Cuneiform 101 · Chapter 05

Counting like a Sumerian

This is the numbers chapter. Three of its four new signs are the number-atoms of the entire script — each a single press of the stylus (the fourth, a measure for the counting, joins further down):

You met these three shapes as bare strokes in chapter 01’s anatomy lesson; here they take their seats as signs — the workhorses of a hundred thousand receipts. What this chapter adds is what they can do once you let them repeat.

Numbers came first

The oldest tablets that survive are not stories, hymns, or letters — they are accounts: so many sheep, so many jars of grain, so many days’ labor. The standard introductions to the script make this claim plainly: counting is close to the native tongue of the writing system, not a later add-on. The wedge that means “one” is older, on the evidence of the earliest tablets, than most of what it would go on to write.

The sexagesimal idea

Sumerian counted in base 60 — but not as sixty unrelated number-words. Underneath, there is a base-10 step: units are built from the vertical wedge 𒁹DIŠ · [diš] · one; item marker, repeated one to nine times; tens are built from the corner wedge 𒌋U · [u] · ten, repeated one to five times, for ten through fifty. Put a run of tens before a run of units and you have any number up to fifty-nine — the whole first “digit” of a base-60 system, spelled with two shapes.

Scribes did not usually leave nine wedges in one long undifferentiated row — accounts arrange them in tidy short rows so the eye can take in a quantity at a glance rather than counting stroke by stroke. The table below groups them the same way.

Nothing here beyond this chapter’s own atoms — the same vertical and corner wedges, put to their counting job by pure repetition.

Sixty and beyond

Here is the turn that gives the system its name. At sixty, Sumerian does not invent a sixty-first sign — it starts over, the way our own decimal system starts over at ten. And it starts over with the same shape it began with: sixty is written with a vertical wedge again, 𒁹DIŠ · [diš] · one; item marker, only now standing one place higher, so the very same mark can mean “one” or “sixty” (or thirty-six hundred) depending on where it sits. This is place-value notation, the same principle as our own “1” meaning one, ten, or a hundred depending on its column — just built on a base of sixty instead of ten. We will not build compound sixty-plus numbers by hand in this chapter; the point to hold onto is conceptual: the count keeps its shape and changes its weight.

Why sixty, of all bases? The question is genuinely debated — sixty divides evenly by 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30, which makes it forgiving for fractions and for splitting shares, and some scholars see a fusion of an earlier base-10 counting habit with a base-6 or base-12 one; no single account is settled fact. What is not debated is the legacy: our 60-minute hour, our 60-second minute, and our 360-degree circle (360 = 6 × 60) all descend, by a chain of transmission through Babylonian astronomy, from this same base sixty. Every time a clock’s second hand completes a circuit, it is retracing a Sumerian accountant’s number line.

Counting things

Counting needs something to count — so here the chapter’s fourth sign takes its seat, the unit that follows the number on a thousand barley receipts:

A bare number is rarely the point — Sumerian accounts pair a number with what is being counted, number first, then the commodity sign. The examples below are schematic, built only to show the shape of an account line, not a transcription of any particular tablet — with one exception: the last line adds your new 𒄥GUR · [gur] · gur — the great capacity measure of grain accounts, in the standard barley-account pattern the real corpus repeats endlessly.

Number, then commodity: that two-part shape — quantity plus the thing counted — is the single most common sentence in the entire cuneiform corpus, repeated across hundreds of thousands of tablets of grain, sheep, silver, and labor.

Drill before you go on

1. Write, from memory, the numbers 1 through 9 using only 𒁹DIŠ · [diš] · one; item marker, grouped in short rows.
2. Write 10, 20, 30, 40, and 50 using only 𒌋U · [u] · ten.
3. Compose 7, 23, and 45 again without looking at the table above, then check yourself against it.
4. Read back, aloud, the three barley lines in the reading panel — cover the translit and gloss columns first.
5. Anything shaky — write it five more times. Chapter 06 assumes you can compose any number up to fifty-nine without pausing to think.

Where this leads

This course’s own frequency counts over the CDLI corpus put 𒁹DIŠ · [diš] · one; item marker — the plain counting stroke — at the very top of the entire administrative record: the single most frequent sign, over a million lines of text. For most of the cuneiform corpus, number literacy is reading literacy. Chapter 06 takes you into the seals-and-bricks world of ownership marks, where these same counting habits sit alongside names and titles on the receipts, tags, and dockets that make up the bulk of what survives.

Next: seals and bricks — ownership, naming, and the everyday objects that carried writing into daily life.