Embedded Files
One way to model the bloom and decline of layered complexity, with 100 individuals (one circled) showing 6 ternary views of the 5-simplex for displaying all 6 normalized attention-slice fractions.
One reason that number of choices W works so well as an order parameter [1] in this application may be its connection to state uncertainty S, a useful order parameter in many other complex systems e.g. via Boltzmann's S = k ln W and Shannon's #choices = 2#bits. Uncertainty (e.g. in bits or J/K) is more useful, of course, when you have way more than 6 choices.
In fact one of the five "tail-wagging ideas" mentioned on our poster about that subject was energy's uncertainty slope or "coldness" β ≡ ΔS/ΔE = 1/kT where entropy S = k ln[#choices], which provides insight into not only why temperature works (and what its natural as distinct from historical units are [2]) but also the assumptions behind the ideal gas law, equipartition, and chemistry's law of mass action. It also allows extension of the temperature concept to use on negative absolute temperature systems (hotter than positive absolute temperature systems) like LASER inverted-population states and spin systems in general.
This entropy-first approach also opened the door to study of applications for "Bayesian" statistical inference to more complex systems. One of these gave rise to the idea of layered complexity involving natural selection beyond the organism to include gene-pool and idea-pool lifeforms, and to an activity-layer multiplicity measure of community-level health [3-5] designed to recognize the physical importance of family and culture in the quality of individual lives. In other words, just as #choices = eS/k = 2#bits in thermal and information systems, the geometric average of activity-layer choices for population N i.e. Mgeo ≡ (Πjmj)1/N = eΣjsj/kN ≡ eSavg/k (where mj = Πi(1/fij)fij ≡ esj/k is the choice multiplicity for the jth individual with attention fraction fij for the ith of 6 layers, and k determines units for uncertainty) may be "the dog that wags" the quality of life for individuals in human communities.
Let's break it down more simply. If you, as person j out of N, divide your time between the L = 6 activity layers (f1j self/fitness, f2j friend/mentor, f3j relative/family, f4j community/politics, f5j tradition/beliefs, and f6j profession/science) according to the fractions fij where Σifij = 1, then the effective number of activity choices that complicate your life is:
where the "information units" for your "state uncertainty" sj is bits, giving us nothing more than a "logarithmic" way to describe layer multiplicity mj.
Thus your "activity-layer multiplicity" mj is 6 if you spend equal amounts of your "active time" in each of the 6 activity layers, 5 if you spend equal amounts of time in only 5 of the 6 activity layers, and only 1 if you spend all of your time in only one. This is a kind of empirical measure of the breadth of your opportunities in life, as well as of its layer complexity. It also characterizes the nature of your role in society.
To characterize a community of j = {1,N} organisms in this context, the natural extension of this (which also was easier to determine the "uniform distribution" value of Mgeo to be e29/20 ≈ 4¼) is the geometric mean choice multipicity, i.e.
This number gives a sense of how many layers, on average, each individual is involved in. It is always less than the "center of mass" choice multiplicity Mcm of a given community, defined as
This "center of mass" multiplicity describes the span of layers dealt with by the community as a whole, rather than span of individual domains. Thus, for instance, gender based divisions of labor might keep Mgeo closer to 3 if say one gender focused on odd numbered (inward-looking) layers and the other focused on even numbered (outward-looking) layers. This in spite of the fact that all six layers are spanned by Mcm for the community as a whole.
This sort of analysis is in principle possible for multi-celled organism communities of all sorts. Thus, for example, a "nearly pure" gene-pool lifeform community like that of the eusocial insects [6] might be characterized with most activities focused on subsystem correlations looking in/out from the gene-pool boundary i.e. on f3 (relatives/family) and f4 (community/politics). Hence Mcm might be not much above 2, and Mgeo might be nearly that with only a small amout of individual organism activity e.g. focused on taking care of themselves (f1) and their colleagues (f2). For human communities, we might hope that Mcm is about 6, and Mgeo e.g. in the "all possible combinations case" would be around 4¼.
References:
[1] James P. Sethna (2006/2021) Entropy, order parameters and complexity (Oxford U. Press, Oxford UK) (book webpage, edition 2).
[2] P. Fraundorf (2003) "Heat capacity in bits", Amer. J. Phys. 71:11, 1142-1151 (link video abstract).
[3] P. Fraundorf (2019) "Task layer multiplicity as a measure of community level health", Complexity 2019, 1082412, 8 pages, hal-01503096, new/earlier google sites, laTeX pdf.
[4] P. Fraundorf (2013) "Layer-multiplicity as a community order-parameter", arXiv:1306.5185 [physics.gen-ph] mobile-ready version.
[5] P. Fraundorf (2008) "A simplex model for layered niche-networks", Complexity 13:6, 29-39 abstract e-print.
[6] Martin A. Nowak, Corina E. Tarnita & Edward O. Wilson (2010) Nature 466, 1057-1062 abstract supplement.
Page updated
Google Sites
Report abuse