG (clothes, x2, incl. 1 SIG night), MA2 (boat x1, hollow? BU) Places: NIM (Elam, high, x1) NUN (god Enki, Eridu, x1), SZU2 (cover, x1) IB (corner) Participants: PU2, NIR (prince) ME (priest) UKKIN (assembly) Other: PAP (check or verify) LAGAB (total?), LA? | Uruk V tablets |
Uruk IV | 3350-3200 BCE | 1861 | 98% (1833) tablets <1% (14) tags | Uruk Expansion? Tablets are mostly complex numero-ideographic with multiple cells per tablet, and some double-sided with front containing detailed breakdown and reverse containing rolled up sum. Signs are proto-cuneiform. We now see the temple economic organization, with non-commodity signs EN, SANGA, UNUG. | Uruk IV tablets |
Uruk III/Jemdet Nasr | 3200-3000 BCE | 4922 | Uruk hegemony and administrative standardization. Signs are simplified proto-cuneiform. Additional place signs possibly indicate the increased flow of economic goods, trade, tribute between cities. Before the Flood. | Uruk III tablets | |
Egyptian 0. | 3300-3000 BCE | 186 | Mainly tags with ideographs. | Archaic Egyptian artifacts | |
Proto-Elamite (Susa) | 3100-2900 BCE | 1636 | Numerical signs shared, but diverge to decimal system. Some proto-Elamite signs shared with proto-cuneiform (e.g. UDU), rest divergent. Record layout reversed: first commodity, then quantity. | Proto-Elamite artifacts | |
Early Dynastic I-II | 2900-2700 BCE | 1189 | After the Flood. Kish hegemony according to Sumerian King List. Kish: Enmenbaragesi, Aga. Uruk: Enmerkar and Aratta. Transition from Proto- cuneiform to cuneiform (nail writing). Expansion of vocabulary, scribal schools, first attestation of lexical lists, Ex: LU A list | Early Dynastic tablets (ED I-II) | |
Early Dynastic IIIa | 2600-2500 BCE | 1895 | City state rivalry. Gilgamesh? (Uruk) | ED IIIa tablets | |
Early Dynastic IIIb | 2500-2340 BCE | 5053 | Fara school. Akkadian influence. Transition to syllabic writing for dual Sumerian/Akkadian texts. Lexical lists. | ED IIIb tablets | |
Ebla (Syrian empire) | 2350-2250 BCE | 7105 | Old Eblaite tablets | ||
Old Akkadian (empire) | 2340-2200 BCE | 10,164 | Sargon | Old Akkadian (Sargonic) tablets | |
Lagash II (empire) | 2200-2100 BCE | 4,551 | Gudea | Old Gudean tablets | |
Ur III (empire) | 2100-2000 BCE | 109,734 | Ur-Nammu, Shulgi | Ur III tablets |
[add table – frequency of signs in Pre-Uruk V, Uruk V, IV, III, across professions list, deities, places, and commodities]
In this context, Uruk in southern Iraq was the centre of excellence and innovation, with its influence radiating outward alongside the projection of its trade, economic, and military power. Susa in western Iran (Khuzistan) was a rival, adopting what appears to be the core early system (tokens, envelopes, tablets, numbers, ideographs) and then innovating this in its own direction (a decimal-based system, commodity then quantity, different ideographs, proto-Elamite).
[figure – map]
Over the next 500 years (2500 BCE), across the southern Mesopotamian and Zagros region, this system was refined and scribal schools were established to teach the ways of literacy, most notably in Shurrupak (modern Fara). The ideographic signs (proto-cuneiform), produced with the sharp end of a stylus for drawing the various curves involved, began to be simplified, and mimicked using the wedge end of the stylus and straight line-segment impressions.
[figure – evolution of signs, Nissen, Englund, and CDLI sign list]
Appendices
Appendix 1: Learning the Ancient Skills
If you live in a British city of reasonable size, you are likely to find, nearby, opportunities to learn the skills recorded by the ancient peoples, and taste what parts of their lives might have been like. Below some options accessible to residents of Hertfordshire, 30 minutes north of London. If you happen to live in Devon or holidaying there, you’re in a craft center of Britain (Devon Guild of Crafts, workshops) with plenty of ancient skills to explore.
- Pottery – pinch-forming, coil-forming, wheel throwing, creating clay from mud, finishing and firing, painting and glazing
- Muddy Pots – Dig your own clay and make pots, £45/3hrs, 2-3 sessions, M/T/Thu
- Kate Radford Pottery, Harpenden, £20/course or £12.50 per child
- Wheel throwing party £40 per child
- Clay Time, open access studios, 30m from BAI, 50m from KL
- Elaine Wells, 25min from KL (Amersham)
- Maggy Gardiner, £25/2 hrs, 50 min from KL (Bishops Stortford)
- DCPG (Dacorum & Chiltern Potters Guild) – Potters Open Day 7th Mar, Monthly meetings
- Fishing
- Weaving mats / baskets
- 4-day basket-making course from reeds to baskets course, £340 (incl. lunches) Tim Johnson
- Weaving with willows
- Weaving rope
- Weaving cloth (wool/flax)
- Susie Gillespie, weaving from flax, nettles, antique linen yarn, from flax seeds to linen, a pictorial and process description, 4-day flax processing & handweaving course from flax seed to linen £340 (incl. lunches), 2-day handweaving course £180 (incl. lunches)
- Weaving with a Loom, £30 afternoon course
- free-form weaving
- Devon weavers workshop, formed in 2005 to preserve handweaving which was on the brink of disappearing from Devon
- Fibre shop!
- Cultivating barley to make flour and bread
- From Raw Wheat to Flour, Milling Flour at Home
- Flour ideas: barley flour, wheat flour, red bean flour, corn flour, lentil flour (green, purple, orange), almond flour, cashew flour, dried date flour
- An electric grain mill for your kitchen, £73 (amazon.co.uk): 2500W motor, 500g grain capacity (takes ~3 cups of grain and makes ~4-5 cups of flour in c.60 seconds), 5 min max recommended running time with 33% duty cycle, produces superfine grain flour @5min and coarser grain with less grinding time
- Recipes:
- almond flour – there are oils in almonds, so this requires 2-3 grinds, each time scraping out the pasty/flour.
- barley flour –
- popcorn flour – 1 cup of kernels, makes 1.5 cups of fine yellow cornmeal flour in 60 sec.
- red kidney bean flour – 1 cup of red kidney beans makes 1.5 cups of pale reddish bean flour in 60 sec.
- super cookies (6 wholesome ingredients): 2.5 cups of flour, 3 eggs, 1/2 cup of milk, 1/3-1/2 cup of oil, 1/4 cup of sugar (up to 1/2 cup if want it sweeter), mix with fork, drop dollops onto wax paper baking tray, bake at ~170*C for c.10 minutes till crusted outside but still soft inside.
- SZE-LAM cookies (barley-almond, 2 cups/0.5 cups of flour), with GA (milk), NUNUZ (eggs), NI (oil), and SA6 (sweet)
- CORN-BEAN-BARLEY cookies (1.5 cup/0.5 cup/0.5 cup), rest as above (less sugar)
- Baking the ancient way (honest bread), £95 1 day course, Wed/Sun
- Real Bread
- Chorleywood process for making Wonderbread, and why it is not so wonderful, CBP (Wikipedia).
- Higher Protein, No Powders, Tiffany T.
- Making soap from plants (NAGA)
- Cold process solid soap making from plants, 1 day £75
- Pure natural liquid soap making from plants, 2 days £155
- Blacksmithing course
- Animal rearing, natural butchering, meat curing
Appendix 2: Map of Places
References
- [Charvat, 2002] – Petr Charvat, Mesopotamia Before History, Taylor & Francis (Revised edition of Ancient Mesopotamia 1993), [Charvat/2002] – This book provides a detailed description, based on archaelogical finds, of how the Near East went from Paleolithic to Mesolithic to Neolithic to Chalcolithic, before arriving at the Uruk period of city states. Each find site is reviewed in detail, and an interpretation is given covering all aspects of the associated culture (material conditions, social practice, art and ritual, modes of sustenance, food and commensality, individual work profiles, housing conditions, etc.)
- [Nissen 1993] – Hans Nissen, Peter Damerow, Robert Englund, transl. Paul Larsen – Archaic Bookkeeping: Early Writing and Techniques of Economic Administration in the Ancient Near East.
- CDLI – Cuneiform Digital Library Initiative
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