Xi’an Lectures
It is an enormous honor to be invited to Xi’an Jiaotong University, and be invited to give two
public lectures, each an hour long, with questions. I thank you for your invitation and your
hospitality. This invitation results from contacts that were made through the Santa Fe Institute
for Complexity Studies and through common interests in the study of social networks. I was
asked to give a first lecture on social networks and a second on complexity. Because these
two are intimately connected, I address the first in terms of foundations and the second in
terms of conclusions. The foundations are those of the human sciences, or better, humanizing
of science, with a focus on the role of Anthropology as providing integrative perspectives.
The conclusions are those of networks and complexity as a central integrative perspective.
Lecture I. Foundations (society and networks)
The foundations I will speak about, then, are those of Anthropology as a discipline, in relation
to the other disciplines; and the contribution of anthropological (w)holism to human
knowledge and problem solving. Anthropology is holistic in the integrative sense, across
disciplines, as well as across the various aspects that constitute human beings – physical and
material, biological, historical, linguistic, cultural, and social. At a larger scale, this plays out
as integration of disciplinary perspectives between the nomothetic sciences (searching for
regularity) and the idiographic humanities (concerned with interpretive validity).
Nomothetic
Holistic
Idiographic
Physics
Sociology
Anthropology
History
Ethnography
Generality
Rigor
Integrative
Process
Meaning
Primary
<-------------- Integration -------------->
Deutero- (second-order)
<-------------- Integration -------------->
<--------------
-------------->
Networks
Networks
Networks
Networks
Networks
Theory
Theory
Theory
Theory
Theory
Figure 1: Integration across disciplines from a Human Complexity Sciences Anthropology
Figure 1 is a crude representation of the kind of integration I am interested in and its relation
to illustrative disciplines from the perspective of anthropology as a Complexity Science.
These compartments are not airtight and should not be seen as separate. Each, for example,
studies networks, albeit in a different way. Each has its own theory, albeit different.
Figure 2 shows how another discipline, Sociology, might relabel these columns differently.
Nomothetic
Social
Physics
Holistic
Sociology
EthnoSociology
Idiographic
Historical
Sociology
Ethnographic
Sociology
Primary
<-------------- Integration -------------->
Deutero<-------------- Integration -------------->
<--------------
-------------->
Networks
Networks
Networks
Networks
Networks
Theory
Theory
Theory
Theory
Theory
Figure 2: Integration across disciplines from a Human Complexity Sciences Sociology
One of the challenges for interdisciplinarity to succeed is to find common languages in spite
of differences in perspective, differences in terminology, differences in methodology,
differences in modeling, and differences in theory. To bridge some of these differences at the
personal level, as a network researcher, I might call myself an anthropologist but also an
ethno-sociologist. I can easily call my discipline ethno-sociology. Relabeling of this sort
might help to establish an interdisciplinary identity when giving a paper at a conference or
teaching in a summer school, but it does not solve the problem of common languages across
the sciences and humanities.
You can see why I do not want to give a public lecture on social networks or to identify
myself as a social network researcher. You can also see why I do not believe that it is useful
to create a taxonomy of networks, organized by disciplinary definitions, as in Figure 3.
Taxonomy?
Physical
Networks
Biological
Networks
Social / Kinship?
Networks
Historical
Networks
Personal?
Networks
Figure 3: A Spurious Taxonomy of Networks: NOT a Complexity Sciences Perspective
The fields of networks, bottom-up or adaptive simulation1 and complexity were already
building common languages across disciplines in the 1960s (the period of my early
1
Agent based modeling (ABM), Complex adaptive systems (CAS), parameterized analytical simulations of emergent
phenomena, and related approaches.
2
professional life), each on the basis of interdisciplinary research communities. Integration
between these approaches, however, had already begun. Ithiel de Sola Pool, for example,
made major contributions, during WW II, to quantitative analysis of networks and complexity
in his studies of communications content and political elites, to “computer simulation of
social processes, including the first computer simulation of decision making in international
crises”2 and did “the first major computer simulation of the American electorate based on
public opinion data and used to advise President Kennedy's campaign for the Presidency in
1960” (Etheredge 1997:1, see also Deutsch 1971). Stanley Milgram’s (1971) small-world
problem is a good example of a general concept spoken in a common language, across
disciplines.3 Network concepts, measures, processes, and models have become part of a larger
scientific common language in the last few decades, and they are now widely studied not only
empirically and theoretically but used in simulation studies and recognized as an essential
way to formulate, compare, and analyze basic processes in the complexity sciences.
For my part, it would be incorrect to say that I simple study “social” networks, as a part of
social reality and theory, as in Figure 3. Rather, networks are part of my conceptual language
for analyzing phenomena of all sorts, across the spectrum in Figures 1 and 2. This specialized
common language is also fit – well suited – for historical, humanistic (e.g., text-based), and
ethnographic studies. Network concepts also translate into several branches of mathematics.
They complement and relate to other branches of mathematics – such as probability theory
and calculus and differential equations among many others – that are used in scientific
analyses and theory.
Testable models and theories in my ethnography with Ulla Johansen, Process models of a
Turkish Nomad Clan, for example (now being translated by Xi’an Jiaotong Professor Haifeng
Du), are stated in a language of network concepts that connect to empirical social networks as
understood and recorded through participant and systematic observation, on the one hand,
and, on the other, to graph-theoretic models and mathematical theorems that provide the basis
for testable theoretical explanations, as in Figure 4.
Ethnographic data <--------------> Network measures <--------------> Formal theorems
e.g.
e.g.
e.g.
e.g.
nondeterministic
probabilisitic
complex
multivocal
dynamical
nondeterministic
probabilisitic
complex
multivocal
dynamical
Figure 4. Explanatory Models, but not based on (Referential) Correspondence Theory
What is interesting about the mappings in Figure 4 is that they are not based either on the
classical theory of Aristotle where words and things are in 1-to-1 (referential)
2
Simulating the processes involved in the outbreak of World War I ("The Kaiser, the Tsar, and the Computer"). Sola Pool
also contributed to the study of contact networks and influence and the impacts of new communication technologies.
3 The fields of networks, adaptive simulation, and complexity rediscovered themselves in an increasingly interdisciplinary
complex systems science and in the late 1990s rediscovered the links between physics and social sciences when so many
physicists were attracted to the parameterized small-world problem of Milgram as posed by Watts and Strogatz (1997).
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correspondence, nor on deterministic physical theory, nor are they based on equation-based
deterministic modeling. The links between data, measurable quantities, “entities” and theory
in this case are often nondeterministic, complex, multivocal, and dynamical, and may also be
probabilisitic. I can best illustrate this through my own work. Two contributions to network
theory and research that I am known for are:
a. Abstract role theory and the identification of multivocal roles in networks.4
b. Structural cohesion theory and multilevel cohesion in networks.5
These are models, respectively, that provide generally applicable identification of roles and
groups in networks, be they in physical phenomena, biology, sociology, kinship and marriage
(classical domains of anthropology, history, ethnography, and “network studies” proper,
whether in technology (the Internet, power grids), biology (protein interaction), or culture
(networks of meanings in texts). Note that meanings are parsed from their contexts by a set of
inferences which do not include the idea that a single word has a single referent. Rather, what
appear to be the same words (spelling, pronunciation), where they occur in mutually
exclusive and contrastive contexts, are initially assumed to have different meanings.
In general, it is relationships (i.e., networks) that define contexts. The extent of equivalence of
positions of elements in networks – their abstract role (as above) – is determined by whether
elements hypothesized to occupy the same role do in fact occur in the same contexts, and
whether those that occupy different roles occur in the different contexts. Figure 5 shows how
regular role relations are not necessarily unique but admit of multiple contradictory models.6
Figure 5: The Non-Uniqueness of Regular Roles
4
White and Reitz (1983), Reichardt and White (2007, 2008).
Moody and White (2003)
6 Figure 5 is from White and Reitz (1983:210).
5
4
In Figure 5, we start with twelve people in the graph (network) to the upper left, each person
or node with a kinship link R to a relative on their right, and with a sexual link S to a partner
on their left. Here, there are two possible role structures. One is the structure-preserving map
to the 4-role structure on the upper right, where each of the upper and lower nodes has a link
S on one side and a link R on the other. We cannot map the upper and lower node together in
a 3-role structure or get a 2-role structure because each would then be represented as
committing incest, with R and S links to occupants of the same role. These R and S links
could then be linked simultaneously to the same person, but this does not occur in reality. A
mapping of the same quality – an accurate mapping of roles – occurs in the bottom graph, but
now we have people assigned to six roles that are inconsistent with those in the upper right.
Persons 1 and 3 are in the same role in the first role model but in different roles in the second.
Thus there is no Aristotelian necessary referential 1-to-1 correspondence between person and
role. Rather, there is a higher order correspondence based on structural or regular
equivalence. This disjunction of role models – each with a different irreducible roleperspective – occurs once we admit that role relations that may be composed of multiple
relations (so that you and I may be friends, relatives, or both friend and relative, with each
possibility distinguished). This 1-to-many correspondence is unstable, and our perception of
roles could shift between one and the other and both be correct but their intersection
incorrect.7
Similarly, but for a different reason, there is an unstable ambiguity about the concept of
cohesive group, which is another area of my contribution to network theory and analysis,
along with important empirical discoveries where structural cohesion makes important
empirical predictions (Powell et al. 2005). Johansen and I showed in our book, Network
Analysis and Ethnographic Problems: Process models of a Turkish Nomad Clan, an
ethnographic case where our nomads use the same word, “kabile”, in different contexts, for
extended patrilineages, intermarried lineages forming a clan, and intermarried clans when
they form a single tribe or subtribe. As you might guess, it is the notion of intermarriage as
forming larger cohesion social units – although variable in size – that constitutes the common
but sliding signification. So context itself is not always an absolute criterion for meaning. In
this case the contextual variable of size is ignored. But a speaker might use the word kabile
extended to larger units when stressing integration, and choose instead the word “aile”,
meaning family, when the intent is to signal that the interests of “smaller” families might be
opposed. Here, the conceptual structure underlying the use of words is fluid and shifting, not
arbitrarily but signaling differences between integration and opposition, and reflects a larger
social fields of potentially shifting alliances.
The formal definition of structural cohesion at a given level k – subnetworks that cannot be
disconnected without removal of k or more members – works perfectly in this case of shifting
alliances, and works in many (indeed most) other kinds of applications of network theory
because it intrinsically defines a determinate and powerful measure of how well a unique and
Moreover, we could imagine the males in Figure 5 as exclusively on the “outside” in these role structures or on the
“inside,” and still both perceptions of the role models would be correct.
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perfectly defined maximal group of elements hangs together through bonds of positive
relations.
If people refer to their kabile at large, medium and smaller scale (tribe, clan, lineage;
depending on context), moreover, they are technically correct that if each unit is connected
cohesively (structural cohesion level 2 = biconnected, where every pair of couples has two or
more connecting kinship paths) they are in one sense equivalent, but in another sense, the
difference of scale in these three types of units will differ by the average length of the paths
by which people are multiply connected in a structurally cohesive kinship and marriage
group. Every such group, however, is uniquely defined by a chosen network of genealogical
relations, with a determinate boundary that we call that of structural endogamy. (White
1997).
Fast and Frugal (FF) Heuristics and Ecological Rationality
I spoke of intention in how we use words and how we see patterns and showed the potential
for complex interactive stability or instability that needs to exist in our models when we use
networks, simulations, probabilies, or complexity in our empirical studies. Still, even with
these instabilities, we can – and must – talk about causality through the study of dynamics.
Rather than Aristotelian entities that are always fixed in nature, we have entities that are
emergent.
Human beings possess emergents that evolved from their adaptive histories. Here is an
example of a FF heuristic for individuals to compute their membership in structurally
cohesive groups. People can easily consider and experience socially how they are connected
in two different ways to other people. If I have two different paths to person x in my social
environment, it is likely that I will meet at one time person z who connects to x by one path,
and at another time or even the same time meet w who connects to x by another path. In my
world I can meet some distant x and in our discussion it turns out that we both know w and z,
and we exclaim “Small world!” (even before or without knowing about Watts and Strogatz
1998 or Travers and Milgram 1969). People thus can easily identify many of those in their
network bicomponent, their “social group” with reference to some relation. It is an easy
theorem to prove that if everyone in a subset of people in a given radius (defining a network
perimeter by geography or network distance across contexts or settings) belongs to ego’s
“bicomponent” and this is true for most egos within this social perimeter, then it will contain
a network “bicomponent” that is mostly valid for each and every person within it. This is a
variant of the theorem that states: in a network connected by positive and negative ties, if
each ego can trace only cycles of connections that are “balanced” (product of signs is
positive, where ++ and – are balanced, and -+ +- are unbalanced), then the entire network is
divisible into two sides, each with only positive internal connections and only negative
intergroup connections. Going back to if we allow the perimeter for bicomponents to vary
from person to person, of course these bicomponents will overlap and form larger
communities.
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In both these cases, bicomponents and polarized social worlds, people can solve a complex
assignment problem by using only local knowledge by using a fast frugal (FF) heuristic, and
their solution will match the solution of this problem by optimization methods applied to the
whole network, but using many many more steps in the computation. The problem of finding
all k-components of a rather dense network is maximally difficult computationally, but a
problem that has fairly obvious and intuitively accurate solution for individuals in
communities.
Two competing paradigms of human sciences: Network Complexity versus Rational Choice
So, it is time to talk about the alternative paradigm: the illusion that it is only “unbounded
rationality” that is truly rational when there are FF heuristics for many problems that humans
face recurrently where they can obtain solutions equally good or better using the human
adaptive toolkit of FF heuristics. The study of the contexts in which FF heuristics outperform
computer optimization methods is the field of ecological rationality studied by Gert
Gigerenzer (2007) and researchers at the Max Planck Center for Adaptive Behavior and
Cognition. They investigate reasoning and decision making under uncertainty at the levels of
both individuals and social groups and find a large proportion of problems where humans
outperform optimization algorithms.8
What the research on FF heuristics (ecological rationality, Gigerenzer, 2007) refutes is the
idea that the theory, methods and models of “Rational choice”, including dynamical Game
Theory, “Optimality”, and classical microeconomic optimization, which is “unbounded”
constitute the only valid formal definition of rationality (e.g., Simon argues that people who
make actual economic decision do not meet all the assumptions that the model requires,
including perfect information and unbiased processing of the imperfect information they
have)9, a premise that until recently has dominated mathematical economics and utility
theory, especially after the advent of formal economics, Von Neumann and Morgenstern’s
(1953) invention of Game Theory, and modern computational methods. These are useful
“ideal models” of something, but that something is retrodictive, asking: Was a given behavior
unboundedly rational, computationally optimal, as defined in the theory of “Rational choice”,
even if bounded rationality is better at solving the problem?
Network complexity, in contrast, is one of the areas where local behavior in the adaptive
behavioral toolkits that have evolved, not only those of humans but of other organisms, yield
in many cases to simpler, faster, and more efficient solutions to complex problems of
perception and choice, and often better optimization that formal computational optimization.
That is, the best decision algorithms are often not those of “Rational choice”.
What his implies is that we should study actual networks, actual behavior, and actual
heuristics used in cognition, those called, until now dismissively, “gut feelings” or
8
This also suggests that we would do well to put FF heuristics with contingent strategies for local behavior (depending on
the problem) in our simulations if they are to be useful in understanding real-world behavior of humans and other living
organisms. This is a goal of contemporary work in digital evolution models, formerly know as “Artifical life.”
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Leaf (2008:6).
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“intuition”, if we want to understand causality, the dynamics of complex interactions, make
better predictions, design better policies, and design better solutions to human and ecological
problems.
Implications for studies of networks and society
Society is not a self-organizing, stable, self-contained system, but like migration, politics,
economics, and any other area of life, consists of networks of processes, internal and
exogenous, in which there are many dynamically reactive processes. If used wisely, network
studies include the time dimension and try to focus on those problems and areas where the
data on the networks studied are taken to represent channels of actual interactive effects on
other outcomes. With refinement of our methods of testing causal models, we might be able
to identify causal interactions. But if we fit all of our data to a given model, even if fit to the
is perfect, we do not have evidence of causality. Only if we set half our data aside to build a
model, for period 1, and test the predictions of the model for period 2, and do this over many
different contexts, times and places, will we have evidence of causality. To do this we can
usefully combine the approaches of physics, concerned with generality, sociology, concerned
with reliability and validity, anthropology, concerned with a holistic view of how pieces of
the puzzle fit together and how to reconceptualize our research problems, history, concerned
with valid inferences from data in space and time about actual temporal processes, and
ethnography, concerned with what human life looks like in the full dimensions in which it is
experienced.
Formal modeling and mathematics has a vitally important place in understanding networks
and society, or social processes. Mathematics – from graph theory to differential equations,
and all the rest – has a role equally important to that of data collection and analysis because
inductive inference alone cannot provide causal explanation. There are aspects of causation
and explanation that are reached by deductions from axioms to consequences, and if these can
be proven a priori they do not require empirical evidence. Rather, if the consequence does
not follow in the empirical world to which the theory is applied, it must also be the case that
the axioms did not apply in this case. The strategy I have used in my work – like that of
measuring cohesion or role structure – is to weaken the axioms of model that might lead to
explanatory causality until they can be weakened and generalized no further and still help to
explain the phenomena.
References
Deutsch, Karl W., Platt, J. & Senghaas, D. 1971. “Conditions Favoring Major Advances in
Social Science.” Science 171(3970): 450-459.
Etheredge, Lloyd S. 1997. What Next? The Intellectual Legacy of Ithiel de Sola Pool
http://web.mit.edu/comm-forum/papers/etheredge.html MIT Communications Forum.
http://web.mit.edu/comm-forum/papers.html
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Gigerenzer, Gerd. 2007. Gut Feelings - The Intelligence of the Unconscious. New York:
Viking Press.
Moody, James, and Douglas R. White. 2003. Structural Cohesion and Embeddedness: A
Hierarchical Conception of Social Groups. American Sociological Review 68(1):1-25.
http://www2.asanet.org/journals/ASRFeb03MoodyWhite.pdf Outstanding Article Award in
Mathematical Sociology. American Sociological Association, 2004.
Powell, Walter W., Douglas R. White, Kenneth W. Koput & Jason. Owen-Smith. 2005
Network Dynamics and Field Evolution: The Growth of Interorganizational Collaboration in
the Life Sciences. American Journal of Sociology 110(4):901-975. Viviana Zelizer Best
Paper in Economic Sociology Award (2005-2006), American Sociological Association.
http://www.journals.uchicago.edu/doi/abs/10.1086/421508
Reichardt, Jörg, and Douglas R. White. 2007 Role Models for Complex Networks. European
Physical Journal B 60: 217-224. http://intersci.ss.uci.edu/wiki/pw/ReichardtWhite.pdf
http://eclectic.ss.uci.edu/~drwhite/pub/RW_6Page_JournalFormat.pdf Selected for
Europhysics News 8(1) 2008 “Highlights”.
Simon, Herbert A. 1957. Models of Man. New York: Wiley.
____. 1986. Rationality in Psychology and Economics. The Journal of Business
59;4, part 2, The Behavioral Foundations of Economic Theory, pp. S209-S224.
Travers, Jeffrey & Stanley Milgram. 1969. “An Experimental Study of the Small World
Problem.” Sociometry 32(4): 425-443.
Von Neumann, John, and Oscar Morgenstern. 1953. Theory of Games and Economic
Behavior, Third Edition, Princeton University Press.
Watts, Duncan J., and Steven H. Strogatz. 1998. “Collective dynamics of 'small-world'
networks”. Nature 393: 440-442.
White, Douglas R. 1997. Structural Endogamy and the Graphe de Parenté. Mathématiques,
Informatique, et Sciences Humaines 137:107-125. http://eclectic.ss.uci.edu/~drwhite/pw/strendo.pdf
White, Douglas R., and Ulla Johansen. 2006. Network Analysis and Ethnographic Problems:
Process Models of a Turkish Nomad Clan. Boston: Lexington Press. 2006 Paper
http://eclectic.ss.uci.edu/~drwhite/pub/PMContFwd01.pdf
White, Douglas R., and Karl P. Reitz. 1983. Graph and Semigroup Homomorphisms. Social
Networks 5:193-234. http://eclectic.ss.uci.edu/~drwhite/pub/whitereitz.pdf
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Lecture II. Conclusions (networks and complexity)
I had six very good teachers of complexity. One’s interest is directed toward those
approaches that inspired you. Each of these teachers pointed toward the links between
networks and complexity.
1. Buckminister Fuller, Engineer and Designer, taught me the relation between dynamics
and structure: the dymaxion house, the fuller dymaxion dome, dymaxion
transportation systems, dynamical earth. At the heart of Buckminster Fuller's
Dymaxion concept is the idea that rational action in a rational world demands the
most efficient overall performance per unit of input. His Dymaxion structures, then,
are those that yield the greatest possible efficiency in sustainable (hence alternative)
technology. His belief was that several hundred years would be required for these
advances to come forth into practice. Dynamical equipartition and utilization of
energies were the basis of dymaxion designs. The heart of complex, efficient,
sustainable structure and dynamics is simplicity in design.
2. Wikipedia:Adamson Hoebel, process models, cooperation and conflict, and an
introduction to the Manchester School of Max Gluckman and his students and
colleagues (Clyde Mitchell, Elizabeth Colson, Thayer Scudder)
3. Eric Wolf, the best of my seminar teachers, among many of the greats at the
University of Michigan: “Anthropology is both a science and a humanity”
('Anthropology 1964 Englewood Cliffs: Prentice-Hall).
4. Edward Tufte, who taught the principles of visualization, visualizing quantitative
information, one-day seminars.
5. Arthur Iberall, Engineer and Physicist, designer of the space suit for the first
American space voyage, developed homeokinetics as a theory of causal complexity
6. Frank Harary, my teacher of Graph Theory (University of Michigan) and a delightful
coauthor
…
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