Analogies

I was asked to write about the ‘Evolution of Science’. This is an enormous subject and would take a historian to do it justice. I am not a historian. I am a scientist with a smattering of knowledge about history. I prefer to write about things I know. Here, I tell stories rather than digging deep into the sources of historical truth. I write about astronomy, which is one little corner of science, and about recent events with which I am familiar. I use the recent history of astronomy to illustrate some evolutionary themes, which may or may not be valid when extended to earlier periods or to other areas of science.

My approach to evolution is based on analogies between biology, astronomy and history. I begin with biology. The chief agents of biological evolution are speciation and symbiosis. In the world of biology these words have a familiar meaning. Life has evolved by a process of successive refinement and subdivision of form and function; that is to say, by speciation, punctuated by a process of bringing together alien and genetically distant species into a single organism, i.e. symbiosis. As a result of the work of the biologist Lynn Margulis and other pioneers, the formerly heretical view, that symbiosis has been the mechanism for major steps in the evolution of life, has now become orthodox. When we view the evolution of life with an ecological rather than an anatomical perspective, the importance of symbiosis relative to speciation becomes even greater.

As a physical scientist, I am struck by the fact that the borrowing of concepts from biology into astronomy is valid on two levels.

If evolution is the process of cumulative change then cities can be characterized as metabolisms that adapt over time in order to survive. In this chapter I argue that London, like other complex urban systems, is a fragile and delicate structure that has come full circle in the cycle of evolutionary change. The city is now facing an environmental, social and political crisis that threatens its very existence. Its future cannot be left to processes of random mutation, where market forces determine the policies and shape of its physical fabric. Intelligent forward planning, anticipatory design and government intervention are necessary to avoid the process of gradual decline and eventual extinction that has affected urban cultures in the past.

As the magnitude of the global environmental crisis comes to light, the design and management of our cities (the major consumers of world energy and producers of pollution) are becoming more critical to the survival of the planet. The solution lies in cities such as London becoming sustainable – circular metabolisms that conserve resources, use renewable energies and recycle waste, providing an equitable and stable social environment for future generations.

Sustainable growth

London is not alone in the struggle for urban survival. Human life has always depended on three variables: population, resources and environment. Today, we are the first generation of human inhabitants of the planet to face and be aware of the simultaneous impact of expanding populations, depletion of resources and erosion of the environment. All this is common knowledge, and yet, industrial expansion and urban growth carries on regardless.

This chapter sets itself the modest task of explaining the broad pattern of history on all the continents for the last 13 000 years. Why did history take such different courses for peoples of different continents?

Eurasians, especially peoples of Europe and eastern Asia, have spread around the globe. They and their overseas descendants now dominate the modern world in wealth and power. Other peoples, including most Africans, survived and have thrown off European domination but remain far behind in wealth and power. Still other peoples, including the original inhabitants of Australia, the Americas and southern Africa, are no longer masters of their own lands but have been decimated, subjugated and even exterminated by European colonialists. Why did history turn out that way, instead of the opposite way? Why were American Indians, Africans and Aboriginal Australians not the ones who conquered or exterminated Europeans and Asians?

This question can easily be pushed back one step further. By the year A.D. 1500, the approximate year when Europe's overseas expansion was just beginning, peoples of the different continents already differed greatly in technology and political organization. Much of Eurasia and North Africa was occupied by Iron Age states and empires, some of them on the verge of industrialization. Two Native American peoples, the Incas and Aztecs, ruled over Stone Age or nearly Bronze Age empires. Parts of sub-Saharan Africa were divided among small indigenous Iron Age states or chiefdoms. All peoples of Australia, New Guinea and the Pacific Islands, and many peoples of the Americas and sub-Saharan Africa, lived as Stone Age farmers or hunter–gatherers.

It seemed at first paradoxical to find myself invited to write about ‘The Evolution of the Novel’ since I do not believe that the novel evolved, and have spent some work demonstrating that this is one among a number of misplacements of the evolutionary metaphor – misplacements that have caused confusion (and worse) in other areas of experience (musicology and race-relations are two). But the invitation has allowed me to discriminate between, on the one hand, the effects of this misapplied metaphor on the history of past fiction and, on the other, the creative urgency with which writers have responded to evolutionary ideas in all their contradictory implications – indeed, for their contradictory implications. What has most drawn novelists, I argue, are the tensions within and between Darwinian ideas, as well as the pressures in the relation of such ideas to the human.

Fiction thrives always at points of contradiction, and evolutionary theory offered contradictory stories and contrasting trajectories for interpretation. Was this an account of development or decay? Did development inevitably imply progress, or was this a new version of the Fall? Did evolution make room for disinterestedness or did it necessitate always a ghastly struggle for too few resources? Was it communitarian or individualistic? What made evolutionary theory so fruitful for fiction was not only its coherence but its contradictions. True, it proposed a universalizing theory that would explain the history of all kinds on the earth: descent with modification, predominantly by means of the newly described and named principle, natural selection.

Cosmologists study evolution on the grandest scale of all. They aim to set our earth and our solar system in an evolutionary scheme stretching right back to the formation of the Milky Way galaxy – right back even to a so-called ‘Big Bang’ that set our entire observable universe expanding and imprinted the physical laws that govern it.

Evolution within our galaxy

Let us start with something fairly well understood – the life cycle of our sun, a typical star. About 4.5 billion years ago it condensed from an interstellar cloud, and contracted until the centre became hot enough to ignite fusion of hydrogen into helium. This process will keep it shining until, after another five billion years, the hydrogen runs out. The sun will then flare up, becoming large enough to engulf the inner planets, and to vaporize all life on earth. After this ‘red giant’ phase the inner regions contract into a white dwarf – a dense star no larger than the earth, though nearly a million times more massive.

We are quite confident about these calculations because the relevant physics has been well studied in the laboratory – atomic and nuclear physics, Newtonian gravity and so forth. Astrophysicists can just as easily compute the life cycles of stars with half the sun's mass, or twice, four times, etc. Heavier stars burn brighter, and trace out their life cycle more quickly.

Stars live so long compared to astronomers that we are granted just a single ‘snapshot’ of each star's life. But we can test our theories, by looking at the whole population of stars.

The concept of evolution means different things to different people. To a biologist it simply means genetic evolution, whereas in many other disciplines it can mean change, or unfolding, with time – sometimes with an implicit gradualness to distinguish it from revolution.

This collection of essays is the result of asking eight well-known communicators from separate disciplines to discuss evolution. It will be seen that most of them tell us how the topic has arrived where it has: the Darwinian concept of evolution itself from Stephen Jay Gould; cells and the embryo from Lewis Wolpert; the current human political divide (with a very broad brush) from Jared Diamond; society from Tim Ingold; the universe from Martin Rees; the scientific enterprise from Freeman Dyson; Richard Rogers on the evolution of cities concentrates on the current state of London and Gillian Beer considers whether novels have evolved at all and then tells us how the concept of evolution has permeated through fiction.

The essays were originally given as the Tenth Darwin College Lecture Series in early 1995. These Series have become an institution for some in Cambridge and are open to, and well attended by, the public as well as members of the College and University. The Lectures are intended to be interdisciplinary and to that end we select for each Series a group of well-known communicators, mostly from the academic world, and ask them to talk on a chosen theme. We have now had Origins, the Fragile Environment, Predictions, Communicating, Intelligence, Catastrophes, Colour and now Evolution. A greater appreciation of the overall result can best be obtained by looking at more than one volume.

The evolution of the cell is nature's greatest evolutionary triumph. That may sound rather presumptious when one compares the apparently humble cell with the complexity of organisms such as human beings, with their extraordinary brains. But in evolutionary terms, it was only once the cell had evolved that multicellular organisms became possible. Moreover, I suggest that given the eukaryotic cell – which has a nucleus, contains organelles such as mitochondria, is capable of movement and is itself evolved from the simpler bacteria – the evolution of complex structures, even the brain, was by comparison relatively simple.

Evolution as the modification of development

Development is central to the evolution of multicellular organisms: evolution proceeds by the modification of the embryo's developmental programme to produce differences in the adult. This modification is due to changes in the genes controlling development; they act by controlling cellular behaviour during development. It is by this process that, to use the French molecular geneticist Francois Jacob's phrase, evolution can tinker with embryos, using its bits and pieces to make new structures. This can be seen very clearly when one looks at the early embryos of vertebrates: they all look remarkably similar at one stage (known as the phylotypic stage) and then diverge (Figure 1). Evolution has tinkered with the basic body plan.

A clear example is the limb. While the basic form of the limb has been retained in many land vertebrates, its development has been ‘tinkered with’ to provide the bird's and bat's wings, the horse's leg and our own manipulative hand.

Adaptive continuity

Perhaps there will not always be an England (particularly on time scales favoured by palaeontologists), but a few miles of Channel and nearly a thousand years of freedom from full-scale invasion (1066 and all that) have produced a plethora of British distinctions, both idiosyncratic and deeply philosophical, from continental preferences and modes of thought. (A common language across 3000 miles of ocean can inspire more closeness than twenty miles of La Manche accompanied by a divergence of tongues – hence the similarities between American and British histories of evolutionary thought, as discussed in this article.) In this work, I try to identify adaptation as the most distinctly anglophonic subject of natural history and subsequent evolutionary ideas. I set out to show that Charles Darwin's (Figure 1) decision to site his defence and mechanism of evolution in the explanation of adaptation has roots in a long tradition of English natural history and theology that never provoked much continental attention. Our current struggles over ‘ultra-Darwinian’ versus structuralist modes of thought continue the same debate and establish a particularly English continuity across several centuries.

In the operative paragraph of his Introduction to The Origin of Species, Charles Darwin stated (1859, p. 3) that the classical subjects of natural history could provide sufficient evidence for the factuality of evolution:

Evolution

Many years ago I heard a lecture on evolution by a distinguished geneticist. Holding a stone in his hand, he observed that, were he to let it go, there was a fair degree of certainty that it would fall to the ground. With that, I am sure everyone in his audience agreed. It is equally certain, he then went on to declare, that species have evolved. This beguiling analogy has stuck in my mind ever since, for three reasons. First, declarations of certainty seem an odd place from which to start doing science. After all, it was only because Darwin refused to accept the certainty that species had been created to divine order that we have a theory of evolution at all. Secondly, I was put in mind of the objection lodged by Canon Kingsley, over a century ago, to the claim that there was a similar inevitability about the evolution of society. A dropped stone, Kingsley noted, would not necessarily hit the ground if someone decided to catch it. His point, of course, was that human freedom could not readily be comprehended within a framework of mechanical law. Thirdly, I was moved to reflect that had it not been for a colossal misunderstanding in the history of their subject, brought about through an uncritical extension of widely held ideas about social evolution to the organic domain, contemporary biologists would now be telling us that to believe that species have evolved is profoundly misguided.

Shortly after Robert Grosseteste completed the first full translation of the Nicomachean Ethics into Latin, Albertus Magnus prepared a detailed commentary on it in the course of a series of lectures given in Cologne c. 1250. More than a decade later, Albert returned to the Ethics with a second commentary. Thomas Aquinas was one of Albert's students during the period of the Cologne lectures. In the mid–1206s Aquinas wrote his own commentary on the Ethics, based on a revised Latin translation, which showed the continuing influence of Albert's teaching. The primary intent of both Albert and Aquinas in their commentaries was straightforward clarification and explication of the text. For the most part they resisted introducing their own or orthodox positions in contrast to Aristotle's formulations, even though a detached presentation of this pre-Christian ethical system presented considerable doctrinal difficulties.

There was a great deal in the Ethics, including Aristotle's decidedly mathematical treatment of economic exchange in Book v, that was new and indeed foreign to medieval thinkers. Additional problems of interpreting Aristotle's economic thought were presented to the commentators by the imperfections of the Grosseteste translation and by the many inconsistencies found within the text itself of Book v. The early commentaries of Albert and Aquinas were remarkably successful in clarifying Aristotle's most difficult passages, and nowhere more so than in the chapters dealing with economic exchange. The influence of these first Latin commentaries on the study of the Ethics in general and on Aristotle's economic thought in particular proved long-lasting.

A complex and dynamic vision of the natural world emerged within fourteenth-century natural philosophy and, with it, a cluster of logico-mathematical languages capable of describing and bringing order to this vision. Over the course of the century, the traditional image of a world of hierarchically fixed and absolute values began to dissolve, gradually replaced by a shifting, relational world in which values were in constant flux. As philosophers turned from the investigation of perfections and essences to the investigation of motion and change, questions of measurement and gradation came to dominate scholastic discourse. Since the pioneering work of Pierre Duhem in the early years of this century, historians of science have come to recognize the critical place this shift in philosophical concern played in the development of modern scientific thought. The concluding chapters of this book examine the many ways in which the intellectual process of scientific innovation was tied to the social experience of monetization and market development.

The suggestion that fourteenth-century philosophical speculation was influenced by social developments taking place in the society beyond the schools raises a number of questions. If natural philosophers were deeply involved in the world beyond the classroom and sensitive to its changes, why is the phenomenal world – including the world of social experience – so absent from their speculation? Why in the study of nature to empirical observations play a minuscule part within arguments dominated by technical logic?

Introduction

The differential operator introduced by Dirac in his study of the quantum theory of the electron has turned out to be of fundamental importance both for physics and for mathematics. Essentially the operator is a formal square-root of the wave operator or, with a different signature, of the Laplacian. In this lecture I will attempt to survey its role in mathematics. I will begin with the algebraic underpinnings, which go back to Hamilton and Clifford, and I will then go on to the role of the Dirac operator in Riemannian geometry. In particular I shall discuss various aspects of the index theorem. Finally I will briefly allude to the very recent results on four-dimensional manifolds, arising from new physical ideas of Seiberg and Witten.

Algebraic background

Let us begin by recalling Hamilton's quaternions. These are generated, over the real numbers, by three ‘imaginary” quantities i, j, k, satisfying the relation:

For a general quaternion

We define its conjugate by

Then the norm-squared of x is given by

The quaternions of unit norm form a group (the 3-sphere S3) with the inverse given by

This group acts by left and right multiplication on R4 = C2, giving the two ‘spin representations’ of S3. The group also acts by conjugation

on R3 (the imaginary quaternions, where x0= 0). This gives a double covering

with kernel ± 1.

For three and four dimensions the quaternions provide all one needs to understand spinors (and in due course the corresponding Dirac operator).

By the second half of the thirteenth century, the social conception of a world connected by commerce and held together by a monetarily measured and regulated “flux and reflux of services” was being articulated in the Ethics commentaries of Albertus Magnus and Thomas Aquinas. As the social process of monetization gathered speed, scholastic thinkers expanded Aristotle's geometric model of exchange from its base in personal relationships to a supra-personal system of relations in which aggregate needs and decisions determined value. The great claims Aristotle made for the success of money as a measuring and commensurating medium were expanded as well. In the writings of the most sophisticated economic thinkers of the fourteenth century, the use of money as an instrument of equalization was understood to permit exchangers of unequal social status and occupation, at crossed purposes (each wanting to buy cheap and sell dear), with unequal needs, exchanging unequal goods of unequal value, to arrive, nevertheless, at an approximate equality in their economic transactions – an equality, moreover, sufficient to be named “just.” The monetized marketplace was seen to bind all producers and consumers into a geometrically conceived, self-equalizing system, regulated through a shifting market price determined by common need and estimation.

In order to show that the experience and comprehension of this social context influenced the development of scientific thought, I have been following six clusters of insights, organized into category headings, that in my view characterize the most innovative aspects of both economic thought and natural philosophy in the fourteenth century.

When economics and science are viewed in modern terms as separate and self-contained subjects of inquiry, it is difficult to envision how easily medieval thinkers exchanged approaches, models, and insights between these spheres. Philosophers of the thirteenth and fourteenth centuries show no hesitation in linking their economic thought (at that time considered under the larger heading of scientia moralis) with their speculations on nature. In the Aristotelian system of classification, “practical science” governing the investigation of ethical questions, including the question of justice and just exchange, utilized the same methodology as “theoretical science” governing physical thought; they differed in degree of certainty but not in approach.

The previous chapter outlined social and material developments in the thirteenth century that led to the intensification of monetary consciousness and encouraged the transference of perceptions and techniques from the economic sphere to other spheres of knowledge. From the middle of the thirteenth century this transference was encouraged from within the intellectual culture of the university as well, as the writings of Aristotle came to occupy an ever greater position within the curriculum. Given the great prestige of Aristotle within the university, his mathematical, geometrical, and markedly “scientific” treatment of economic exchange in Book v of the Nicomachean Ethics provided an influential, even authoritative, textual ground for the linking of scholastic economic thought and scientific speculation.

Aristotle's two most concentrated discussions of economic questions are found in Book i of the Politics, chapters 8–11, and Book v of the Nicomachean Ethics, chapters 3–5.