Sided with Omaha but no Twist:
Three Logics of Alyawarra Kinship
• Woodrow W. Denham,
• Douglas R. White,
American University,
University of California,
Dubai, wdenham@ncia.net
Irvine drwhite@uci.edu
U. A. E.
U.S.A.
Cultural Structures and Distributed Cognition
Session 2: Ethnographic Cases for Potential Formalization.
Cultural Structures and Distributed Cognition
Chair: Dwight Read
Anthropological Sciences Meeting, New Orleans 2002 Friday
1:30-1:45
Air photo of Gurlanda Camp 1972.
The Fieldwork Experiment
• This paper derives from an experiment in quantitatively
oriented fieldwork conducted by Denham in Central
Australia thirty years ago.
• The experiment was designed explicitly to explore
differences between what Aborigines actually did and
what they said they did when anthropologists interviewed
them.
• The attempt to discover what they did rested on observing
and recording their activities, then using computers to
seek and extract patterns in the coded data that would
not have appeared in traditional ethnographic data.
Domestic activities.
Denham fieldwork ’71-2: data
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File01 Genealogies and vital
statistics - 377 records – one focus here
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File02 Census data - 264 records
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File03-20 digitized maps of 17
Alyawarra camps
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File21 Meteorological records - 146
days
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File22 Kinship term applications
- 104 egos x 225 alters = 23,400
applications – the other focus here
¨
File23 Sleeping Group
Compositions - 162 records
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File24 Residential Group
Compositions - 258 records
¨
File25 Task Group Compositions 2490 records
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File26-27 Observation distribution
records
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File28-78 Behavior Observations 41,809 records of numerically coded
data derived from 200 hours of
observations spanning 86 days
¨
Documents - 500+ pages of field
notes and historical letters
¨
Photographs - 217 portraits, 90
B+W prints, 230 color slides, 7 air
photos
¨
Other graphics - 3 Alyawarra
Territory Dreaming maps,17 camp
maps, 12 residence plans, 30 sketches
¨
Genealogical diagrams containing
all people belonging to the 17 countries
represented in the research population
¨
Audio recordings - 14 hours raw,
77 minutes edited
Some members of the research population.
Alyawarra fieldwork: one of the methods used is Photodeck
Cards for data collection on kin-term usage
This person’s use of kinship terms for
while they view other cards containing
alter’s card in the area indicated by the
others numbered 1-225 is recorded here
each alter’s photograph as mounted on
arrow
Our reanalysis
• Our new analysis examines the kin-term usage data elicited with the
Photodeck cards on each of 104 egos x 225 alters, in relation to a
• network analysis of regular equivalence in marriage patterns
between lineages using the genealogical and marriage data on all
264 individuals in the region studied, plus 113 ancestors. Lineages
are treated as regular-equivalent if they have equivalent relations to
equivalent sets of other lineages (White and Reitz 1983).
• We examined these data in the light of discrepant logics noted by
Denham, Chad McDaniel, and John Atkins (1979) in Aranda and
Alyawarra Kinship: A Quantitative Argument for a Double Helix
Model. American Ethnologist 6(1):1-24.
The original and new results:
an overview
• Denham, McDaniel, and Atkins (1979) found evidence for a Cultural
Model of the Alyawarra (and Aranda) kinship system as one where
– generational times were 50% longer for males than for females,
– but the discrepancies of actual kin term usage and this model were
about 23%,
– some of which was due to use of Omaha terms that merged
generations, and some to nonreciprocal use of terms.
• We reevaluate these discrepancies by
– a network analysis of equivalence classes in marriage behavior,
– locating the discrepancies in kin-term usage within the kinship
network, and
– deriving an analysis of the different logics-in-play from this evidence
Four Logics Operative in Alyawarra Kinship: Summarized
Logic
Description
Percentage Fit of Behavior
Logic0
Shared Semantic Rules for Named Sections:
Membership rules as applied by individuals
100% for patri-descent
99% in marriages
Logic1
Shared Kin Terms, as applied by individuals
87% in Opposite patri-side
67% in Same patri-side *
Logic2
Social Organization via Emergent Behavior,
sensitive to age groupings
75% +/-
Logic3
Variable use of Omaha Terms,
signaling marital exclusions and lineage-based inclusions
16% in W,WB terms and
in M,MB terms *
* Denham et al. 1979: p. 12 for row 2, overall fit; p. 10 for row 4, where we find a potential W is
often equated with M, and a WB with MB (the Omaha pattern of terminology). A sided marriage
network is one in which marriages can be classified into two supersets such that parents of bride
and groom tend to come from opposite sides. A viri- or uxori-sided network is one that is sided, with
sidedness respectively assigned to males by patrilineal inheritance, or to females by matrilineal
inheritance. The Alyawarra are a case in which both tendencies exist, i.e., the marriage network is
both viri- and uxori-sided (Houseman 1997).
Logic0: Tetradic rules for (four-) named marriage sections are
constituted by three local principles of equivalence classes
amongst relatives, plus a proviso that the rules apply uniformly:
=
Triangles -male sibling
equivalence classes
Circles - female sibling
equivalence classes
Marriage
=
=
• 1. Equivalence of siblings but nonequivalence of cross-cousins.
• 2. Equivalence of alternating generations in male and female lines.
• 3. Marriage cannot take place between those of the same equivalence class.
• 4. All rules apply uniformly, and uniformly to equivalence classes (if the
brothers in an equivalence class marry into another such class, then so do the
sisters, and vice versa).
• Note that these might well be rules that hold for all four-section systems.
Tetradic Logic0 (e.g., Section Memberships): Egocentric
1
2
3
Kamara =
7
8
Burla
13
14
Kamara
4
5
6
Pityara
9
Kamara
10
11
Ngwariya =
15
Pityara
16
12
Burla
17
18
Kamara
= Pityara
Solid lines assign relative equivalence classes both by descent rules
(patrilines, matrilines) and by affinity (marriage). The equivalence classes
would hold from the perspectives of sibling sets 1/2, 9/10, and 17/18, .
Dotted lines show the variety of equivalence classes to which children
might be assigned for women in equivalence class 4.
Alyawarra section names are Kamara, Pityara, Burla and Ngwariya
Section Rules (Logic0): Neither
Genealogical nor Static
• More general than kinship: section rules are also used in
ceremonials, beyond kinship proper
• Based on an equivalence-class logic that applies to but
is not subsumed by genealogical relationships
– Anthropological models of sections often infer marriage patterns
from equivalence-class logics as if the genealogical marriage
rules were implied by these rules when in fact they are not.
– Kinship terminologies often fit the section logic and again are
often used by anthropologists to imply marriage rules that do not
in fact match actual behavior.
– Classificatory kinship terminologies consistent with sections
require careful consideration of equivalence-classes among
complex bundles of genealogical relationships.
Ceremonial activities.
Kinship Dynamics of Sections:
Historically, 0 to 4 to 8, in 30 years
• The four-section system of Logic0 was probably adopted by
the Alyawarra in the 1850s from a society just to the west, at the
same time as is documented for their Aranda neighbors.
• Ditto for an eight-subsection variant of that system, which was
adopted by the Northern Aranda in the 1880s. What we call
Logic1 — Models of the Kin Term System— includes
Radcliffe-Brown’s model of this system.
• The Northern Aranda have eight named subsections, while
only four sections are named among the Alyawarra, with
eight unnamed subsections implicit in the kinship terminology
Octadic Logic0: Tetradic Logic0 extended to 8 subsections
1
2
3
4
5
1Kamara = 2Pityara
7
8
9
2Burla
13
10
6
2Kamara
11
12
1Ngwariya = 1Burla
14
15
1Kamara
16
17
Modified
18
2Pityara
2Kamara = 1Pityara
1Ngwariya
1Burla
2Ngwariya = 2Burla
Original
1Pityara
Historically, ca. 1880: “each of [the] sections was divided into two, so that, to a
[Ngwariya] man, for example, only half of the [Burla] women were eligible as wives,
the other half being Unkulla or forbidden to them” (Spencer and Gillen 1927:320-322).
Octadic Logic0 provides a basis for a complete inventory of
fit not only to the implicit eight-subsection groupings implied
by informants’ designations of their first choice in appropriate
usage of kinship terms applied to specific alters, but also:
  Where and to what extent do violations of subsection logic
correspond to irregularities in the network patterns of Logic2
  To what extent usages are systematically non-reciprocal
(i.e., not merely as a result of the elicitation methods) given
both the network and subsection framing of Logic2
  Where precisely and exhaustively Omaha terms are
employed in Logic3
  These questions will be the subject of a separate
article. Meanwhile, partial answers are provided by our
network analysis.
Anthropological Fictions and Generalizations (Logic1)
Artificial closure of equivalence class
marriage rules in Radcliffe-Brown’s
‘Kariera’ model: one of “repeated
sister exchange”
Artificial closure of
equivalence class marriage
rules in R-B’s ‘Aranda’
model: “sister exchange in
alternate generations”
From Logic1  Logic2,
‘open’ format: one of
many possibilities,
(Denham et al., 1979 and
Tjon Sie Fat 1981, 1983)
Logic1, but a false image: Kin terms ‘fit’ R-B’s 8-subsection
‘Cultural Model’ of ‘normative’ Alyawarra and Northern Aranda
kinship (Aranda-type). A good ‘fit’ of model and terminology but
not to behavior: the Alyawarra have no sister exchanges, etc.
Other Generalizations of Logic1  Logic2:
Network Models of Kinship Organization,
attuned to age differences and strategies
‘open’ format: 0
age difference
between spouses
‘open’ format: 14
year age difference
(as per Denham et
al. 1979)
‘open’ format: 28 year
Figure same as above, but
age difference
steeper diagonal
Logic2 is a Logic1 kin-term pattern, but now analyzed in relation to
social (network) organization, not just the kin-term pattern alone
Logic2?: The ‘Open Format’ proposed by Denham et al. (1979)
A1
K1
D1
N2
B2
P2
B1
D1
N1
C1
K2
A2
B2
C1
K2
D2
P1
B1
N1
C2
B1
D2
P2
D1
N2
A1
K1
C2
B1
Red=
matri
lines
P2 B 2
D1
N1
C1
K2
A2
B2
C1
K2
D2
P1
N1 B 1
D2
P2
K1
A1
C2
B1
N2
Key: Assuming that ego is in section K, then K,P,B,N are section designations and
K1,K2, through N1,N2 are implicit 8-subsection designations. A 1, A 2, B 1, B 2, C
1, C 2, D 1 and D 2 are distinct kin terms consistent with 8 implicit subsections.
To see if Denham et al.’s Logic2 is a
network pattern
• We place Alyawarra lineages into regular equivalence
classes in a network diagram according to whether they
have equivalent relations to equivalent sets of other
lineages (White and Reitz 1983), using the genealogical
and marriage data on all 377 individuals.
• Actual patterns of marriage choice, social organization,
and patterns of alliance then emerge as an element of the
logic, i.e., a logic realized in the context of the social
network. This is the real-time decision-making ‘realization’
of cultural models, complete with a time dimension.
• In the following results, we find the ‘open’ format model
of Denham et al. (1979) does fit the equivalence-class
patterns of actual behavior ‘roles’ in the social network.
Logic2: The actual kinship network with social organization
given by regular equivalence analysis of inter-lineage marriages
(key: red =mothers, black =fathers, lite marriages
)
key
N=all 377
individuals
K’
L’
M’
N’
O’
P’
Q’
Node Colors: blue-Kamara, green-Burla, yellow-Pityara, orange-Ngwariya
Node Size: proportional to age (smallest black nodes are unknown/deceased)
Logic2: The actual kinship network and social organization; this
time the colors are those of the languages spoken by individuals
K’
L’
M’
N’
O’
P’
Q’
Key to Languages Spoken: blue-Aranda, yellow-Alyawarra , green-in between
Logic2: The actual kinship network and social organization, with
a close-up of the network of Alyawarra speakers
(red and black arrows=mothers, fathers; green lines=marriages)
•6 (early) red lines correspond to “open format” 28 year difference
•87 red lines correspond to “open format” 14 year difference
•7 red lines correspond to “open format” 0 year difference
Logic3: The actual kinship network, social organization,
showing Omaha usage within the network of Alyawarre speakers
blue lines=marriage, green lines=Omaha terms such as W=M,
WB=MB, found to be non-reciprocal and to exclude marriage
Use of Omaha terms excludes possibility of marriage
Difference between the Logics
• The standard interpretation of kin-term Logic1 models of
Aranda-type (including Alyawarra) kinship (e.g., by R-B
and Lévi-Strauss) is that of symmetric or direct exchange.
• The actual kinship network, where Logic1  Logic2,
confirms Denham et al.’s (1979) ‘open format’ model, one
of asymmetric or generalized exchange. It has:
– No generational closure (no cycles of siblings-in-law)
– No algebraic closure (rather there are open-ended alliances)
– dynamically ‘open’ and subject to adjustments that follow from
marriage strategies (not static or locked into prescriptive rules)
• Analysis of signaling in Logic3 is
– Consistent with this dynamic, signaling non-marriageable
– Non-reciprocal in use of terms at behavioral level
Further, we see these results…
• Kinship terminologies are egocentric
• But local rules have implications for the larger network
structure, a point evident to participants: e.g., choices as to
age of spouse co-vary with implications for reciprocity
(same age) versus asymmetry (large age differences)
• The global network structure is the social organizational
context in which to evaluate the terminologies, cultural
models and decision models
… as consistent with Read’s theory of
kinship terminologies as applied to
classificatory kinship
And that’s a good place to stop
PHENOTYPE
Our additions
to Read’s
model of
behavioral
realization of
last year
Symbol System
Conceptual
Structures
Instantiation
Goals/ Strategies
Mental
Representation 2
Actor and Group
Positions in Social
Network
Use of signaling
External
World
(continuous)
Senses
Sensory
Processing
Sign
System
Units
Cognitive
System
Decision
Behavior
Mental
Representation 1
Responses of others and behavioral effects on context
Dwight Read 2001 Symposium: Cultural Idea Systems: Logical Structures and the logic of Instantiation (AAA Annual Meetings)
Concluding note on methods
• It is easy to misunderstand the logics of equivalence classes in
Australian systems. Denham’s experimental field methods provided
a different set of understandings of these logics.
• Anthropologists concerned with ‘modeling’ kinship, from R-B to
Lévi-Strauss, have inferred prescriptive marriage rules from kin
terms in interpreting their models. Denham’s methods also permit a
network analysis that gives a better understanding.
• The Alyawarra case, we think, exemplify the underlying dynamics
of the adaptive social organization that accompanies section systems
generally. Denham’s methods might have benefited from interviews
on how and when sections and subsections were introduced, how the
unnamed subsections are reckoned, if at all, and informants’
reflections on how they determine the ‘Alyawarra way’ of reckoning
the correct kinship term for alters.
Four Logics Operative in Alyawarra Kinship, recalled
Logic
Description
Percentage Fit of Behavior
Logic0
Shared Semantic Rules for Named Sections:
Membership rules as applied by individuals
100% for patri-descent
99% in marriages
Logic1
Shared Kin Terms, as applied by individuals
87% in Opposite patri-side
67% in Same patri-side *
Logic2
Social Organization via Emergent Behavior,
sensitive to age groupings
75% +/-
Logic3
Variable use of Omaha Terms,
signaling marital exclusions and lineage-based inclusions
16% in W,WB terms and
in M,MB terms *
* Denham et al. 1979: p. 12 for row 2, overall fit; p. 10 for row 4, where we find a potential W is
often equated with M, and a WB with MB (the Omaha pattern of terminology).
A more detailed summary
•
•
•
In Logic1 the Alyawarra strictly adhere to marriage rules and ‘normative’ kinship
terms that conform to marriage sections (cross-cutting exogamous sides) and
unnamed endogamous matrimoieties that unify interleaved alternating generations.
In Logic 2, the axiom of generational closure – that successive sibling-in-law links
close into cycles in an endogamous group – does not apply because female age at
marriage is significantly lower than that of males. The resulting extra-normative age
bias yields recurrent patterns of marriage between patrilineages that are much more
likely to be asymmetric than symmetric (as with sister exchange, for example).
Patterns of marriage among the deceased are quickly forgotten, and no longer cast
their shadow as a constraint on future behaviors. Thus wife-givers and wife-takers
may engage in exceptional marriages that inflect Logic2 behaviors into new
systemic patterns leading to lineage remapping of generations. This allows the
“kinship system” to evolve dynamically across a class of network models influenced
stochastically by age distributions at marriage.
In Logic3, the unintended effect of demography (H>W age differences) is
supplemented by widespread and intended use of extra-normative Omaha
terminology as an exclusionary device that says, “don’t marry here”, but does so
nonreciprocally.
The field data collected
by Denham in 1971-72
are available in the
Group Compositions in
Band Societies archived
on-line at
http://eclectic.ss.uci.edu/
~drwhite/