Transcript Social physics: Networks & causal chains (emergent causality in network cohesion) "Life and the Sciences of Complexity" Iberall Distinguished Lecture Series C:\Documents and Settings\User\My.

Social physics: Networks & causal chains
(emergent causality in network cohesion)
"Life and the Sciences of Complexity" Iberall
Distinguished Lecture Series
C:\Documents and Settings\User\My Documents\pub\SocialPhysics
Douglas R. White
workshop December 4, 2008
1
Outlines for Workshop
with some examples from the Talk
1. Anthropology and Physics as experimental sciences
2. Cohesive Causality: Schools to industrial organization ..a few examples..20
3. World economy and historical dynamics
… left for the main talk
4. Cohesion in Kinship groups (32-…)
a Cohesion in kinship networks as constituents of society
b Simulation
c Mapping data onto networks and further findings
d Conclusions: a concrete implicate order
2
Anthropology as an experimental science
•
Anthropologists are the experimentalists of the social sciences.
•
They gather meticulous data (ethnography)
•
About 40% of the best ethnography adds a time dimension (the rest
are “idealized” static structures). Iberall’s advice: you have to do your
case studies through time (and study process, i.e., dynamics).
•
Using the temporal access, the dynamics of social processes can be
studied in all of its “compartments.”
•
I followed his advice.
3
Anthropology as diachronic/policy science
•
I followed that advice by teaming up with one of the best time-series
projects in Africa, one that did before-after studies of the impact of
relocation of 100,000+ people with building the Kariba Dam in Zambia
•
Rather than changes from one “static” state to another, their blanket
ethnography, every 2-3 years, showed new emergents and massive
changes in everyone of a dozen of these short time period, and no
emergent stability.
•
Their study “informed” World Bank and IMF policy on resettlement
projects: contrary to economists’ views, people were not “open” to
innovation after resettlement, they were instead oriented more
conservatively toward reestablishing their life-ways, which took about
four years, after which they were more open to innovation.
•
(By that time economists would have implemented their plan, failed, and
tried to erase the tracks of their failures, which are nonetheless in the
documentary records of development programs).
4
Cohesive emergence in the sciences
• Given atomisms interacting at one “level” of study that are made up
of smaller atomists at a finer scale, interacting to form the larger
units, it is not experimentally proven that the relation among levels
is strictly hierarchical. Thus no strict “vertical reduction” principle
of explanation in the sciences. Explanations do not apply as
hierarchical reductionism but laterally. In complex systems,
through memory, storage bins, interactions, cohesive emergence of
atomisms, how atomisms are built, with cohesion linked to stability.
• This observation has two consequences: (1) a key measure of
complexity is the extent to which at any level the interaction of
entities is subject to time-lagged effects internal to their
atomisms that resurface to alter their interactions (bins,
processes and memory). (THAT COMPLEXITY WILL BE IN
EVIDENCE IN THE COHESIVE GROUPS WE STUDY)
5
The Lateral principles of science
• Consequence (2): general principles do not apply so much vertically
(hierarchical reductionism) but laterally. Phil Anderson agreed as
do many physicists today.
• Iberall viewed the study of processes at any level as “chains of
causality.” These form networks. Networks don’t simply link
elements. They form cohesive units that represent emergence of a
higher out of a lower level of atomisms.
• Interactions leading to emergent cohesion of atomisms at one
scale may produce atomisms at a larger scale.
6
The Network principles of science
• Iberall and I had in common a view of atomisms and
networks at all these non-strictly hierarchical levels.
My “networks of processes” are his “chains of causality”
but they take a different shape with cohesive units.
• In the past four decades, especially the last, the
“network sciences” have become a lingua franca of
experimental science (simulation & observational) in
physical, chemical, biological, social, economic & now,
anthropological and political sciences. Emergent
causality has yet to be fully incorporated into the
network sciences.
7
What are atomisms?
• At any level of study, the atomisms are the entities that persist so
as to interact at some time scale (“asts”), so as to produce effects.
The very concept of atomism is linked to causality as observable
effects asts.
• Entities that persist so as to interact => interact to persist must
have the two key properties of cohesion: (1) resistance to
destruction (asts) by external shocks and (2) interactions among
their components (internal bonds) that not only resist destruction
but that facilitate the coordinations that enable persistence and
activity (asts) that produce external effects – thru cohesion.
8
So what are the “cohesive units” of
networks?
It was Iberall who convinced me that networks don’t
just link elements, i.e., without strictly bounded units
larger than a single node, but that there are cohesive
units within networks. Investigating this possibility led
me to an unusual idea of how groups are constituted in
networks.
The idea is based on a fundamental formalism of
network and graph theory that defines the boundaries
of cohesion. (e.g., Harary 1969)
9
Structural k-cohesion: a
fundamental definition
• Within a network, subnetworks of cohesive webs (kcomponents) occur where each node is a hub with at
least k connections to others SUCH THAT each node has
at least k node-independent paths (no shared
intermediaries) to every other.
• For each value of k all the maximally large webs can
be found, they will be nested, they may overlap, and
they are nonseparably connected without removal of a
minimum of k nodes (the Menger theorem)
10
4-component
structurally 4cohesive
network
4-inseparable
≡
4 independent
paths for each
pair of nodes
Here: THERE IS NO
CENTRAL NODE
11
4-component
structurally 4cohesive
SCALABLE
network
4-inseparable
≡
4 independent
paths for each
pair of nodes
Here still: NO
CENTRAL NODE
12
4-component
structurally 4cohesive
SCALABLE
network
4-inseparable
≡
4 independent
paths for each pair
of nodes
NO CENTRAL NODE:
but there could be
This 4-cohesive network can be expanded INDEFINITELY with a cost of only four new
edges for each new node, and they may attach ANYWHERE in the 4-component.
13
A science of cohesion & causality
• Hypothesis: Its not single causal chains that have
major abiding causal effects, but the emergent
cohesive entities at different spatial and temporal
scales that have major causal effects but also
metastable tendencies in their fluctuations.
• Proper identification of emergent network- cohesive units makes
this sciences easier and much more grounded than you would
think.
14
These k-cohesive “units” define
scalable human groups
Since k-cohesion in a network with n nodes requires only a
constant number of ties (k) per person, a k-cohesive group
can expand indefinitely at a constant cost per person. This
entails that k-cohesive groups are scalable, that is, they
are able to scale-up in number or grow indefinitely without
extra costs per person. The growth of cohesive ethnicities
plays a fundamental role in historical dynamics.
The minimum benefit b of independent cycles per person is nearly
constant (b < (k-1)/2) while the non-independent cycles per person
grow exponentially, offsetting the effects of distance. Excess in m
links above the minimum k*n/2 for k-cohesion can provide
centralization, additional local cohesion, etcetera.
15
These units of human groups are our
informal superatomistic organizations
Normally we think of “groups” as necessarily having leaders, names, lists
of members known to each other through communications from central
to peripheral members or through face-to-face meetings. Sociologists
since Durkheim have a conception of a social ”group” as having an
implicit charter and constitution, a kind of corporation, analogous to the
idea of a formal organization. Structural cohesion is a more generic idea
of a group more on the model of a community, where people may be
multiply and densely connected, operating as organizations but
informally, and scaling up even to ethnicities and their inclusions in the
lesser cohesive nationalities.
16
with effective causality and agency
• I am not saying that structurally cohesive groups (of kin, in
schools, organizations, politics, science, industry, etc.) have the
agency and decision-making analogous to individuals (clearly
ethnicities do not, tho nationalities as national governments do).
But structurally k-cohesive groups do have k times greater
efficacy to do so with k-times the potential :
• 1) for internal group coordination through mutual influence and
communication
• 2) for external causality, whether through agency or
unintended effects
• 3) to operate as organizations, even without central leadership.
17
So what are the “units” of human
groups? The nested atomistic levels?
So a more general idea of a group, more on the model of a community
core can be based on the formalism of k-cohesion, where people are
not only more densely connected but all pairs of members are kcohesive with one another. This definition does not require that the
group is named, with a formal organizational charter or membership,
but implies the capacity for a level k of intensity of redundancy in
communication and resistance to disconnection.
Nesting of cohesive groups occurs by virtue of intensity: a group
where all pairs have connection intensity k are a subgroup of those
with intensity k-1. These groups are not just named entities but have
interaction intensities.
18
The “units” of human groups and
nested atomistic levels
In kinship and other networks, there are entities that we
can identify as “groups” because they are cohesive, they
coordinate their actions, have divisions of labor, and may
carry distinctive recognizable markers, including selfrecognition and identity.
Cohesive groups of this sort may define community, social
class, ethnicities, the stable cohesive local subgroups of
populations as distinct from migrants.
19
Topical Examples: Cohesive Causality
•
•
•
•
•
•
•
•
•
Education
Social Groups
Political Parties
Science
Industry
Kinship
Cities & Trade
Warfare/Empire
World Economy
Workshop examples: bolded;
others in the public talk
•
•
•
•
•
•
•
•
•
School attachment
Organizational fragmentation
Bifurcation/Competition/Collusion
Transmission lines and cores
Collaboration/Innovation
Complex tasks/Cohesion
Balance/Cycling/Innovation
Resistance/Replacement
Metastable oscillatory cycles
20
Longitudinal Network Studies and Predictive Social Cohesion Theory
overlapping k-components in high schools predict school attachments
The algorithm for finding social embeddedness in nested
Fig Structural Cohesion of Friendships
cohesive subgroups is applied to high school friendship _______in an American high school
networks ( boundaries of grades are approximate). The
11-12th grade
measures of cohesive embeddedness are tested against
outcome variables of school attachment in the friendship
study. The cohesion variables outperform other network
and attribute variables in predicting the outcome
variables using multiple regression.
Nearly identical findings are replicated for school
attachment measures and friendship networks in 12
American high schools from the AddHealth Study
(http://www.cpc.unc.edu/addhealth/), Adolescent Risk and
Vulnerability: Concepts and Measurement. Baruch
Fischhoff, Elena O. Nightingale, Joah G. Iannotta,
10th grade
Editors, 2002, The National Academy Press.
2003 James Moody and Douglas R. White, Social Cohesion
and Embeddedness: A Hierarchical Conception of Social
Groups. American Sociological Review 8(1)
9th
8th grade
Interpretation: 7th-graders- core/periphery; 8th- two cliques, one hypersolidary, the other marginalized; 9th- central transitional; 10th- hang out on 7th grade
margins of seniors; 11th-12th- integrated, but more freedom to marginalize
21
Education: School attachment
Levels of K-cohesion in these schools vary from 1-8
• In general, within a network, a k-component is a
maximal subgroup in which
– Every pair is connected by at least k node-independent paths
– A group is not separable without removal of k nodes
• Level of k-cohesion predicts school attachment
(replicated in 10 schools, complete network
Adolescent Health Surveys)
• LR Odds 9.1 p=.002 Moody & White 2003:10
22
Organizational Fragmentation
(how a karate club splits in two)
• Levels of k-cohesion apply to friendships: k=1, 2, 3, 4components (White & Harary 2001)
– Every pair is connected by at least k node-independent paths
– A group is not separable without removal of k nodes
• As the teacher and owner compete people forced to
choose:
• The order of dropping ties is predicted by least
cohesion (R2 = .94) p < .0000000001
23
.
Longitudinal Network Studies and Predictive Social Cohesion Theory
A test of the k-cohesion measure
is exemplified by successful
prediction of how a group,
studied longitudinally during a
period of conflict between
leaders, divides into two (Fig 1).
Fig. Snapshot of friendships at an early point
in time in a longitudinal study of friendship
in a Karate club, with leaders labeled T and
A and levels of cohesion coded by color.
2001 Douglas R. White and Frank
Harary, The Cohesiveness of
Blocks in Social Networks: Node
Connectivity and Conditional
Density. Sociological Methodology 2001,
31(1):305-359. Blackwell Publishers, Inc.,
Boston, USA and Oxford, UK.
Connectivity: Blue=4 Red=3
Green=2 Yellow=1
Ethnography and data source: Wayne Zachary
24
Loss of cohesion
T
A
T
T’s side
T and A start to fight: some must choose sides
members of a
group with
cohesion level
k automatically
have at least k
different ways
of being
connected
through (k)
nodeindependent
paths
A
A’s side
Opposing cohesive sides emerge
T = karate teacher
A = club administrator
Block Connectivity:
Blue k=4 (quadricomponent)
Red k=3 (tricomponent)
T
A
Green k=2 (bicomponent)
Yellow k=1 (component)
Figure 1a,b,c Data source: Wayne Zachary, 1977. An Information
Flow Model for Conflict and Fission in Small Groups. Journal of
Anthropological Research 33:452-73.
25
The sides separate along cohesive fracture
Industry (Biotech)
In 12 successive years, what predicts collaborations?
• LR log-ratio odds (DBF=Dedicated Biotech Firm)
• DBF to DBF
DBF to nonDBF
• New
Repeat
New
Repeat
• 1.06
• P<.05
» SHARED COHESION
1.1
n.s.
» PARTNER COHESION
5.33
p<.0001
1.91
<.001
• 1.43
2.6
1.67
1.08
• P<.01
.001
p<.001
n.s.
• (Diversification is the other strong predictor)
26
all ties for a year, Biotech,
1997
Attractor
Flip forward
and back for
a sense of
dynamic
alternation
of
consolidatio
n and
reaching out
for
innovation:
all ties /
new ties
is kcohesion
27
New ties, Biotech, 1997
Attractor is
k-cohesion
and
diversity
(flip back)
28
Longitudinal Network Studies and Predictive Social Cohesion Theory
Structural Cohesion predicts collaborative Attachment Dynamics of
collaborations in Biotechnology (2,899 firms) longitudinally
Fig Biotech Collaborations
To account for the development of collaboration among organizations in
the field of biotechnology, four logics of attachment are identified and
tested: accumulative advantage, homophily, follow-the-trend, and
multiconnectivity. We map the network dynamics of the field over the
period 1988-99 (Fig 1999). Using multiple novel methods, including
analysis of network degree distributions, network visualizations, and
All ties
multi-probability models to estimate dyadic attachments, we
1989
demonstrate how a preference for diversity and multiconnectivity in
choice of collaborative partnerships shapes network evolution.
Cohesion variables outperform scores of other independent variables.
Collaborative strategies pursued by early commercial entrants are
supplanted by strategies influenced more by universities, research
institutes, venture capital, and small firms. As organizations increase
both the number of activities around which they collaborate and the New ties
diversity of organizations with which they are linked, cohesive
1989
subnetworks form that are characterized by multiple, independent
pathways. These structural components, in turn, condition the choices
and opportunities available to members of a field, thereby reinforcing
an attachment logic based on connection to partners that are diversely
and differently linked. The dual analysis of network and institutional
evolution offers a compelling explanation for the decentralized
All ties
structure of this science-based field.
1990
2003 Walter W. Powell, Douglas R. White, Kenneth W. Koput and Jason
Owen-Smith. Network Dynamics and Field Evolution: The GrowthAnd
of so on
Interorganizational Collaboration in the Life Sciences, 1988-99.
to 1999
Submitted to: American Journal of Sociology.
29
Science transmission
• This example gives an aspect of the social
transmission of science in terms of genealogical
relations among scientists in Geneva, 16th-19th
centuries (Eric Widmer 1998).
• Cohesive & (connected but noncohesive) groups differ
in their specialties, with physics, math, law and
theology in the temporally early cohesive core
• Transmission gives way to universities at later time
periods
30
Kinship cohesion in Science
3 physics 3 theology 2 hebraic studies 1 law 1
math
3rd cousin
31
Cohesion in kinship networks
as constituents of human societies
A. What are the atomisms of human kinship? Persons,
couples creating children and reproduction, and larger
cohesive units (superatomisms) of social coordination
multiply connected through marriage.
B. This opens the study of cohesive kinship units and of the
constituents of these units that lend cohesion.
C. For kinship networks this defines structurally
endogamous groups with identifiable boundaries to
discrete cohesive groups
D. A key question concerns the mutually causal correlates
of these cohesive groups
32
The idea of consequences is that structurally
endogamous units define the local boundaries of one
or more concrete implicate order groups that gain
cohesion or are the cause of cohesion, such as:
ethnicities, religious groups, community, stayers
versus migrants, social class, endo-clans, factions,
regions of exchange, markets, etc. The
consequences may run from or to structural
endogamy groups as implicated in the actions or
activities of those inside or outside the group.
Example: Canaanite Structural Endogamy
33
E.g., Measuring boundaries of structural endogamy
Jacob and Esau are
included in the main
unit of structural
endogamy of Canaan land
Lot married to
his daughters
Abram
Sarai
Abram
Hagar
Ishmael
Male Descent
Female Descent
Same person
(polygamy)
Structurally endogamous Canaanite Marriages in the
narrative of the Patriarchs (White/Jorion) 34
This is Case 1: The Patriarchs and the Matriarchs
The graph tells a story of the
Old Testament covenant that
established monotheism
M
Become Abraham
and Sarah
M
M
M
35
The stacking of kinship atomisms and
their nested levels
Persons–&–couples creating children & reproduction
The larger units of social cohesion/coordination
(superatomisms) created by coupling or marriage
bicomponents (cohesive linkages) that may define
community, ethnicity, emergent from networking.
To observe this stacking of atomisms we create an
appropriate formalism that includes such ideas as larger
units that have cohesion because of redundant linkages,
like multiple overlapping social circles.
36
1.
Define a graph
that represents how marriages form
cycles
(P-graphs and P-systems)
where P is for the parental relations
that constitute kinship and in a P-system
nodes may contain embedded graphs of
smaller-scale networks
37
Data and Representation:
P-graphs link parents (flexible & culturally defined) to offspring
They are constructed by showing:
•Each couple (as) a node
• Each individual a line
•Each gender a different
type of line
•A marriage node includes the
husband and wife as an
embedded graph
•i.e., a P-system
38
It is a Good Formal Representation
(commentary slide of Dwight Read)
1.
Removes aspects of concrete situation
not relevant to structural relations of
interest
2. Faithfully represents structural
relations of interest
3. Properties of the representation derived
through analysis using the representation
can be mapped back to the original
context faithfully.
4. Enables structural similarities to be
identified between disparate contexts
39
2. This representation captures
independent nuclear families,
networks of marriage between them,
how families form descent groups &
marriages within and between them
40
3. Now link this representation
to actual marriage network data
41
Data and Representation:
Building Kinship Networks
P-graphs link pairs of parents (flexible & culturally defined) to their decedents
P-graphs can be constructed from
standard genealogical data files
(.GED, Tipp), using PAJEK and a
number of other programs.
See:http://eclectic.ss.uci.edu/~drwhit
e for guides as to web-site
availability with documentation (&
multimedia representations)
42
4. What are the properties
of how marriages form cycles?
they form bicomponents =
maximal sets of nodes, in which
each pair is connected in two or
more independent ways
43
This is a bicomponent with no
cut-point and with two+
independent paths between
every node pair.
By Menger’s
theorem, these are
equivalent.
It has 8
independent
cycles m-n+1
m=24 (parentchild) edges
n=17 nodes
(couples)
44
The same bicomponent with
no cut-point and with two+
independent paths between
every node.
And 8 corresponding
named cycles
WB
MBD
FZ
MZD
ZDDD
FZD
(the 8
independent
cycles m-n+1
for m edges
& n nodes)
MMZDD
FZDD
It’s also ORDERED, by
a time dimension,
through generations.
45
The formalism helps Identify Ambiguities
(commentary slide of Dwight Read)
Ancestral generation 1
Generation 2
Generation 3
Why not generation 3?
(optionally 3 or 4)
Generation 4
Generation 5
Ambiguous generation 4 or 5
depends on the path taken
46
And to identify the
micro-structures that
create cohesion
Ancestral generation 1
Generation 2
Generation 3
WB
marriage cycles
MBD
ZDDD
MMZDD
The 8 constituent marriage
cycles of the bicomponent
each of a given type
Generation 4
FZ
MZD
FZD
FZDD
Generation 5
47
How to “see” the atomisms of human kinship
at nested atomistic levels?
The network formalism identifies distinct levels with distinct types of
units: persons, couples, families and cohesive clusters of families and
groups like those that self-identify by descent or intermarriage.
It allows us to see how units at a smaller scale are embedded in those
of a higher level. If we take P to denote the Parental ties that form
into kinship networks, we can name the formalisms as P-systems,
graphs of networks where graphs for relations among atomists can
contain other graphs.\
The micro-macro links allow us to see a concrete implicate order
relation exists between the macro parameters of the structural
endogamy group and its micro patterns of marriage-type frequencies,
e.g. MBD, FZD, MMBDD, etc.
48
The “cohesive units” of kinship
restated as k-cohesion, limited to k=2
(graph-theoretic term bicomponents)
Here a fourth part is added to formalism (i-iv)
Let G=<V,A> be a graph of n vertices in set V with m pairs u,v
in VxV of directed or undirected links. A graph of G΄≤G is kcohesive if (i) every pair of its n΄ nodes has k or more
independent paths between them and (ii) cannot be
disconnected without removal of k or more nodes. (iii) By
Menger’s theorem (i) and (ii) are equivalent. Further (iv) there
are m-n+1 independent cycles (m edges, n nodes) in every kcohesive graph with k ≥ 1. (This links the micro structure to to
the macro structure of the cohesive group).
49
Capturing the “units” and nested
atomistic levels of human kinship
The idea of the P-system formalism is to capture
overlapping cycles in (micro-structure of marriage) to find
the boundaries of 2-cohesive (bi)components (macrostructure) of kinship networks. In these bicomponents,
every person or couple is linked by at least 2 independent
paths (marriage circles) that overlap to form in larger
cohesive subsets of structural endogamy as a special case
of structural 2-cohesion (k-cohesion with k=2).
50
Concrete implicate order
Local structure, ranging from marriage rules to
the appearance of nuclear families as
autonomous, may be part of a concrete
implicate order of wholeness within structural
endogamy, and structurally endogamous
groups part of a larger implicate order.
Unlike David Bohm’s implicate order this
concrete order of micro-macro linkages is
based on mathematical proofs with
explanatory purchase.
51
5. Bicomponents (I), as
maximal sets of marriages, each pair
connected in two independent ways,…
... identify
the boundaries of structural
endogamy (& so - define new terms,
bicomponent=structural endogamy).
I focus on the consequences and causes of these
units – part of the concrete implicate order of
structural endogamy.
52
Kinship and cohesion:
5. examples
of mutual causality or causal effects
• Case 2. Kinship cohesion and Social Class in an
Austrian farming community
• Heirship/Structural endogamy R2>>.29(.9?)
– (Structural Endogamy <–> Social Class)
• Case 3. Kinship cohesion and Stayers/Leavers
in a Turkish Nomad clan
• Stayers/Structural endogamy R2 =.90
• Case 4. Cohesive sidedness for Garo Moieties,
– 23 cycles, R2 =1.0 p<.00001
53
The Middle-Eastern Example from Case 1
showed marriages with relatives by common
descent (here, same patrilineage) and
membership in a founding religious group
(Judiasm).
by way of contrast: we apply
marriage bicomponent analysis to a European
town (Case 2)
54
6. Case 2: here, a European village, no blood
marriages
How do marriage cycles and structural
endogamy have consequences in this case?
Relinkings are structurally endogamous
marriages that reconnect 1 or more
families; they overlap to form cohesive
groups
55
Feistritz, Austria – structural endogamy by affinal relinking
THE NEXT SLIDES WILL TREAT
THESE
with heirship
56
Feistritz, Austria – structural endogamy by affinal relinking (no
blood marriages)
Attribute endogamy = e.g., heirs marry heirs
Pearson’s R
=.29 to .90?
8. There are consequences but not that heirs marry
heirs – its THOSE IN THE BICOMPONENT WHO DO RELINK THAT
BECOME THE HEIRS
57
The stemline
social class of
farmstead
inheritors,
1510-1980
58
Feistritz Austria – structural endogamy
1520
9. This is social class constituted by marital
relinking
T
h
e
T
i
m
e
D
i
m
e
n
s
i
o
n
1970
59
Feistritz Austria – structural endogamy by affinal relinking
10. BUT IS IT JUST RANDOM CHOICES THAT
CREATE THE MARRIAGE BICOMPONENT IN THIS
TOWN? OR IS THIS BEHAVIOR TARGETED AND
INTENTIONAL?
60
Feistritz Austria – structural endogamy
(i.e., bicomponent) with heirship
11. Pearson’s R = .54
61
12. Simulation tests of randomness
are critical to identify for each
generation“non-intentional behavior”
For each generation,
permute the marriages randomly,
in context, holding all else constant
62
For example, take these three generations and permute the
red lines so existing marriage and child positions are
occupied
63
64
65
66
67
68
13. Comparing Feistritz actual to simulated rnd relinking
frequencies:- Relinking frequency >> random back 1 and 2
generations, those where there is most knowledge & availability
Random in all higher generations 3+
69
Structural Endogamy among known relatives
Social Class: Carinthian Farmers of Feistritz:
Comparison of Relinking Frequencies
for Actual and Simulated Data (*=actual frequencies greater than chance as determined by simulation)
Number of Structurally Endogamous Marriages
Generation
1
2
3
4
5
6
by Ancestral Levels
Present:
Actual
8*
16*
70*
179
257
318
Simulated
0
0
32
183
273
335
by Ancestral Levels
Back 1 gen:
Actual
8*
58*
168
246
308
339
Simulated
0
18
168
255
320
347
by Ancestral Levels
Back 2 gen:
Actual
26*
115*
178
243
278
292
Simulated
0
98
194
262
291
310
Statistical
conclusion:
conscious
relinking
among
families
creates
structural
endogamy
Source: 1997 “Class, Property and Structural Endogamy: Visualizing Networked Histories,” Theory and Society 25:161-208. Lilyan Brudner
and Douglas White
70
Case 3. We look next at Arabized Turkish
Nomads, similar in structure to the
Canaanites, and show how a similar concrete
implicate order of structural endogamy
applies to how lineages are linked into
clans, and consequences for those who stay
and those who leave the clan.
71
Applications of Structural Endogamy
A Turkish Nomadic Clan as prototype of Middle Eastern segmented lineage systems:
The Role of Marital Cohesion
Sources:
2002 Ulla Johansen and Douglas R. White, Collaborative
Long-Term Ethnography and Longitudinal Social Analysis
of a Nomadic Clan In Southeastern Turkey, pp. 81-99,
Chronicling Cultures: Long-Term Field Research in
Anthropology, eds. R. van Kemper and A. Royce. AltaMira
Press.
2005 Douglas R. White and Ulla Johansen. Network
Analysis and Ethnographic Problems: Process Models of a
Turkish Nomad Clan. Lexington Press.
See also:
2003 Douglas R. White and Michael Houseman The
Navigability of Strong Ties: Small Worlds, Tie Strength
and Network Topology, Complexity 8(1):72-81.
(How highways of trust are established through reciprocal
ties in structurally endogamous conical clan systems)
72
Turkish nomads
Names of members
all
members
Black=patriDescent lines
Blue=female lines
73
74
Turkish nomads
SCALING
All known
members but
many have
emigrated
dotted=
female lines
Black=patridescent lines
75
Turkish
nomads:
Relinking only
(Structural
Endogamy)
Stayers in the
community ~
cohesive core
Relinking
+yes no
160 14 Stay
18 71 Leave
Pearson’s R
=.73
Dotted=female
lines
Black=patriDescent lines
76
Applications of Structural Endogamy
A Turkish Nomadic Clan as prototype of Middle Eastern segmented lineage systems:
The Role of Marital Cohesion
Does marital relinking predict staying with the clan, as predicted by PCT?
Results: Yes !
Testing the hypothesis for stayers versus leavers
Relinked
Marriages
Non-Relinking
Marriages
Totals
villagers who became clan members
2**
1**
clan Husband and Wife
148
0
“ Hu married to tribes with reciprocal exchange 12
14
“ Hu left for village life
13
23
“ Hu married to village wife (34) or husband (1) 11
24
“ Hu married to tribes w/out reciprocal exchange 2
12
“ members who left for another tribe
0
8
villagers not joined to clan
1
3**
* tribes
**non-clan by origin
Totals
189
85
3
148
26
36
35
5
8
4
274
Pearson’s coefficient r=.95 without middle cells
77
15. Cycles within Structural Endogamy
A Turkish Nomadic Clan prototype of Middle Eastern segmented lineage systems:
The Role of Marital Cohesion
Rather than treat types of marriage one by one: FBD, MBD etc., we treat them as an ensemble
and plot their frequency distribution
Frequencies of more distant endogamous marriage-types has power-law decay as against
the individually more frequent closer marriage types.
180
This is an ancient (4500
year old ) complexsystem integration of
scalable integration
from families to
subcontinents and from
small feuds to
international conflicts.
Already present in the
Canaan conical lineage
as a form of
organization.
160
140
M
Frequency
M =206/x
0 + 156/x^2
2
120
of Types
##of
kin types
100
(power law preferential curve)
80
60
couples
##
of of
Couples
40
FFZSD FFBSD:10-11 FZD:14 MBD:16
FFZSD FFBSD FZD
20
MBD
FBD:31
FBD
0
0
Raw
frequency
5
10
15
20
25
78
Cycles within Structural Endogamy: log-log
A Turkish Nomadic Clan prototype of Middle Eastern segmented lineage systems:
The Role of Marital Cohesion
types of marriage are ranked here
to show that
numbers of the types of
blood marriages follow a
power-law (indexical of selforganizing preferential
attachments)
while affinal relinking
frequencies follow the exponential
distribution associated with
randomness
79
Constituent Elements of Structural Endogamy
Ethnographers characterize marriage systems by “rules” of
preferential behavior. This may be sufficient for some societies, E.g.,
which cousin marriages are favored over others.
Networks show a much broader range of marriage behaviors in most
cases, e.g., Australia, East Asia, Africa. There are complex
distributions of behavioral frequencies – e.g., power laws for blood
marriage frequencies (Middle East) or for broad in-law relinking cycles
(Europe) – and demographic constraints and factors like relative
marriage ages that alter marriage probabilities. A coherent
probabilistic approach is both possible and needed. Why is this
important?
Structural endogamy and cohesion have huge social consequences
that need to be properly understood.
80
Case 4. Uxori-sides for the Garo found independently of
the names for matri-moiety dual organization
23 cycles all sided p<.00001
81
Mapping data
onto networks
Analyses of such data
can be crossed:
• By structural endogamy
• Migration
• By generation time-series,
• Residence
patrilineages, matrilineages
• Wealth owned
• Heirship
• By viri-sides, uxori-sides
--- PLUS
• Kin Behaviors
• Kin Terms &
Products in relation
to marriage
82
e.g., Data about kin behavior
• Kin behaviors mapped by kin type/kin term
–
–
–
–
–
–
Avoidance
Sexual Prohibition
Respect
Informality
Joking
Privileged sexual relation
• Associated expectations
– (additional features for a given society)
83
structural cohesion
and structural endogamy
Local structure – exemplified by the range of marriagetype rules and their frequencies to the appearance of
autonomous nuclear families linked in structural
endogamy – may be part of a concrete implicate order
of wholeness within structural endogamy.
Structurally endogamous groups and their microstructures as part of a larger concrete implicate
order has only begun to be explored …
84
Can also look at changes in structural
endogamy (cohesion) through time
Networks of Omaha tribe, for example, the
structural endogamy is fragmented early on
into factions and decays in later
generations. More severe decay of cohesion
because chiefly elites were stratified and
did not relink with other social strata.
85
Omaha Genealogies – Chiefs and Siblings – no
relinking of chiefly lines:- disconnected
ELK CLAN
86
Omaha – top 4 generations - structural
endogamy weak
Five disconnected components in the top four
generations:
of sizes 643, 46, 38, 29, 15
Bicomponents of sizes 141, 4
87
Omaha – all generations – structural endogamy
88
Omaha – 8 generations – disintegration
89
Omaha – loss of structural endogamy
1
2
Bicomponent
Omaha
relinking
marriages
Nonrelinked
singles
Genera 1
tion
2
Levels 3
29
41.40%
41
58.60%
70
50
32.90%
102
67.10%
152
60
22.60%
205
77.40%
265
4
36
12.70%
248
87.30%
284
5
18
8.70%
188
91.30%
206
6
7
15.60%
38
84.40%
45
7
3
17.60%
14
82.40%
17
8
1
4.80%
20
95.20%
21
1 early
3
Tota
l
8
late
Relinking
marriages decrease in later generations
4
5
6
7
8
90
Changes of cohesion by generation
• Over dozens of communities studied (disregarding unmarried
children)
• cohesion is decreasing
• which implies more people leaving their communities and
marrying outside
• And this creates larger ethnicities on a more global basis
• Kinship cohesion through time is decreasing locally in
communities but increases at larger spatial scales and is
transforming world ethnicities and cultures.
• implications turn out to be massive, global, and as relevant to
understanding the global economy and global conflicts as in more
localized anthropological studies.
91
Conclusions: Advances & Benefits
• Network Visualization of Kinship
• Variables for testing theory
• A coherent probabilistic approach in this
framework includes not only comparisons
against the null hypothesis, as shown, but
bootstrap inferential methods for testing
complex models of kinship structure, given
discrete constraints where they occur
(strict Australian section rules, or incest
prohibitions).
92
end
93