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
December 5, 2008 (& workshop Dec 4)
1
Outlines for Talk and Workshop
1. Anthropology and Physics as experimental sciences
2. Cohesive Causality: Kinship to industrial organization ..slide 21
3. World economy and historical dynamics
4. Afterword and forward
… 55, ends at 85
… slide 86
Workshop on Cohesion in Kinship groups (87-130)
2a Cohesion in kinship networks as constituents of society
2b Mapping data onto networks and further findings
2c Simulation
2d Unsolved problems and solutions
2e Conclusions: Tying it all together for kinship
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
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.
11
4-component
structurally 4cohesive
network
4-inseparable
≡
4 independent
paths for each
pair of nodes
Here: THERE IS NO
CENTRAL NODE
12
4-component
structurally 4cohesive
SCALABLE
network
4-inseparable
≡
4 independent
paths for each
pair of nodes
Here still: NO
CENTRAL NODE
13
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.
14
Metaphors for the new science
• Intuitive models for network-cohesive units in this
new science are (1) Bucky Fuller’s geodesic domes with
many elements cohesively connected (2) Art Iberall’s
spacesuit design with the stable points of bodily
dynamics linked by a flexible web.
• I am going to run quickly through 50! slides for a
series of examples of causal impacts of structural
cohesion that give the core ideas of how this science
applies everywhere, with myriad applications.
15
Topical Examples: Cohesive Causality
•
•
•
•
•
•
•
•
•
Kinship
Education
Social Groups
Political Parties
Science
Industry
Cities & Trade
Warfare/Empire
World Economy
•
•
•
•
•
•
•
•
•
Complex tasks/Cohesion
School attachment
Organizational fragmentation
Bifurcation/Competition
Transmission lines and cores
Collaboration/Innovation
Balance/Cycling/Innovation
Resistance/Replacement
Metastable oscillatory cycles
16
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.
17
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.
18
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.
19
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.
20
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.
21
(2a) 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. A key question concerns their mutually causal
correlates
22
Kinship and cohesion: examples
mutual causality or causal effects
of
• Kinship cohesion and Social Class in an Austrian
farming community
• Heirship/Structural endogamy R2>>.29(.9?)
– (Structural Endogamy – Social Class elsewhere?)
• Kinship cohesion and Stayers/Leavers in a
Turkish Nomad clan
• Stayers/Structural endogamy R2 =.90
• Cohesive sidedness for Garo Moieties,
– 23 cycles, R2 =1.0 p<.00001
23
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.
24
How to “see” the atomisms of human
kinship at nested atomistic levels?
The network formalism that is needed identifies distinct levels
with distinct types of units: persons, couples, families and
cohesive clusters of families and groups like those that selfidentify 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.
25
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 micro to macro structure).
26
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).
27
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
28
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
29
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
30
2. This representation captures
independent nuclear families,
networks of marriage between them,
how families form descent groups &
marriages within and between them
31
3. Now link this representation
to actual marriage network data
32
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)
33
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
34
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)
35
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.
36
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
37
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
38
Example: Patriarchs and Matriarchs
The graph tells a story of the
Old Testament covenant that
established monotheism
M
Become Abraham
and Sarah
M
M
M
39
Uxori-sides for the Garo found independently of the
names for matri-moiety dual organization
23 cycles all sided p<.00001
40
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
41
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)
42
Education: School attachment
• 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
• 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
Levels of K-cohesion in these schools vary from 1-8
43
Longitudinal Network Studies and Predictive Social Cohesion Theory
D.R. WHITE, University of California Irvine, BCS-9978282
Topology: Overlapping hierarchies (Empirical Results)
The algorithm for finding social embeddedness in nested
Fig 2. Structural Cohesion of Friendships
cohesive subgroups is applied to high school friendship _______in an American high school
networks (e.g., Fig 2; boundaries of grades are
11-12th grade
approximate) and to interlocking corporate directorates.
The usefulness of the measures of cohesion and
embeddedness are tested against outcome variables of
school attachment in the friendship study and similarity in
corporate donations to political parties in the corporate
interlock study. The cohesion variables outperform other
network and attribute variables in predicting the outcome
9th
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
th
(http://www.cpc.unc.edu/addhealth/), Adolescent Risk and 10 grade
Vulnerability: Concepts and Measurement. Baruch
Fischhoff, Elena O. Nightingale, Joah G. Iannotta,
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)
8th grade
7th grade
Interpretation: 7th-graders- core/periphery; 8th- two cliques, one hyper-solidary, the other marginalized; 9th44
central transitional; 10th- hang out on margins of seniors; 11th-12th- integrated, but more freedom to marginalize
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
45
Longitudinal Network Studies and Predictive Social Cohesion
Theory
D.R. WHITE, University of California Irvine, BCS-9978282
Part 1. Development of a Methodology for Network Research on Social Cohesion
An operational definition of social cohesion
based on network connectivity measures
cohesiveness as the minimum number k
of actors whose absence would disconnect
a group. Two members of a group with
cohesion level k automatically have at
least k different ways of being connected
through independent paths.
Fig 1. 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.
A test of the measure is exemplified by
successful prediction of how a group,
studied longitudinally during a period of
conflict between leaders, divides into two
(Fig 1).
2001 Douglas R. White and Frank Harary,
The Cohesiveness of Blocks in Social
Networks: Node Connectivity and
Conditional Density. Sociological
Methodology 2001, vol. 31, no. 1, pp. 305359. Blackwell Publishers, Inc., Boston,
USA and Oxford, UK. SFI Posting
Connectivity: Blue=4 Red=3
Green=2 Yellow=1
Ethnography and data source: Wayne Zachary,
1977. An Information Flow Model for Conflict
and Fission in Small Groups. Journal of
Anthropological Research 33:452-73.
46
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.
47
The sides separate along cohesive fracture
Political Parties and Business
• Closeness in k-cohesion of business practices
(interlocking directorates, stockholding etc-Mizruchi
1992) predicts similarity in (2 party) political
contributions ~ collusive interests.
• LR Odds 4.9 p=.004 Moody-White 2003:11
• In general, within a network, k-component embedding
similarity is the level at which pairs intersect in their
k-component memberships
– Pairs are connected by at least k node-independent paths
– Not separable without removal of k nodes
48
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
49
Kinship cohesion in Science
3 physics 3 theology 2 hebraic studies 1 law 1
math
3rd cousin
50
Industry (Biotech)
In 12 successive years, what predicts collaborations?
• LR 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)
51
Longitudinal Network Studies and Predictive Social Cohesion Theory
D.R. WHITE, University of California Irvine, BCS-9978282
Topology: Stacked hierarchies and Dynamics (Empirical Results)
Longitudinal Validation of Structural Cohesion Dynamics in Biotechnology
Fig 3. 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 3 1999). Using multiple novel methods, including
analysis of network degree distributions, network visualizations, and
multi-probability models to estimate dyadic attachments, we
demonstrate how a preference for diversity and multiconnectivity in All ties
1989
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
diversity of organizations with which they are linked, cohesive
New ties
subnetworks form that are characterized by multiple, independent
1989
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
structure of this science-based field.
All ties
1990
2003 Walter W. Powell, Douglas R. White, Kenneth W. Koput and Jason
Owen-Smith. Network Dynamics and Field Evolution: The Growth of
Interorganizational Collaboration in the Life Sciences, 1988-99.
And so on
Submitted to: American Journal of Sociology.
to 1999
52
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
53
New ties, Biotech, 1997
Attractor is
k-cohesion
and
diversity
(flip back)
54
Cities and Trade
• Medieval Renaissance: trade routes are
cohesive, equalization of trade benefits
• Banking routes are hierarchical, tree-like,
noncohesive, unequal advantage
• Commodity wealth accrues to Genoa, via shortpath betweenness centrality
• Over 3 centuries trade flow centrality brings
financial profits to the Low Countries banking
cities.
• 20th century trade-commodity flows are
hierarchical, unequal position in trade relations
55
Because sea routes opened cohesive exchange cycles as
alternatives to land routes, a positional similarity analysis
reflects a cohesive and non-monopolistic trade network
Venice
The importance of land
versus sea routes
oscillated during the
12th-15th centuries..
The split in Genoese
(western and Atlantic)
and Venetian (eastern)
routes is also reflected in
the circular positional
structure, showing how
they compete for trade.
Regular equivalence
analysis with
normalized SVD scaling
based on valued
{1,2,3,4} ties =
{Aux,Prin} banking
{Venice,Geneva} Ports
Genoa
Genoa dominates the core
cities at the lower right,
but their cluster and
that of more peripheral
cities at the upper left
each has its banking
cities. Venice is more a
single eastern bridge
between land and E.
Mediterranean.
Later: a look at how population cycles and trade networks promote/demote industries
56
the banking network, main routes only (geographic locations).
Control networks often rely
on unambiguous centralized
spines but their operation
relies on feedback in
cohesive networks.
the spine of the exchange system
is tree-like and thus centralized. It
is land based. Linking the four
parts was Alessandria, a small
stronghold fortification built in
1164-1167 by the Lombard League
and named for Pope Alexander III.
At first a free commune, the city
passed in 1348 to the duchy of
Milan.
Note again the closeness of Genoa
to the center, and the exclusion of
Venice.
57
Flow centrality (how much total network flow is reduced with removal of a node)
predicts something entirely different: the potential for profit-making on trade
flows. It necessarily reflects flow velocities central to the organizational
transformations undergone in different cities, as Spufford argues.
This type of
centrality is
conceptually very
difference and
distributes very
differently than
betweenness and
strategic centers
like Venice or
Genoa, which are
relatively low in
flow centrality.
58
Cohesive nodes (gold and red) in an expanded exchange network and road
identification (red=3-cohesive) shows two cohesive accumulation regions -- such
cohesion supported the creation of wealth among merchants and merchant cities,
with states supported by indirect taxation and loans.
In Northern Europe the Hanseatic port of Lubeck had about 1/6th the trade of Genoa, 1/5th that of Venice.
Red 3-components
Middle East and
its 3-core not
sampled
59
Northern Hanse Trade Organization:
Saintly Brotherhoods
Highly regulated
trade works but
goes extinct
through competition
from London-Holland
global profit centers
Northeast
Southwest
v
v
v
v
Other Eastern Hanse
German Towns, 1470
60
Warfare/Empire
Effective number of polities, based on area and on population (courtesy of
Taagepera 1997, who notes that polities that expand slower tend to last longer
[80:475]; arrows mark his dates for large polity concentrations; others are marked
by lighter lines) AREA SIZES ARE MORE VARIABLE THAN POPULATION SIZES
61
Political and warfare dynamics (Turchin 2004) and constraints
12thC.jpg polities, with conflict frontiers, ethnogenesis across
metaethnic political boundaries, and arrows showing movement in the
next time frame
Warfare on the
frontiers of Europe
were primarily along
religious boundaries.
In the center were
the fractured
remnants of the
Holy Roman Empire,
a zone of
competition but
‘relative’ peace and
trading fairs
Source: Peter
Turchin 2004
62
13thC.jpg polities, with conflict frontiers, ethnogenesis across
metaethnic political boundaries, arrows showing movement in the next
time frame
Christian
Crusades run
into the Baltic
The European
polities are so
weak compared
to the Mongol
military they
would have been
no match
whatever, but
the Mongols turn
back to China
over an issue of
succession.
Source: Peter
Turchin 2004
63
14thC.jpg polities, with conflict frontiers, ethnogenesis across
metaethnic political boundaries, arrows showing movement in the next
time frame
As velocity of trade
transforms
European
organizations, small
polities harden,
Castile expands,
France expands,
Leagues form in
Germany, the
Ottoman push
against
Constantinople.
Source: Peter
Turchin 2004
64
15thC.jpg polities, with conflict frontiers, ethnogenesis across
metaethnic political boundaries, and arrows showing movement in the
next time frame
Velocity of trade
decreases, Paris
becomes a remnant,
but Europe remains
a trading zone...
Ottomans take
Constantinople in
1442, and then the
Aegean-Balkan
south. The
Renaissance is
fueled by recovery
of materials from
Constantinople
Source: Peter
Turchin 2004
65
Historical Cycles
• Peter Turchin shows agrarian empire
metastabilty in 200+ year “secular” cycles of
growth/decline in people/resource ratios
leading internecine conflict cycles by ¼ cycle
(+) feedback, conflict leads negative (-)
feedback on people/resource ratios.
• Longer and many successively shorter cycles
have temporal phase-length doublings; conflicts
alternately open and close exchange
boundaries as doublings.
66
Turchin
2005:
Dynamical
Feedbacks in
Structural
Demography
Key:
Innovation
Chinese phase diagram
67
J. S. Lee measure of SPI for China region
(internecine wars )
68
city systems in the last millennium
Dynamics of groups and institutions: Their emergence, co-evolution and environment:
Environmental limits interact with population and sociopolitical violence
In periods of crisis, further monetization (which proceeds today) drives
Volume of trade (velocity of money)
which will transform those organizations and institutions
situated at predictable network junctures
The dynamics of the modern world system is evident in the long 13th century
Arrighi's thesis of an alternation of commodity and financial capital intensity
fits into the periodization of the pop-war interactive cycles
and the inflationary price cycles
Each cycle leaves institutions, transportation, technology transformed
and the next cycle builds upon these, so
there are millennial trends and increasing environmental capacity
that also predict network-situated innovation
69
Cities in Historical Dynamics
• Cities and their size distributions are affected by
agrarian empire metastabilty in 200+ year “secular”
cycles of growth/decline in people/resource ratios
leading internecine conflict cycles by ¼ cycle (+)
feedback, conflict leads negative (-) feedback on
people/resource ratios.
• Zipfian balanced “power law” distributions are not
constant but metastable: tails are affected by global
trade, smaller sizes by fluctuations in rural trade and
land routes.
70
Color key: Red to Blue:
Early to late city
entries
The world system &
Eurasia are the most
volatile. Big shifts in
the classical era until
around 1000 CE.
Gradual reduction in
shifts until the
Industrial Revolution.
US shift lower, largest
1830-90. UK similar,
with a 1950-60
suburbanization shift
INDIVIDUAL CITY
SIZES
UK
Worl
d
Slides from Michael Batty, Nature 2006
71
city systems in the last millennium
Zipf’s law metastable
Population at rank
Rr
Tr
r
=

Mi

i 1
M the largest city and α=1
Take a
closer
look:
Lots of
variation
from a
Zipfian
norm
city rank distributions over 50 year intervals
city systems in the last millennium
1
2
3
4
5
6
7
8
9
10
11
top20
12
13
14
72
15
City Size Distributions for Measuring
Departures from Zipf
construct and measure the shapes of cumulative city size distributions
for the n largest cities from 1st rank size S1 to the smallest of size Sn
as a total population distribution Tr for all people in cities of size Sr or
greater, where r=1,n is city rank
P(X≥x)
Empirical cumulative
city-population
distribution r
Tr=  Si
i 1
Rank size power law M~S1
r
RTr =
 Mi

i 1
73
Partial independence of q and β
TAILS AND BODIES OF CITY-SIZE DISTRIBUTIONS VARY INDEPENDENTLY
74
Probability distribution q shapes for a
person being in a city with at least
population x (fitted by MLE estimation)
Pareto Type II
Shalizi (2007) right graphs=variant fits
city systems in the last millennium
75
Examples of fitted curves for the cumulative distribution Curved
fits measured by q shape, log-log tail slopes by β
Pβ (X ≥ x) = (x/xmin)-β
(top ten cities)
city systems in the last millennium
76
Variations in q and the power-law slope β
for 900-1970 in 50 year intervals
3.0
2.5
2.0
China
Mid-Asia
Europe
MLEqExtrap
Beta10
1.5
MinQ_Beta
1.0
0.5
0.0
911111111111111111111111191111111111111111111111119111111111111111111111111
001122334455566778888999900112233445556677888899990011223344555667788889999
000505050505705050257025700050505050570505025702570005050505057050502570257
000000000005000005050500 000000000005000005050500 000000000005000005050500
date
city systems in the last millennium
911111111111111111111111191111111111111111111111119111111111111111111111111
001122334455566778888999900112233445556677888899990011223344555667788889999
000505050505705050257025700050505050570505025702570005050505057050502570257
000000000005000005050500 000000000005000005050500 000000000005000005050500
date
77
Random walk or Historical Periods?
Runs Test Results
Runs Tests at medians across all three regions
Test Value(a)
Cases < Test Value
Cases >= Test Value
Total Cases
Number of Runs
Z
Asymp. Sig. (2-tailed)
MLE-q
1.51
35
36
71
20
-3.944
.0001
Beta10
1.79
36
37
73
22
-3.653
.0003
Min(q/1.5,
Beta/2)
.88
35
38
73
22
-3.645
.0003
city systems in the
last millennium
Runs Test for temporal variations of q in the three regions
mle_Europe
mle_MidAsia
mle_China
Test Value(a)
1.43
1.45
1.59
Cases < Test Value
9
11
10
Cases >= Test Value
9
11
12
Total Cases
18
22
22
Number of Runs
4
7
7
Z
-2.673
-1.966
-1.943
Asymp. Sig. (2-tailed)
.008
.049
.052
a Median
78
Fitted q parameters for Europe, Mid-Asia, China, 900-1970CE, 50 year lags. Vertical lines show
approximate breaks between Turchin’s secular cycles for China and Europe
Downward arrow: Crises of the 14th, 17th, and 20th Centuries
79
Time-lagged cross-correlation effects of the Silk Road trade on Europe’s City
Size tail
logSilkRoad with EurBeta10
(50 year lagged effect)
Coefficient
Upper Confidence
Limit
0.9
Lower Confidence
Limit
0.6
mle_MidAsia with mle_Europe
0.3
Upper Confidence
Limit
0.0
Lower Confidence
Limit
0.6
0.3
-0.3
CCF
CCF
Coefficient
0.9
-0.6
0.0
-0.3
-0.6
-0.9
-0.9
-7
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
Lag Number
Lag Number
80
Time-lagged cross-correlation effects of Europe’s City Size distribution body
on % of French population in Paris (trade  cities benefit  migration to
capital)
mle_Europe with ParisPercent
Coefficient
Upper Confidence
Limit
0.9
Lower Confidence
Limit
0.6
CCF
0.3
0.0
-0.3
-0.6
-0.9
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
Lag Number
81
City Size Distributions as Measured by q Departures from
Zipf are correlated with instability: China
SPIm with q
Coefficient
0.9
Upper Confidence
Limit
0.6
Lower Confidence
Limit
CCF
0.3
0.0
-0.3
-0.6
-0.9
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
Chinese PIm=Sociopolitical
Instability (moving
average) as measured by
Internecine wars (Lee
1931), 25 year periods
interpolated for q
Lag Number
82
Warfare & Resistance to Empire
Turchin empire/resistance dynamics
Turchin’s 50 cultural regions used as geographical units in the
statistical analysis of the relationship between metaethnic
frontiers and polity size (courtesy of the author)
83
Empire/resistance dynamics
0-1000CE
Region
Becomes
Empire
No Empire
ontier
1
34
Starts as
Frontier
11
4
Region in
50
regions
p<
.0000004
No
Frontier
1
50
Likelihood
ratio 28.6
regions
p<
.0000004
34
10001900CE
Becomes
Empire
No Empire
Starts as
Frontier
22
6
10001900CE
Becomes
50 regions
Empire
No Empire
Starts as
Frontier
22
6
Likelihood
ratio 22.6
No
Frontier
3
p<
.0000004
19
polities that start on multiethnic frontiers, resisting empires, end as empires a
millennium later; if not then not. Most empires (75%) were resistive frontiers.
84
Warfare & Resistance to Empire
• The scalability of decentralized cohesion can promote steady
low-cost growth of counter-ethnic resistance movements over
100s of years; cohesion promotes the resistive counter-ethnicity
bounded by the meta-ethnic frontier
• As a decentralized form of organization, growth of a k-cohesive
group has no increase in cost with scale-up in size, simply that
each new member has k links to those already in the group
• In the absence of such conflicts and boundaries, k-cohesion
can spread and promote cooperation.
• A pity that Bush and Cheney chose war over diplomacy !
85
Afterword to structural cohesion
Foreword to 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 …
86
Kinship: in detail (workshop)
• This is where the structural cohesion studies
began, with structural endogamy
• The implications turn out to be massive,
global, and as relevant to understanding the
global economy and global conflicts as in more
localized anthropological studies.
• Kinship cohesion through time is decreasing
locally in communities but increases at larger
spatial scales and is transforming world
ethnicities and cultures
87
5. Bicomponents (I), as
maximal sets of marriages, each pair
connected in two independent ways,…
... identify
the boundaries of structural
endogamy (& so - define a new term).
I focus on the consequences and causes of these
units – part of the concrete implicate order of
structural endogamy.
88
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, social class,
stayers versus migrants, endo-clans, factions,
regions of exchange, markets, etc. The
consequences may run from or to structural
endogamy as implicated in the actions or activities
of those inside or outside the group.
89
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) 90
6. That Middle-Eastern Example
shows for marriages with relatives by
common descent (here, same
patrilineage) and membership in a
founding religious group (Judiasm). So
…
by way of contrast:
91
7. Apply marriage bicomponent analysis to a
European town
(here, no blood marriages)
How do marriage cycles and structural
endogamy have consequences in this case?
Relinkings are marriages that reconnect 1
or more families
92
Feistritz, Austria – structural endogamy by affinal relinking
THE NEXT SLIDES WILL TREAT
THESE
with heirship
93
The stemline
social class of
farmstead
inheritors,
1510-1980
94
Feistritz, Austria – structural endogamy by affinal relinking (no
blood marriages)
Attribute endogamy = e.g., heirs marry heirs
Pearson’s R
= .15
8. There are consequences but not that heirs marry
heirs – its THOSE IN THE BICOMPONENT WHO DO RELINK THAT
BECOME THE HEIRS
95
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
96
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?
97
Feistritz Austria – structural endogamy
(i.e., bicomponent) with heirship
11. Pearson’s R = .54
98
12. (2c) Simulation tests of
randomness as “non-intentional
behavior” for each generation
For each generation,
permute the marriages randomly,
in context, holding all else constant
99
For example, take these three generations and permute the
red lines so existing marriage and child positions are
occupied
100
101
102
103
104
105
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+
106
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
107
14. 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.
108
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)
109
Turkish nomads
Names of members
all
members
Black=patriDescent lines
Blue=female lines
110
111
Turkish nomads
SCALING
All known
members but
many have
emigrated
dotted=
female lines
Black=patridescent lines
112
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
113
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
114
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
115
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
116
16. We look next at the Omaha, where
chiefly elites are stratified and do
not relink with other social strata.
Their structural endogamy is
fragmented early on into factions and
decays in later generations.
117
Omaha Genealogies – Chiefs and Siblings – no
relinking of chiefly lines:- disconnected
ELK CLAN
118
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
119
Omaha – all generations – structural endogamy
120
Omaha – 8 generations – disintegration
121
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
122
Correlating cohesion with
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
123
17. (2d) An age-bias simulation problem
• The current random-simulation of marriage
solution assumes that persons in the same
structural generation have a uniform age
distributions, a biased assumption.
• But if there are Hu-Wife age differences,
then successive WiBr linkages generate
younger and younger men in the same
structural generation, as seen for the actual
Alyawarra case where ages are known, next
slide.
124
Systemic age differences of wives and husbands complcates generational simulation: Alyawarra. Australia
G2
G3
G1
G4
G2
G5
G3
G6
G4
G7
G5
G8
G6
Key: Vertical black lines male descent, red dots, females: the G7
generations are sloped (pink and blue) in a P-graph.
125
18. Solutions to the simulation problem
• (Problem here is that “same generation” WiBr chains are not a
group of contemporaries but stretched in time)
• Simulation for Alyawarra and similar examples can be done
considering male and females to have different average
generational time, α and ß, where Δ= ß-α is the average
age preference Δ ± ε for a younger spouse. We can get
ß/α ratios without knowing actual ages. Varying α, ß, ε,
these parameters define marriage-age probability
distributions for simulations where wives can come from
different generations.
• E.g., given section rules for marriage in Australia,
different parameter ranges, generate varying
distributions of marriage types and configurations of
successive and branching WiBr chains.
126
Daughters are moving to husbands in groups that are “adjacent” in a flow of
directed (asymmetric, “generalized”) exchange. The flow of personnel, however,
like a terracing model, also has constrained alternative flows. All these
elements allow more generalizable probabilistic modeling.
127
That is
• Inside the structurally endogamous group we have
– A “random” distribution of simulated types of marriage,
constrained by age-bias parameters and section rules and the
– Compared to the actual distribution of types of marriage
• And that actual distribution might be a function of
the age-biases.
• In general, a concrete implicate order relation exists
between the macro parameters of the structural
endogamy group and its micro patterns of marriagetype frequencies, e.g. MBD, FZD, MMBDD, etc.
128
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.
129
(2e) Conclusions: Advances & Benefits
• Network Visualization of Kinship
• Variables for testing theory
• The coherent probabilistic approach that is
needed can include 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).
130
Tying it all together for Kinship: 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.
131
132
Ancestral generation
1
Generation 2
WB
MBD
Generation 3
The 8 constituent
marriage cycles of the
ZDDD
bicomponent (PART
MMZDD
II)
Generation 4
FZ
MZD
FZD
FZDD
Generation 5
It’s also ORDERED,
by a time
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dimension, through
18. Solutions to the simulation
problem
• (Problem here is that “same generation” is not
a group of contemporaries but stretched in
time)
• With known ages of marriage data, simulation
for Alyawarra and similar examples can be
done considering marriages “filled”
sequentially in time, 1-by-1, from
marriageable-age probability distributions.
• Where actual ages are unknown, they can be
estimated from successive WiBr chains and
guesstimates from ethnographers of average
Hu-Wife age differences.
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(2B) What are the “units” of human
groups? The nested atomistic levels?
But to say that a k-cohesive component of a network
coordinates activity requires that (a) group membership as
defined by its boundaries has causal effects within or
outside the group, or (b) it acts as an attractor for new
members, or both (a,b). So for a k-cohesive component of
a network to act as a group, it must be implicated in
causal relations. The probability that this is true is higher
given the Menger properties (i,ii,iii) but requires
demonstration in specific empirical cases. And (iv) links
these larger units of cohesion to the minimal units of
cycles, or multiple circles of cohesive ties.
135
Learning to overlay networks on geophysical
terrains (press for zoomable GIS images)
A preview of things to come: the
network shown will be capable of
changing dynamically from the activated
website to show evolution through time.
The svg projection also has the
capability of showing agents moving over
the network and geographic space
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