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a network theory of everything? Fox-Keller says: no way!

Omar

In the miasmic pool of academic production, disciplinary globules constantly bump against another and some even extend their pseudopods into other disciplinary turfs. The recent of explosion of “network physics” for instance has provided the opportunity for one such increase in cross-disciplinary contact and trans-disciplinary invasions. Physicists, armed with graph theory and simple computational models that recover various graph-level statistics (such as degree distributions) have attempted to draft network “theories of everything” suggesting that a similar set of simple principles govern the organization of the internet, molecules and society among other “self-organized” systems. The Center for Complex Network Research right here in South Bend is one of the main command and control outposts from which the network physics invasion is being launched.

In a previous post, I have expressed my dissatisfaction regarding this approach to the study of network phenomena. For one it attempts to import certain thought styles into other disciplines, that while successful in physics, are of little use to other scientists who are usually cognitively embedded in different epistemic cultures. The search for “general network laws” is one of them. The inattention to the specificities and the peculiarities of generative mechanisms characteristic of certain systems (such as social systems) and absent in others is another one.

In a position paper that I highly recommend, iconoclastic biologist Evelyn Fox-Keller provides an (infinitely much more sophisticated) argument along the same lines for the field of biology. She reviews the history of “power laws” in the social and physical sciences, pointing to the neglect of Pareto and Simon’s work by the physicists, which they essentially reinvented. The main thrust of the piece however, is that power law distributions can be generated by a large set of processes of which the Barabasi favored “preferential attachment” model is only one. This model, while appropriate for some delimited classes of social phenomena (i.e. fads, scientific citation patterns), may not be the underlying generative mechanism responsible for the existence of power-law distribution in other systems, especially biological and technological systems.

She points out that referring to the network structure of these various networks as “scale free” is misleading, since while this term has a specific sense in the Physics of phase transitions, it is meaningless when used for such systems that not organize in sudden “jumps” from disorder to order, but whose structures emerges in a gradual manner. Fox-Keller concludes that

The search for unifying laws, for universal principles that can bypass the specificity of particular systems to capture the underlying unity of the world, is a deeply established tradition in physics, and the discovery of such laws has long represented the highest possible achievement of that discipline. Yearnings of this sort are not absent in biology—witness the search for unifying laws in the neo-Darwinian theory of evolution by natural selection, or in the Central Dogma of molecular biology—but in the history of the life sciences such aspirations have long been countered by a very different tradition, one rooted in respect for and even veneration of diversity. Indeed, philosophers of biology now debate the question, Are there laws of biology?…Physicists, however, rarely have such misgivings. It is Barabasi’s experience in the statistical mechanics of critical phenomena that imprints his faith in, as he says, ‘‘the unique and deep meaning of power laws’’. As he himself reminds us, it is the fact that, in the theory of phase transitions, power laws signal self-organization and the emergence of order from disorder, that underlies his excitement at finding these same laws show up in completely different contexts. here too, he cannot but believe, they must be ‘‘nature’s unmistakable sign that chaos is departing in favor of order.’’

But what in fact do network structures actually have to do with phase transitions, with criticality, or for that matter, with self-organization? And what do Barabasi and his colleagues mean by the term ‘‘scale-free’’? These are all terms that have acquired considerable fluidity as their use becomes widespread; indeed, their very fluidity contributes to their popularity. but my own take is that, while their original technical meanings may play a substantial role in the reception of the arguments that have been put forth, the role that these terms have played in the actual construction of arguments has been primarily evocative (1065-1066).

Written by Omar

April 17, 2007 at 12:59 am

Posted in networks, omar

One Response

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  1. Take the plot of y=x^2, the common parabola. Just by looking at the graph you cannot tell what are the units in the axis; they could be milimeters, yards or light-years. Now take the sine function, the distance between two intersections in the X-axis should be 2*pi and the vertical distance between a maximum and a minimum should be 2. The parabola is scale-free, the sine is not. As simple as that.

    Like

    Pedro Miramontes

    May 22, 2012 at 6:58 pm


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