The Zagi Family

Üksküla sees a “genealogical primer for the clan of Zagi” in the Zagi documents. I think it’s more likely to be a very simple list of family relations in a small clan or band.

Inrik Üksküla’s The Clan of Zagi: Numeric Calculus or Genealogical Primer? A Structural Analysis of the Kristiansen Cuneiform Corpus is a structural study of a small corpus of clay tablets written in the Kristiansen glyph system, all headed in Akkadian as “the clan of Zagi” (𒅎𒊑 𒍝𒄀𒀝, imri Zagi-ak). The author treats a machine-readable transcription of 104 short, highly formulaic sentences built from just 46 composite signs.

Quantitative analysis shows that the corpus is dominated by a few “pivot” signs that organize sentences into rigid templates, a tightly constrained paradigm of four markers (glossed ONE to FOUR) that always combine with a special UNIT sign, and a restricted linker (AND_PLUS) that only appears in certain fixed trigrams. Many sentences occur as near-reversal pairs, suggesting a learned formalism rather than free prose.

On this basis he develops and tests two main interpretations. Hypothesis A sees the tablets as a didactic introduction to a small numeric or proto-algebraic calculus, with UNIT as a base quantity, ONE-FOUR as small numerals, and the pivots DEF_PIVOT marking “is defined as” vs EQ_PIVOT for “is equal to.” Hypothesis B instead reads the same structures as a genealogical primer for the clan of Zagi, where UNIT means “clan member,” ONE to FOUR encode ordered child positions, and the templates assign and identify roles within the lineage. A comparative evaluation finds that both models fit the internal structure, while earlier Kristiansen material favors the numeric reading and the heading favors the genealogical one. The author ultimately leans toward a hybrid view: the tablets show a formal, possibly numeric notation being used to model and teach the internal structure of a specific kin-group, while stressing that the limited data do not allow a definitive choice between the pure or hybrid interpretations.

In the genealogical primer hypothesis, Uksküla’s UNIT sign C01-M03-S01-C02 is a kind of generic clan member, an abstract Zagi-descendant, not a specific person. That’s already a kinship reading, just a very cautious and abstract one. What I want to do here is push that a step further. What if C01-M03-S01-C02 isn’t UNIT at all, but just straight-up CHILD? Not “a generic Zagi-descendant” in a theoretical sense, but the ordinary kin term you’d use when you say “child one”, “child two”, “they have three children”.

Once you flip that switch, a big chunk of the tablets stops looking like algebra and starts reading like a regular example family tree.

Two key patterns: “X has N CHILD” and “CHILD N is Y”

Let’s look at how C01-M03-S01-C02 behaves in the corpus (I’ll call it CHILD from now on, to keep the discussion readable). There are 26 occurrences of this sign in the 104 sentences. They fall into two very tight patterns:

Pattern A: X DEF_PIVOT N CHILD

This looks like

X C03-M03-T02 N C01-M03-S01-C02

Where

• C03-M03-T02 = DEF_PIVOT
• N = ONE / TWO / THREE / FOUR
• C01-M03-S01-C02 = (let’s assume) CHILD

Every single DEF_PIVOT + CHILD line in the corpus matches this template. For example (tokens anonymised, but structure preserved):

F3_44: X₁ DEF_PIVOT TWO CHILD
F3_45: X₂ DEF_PIVOT TWO CHILD
F3_51: X₃ DEF_PIVOT TWO CHILD
F3_70: X₁ DEF_PIVOT THREE CHILD
F3_71: X₄ DEF_PIVOT THREE CHILD
F4_83: X₅ DEF_PIVOT FOUR CHILD

If we stop calling this “DEF_PIVOT” and just read it as HAVE, these become very natural genealogical statements:

• “X₁ has two children.”
• “X₂ has two children.”
• “X₃ has two children.”
• “X₁ has three children.” (repeated or corrected entry, or perhaps a second person with the same name)
• “X₄ has three children.”
• “X₅ has four children.”

That’s already a perfectly ordinary way to talk about a family.

Pattern B: CHILD N EQ_PIVOT Y

The second cluster of sentences looks like this:

C01-M03-S01-C02 N C03-M03-L01 Y

Where:

• C03-M03-L01 = EQ_PIVOT
• N again is ONE / TWO / THREE / FOUR
• Y is some other token, which I would posit as a candidate personal name

Examples:

F3_47: CHILD ONE EQ_PIVOT Y₁
F3_48: CHILD TWO EQ_PIVOT Y₂
F3_54: CHILD ONE EQ_PIVOT Y₃
F3_55: CHILD TWO EQ_PIVOT Y₄
F3_73: CHILD TWO EQ_PIVOT Y₅
F3_74: CHILD THREE EQ_PIVOT Y₆
F4_84: CHILD ONE EQ_PIVOT Y₇
F4_85: CHILD TWO EQ_PIVOT Y₈
F4_86: CHILD THREE EQ_PIVOT Y₉
F4_87: CHILD FOUR EQ_PIVOT Y₁₀

If CHILD is really “unit”, these become quite abstract:

“unit one equals [token]”
“unit two equals [token]” …

If CHILD is a lexical noun and EQ_PIVOT is BE , they become extremely prosaic:

“Child one is Y₇.”
“Child two is Y₈.”
“Child three is Y₉.”
“Child four is Y₁₀.”

Now combine Pattern A and Pattern B.

2. Document 4 as a worked example family

Document 4 gives us a beautifully clean block:

• F4_83: C07-S02-C06 DEF_PIVOT FOUR CHILD
  “X₅ has four children.”
• F4_84: CHILD ONE DEF_PIVOT C07-S01-A05-S01
  “Child one is Y₇.”
• F4_85: CHILD TWO DEF_PIVOT C05-C01-T02-C06-T02
  “Child two is Y₈.”
• F4_86: CHILD THREE DEF_PIVOT A04-T02-A01-T02
  “Child three is Y₉.”
• F4_87: CHILD FOUR DEF_PIVOT M01-T02-B02-T03
  “Child four is Y₁₀.”

So the tablet is essentially saying: “X₅ has four children. Child one is Y₇, child two is Y₈, child three is Y₉, child four is Y₁₀”. That’s astonishingly straightforward if you allow yourself the word CHILD.

No algebra is required. The numerals are doing what numerals do in any family tree: differentiating “first child”, “second child”, etc.

3. Couples: AND_PLUS as parental pairing

Now let’s bring in the AND_PLUS sign A02-L01. In the wider dictionary it’s labelled as a special “and” used with numbers, but in this genealogical view it aligns almost too neatly with “A and B”, i.e. parental couples.

Here are some of the most common AND_PLUS pairs:

C02-S01-M03-S01 AND_PLUS C05-C02-T02-M03-T03
B03-T02-B05-L01-S01 AND_PLUS A01-L01-B03-T02
C02-S01-M03-S01 AND_PLUS C06-S01-C02-S01-C01-T02

These specific pairs then turn up in CHILD-definitions:

• F3_46: C02-S01-M03-S01 AND_PLUS C05-C02-T02-M03-T03 DEF_PIVOT TWO CHILD
  “P and Q have two children.”
• F3_53: B03-T02-B05-L01-S01 AND_PLUS A01-L01-B03-T02 DEF_PIVOT TWO CHILD
  “R and S have two children.”
• F3_60: C02-S01-M03-S01 AND_PLUS C05-C02-T02-M03-T03 DEF_PIVOT TWO CHILD CHILD ONE EQ_PIVOT B03-T02-B05-L01
  “P and Q have two children; child one is T.”
• F3_72: C02-S01-M03-S01 AND_PLUS C06-S01-C02-S01-C01-T02 DEF_PIVOT THREE CHILD CHILD ONE EQ_PIVOT A01-L01-B03-T02
  “P and U have three children; child one is S.”

Again, if UNIT is abstract, these lines are clever little set-theoretic statements about cardinalities of groups. If it’s CHILD, they’re the most ordinary genealogical sentences imaginable:

“P and Q have two children. Child one is T.”

“P and U have three children. Child one is S.”

The arithmetic is still there, as we’re absolutely using numerals and a pivot to define cardinalities, but it’s arithmetic about people and their kids.