The Equations of Life

How Physics Shapes Evolution


By Charles S. Cockell

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A groundbreaking argument for why alien life will evolve to be much like life here on Earth

We are all familiar with the popular idea of strange alien life wildly different from life on earth inhabiting other planets. Maybe it’s made of silicon! Maybe it has wheels! Or maybe it doesn’t. In The Equations of Life, biologist Charles S. Cockell makes the forceful argument that the laws of physics narrowly constrain how life can evolve, making evolution’s outcomes predictable. If we were to find on a distant planet something very much like a lady bug eating something like an aphid, we shouldn’t be surprised. The forms of life are guided by a limited set of rules, and as a result, there is a narrow set of solutions to the challenges of existence.
A remarkable scientific contribution breathing new life into Darwin’s theory of evolution, The Equations of Life makes a radical argument about what life can — and can’t — be.



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Extra-Terrestrial Liberty: An Enquiry into the Nature and Causes of Tyrannical Government Beyond the Earth

Space on Earth: Saving Our World by Seeking Others

Impossible Extinction: Natural Catastrophes and the
Supremacy of the Microbial World

An Introduction to the Earth-Life System

Biological Processes Associated with Impact Events

Ecosystems, Evolution, and Ultraviolet Radiation




Image of Lesser Mole-Rat (Nannospalax leucodon)

by Maksim Yakovlev.




SOME OF THE MOST fascinating questions whose answers still remain obscure to science lie at the interface between traditional fields. Of course, disciplines are not real entities. They are artificial constructs made by people. Collecting scientific questions into neat disciplinary boxes is administratively useful but artificial and sometimes intellectually counterproductive. The unguided processes of the cosmos do not recognize these neat divisions, either. There is just the universe, about which a civilization can ask questions.

This book explores one line of thinking that tries to make sense of diverse areas of science that straddle the living and the nonliving, the indefeasible links between physics and evolutionary biology. The connections reflect the reality that life is just a form of reproducing, evolving matter in a universe with many interesting and distinctive types of matter.

The reader should know from the outset that this book is not a sterile attempt to demonstrate that evolution is an utterly predictable product of physics. Historical quirks and chance do play a part, and that point is indisputable. They result in the remarkable plethora of detail and the kaleidoscope of forms that we observe in the great evolutionary experiment occurring on our planet. Travel to the Indonesian islands of Lombok and Bali, and despite their similar size, location, and a mere thirty-five kilometers between them, the fauna of each island is distinct. Life on the islands is the evolutionary progeny of that invisible Wallace Line that carves through the deep waters of the Lombok Strait, placing Bali within the historical trajectory of Southeast Asia’s particular evolutionary journey. Bali’s forests echo with the calls of Asian woodpeckers and barbets, while Lombok, alive with the shrill cries of cockatoos and honeyeaters, lies within the fold of Australasia’s evolutionary umbrella. But lurking within this riot of evolutionary experimentation are unyielding principles of physics. It is those that concern me in this book, principles that have increasingly explained many facets of biology, from the subatomic scale to whole populations—biological observations that were previously assumed to be flukes of history and beyond prediction.

Which features of life are deterministically driven by physical laws and which are mere chance, contingent events decided by a metaphorical role of the dice? This question remains one of the most cogent and interesting puzzles about life and its evolution. I do not intend to provide a definitive answer to this question; I’m not convinced anyone currently has the knowledge to do so. However, I do intend to shed light on the growing understanding of the principles that channel life at all levels of its structure and how this expanding corpus of work shows that life is firmly embedded within the basic laws that shape all types of matter in the universe, much more so than a cursory glance at the menagerie on Earth might suggest.

From this view of life emerge conclusions that some people might find sobering, others might find frightening, and still others thrillingly comforting. For people who share with me a fascination for life on Earth, there is something reassuring about our increasing ability to demonstrate that the apparently fathomless profusion of living things on this planet conforms to simple principles that apply to all other types of matter. For those people who also enjoy speculating about what life on other planets might look like (if it exists at all), a conclusion might be that at all levels of its structural hierarchy, alien life is likely to look strangely similar to the life we know on Earth.

As we let go of many of our ancient traditions of thought that have separated life from inanimate matter, we may find that our fear that this will dangerously consign people and other creatures to what is often viewed as the blandness of physics that determines the fate of most matter in the universe is unfounded. Instead, the unity of evolution and physics brings a new richness to our view of life, an appreciation that within the simplicity of rules that govern and limit the forms of living things there is remarkable beauty.



A SHORT WALK THROUGH the Meadows in Edinburgh would leave most people in little doubt that life on Earth is a remarkable anomaly in a universe of bland conformity. Trees of various shades of green rustle in the wind, birds take to the air in gymnastics that left the ancients aghast at the agility of these heavier-than-air flying machines, and along the ground run all manner of animals; the smallest ladybugs land on picnicking tourists, while domestic dogs leap and cavort across the grass.

Compare this spectacle with the velvet black emptiness of space seen with some of our best telescopes. Images of galaxies colliding in astrophysical violence, the light of these long-since-dead encounters collected after traveling billions of years through an empty void almost unimpeded. In this vast, infinite vacuum, punctuated by a collection of stars, planets would materialize. And on one planet, tourists would be swatting flies in a meadow below a castle. What could be more of a contrast between the apparently simple laws that govern the gravitational rotation of a collection of stars—mere balls of fusing gas in the rarefied expanse of space with their attendant planets—and the unpredictable leaps and bounds in something as complex as a pet Labrador, the phenomenon of life?

I once heard a distinguished astrophysicist declare that he was glad to be studying stars, since a star is much easier to understand than an insect.

As we peer into outer space, we can certainly find merit and empathy in this view. Even at the intimidating scale of a massive star, we find simplicity. As the star burns, fusing gaseous elements and releasing energy, so these building blocks successively grow in atomic mass. We begin with hydrogen atoms, the universe’s most abundant element, which joins with other hydrogen atoms to form helium. Other helium atoms combine to form carbon and so on, until successive layers are formed—oxygen, neon, magnesium; the atomic mass of the elements grow as the products of each new round of fusion are formed. In the center of the star is iron, which cannot fuse to form any other elements. Iron is the last stage of fusion, and the result of this sequence of relatively simple atomic additions is layer upon layer of heavier and heavier elements from the surface to the core of the star. Elements heavier than iron are formed by other means, such as in the catastrophically energetic explosions of stars that herald the spectacle of a supernova.

Compare the onion-like arrangement of elements in a massive star, over a million kilometers in diameter, to our ladybug (a ladybird in many places in the world), just seven millimeters long, sitting on the thumbnail of a sleeping tourist in the Meadows.

The little oval ladybug, a beetle, is just one insect among many species that inhabit the planet. (We do not know how many species there are. About a million are known, and there are likely to be many more still undiscovered.) However, this unassuming creature is full of complexity and comprises eight major parts. Its head is one discrete portion and contains its mouth. The ladybug has antennae and eyes for sensing the world around it, with the antennae considered a separate part. The pronotum, a tough protrusion behind the head, protects it from damage. Behind this are the thorax and abdomen, the body section to which the wings and legs are attached. Finally, this complex machine has elytra, wing cases that protect its vulnerable and delicate flying apparatus.

Yet like the star, each of these features is molded by physical laws. The power of flight conferred by wings means the ladybug must observe the laws that govern aerodynamics, as must all flying creatures. And as for its legs—well, why not wheels? Like all land animals, besides snakes and some lizards that lack limbs altogether, ladybugs evolved legs instead of wheels. There are physical reasons for that, rooted in the relative effectiveness of legs in navigating the irregular terrain of our planet. In protecting their gossamer wings, the elytra must observe rules that pertain to the behavior of tough materials, such as abrasion resistance and flexibility.

In all segments of the ladybug, we can identify the principles of physics. The apparent complexity of the ladybug compared with a star lies merely in the greater number and variety of principles embedded within the insect and which it uses to live its life. Evolution is simply a very good process for assembling different principles, which we can represent as equations, into an organism. Any natural environment usually presents multiple challenges to survival. If a physical process leads to a living thing’s development of a characteristic that makes the living entity less likely to be eliminated before it reproduces (reproduction being the measure of evolutionary success), then creatures will evolve over time and can be thought of as containers manifesting diverse physical laws.

The menagerie of life, impressive enough even on a casual walk in the Meadows, grows in variety as you explore its forms through time. Equipped with every scientist’s favorite improbable toy, the time machine, we might revisit the Meadows 70 million years ago. Then, we would find forms of life very different from today. Like modern birds, the reptilian pterodactyls had mastered aerodynamics, some with ten-meter wingspans. Feathered dinosaurs and strange insects roamed the land, and in ponds or lakes, reptiles, slender and long, achieved mastery in their watery habitats. If we hop back into our machine and return to about 400 to 350 million years ago, we would find Edinburgh in the site of immense volcanic activity, thick mat-like conglomerations of microbes growing here and there. Across the land, between the volcanic cones, the earliest land plants, the Cooksonia, stake their claim to the new habitat. Scurrying among their short knobbly stems of just a few centimeters’ height were early insects and the now extinct eight-legged beetle-like trigonotarbids. Return just a few tens of millions of years later and you would have seen four-legged Pederpes, a forerunner to modern land vertebrates, awkwardly shifting its one-meter-long slithery body through the undergrowth, peering this way and that with its triangular head to chart its way through.

But impressed though we may be with all the wonderful life forms we have observed in our excursion through time, there is a strange familiarity about all these living things. Their shapes and forms, although different, share fundamentally the same types of solutions to living as we see in modern forms. These similarities are not merely an artifact of evolutionary descent. The growth of early plants against gravity, the size of bones that hold up a dinosaur, the sleek shapes of water-bound animals, and the features of wings that allow a pterodactyl to fly lead to evolutionary forms similar to modern-day organisms faced with the same unyielding laws.

The complexity and sheer diversity of life in time and space could convince anyone that life represents something quintessentially different from physical processes, a divergence of form that transcends the simple principles that seem to fashion the apparently predictable structure of the inanimate world.

Yet physical laws restrictively drive life toward particular solutions at all levels of its assembly. The outcomes are not always predictable, but they are limited. It does not matter at what level those requirements are operating, from the subatomic to the population scale: the results are various, but not boundless.

Even at the smallest scale, we can see these narrow channels of evolution. Consider molecules, such as the proteins, from which the eclectic mixture of monsters on Earth is assembled. Like life at the larger scale, proteins do not display untrammeled potential. Rather, in observing the limited ways that proteins (including enzymes, biological catalysts) can be folded together, some scientists have argued that these configurations reflect a set of forms analogous to the perfect and unchanging forms of things espoused by Plato. To some people, such a view seems to contradict the Darwinian view of life, which emphasizes natural selection’s tendency to produce apparently unlimited variety.

Science can sometimes be unnecessarily polarized, and, of course, challenging the Darwinian view is always popular, edgy, and controversial. In the synthesis I present here, there is no challenge to Darwin’s basic precept that natural selection can fashion an extraordinary range of creatures or even proteins. I merely illustrate how this process is limited in the basic pattern of its products, not just at the level of the organism, but in any part of its construction, from populations down to proteins and down to the atomic level. I gather evidence from what has become an impressive corpus of work by many researchers to show how physical principles sharply narrow the scope of the evolutionary process at all levels of life’s structure.

My view is underpinned by a simple proposition. Evolution is the process by which the environment acts as a filter to select units of organic mass in which a mosaic of interacting physical laws are optimized sufficiently to allow for reproductive success. The environment in this context can include a whole range of challenges—from weather phenomena such as storms to the appetites of predators— that might prevent an organism from reproducing. Evolution is just a tremendous and exciting interplay of physical principles encoded in genetic material. The limited number of these principles, expressed in equations, means that the finale of this process is also restrained and universal.

Equations are merely a means to express in mathematical notation the physical processes that describe certain aspects of the universe, including features of living things. The phrase equations of life is shorthand for this growing capacity to use physical processes, and often their mathematical formulations, to describe life at different levels of its hierarchy. Throughout this book, I will provide some examples of these equations, but I do not expect you, the reader, to have to understand their nuances and details or how to use them. I show them to illustrate how physical principles that underlie evolution can often be expressed in these conveniently shortened mathematical forms.

That the laws of physics should bound life is hardly a controversial statement. The ladybug in the Meadows does not exist outside the same principles that govern the formation of the Sun that warms it on a sunny day. Life is very much part of the universe: it cannot operate outside its rules. Yet although this observation seems trite, we are often remarkably unwilling to accept the extent to which life is tightly constrained by physical laws. When observing living things, we can easily forget that the rules that govern their architecture set a harsh perimeter; the extravagance of life can appear, to the unreflective observer, to be limitless in its variety.

For me, what is surprising about the journey through the different scales of life’s structure, accompanied by our growing knowledge, is that life is much more amenable to description in terms of physical processes, and thus simple mathematical relationships, than once was thought, and that these principles are now being elaborated at many different levels of its hierarchy. These insights also suggest that life is much more narrowly circumscribed than those who favor the role of chance and history would like to think. Accordingly, life is more predictable and potentially universal in its structure than is sometimes assumed.

In their details, living things do show apparently illimitable embellishments. The vastness in the details of living things has probably caused a divergence between the biological and physical view of the universe. Yet if we return to our facile observation that biology operates within the laws of physics, then we should be able to more comprehensively reconcile this division.

When I joined a university physics department a few years ago as an astrobiologist, I was asked to teach an undergraduate physics course called Properties of Matter. For me, with a background in biochemistry and biology, a semester of this material would be unpalatable without some biology, so I set about modifying my task by using biological examples to illustrate the physical laws and ideas I needed to teach. The inclusion of some biology improved my own motivation, and I also thought that doing so would be interesting for undergraduates.

It was not a difficult task to find these examples. At the molecular level, the van der Waals forces that hold molecules together—these feeble forces from the inherent polarity in molecules make the molecules behave like little bar magnets (even the unreactive noble gases such as neon can behave like this)—can be illustrated with a gecko. These agile desert lizards have an abundance of tiny hairs on their toes; the hairs allow the combined van der Waals forces on all four feet to hold the creature fast on a vertical surface, allowing it to run up a shiny glass window with ease.

The two strands of the genetic material DNA, the molecule that encodes the information in your cells and all other cellular life, are held together to make the familiar double helix by links called hydrogen bonds. The forces involved in these links are just enough to hold the strands together and maintain the integrity of the molecule, but just weak enough that the two strands can be easily unzipped when the cell is dividing in two and the information in DNA must be copied. The replication of DNA and the architecture of its multiplication can be understood as the forces between atoms.

At higher levels of its hierarchy, biology still came to the fore. In explaining phase diagrams (graphs that show the state that matter adopts at given pressures, temperatures, and volumes), I found some illustrations from the world of biology useful. The fish that swim unmolested by predators and in the comparatively warm water trapped beneath the ice on a frozen wintry pond take advantage of the negative gradient of water’s melting curve on a phase diagram. Put simply, when water is frozen, it becomes less dense and floats. Fish that remain active in the winter have evolved to cope with living in the habitat under ice—their behavioral evolution is constrained by some simple facts about the behavior of water that can be manifested in a phase diagram.

Even at the macroscopic scale, physics both explains biological systems and constrains their operation. When clarifying how large creatures travel through water, we are confronted with questions such as why fish lack propellers—what physical laws make a flexing body a better way to get through the ocean and away from a shark than a propeller, the solution of choice to human engineers? The behavior of fluids and the objects that travel through them provides extraordinarily tight constraints on the organisms that can evolve and the solutions they find to live within these constraints.

After teaching this course, I was surprised not by how we could find biological examples of physical laws in action, but by how deeply simple physical rules fashion and select features in life at all levels of its hierarchy, from an electron to an elephant. I was well aware of how physics can shape whole organisms, but I was awed by the sheer pervasiveness of the reach of physical principles, like tentacles, stretched through the entire fabric of life. And despite the inherent uncertainty swirling around subatomic particles in the quantum world— uncertainty that might reasonably make a cautious physicist wonder about how confidently we can bring biology and physics together—the shape and chemical composition of Schrödinger’s cat and the height of Werner Karl Heisenberg himself are highly predictable, convergent features of physical principles operating in biology.

Sometimes, scientists use the oceans as an analogy to evolution. Different animals represent islands of biological possibility, where solutions to successful adaptation to the environment are constrained by what is physically possible and what an organism already has on hand: its history. Between these islands, there are vast oceans of impossible solutions that life must navigate between to find new islands of possibility. Its seems extraordinary that life manages to home in on these islands and that living things seem to arrive at the same haven, like a party of separated shipwrecked seafarers that find themselves marooned on the same deserted outcrop in the middle of the Pacific Ocean. How is it that two animals, such as a bat and a bird, home in on the same functional solution to flight? This convergence cannot be easily explained by a common ancestor, since their ancestors lacked wings, a fact borne out by the very different wing anatomy in the two creatures. However, there is nothing uncanny about life’s ability to land on the same solutions. Impossible solutions are impossible solutions, which means that the ocean of impossibility does not exist at all.

We might instead try to visualize the physical aspects of evolution as like a chessboard. Each square is a different environment, a different set of physical conditions to which life must adapt. When a living thing moves across the board, it automatically finds itself in another space to which it must adapt using a range of well-defined physical laws. For example, the laws of hydrodynamics that enforce certain forms in a fish would be replaced by the dominance of new rules when it crawls onto land. Limbs that allow movement against a more dominant influence of gravity and equations that determine the rate of evaporation as the midday sun mercilessly tries to desiccate our new denizen of the landmasses become some of the shapers of evolution. But there is no intermediate ocean of impossibilities. There are only physical principles seamlessly operating together in different combinations and magnitudes in different environments. Life moves from one environmental condition to another, those laws operating all the time to select successful conformists to physics, while the environment or competitors ruthlessly eliminate the forms whose adaptation to the unwavering requirements of these laws fails to allow them to reproduce.

There is a distinction worth making here. The ocean analogy works rather better when we think about how effectively creatures are adapted to their environment. In the extreme example, an insect born with a missing wing is likely to be severely handicapped in its ability to succeed in the evolutionary game. The idea of organisms occupying a vast landscape where islands and the peaks of mountains represent organisms best adapted to their environment and the plains and oceans between as the organisms less well adapted and less likely to succeed forms the basis of the concept of adaptive landscapes. However, there is nothing strange about life’s ability to find similar evolutionary solutions to environmental challenges. There is no empty space to explore. Living things just move from one place to another; when the physical laws confront them, they must adapt to reproduce. If they do not, we never see them again. Those physical laws often demand similar solutions.

In this book, I do not expect the reader to be surprised that biology and physics are inseparable, that physics is life’s silent commander. Instead, I intend to illustrate the wonderful simplicity of life from population to the atomic scale. I also suggest that these laws are so ingrained, from the atomic structure of life to the social behavior of ants, that life elsewhere across the universe, if it exists, will show similar characteristics.

Surely, though, we might say, “Life cannot just be about physical principles. What about the cheetah that chases the gazelle? Not merely a physical effect on the gazelle, but a true biological interaction.” The cheetah that races across the African savanna to catch the hapless gazelle for its next meal is exerting a selection pressure on the gazelle, and this pressure is, at the level of the biological response, physical. The gazelle will survive this encounter if it can outpace the cheetah. Whether the gazelle can escape depends on how quickly it can release energy in its muscles or how deftly it can twist and turn as it seeks to evade the oncoming predator. This ability is itself a product, among other things, of the forces that the knees of the gazelle can endure and the torsion that its leg bones and muscles can accept as it seeks freedom. These factors ultimately are determined by the structure of muscles, bones, the acuity of eyesight, and so on. Either the gazelle will survive to get closer to reproductive age, or it will not. This selection pressure cares not that the cheetah is another biological entity. It could just as well be a fast-running robot built in a physics laboratory at the University of Edinburgh programmed to run across the savannas of Africa, randomly intersecting and killing gazelles. The only matter of importance is whether the biological, and ultimately physical, capabilities of the gazelle allow it to survive the cheetah and what adaptations in muscular properties, bone strength, and other factors allow its offspring to be the successful successors.

The points I make above apply equally to the evolutionary changes that occur in organisms not just from selection restrictions in the environment, such as predation, but also by new expansive opportunities provided, for example, by unexplored habitats and food resources. Many of these changes, both in the short term and ultimately in evolutionary terms, projected onto living things in their environment may be caused by fellow biological travelers on Earth. However, the adaptations required to ultimately survive or exploit the changes in the environment or other organisms are often tightly channeled by physical principles.

All these adaptations are, of course, bounded by the restrictions that may be imposed by the prior shape and form of the organism’s ancestors or in its developmental patterns. These historical architectures and limits in how living things can develop and grow are in themselves boundaries set up by previous evolutionary selection, and these boundaries merely constrain how an organism can respond to the full set of physical laws theoretically available to it and imposed on it. They narrow the field of play further.


  • "In a fascinating journey across physics and biology, Cockell builds a compelling argument for how physical principles constrain the course of evolution."—Science
  • "Cockell's book lucidly addresses biology's great mystery: If we grant that life is an interplay of chance and necessity, in the words of the French biochemist Jacques Monod, then which has the upper hand?"—New York Times
  • "If a ladybug lands on you while reading this provocative perspective, don't swat it away before you've taken a good look. Astrobiologist Cockell uses the insect, along with assorted microbes and other earthly residents, to reassess the story of life both on and beyond our planet."—Discover Magazine
  • "Both magisterial and collegial, this may be the biology book of the year."—Booklist
  • "Many readers...will relish a lucid, provocative argument that the dazzling variety of organisms produced by 4 billion years of evolution may seem unbounded, but all follow universal laws."—Kirkus Reviews
  • "Life as we know it arises from an interplay between biological chance and physical necessity. What about life as we don't know it? To think about life on other planets, we need to understand how things could have been different. Charles Cockell's book is a fascinating new look at this question, offering surprising insights on just how constrained biology can be by the laws of physics."—Sean Carroll, author of The Big Picture
  • "Nature's intricate diversity offers immense challenges to biologists--and inspires the rest of us with wonder and delight. But despite its diversity, the entire biosphere is governed by unifying principles--all living things are assemblages of atoms, governed by gravity and other basic forces. This riveting book--fully accessible to the general reader--shows how all Earthly life (and indeed any alien life elsewhere in the universe) emerges through the operation of basic physical laws and is constrained by what these laws permit. Charles Cockell is not only a fine scientist but a fine writer too." —Lord Martin Rees, Astronomer Royal, past President of the Royal Society
  • "Want to know about alien life? According to Charles Cockell, you can learn from the living things all around you, right here on Earth. Whether on this third rock from the Sun or another planet in a far-distant galaxy, creatures should share forms and behaviors shaped by the forces of natural selection and the fundamental laws of physics that reign throughout the universe. In this enlightening, entertaining book, Cockell explains how extraterrestrials might not be quite so 'alien' after all."—Lee Billings, author of Five Billion Years of Solitude
  • "Fascinating. A profound exploration of the deep nexus between physics and biology."—Andreas Wagner, professor of evolutionary biology at the University of Zürich and author of Arrival of the Fittest
  • "An intriguing and enthralling adventure into the physics of life that is all around us and inside us. Cockell provides a reminder of the seeming rarity of all this beauty but also an invitation to look up to the skies and ask 'where else might something like this be?'"—Robin Ince, co-host of The Infinite Monkey Cage and co-author of How to Build a Universe (with Brian Cox)

On Sale
Jun 19, 2018
Page Count
352 pages
Basic Books

Charles S. Cockell

About the Author

Charles S. Cockell is a professor of astrobiology at the University of Edinburgh and the director of the UK Centre for Astrobiology. He lives in Edinburgh, UK.

Learn more about this author