Writing-Cuneiform

Cuneiform Tablet

Account of Rations for Six Persons
Working as Messengers for the City Governor

Mesopotamia, Umma.

ca. 2040 B.C.

x 3.23

This tablet was taken by astronaut Sonny Carter, an Emory University alumnus, on the November 1989 mission of the space shuttle Discovery as part of NASA's Object in Space Program. Representing the oldest human artifact to have traveled in space, the cuneiform writing on the tablet lists rations for 6 messengers undertaking a journey:

Here is the translation:

For Bama: 5 quarts beer; 5 quarts bread; 5 ounces onions; 3 ounces oil; 2 ounces alkali

For Baza: the menial: same amount

For Lugal-sazu: same amount

For Su-Esdar: 10 quarts beer; 10 quarts bread; 5 ounces onions; 3 ounces oil; 2 ounces alkali

For Mas: 5 quarts beer; 5 quarts bread; 5 ounces (onions); 3 ounces oil; 2 ounces alkali

For Ubarum: 3 quarts beer; 2 quarts bread; 56 ounces (onions); 3 ounces oil; 2 ounces alkali

Day; 24 Year: Huhnuri was raided (=Amar-Suen 7, 2040 B.C.)

Cuneiform numbers

Cuneiform numbers were written using a combination of just two signs: a vertical wedge for '1' and a corner wedge for '10'. Handwriting varied as much in Old Babylonian times as it does now but the basic system of numbers is illustrated below.

	1		2		3		4
	5		6		7		8
	9		10		11		12
	13		14		15		16
	17		18		19		20
	30		40		50		60

Some common variants are

	for 4
	for 7
	for 8.

Occasionally, 19 was written as something like , meaning 20 - 1, although there are a huge number of minor variations in the way this sign is written.

Additionally, there were special signs for some common fractions. These were used when the numbers stood for metrological quantities, such as 1/2 gin.

	1/2
	1/3
	2/3
	5/6

Larger cuneiform numbers

For computation, the Mesopotamians used what is usually referred to as a 'sexagesimal' (i.e., base-60) system. Technically, this is a slightly inaccurate designation as they used only combinations of two symbols bundled together for writing numbers up to 60. For writing numbers greater than 60, they just repeated the symbols in different columns, just as we do, except that where for us a '1' in the 'tens' column means 10, for the Babylonians a in the 'sixties' column meant 60. Each column increased the value of the number by a factor of 60, and the Babylonians wrote their numbers with the largest values to the left, just as we do. Here are some examples of cuneiform numbers, their transliterations and values in our notation.

Cuneiform	Transliteration	Decimal value
	1,15	75
	1,40	100
	16,43	1003
	44,26,40	160000
	1,24,51,10	305470

There are a few differences between the way we write our numbers and the way the Babylonians did. First, they had no special way to mark an empty column. We would write a zero to mark the place, they would often leave a space, but not always. For example, it is not always clear if should mean '2' or '61', or even '3601'. In practice, empty columns don't arise that often in a base-60 system and so this was not such a problem as you may think. Later on, in the Neo-Babylonian and Seleucid times, when astronomers needed to do lots of many-place sexagesimal computations, they did introduce an empty-column marker.

One of the great advantages of a place-value system is that you can use the same symbols to make ever larger numbers. There is no limit to how large a number you can write down. Another advantage is that you can continue writing numbers in places to the right of the units column in order to denote fractions. All that distinguishes the number 1234 from the number 1.234 is the use of a decimal point (or comma in Europe) to mark where the units come. Computations with fractions are just the same as computations with whole numbers. The Babylonians used the same idea, except that they did not bother with a decimal point - that absolute size of a number was 'determined by inspection.' For example, the number could mean 160000, as noted above, but it could also be 1/81, the reciprocal of 81, which is why it was widely used. In the early days of deciphering Mesopotamian mathematics, people were puzzled as to why they would go to the trouble of writing a 160000-times multiplication table. The last sexagesimal number given in the table above, , also has a more useful meaning than 305470.