Ball’s Critical Mass

Posted by jns on February 25, 2007

A week or two ago I finally finished reading Philip Ball’s Critical Mass : How One Thing Leads to Another. New York : Farrar, Straus and Giroux, 2004. (My book note about it, with different quotations, is here.)

I’ve become quite a fan now of Philip Ball’s writing; previously I was wowed by Bright Earth, and The Ingredients. Happily for me, there are still some of his books that I haven’t read.

This one struck me very personally in a couple of ways. Loosely speaking, it’s about modern attempts to apply modern concepts in condensed-matter physics (encompassing thermodynamics, statistical physics, fluid dynamics, critical phenomena, chaos theory and others) to social systems and the collective behavior of humans. Once upon a time I did experimental research in condensed-matter physics, including several of the disciplines he talks about. Today, with Ars Hermeneutica, I’m quite interested in what I call “appropriate quantification”, or how to apply statistical models to collective human behavior. Thus, there is a lot of resonance here. When I think about how irritating this book could have been had it been written by a less-accomplished science writer, it makes me admire Ball’s talents that much more.

These are some excerpts that I marked to keep here in my common-place book.

To kick things off, here’s an excerpt he quotes from C.P. Snow’s famous book The Two Cultures, about the divide (real or imagined) between the sciences and the humanities. This is all Snow:

A good many times I have been present at gatherings of people who, by the standards of the traditional culture, are thought highly educated and who have with considerable gusto been expressing their incredulity at the illiteracy of scientists. Once or twice I have been provoked and have asked the company how many of them could describe the Second Law of Thermodynamics. The response was cold: it was also negative. Yet I was asking something which is about the scientific equivalent of: Have you read a work of Shakespeare’s. [p.38 of Critical Mass]

Ball began his discussion by looking at the earliest attempt to make a science of social interaction, Hobbe’s Leviathan. Later on, he wrote about how earlier ideas propagated into today’s economic thinking.

The social contract proposed by Hobbes might sound like a forerunner of those advocated by John Locke (1623–1704) and Jean-Jacques Rousseau (1712–1778), but it is instead the reverse. To Locke and Rousseau, the power conferred upon the head of state comes with an obligation to serve the interests of the populace; for Hobbes, the common people are contracted to serve their ruler. For Hobbes, the principal fear was of anarchy; for Locke it was the abuse of power, which is why he saw the need for safeguards to avoid absolutism.

But although apparently a proponent of autocracy, Hobbes also provides arguments that can be used to support both bourgeois capitalism and liberalism. Although he expressed an aversion to the way the mercantile society bred men whose “only glory [is] to grow excessively rich by the wisdom of buying and selling,” which they do “by making poor people sell their labour to them at their own prices,” he saw bourgeois culture as largely inevitable, and sought a system that would accommodate its selfish tendencies without conflict. To this end he left it to the market to assign the value of everything, people included: “The value of all things contracted for, is measured by the Appetite of the Contractors: and therefore the just value, is that which they be contracted to give.” This fee-market philosophy found voice in Adam smith’s Wealth of Nations in the following century. Those in Britain and the United States (and indeed elsewhere) who lived through the 1980s will recognize it as an attitude that did not wane with the Age of Enlightenment. [p. 29]

After we’d spent quite a bit of time using scientific models to understand some of the complexity of the market and larger economic systems, suddenly traditional economic theories seems hopelessly naive and more the product of wishful thinking than critical thinking.

So deeply entrenched is the free-market philosophy in American economic theory today (I am talking here about the pundits who exert a real influence–the TV analysts, the Wall Street Journal op-ed columnists, the think-tankists, and all too often the White House advisors–but not the academic economists) that the supporters of this creed are hoping even to ride out the catastrophic stock market collapse that is proceeding at full throttle at the time of writing. They place the blame on a few corrupt CEOs, on government policies, on fickle small investors, on labor unions, on left-wing critics who spread doubt and negative thinking–anywhere but on the market itself. If only all these people would behaved, say the free-marketeers, stocks would keep rising forever. [pp. 224--225]

Later, he moved on to using ideas from critical phenomena to look at systems that can apparently change their states spontaneously and suddenly. The key concept here is that of thermodynamic fluctuations.

One experimental peculiarity that the theory [a late 19th century by physicist van der Waals) did embrace was the extraordinary sensitivity of the critical point. A system near its critical state becomes extremely responsive to disturbances. If you squeeze a substance, it shrinks in volume. The resistance it offers to the is compression is a measure of its so-called compressibility A rubber ball is more compressible than a steel, ball, and a gas is typically much more compressible than a liquid--one can squeeze it more easily. At the critical point of a liquid and gas, the fluid becomes absurdly compressible--in fact, more or less infinitely so. In principle, the gentlest squeeze is sufficient to collapse a critical fluid into invisibility. This sounds absurd, and experimentally one can never observe such extreme behavior, because maintaining a substance exactly at its critical point is too difficult--the critical state is too unstable. but one can see the compressibility start to increase very rapidly as the critical point is approached. [p. 228]

A correction: the fluctuations are unstable only below the critical temperature; above, they are stable and can grow very large if one can contrive to get the fluid close enough to the critical point and keep it there. I once was able to do that. It was such fluctuations that we were studying with our Zeno space-shuttle experiment in the early 90s. We were able to keep a very small fluid sample stably poised some 3-millionths of a Kelvin (i.e., a centigrade degree) above its critical temperature to study the density fluctuations. The compressibility was so high that we had to do this in earth orbit (so called “micro-gravity”) so that gravity itself would not move the fluid away from the critical point.

Still later the topic was networks and how they organize their connections and related topics, including a discussion of the Kevin Bacon degrees-of-separation game. Can all actors be connected to Kevin Bacon in just 6 or fewer steps? Is this deeply significant? Not really.

And what of the must burning issue: Is Kevin Bacon really the center of the movie universe? To answer this, one must calculate the average Bacon Number for the entire network and see how it compares with the equivalent measures for the other actors: the Elvis Number, the Bogart Number, the Brando Number, and so on. If Kevin Bacon really is the most important linchpin in the network, all other actors will, on average, be closer to him than to anyone else.

It turns out that not only is Kevin Bacon not the most important hub of the network, he is not even in the top one thousand (the list of course changes daily as new films are made). Currently up at the top is Rod Steiger (the average Steiger Number is 2.652), followed by Christopher Lee, Dennis Hopper, Donald Pleasence, and Donald Sutherland (who appeared in the movie version of Six Degrees of Separation). Marlon Brando is number 202, Frank Sinatra number 443. By the time we get to Kevin Bacon’s level., the differences in the average Actor Number that separate successive actors in the list are tiny, about 0.0001.

So why was Kevin Bacon picked for this game? The answer contains the entire essence of a small world: in such a network, everyone appears to be at the center. Some are more “central” than others–but not by very much. Even relatively minor actors like Eddie Albert have a comparable network status to major stars. (Donald Pleasence was a fine actor but hardly a superstar.) [pp. 369--370]

Finally, a little quotation from Pericles [quoted on p. 425]:

Even if only a few of us are capable of devising a policy or putting it into practice, all of us are capable of judging it.