# Realistic modeling of complex interactive systems

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## Contents

- 1 Lectures -
**Human Social Dynamics: Realistic modeling of complex interactive systems** - 2 Some core readings
- 3 Assignments/exercises (please Post here or intersperse edits, pose questions, post results elsewhere on the wiki)
- 4 (1) Realistic evolutionary process models and ethno-sociological dynamics (autocorrelates, dynamics, realism) ppt1pdf [6]
- 5 (2) Realistic simulation and retrofitting parameters (social circles feedback model, old and new parameters) Kejžar slides [13] ppt2pdf [14]
- 6 (3) Realistic dynamical modeling ppt3pdf [17]
- 6.1 _____ Empirical Scaling Baselines for City Growth
- 6.2 _____ A Link to Social Networks
- 6.3 _____ Alternative hypotheses about City Size and City System Fluctuations
- 6.4 _____ Scaling Changes in Historical City Sizes
- 6.5 _____ Background to Scaling of Historical Eurasian City System Dynamics
- 6.6 _____ Causes of Failed States, and their Consequences for Global destabilization
- 6.7 _____ Historical Scaling of Changes in Eurasian Regional City Size Distributions

- 7 Conclusions
- 7.1 _____ Conclusions: Part 1
- 7.2 _____ Conclusions: Part 2 (parameterized simulation and measurement of feedback networks)
- 7.3 __________ QML estimation of retrodictive feedback model outcome parameters
- 7.4 _____ Conclusions: Part 3
- 7.5 _____ Auxiliary powerpoint, beyond the conclusions: Multilevel Networks and Historical Dynamics
- 7.6 _____ Period-Doubling and the Road to Chaos
- 7.7 _____ Beyond the scientific conclusions

- 8 Highly provisional graphic
- 9 Schedule of these lectures

## Lectures - **Human Social Dynamics: Realistic modeling of complex interactive systems**

Douglas R. White Paris 2007. Paris lecture site: http://iscpif.fr/Realistic+modeling+of+complex+interactive+systems. ISC-PIF Complexity summer school [1] :- all students, faculty, staff are free and invited to add/edit these pages in the spirit of increasing scientific objectivity, criticism, and realism.
(These notes are now substantively complete and open for review)

**Abstract of the lectures**
I will illustrate a layer-embedded networks (LEN) approach to emergence and complexity. Unlike discovery of simple interactive principles that generate complex emergent behavior (e.g., agent-based modeling, self-organized criticality), networks of interaction in the multi-layer approach occur between elements with internal processing and time-delayed responses, such as humans with biosocial and cogni-cultural reactivities. In several of these studies, response times are at generational time-scales. These embed linked phenomena at shorter spatio-temporal and spatial scales and are embedded in those of longer and larger scales. LEN models allow multiple levels of embedding, with some interactions occurring at faster time scales and others that affect them occurring at successively slower scales. The principles here may be simple, but how these levels interact requires a very delicate and new understanding of layering and feedback. I use examples from human evolution and dynamical organizational oscillations at different spatiotemporal scales, from long-term evolution over tens of thousands of years to those of generational and shorter time scales. Looking at longer-term trends and oscillations around those trends some crucial problems to our survival can be projected into the near term decades of our future and the importance of choices we make regarding our behaviors and policies in the very near term. Many sources of data and methods of modeling are illustrated here but there is a clear need in the human sciences for integrated reconstructed datasets that tie together at multiple levels of embedding. My objective and the problems I have posed in my career, as illustrated here, have concerned how to bring methods belonging to an emergent field of complexity sciences to bear on problems at the various scales of human behavior, and to bring what we have learned in the social sciences and humanities back into the approaches we use in the sciences.

- Part 1 Realistic evolutionary process models and ethno-sociological dynamics (autocorrelates, dynamics, realism) undertakes a quantitative review of ethno-sociology as a comparative field continually rediscovering complexities that do not fit the standard models and that require dynamical modeling of interdependencies. The introduction to historical dynamics provides a basis for continuation in part 3, mediated by understanding of the generative network model in part 2.
- Part 2 Realistic simulation and retrofitting parameters (social circles feedback model, old and new parameters) explores a new kind of
*platformed*simulation in which a few elementary parameters generate many of the kinds of diversity that we observe in real networks. It is constructed probabilistically to allow a 1-to-1 mapping to and retrofitting from the parameters of empirical networks. Where these 1-to-1 mappings exist is of considerable interest because this kind of simulation*platforming*suggests that modularity in simulated processes can deal with compound processes whose interactivity in the models can be parametrically retrofitted to interactivity in real world social processes. - Part 3 Realistic dynamical modeling. This builds on findings about historical dynamics from part 1, and continues into new terrain that ties in with the feedback simulation modeling in part 2, now exploring the historical dynamics of city systems. Links to the sandbox where math formuli are possible provide the background mathematics where I connect the Bettencourt et al. 2007 PNAS work on city growth and metabolics with the city size and population growth dynamics.

## Some core readings

For an overall review of selected ethno-sociological work by me and others in these areas covered, see the **topical bibliography**

- To what theories are these approaches and findings relevant? #Conclusions

## Assignments/exercises (please Post here or intersperse edits, pose questions, post results elsewhere on the wiki)

##### _____ Using R for Stats and Graphics

- Using R for statistical research [2](Please turn in R code and results---create your user and home pages on this site, and also post your code and results to your page): Comparative research tools [3]. The idea here is to download one of the comparative/coded ethnographic databases (in R or Spss), review items 1-7 in the topical bibliography and the codebook [4], and then use R (alternately Spss) to try to identify a single factor structure for a group of variables that measure the same thing, a major dimension of sociocultural organization, and correlate that in turn with other single variables. We will discuss this pattern where one factor correlates with many other variables that have little correlation amongst themselves, as one of Guttman's radex [5]
^{pdf}patterns, a*stardex*representing a factor that includes measures that vary by complexity but not by kind, and the one-to-many pattern a factor generalization that has variation both in kind and complexity, but with a kind of central causal element (the core factor). Then try a regression analysis where two or more factors or independent variables are regressed on a dependent variable, and analyze the residuals for autocorrelation (cases are ordered by proximity, but there are intersociety matrices for distance, language similarity, etc.) This illustrates the**general nonindependence problem for all sorts of survey data**which is a tipoff for a more general****Radex theory of complex interactions****in which I develop a theoretical perspective capable of integrating comparative analysis of multiple cases with network analysis with historical and dynamical analysis.- factor analysis: install R, load R for comparative research, select variables, run factor analysis, try to find a single factor structure; you can alternatively use Spss
- autocorrelation in multiple regression (see
**Anthon Eff**): His 186x186 language similarity matrix can be downloaded from http://intersci.ss.uci.edu/wiki/drw/AnthonEff/wmlang02112006.xls and the another version plus the distance matrix from the exercise pages. - time lagged regression for 2-equation endogenous dynamics (time-lagged negative feedback)

##### _____ Using Python for Networks

- Using Python for networks, Networkx for feedback networks, R for networks, R for simulation and R for MLE of the Pareto and Pareto II distributions, Pajek and R for graphical results
- Social circles generative feedback model: The complex network problem Kejžar slides
- Pajek network graphics/analysis and output of degree distributions
- Degree distribution parameters http://eclectic.ss.uci.edu/~drwhite/0/parameter_values1.html
- Computing retrofit of parameters

##### _____ Using R, Excel, ... for macro-system dynamics

- Using R, Excel, ... for macro-system dynamics
- MLE of city size distributions: Probability distributions

##### _____ Sketches and ancillary materials for the lectures

-- check back, **under construction**--Doug 15:43, 25 June 2007 (PDT). Once finished, the powerpoints for each part will be available under the main headings as viewable ppt_pdf files.

## (1) Realistic evolutionary process models and ethno-sociological dynamics (autocorrelates, dynamics, realism) ppt1pdf [6]

Social science may have missed some of the big stories of human evolution. Starting with comparative ethnographic data over time, the dimension of modernity is neither correlated with complexity nor with the advancement of human rights. It is correlated with inequality, including beliefs in female inferiority, etc. Once we get past hunter-gatherer-pastoralists, morality and religion, not functionality, have tended to shape social organization and institutions. The biggest “jump” in evolution occurred in the twentieth century forward and its two biggest correlates are part of the story of 1 and 2 below.

##### _____ Social evolutionary processes

- hyper-exponential growth in population [7] - city growth and scale treated in part 3
- major increase in internal wars (my finding) method: Trevor Denton
- major recent increase and short run trend in external wars Trevor Denton 2007 (the long-run trend was toward decrease but the short run trend to the present possibly indicative of the future was to increases in external wars).
- major recent increase and short run trend in population density, food stress: Trevor Denton 2007 (other trends halted and stabilized: Money, political integration, stratification, divorce, wife-beating, adult mobility, formal education.)
- correlation between internal wars and population density/modernization masked by dynamics, unmasked by sufficient aggregation: Peter Turchin
- for the last two millennia ideology and religion account for the major ways in which differentiation of social organization has occurred worldwide: Andrey Korotayev
- external warfare across ethno-religious boundaries affects formation of resistive cohesive groups: see Peter Turchin

- Key causal variable in formation of ethnicity, linguistic differentiation, social class, power elites: structural endogamy [8] and structural cohesion -- [9]
- The role of open boundaries in societal resilience, i.e., cohesive overlap[10]; not unrelated to valid competing claims over disputed territory.

##### _____ Consequences of Human evolutionary processes

Consequences include disruption and impoverization caused by internal wars have fueled the population explosion, while external wars precipitate cohesive resistance, 'formation of nationalities,' and competing/overlapping historical claims over territoriality. Massive crashes in the earth ecosystem will occur with near certainty in the next 50 years with global climate change, warming and variability, and massive species die-off. Some of these big stories of human social structure are missed or neglected by social network and complexity science.

- massive disruption of ecosystems – structurally cohesive or redundant network pathways are essential to maintain a viable ecosystem
- eradication of variability in relatively autonomous cultures and variability in plant species – when the redundant pathways (or structural cohesion) in the networks that support these systems are disrupted, even by overlay networks such as those called “globalization” the effects are massively destructive

##### _____ Role Modeling of Exchange Structure in World Trade

Network studies of world trade flows made an important transition between Nemeth and Smith (1985) and Smith and White (1992) [11]^{pdf} summary [12]^{pdf}. The transition in methods was from network analysis of position using structural equivalence measures to those of regular equivalence. The earlier analysis identified blocks of countries on the basis of having approximately same sets of trading partners, and showed only regional blocks in the world economy. The regular equivalence analysis showed blocks that had equivalent members in other blocks: "Regularly equivalent [actors, countries] are connected in the same way to matching equivalents." "Regular equivalence yields groupings of [actors, countries] in which for every pair of factors, countries] in the equivalent position, if one has a relation with [another] in a second position, the other has an identical relation with a counterpart in that position" (White and Reitz 1983:200,214). This analysis showed for each successive time period (1965, 1970, 1980) a core-periphery structure in the world economy that could be mapped onto a single quantitative dimension in a hierarchy of inequality. The stability or mobility of countries could be mapped in terms of vertical position along this hierarchy.

Smith-White 1992 regular equivalence model of world economy 1965-1970-1980

link to new world economy blockmodeling paper with Jörg Reichardt via a review by Cosma Shalizi

##### _____ Replication of Unequal Exchange in World Trade

Matthew Mahutga (2006) used an improvement of the Smith-White (1992) methodology for measuring regular equivalence in world commodity flows, this time expanding to five time periods (1965, 1970, 1980, 1990, 2000) and reducing the countries to 53 in order to include only those with complete data in all periods. He tested the hypothesis that the new industrial division of labor (NIDL) encouraged upward mobility for historically poor countries and found the opposite: "NIDL and globalization have benefited a few exceptional countries while at the same time producing structural inequality."

These findings are cited in http://cos.sagepub.com/cgi/content/abstract/48/1/43 International Journal of Comparative Sociology 48(1):43-72 (2007) "Ecological Unequal Exchange: Consumption, Equity, and Unsustainable Structural Relationships within the Global Economy" by James Rice.

The diagram in my pdf/ppt of Mahutga's full 5-period results uses a summary figure made by Carl Nordlund (University of Lund) in Chapter 8 draft of his dissertation, "International trade, network analysis and ecological conceptualizations of unequal exchange." He ranks each country by its scaling value on the first component of variation for the regular equivalence coefficients as found by Mahutga, and then shows the clustering of core, SP1 and SP2 (semiperipheries) and P1-P1 (countries occupying the periphery in the world trade network). My interest is in the mobility of countries over time and in the mobility of the blocks, and I superimpose on Nordlund's graph a transparent coloring to show block mobility.

Is there a G7 production cycle? (2001) shows downturns in average production in the six major G7 and U.S. economies in >1971 (-6) 1975 (-9), 1983 (-8), and 1993 (-4), a relatively positive period 1964-1968 (+2) and upturns in 1974 (+7), 1979 (+5), and 1989 (+3). Mobility is perfectly in line with predictions from a network economics model made by White and Smith in 1988 (unpublished: figures separate, a study never published because we had only two inter-period mobility series. World Gini index aveerages show inequality grows when the economy expands -- cores and SP 1 move up --, while equality increases when the economy shrinks.

Stock market fluctuations, as expected, are not correlated with rise and fall in production, which is the real business cycle. Nor do stock market fluctuations correlated across countries.

At this point in the summer school, Joerg Reichardt gave a presentation on blockmodeling from our new paper, 2007 Role Models for Complex Networks, (http://arxiv.org/abs/0708.0958 - Jörg Reichardt. Our joint paper weights for structural equivalence of countries in the world trade-flow network. Symmetries in the role structure image graph suggest a more one-dimensional core-periphery structure or central axis of centralization and peripheral organization. Our next paper will weight our quality function for regular equivalence. The outcome is predicted to be a highly one-dimensional role structure, supporting the findings of Smith and White (1992) and Mahutga (2006) discussed above.

## (2) Realistic simulation and retrofitting parameters (social circles feedback model, old and new parameters) Kejžar slides [13] ppt2pdf [14]

How do we in the human simulation sciences connect to social realism? So much of the data we use to develop and test models are about our own citation networks, our internet, our email messages, our router systems, our on-line movie databases, our own society, the boards of directors of firms without knowledge of ownership, shareholding, private equity, etc. The in-depth data we need to understand our planet and ourselves as its inhabitants may take years to develop. (See: The complex network problem). The best-known**complex network**models tend to oversimplify to too-few dimensions or parameters (scale-free models) and to overgeneralize interpretations, or to show that parameters such as path length and clusters create such an inclusive space of networks that they are of little use in empirical studies (small-world models). The complex network problem[15], this text, and the exercises examine the social-circles network model [

**social circles**generative feedback model] as an alternative to those of small-worlds and scale-free networks. These simulations are intended to model such examples as the formation of trade networks, business partnerships such as the biotech industry, social classes linked by structural endogamy, and autocatalytic networks.

Feedback in a network entails either mutuality between 2 nodes or cycles of 3 or more. Lacking cycles every node is a cutnode or an endnode, and all routings are uniquely determined. Alternatives, and hence dynamics, depends on cycles.

Networks have two fundamental aspects: structure and traversal; traversal or transport is the function of providing routes of transmission. Network theory requires that we connect these two concepts to understand dynamics. The Menger theorem, for example, states the fundamental isomorphism or identity between *structural cohesion* as the minimum number of nodes needed to disconnect a group and *structural traversal* as the maximum number of node-independent paths that holds between every pair of nodes in a group. For any given number k, the there are a unique set of maximal subgraphs with these two identical properties, each with n > k nodes. The minimum number of independent cycles (where each has at least one unique edge) within each such k-connected group of size n is (n(k-2)-2)/2.

How feedback cycles are structured within a network has implications for the structure-traversal identity. Dyad and triad censuses of a network may not give us sufficient information to study dynamics. Cycle censuses are not unique because there are many ways to construct the minimum number of independent cycles. The k-connected groups of a network are unique, and they have predictive consequences in terms of structural cohesion predicting patterns of influence and structural division (cleavages in cohesion, which may include overlaps).

Hence one of the fundamental properties of complex networks that we need to understand are feedback effects that operate through structural cohesion-traversal properties. If causal effects operate as positive feedback they are either runaway or self-destructive systems. Negative feedback can lead to self-correcting systems tending to equilibrium, but in living systems these are more commonly only near equilibrium because of time lags effects, and these lags may operate over very different time scales. Part 3 considers *kinds* of feedback with respect to the dynamics of city systems.

Where network links represent the channels for proximal influences in propagating social effects (the spread of a fad or a disease, for example), to understand complex dynamics in which structural cohesion-traversal have effects, it is of crucial importance to understand the dimensions of variability in network structures in order to study their effects. Analyzing network structure by the scale-free model, with a single fitted parameter related to attachment probabilities, may be of very limited use because very different processes may lead to similar outcomes. Similarly, analyzing network structure in the context of the small-world model (more clustering and lower average distances than expected if the network links were more randomized) may only succeed is placing the network in a broad class with little analytical purchase.

##### _____ Realistic parameters of the feedback model

The **generative feedback network** or **social-circles network model** (please go to this link for synopsis and mathematical formuli)

...was developed to provide greater analytical purchase by having three basic parameters represent the most common variants of human (or living system) behavior:

- alpha - like the scale-free parameter, the probability of a new behavior reflects past behaviors (0=equiprobable)
- beta - the viscosity of the network, the ease or difficulty of traversal (>1 but ~1 inversely proportional to distance)
- gamma - the extent to which traversals or searches are conducted with a bias towards hubs (0=equiprobable).

Here, viscosity plays the role of clustering in the small-world model, but is not limited to clustering in the neighborhood of immediate adjacency. This contrasts with the small-world model, in which cluster density for egocentric cliques gives no information about larger cohesive structures. Viscosity in the generative feedback model represents structural cohesion-traversal, or **social circles which are scalable in that relatively low cluster density may expand indefinitely in size and still have very high k-connectivity**.

One of the crucial findings of the simulations as concern the self-scaling property of structural cohesion-traversal, in which the network grows indefinitely, and for alpha>1 or gamma>1 grows a power-law tail in hubs according to degree distributions, but the average of links per node may remain very low (circa 1.5 and but no more than 5 on average, although the tail of the degree distribution is power-law). These are density ranges that Stuart Kauffman identifies as ideal for complex dynamics that do not settle down to an equilibrium or that form recurrent nondeterministic patterns. Still, except for parameter settings that produce a nearly random graph given clustering, almost all of the networks generated are small-world in having both clusters (because of viscosity) and much lower average pairwise distances than Erdös-Rényi random graphs of the same density due to the presence of hubs if either alpha or gamma are greater than zero.

Distributions of degree (number of edges) cumulated for different parameter values form a single universality class in the social circles model, one which includes power-laws at one end of the spectrum and the type of exponential distributions found with Erdös-Rényi random graph at the other. The distribution which includes this range of outcomes corresponds to Tsallis entropy with a shape parameter q>0 that associates to the exponential distribution at q=1 and asymptotes to a power-law tail of slope 1/(1-q) where q>1. As *q* → 1, Tsallis entropy converges to the Boltzmann-Gibbs entropy characteristic of random motion under the gas laws, for example.

The low average degree in these graphs may contrast with many real networks, but the shape of real networks may often be *q*-exponential, and it may be the ties that generate useful 'feedback' in social networks that generates both the clustering and the hubs and many networks.

The feasibility of retrofitting the social circles model has been demonstrated in a social network study of migrants to urban neighborhoods in Chinese cities carried out in cooperative demographic research between Stanford and Xi'an universities. In this study five common-neighborhood, residence, or work groups, each of about size 200, were each completely canvassed to collect network interview data on all within-group ties. Seven different types of ties were pretested and collected in the final studies. This gave 7x5 or 35 networks in total, almost all of which had degree distributions that fit the *q*-exponential better than the scale-free model, or, due to the present of hubs and network centralization, the small-world model. Retrofitting to the *q*-exponential parameters for degree distributions proved to be consistent for 5 of the 7 relations.

Because Nataša Kejžar (2007) has recently completed the parameterization of directed degree distributions and path lengths for the feedback network model, it will now be possible to fit and then retrofit the empirical *q*-exponential parameters of the 35 Chinese migrant networks to the model (aka social circles model). Successful retrofitting of multiple parameters increases the probability that this model has explanatory power, compared to other models, as to how actual social relationships are formed, and as to their dynamics.

##### _____ One-to-one retrodictive mapping of feedback model parameters to q parameter

To reiterate details of the social-circles or generative feedback model, the topology of outcome networks depends on parameters α,β,γ as exponents governing probabilities (proportionality effects) *following path dependent behavior in a growing network*. The surprising result is that the parameters of Tsallis entropy (shape parameter q, scale parameter κ and density parameter δ) that fit the degree distributions of the networks with α,β,γ generating parameters
have continuously 1-to-1 mappings between their parameter sets.

Degree distributions are only one of many properties of the networks generated by the feedback network model that might exhibit 1-to-1 mappings between the parameters that describe these properties statistically and the parameters generating the networks. Nataša Kejžar (2007) has recently shown the model to be robust, properly modeled for outcome distributions of degree, and realistic for empirical networks. She examined:

- degree distributions for directed edges (indegree, outdegree)
- densification
- shortest paths distributions
- variation in path length distributions

Other properties that might be examined are:

- transitivity
- reciprocity
- triad census
- degree correlations (assortativity)
- searchability: whether hub search outperforms random search (Adamic et al.)
- component and k-component size distributions
- clustering coefficient distributions
- emergence of giant bicomponent
- node centrality distributions and graph centralities

- betweenness
- closeness
- flow
- eigenvalue (Bonacich)
- subgraph centrality

These are properties that can be studied with the Python feedback network simulation and Networkx analysis of the networks generated. The question is whether there are other QMLE retrodictions for some of these properties.

##### _____ Studies of additional properties of simulated feedback/Social circles networks

The way forward here is described in the Assignment/exercise materials for part 2 above, that is, using the Python simulation in a do loop that varies the three parameters, but perhaps stopping at 250, 500, or 1000 nodes. Once can then choose a network dimension like defining a searchability parameter and study how it varies with the generating parameters *alpha, beta, gamma* and whether this adds to retrofitting combined with the degree distribution parameters. (We have an excel file download [16] with those values together with the generating parameters. The retrofitting procedures are linear and nonlinear regression).

##### _____ Reconstruction of Networks

System reconstruction has become a major theme of complex systems analysis. The network feedback model provides one means of doing reconstruction by estimating generating parameters for large classes of empirically studied social networks. These estimated generating parameters plus the network sizes can be used in the feedback or "social circles" simulation and compared to each individual empirical network. It will be useful in such comparisons to observe what are the remaining discrepancies between the observed and the theoretically generated networks. The network software of Carter Butts may be especially useful in this regard. (further development needed here).

## (3) Realistic dynamical modeling ppt3pdf [17]

The next two decades are critical for determining the survivability of city systems. This is not a simple problem of resources or potentially reversible environmental degradation. Cities now hold the majority of the world’s population (Bettencourt et al. PNAS 2007). A large part of urban growth is due to displacement of impoverished rural populations and to the displacement of refugees from war-torn region. Rural impoverishment and displacement to crowded urban areas are often compensated by having children as a safety net for mutual aid and needs for labor.

At any one point in time there is little correlation between population density and levels of violence, but when tracked over time (Turchin & Korotayev, as above), as populations with limited resources grow beyond capacity (Bettencourt et al. 2007), regional sociopolitical violence is an observed outcome, with slow but quickening historical cycling within large politically enclosed regions. In a world cross-cultural sample, correlations appear between increased internal conflict within polities and averaged by levels of consolidation of political hierarchy or subsistence/production mode (Turchin & Korotayev). Our analysis, using the same sample of 186 societies ethnographically described at different points in time, shows significantly higher average levels of internal warfare for the 20th century (drw 07) than previous centuries. Some observers have noted that governments in the 20th century were the biggest killers of their own populations. The massive growth of urban populations and proportion urbanization occurred in the last 19th and 20th centuries. After 1962 world population growth slowed but not percent urbanization, which is slowly climbing an S-curve as it leaves a largely impoverished minority in rural areas. Mega-cities will undoubtedly continue to grow. With global warming on an unprecedented scale, questions of sustainability of city systems take on new urgency. This poses problems not only of individual city management (Bett. et al. 2007), but of regional systems interaction and the effects of wars on city-system viabilities and of system failures of the world economy.

##### _____ Empirical Scaling Baselines for City Growth

We begin the study of regional city systems with results from the study of urban growth. The growth of cities is constrained by availability of resources and rates of their consumption. The general growth equation (Bettencourt, Lobo, Helbing, Kühnert, & West 2006 [18] assumes a quantity *R* of resources used per individual, on average, per unit time, while a resource quantity *E* is required to add one person to the population. An allocation of resources is expressed as , that is, sustenance and replacement, where is the growth rate. Then

The solution to this equation is given by

When , population growth ceases at large times as a finite carrying capacity is reached, which is characteristic of biological species. In this case, “cities and, more generally, social organizations that are driven by economies of scale are destined to eventually stop growing”

Exercise: Create a distribution with (2) and grow it by (1), with . Use Excel to fit to a power-law (Pareto), the R programs to fit to a *q*-exponential (Pareto II). Does the growth curve follow a power law, as claimed? (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=961842) You can also fit the power-law (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=961842) and q-exponential growth formulas. (See q-exponential,
q-analog).

- (The exercise here is to generate a superlinear city-size distribution, then grow the distribution by the solution to its derivative, and compare those size distributions before and after growth to the
*q*-exponential.)

- (The exercise here is to generate a superlinear city-size distribution, then grow the distribution by the solution to its derivative, and compare those size distributions before and after growth to the

Ref B. 2007 *Growth, innovation, scaling, and the pace of life in cities*. Luís M. A. Bettencourt, José Lobo, Dirk Helbing, Christian Kühnert, and Geoffrey B. West **PNAS 104**(17):7301-7306. http://www.pnas.org/cgi/content/abstract/104/17/7301 http://www.pnas.org/cgi/reprint/104/17/7301 supplementary: http://www.pnas.org/cgi/content/full/0610172104/DC1

##### _____ A Link to Social Networks

Bettencourt et al. (2007, Appendix) model the potential links between variations in for**productive activities in cities and human cognitive capacities**. They note, however, "The exponents are commensurate for many social quantities, but there is no strong indication that they must be identical for different urban systems." For productive activities, however, tend to vary between , in general accord with their model of limits on the acceleration of human cognitive capacities to deal with complex task activities {Milgram's information saturation).

Higher for productive activities also imply a faster pace of life for cities, as shown in the insert. This contrasts with living species, which have slower pace of life the larger the organism, a log-log scaling law which implies energetic conservation. Cities in this sense are non-conservative and inefficient: they burn more energy superlinearly with city size and spatial scale.

##### _____ Alternative hypotheses about City Size and City System Fluctuations

Individual city populations vary over time and have different values of for city growth. Is this variation related to broader patterns of historical dynamics, such as that we have reviewed for Goldstone's structural demography and Turchin's historical dynamics? Possible answers to these questions can be studied using data from Tertius Chandler (1987). Chandler's data may be downloaded in the form of an excel file of largest cities in comparable historical periods, and either city sizes and rank or estimated size rank alone.

Individual cities are often treated (e.g. by Denise Pumain and colleagues) as following a stagewise development from early growth due to innovative industries to mature growth to deadline due to industrial obsolescence. Modelski and Thompson (1996) develop a comprehensive alternative to the single-city perspective, showing that it is economic regions of innovation, maturation and decline that evolve through competition with other regions, following a temporal logic of Kondratiev cycles based on construction and decay of industrial infrastructures. They also show how polities benefit from successful competitions and tend to emerge competitively into positions of political hegemony on a slower temporal scale, often with a first Kondratieff cycle marking their competitive emergence, followed by external wars to establish hegemony, and than a second Kondratieff cycle as the hegemonic polity reinvests in a more global economic/industrial expansion.

##### _____ Scaling Changes in Historical City Sizes

To answer these questions about city size fluctuations, collaborative work involving myself, Tambayong, Kejžar, and others, undertook an evaluation of historical changes in regional size distributions, using a sample of regional city size data from Chandler (1987), which can be downloaded and analyzed. My hypothesis was that these distributions: (1) will go through oscillations related to various aspects of historical dynamics studied by Turchin, Modelski and Thompson (1996), and others, (2) will follow a distributional form that reflects the underlying network processes that are associated with urban industrial innovation and decline, but that (3) city system declines are often related to conflicts with major political competitors.

Michael Batty's (2006, *Nature*) *rank clocks* study of Chandler's data, classified by time periods that reflect alternations in economic dominance of different historical regions, supports our view that city systems are highly dynamic. His methods of analysis and results eliminated Pumain's hypothesis that these fluctuations are simply those of individual city dynamics, but did not provide answers as to whether rise and fall of city systems is more affected by regional urban system competition, major wars, political alliances, or other factors.

##### _____ Background to Scaling of Historical Eurasian City System Dynamics

The theoretical context of our study of city system dynamics is linked to two observations, one for agrarian political regimes (as studied by Turchin and Goldstone, for example), and the other for modern industrial and post-industrial regimes. In the first case, it has been know since Malthus that if population grows at a constant rate of change (exponential growth) while food productivity grows at a linear rate, population will outstrip food supply to create a crisis of overpopulation.

- "The power of population is so superior to the power of the earth to produce subsistence for man, that premature death must in some shape or other visit the human race. The vices of mankind are active and able ministers of depopulation. They are the precursors in the great army of destruction, and often finish the dreadful work themselves. But should they fail in this war of extermination, sickly seasons, epidemics, pestilence, and plague advance in terrific array, and sweep off their thousands and tens of thousands. Should success be still incomplete, gigantic inevitable famine stalks in the rear, and with one mighty blow levels the population with the food of the world." Malthus Essay on the Principle of Population 1798

The elements of this dynamic are shown in the power point, which has figure from some of the following data sources.

Three major comments are in order.

- One is that power-law population growth in the "modern" period, with its rate-change exponent of 1, has never been fully understood, nor has the observation that power-law growth has occurred in earlier historical periods, ones in which the crisis of growth resulted in periods of collapse of growth.
- A second is that while population growth followed a power-law trend (coefficient 1) in the modern era, world GDP (GWP) has grown by a power-law trend with coefficient 2 (Kremer 1993). In a temporal perspective from the historical period of Malthus, Adam Smith, or Darwin, a power-law trend with coefficient 2 for resource productivity would appear to be linear in comparison with a population growth trend with a power-law coefficient of 1. The "modern" distortion introduced by this power-law disparity between resource and population growth is the "optimistic" view that technology and resource productivity will "always" increase faster than population. What this modern deception ignores is that both these power-law trends have a expiration date that is built-in by the singularity of power-law growth of any sort. We are quite close to the singularity or expiration dates of both trends (2026 CE as dated by von Foerster, although population growth toward singularity already started to level after 1962; GDP singularity according to Kremer's figures occurs earlier).
- Third, higher population and GDP (GWP) produce greater entropic costs of burning or utilizing resources which has environmental effects. With power-law growth these destructive effects grow super-exponentially. This produces the massive effects that we are discovering and experiencing today as global warming, species destruction, and ecological niche destruction on world scales.

Refs.

- von Foerster, H., P. M. Mora, and L. W. Amiot. 1960. "Doomsday: Friday, 13 November, A.D, 2026," Science 132:1291-1295. http://www.sciencemag.org/content/vol132/issue3436/index.dtl#articles (Written tongue-in-cheek, commentaries [19])[20])
- Kremer, M. 1993. Population Growth and Technological Change: One Million B.C. to 1990. The Quarterly Journal of Economics 108: 681–716. http://ideas.repec.org/a/tpr/qjecon/v108y1993i3p681-716.html
- Reviewed by White 2002 http://eclectic.ss.uci.edu/~drwhite/pub/FoersterShort1.pdf
- Further pdf references White Malkov Korotayev 2005 http://eclectic.ss.uci.edu/~drwhite/pub/WorldPopulations.pdf

##### _____ Causes of Failed States, and their Consequences for Global destabilization

One of the most pernicious effects on global destabilization, global warming, and world-scale ecological destruction on the contemporary era is failed states.

Failed states are caused by

- major increase in the widening occurrence of internal wars
- major increase in the intensity and destructiveness of internal wars
- major increase in the widening occurrence of external wars
- major increase in the intensity and destructiveness of internal wars
- consequent impoverization in failed states and the regions of failed states
- including refugee populations from failed states
- homeless and homeless children, adolescents
- recruitment of adolescents or preadolescents into private and child armies
- the viscious cycle of these effects

Examination of the following maps may help to describe the problem and the regional effects of each variable on others.

Failed states index 2007 Demographic transition? Birth rates / Death rates 1999 - Which is closer to Failed states? - Projected growth rates (net) Fertility 1999 - Which is closer to Failed states? - more fertility

Birth rates 2000 Demographics 2000

##### _____ Historical Scaling of Changes in Eurasian Regional City Size Distributions

The final segment of this part will be a sketch of findings of White, Tambayong and Kejžar, covered in the powerpoint.

## Conclusions

All three parts of these lectures are relevant to feedback processes and modeling the "Dynamics of human behavior". Part 1 deals with positive feedback loops, which Gregory Bateson called "schismogenesis", in the case of comparative studies of human evolution, and Edmund Leach called a "runaway world." Part 2 deals with the formation of network linkages into feedback cycles, whether the feedback is negative or positive, but where the generative network structures themselves tend toward equilibrium. Part 3 deals with negative feedback loops whose time delays do not tend toward equilibrium but are discovered in the case of the variables examined in part 1 but not in a longitudinal and historical context, to produce major fluctuations that are disruptive both to social and economic networks at different scales, and ultimately, to the global ecologies in which or urban and production economies operate.

##### _____ Conclusions: Part 1

Synchronic correlations in observational rather than experimental data are notoriously prone to radical problems of statistical misestimation. One such problem is the nonindependence of cases, which means that variance is likely to be highly underestimated, producing spurious correlations (overrated by significance tests) that will fail in replications (type I errors). Further, attempts to replicate valid statistical results from different samples will fail (type II errors). Another factor is that of time-lags in causality that may nullify synchronic correlations, leading to misattribution about the absence of relationships. In social and cultural data, the indicators of these problems, which are also indicators of complexity, are everywhere once you know to scan for them, and almost everywhere overlooked and ignored in social science research. The other ubiquitous indicator of complexity is not only nonlinearity, but higher-order interactions than the common assumption of bivariate interaction, as assumed in scaling models, and of the absence of higher order interactions.

One of the observations here was that once we move away from looking for synchrony only at an everyday time-scale is that larger processes operate at such large time scales that they are invisible through correlation studies. The correlation between (rising) population density and (rising) levels and intensities of internal warfare and endemic conflict is zero in a sample of human cultures. As citizen observers of human history and our own, the mutually upward trend of these two variables is not evident because there are dynamical oscillations in population relative to resources and in the outbreaks of internal wars at different times and places so that we simply do not perceive the global trend and our politicians and journals fail to believe the connection, just as they fail in the U.S. to believe in global warming. The same invisibility occurs, of course, at smaller time and spatial scales, but there we are used to looking at these scales with specialized instruments. We need comparable quality of instruments to look at the various time scales in which humans are embedded, and to scan for dynamics.

An aggregation approach using the conceptual framework of sufficient statistics begins to show macro-correlations, for example, between aggregated societal-scale and the average intensity of internal wars at those scales. Temporal reconstructions and of long-term trends show how large are the long-term trends that may mask the dynamics operating at the level of populations.

All the methods used in part 1 -- including tests and controls for autocorrelation, the autocorrelation simulation, the stardex findings about core variables in the cross-cultural database and how they connect to peripheral variables, nonlinear modeling such as entailment analysis and Galois dual-intersection lattices that show higher order n-way interactions among variables -- all give evidence of nonlinearities that point to complex interactions that are not captured by the conventional strict-bivariate interaction assumptions of scaling methods. Nearly all survey data, in fact, manifest nonlinearities such as autocorrelation, and require consideration of complex interactions.

All these results, as examined in part 1, point to the need for empirical longitudinal measurement and testing of dynamical models for human behavior, going beyond simulations to test hypotheses and models with actual historical or longitudinal data.

Fortunately for cross-cultural studies, dynamicist Peter Turchin's collaboration with comparative researcher Andrey Korotayev provided a key example of the kind of dynamics at the societal or population level that wash out synchronic correlations of variables across cases that are not delineated according to the levels of aggregation at which dynamically related variables may affect one another over time, cumulatively. Returning to this problem in Part 3, we will see that the trends produced by these particular dynamics, and the dynamical pressures produced by these trends, are interlocked in a larger configuration of sociopolitical processes.

##### _____ Conclusions: Part 2 (parameterized simulation and measurement of feedback networks)

Networks are not only discrete structures that offer the opportunity to measure and calibrate the effects of structure on dynamical outcomes but can be simultaneously conceived and specified in terms of the tangible links or vehicles for the traversal of influence or causal effects. The close links between traversal-properties and structural-properties in graphs have offered some of deepest theorems about such things as structurally cohesive nested and overlapping entities created by structure-traversal synergies and their internal and external causal effects.

The statistical study of networks has advanced to the level of modeling structure within the explosive combinatorial space of all possible graphs (exponential random graphs or ergs), which gives the possibility of grounding some of our maximal likelihood estimates for complex structures. For distributions of network characteristics, like degree, for instance, solid MLE statistics have been worked out for many useful and realistic models, some among many possibilities.

The popular models of complex networks are, in general, however, somewhat pathetic. The scale-free model, the dream of the universalizing physicist, has too few parameters and too many possibilities as to how power-law distributions can be generated. The small-world model captures some robust properties of networks, but in stopping at three parameters (average path length approaching that of a random Erdös-Rényi graph with the same number of nodes and edges, clustering, and lack of centralization), is woefully inadequate to characterize differences among real networks.

To evaluate simulations, unless they are as elementary as those of John Holland, one approach is to insert network probes into the simulation to observe changes in network structure and traversals, and to try to explain outcomes in the ways we might like, i.e., to explain interpersonal or live networks.

In that respect and in the modeling of social networks, a complex network with more verisimilitude is the social-circles or generative feedback network. Its parameters are few but they capture basic network processes, including the potential for *agency* among originators and the mediators in traversal events that leave structural effects. One of the beauties of this model is that the combinatory dimensions of its three produce outcome networks with parameters that map back 1-to-1 to the generating parameters.

These retrofitted mappings suggest the construction of a simulation platform of generating models that have not just local biases, e.g., toward transitivity, symmetry, coparental or sibling biases, local hierarchy, clustering, etcetera, but somewhat more global processes like the effects of longer path traversals, long distance correlations, correlated diffusion, and the like. The social circles model is one the few to focus on cycle formation. Understanding cycle formation, structural cohesion emergent from cycles, and feedback in cycles, is theoretically central to the understanding of dynamics. The first retrofitting relations to be mapped were those between degree distribution parameters and generating parameters. Next to be mapped and retrofitted were the parameters of directed degree distributions, their relations to densification, and path length distributions. As more such parameters are mapped and retrofitted we will undoubtedly see that generating parameters map to a great many outcome parameters, all of which form a systemic and comprehensive relational pattern and dynamical model of network topology. To a core or baseline model such as this, additional local-structure generating parameters can be added and their effects observed.

One of the conceptual features of a core parameter-modeling and retrofitting strategy (and extensible research program) such as this is that the properties of the outcome distributions map onto a generalized mathematical formulation of complex dynamics, *q*-entropy, that generalizes the Boltzmann-Gibbs statistics of minimum energy interactions into the gradient processes that we see in thermodynamics. These general families of models are not highly constrained by specific limiting external conditions (which can always be specified as additional constraints) but have self-organizing characteristics. That is, energy and materials diffuse through these kinds of processes, but maintain heterogeneity and differential structures and traversals. These properties might relate to those of geography and differential resources, economics, and social practices in actual exchange and organization. Core parameters in these models can also be seen to be in endogenous dynamical (time-lagged) interaction with other variables simply because they trace out a limited possible trajectory of oscillations between polar states or nonlinear but recurrent kinds of transformation. This is particularly so for the central shape or *q*-parameters of some of the system that are modeled by networks. These same core parameters, however, may also be subject to external shocks that would reset the starting points for oscillations, speed them up or slow them down, or if delivered as larger synchronous shocks, to coordinate oscillations in different regions. Thus, there is a foretaste or even forecast in the generative feedback network modeling for this kinds of analysis of dynamical systems that we see in the next part of these lectures.

##### __________ QML estimation of retrodictive feedback model outcome parameters

Can we describe through appropriate MLE statistics a clear inferential route to explanatory modeling with the social circles model? Halbert White (1982, 1994) states some conditions for a quasi-maximum likelihood estimator or QMLE to describe the problem posed. The equation that fits the degree distributions passes most of the tests that qualify for a quasi-maximum likelihood estimator, must converges under conditions given by White (1982,1994) to the solution to the problem max[κ,δ,q] = ℓ(δ,κ,q;α,β,γ) ≡ ∫ ln p(κ; δ,κ,q)( κ;α,β,γ) dη(κ), where η is the counting measure on the integers.

When, as is typically the case, the above maximization problem satisfies the hypotheses of the theorem of the maximum (e.g., Berge, 1963), the 1-to-1 mapping condition is satisfied. Halbert White and Chalak (2006, Theorem 4.2) give conditions for application of the theorem of the maximum in a related context.

If quasi-maximum likelihood estimators (QMLE) can be found for parameters of degree (so far, we have just approximations) and other distributions that describe the family of feedback networks, then empirical studies of network phenomena occurring in realistic settings, repeated network surveys, and longitudinal or historical contexts, may show which kinds of phenomena correspond to a social-circles network process, and what the network parameters reflect or are affected by in terms of causality.

If this kind of work pans out, i.e., proves itself, we can envision a simulation platform in which additional generative modules might be adding with extra parameters (e.g., a reciprocity bias), and matching of parameters of outcome network distributions can be systematically compared and retrofitted to generating parameters to the model. The advantage here over fitting statistical models which combine strictly local biases is that the effects of biases that compound over network traversal processes can be investigated. These kinds of investigations could also be compared to monitoring network interaction probes into other simulations for which no analytic representations are known.

##### _____ Conclusions: Part 3

Part 1 showed how dynamics may be masked and made invisible to the ordinary human observer because of time-lagged effects. Visualizing and testing time-lagged effects involves constructing variables on appropriate time scales, and with a sufficient run of independent observations. The example was the "secular cycle" so-named because of the centuries-long (Latin saeculum=generation, age, century) structural demographic interaction between population growth/decline and growth/decline patterns of internal sociopolitical violence in the context of agrarian states and empires.

What I noted in part 1 is that states and empires arise with markets and exchange economies that produce an unusual kind of population growth in the first phase of the secular cycle: growth not at a constant rate but proportional to size, i.e., power-law rather than steady or logistic growth. Growth of this sort necessarily outruns its resource base and precipitates its later period of instability and relative decline.

Because what enables power-law growth is uniquely human – technology, the use of tools to enhance productivity – and because technology as a cultural artifact can be preserved through periods of conflict and destruction, the secular cycles of exchange economies create a lasting long-term trend of growth in aggregate population. Whatever the level of aggregation, however, these trends are necessarily interrupted because power-law growth by definition cannot continue indefinitely. Hence the aggregate growth curve is one of power-law growth alternating with flattening of growth, or “periods of crisis,” although crises do not occur uniformly across the populations aggregated. To capture the dynamics of these systems, Turchin and others have used “sufficient statistics” of total population numbers defined for large regional populations within the political systems that contain them. It is only when the boundary conditions for structural demography are well specified and defined for a period of relatively low “outside” perturbation (see Kohler et al. 2006) that we can properly focus on the dynamics. These bounded units might be found to exhibit self-bounding “structural cohesion” consistent with the multiple-levels and emergent aggregates approach to network phenomena.

Parallel to the consideration in Part 1 of sociopolitical units that “fall apart” to some degree in periods of internal crisis (and are then also vulnerable to outside attack), we also considered in Part 1 the tendencies of successful polities to expand their sphere of control over exchange relations, revenues, and population numbers by expansion of territory (common in state and imperial systems but rare in prestate societies) either through colonies or conquest. When the vehicle of expansion is that of military attack, however, Turchin’s work has shown that the peoples who are attacked, if they are sufficiently different in language, ethnicity, religion or other cultural markers, begin to rally their own forms of resistance through increase in the size of structurally cohesive subnetworks. As these scalable but decentralized forms social organization increase numerically and in resistive organization and capacity, they may eventually overrun the attacker. Turchin shows that these struggles over dominance and resistance are important generators of new “ethnicities,” initially resistive groups that emerge to have broad named cultural entities and a lasting historical memory of their identity.

The general perspective employed in these studies of networks and complexity is that of multi-level emergent units in networks where structural cohesion is one of the key components providing the vehicle through which new groups and new types of entities emerge. The complex network generative model studied in Part 2, and its focus on the generation of cycles (which produce structural cohesion), comes out of this motivation, or, better said, theory.

The focus of part 3, then, was to bring the historical dynamics methodology forward to study the dynamics of city systems. The initial research question was whether, if we take city systems as a focus of study, regional city systems exhibit the same kinds of characteristics of oscillating periods of growth and decline in population relative to overall trends of aggregate population and resource growth.

From an embedded-levels network approach, the first observation to underscore is that cities and regional city systems are embedded in one or more regional territorial polities, i.e., in units at which, at least for agrarian polities, we observe the dynamics of secular cycles. Cities, then, are subjected to the events within these secular cycles. But a second question is: What happens once technology changes the form of political aggregation from that of an agrarian polity to an industrial polity?

To implement this research, we took Chandler’s (1987) data on the largest 75 or more cities in each 50 year period in which data on city size, or historical-archaeological estimates that can be considered reliable, are available. Our research team (including Tambayong and Kejžar, but assisted methodologically by many others) took the period from 900 CE to the present as the period of study and sorted the data for Eurasian cities into three or more subgroups – China, Europe, and Mid-Asia (everything between China and Europe, with some further subdivisions for purposes of comparison). For each time period and each region, then, the data consisted of a ranking of largest cities within that region by size. Where there were sufficient numbers of cities whose population was estimated, and some cities were ranked but not estimated, we developed careful extrapolation procedures to estimate the actual size distributions. These distributions were then subject to scaling. Even for the largest cities (varying by region and time period in the proportions of the largest 75 world cities), however, it was evident that these distributions did not uniformly follow either a Zipfian rank-size distribution or Pareto distributions with varying slopes.

What these distributions did follow, uniformly, was the same distribution observed in part 2 for the degree distributions of the networks generated in the social-circles feedback network model: cumulative distributions in the *q*-exponential family. For any given region, what these showed for any given region, over time, were statistical runs of proximally-bunched values of *q*, the shape parameter analogous to that of the Pareto II distribution. Values of *q*, then, took the form of historical periods of normal *q*, followed by punctuated declines, and then rises again to normal *q*, sometimes excessively large *q*, and so forth.

These time series were not only historically interpretable within regions as times of rise and fall in the fortunes of the regional city system, e.g., for China and Europe, but with China as the early innovator in these time periods, the variations of *q* in China were significant time-lagged predictors of the variations of *q* in Europe. It is known historically that China contributed the inventions of productive technology, monetary instruments of credit (like paper money), and elements of military weaponry that were slowly adopted by Europe over such means of network transmission as the Silk Routes. It is significant, then, that variations in *q* for Europe are predicted by expansion or contraction of variations in the Silk Routes trade.

Given these results, and the efforts we made to develop reliable and accurate estimation procedures – with crucial help from Cosma Shalizi who provided MLE procedures – we were fairly confident that the historical variations we observed in *q*, at least for Europe and China, were valid measures of the relative fortunes of city systems in the two regions. Mid-Asia is more problematic given that core city-system regions change over time.

Now, we could evaluate hypotheses about possible causal interactions between variations in *q* and the secular cycles variables of regional population pressure (population on resources) and levels of internal sociopolitical violence.

First we had to clarify through proper measurement, the observation that for each of our regions the behavior of the extreme tails of our city-size distributions – the slope of the power-law curve for the top 10 largest cities – tended to vary with considerable independence from the behaviors (slopes) consistent with *q* as estimated from the overall distribution. Hence, we took careful measurements of the Pareto slope *p* ( in our cities paper) for the 10 largest cities in each period, and began to consider how the “tails” and “bodies” of our distributions interacted over time, either in terms of correlations or time-lagged regressions.

What we found in addition to generational time-lagged effects of *p* on *q* and *q* on *p* was that “shock level” sociopolitical violence, indexed by *I*, had an effect on their relationship, where C_{p} and C_{q} are constants:

*p*_{ t+1} ≈ -*q*_{ t} + *q*_{ t}*p*_{ t} + C_{p}

(overall R^{2} ~ .78, China ~0.74, Europe ~0.67) (3)

*q*_{ t+1} ≈ -*p*_{ t} + *q*_{ t}*p*_{ t} + C_{q} - *I*_{t}

(overall R^{2} ~ .50, China ~0.43, Europe ~0.62) (4)

Without the effect of *I*, these two equations would predict positive feedback between *p* and *q* that would result in either a convergent or a divergent time series. The effect of *I* is to reset the values in this series through a city-system collapse. These collapses conform to Michael Batty’s (2006, *Nature*) findings, although he did not provide an explanation.

##### _____ Auxiliary powerpoint, beyond the conclusions: Multilevel Networks and Historical Dynamics

##### _____ Period-Doubling and the Road to Chaos

The relation between period doubling in historical dynamics (such as the series of temporal scalings for oscillatory phenomena at the level of business cycles, generations opposing or double generations, ..., Kondratieff cycles, political hegemony cycles, regional and city size cycles, historical epochal cycles) and period doubling in the q-exponential "road to chaos" has not yet been explored as a topic in dynamics. There is evidence (White 2006) for both attractors and repulsion in the period doubling of historical dynamics: ego, children repeat the careers of parents; children oppose the wars of parents, thus repeating the warfare behavior of grandparents, and so forth.

http://www.math.montana.edu/frankw/ccp/calculus/discdynm/perddble/learn.htm

http://www.math.montana.edu/frankw/ccp/calculus/discdynm/perddble/answer.htm

http://prola.aps.org/abstract/PRA/v40/i9/p5305_1 Scaling and multifractality in one-dimensional asymmetric maps - 1989 Sousa Vieira and Tsallis

http://astro.uchicago.edu/~voort/mla315glossary.htm

Google: doubling period "road to chaos"

Cosma Shalizi: see Tsallis 2005 long Letter to the Editor, second half of p. 1 first half of page 2.

##### _____ Beyond the scientific conclusions

Science is a practice and an ideal: unfettered by politics and objective by means of a community of criticism.

The practices of technology are necessarily more embedded within culture. They are shaped in part by what we know from science and what can be done, but what should be done and what is done in the name of technology is of a deeply political and instrumental nature.

Science has come under the knife of political criticism from the right in the "White House declaration" that science must be censored to fit the needs of policy, which has not been reviewed by the U.S. legislature or judiciary. It has also been criticized from the left in the attack on "Science as culture," an attack that often turns to antiscience. The antiscience movement is also enjoined by various creeds of fundamentalism and the denial of evolution.

The distinction between science as a practice and ideal is also compromised by the fact that certain of our social sciences -- especially economics and political science - are defined at their core as policy science. Physics and chemistry, in their classical formulations, do not define themselves as policy sciences. This is changing as physicists enter the domain of the social. Barabási's popular book, *Linked* (2002), crosses this Rubicon to declare a universalizing science of networks in which competition is the sole dynamic and the scale-free network is the measure of success, harking back to the social Darwinism of the 19th century. The *Tipping Point* by New Yorker journalist Malcolm Gladwin (2000), now the nonfiction work longest on the best-seller list, places *policy implications* of complexity science in this same light. Morton Grodzins coined the term "tipping point" in its sociological sense in his books on white flight such as *The metropolitan area as a racial problem* (1958). In popular culture Gladwin's book is much used as a recipe for self-styled mavens and salespeople in marketing and business, and in political “clean-up” operations where Gladwin gives Giuliani credit for reducing crime in NYC (other studies give a demographic explanation in the number of kids born to single welfare mothers, for example, thinning the cohort of teenagers in NYC during Giuliani’s term of office).

"Tipping points" thus represent a popularized simplification of elements of the complexity sciences, used to suggest that policy levers can be used to turn seemingly impossible situations around by sheer force of political will, a bankrupt idea from the start.

The analysis of multiple levels of complex dynamics presented here, in contrast, illustrates the need for serious scientific exploration of historical dynamics and diagnosis of trends -- global warming, overpopulation, politically motivated violence, emiseration -- that require whole new ways of thinking about technology. Some diagnosticians (Jared Diamond? -- attribution not certain) have said that unless humans are part of nature, they are a dead species in the longer run. Others, such as Michael Braungart (my Stability domains group page), have spearheaded revolutions in manufacturing practices, now beginning to diffuse widely, in which products are made whose components are reusable.

## Highly provisional graphic

Some of the variables in city-system dynamics.

## Schedule of these lectures

http://www.timeanddate.com/calendar/?country=1&year=2007

Mon July 30. 1.5 hours. 9:00 Part 1. (Run the drw pdf, do the exercises, run the analyses)

Tue July 31. 2 hours. Part 1, review exercises 1, Part 2. (Run the NK pdf, run the drw pdf, run the simulation and analyses)

Wed Aug 1. 2 hours. review exercises 2, Part 2

Thu Aug 2. 1.5 hours. 9:00 Part 3, also review exercises 3

Fri Aug 3. 1.5 hours. 9:00 Part 3, continued (Run the drw pdf), including a city system dynamics model briefly presented by Tambayong (Run the pdf if there is one); final review of exercises