In February 1943, Erwin Schrödinger delivered a series of three lectures in Dublin. A year later, they were published as a book, under the title What Is Life?, so ensuring that Schrödinger’s ideas reached an audience far larger than the four hundred – a number, he wryly notes, which ‘did not substantially dwindle’ over the three lectures – who originally heard him. Together with Max Delbrück, another physicist, Schrödinger subsequently inspired a postwar generation of scientists to think of biology as a place where exciting physical work might be done. The final chapter of What Is Life? suggests that the problem of understanding biological organisation and order might lead to the uncovering of new physical principles. As we investigate the structure of matter, Schrödinger wrote, ‘we must be prepared to find a new type of physical law prevailing in it.’
In the late 1940s and 1950s, molecular biology was born, and it has grown at an astonishing and still unslackening pace. Researchers have by now discovered the nature of the hereditary material, the structure of DNA, the form of the genetic code, the functions of RNA, the molecular control of gene expression, and the complexities of the route leading from genes to proteins. They have learned how to distinguish the sizes of biologically significant molecules, to copy arbitrary DNA sequences, to map and sequence genomes. They have bred mutant organisms, some of which are able to churn out desired proteins, others to reveal the ways in which particular molecules interact in the early stages of development. In sum, these achievements amount to one of the greatest of all scientific revolutions (it may turn out to be the greatest). Yet, by an interesting irony, Schrödinger’s great hope, that new physical principles would emerge, has so far been unfulfilled. The overwhelming message of molecular biology is the particularity of molecular systems: while we now have a vast amount of detail about the mechanisms that govern the lives of cells in specific organisms, there seems to be no general picture. Furthermore, the question Schrödinger took for his title – ‘What is life?’ – has almost disappeared from view.
Perhaps that question is best left to philosophers while the biological community takes the next steps in fathoming out cellular metabolism or the differentiation of cells that occurs in the development of multicellular organisms. Yet there are contexts in which the question matters: students of the origins of life need a clear view of just what transition it is they are aiming to explain; researchers in exobiology (life beyond the Earth) need to know what they are looking for. Are there general principles that characterise all living things? Or is Schrödinger’s essay merely a quaint work of prophesy, dwarfed by the vastly successful science it helped to inspire?
Stuart Kauffman believes that it’s time to return to Schrödinger’s hopes and the questions he asked. His title echoes Wittgenstein, with whose Philosophical Investigations he sometimes labours to link his project, but the deeper connection is with the Dublin lectures. Kauffman, too, yearns for a general biology that will expose a significant pattern in the mass of molecular detail, and his discussions embrace those areas – origins-of-life research, extra-terrestrial life – for which a broad biological perspective is most needed. He confesses that many of his ideas are mere glimmerings of future projects whose contours he may not yet see clearly. Investigations is far more than ungrounded conjecture, however, for Kauffman draws on a broad knowledge of molecular biology and biochemistry, as well as an eclectic range of ideas in mathematics, physics and the social sciences. His way of being an original thinker is to be both a maverick and a polymath.
Kauffman starts by outlining what he thinks the form of a general biology ought to be and why he believes we need one. He next offers a scenario for how life might have originated, together with some proposals for refining (or even refuting) his own suggestions. Responding to Schrödinger’s question, he offers an account of living things (or ‘autonomous agents’ as he calls them): a living thing is a reproducing system able to carry out at least one thermodynamic work cycle – i.e. which has the capacity to fend off the degradation that the second law of thermodynamics sees as affecting all closed physical systems.
The central part of Investigations is more programmatic. Kauffman here explores the possibility of a ‘physics of semantics’, or a scientific account of the relations between signs and what they signify. Although this is territory that philosophers have begun to chart in recent decades, Kauffman proceeds without much awareness of the avenues already pursued and the problems that have arisen. But he has his sights set on a larger goal. Believing that we need a new type of science, he proposes that if we are to do justice to major aspects of the human (and the living) world we must go ‘beyond Newton, Einstein and Bohr’ and the kinds of inquiry they have made familiar.
The last four chapters provide more detailed explorations of how this new science might go. Kauffman begins by defending the claim that the history of the universe so far doesn’t provide enough time for more than a minute fraction of the physical possibilities it contains to have been realised: the complex organic molecules that do occur are only an infinitesimal subset of those that are possible. He argues further that the number of different possibilities is itself constantly being increased, and that this expansion could be the source of the new laws of nature that Schrödinger was seeking.
He goes on to probe candidates for such laws in more detail, focusing first on the biosphere. His examples seek to identify the kinds of diversity among biological entities that we should expect to find: among his proposals is that the evolution of ‘autonomous agents’ (roughly speaking, organisms) will take them to the ‘edge of chaos’ – a state in which they still display stable patterns of behaviour but close to one in which their behaviour would be chaotic in the technical sense. I will return to this idea in a moment.
In his last two chapters Kauffman moves beyond biology. In one he attempts to do for the social sciences – what he calls the ‘econosphere’ – what he has just done for the biosphere. Arguing that economists define their discipline too narrowly, by concentrating on states of equilibrium in situations that can be precisely circumscribed, Kauffman urges them to consider economies, and societies, as ‘burgeoning with new ways of making a living’, i.e. as evolving systems, subject to general principles which he tries to enunciate. In the last chapter, he outlines an equally ambitious approach to the cosmos, as he wrestles with the problems that have inspired others to invoke anthropic principles or talk of cosmic ‘selection’ (roughly, the idea of there existing a whole population of universes subject to a process analogous to natural selection). Here, as he cheerfully acknowledges, he is close to, or possibly beyond, the limits of his expertise, and the discussion is openly incomplete.
It would be easy to sneer at Kauffman’s closing words – ‘We enter a new millennium. There will be time for new science to grow.’ (Do we hear strains of Also Sprach Zarathustra?) It’s easy, too, to scoff at the hubris of treating difficult problems in physics, biology and social science in such bold strokes, and although he concedes that he will appear over-ambitious, Kauffman doesn’t help his cause by inserting occasional purplish passages that seem to betray an urge to write middlebrow fiction. There are also a few points at which the discussion is foggy, tentative and even uninformed – the discussion of semantics is the most obvious example. But the flaws should be forgiven, in recognition of the many places where Kauffman writes with acumen, erudition, clarity and, above all, great originality. A prime instance is his exposition of his ‘first candidate law’.
Living cells are complex biochemical factories in which many different reactions are always going on. Conventional molecular biology studies the sequences of reactions in processes that seem particularly important, like the copying of DNA or the production of proteins out of genes. Kauffman asks a general question: how should we think about the ways in which one state, in which a particular array of genes is ‘expressed’ (i.e. activated), gives way to another state in which a different array is activated? Suppose (ludicrously) that there are just two genes in the array. It then has four possible states: both genes may be expressed (‘on’), both may be ‘off’, the first may be on and the second off, or the first may be off and the second on. It’s not hard to see that if there are 80,000 genes in the array (Kauffman takes this as the number of genes in a human cell, an estimate that now appears about twice as big as it should be), it has 2 to the power of 80,000 possible states, or roughly 1 followed by 24,000 zeroes.
We’re now invited to think about the ways in which the states may succeed one another, which we can represent by rules that tell us how a given state will give rise to a successor. Once again, Kauffman abstracts from the details, and considers general possibilities. Suppose that an organism begins in a particular state, characterised by having such and such genes activated and the rest unactivated. What will happen? Perhaps the organism will now pass through a succession of states of gene activation, ending up with a particular pattern which it thereafter maintains. (Imagine that our two-gene organism goes from a state of having both genes off to one in which both are on, and that this is thereafter maintained.) Or perhaps the organism will go through a sequence of states that culminates in a repetitive pattern (the two-gene organism ends by regularly oscillating between the state in which both genes are off and the state in which both are on). In this instance, we may say that the final behaviour is a cycle, the measure of whose length is the number of states the organism passes through before the pattern repeats itself. If it has 80,000 genes, then the cycle can, of course, be quite long. Chaos (in the technical sense) occurs when the cycles of successive states become very long, and when starting states that are very similar to one another go through sequences that are very different. (Imagine an organism with a large number of genes, and initial states that differ only in the activation of a single gene – one has 40,000 genes on, while the other has the same 40,000 activated and just one more besides. That tiny difference might give rise to highly divergent sequences of later states.)
Drawing on the mathematics of chaos theory, Kauffman points out that organisms which behave in an orderly way but are close to chaos will have cycles of a length close to the square root of the number of genes they contain; those that behave chaotically will have cycles of a length close to the square root of the number of possible states of gene expression. In the former case, using his estimate of 80,000 genes in a human cell, the expected cycle length would be around 270, in the latter a staggeringly large number (1 followed by 12,000 zeroes). Using the standard data on rates of cell division, Kauffman concludes that cycles of 270 states are perfectly possible for organisms like ourselves (we can handle the fact that our cells go through sequences of patterns of gene activation in which about 270 different states occur before they return to the initial configuration), while the staggeringly long cycles would require a time orders of magnitude vaster than the number of seconds that have elapsed since the Big Bang. As he remarks: ‘Not in my body, thank you very much.’
So we have the suggestive conclusion that our cells and those of other organisms are engaged in biochemical behaviour that is about as complex as it can be while remaining co-ordinated. This is only the beginning of Kauffman’s subtle and powerful discussion of the issue, however. He continues to refine his approach by drawing on further mathematical ideas and linking them to experimental data, much of it acquired by himself and his colleagues.
In many other discussions throughout Investigations the same powerful method is at work. Begin with a basic fact about life (or about economic systems). Abstract from the complexities attending on that fact in nature, focusing on some general feature of the situation – like the capacity of genes to be on or off. Think about the general possibilities, and employ a mathematical idiom for representing them. Use that representation to generate surprising consequences. Link those consequences back to the biological (or economic) world.
Centuries before Schrödinger, another great physicist campaigned for the adoption of a similar method in opposition to those who stressed the particularity of natural phenomena. Committed Aristotelians were convinced that no mathematical description could capture the rich diversity of processes of change, among which they counted processes of local motion. Although some of his medieval predecessors had fought in the same cause, Galileo argued successfully for a new style of physics, one that sought to establish mathematical generalisations about the motions of bodies. Molecular biology has shown that we can have a powerful, but particular, science of the mechanisms of life, exposing their detail and diversity, but Kauffman, like Schrödinger before him, longs to find a counterpart to Galileo’s achievement. Much of Investigations contains imaginative developments of a Galilean method; although we cannot yet know whether that method will succeed in establishing precise laws of a mathematical biology (or social science), Kauffman has made a strong case for its promise.