Soft correlations in layered niche-networks

Notes from papers for Complexity on
the roots of correlation-based complexity,
and a simplex model for community correlations;
also media dynamics and dividing your attention.
The notes here on scaling time connect to
our broader foray into multiscale thought,
as does this nanoscience intro to mean free path.

[abstract] [intro] [inventories] [rates] [discuss] [refs] [credits]


Multiscale correlations in biological communities are sometimes challenged by limits on free energy per capita, as well as by environmental change. The standing crop of such correlations might be assessed by an inventory of niche structures focused inward and outward from the physical boundaries of skin (self), gene-pool (family), and meme-pool (culture). Such measures, with roots in physical representation theory (see Lapilli et al., Phys Rev Lett 96, 2006, 140603 for something related), might be useful for monitoring the effect on communities of policy changes as well as of naturally-ocurring events. They also point the way to more explicit analysis of our relationship to those replicable codes which help and/or hinder our ability to maintain correlations, particularly in context of our shared pre-historic adaptation for supporting only five of the six niche layers mentioned above.


Why might we want to quantify "soft" correlations in complex systems, like that of a biological community [cf. Carel Van Schaik, Sci. Am. (April 2006)]? Perhaps the simplest reason is to provide a handle on the rise and fall of life's quality. Some of these correlations are already inventoried in piecemeal fashion, for example through population counts, census data, and employment statistics.

The information theory insight that subsystem correlations lie at the heart of thermal physics, as well as of generalized availability measures like net surprisal (Kullback-Leibler divergence) and mutual information [cf. P. Fraundorf, Am. J. Phys. 71 (2003) 1142-1151], makes possible an integrative approach to this problem that may come in handy as we explore the limits of our planet's ability to sustainably support human communities in the years ahead [cf. Brownlee and Ward, The Life and Death of Planet Earth (Owl Books, 2002)]. For example, what behaviors and physical limits constrain these measures? What changes in life's quality have emerged in societies on the verge of collapse [cf. J. Diamond, Collapse (Viking/Penguin, 2004)], and where and how have communities managed to reverse these changes in the past? Most importantly, how can we make the most of this information in charting the downstream course of our now-global community?

Monitoring standing crop

Perhaps the simplest thing to do is to count niches. Think of it as a census on steroids, designed (as much as possible) to work for complex systems of all sorts. Operational definitions, as well as objective implementation in practice, will require much discussion and perhaps locally subjective fine-tuning as well. In some cases, existing measures (like census and employment data) can be integrated into the layered niche analysis. Before we address these, the following subsection is to discuss the integrative physical context, application to underlying subsystems, and possible ennumeration of accessible states for putting these measures into second law terms.

An integrative physical context

To provide a robust multiscale setting, one might cartoonify hypothetical correlation measures in the following way across three quite different levels of complex system organization: the state of a molecule, a metazoan, and a community of individuals.

Here the number of states or assignments or niches per agent is in effect an average, so that each total can also be determined by a sum of all the states or assignments or niches in the larger unit. Each of the three items in sequence assesses the mutual-information associated with order on a larger size scale. Thus each assignment of a metazoan molecule builds on a certain number of correlated fermion-states within that molecule, just as each niche for a community metazoan will build on a certain number of correlated molecule-assignments with that metazoan. Nonetheless each assignment or niche, as an emergent phenomenon, is quite distinct from (hence something more than) the sum of its constituent states or assignments, respectively.

Concerning the parenthetic ``max 6 in \& out from...'' clauses, these basically figure that individual elements within a given level of system organization occupy a finite number of correlated state types. Put another way, we plan to categorize each element's ``correlation collection'' by viewing it as directed inward and outward with respect to a set of (in the examples above three) sub-system boundaries.

For instance, quantum statistics might first consider that single bit of mutual information between up-spin and down-spin electrons that comprises a carbon atom's ground state K-shell. This amounts to a pair correlation (wave-packet:OUT) between two intact electrons whose internal structure (wave-packet:IN) is a separate subject. The other electrons in a ground state atom occupy sites which correlate with one another, complete their respective shells (shell:IN), and moreover occupy those shells in the sequence of increasing energy (shell:OUT). We can presently take these correlations for granted, since most carbon atom electrons (except those inside stars) have too little energy to access electronic excited (atom:IN) states.

The question of intra-molecule correlations between electrons (atom:OUT) of course remains an interesting question at room temperature and below, sometimes with thermodynamic consequences in everyday life. Thus for example electrons involved in covalent bonds, or scattering experiments, are participating in correlations directed outward from the atom to which they were initially assigned. This is also true for electrons participating in collective solid state excitations, like Bose pairs or the conduction band of an operating semiconductor device.

On the level of a metazoan organism, we might similarly consider molecule assignments pointing inward and outward with respect to molecule surface, cell-membrane, and organ. For example, hormone molecules required to convey signals from one organ system to another might be seen as charged with an inter-tissue (organ:OUT) assignment.

Community Inventories

The motivation for the correlation scheme outlined above was its use for layered-niche networks in human communities. In this case, humans seem to naturally conceptualize niches as directed inward and outward with respect to the boundaries of self, family, and culture. Roles (cf. the figure above) taking care of self, friends, family, hierarchy, culture, and profession have thus developed, as have (respectively) the lore and participant/leadership obligations of patient/doctor, colleague/mentor, sibling/parent, citizen/leader, dancer/priest, and professional/scholar.

In other words, this inventory for the case of a community simply asks: In how many of these six areas are individuals able to make a name for themselves? If this is decreasing, things are perhaps getting worse for the community, independent of what other indicators have to say. The correlation scheme in principle will work for organism communities with meme-pools less developed than in the human case, as well. In this context, the clickable image at left illustrates one way to visualize the assignment of focus by communities and individuals on these six layers of community correlation.

Process indicators

One might also be interested in the rates at which correlations above are created, and/or the rates at which they are lost. One strategy may be to track the inventories above, since the rate of change of standing crop should equal the rate of creation minus loss. Thus inventories could at least be checked for consistency with more direct measures of process dynamics.

Thanks to the second law of thermodynamics, we also have the fact that rates of reversible thermalization are less than or equal to the rates of available work used up. Hence the rate at which available work is fed into the system (i.e. at which energy is thermalized on the left side of the figure above) provides an upper limit on the rate (when converted into second law terms) at which correlations are gained (on the right side of the figure). Such energy-based measures include the power stream accessible to life, and for evolving complexity in a more general sense Eric Chaisson's free energy rate density, cf. [BioSystems 46 (1998) 13-19] and [Complexity 9 (2004) 14-21].


A variety of questions are unanswered. For example, how do statistical properties of layered niche-networks affect information flow, and the capability of organisms involved in adapting to change? Are there objective ways to inventory the connections discussed here in human and non-human communities, and what perturbations to those connections would occur as a result? How might existing instruments of population and employment statistics be used to augment such network inventories? How are recent changes in demographics and communications affecting these networks? Can measures of this sort assist economists e.g. in looking at the long term costs of a given activity, as issues of sustainability become more difficult to ignore?

Nonetheless correlation inventories like this, with roots in the physical sciences, may prove useful for monitoring the state and process dynamics of layered niche-networks including the metazoan communities of which we are a part. Other corollaries of the approach include these observations: that idea sets (e.g. values) targeted toward the maintenance of specific levels of correlation in such inventories are easily identified, and that the stone age history which most humans share [cf. J. Diamond, The third chimpanzee (Harper Collins, 1992)] likely adapted us primarily to deal with only five of these six levels. Thus as free energy per capita for humans declines, the pressure to blur the lines between levels (e.g. politics, religion, and science) will increase.

One hedge against this trend might involve reporting on the dynamics of non-constructive idea sets easily amplified in this digital age. For example saying bogeyman code to terrorists, and observation to intelligent designers & deconstructionists, may be more effective than saying "evil" or "consensus" respectively. This is because the latter concepts echo ideas that drive each of these conflicts to begin with, while the former concepts address the problematic codes on their own field of play. Thus the dynamics of replicable codes are important for journalists as well as for biologists, making multi-disciplinary complex-system informatics courses a promising place to forge collaborations between both. Of course, without attention to the correlation inventories that memetic codes impact, the need for such collaborations might continue to be missed.

Read more about it:

Most of the references have been placed directly in the text. A citable eprint is also available [pdf]. If you'd like a few more clues to the math and physics behind these reflections, check out this draft for the 2005 Understanding Complex Systems Symposium at UIUC. Our ``heat capacity in bits'' page is here, and our even older ``information physics'' page is here. Suggestions are welcome/pf.

Developments after 2010 include:

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