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