Xi’an Lectures I and II XianPublic1.ppt http://intersci.ss.uci.edu/wiki/index.php/Xi'an_Jiaotong_University_lectures

It is a great 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 wan to speak about 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.

A Unifying Perspective on the Disciplines. Holism plays out as an integration of disciplinary perspectives between the nomothetic sciences, searching for regularity, and the idiographic humanities, concerned with interpretive validity.

Nomothetic Holistic Idiographic

(I.) (II.) (III.) (IV.) (V. individual)

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

2 Slides: Feedback Networks (simulations linking physics and sociology)

Interdisciplinary common languages. My slides on physics and sociology (social networks) can extend through simulation to physics and anthropology (social networks), or physics and history (social networks), or physics and ethnography (social networks), as I will show in the next few examples. The same simulation could apply to problems in each area, as could the same network concepts and measures.

Thus, I do not believe that it is useful to create a taxonomy of networks, organized by disciplinary definitions, as in Figure 3. These disciplinary compartments should be integrated and not seen as separate. Each can study networks, albeit in different ways. Each has its own theory, albeit with different goals, but the theories can be linked.

Taxonomy?

Physical Biological Social / Kinship? Historical Personal?

Networks Networks Networks Networks Networks

Figure 2: A Spurious Taxonomy of Networks: NOT a Complexity Sciences Perspective

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. I might call myself an anthropologist in one context but an ethno-sociologist in another. From that perspective I might call my discipline ethno-sociology. Figure 2 shows how another discipline, Sociology, might relabel the columns of Figure 1 differently.

Nomothetic Holistic Idiographic

Social Sociology Ethno- Historical Ethnographic

Physics Sociology Sociology Sociology

Primary

<------Integration ------>

Deutero-

<------<------Integration ------> ------>

Networks Networks Networks Networks Networks

Theory Theory Theory Theory Theory

Figure 3: Integration across disciplines from a Human Complexity Sciences 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. The earlier Figure 1 and the powerpoint on Feedback Networks simulations linking physics and sociology illustrate the kind of integration I am interested in and their relation to representative disciplines from a perspective of anthropology but within an interdisciplinary Complexity Science. And 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.

For my part, it would be incorrect to say that I simply study “social” networks, as a part of social reality and theory, as in Figure 2. Rather, networks are part of my conceptual language for analyzing phenomena of all sorts, across the spectrum in Figures 1 and 3. 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.

Explanation and Explanatory Models. 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) 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 probabilisitic.

Formal theorems <------> Network measures <------> data

Ethnographic

nondeterministic nondeterministic Historical

e.g. probabilisitic probabilisitic Sociological

e.g. complex complex Ecological

e.g. multivocal multivocal Physical

e.g. dynamical dynamical

Figure 4. Explanatory Models, but not based on (Referential) Correspondence Theory

Explanatory Principles. In principle, then, similar approaches can be taken across the nomothetic-idiographic continuum. But at each of these levels different approaches may be applied. Krakauer (2008), for example, writes of the arbitrary present (AP) in history – a date for which we could seek an explanation in terms of antecedent events – by study of

(1) unifying mechanisms and boundary conditions, including evolutionary theory generally without making use of common descent, such as

a.  Abstract role theory and the identification of multivocal roles in networks.[1]

b.  Boundary condition equivalence in context.

c.  Structural cohesion theory and multilevel cohesion in networks.[2]

or,

(2) the regular component in a time series, statistical and contingent.

I can best illustrate (1), unifying mechanisms and boundary conditions, through my own work. Three contributions to network theory and research that I am known for are:

a. Abstract role theory and the identification of multivocal roles in networks. 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) are initially assumed to have different meanings, where they occur in mutually exclusive and contrastive contexts.

Slides on Role structure in networks. These are slides on how a modern network approach evolves out of social anthropology and the study of role systems, pioneered by A. R. Radcliffe-Brown, Lloyd-Warner (slide: Murngin), André Weil (1949), graphics of Guilbaud, G. Th. 1970 and Bertin, Jacques. 1983. Semiology of Graphics, Trans. William J. Berg; University of Wisconsin Press, Madison, Wisconsin, (trans. of 1967: Semiologie Graphique, Editions Gauthier-Villars, Paris). Hèran, François. 1995. Figures et Légendes de la Parenté. Paris: INED. François Lorrain (1968), and others, and from there into Lorrain and White (1981) to feed foundational work in network sociology. (two slides: Alyawarra genealogy and role structure à http://eclectic.ss.uci.edu/~drwhite/pw/Classificatory.htm

Recurrence and emergence. What is it about the study of role structure that fits Krakauer’s “unifying mechanisms and boundary conditions”? Invariably, its is patterns of dense and repetitive interaction that form into emergent role structures, and their recurrence as types of role systems (center/periphery, hierarchy, reverse hierarchy, circular flow, etcetera) as global patterns emerge directly out of specific (and often surprising! – like the hierarchies of egalitarian chickens) local mechanisms. The theory here is the duality of local-global co-evolution in networks. The generality of this theory is developed most fully by Harrison White (2008) in the forthcoming revision of his book, Identity and Control: A Structural Theory of Social Action.

World systems (Slides and Studies). Reichardt and White (2007) are the latest iteration in a series of temporal snapshots of the world economy (e.g., Smith and White 1992, Mahutga 2006). What makes these more than contingent time-series are findings like those of Emily Erickson and Peter Bearman (2006 “Routes into Networks: The Structure of English East Indian Trade, 1600-1831”. American Journal of Sociology 112(1):195-230) that show how the malfeasance of sea-captains in the Indian ocean trade created patterns of dense and repetitive interaction that formed into the emergent role structures of modern capitalism. Avner Greif’s (1997) intensive historical study of institutions that facilitate impersonal exchange in pre-modern Europe http://www-econ.stanford.edu/faculty/workp/swp97016.pdfgives a land-based mapping of the historical processes involved in this transformation into appropriate game theoretic models for experimental studies. Kimbrough, Smith, Wilson (2006:1) then explore in well-designed laboratory experiments the conditions for emergence of impersonal markets.

But Greif (1993, 2006) also reconstructs two specific lost histories of community-based systems of responsibility that supported impersonal exchange in medieval Europe and that laid the foundation for broader, law-based systems to eventually supplant them. Using the experimental method, Kimbrough, Smith, Wilson (2006) attempt to reconstruct our understanding of such transitions by directly observing how Adam Smith’s natural propensity expresses itself as cash-motivated participants discover and implement local and distal exchange networks in the laboratory.

Ethnographic Recurrence in Social Structure. 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.

b. Equivalence in Context. 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. But Figure 5 shows how regular role relations are not necessarily unique but admit of multiple contradictory models.[3] The evolution of role structures is not deterministic but includes the possibility of structural bifurcations.

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.

Figure 5: The Non-Uniqueness of Regular Roles

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 role-perspective – 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.[4]

And as distinct from Krakauer’s more regular views of historical explanation as (1) mechanisms and boundary conditions or (2) regular components of statistically contingent patterns, we need a more refined view of bifurcation and of memory:

“Memory is life. It is always carried by groups of living people, and therefore it is in permanent evolution…. Sometimes is remains latent for long periods, then suddenly revives…. Memory always belongs to our time and forms a lived bond with the eternal present.” Eric Hobsbaum (Tr. Paris 1984 v.1 p xiv by Pierre Nora, ed., The age of Empire) Les Lieus de la memoire.

c. Cohesive resistance and impact. 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 consistent empirical predictions in all kinds of arbitrary present (AP) situations (e.g., Brudner and White 1999, White and Johansen 2004, Powell et al. 2005).

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 perfectly defined maximal group of elements hangs together through bonds of positive relations.

Structural cohesion: Biotechnology Slides. To shift now to an integrative example from a sociology-ethnosociology perspective my 2 powerpoint slides here are from a collaborative sociological study of the biotech industry (analyses linking sociology and network anthropology). These are followed by a scaling plot, and then a dynamical plot, year by year.