Section system simulator: moieties, four sections and eight subsections as rule tables

One plain statement first. Section and subsection systems are not museum pieces. In many Aboriginal communities, notably in Central and northern Australia, people use their section or subsection names, widely called skins, every day, and someone who spends time in a community may be given one. The simulator shows only the rule tables underneath, the way a grammar sits under a language. It says nothing about how people speak, joke, argue or look after one another inside the system, and it should not be read as a puzzle someone solved.

Notation: F father, M mother, B brother, Z sister, S son, D daughter, read from the person, so MMBDD is the mother's mother's brother's daughter's daughter. The notation guide has the rest.

The rule tables

Every setting is two rules: whom a person of each group marries, and where a man's children go. A woman's children go where her husband's children go. With two moieties, A marries B; children take the mother's moiety in one setting and the father's in the other.

Four sections (Kariera type):

Eight subsections (Aranda type):

Drop the numbers and the second table collapses into the first: each section splits in two. Marriage keeps the number, descent between A and C keeps it, and descent between B and D swaps it.

Why the labels are abstract

Real systems have names in their own languages, and the same structure carries different names from one community to the next. In some languages each name has a man's form and a woman's form. The names belong to the people who use them, so the tool uses letters, as textbooks do. The tables follow documented systems: the four-section rules have the structure of the Martuthunira system of the Pilbara, the eight-subsection rules that of the Lardil of Mornington Island. Letters also differ between books. In A. R. Radcliffe-Brown's The Social Organization of Australian Tribes (1931), a man of A has children in D, not C. Compare patterns, not letters.

Reading the ring

Each group is a circle on a ring. Double lines join groups that marry each other; dashed arrows run from a father's group to his children's. The chosen group is red, the spouse's group pale peach, the children's group pale yellow, and the marriage line touching the chosen group is drawn in red. In four sections, A sits top right and the others follow clockwise, so the marriage lines are the two sides and the arrows cross as diagonals. In eight subsections A1 is at the top, again clockwise, and the arrows meet in the middle. The patrilineal moiety view shows no arrows at all, because a man's children stay in his own group.

Worked example: a man of A in four sections

This is the default. The result line reads "A man of A marries into B; his children are C", and the table gives:

Check each line against the table. A man of C has children in A, so the father is C. A woman of D marries C and her children are A, so the mother is D. FF: a man of A has children in C, so A. MM: a woman of A has children in D, so A. FZ is C like her brother; she marries D, and D's children are B. MB is D like his sister, and his children are B. Both kinds of cross cousin land in B, the spouse's section, so first cross cousins are marriageable: Radcliffe-Brown's Kariera norm of bilateral cross-cousin marriage.

Parallel cousins come out differently. FB is C, so his children are A; MZ is D, married to C, so hers are A too. They share Ego's section, like the Iroquois split on the kinship terms chart. The male line runs A, C, A and the female line A, D, A, which is why the tool reports a return after 2 generations in each.

Second example: a man of A1 in eight subsections

Switch the system; the person resets to A1. The tool reports spouse B1, children C1, father C1, mother D1, FF A1, MM A2, and both kinds of cross cousin in B2. B2 is in the right section but the wrong subsection, since B2 marries A2. So first cross cousins are not marriageable.

The path to B1 runs through the mother's mother. Mother D1 (a D1 woman marries C1, children A1). MM is A2, since an A2 woman marries B2 and B2's children are D1. Her brother is A2 too, and his children are C2. That daughter, a C2 woman, marries D2, and her children are B1. MMBDD = B1, the spouse's subsection.

Radcliffe-Brown made MMBDD the defining marriage of his Aranda norm and listed four second-cousin kinds who qualify: MMBDD, FMBSD, FFZSD and MFZDD. Run the other three through the table and each lands in B1. The female line takes four generations to return (A1, D2, A2, D1, A1), the male line two.

Limits

The tool places categories, not people. A rule that names MMBDD admits any woman of her category, and real marriages do not always follow the ideal. Radcliffe-Brown's types describe terminology and marriage, and Patrick McConvell and Rachel Hendery (2017) argue that the Kariera pattern is independent of four sections, which developed later. The note on closure in Aboriginal kinship looks at what the tidy diagrams leave out, and the explainer on Kariera and Aranda systems covers their history.

Questions

What changes if the person is a woman?

Her spouse's group is the same, but her children follow her husband's arrow. A woman of A in four sections has children in D; a woman of A1 in eight subsections has children in D2.

Why are cross cousins marriageable in four sections but not in eight?

In four sections the spouse's group is defined by the section alone, and both cross cousins fall in it. Eight subsections split that section in two, and first cross cousins land in the other half.

Why does the female line take four generations in eight subsections?

A woman's children stay in her matrilineal half and move one place along it each generation. In four sections that half has two members, A and D, so the line returns after two steps. In eight subsections it has four, A1, D2, A2 and D1, so it needs four.

Are these systems still in use?

Yes. In many communities they are part of everyday life, used to work out how people are related and what that asks of them. The tables here are a simplified outline of that knowledge, not a substitute for it.