Complexity in human behavior

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Social Networks Course: social networks & complexity

Complexity in human behavior

New references: Language Networks

Historical Memory as a basic property of Complex Systems

One of the fundamental aspects of complex systems is that they have biographical or historical memory: their behavior is not independent of their history. We need to understand this before we begin to study other aspects of complexity. Lacking this property, systems are mere mechanisms. Descartes made the mistaken argument that animals as opposed to humans are machines, and simply operate on fixed rules or fixed (Markovian) state-to-state probabilities without behavioral learning or adapting through experience, i.e., in more modern terms, programmed from birth by inherited genes or with programs modified only by genetic mutations and natural selection. Descartes was wrong: all forms of life are complex. Some nonliving systems are also complex because their structures, laid down historically (or by computer simulation), both influence and are modified by their history. Complex systems do not belong to the world of Newtonian physics on which early scientific positivism was applied to the social sciences.

Comparative research in anthropology is often criticized because the cases chosen for comparison are not independent, and therefore statistical tests under the assumption of independence. as they were employed by the Newtonian positivists, do not apply. Anthropological critics such as Eric Wolf, in his book Anthropology (1964), were correct in that anthropology must be also an historical science, a composite of science and humanities.

Statistics and the Problem of Nonindependence

There are two kinds of statistics: those that take complexity, and thus historical memory, into account; and those that do not. The latter rely on the assumption of statistical independence to apply the logico-deductive laws of probability directly to observed data without taking nonindependence into account. Nonindependence includes common origin, stimulus diffusion (A's past affecting B's future through the transfer of ideas, for example), and contemporaneous (A-B-C) interaction.

An example of the first kind of statistics is that of reconstructing evolutionary trees from data about living or social entities that have evolved from common origins. This is a problem that has been solved by complexity scientists using the total complex of nonindependent data, to find a maximal likelihood estimate of the best-fitting evolutionary tree (with splitting of branches ordered in time) that would account for observed similarities. As the authors of this new procedure state "CoRind" (acronym, roughly, for controlling to obtain CoRrelational independence) "is a program that corrects for phylogenetic correlations in pairs of columns of a multiple alignment, allowing statistical tests of covariation to be performed.... [while] the software itself has no tuned parameters whatsoever." If we know by this means how a collection of observed cases derive similarities from common origin, we have both an explanation and a model for these similarities, provided always that the model we used is based on observed processes that have independently testable effects. Further, by controlling for these common evolutionary similarities, we can use the remaining independent variance to test other hypotheses. These latter are known as autocorrelation tests that provide a valid correction for statistical nonindependence in order to test other hypotheses, as for example, learning from experience, adapting to environment, independent invention, and other sources of creativity. Thus, we combine history with science with humanities.

This approach is being applied to the evolution of interacting human proteins, but will be applied to interacting language groups, cultures, data on mitochondrial DNA and Y chromosome evolutionary trees, and can be applied to all these human databases taken together. One finding to date is that evolutionary divergence of human characteristics tend to pattern into groups that split quickly in periods when diversity is generated and groups that preserve a long line without splitting, taken to be evidence of evolutionary bottlenecks where side branches went extinct. This could entail that there were many languages, cultures and genetic populations in the past than those that left descendants, and that many of these died out historically. Comparing living cultures at a time when they were observed, compared to archaeological or paleontological traces of human groups that died out, poses a profound sort of nonindependence that suggests that hypotheses about causal or historical effects and relationships in human, as in other groups and species should be prefaced with "among surviving groups or species..." there appears to be an effect of A and B, controlling for common evolution, or, one could say in some cases, "the strongest effect on X" (say sexual dimorphism among primates) "appears to be phylogeny, i.e., a long, slow, evolutionary transmission of this characteristic, with very slow divergence." Such was one of the findings of my former student, Malcolm Dow, in his coauthored study of primate dimorphism. This case was not one of rapid adaptation, say, to climate, such as we find with mutations in mitochondrial DNA that may show rapid spread in surviving populations during folowing periods of environmental change.

In Wolf's insistence that anthropology is both science and humanities, part of the science needs to involve interdisciplinary collaboration among social and cultural anthropologists, archaeologists, geneticists and molecular anthropologists, linguists, biologists, and others.

Scalability and Self-Similarity

James H. Brown, Vijay K. Gupta, Bai-Lian Li, Bruce T. Milne, Carla Restrepo and Geoffrey B. West’s <The fractal nature of nature: power laws, ecological complexity and biodiversity (2002) is one of the most important articles you can read to understand the scalability of a common life-design for the species that have evolved on our planetary. Basically, the networks that support life internal to organisms and ecosystems are fractal in nature, like the mammalian arteries that divided into smaller but more numerous branches to distribute blood while rougly conserving cross-sectional area (which, with greater frictional resistance, also slow in rate of flow as they reach their target areas for distributing nutrients). Carrying these ratios (scalar constants) up to larger organs and organisms with greater mass and volume (with lessened surface area per unit mass) we find that the slowing of metabolism B with mass M slows or scales down at a ¾ power-law (B ~ M-¾), a design that is conservationally efficient and that generates an equal playing field for species diverse in body sizes and a host of other characteristics. In short, life is scalable from small to large, with limits at both extreme. Scalable regularities also apply to the packing of diversity, distances, and interdependencies in ecological systems.

(To keep track of terminology in these fields, "power law" and "large tails" refer to distributions such as those for animals ranked by size, with numbers decreasing with size: plotted in x=log-size y=log-numbers a scalable or scale-free graph is linear. Brown and Geoff West and others show the power-law graphs for x=log body mayy and y=log metabolism and a host of similar with linked parameters in biology and ecology).

Hamilton, Marcus J., Milne, Walker, Burger, and Brown.. <The complex structure of hunter–gatherer social networks. Proceedings of the (UK).Royal Society B (2007) shows how these considerations apply, similar to those of ecological systems, to human societies in their prototypical form, that of hunter–gatherers.

This structure is often preserved in the more decentralized forms of human social interactions, such as the self-similar distribution of email network community sizes, studied in Self-similar community structure in a network of human interactions (2003) by R. Guimerá, L. Danon,. A. Dıáz-Guilera. F. Giralt,. 1. and A. Arenas.

Some of these themes are treated in the <Self-similarity algorithm> by Song et al.

The exceptional scalability of human societies

Fractal growth per se may involve branching that grow by multiples (exponential growth, e.g., even you savings account grows by a yearly multiple, say 1.03 for 3%). If population growth were fractal or a constant multiple (say 2% per year) population would grow exponentially. Thomas Malthus thought if population grows exponentially at a constant percent of increase, while food productivity grows at a linear rate, population will outstrip food supply to create a crisis of overpopulation. This Malthusian "observation" seems to works well for agrarian polities, as in Peter Turchin's (2004,2006) model of historical dynamics.

"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
Figure 1. World Population Crises from Power-law growth, Kremer 1993 data
But for post-agrarian or industrial economies, it has only been known since von Foerster, Mora and Amiot (1960) that world population over long periods tends to grow superexponentially, that is, according to power-law growth where the percentage of population increase accelerates proportionally to the size of the population. Population scales according to some power of the current population, e.g., Pt+1=Pt1.001 instead of exponentially at Pt+1=1.03 Pt. This happens in cities. It does not happen because of increasing fertility in cities but by attraction of migrants to cities, and what would be the emptying of rural areas if it were not that rural areas compensate by raising their total fertility, achieving population growth or stability in rural areas while feeding generations of new migrants into cities.

This is a very special problem of the "modern" era, with its spiking rise in world population up to 1962, rise in urbanization, and impoverization of rural areas. When superexponential growth take the power-law form of growth it rises toward an infinite population in a finite time. The finite time period is called the singularity of power-law growth. The year 1962 marked a (necessary) transition in world population from a power-law growth trend with a singularity in 2027 to a lower and apparently more stable or exponential rate of increase.

That is not the end of the story, however. The early stages of power-law growth curves are so gradual as to be almost indistinguishable form constant percentage (ordinary exponential) growth. When we go back to historical and archaic population growth, we find oscillations in which power-law growth does describe long historical periods, and in each of these periods (which themselves get shorter and shorter), the trend terminates with a population crisis, after which population levels or declines or destabilizes, and then resumes an initially slow power-law rise once again. This patterm, for both world and regional populations, tends to repeat over and over again, in increasingly short time intervals.

The consequences of hyper-Malthusian crises: Increase of internal war

Figure 2. Population crises, exceeding resource capacity, produce sociopolitical conflict and internecine warfare. This cannot be verified by correlations between these two variables because the time-lag between population increase relative to resources and the ensuing conflicts in competition over resources do not occur immediately but with a generation or more time lag. Scarcity of resources affects the owners of productive resources in one way -- as owners of scarce resources they are advantaged -- and workers, peasants, landless and proletarians in another because prices of scarce resources go up and their purchasing power goes down. For those without property, effective wages go down, and because there is a surplus of people there is a surplus of labor, pushing wages down even further. If government policies provide for redistribution of goods, minimum wages, or limits on pricing some of the effects on social conflicts can be abated. It may take a generation, however, for those who are in the majority that is disadvantaged by this situation to realize that their situation will or cannot be ameliorated by government policies, or for government to run out of resources for redistribution or to be unable to resist the social pressure exerted by the wealthy to benefit from the situation. After a generation, however, as shown by the research Peter Turchin (2004, 2005, 2006, 2007) and others on historical dynamics in agrarian polities, the likely and recurrent outcome of population crises is the outbreak of internecine warfare.

Although there is no cross-correlation between population density and warfare, when Turchin and Korotayev (2006) used the SCCS to correlate these two variables when averaged for the succession of types of productive and subsistence economies in our human evolutionary history, and rising levels of modernization, we see a disturbing trend (shown in Figure 2): the frequency of internal war increases with modernization increases in the economy.

The problems of showing these connections using cross-cultural comparisons increase with this kind of process-driven historical causality, of course, because in addition to the autocorrelation of the branching historical phylogeny and the spatial or network autocorrelation of borrowing, diffusion, trade, and intersociety warfare, we have a third autocorrelation: that of temporal autocorrelation (the present is roughly continuous from the past) and temporal lag (causal effects may operate with time delays).

The principle of "sufficiency" is that sometimes to see statistical effects we have ignore what seem to be the details and look at a higher level of aggregation, as in Figure 2: here, perhaps because the population trend is rising, because it is not just rising but rising superexpontially, and possibly because polities are getting larger, the frequency of internal wars is rising with degree of modernization. We know as well that the destructiveness of weaponry and the severity of warfare is rising.

Another way to test statistical effects is by "replication." I tried to test the hypothesis of internal warfare rising with modernization in the SCCS societies in Figure 2 by considering date of observation. A huge effect emerged: internal warfare was statistically (and significantly) more frequent in those societies observed in the 20th century than those observed before. There may be an article by Trevor Denton that could be searched in the library that has a similar finding when archaeological data are also considered as part of the comparison.

The dynamic oscillations of population growth and internal war

dynamics of population density and internal war

Networks and complexity

"Complex networks"


Back to Lectures: HSC and World Cultures

Back to Network Theory and Social Complexity

Carl Simon's pdf describing the Center for the Study of Complex Systems] (CSCS, University of Michigan) Complex System Approach

  1. Heterogeneous agents/ diversity
  2. Nonlinear dynamics
  3. Contact structure; networks; organization
  4. Feedback, adaptation, learning, evolution
  5. Stochastic with concern for “tails”
  6. Emergence