Category Archives: Plectics

Multiscale Structure, Information Theory, Explosions

I’d like to talk a bit about using information theory to quantify the intuition that a complex system exhibits structure at multiple scales of organization. My friend and colleague Ben Allen wrote an introduction to this a while ago:

Ben’s blog post is a capsule introduction to this article that he and I wrote with Yaneer Bar-Yam:

I also cover this topic, as well as a fair bit of background on how to relate probability and information, in my PhD thesis:

In this post, I’ll carry the ideas laid out in these sources a little bit farther in a particular direction.
Continue reading Multiscale Structure, Information Theory, Explosions

Multiscale Structure in Eco-Evolutionary Dynamics

I finally have my thesis in a shape that I feel like sharing. Yes, this took over three months after my committee gave their approval. Blame my desire to explain the background material, and the background to the background….

In a complex system, the individual components are neither so tightly coupled or correlated that they can all be treated as a single unit, nor so uncorrelated that they can be approximated as independent entities. Instead, patterns of interdependency lead to structure at multiple scales of organization. Evolution excels at producing such complex structures. In turn, the existence of these complex interrelationships within a biological system affects the evolutionary dynamics of that system. I present a mathematical formalism for multiscale structure, grounded in information theory, which makes these intuitions quantitative, and I show how dynamics defined in terms of population genetics or evolutionary game theory can lead to multiscale organization. For complex systems, “more is different,” and I address this from several perspectives. Spatial host–consumer models demonstrate the importance of the structures which can arise due to dynamical pattern formation. Evolutionary game theory reveals the novel effects which can result from multiplayer games, nonlinear payoffs and ecological stochasticity. Replicator dynamics in an environment with mesoscale structure relates to generalized conditionalization rules in probability theory.

The idea of natural selection “acting at multiple levels” has been mathematized in a variety of ways, not all of which are equivalent. We will face down the confusion, using the experience developed over the course of this thesis to clarify the situation.

(PDF, arXiv:1509.02958)

My Year in Publications

This is, apparently, a time for reflection. What have I been up to?

And so this is Korrasmas
Things have been Done
Kuvira is fallen
A new ‘ship just begun

We all knew it

Well, other than watching cartoons?

At the very beginning of 2014, I posted a substantial revision of “Eco-Evolutionary Feedback in Host–Pathogen Spatial Dynamics,” which we first put online in 2011 (late in the lonesome October of my most immemorial year, etc.).

In January, Chris Fuchs and I finished up an edited lecture transcript, “Some Negative Remarks on Operational Approaches to Quantum Theory.” My next posting was a solo effort, “SIC-POVMs and Compatibility among Quantum States,” which made for a pretty good follow-on, and picked up a pleasantly decent number of scites.

Then, we stress-tested the arXiv.

By mid-September, Ben Allen, Yaneer Bar-Yam and I had completed “An Information-Theoretic Formalism for Multiscale Structure in Complex Systems,” a work very long in the cooking.

Finally, I rang in December with “Von Neumann was Not a Quantum Bayesian,” which demonstrates conclusively that I can write 24 pages with 107 references in response to one sentence on Wikipedia.

Lacking Tonka

Dawkins claims that Hölldobler has “no truck with group selection”. Wilson and Hölldobler (2005) proposes, in the first sentence of its abstract, that “group selection is the strong binding force in eusocial evolution”. Later, Hölldobler (with Reeve) voiced support for the “trait-group selection and individual selection/inclusive fitness models are interconvertible” attitude. Hölldobler’s book with Wilson, The Superorganism: The Beauty, Elegance, and Strangeness of Insect Societies (2008), maintains this tone. Quoting from page 35:

It is important to keep in mind that mathematical gene-selectionist (inclusive fitness) models can be translated into multilevel selection models and vice versa. As Lee Dugatkin, Kern Reeve, and several others have demonstrated, the underlying mathematics is exactly the same; it merely takes the same cake and cuts it at different angles. Personal and kin components are distinguished in inclusive fitness theory; within-group and between-group components are distinguished in group selection theory. One can travel back and forth between these theories with the point of entry chosen according to the problem being addressed.

This is itself a curtailed perspective, whose validity is restricted to a narrow class of implementations of the “multilevel selection” idea. (Yeah, the terminology in this corner of science is rather confused, which doesn’t make talking about it easier.) Regardless, I cannot think of a way in which this can be construed as having “no truck with group selection”. The statement “method A is no better or worse than method B” is a far cry from “method A is worthless and only method B is genuinely scientific”.

If Dawkins has some personal information to which the published record is not privy, that’s fine, but even if that were the case, his statements could not be taken as a fair telling of the story.

EDIT TO ADD (21 November 2014): I forgot this 2010 solo-author piece by Hölldobler, in a perspective printed in Social Behaviour: Genes, Ecology and Evolution (T. Székely et al., eds). Quoting from page 127:

I was, and continue to be, intrigued by the universal observation that wherever social life in groups evolved on this planet, we encounter (with only a few exceptions) a striking correlation: the more tightly organized within-group cooperation and cohesion, the stronger the between-group discrimination and hostility. Ants, again, are excellent model systems for studying the transition from primitive eusocial systems, characterized by considerable within-group reproductive competition and conflict, and poorly developed reciprocal communication and cooperation, and little or no between-group competition, one one side, to the ultimate superorganisms (such as the gigantic colonies of the Atta leafcutter ants) with little or no within-group conflict, pronounced caste systems, elaborate division of labour, complex reciprocal communication, and intense between-group competition, on the other side (Hölldobler & Wilson 2008 [the book quoted above]).

And, a little while later, on p. 130:

In such advanced eusocial organisations the colony effectively becomes a main target of selection […] Selection therefore optimises caste demography, patterns of division of labour and communication systems at the colony level. For example, colonies that employ the most effective recruitment system to retrieve food, or that exhibit the most powerful colony defence against enemies and predators, will be able to raise the largest number of reproductive females and males each year and thus will have the greatest fitness within the population of colonies.

Google Scholar Irregularities

Google Scholar is definitely missing citations to my papers.

The cited-by results for “Some Negative Remarks on Operational Approaches to Quantum Theory” [arXiv:1401.7254] on Google Scholar and on INSPIRE are completely nonoverlapping. Google Scholar can tell that “An Information-Theoretic Formalism for Multiscale Structure in Complex Systems” [arXiv:1409.4708] cites “Eco-Evolutionary Feedback in Host–Pathogen Spatial Dynamics” [arXiv:1110.3845] but not that it cites My Struggles with the Block Universe [arXiv:1405.2390]. Meanwhile, the SAO/NASA Astrophysics Data System catches both.

This would be a really petty thing to complain about, if people didn’t seemingly rely on such metrics.

EDIT TO ADD (17 November 2014): Google Scholar also misses that David Mermin cites MSwtBU in his “Why QBism is not the Copenhagen interpretation and what John Bell might have thought of it” [arXiv:1409.2454]. This maybe has something to do with being worse at detecting citations in footnotes than in endnotes.

Multiscale Structure via Information Theory

We have scienced:

B. Allen, B. C. Stacey and Y. Bar-Yam, “An Information-Theoretic Formalism for Multiscale Structure in Complex Systems” [arXiv:1409.4708].

We develop a general formalism for representing and understanding structure in complex systems. In our view, structure is the totality of relationships among a system’s components, and these relationships can be quantified using information theory. In the interest of flexibility we allow information to be quantified using any function, including Shannon entropy and Kolmogorov complexity, that satisfies certain fundamental axioms. Using these axioms, we formalize the notion of a dependency among components, and show how a system’s structure is revealed in the amount of information assigned to each dependency. We explore quantitative indices that summarize system structure, providing a new formal basis for the complexity profile and introducing a new index, the “marginal utility of information”. Using simple examples, we show how these indices capture intuitive ideas about structure in a quantitative way. Our formalism also sheds light on a longstanding mystery: that the mutual information of three or more variables can be negative. We discuss applications to complex networks, gene regulation, the kinetic theory of fluids and multiscale cybernetic thermodynamics.

There’s much more to do, but for the moment, let this indicate my mood:

Delayed Gratification

A post today by PZ Myers nicely expresses something which has been frustrating me about people who, in arguing over what can be a legitimate subject of “scientific” study, play the “untestable claim” card.

Their ideal is the experiment that, in one session, shoots down a claim cleanly and neatly. So let’s bring in dowsers who claim to be able to detect water flowing underground, set up control pipes and water-filled pipes, run them through their paces, and see if they meet reasonable statistical criteria. That’s science, it works, it effectively addresses an individual’s very specific claim, and I’m not saying that’s wrong; that’s a perfectly legitimate scientific experiment.

I’m saying that’s not the whole operating paradigm of all of science.

Plenty of scientific ideas are not immediately testable, or directly testable, or testable in isolation. For example: the planets in our solar system aren’t moving the way Newton’s laws say they should. Are Newton’s laws of gravity wrong, or are there other gravitational influences which satisfy the Newtonian equations but which we don’t know about? Once, it turned out to be the latter (the discovery of Neptune), and once, it turned out to be the former (the precession of Mercury’s orbit, which required Einstein’s general relativity to explain).

There are different mathematical formulations of the same subject which give the same predictions for the outcomes of experiments, but which suggest different new ideas for directions to explore. (E.g., Newtonian, Lagrangian and Hamiltonian mechanics; or density matrices and SIC-POVMs.) There are ideas which are proposed for good reason but hang around for decades awaiting a direct experimental test—perhaps one which could barely have been imagined when the idea first came up. Take directed percolation: a simple conceptual model for fluid flow through a randomized porous medium. It was first proposed in 1957. The mathematics necessary to treat it cleverly was invented (or, rather, adapted from a different area of physics) in the 1970s…and then forgotten…and then rediscovered by somebody else…connections with other subjects were made… Experiments were carried out on systems which almost behaved like the idealization, but always turned out to differ in some way… until 2007, when the behaviour was finally caught in the wild. And the experiment which finally observed a directed-percolation-class phase transition with quantitative exactness used a liquid crystal substance which wasn’t synthesized until 1969.

You don’t need to go dashing off to quantum gravity to find examples of ideas which are hard to test in the laboratory, or where mathematics long preceded experiment. (And if you do, don’t forget the other applications being developed for the mathematics invented in that search.) Just think very hard about the water dripping through coffee grounds to make your breakfast.

Modern Evolutionary Theory Reading List

The following is a selection of interesting papers on the theory of evolutionary dynamics. One issue addressed is that of “levels of selection” in biological evolution. I have tried to arrange them in an order such that the earlier ones provide a good context for the ones listed later.

I’ve met, corresponded with and in a couple cases collaborated with authors of these papers, but I’ve had no input on writing or peer-reviewing any of them.
Continue reading Modern Evolutionary Theory Reading List

Currently Reading

T. Biancalani, D. Fanelli and F. Di Patti (2010), “Stochastic Turing patterns in the Brusselator modelPhysical Review E 81, 4: 046215, arXiv:0910.4984 [cond-mat.stat-mech].


A stochastic version of the Brusselator model is proposed and studied via the system size expansion. The mean-field equations are derived and shown to yield to organized Turing patterns within a specific parameters region. When determining the Turing condition for instability, we pay particular attention to the role of cross-diffusive terms, often neglected in the heuristic derivation of reaction-diffusion schemes. Stochastic fluctuations are shown to give rise to spatially ordered solutions, sharing the same quantitative characteristic of the mean-field based Turing scenario, in term of excited wavelengths. Interestingly, the region of parameter yielding to the stochastic self-organization is wider than that determined via the conventional Turing approach, suggesting that the condition for spatial order to appear can be less stringent than customarily believed.

See also the commentary by Mehran Kardar.

Currently Reading

A. Franceschini et al. (2011), “Transverse Alignment of Fibers in a Periodically Sheared Suspension: An Absorbing Phase Transition with a Slowly Varying Control Parameter” Physical Review Letters 107, 25: 250603. DOI: 10.1103/PhysRevLett.107.250603.

Abstract: Shearing solutions of fibers or polymers tends to align fiber or polymers in the flow direction. Here, non-Brownian rods subjected to oscillatory shear align perpendicular to the flow while the system undergoes a nonequilibrium absorbing phase transition. The slow alignment of the fibers can drive the system through the critical point and thus promote the transition to an absorbing state. This picture is confirmed by a universal scaling relation that collapses the data with critical exponents that are consistent with conserved directed percolation.

Adaptive Networks

In network science, one can study the dynamics of a network — nodes being added or removed, edges being rewired — or the dynamics on the network — spins flipping from up to down in an Ising model, traffic flow along subway routes, an infection spreading through a susceptible population, etc. These have often been studied separately, on the rationale that they occur at different timescales. For example, the traffic load on the different lines of the Boston subway network changes on an hourly basis, but the plans to extend the Green Line into Medford have been deliberated since World War II.

In the past few years, increasing attention has been focused on adaptive networks, in which the dynamics of and the dynamics on can occur at comparable timescales and feed back on one another. Useful references:
Continue reading Adaptive Networks

Of Predators and Pomerons

Consider the Lagrangian density

\[ \mathcal{L} (\tilde{\phi},\phi) = \tilde{\phi}\left((\partial_t + D_A(r_A – \nabla^2)\right)\phi – u\tilde{\phi}(\tilde{\phi} – \phi)\phi + \tau \tilde{\phi}^2\phi^2. \]

Particle physicists of the 1970s would recognize this as the Lagrangian for a Reggeon field theory with triple- and quadruple-Pomeron interaction vertices. In the modern literature on theoretical ecology, it encodes the behaviour of a spatially distributed predator-prey system near the predator extinction threshold.

Such is the perplexing unity of mathematical science: formula X appears in widely separated fields A and Z. Sometimes, this is a sign that a common effect is at work in the phenomena of A and those of Z; or, it could just mean that scientists couldn’t think of anything new and kept doing whatever worked the first time. Wisdom lies in knowing which is the case on any particular day.

[Reposted from the archives, in the light of John Baez’s recent writings.]


In the wake of ScienceOnline2011, at which the two sessions I co-moderated went pleasingly well, my Blogohedron-related time and energy has largely gone to doing the LaTeXnical work for this year’s Open Laboratory anthology. I have also made a few small contributions to the Azimuth Project, including a Python implementation of a stochastic Hopf bifurcation model.

I continue to fall behind in writing the book reviews I have promised (to myself, if to nobody else). At ScienceOnline, I scored a free copy of Greg Gbur’s new textbook, Mathematical Methods for Optical Physics and Engineering. Truth be told, at the book-and-author shindig where they had the books written by people attending the conference all laid out and wrapped in anonymizing brown paper, I gauged which one had the proper size and weight for a mathematical-methods textbook and snarfed that. On the logic, you see, that if anyone who was not a physics person drew that book from the pile, they’d probably be sad. (The textbook author was somewhat complicit in this plan.) I am happy to report that I’ve found it a good textbook; it should be useful for advanced undergraduates, procrastinating graduate students and those seeking a clear introduction to techniques used in optics but not commonly addressed in broad-spectrum mathematical-methods books.

REPOST: Scathing Review Fail

A discussion elsewhere on the ‘tubes this morning reminded me of this, so I decided to dig it out of my archives. Short version: people complaining that something sounds silly got it coming right back at them because they have no clue what they’re talking about.

I haven’t yet seen the remake of The Day the Earth Stood Still. Generally speaking, I haven’t been terribly speedy about seeing movies as they come out; sometimes, I just wait until they’re available on mplayer. The reviews have not been kind, but on the flipside, not all the reviews have been particularly insightful. To wit, here is Alonso Duralde at

The new “Day” can’t be bothered to include the thought-provoking dialogue of the original, choosing instead to bury the audience with special effects that are visually impressive but no substitute for an actual script. And what words do remain are so exquisitely awful that they provide some of the season’s biggest laughs.

OK, bring it.

My personal favorite? Astro-biologist Helen Benson (Jennifer Connelly) takes alien Klaatu (Keanu Reeves) to see a Nobel Prize-winning scientist and notes that her colleague was honored “for his work in biological altruism.” What would that entail, exactly? Helping frogs cross the street?

The sound you hear is my palm hitting my forehead, rather emphatically, followed by a howl from deep within my thorax: “Learn to [expletive deleted] Google, you [anatomically uncomplimentary compound noun]!” Just because Chris Tucker of the Daily Mail can’t do a simple web search doesn’t give you an excuse.

Claudia Puig at USA Today is no better:

What, exactly, would that entail? It sounds like something Cleese and his fellow Monty Python wits might have dreamed up.

You ignorant [epithet derived from SF television show]. Why don’t you go [verb unsuitable for a family blog] with Dave White, who apparently thinks that the mere mention of an actual scientific subject makes a movie instant MST3K fodder.

In Scientific American, Michael Shermer gives the movie a mostly positive review, and indicates that “biological altruism” is a real subject. Kenneth Turan of the LA Times is also mostly happy with the film, and he doesn’t crack wise about the “biological altruism” business, though I’m not sure about his grasp of it:

Aside from Klaatu and Gort, the “Day” team claims to have retained the original’s snappy catchphrase, “Klaatu barada nikto,” but it’s so hard to hear that viewers will be forgiven if they miss it. Also still around is the charming blackboard scene, in which Klaatu solves an equation for Professor Barnhardt (John Cleese), a man smart enough to have won the nonexistent but indisputably high-minded Nobel Prize for biological altruism.

Supposing that Barnhardt did work in the field of kin recognition, evolutionary ecology or some such topic which was honoured with a Nobel Prize, it wouldn’t be “the Nobel Prize for biological altruism”, but rather the Nobel Prize in Physiology or Medicine or, possibly, Economics (if Barnhardt’s research focused on, say, evolutionary game theory).

MTV’s Kurt Loder calls the film “boldly mediocre” but says that “biological altruism” is “a very Pythonian name for an actual subject of scientific inquiry”. Stephen D. Greydanus has a similar attitude. The recapper at the Agony Booth was also underwhelmed, by this part and by the rest of the movie:

Helen explains that Karl won the Nobel “for his work in biological altruism.” This sounds like something goofy they made up to make Karl sound noble, but in fact it’s a real field of philosophic study that investigates why, in times of limited resources, individual organisms throughout the animal kingdom occasionally produce fewer offspring (which, in Darwinian terms, is self-abnegation) for the good of the community. Which is great, but since it’s not explained, most of the audience is left to think that it’s something goofy the filmmakers made up.

So, I guess you can still dislike the movie after you’ve looked up the relevant science.

Colloquium on Complex Networks

I might be going to this, because it’s in the neighbourhood and I suppose I ought to see what colourful examples other people use in these situations, having given similar talks a couple times myself.

MIT Physics Department Colloquium: Jennifer Chayes

“Interdisciplinarity in the Age of Networks”

Everywhere we turn these days, we find that dynamical random networks have become increasingly appropriate descriptions of relevant interactions. In the high tech world, we see mobile networks, the Internet, the World Wide Web, and a variety of online social networks. In economics, we are increasingly experiencing both the positive and negative effects of a global networked economy. In epidemiology, we find disease spreading over our ever growing social networks, complicated by mutation of the disease agents. In problems of world health, distribution of limited resources, such as water, quickly becomes a problem of finding the optimal network for resource allocation. In biomedical research, we are beginning to understand the structure of gene regulatory networks, with the prospect of using this understanding to manage the many diseases caused by gene mis-regulation. In this talk, I look quite generally at some of the models we are using to describe these networks, and at some of the methods we are developing to indirectly infer network structure from measured data. In particular, I will discuss models and techniques which cut across many disciplinary boundaries.

9 September 2010, 16:15 o’clock, Room 10-250.