Good Read on Modeling Social Emergent Phenomena - But Still Not There Yet!

Philip Ball - Critical Mass

The most important thing we can do right now - given the huge changes ahead of us - both in society, the world, and technology - is to get some sort of "handle" on what's coming up. By that, I mean a good set of models.

And as a result, I'm on a search for good models. Those that I know, those that are new. Those that make sense, and those that don't. (We need to relegate them to the "don't work" bin - but we need to know what we're relegating where.)

I'm starting to re-invigorate my modeling, and to connect with others about this. And along these lines, a dear colleague recommended one of his favorite books - Philip Ball's Critical Mass. I've had a good look at the Amazon "Look Inside" feature, which offers both the intro and first chapter, and the notes/references at the end.



Overall this book is great - I'm going to get a copy (from my public library, of course!) - but - it just doesn't go far enough.

Don't get me wrong. I'm all in favor of books that lay the groundwork and set the stage. Critical Mass definitely serves this need. However, we'll need to actually go beyond what is offered and discussed here to get what we really need right now: A robust set of very basic but useful models, with a clear set of what models apply to what situations, what assumptions and constraints have to be made, how we interpret the model variables, and what the model parameters actually mean.

And oh yes. This is what differentiates this new set of models and modeling tools from the previous generation. These models need to deal with nonlinear and (fairly often) non-equilibrium systems.

That said, Critical Mass looks well worth the read, and I've already looked up several of the references, and either read them online or plan to get the books.

Good job, Philip! And thank you!

Analytic Single-Point Solution for Cluster Variation Method Variables (at x1=x2=0.5)

Single-Point Analytion CVM Solution Involves Solving Set of Nine Nonlinear, Coupled Equations

The Cluster Variation Method, first introduced by Kikuchi in 1951 ("A theory of cooperative phenomena," Phys. Rev. 81 (6), 988-1003), provides a means for computing the free energy of a system where the entropy term takes into account distributions of particles into local configurations as well as the distribution into "on/off" binary states. As the equations are more complex, numerical solutions for the cluster variation variables are usually needed. (For a good review, see Yedidia et al., Constructing free energy approximations and generalized belief propagation algorithms.

When allowed to stabilize, the system comes to equilibrium at free energy minima, where the free energy equation involves both an interaction energy between terms and also an entropy term that includes the cluster variables. This computation addresses a system composed of a single zigzag chain.

I have computed an analytic solution for representing one of the cluster variables, z3, as a function of the reduced interaction energy term:

The equation details are presented in a separate Technical White Paper; I'll include a link to it as soon as I post it on my website, http://www.aliannamaren.com.

This pattern of CVM variables follows what we would expect.

The point on this graph where h=1 (the x-axis is 10) corresponds to h = exp(beta*epsilon)=1. Effectively, beta*epsilon => 0. This is the case where either the interaction energy (epsilon) is very small, or the temperature is very large. Either way, we would expect - at this point - the most "disordered" state. The cluster variables should all achieve their nominal distributions; z1=z3=0.125, and y2=0.25. This is precisely what we observe.

Consider the case of a positive interaction energy between unlike units (the A-B pairwise combination). The positive interaction energy (epsilon>0) then suggests that a preponderance of A-B pairs (y2) would destabilize the system. We would expect that as epsilon increases as a positive value, that we would minimize y2, and also see small values for those triplets that involve non-similar pair combinations. That is, the A-B-A triplet, or z3, approaches zero. We observe this on the RHS of the above graph. This is the case where as h = exp(beta*epsilon) moves into the positive range (0-3), we see that y2 and z3 fall towards zero. In particular, z3 becomes very small. Correspondingly, this is also the situation in which z1 = z6 becomes large; we see z1 taking on values > 0.4 when h > 2.7.

This is the realm of creating a highly structured system where large "domains" of like units mass together. These large domains (comprised of overlapping A-A-A and B-B-B triplets) stagger against each other, with relatively few instances of "islands" (e.g., the A-B-A and B-A-B triplets.)

Naturally, this approach - using a "reduced energy term" of beta*epsilon, where beta = 1/(kT), does not tell us whether we are simply increasing the interaction energy or reducing the temperature; they amount to the same thing. Both give the same resulting value for h, and it is the effect of h that we are interested in when we map the CVM variables and (ultimately) the CVM phase space.

At the LHS of the preceding graph, we have the case where h=exp(beta*epsilon) is small (0.1 - 1). These small values mean that we are taking the exponent of a negative number; the interaction energy between two unlike units (A-B) is negative. This means that we stabilize the system through providing a different kind of structure; one which emphasizes alternate units, e.g. A-B-A-B ...

This is precisely what we observe. The pairwise combination y2 (A-B) actually increases slightly beyond its nominal expectation (when there is no interaction energy), and goes above 0.25, notably when h is in the range of 0.1 and smaller. Also, as expected, the value for z1 (A-A-A triplets) also drops towards zero - triplets of like units are suppressed when the interaction energy between units is positive.

Somewhat surprisingly, z3 (A-B-A triplets) also decreases as h approaches 0.1. This means that the increase to above-nominal distributions for the CVM variable goes to z2 (A-A-B). Given that this is an even distribution of A and B units (x1 = x2 = 0.5), another way to think of the far LHS is when the temperature is very large. (We then have the exponent of a negative interaction energy over a large temperature, and can think of the increased temperature as producing greater "disorder" in the system - moving us away from the highly structured A-B-A-B-A order that would otherwise exist if y2 (A-B) predominated with no other influence.

"Nonadditive Entropy" - An Excellent Review Article

New Advances in Entropy Formulation - "Nonadditive Entropy"

Well, chalk it up to being newly returned to the fold - after years of work in knowledge discovery, predictive analysis, neural networks, and sensor fusion, I'm finally returning to my roots and re-invigorating some previous work that involves the Cluster Variation Method. In the course of this, I've just learned (as a Janie-come-lately) about the major evolution in thinking about entropy, largely led by Constantino Tsallis. He has an excellent review paper, The nonadditive entropy Sq and its applications in physics and elsewhere: some remarks. Beautifully done; elegantly leads the reader through the somewhat complex and subtle arguments leading to major breakthroughs in entropy formulation.

Modeling Trends in Long-Term IT as a Phase Transition

The most reasonable model for our faster-than-exponential growth in long-term IT trends is that of a phase transition.

At a second-order phase transition, the heat capacity becomes discontinuous.

The heat capacity image is provided courtesy of a wikipedia site on heat capacity transition(s).

L. Witthauer and M. Diertele present a number of excellent computations in graphical form in their paper The Phase Transition of the 2D-Ising Model.

There is another interesting article by B. Derrida & D. Stauffer in Europhysics Letters, Phase Transitions in Two-Dimensional Kauffman Cellular Automata.

The divergent increase in heat capacity is similar in form to the greater-thean-exponential increase in IT measurables, as discussed in my previous post, Going Beyond Moore's Law and identified in Super-exponential long-term trends in IT.

In one of my earlier posts, starting a modeling series on phase transitions from metastable states (using the Ising model with nearest-neighbor interactions and simple entropy), I identified a key challenge in identifying what it was that we were attempting to model. That is, What is x?. When we identify what it is that we are trying to model, we can figure out the appropriate equations.

Now, we have the same problem - but in reverse! We have an equation - actually, an entire modeling system (the Ising spin-glass model works well) - that gives us the desired heat capacity graphs. What we have to figure out now is: What is it exactly that is being represented if we choose the "phase transition analogy" for interpreting our faster-than-exponential growth in IT (and in other realms of human experience)?

That will be the subject of a near-term posting.

(Another good heat capacity graph is viewable at: http://physics.tamuk.edu/~suson/html/3333/Degenerate_files/image108.jpg)

Going Beyond Moore's Law

Super-Exponential Long-Term Trends in Information Technology

Interesting read for the day:
Super-exponential long-term trends in Information Technology by B. Nagy, J.D. kFarmer, J.E. Trancik, & J.P. Gonzales, shows that which Kurzeil suggested in his earlier work on "technology singularities" is true: We are experiencing faster-than-exponential growth within the information technology area.

Nagy et al. are careful to point out that their work indicates a "mathematical singularity," not to be confused with the more broadly-sweeping notion of a "technological singularity" discussed by Ray Kurzweil and others.

Kurzweil's now-famous book, The Singularity is Near: When Humans Transcent Biology, was first released as a precis on his website in approximately 2000. His interesting and detailed graphs, from which he deduced that we were going "beyond exponential growth," had data points up through approximately 2000. In contrast, Nagy et al. are able to produce data points typically through 2005.



The notion of "singularity" is both interesting and important now. Sandberg (2009) has published an interesting and readable paper, An overview of models of technological singularity".

"Knowledge Management" - Key Element for Start-Up Businesses

Knowledge Management - the "Middle Road" for Large and Small Businesses

If you're a small business entrepreneur (like me), or managing a role in a large organization, you probably wake up every morning with a single, compelling question: "What's the best use of my time today?" (And best use of time for the week, month, season ahead, etc.) For all of us, our time is the most valuable, and completely unrenewable resource.

So over the past three months - with a product launch on the horizon (we launched in late July; first book published by Mourning Dove Press, my new publishing company), my focus was - of all things - on databases. Particularly, on cleaning up my databases, transitioning to ACT! as the "main" data repository (instead of having duplicate contact cards in Outlook, for different taxonomy areas), and totally rethinking, rebuilding, and overall retooling our taxonomies.

Everything that I learned about taxonomies, knowledge management, and data organization while at EagleForce, and then later at Viziant, is becoming real and important in the most meaningful way.

And by "meaningful," I mean: This is where I'm spending my "time dollar." Over the past three months, I and my associates have spent more time on the database than on ANY OTHER ACTIVITY - and there's more to be done. (And there will ALWAYS be more to be done.)

We've put more time into the database than into the website, or even into our social media and public presentations. And we've done more head-scratching about how to organize our people-information than we've done about designing our website.

This is a really important point, because after teaching at both Marymount and George Mason University's Applied Information Technology programs over the past two years, where the focus for each course was essentially on "business process transformation," the one thing that we did not address was data management. That was always sort of a "sidebar." As in, "let's put in a user login system."

That's right. In teaching over nine different courses, at three major universities (and I'll throw in the course I taught on Knowledge Discovery at Georgetown many years ago into this mix), not once did I encounter the practical and very real-world importance of really focusing on and managing the corporate taxonomy and databases.

We worked on taxonomy-development and knowledge population for the Air Force, and for a number of smaller accounts while at EagleForce. Again, the overwhelming time-intensity of the task hasn't struck me until now - managing a much smaller, structured-data, information set.

Whenever I go back to teaching, and from now on, whenever I talk with teachers - especially in the business, IT, marketing, or related areas - I will in the future focus on the crucial role of getting the corporate taxonomies, or "world view" right. And putting people and other entities into the right taxonomies. And finding the right tools to manage the data, and to also integrate with the "communications" tools.

This is an important topic, and I'll be returning to it as time goes on.

What Makes a Metastable State Happen?

Metastable States - the Meltdown Precursors

I've just read a recent column by JL, one of the editors from Taipan Daily. He states, in his column "There Will Be Blood in Europe":

Stepping back a bit: What is so frightening right now, not just in Europe but China and America and Japan too, is the presence of fraud-fueled "Lehman 2.0" catalysts threatening to explode.

One could say that the 2008 financial crisis was the mother of all wake-up calls. But instead of actually waking up, the powers that be slammed the alarm clock, choked down a fistful of Ambien, and rolled back to sleep.

As a result, the world is going to get an even bigger wake-up call in the not-so-distant future.

This current Case Study is using the 2008-9 financial systems meltdown as the focal point. Starting today, I'm going to begin making the crucial parameter identifications that indicate when a metastable state will collapse, so that a "meltdown" occurs.

The most important thing to note right now is that - both in the model predictions AND in the real-world events that we've been observing - meltdowns happen fast. We can be in a metastable state that lasts so long, and is so extreme, that many people believe that the situation will last forever.

But it doesn't. This Case Study will show the underlying dynamics, and how these "meltdowns" are set up, and what happens when they collapse - all using the very simplest model possible from statistical thermodynamics.

In the last post, I characterized a state where very few institutions ("units" in the statistical thermodynamics model) were involved in risky (overly-leveraged) situations. This occurs when the free energy minimum occurs for a low value of x, where x is the decimal fraction of total units (institutions) involved in risky deals. It corresponds to Region A of the phase space diagram, shown two blogposts ago, and also previously.

With this posting, we move on to Region D, which is the one where metastabilities exist. That means that there are two free energy minima, throughout all points in Region D. (If you'll refer to the phase diagram, you'll see that Region D is the pink area in the middle; bordered by Region A at the top and Region G below, where both A and G are light blue.)