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Convergence - Peter Watson

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Preface: Convergence: The Deepest Idea in the Universe

Introduction: The Unity of the Observable World

Part One

The Most Important Unifying Ideas of All Time

1. The Greatest of All Generalizations

2. A Single Stroke Unifies Life, Meaning, Purpose, and Physical Law

Part Two

The Long Arm of the Laws of Physics

3. Beneath the Pattern of the Elements

4. The Unification of Space and Time, and of Mass and Energy

5. The Consummated Marriage of Physics and Chemistry

6. The Interplay of Chemistry and Biology: The Intimate Connection Between Two Kingdoms

7. The Unity of Science Movement: Integration Is the New Aim

8. Hubble, Hitler, Hiroshima: Einstein’s Unifications Vindicated

Part Three

The Friendly Invasion of the Biological Sciences by the Physical Sciences

9. Caltech and the Cavendish: From Atomic Physics to Molecular Biology via Quantum Chemistry

10. Biology, the Most Unifying Science: The Switch from Reduction to Composition

Part Four

The Continuum from Minerals to Man

11. Physics + Astronomy = Chemistry + Cosmology: The Second Evolutionary Synthesis

12. A Biography of Earth: The Unified Chronology of Geology, Botany, Linguistics, and Archaeology

13. The Overlaps Between New Disciplines: Ethology, Sociobiology, and Behavioral Economics

14. Climatology + Oceanography + Ethnography → Myth = Big History

15. Civilization = The Orchestration of Geography, Meteorology, Anthropology, and Genetics

16. The Hardening of Psychology and Its Integration with Economics

17. Dreams of a Final Unification: Physics, Mathematics, Information, and the Universe

18. Spontaneous Order: The Architecture of Molecules, New Patterns in Evolution, and the Emergence of Quantum Biology

19. The Biological Origin of the Arts, Physics and Philosophy, the Physics of Society, Neurology and Nature

Conclusion: Overlaps, Patterns, Hierarchies: A Preexisting Order?


About Peter Watson

Notes and References


For David Henn and David Wilkinson

It is a wonderful feeling to recognize the unity of a complex of phenomena that to direct observation appear to be quite separate things.


The history of science teaches us again and again how the extension of our knowledge may lead to the recognition of relations between formerly unconnected groups of phenomena.


By tracing the arrows of explanation back toward their source, we have discovered a striking convergent pattern—perhaps the deepest thing we have yet learned about the universe.


We are at a moment of great convergence, when data, science, and technology are all coming together to unravel the biggest mystery yet—our future, as individuals and as a society.


We shall not rest satisfied until we are able to represent all physical phenomena as an interplay of a vast number of structural units intrinsically alike.


Nature is pleased with simplicity.


Everything is made of one hidden stuff.


All of us secretly wish for an ultimate theory, a master set of rules from which all truth would flow.


Reality, in the modern conception, appears as a tremendous hierarchical order of organised entities, leading, in a superposition of many levels, from physical and chemical to biological and sociological systems.


As scientific knowledge advances, previously unrelated phenomena are found to be related.


The universe is orderly. It has certain built-in characteristics that came we know not whence or why but that are determinable and that have not changed during the course of recoverable history.


Reductionism is the primary cutting tool of science.


We have inherited from our forefathers the keen longing for unified, all-embracing knowledge.


The search for the elementary ingredients making up the universe and the deepest laws governing their interactions may be a search that one day draws to a close. The deeper we look, the simpler and more unified the laws become, and there may well be a limit to this process.


Biology presupposes physics but not vice versa.


Once there was physics and there was chemistry but there was no biology.


Mathematics can expose the underlying unity of phenomena that otherwise seem unrelated.


We live in a world orderly enough that it pays to measure.


Our everyday activity implies a perfect confidence in the universality of the laws of nature.


It is now evident that where one discipline ends and the other begins no longer matters.


In every age there is a turning point, a new way of seeing and asserting the coherence of the world.


Science aims both to detect order and to create order.


There can be no explanation which is not in need of a further explanation.




In early April 1912, the Danish physicist Niels Bohr arrived in the bustling city of Manchester in the north of England. When he had first stepped ashore from Denmark, some months previously, he had never imagined working in the industrial heartland of Britain, where the forest of factory chimneys billowed smoke and soot twenty-four hours a day, and where Market Street was said to be the most crowded in all Europe. Instead, his first destination had been the mellow and stately colleges and quadrangles of Cambridge. He had just completed his PhD, in Copenhagen, on the electron theory of metals, and he went to Cambridge to work with J. J. Thomson, the director of the Cavendish Laboratory and the man who, in 1897, had discovered the electron as a fundamental unit of matter, for which he had won the Nobel Prize.

But although Bohr was always very polite about Thomson in his letters home to his fiancée, Margrethe, Niels and JJ—as he was invariably known—didn’t really hit it off. The Dane, a large-boned, heavyset man, had studied English at school, but his spoken syntax was rather stilted and formal and was hardly helped by the fact that he was trying to polish it by reading David Copperfield. Nor did he do himself any favors by attempting to advance his friendship with the director by pointing out several small errors in the other man’s work. For his part, the notoriously absentminded JJ took weeks to read Bohr’s dissertation, which had been translated from the Danish but by someone who wasn’t a physicist. (The phrase charged particles had been rendered as loaded particles.) Thomson, who in fairness was very busy as director of the Cavendish, just didn’t seem overly interested in Bohr or his work.

And so when, shortly after Christmas, Ernest Rutherford came to Cambridge to speak at the annual Cavendish dinner—a riotous affair, mixing lectures and sing-alongs—Bohr was entranced. Rutherford was a down-to-earth, broad-shouldered man with a ruddy complexion and a reputation for swearing at experiments when they didn’t go according to plan. He was a New Zealander who had done postgraduate work at the Cavendish, and then worked at McGill University in Canada, before returning to Manchester, as professor. Rutherford, who had won the Nobel Prize in 1908, for his investigation of radioactivity, had astonished the world of physics for a second time by discovering the basic structure of the atom in May 1911. He showed that it was a bit like a miniature solar system, with a nucleus of positive charge, surrounded at a great distance by orbiting electrons of equal negative charge. (To put this into context, in the atom the proportions of the nucleus to the electron cloud surrounding it are of the order of a grain of sand in London’s Albert Hall. Put another way, if the nucleus were the size of a basketball, the electrons would be about three city blocks away. In real terms, the largest atom is that of caesium, a silvery-gold alkali metal, similar to potassium, discovered in 1860, which is just 0.0000005 millimeters—5 x 10–7mm—across. It would take 10 million of these atoms laid out side by side to stretch between two points of the serrated edge of a postage stamp.)

After hearing Rutherford, Bohr seems to have decided there and then that he wanted to work with him. He arranged a face-to-face meeting via a friend of his father, who lived in Manchester but had worked in Copenhagen. This was a much more successful relationship than the one with JJ—Rutherford later said that Bohr was the most intelligent man he had ever met.

It was the custom of the Manchester laboratory for all the staff to get together each afternoon, late on, for tea—cakes and bread-and-butter laid out on the lab benches. Rutherford led the discussions, perched on a high wooden stool. The discussions were not confined to physics—everything from theater to politics to the new automobiles were legitimate topics—but it was here that Bohr first tentatively advanced his view that, with the basic structure of the atom now being known, it ought to be possible to further our understanding of the elements. Their different properties, he said, should be related to the way the atom is structured, that structure governing why some elements are metal, say, and others gases, why some are reactive and others inert. He suggested that the radioactive properties of matter stem from the nucleus, while the chemical properties arise from the electrons, on the outside.

It was tidy reasoning but there were problems with it. Matter is both stable and discrete: iron is rigid and hard; other elements are liquids or gases. In chemical reactions, one element interacts with another, to produce a third substance, which is both different from the other two and yet in general stable. However, on Rutherford’s model, according to classical physics, no one could understand why the orbiting electrons didn’t lose energy and spiral down and collapse into the nucleus. Where did this stability come from?

When Bohr arrived in Manchester, Rutherford had just returned from a conference in Belgium where he had met for the first time both Albert Einstein and Max Planck. Both of them had introduced into physics the concept of the quantum, the idea that energy comes in small discrete packets and is not continuous, as classical physics had it. This was very controversial at the time, but it gave Bohr the idea that would make him famous. As he wrote later, In the spring of 1912 I became convinced that the electronic constitution of the Rutherford atom was governed throughout by the quantum of action.

After four months in Manchester, Bohr returned to Copenhagen in July to get married. Over the next months he refined his ideas to show that an atom was formed by the successive binding of electrons. One free electron after another would be drawn into the atomic solar system until the number of electrons equalled the charge of the nucleus and the whole system was rendered neutral.1 But, and this was his real advance, he argued that the binding energy existed as discrete packets—quanta—and so electrons could occupy only certain stable states as they orbited the nucleus at different radiuses. Under certain conditions (in chemical reactions, for example), the electron could move between orbits but only by quanta of action, discrete jumps of a minimum size. And so the arrangement of these orbits explained not only the stability of matter but also how the elements differed. The number of electrons in the successive orbits—particularly the outer ones—gave the elements their characteristic properties.

To begin with, Bohr’s ideas were, as some historians of science have put it, intuitive, even philosophical. Rutherford, a dedicated experimentalist who distrusted theory, was nevertheless supportive of Bohr’s efforts and helped him get his ideas into print, in three seminal papers published in 1913. In these papers, known now as The Trilogy, Bohr explained how the elements fitted into the periodic table, how the electrons were arranged on concentric orbits that related to the element’s atomic weight, how one element was related to others, with similar properties, and why some were more reactive than others, depending on the arrangement of electrons in the outermost orbits.

In other words, Bohr had unified physics and chemistry. It was one of the most riveting and important unifications in science and Bohr’s Trilogy led to the award of the Nobel Prize in Physics in 1922.

Or, it would be truer to say, Bohr had almost unified physics and chemistry. At the time of the Nobel ceremony in 1922 there was one uncomfortable, outstanding problem. At that stage a gap in the table of elements occurred at number 72. According to Bohr’s theory, the missing element should be similar to zirconium (number 40) and titanium (number 22), the two elements in the same column of the periodic table, rather than resemble the rare earths that occupied the places next to it. But in May 1922 the question of element 72 took a new and dramatic turn. Scientists in France claimed to have discovered a new rare-earth element, which they placed at number 72 in the periodic system.2 The new element was named celtium, after France. If celtium was a rare earth, it would be a major embarrassment for Bohr’s theory.

When he had departed his native Copenhagen to travel to Stockholm for the Nobel Prize ceremony he had left two colleagues working on the matter. They were investigating zircon-bearing minerals by X-ray spectrographic analysis. Showing a sense of timing that any theater director would be proud of, the two assistants wired Bohr on the evening immediately before the Nobel ceremony to say that the long-missing element had been found at last and that its chemical properties resembled nothing so much as those of zirconium. The new element was given the name hafnium, for Hafnia, the ancient name of Copenhagen. And so, when Bohr gave his Nobel lecture—as all prize-winners do, on the day after the awards ceremony—he was able to announce this latest result, which did indeed confirm that his theory had successfully unified physics and chemistry.

•  •  •

In the same year that Bohr began his work into the structure of the atom, 1913, Andrew Ellicott Douglass launched his researches, which he wouldn’t feel confident enough about publishing until 1928–29. This was the science of dendrochronology, which exploited the links between astronomy, climatology, botany, and archaeology.

In the notebooks of Leonardo da Vinci there is a brief paragraph to the effect that wet years and dry years can be traced in tree rings. The same observation was repeated in 1837 by Charles Babbage—more famous as the man who designed the first mechanical calculators, ancestor of the computer. But Babbage added the notion that tree rings might also be related to other forms of dating. No one took this up for generations, but then Douglass, an American physicist and astronomer, and director of the University of Arizona’s Steward Observatory, made a conceptual breakthrough.

His research interest was the effect of sunspots on the climate of the earth, and like other astronomers and climatologists, he knew that, crudely speaking, every eleven years or so, when sunspot activity is at its height, the earth is wracked by storms and rain—one consequence of which is that there is well above average moisture for plants and trees. In order to prove this link, Douglass needed to show that the pattern had been repeated far back into history. For such a project, the incomplete and occasional details about the weather reported in newspapers, say, were woefully inadequate. It was then that Douglass remembered something he had noticed as a boy, an observation familiar to everyone brought up in the countryside. When a tree is sawn through and the top part carried away, leaving just the stump, we see row upon row of concentric rings. All woodsmen, gardeners, and carpenters know, as part of the lore of their trade, that tree rings are annual rings. But what Douglass observed—which no one else had thought through—was that the rings are not of equal thickness. In some years there are narrow rings, in other years the rings are broader. Could it be, Douglass wondered, that broad rings represent what the Bible calls fat years (i.e., moist years) and the thin rings represent lean years—in other words, dry years?

It was a simple but inspired idea, not least because it could be tested fairly easily. Douglass set about comparing the outer rings of a newly cut tree with official weather records from recent years. To his satisfaction he discovered that his assumption fitted the facts. Next he moved further back. Some trees in Arizona, where he lived, were three hundred years old. If he followed the rings all the way into the pith of the trunk, he should be able to recreate climate fluctuations for his region in past centuries. And that is what he found. Every eleven years, coinciding with sunspot activity, there had been a fat period, several years of broad rings. Douglass had proved his point: sunspot activity—astronomy—weather and tree growth are related.3

But now he saw other uses for his new technique. In Arizona, most of the trees were pine and didn’t go back earlier than 1450, just before the European invasion of America. At first Douglass obtained samples of trees cut by Spaniards in the early sixteenth century to construct their missions. Later, he wrote to a number of archaeologists in the American Southwest, asking for core samples of the wood on their sites. Earl Morris, working amid the Aztec ruins fifty miles north of Pueblo Bonito, a prehistoric site in New Mexico, and Neil Judd, excavating at Pueblo Bonito itself, both sent samples. These Aztec great houses appeared to have been built at the same time, judging by their style and the objects excavated. But there had been no written calendar in ancient North America, and so no one had been able to place an exact date on the pueblos. Sometime after Douglass received his samples from Morris and Judd, he was able to thank them with a bombshell. You might be interested to know, he said in a letter, that the latest beam in the ceiling of the Aztec ruins was cut just nine years before the latest beam from Bonito.4

A new science, dendrochronology, had been born, and Pueblo Bonito was the first classical problem it helped to solve. At that point, by overlapping samples from trees of different ages felled at different times, Douglass had an unbroken sequence of rings in southwest America going back first to AD 1300, then to AD 700. Among other things, the sequence revealed that there had been a severe drought, which lasted from 1276 to 1299 and explained why there had been a vast migration at that time by Pueblo Indians, a puzzle that had baffled archaeologists for decades. Botany had resolved one of the prime problems of archaeology.

•  •  •

A third kind of unification took place in the wake of World War II. One of the prime problems in psychology at that time was the number of homeless children in postwar Europe. France, Holland, Germany, and Russia, in addition to Britain, had all suffered heavy bombing and the disruption of family life that went with it. John Bowlby, a child psychiatrist and psychoanalyst, and head of the Children’s Department at the Tavistock Clinic in London, was commissioned in 1949 to write a report for the World Health Organization on the mental health of these homeless children. Preparation of the report gave Bowlby an opportunity to pick the brains of many practitioners, and he visited France, Holland, Sweden, Switzerland, and the United States.

Bowlby’s international travels set him on a path that would before long result in the unification of pediatrics, psychoanalysis, ethology—in particular the study of animal behavior seen in an evolutionary context—and the hardening of the idea of the unconscious from a philosophical/psychological concept to a firmly based biological entity. His unification of these disciplines came under ferocious attack at the time from psychoanalysts determined to resist his biologification of their discipline. But Bowlby stuck to his guns, and history has vindicated him.

Bowlby’s report was written in six months and published in 1951 as Maternal Care and Mental Health by the WHO. It was translated into fourteen languages and sold 400,000 copies in its English paperback edition. A second edition, entitled Child Care and the Growth of Love, was later published by Penguin.5

It was this report that first confirmed for many people the crucial nature of the early months of an infant’s life, introducing the key phrase maternal deprivation to describe the source of a general pathology of development in children, the effects of which were found to be widespread. The very young infant who went without proper mothering was found to be listless, quiet, unhappy, and unresponsive to a smile or a coo and later to be less intelligent, bordering in some cases on the defective. No less important, Bowlby drew attention to a large number of studies which showed that victims of maternal deprivation failed to develop the ability to hold relationships with others, or to feel guilty about their failure. Such children either craved affection or were affectless. Bowlby went on to show that delinquent groups were comprised of individuals who, more than their counterparts, were likely to have come from broken homes, where, by definition, there had been widespread maternal deprivation.

This was quite an achievement on Bowlby’s part, but then, in 1951, through Julian Huxley, the eminent biologist, he was introduced to the work of the ethologist Konrad Lorenz, particularly his 1935 paper on imprinting. This is a well-known study now, famously showing that if, at a certain critical stage, young geese are exposed to a stimulus (Lorenz himself in the famous case), they will become imprinted on that stimulus. The photographs and film of Lorenz being followed wherever he went by a line of young goslings caught the imagination of everyone who saw it. From then on, Bowlby embraced ethology as a new discipline which could connect with and enrich pediatrics and psychoanalysis and would in time help refine the concept of the unconscious. He was joined at the Tavistock by Mary Ainsworth, a Canadian who moved to London for a time, following her husband’s deployment there, and then on to Uganda and finally Baltimore. There she carried out parallel studies, using a variety of observational techniques, and ethological comparisons with other species (such as mother-child interaction in monkeys), to build up their notion of what became famous as attachment theory.6

The significance of this was that it showed how linking one science with another could amplify understanding, different disciplines supporting each other, and lead to new methods of treatment. Bowlby and Ainsworth’s alignment of pediatrics and ethology placed the mother-infant bond, and the unconscious motivation that results, on a firm and familiar biological basis and, no less important, situated it in an evolutionary context. According to the Bowlby-Ainsworth theory, attachment was an instinctual response (like imprinting) with the function of binding the infant at a critical period to the mother and vice versa, and in so doing promoting the evolutionary fitness of the offspring.7

And, as part of all this, Bowlby said, the child acquires an internal working model of itself as either valued and reliable, or as unworthy and incompetent. This was, for Bowlby, the best way to understand the unconscious. Internal working models are acquired in the first year of life, well before words, and become less and less accessible to awareness as they become habitual and automatic. This is also because, in mainly dyadic patterns of relating (more or less all that are available at that age), the requirements of reciprocal expectancies are formed exceptionally strongly in such a narrow environment.8 What had begun life, before Freud, as a purely philosophical/psychological entity now had a firm biological underpinning.

From the Big Bang to Big History

These three examples—involving very different subject matter, spreading across many countries, and extending over decades—jointly introduce the theme of this book.

Convergence is a history of modern science but with a distinctive twist. The twist has been there for all to see, but so far it has not been set out as clearly as it deserves. The argument is that the various disciplines—despite their very different beginnings, and apparent areas of interest—have in fact been gradually coming together over the past 150 years. Converging and coalescing to identify one extraordinary master narrative, one overwhelming interlocking coherent story: the history of the universe. Among its achievements, the intimate connections between physics and chemistry have been discovered. The same goes for the links between quantum chemistry and molecular biology. Particle physics has been aligned with astronomy and the early history of the evolving universe. Pediatrics has been enriched by the insights of ethology; psychology has been aligned with physics, chemistry, and even with economics. Genetics has been harmonized with linguistics, botany with archaeology, climatology with myth—and so on and so on. Big History—the master narrative of the trajectories of the world’s great civilizations—has been explained and is being further fleshed out by the interlocking sciences. This is a simple insight but one with profound consequences. Convergence is, as Nobel Prize–winning physicist Steven Weinberg has put it, the deepest thing about the universe.

This story of the convergence of the sciences—their synthesis, symphysis, and coherence—turns out to offer one timeline of history on which all of the major discoveries that have ever been made can fit. It is not a straight line by any means but a definite line nonetheless, not unlike a very long and complicated backbone, or spine, which curves and is made up of vertebrae of different sizes. I further argue that the order that emerges from this convergence—and the way one science supports another—gives scientific understanding an unrivaled authority as a form of knowledge and that we should therefore expect it to extend its reach in the years ahead, into fields not traditionally associated with science. In truth, it is already doing so and we should welcome that fact. The proven interlocking nature of science now helps to guide future research.

Not all the links and overlaps in the story are equally strong. Niels Bohr’s amalgamation of physics and chemistry was fundamental, as was the later linking of quantum chemistry to molecular biology, by Linus Pauling and others (chapter 9). In more recent decades, the linking of fundamental particles to the early history of the evolving universe (chapter 11), and the hardening of psychology—the links between behavior and brain chemistry, for example—are no less fundamental (chapter 16). The same too goes for the overlaps that have also been revealed between genetics and archaeology, and between genetics and archaeology and language (chapter 12). At other times, the overlaps—while not exactly trivial—are more helpful and intriguing than fundamental. The example of tree-ring chronology is a case in point, as are some of the other scientific dating technologies that have been developed, the potassium/argon method, for example (chapter 12). They show that not just botany but also physics, molecular biology, and genetics can help us reconstruct history. Importantly, the different dating mechanisms are consistent with one another, so that ancient history in particular is now an interdisciplinary branch of science.

But—and this is the underlying point—all the connections and overlaps, all the patterns and hierarchies that have been revealed, whether fundamental or otherwise, dovetail together conceptually. There are no exceptions, no important ones anyway. Scientific discoveries repeatedly come together, in all manner of ways, to support one another, to tell one coherent, interlocking story. In an important sense, and to use another analogy, it is as if this story has its own form of gravity as—like particles in cooling gases—the different chapters come together to form a solid narrative.

That narrative leads from the origins of the universe in a Big Bang 13.8 billion years ago, up through the creation of elementary particles, the formation of the lighter then the heavier chemical elements, the formation of the stars and planets, including our own sun, the evolution of the broad structure of the universe (the way the galaxies are laid out), of the gases that coalesced to comprise the rocks of the earth, how those rocks align in the way that they do, how the earth has aged, how the ice ages have come and gone, why the continents are arranged around the globe as they are, why the oceans circulate the planet in a particular pattern, where and when primitive forms of life developed, how ever more complex molecules and organisms came to be, how sex evolved, why trees and flowers take the form that they do, why leaves are green, why some animals have six limbs and others four, why the plants and animals (including people) are distributed across the earth in the way that they are, how major catastrophes have given rise to widespread myths and shape our beliefs, how accuracy developed and became important, how and why and where science itself emerged, culminating (so far) in humankind and the very different civilizations that populate the globe. Indeed, this one story shows why there are different civilizations that populate the globe where they do. The convergence of the sciences helps us explain the greatest single story there could be—Big History.

An Epic Detective Story and a New Dimension

I do not, however, tell the story by beginning at the beginning and ending at the end. It is much more revealing, more convincing, and altogether more thrilling to tell the story as it emerged; as it began to fall into place, piece by piece, chapter by chapter, converging tentatively at first, but then with increasing speed, vigor, and confidence. The overlaps and interdependence of the sciences, the patterns and hierarchies of the discoveries in different fields, the underlying order that they are gradually uncovering, is without question one of the most enthralling aspects—perhaps the most enthralling aspect—of modern science. It is in effect a collective detective story of epic dimensions. The convergence and the emerging order—even a kind of unity—between the sciences is one of the most important and satisfying elements in scientific knowledge, and all the more convincing because nobody went looking for it in the first place.

Nor do I begin, as many science histories do, in ancient Greece, the so-called Ionian Enchantment, or with the discoveries of Copernicus and Galileo, or with the scientific revolution of the seventeenth century. I begin much later, in the 1850s—a crucial decade as I show—because that is when the convergence began, when the interconnections and overlaps between the various disciplines first started to show themselves in two fundamental areas and so added a whole new dimension to science, one that hadn’t been fully grasped until then.

It was in the 1850s that the idea of the conservation of energy was first aired, which brought together recent discoveries in the sciences of heat, optics, electricity, magnetism, food, and blood chemistry. Almost simultaneously, Darwin’s theory of evolution by natural selection brought together the new sciences of deep-space astronomy, deep-time geology, paleontology, anthropology, geography, and biology. These two theories comprised the first great coming together, meaning that the 1850s was in many ways the most momentous decade in the annals of science, and possibly, as it has turned out, the years which saw the greatest intellectual breakthrough of all time: the realization of the way one science supports another, the beginning of a form of understanding like no other. This was in every way a new era intellectually.

I am not aware that anyone has told the history of science, or the history of the universe, in quite this way before. This is the distinctive twist that, I suggest, sets this science history apart.

I am aware that some historians of science, social scientists, and philosophers object to the very idea that there is unity or order in the sciences. But I argue that the story of convergence and the emerging order described in this book speaks for itself, and I address several of their objections in the Conclusion.

The idea that the sciences are linked in some hierarchical way is not new, of course, and is known as reductionism. Although reductionism has been criticized—especially in the last twenty to thirty years, even as the evidence in its favor has grown stronger than ever—for the most part, leading scientists themselves have overridden these objections. Such figures as George Gaylord Simpson, Philip Anderson, Ilya Prigogine, Abdus Salam, Steven Weinberg, and Robert Laughlin (the last five being Nobel Prize winners) have all described themselves as wholehearted reductionists. Edward O. Wilson, the noted sociobiologist, put it this way: Reductionism is the primary cutting tool of science.

As this book was being finalized, there came the news that researchers had inserted two small silicon chips into the posterior parietal cortex of a tetraplegic individual, ninety-six microscopic electrodes that could record the activity of about a hundred nerve cells at the same time. Based on previous work with monkeys, which guided the researchers to a specific area of the human brain, they found that they could reliably read out where the patient intended to move his paralyzed arm by analyzing the differing patterns of these hundred cells. This information was then used—bypassing his damaged spinal cord—to enable him to direct a robot arm either to pick up a beer or move a cursor on a computer screen. The researchers could even predict how fast he wanted to move, and whether he wanted to move his left or right arm. In a related experiment, by showing the activity of a single nerve cell on a screen, the patient was able to modulate the cell activity. The experiment was very specific. One nerve cell, for example, would increase its activity when he imagined rotating his shoulder, and decrease its activity when he imagined touching his nose. The specificity of this experiment, and the fact that it could throw light on the man’s intentions, not just his actual movements, offers great hope for the future, but from our point of view it takes reductionism to a new level, uniting still further psychology and physics.

The Beauty of Deep Order

That said, there is no final order yet, and there may never be. But the order that has emerged already is impressive enough. Order, in particular spontaneous order, is now a major interest of science (chapter 18).

And of course the story of this book is more than just a narrative—for there are two deeper implications of the order that convergence is producing.

The first is that alluded to earlier. Because the convergence—the emerging order—is so strong, and so coherent, science as a form of knowledge is beginning to invade other areas, other systems of knowledge traditionally different from or even opposed to science, and is starting to explain—and advance—them. Science is invading—and bringing order to—philosophy, to morality, to history, to culture in general, and even to politics (see chapters 14, 15, and 19). Critics object that this is a form of intellectual imperialism, but our newspapers are peppered every day with reports, for example, of the latest psychological research having a bearing on our honesty, generosity, trustworthiness, proneness to violence, and much else. This genie can’t be put back into its bottle.

It is not too much to say that the overall coherence and order revealed by the convergence of the sciences is ushering in a new phase of history. No other form of knowledge has the coherence and order that the converging sciences have brought about. The methods and infrastructure of science are invaluable, are indeed unrivaled aspects of modern democracy, and will shape society in all its manifestations even more in the future than they have in the past, and rightly so. This is a quintessentially contemporary story.

The second aspect of the order that is emerging relates to order itself. Order, the way even inanimate matter spontaneously organizes itself in nature (without, it should be said, any input from a supernatural power), has emerged in recent decades as one of the most important new topics. The very idea that there is a preexisting order in nature—a deep order underlying even chaoplexity (a mix of chaos and complexity), as appears to be the case—sounds itself very much like a philosophical conundrum as important as any other. Spontaneous order is being explored by physicists, chemists, biologists, and mathematicians and has been found to occur among elementary particles, among molecules, in complex systems, in living things, in the brain, in mathematics, even in traffic. All of which gives an idea of how central the subject now is (chapters 17 and 18). A breakthrough in this area could have breathtaking consequences, not least for our understanding of evolution (chapter 18).

And so there is no other story quite like the one told in this book. Convergence is, as Steven Weinberg says, and without exaggeration, the most fundamental story that could ever be imagined.

Nor, finally, should we overlook the fact that the way the sciences are coming together may offer comfort of a kind. Not quite a religious comfort perhaps, but the converging sciences—the emerging order in nature—certainly appears to offer an intellectual/philosophical satisfaction, a form of beauty almost and, yes, for the time being at least, a mystery as to what that underlying order might ultimately mean. In this, the converging sciences sustain their power to thrill.



We begin in the mid-nineteenth century, and in the most unlikely of places. Walking on a beach in Cornwall in 1852, a passerby chanced upon a length of driftwood that had been washed ashore following a recent storm. There was writing on the plank. It read: "Mary Somerville." The ship of that name, which had been commissioned in 1834, had plied between Liverpool, India, and China, carrying cotton, tea, and flour. She had foundered on a return journey shortly before.

In that year, 1834, a wealthy Liverpool shipbuilder, William Potter, had asked the real-life Mary Somerville if he could name a merchant ship in her honor and, at the same time, obtain a copy of a bust that had been made of her for use as a figurehead of the ship. The original bust, recently completed, had been carved by Sir Francis Chantrey, the celebrated society portrait sculptor, whose other subjects included such eminences as King George III, King George IV, Prime Minister William Pitt the Younger, President George Washington, and scientists James Watt and John Dalton. The bust had been commissioned by the Fellows of the Royal Society of London and placed in the society’s great hall.1

There was never any question that, as a woman, Mary Somerville would be elected to the Royal Society as a fellow—women were not allowed even to attend lectures there until 1876. But, as the commissioning of the bust and the dedication of the merchantman testify, she had nonetheless made her mark. And though it is unusual, it is by no means unsatisfactory to begin a book about science with an account of a remarkable woman, who so admirably introduces our theme.

She was born Mary Fairfax in Jedburgh, on the Scottish borders, in December 1780. Her mother had only just returned from waving off her husband—a naval officer—on a series of voyages from which he would not return until Mary was a girl of eight. During the intervening years, she received no formal education and was allowed to run wild. When her father eventually returned home, he was alarmed to find that Mary had failed to master the skills of reading, writing, and account-keeping that would make her a suitable wife and so sent her away to boarding school, where she was taught dancing, painting, music, cookery, needlework, and elementary geography.2

She had a more serious cast of mind, however, and taught herself algebra, using puzzles set in popular magazines as a way to begin. Mary found that she had a natural aptitude for mathematics. An avid book lover, she had no fortune to speak of but was fortunate in being beautiful, and at twenty-three, she married. She and her husband, Captain Samuel Greig, set up home in London, where he held a commission in the Russian Navy and was Russian consul. They had two sons, but Mary was lonely inside the marriage, and when her husband died suddenly, although she was inconsolable at first, she returned to Scotland.3 Here, now having a small income deriving from her late husband’s position, she was able to cultivate the kind of life she preferred. All the more so after she met her cousin, William Somerville, who soon proposed. This was a much better match. Both held liberal views on politics, religion, and education and both were interested in science. William, a military doctor, had done pioneering work on natural history and ethnological exploration in South Africa (plus some other, more secret, military duties).

The Most Extraordinary Woman in Europe

It was now that Mary’s intellectual life really began to take off. The couple moved first to Edinburgh. This was the time of the Scottish Enlightenment; many of the men there had liberal views about the role of women, and among the individuals with whom she could share her interest in mathematics were the likes of James Hutton and John Stuart Mill. This was the heyday of the Edinburgh Review, one of the best periodicals in Britain, or anywhere, but in the early nineteenth century the reformers of British science had launched a new journal, which focused on mathematical challenges (this was a fashion of the times). The publication was entitled New Series of the Mathematical Repository, and in June 1811 Mary was delighted to learn that she had won the Prize Question, for which she received a silver medal with her name engraved on it.4

James Secord, the Cambridge-based historian of Victorian science, says that Mary felt most intensely alive and completely herself in mathematics. For her, he writes, the practice of mathematics was a form of theological engagement. . . . For Somerville, the divine transcendence of God’s power could most fully be experienced by those who—like herself—understood the language of mathematics. Or, as she herself put it, These formulae, emblematic of Omniscience, condense into a few symbols the immutable laws of the universe. This mighty instrument of human power itself originates in the primitive constitution of the human mind, and rests upon a few fundamental axioms which have eternally existed in Him who implanted them in the breast of man when He created him after His own image. Mary was from the start interested in how the manifest diversity of the world could be reduced to those few fundamental axioms.

Then she and William moved to London, where they became well known among those with scientific interests: at least twenty-six of their regular friends were Fellows of the Royal Society, possibly the most distinguished corps that any author ever commanded during a lifetime.5 Mary Somerville took this in her stride. She was well connected socially but became famous, says Allan Chapman, in his biography, via her letters, by her conversation, and by the fact that everybody in intellectual London knew of this singular woman who had mastered the most abstruse mathematics of the age, and had acquired from her studies a sophisticated grasp of how physical science worked. Sir David Brewster, a physicist and mathematician who was principal of both St. Andrews and Edinburgh universities, described her as the most extraordinary woman in Europe.6

In the long run, two things set her apart, in addition to that grasp of mathematics. Like other Grand Amateurs of the day, she took part in simple experiments, in her case into the connection between magnetism and sunlight.7 This was in the excited wake of Hans Christian Ørsted’s discovery of a connection between magnetism and electricity (see chapter 1), and the results she obtained were interesting enough for William, her husband, himself an FRS, to read her account of them before the Royal Society. The papers were subsequently published in the society’s Philosophical Transactions and in that way were made available to a much wider range of readers. Offprints were sent to such figures as the astronomer Pierre-Simon Laplace and the chemist Joseph Louis Gay-Lussac in Paris, and to Ørsted himself in Copenhagen.

On the strength of her accomplishments, Henry Brougham suggested that Mary contribute an account of Newton’s Philosophiae Naturalis Principia Mathematica and Laplace’s famous book on the heavens, Mécanique céleste, to the publishing program of the Society for the Diffusion of Useful Knowledge. Brougham—an eccentric Scottish lawyer who was a guiding spirit behind the 1832 Reform Act, and was one of those individuals who had a finger in every pie—had founded the SDUK in 1826 with the aim of spreading knowledge until it has become as plentiful and as universally diffused as the air we breathe. The SDUK published cheap books in weekly parts, topics ranging from brewing to hydraulics and from insects to Egyptian antiquities. Its most successful venture was the weekly illustrated Penny Magazine, which at its peak achieved a circulation of more than 200,000.8

The first books that Mary wrote were too detailed and too thorough for a penny magazine readership and so not at all suitable for the SDUK. She told Brougham along the way that her book would have to discuss the calculus, so that was bound to limit its appeal. But John Murray, the London publisher, who was himself a fixture on the intellectual scene in the capital, snapped it up, and so began Mary’s successful writing career in science, the second thing that set her apart from other women. In all she wrote five books, Mechanism of the Heavens (1831), On the Connexion of the Physical Sciences (1834), Physical Geography (1848), On Molecular and Microscopic Science (1869), and Personal Recollections (1874, posthumous).

The book that concerns us is the second one, On the Connexion of the Physical Sciences, generally regarded as her most important work. She was preparing it at the peak of her renown, when the Chantrey bust for the Royal Society was being carved and when, a year later—to the envy of many—she was awarded an annual pension of £200 by the government for her services to science. (It was later increased to £300, the same as Michael Faraday and John Dalton received.)

The argument in Connexion was sharper then than it might seem now. Its aim was to reveal the common bonds—the links, the convergence—between the physical sciences at a time when they were otherwise being carved up into separate disciplines. Mary was very deliberately her own woman.

Demonstrating the Unity of the Observable World

The professed aim of her book, embodied in the title, was to draw together a range of subjects in the physical sciences that were undergoing unprecedented change. Secord again: "Through its wide readership, Connexion became a key work in transforming the ‘natural philosophy’ of the seventeenth and eighteenth centuries into the ‘physics’ of the nineteenth, demonstrating the unity of the observable world."

A key work, indeed, as we shall see, but not quite the first. The desire for an all-embracing vision, even for a cosmic order, is an ancient concern, dating at least from Aristotle, the so-called Ionian Enchantment. The great chain of being, derived from Plato, Aristotle, and others, specified a hierarchy which ranged from nothingness through the inanimate world, into the realm of plants on up through tame and wild animals and then humans, and above that through angels and other immaterial and intellectual entities, reaching at the top a superior or supreme being, a terminus or Absolute. In the Middle Ages, in his Summa Theologica, Thomas Aquinas had attempted to reconcile Aristotle’s science and Christianity. Four hundred years later, Newton brought order to the heavens and other matters, like motion and light. The Enlightenment held to the idea of the unity of all knowledge, Descartes had a vision of knowledge as a system of interconnecting truths that could eventually be abstracted into mathematics, Condorcet pioneered the application of mathematics to social science, while Schelling proposed a cosmic unity of all things, even though he thought it was beyond the understanding of man. Linnaeus attempted to order the living world in Latin.

Somerville’s approach was much more modern. What she wanted to write about seems to have been clear in her own mind, but the term the physical sciences, which she used in her title, was only then being formulated. By that time, several philosophers had tried to make physics more unified and coherent, of whom the most successful were John Playfair (1748–1819) and John Herschel (1792–1871). As early as 1812, in the first volume of his Outlines of Natural Philosophy, Playfair aimed frankly to have the elementary truths of Natural Philosophy brought into a small compass, and . . . arranged in the order of their dependence on one another. He distinguished natural philosophy from chemistry. Under natural philosophy he grouped dynamics, mechanics, statics, hydrodynamics, astronomy, optics, electricity, and magnetism. His view—widely shared—was that gravitation was the single principle which pervades all nature, and connects together the most distant regions of space, as well as the most remote periods of duration. Playfair thought it probable that a similar principle obtained for non-gravitational matter.9

In his Preliminary Discourse on the Study of Natural Philosophy (1831), Herschel used force, motion, and matter as the basis of categorization of the sub-branches of science. He thought there were two great divisions of the science of force—dynamics and statics—and the subdivisions were: mechanics, crystallography, acoustics, light and vision, astronomy and celestial mechanics, geology, mineralogy, chemistry, heat, magnetism, and electricity. As this shows, people were groping for similarities, but not really finding them. It was a time when the differences between substances and processes were still being explored.

Mary Somerville would also have been aware that the French since the late eighteenth century had recognized "la physique . . . as a branch of science separate from mathematics on the one hand and chemistry on the other. The properties of matter, heat, light, electricity, and magnetism, plus meteorology, comprised la physique."

Connexion was therefore a sort of climax to what was in fact a somewhat untidy and unformed nineteenth-century movement to put some unity into natural philosophy. Her book was forceful, and reviewers praised it for exactly that—for bringing the physical sciences together in a new way. The Mechanics’ Magazine held the book so important that they said it should not be on a bookshelf at all. Instead of that we say—Read it! Read it! James Clerk Maxwell, whose great works we shall meet in chapter 1, said Connexion was among those suggestive books, which put into a definite, intelligible, and communicable form, the guiding ideas that are already working in the minds of men of science, so as to lead them to discoveries, but which they cannot yet shape into a definite statement.10

Somerville presented mathematics as the most promising source of ultimate unity, though she accepted that meant it would only ever be available to a very few. With this in mind, she therefore advanced her argument about mathematics without using a single equation.

She wrote most of the book in secret, uncertain of how its female authorship would be received, though she was already celebrated across Europe for her mathematical accomplishments (which is why Brougham had suggested the SDUK project in the first place). And, as Joanna Baillie, the Scottish poet and dramatist, pointedly remarked, Somerville had done more to remove the light estimation in which the capacity of women is too often held, than all that has been accomplished by the whole sisterhood of poetic damsels and novel-writing authors.11

The first edition of two thousand copies was priced at seven shillings and sixpence and quickly sold out, the book remaining in print for over forty years, in ten editions. It was translated into German, French, and Italian, and publishers in Philadelphia and New York issued pirated editions. The Athenaeum conceded that the book was at the same time a fit companion for the philosopher in his study and for the literary lady in her boudoir.

The Search for Meaningful Patterns and Increasingly Higher Levels of Generalization

The Connexion of the title was further explained in a preface: The progress of modern science, especially within the last five years, has been remarkable for a tendency to simplify the laws of nature, and to unite detached branches by general principles. In some cases identity has been proved where there appeared to be nothing in common, as in the electric and magnetic influences; in others, as that of light and heat, such analogies have been pointed out as to justify the expectation, that they will ultimately be referred to the same agent; and in all there exists such a bond of union, that proficiency cannot be attained in any one without knowledge of the other. And she concluded: Innumerable instances might be given in illustration of the immediate connexion of the physical sciences, most of which are united still more closely by the common bond of analysis which is daily extending its empire, and will ultimately embrace almost every subject in nature in its formulae.12

Kathryn Neeley reminds