armand_marie_leroi's picture
Professor of Evolutionary Developmental Biology, Imperial College; Author, The Lagoon

The Parts & The Whole

Whenever we see highly ordered phenomenon—a baby, a symphony, a scientific paper, a corporation, a government, a galaxy—we are driven to ask: how does that order arise? One answer, albeit a very abstract one, is that each of these is the product of a variation-selection process. By this I mean any process that begins with many variants and in which most die (or are thrown in the waste-paper basket or dissipate or collapse) leaving only a few that are fit (or strong or appealing or stable) enough to survive. The production of organic forms by natural selection is, of course, the most famous example of such a process. It's also now a commonplace that human culture is driven by an analogous process; but, as the above examples suggest, I think that variation-selection processes can be seen everywhere once we know what to look for.

Many others have had this idea: Karl Popper, Donald Campbell, Henry Plotkin, George Dyson are but a few of the names that spring to mind. But none have seen its implications as deeply as George Price, an American living in London who, in 1970, published an equation that describes variation-selection processes of all kinds. The Price equation, as it is now known, is so simple, deep and elegant that it could easily be my candidate explanation. It can be used to describe, inter alia, the tuning of an analogue radio dial, chemical reaction kinetics, the impact of neo-natal mortality on the distribution of human birth weight, or the reason we inhabit this universe out of the multitude that we do not—assuming the others actually exist. But in fact, for me, the real fascination of the Price equation does not just lie in the form that he gave it in 1970, but in an extension that he published two years later.

One of the properties of variation-selection systems is that the selecting can happen at many different levels. Music is clearly the result of a variation-selection process. The composer sits at his piano considering what comes next and chooses one out of the world of possible notes, chords, or phrases that he might. Look at Beethoven's manuscripts (Op. 47, the Kreutzer Sonata is a good example)—they're scrawled with his second thoughts. In 1996 Brian Eno wittily made this process explicit when he used SSEYO's Koan software to produce an ever-varying collection of pieces that he called "generative music."

But the music that we actually have on our iPods is, of course, not merely the result of the composer's selective choices, nor even those made by producers, performers and so on, but ours. As individual consumers we, too, are a selective, and hence creative, force. And we do not only act as individuals, but also as members of social groups. Experiments show that if we know what music other people are listening to we are quite ready to subsume (if not totally abandon) our own aesthetic preferences and follow the herd—a phenomenon that explains why it's so hard to predict hits. So composers, consumers and groups of consumers all shape the world of music. Umberto Eco made much the same point as long ago as 1962 (Opera Aperta-Open Work). Of course, as a literary critic Eco could do no more than draw attention to the problem. But George Price solved it.

In 1972 George Price extended his general variation-selection equation to allow for multi-level selection. This form of the equation has been very useful to evolutionary biologists for it has allowed them to see, for example, the relationship between kin and group selection clearly and so put to rest endless controversies stemming from incompatible mathematical formulations. It hasn't yet been applied to cultural evolution, though it surely will. But I think that the extended Price equation is much more important than even that. I think it slices one of the Gordian knots that scientists and philosophers of science have wrestled with forever.

It is the knot of reducibility. Can the behaviour of a system be understood in terms of—that is, be reduced to—the behaviour of its components? This question, in one form or another, pervades science. Systems biologists v. biochemists; cognitive scientists v. neuroscientists; Durkheim v. Bentham; Gould v. Dawkins; Aristotle v. Democritus—the gulf (epistemological, ontological and methodological) between the holist v. reductionist stances lies at the root of many of science's greatest disputes. It is also the source of advances as one stance is abandoned in favour of another. Indeed, holist and reductionist research programmes often exist side by side in uneasy truce (think of any Biology department). But when, as so often, the truce breaks down and open warfare resumes it's clear that what is needed is a way of rationally partitioning the creative forces operating at different levels.

That is what Price gave. Of course, his equation only applies to variation-selection systems; but, if you think about it, most order-creating systems are variation-selection systems. Returning to our musical world: who really shapes it? Beethoven's epigones tweaking their MIDI files? Adolescents downloading in the solitude of their bedrooms? The massed impulses of the public? This year the UK Christmas No.1 was a ditty, "Wherever You Are," sung by a choir of military wives. How? Why? In 2012? I think that Price's equation can explain. It certainly has some explaining to do.