2
THE SLOW FIRE

DR. COSTARELLIS INSTRUCTIONS were precise: I should arrive for our appointment by public transport, not the bicycle I usually use for short journeys. I should drink no alcohol beforehand—not such a hardship, as we were scheduled to meet at 9 a.m. More onerously, I should also steer clear of caffeine, so I had to forego the kidney-challenging quantity of tea I pour down my throat each morning. And I should skip breakfast.

So I was feeling sluggish and hungry when she met me and led me to her laboratory, a spare white room in the basement of London’s South Bank University. She weighed me, and I lay down on a couch. Her colleague Bill Anderson placed a clear Perspex hood, like a space helmet from a 1950s science fiction film, over my head, and I shut my eyes and relaxed.

For the next 30 minutes, I tried to keep body and mind as inert as possible. I tried—and failed—to remember the last time I had lain still with my eyes closed for half an hour without being asleep. I worried that I wasn’t relaxed enough, then tried to halt this train of thought before it spiraled into hyperventilation. I thought of a technique that had once been recommended to me in a massage workshop at the



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In the Beat of a Heart: Life, Energy, and the Unity of Nature 2 THE SLOW FIRE DR. COSTARELLI’S INSTRUCTIONS were precise: I should arrive for our appointment by public transport, not the bicycle I usually use for short journeys. I should drink no alcohol beforehand—not such a hardship, as we were scheduled to meet at 9 a.m. More onerously, I should also steer clear of caffeine, so I had to forego the kidney-challenging quantity of tea I pour down my throat each morning. And I should skip breakfast. So I was feeling sluggish and hungry when she met me and led me to her laboratory, a spare white room in the basement of London’s South Bank University. She weighed me, and I lay down on a couch. Her colleague Bill Anderson placed a clear Perspex hood, like a space helmet from a 1950s science fiction film, over my head, and I shut my eyes and relaxed. For the next 30 minutes, I tried to keep body and mind as inert as possible. I tried—and failed—to remember the last time I had lain still with my eyes closed for half an hour without being asleep. I worried that I wasn’t relaxed enough, then tried to halt this train of thought before it spiraled into hyperventilation. I thought of a technique that had once been recommended to me in a massage workshop at the

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In the Beat of a Heart: Life, Energy, and the Unity of Nature The author tries to relax while his resting metabolic rate is measured. Credit: Vasiliki Costarelli. University of California at Berkeley. (“Imagine a golden light moving up your body, each part of you relaxing as it bathes in the glow.”) It was all very restful—spring sunshine seeped through the blinds, and the only noises were the hum of the building and a whispered conversation between Anderson and Dr. Costarelli. I tried to stay awake. And every 30 seconds, tubes in the hood carried some air away to an analysis chamber, which measured the amount of oxygen I breathed in. For one of those inhaled oxygen molecules, it was a short, simple trip through my nose and down my windpipe. Then the path forked at my bronchioles, leading down into my lungs. These air passages divide again and again, into a labyrinth of ever-narrowing tubes. Eventually, after crossing more than 20 such junctions, the molecule reached a blind alley—one of the lungs’ air sacs, called an alveolus, where gases move into and out of the blood. The membrane of an alveolus is no barrier to a molecule as small as oxygen, and it slipped easily out of the lungs and into the bloodstream. Instantly, a vastly larger molecule

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In the Beat of a Heart: Life, Energy, and the Unity of Nature called hemoglobin, the protein that moves oxygen around the body, snatched up the oxygen. The next part of its journey was chauffeur-driven, riding in a cleft on the protein molecule. Hemoglobin molecules themselves travel around the body in groups of a few hundred, inside red blood cells—oxygenated hemoglobin is what makes blood red. Snug in its new ride, the molecule moved through the bloodstream. Soon it reached the heart, entering the top left chamber and firing out from the bottom left into the aorta, the body’s biggest blood vessel. The blood cell began moving through the body in jerks, propelled by each beat of my heart. Where to next? Any red blood cell could transport its oxygen to anywhere in my body, but demand is greatest in my brain. Even when I am lying on a couch trying not to send any nerve impulses to my muscles or think any stimulating thoughts, this organ consumes more energy than any other—about one-fifth of my body’s total requirements, despite accounting for only one-fiftieth of its mass. So say that the oxygen molecule went to my head, traveling up my neck via the carotid artery. Here, it entered a network of blood vessels that get narrower and narrower, like leaving a freeway and turning onto a back street. The blood cell eventually reached a single-track highway barely wider than itself, a blood vessel eight-millionths of a meter across with a wall one cell thick, called a capillary. Capillaries are woven into every tissue in my body. They deliver oxygen and food and pick up waste such as carbon dioxide. This capillary snakes alongside a nerve cell. Deep in my tissues, there is less oxygen around than there was in my lungs, and in this environment the hemoglobin loosened its grip on its cargo. The liberated molecule was small enough to slip straight through the cell membrane, driven by nothing more complex than diffusion, the tendency for chemicals to move from where they are common to where they are rare. Inside the cell, the molecule made for a cigar-shaped blob, hanging in space like an airship. This is called a mitochondrion, and it is the unimaginably distant descendent of a bacterium that fused with my unicellular ancestors more than 1 billion years ago. Mitochondria are the cell’s power stations. It is there that the chemical reactions of

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In the Beat of a Heart: Life, Energy, and the Unity of Nature respiration go on, and they are the reason we need oxygen. The diffusion gradient pulls the oxygen in like a tractor beam. Inside the mitochondrion, after crossing yet another membrane, there are more molecular machines that break up food molecules, such as glucose, and use the energy stored in their chemical bonds to fuel life. The main purpose of these reactions is the production of a molecule called adenosine triphosphate, or ATP. ATP is the fuel for every cellular reaction that requires energy. It powers muscles, nerve cells, DNA copying, and everything else, in animals, plants, fungi, and bacteria. At any moment, a human body contains only about 10 grams of ATP, but we make and consume our own body weight of the molecule each day. The oxygen molecule has come to the mitochondrion to pick up the trash. It reacts with the electrons and protons that these molecular machines produce in their fuel-generating work. In the process the molecule, which consists of two oxygen atoms, breaks apart. Each atom forms a new alliance with two hydrogen atoms, in a water molecule. Nothing is ever really destroyed. Each new water molecule will journey through my veins to my lungs, leave my body as vapor, and float into the atmosphere. Here it will become part of a cloud, then a raindrop, and perhaps eventually get taken up by a plant, where it will react with carbon dioxide to become carbohydrate, creating food for animals. Aristotle thought that the function of breathing was to cool the blood. In fact, the opposite is true: By measuring the total amount of oxygen used by my body, Vasiliki Costarelli is measuring the rate at which I use energy. This is why I am lying on the couch—to have my energy consumption, or metabolic rate, measured. The Torch of Prometheus To be alive is to be using up and giving out energy. We understand this instinctively. Many cultures believe an energy field pervades the world and passes through living beings. Taoists call it chi; Hindus, prana. To say that living bodies burn fuel is not a figure of speech. The chemistry of respiration and that of combustion are identical, and the amount of energy released from food when you eat it is the same as when you burn it. Life is a slow fire: Every cell burns fuel to build molecules up

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In the Beat of a Heart: Life, Energy, and the Unity of Nature and break them down. Combustion keeps hearts beating, brains thinking, muscles moving, and bodies building. Chemists came to realize this in the late eighteenth century. The greatest of them all, Antoine Lavoisier, put it best, in 1789, in his Premier mémoire sur la respiration des animaux (First report on animal respiration): This fire stolen from heaven, this torch of Prometheus, does not only represent an ingenious and poetic idea. It is a faithful picture of the operations of nature, at least for animals that breathe: one may therefore say, with the ancients, that the torch of life is lighted at the moment the infant breathes for the first time, and is extinguished only on his death. Lavoisier studied metabolism throughout his life, until his own torch was snuffed out on the guillotine in 1794, during the Reign of Terror that followed the French Revolution. A body’s metabolism is the work of the tiny furnaces and factories in its cells, which in a human body number billions. These fires can be stoked or quenched. When we exercise, we burn more fuel and get hot. When we eat, our intestines and liver crank up to digest the incoming food, and metabolic rate rises by about a third, which is why Dr. Costarelli told me to come to her lab on an empty stomach. When we get a shock, the pulse of adrenaline released revs up our metabolism to provide the energy for fighting or fleeing. When we wrack our brains over a math problem or a tricky piece of map reading, our neurons demand more fuel. When we are infected, we make things uncomfortable for the microscopic invaders by increasing our metabolic rate and raising our body temperature to feverish levels. My half-hour relaxing on the couch revealed that, were I to spend all day like that, I would burn 1,726 kilocalories. (The “calorie” counts given on food packaging are, more often than not, kilocalories. The standard scientific unit of energy is now the joule, which equals 0.24 calories.) If I did nothing all day but sit at my computer writing this book, the fidgeting and extra mental activity would probably push that to a little over 2,000 kilocalories. If I blew the day off and went for a hike, or blew this career off and took a job on a building site, that number would rise above 3,000. The kings of energy consumption—Tour de France cyclists, wildfire fighters, and polar explorers—need about 7,000 kilocalories a day.

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In the Beat of a Heart: Life, Energy, and the Unity of Nature Different parts of bodies demand different quantities of energy. Cells that burn a lot, such as muscle and liver, have more mitochondria. A human liver cell has about 800 mitochondria; the average is about 100. Fat burns less energy than muscle, which is why a woman will usually have a lower metabolic rate than a man of the same weight, because a greater proportion of a woman’s body is fat. Metabolic rate can vary on timescales longer than fright or fever. A cell in a hibernating animal is like a mothballed factory: It keeps ticking over, but only just. Fewer protein molecules are made and broken down, and smaller amounts of substances pass in and out of the cell. Molecular security guards come in to keep key pieces of equipment safe. Energy consumption can drop by 90 percent. The body can also regulate its weight by tuning energy consumption. Fat cells release a hormone called leptin, which raises energy expenditure, so burning off fat, part of a beautifully precise system which means that, although each human in the developed world eats about 1 tonne of food each year, our body weight over the same period changes by only a tiny fraction of this, if at all. Of course, our biology can only adjust to our diets up to a point. Humans evolved in environments where feeding oneself took strenuous effort and where periodic starvation was common. In affluent Western societies—and an increasing number of developing countries—our instincts and tastes lag behind our abundant food and sedentary lifestyles, leading to today’s well-publicized spike in obesity. We combat this trend by becoming acutely aware of our energy budgets, finding out how much fuel our diets contain, and how rapidly different forms of exercise burn it off. Our metabolic rate also declines as we get older—partly because mitochondrial performance drops off—which is why it is harder to stay thin in middle age. The team at South Bank University most commonly measures metabolic rate to help obese people plan their diets. The same measurement is used to ensure that hospital patients who have had major surgery, or been severely burned, get enough food. In concert with hormones such as leptin and adrenaline, the other main controller of metabolic rate is the nervous system. Mostly the brain does this without troubling our consciousness, but Buddhist monks, through deep meditation, can reduce their metabolic rate to

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In the Beat of a Heart: Life, Energy, and the Unity of Nature just a third of its usual level. On the other hand, as I scarf down a Danish pastry in the university canteen, Dr. Costarelli tells me that she was once thrown out of a meditation class for passing notes. Restless, high-energy personalities such as hers will consume more energy than more laid-back people. But the story of my visit to Dr. Costarelli’s lab is about more than discovering whether that Danish will go straight to my hips. This morning Dr. Costarelli is aiming to uncover a metabolic rate that underlies the kerfuffle of exercise, shocks and surprises, big meals, and psychoactive chemicals. This is why I laid off the booze and tea, postponed breakfast, and laid down. The South Bank team is trying to measure how much energy my body uses to keep its parts and processes running—to keep me alive—and nothing more. This measure is called resting metabolic rate, and it is the central rate of life. Metabolic rate is the conductor that sets the tempo for the orchestra of biological processes—feeding, growing, breeding, living, and dying. For centuries, scientists have sought to understand what controls metabolic rate and how living things use energy. Counting Calories The first person to measure life’s energy was Lavoisier. In 1777, in collaboration with the mathematician Pierre Simon Laplace, he put a guinea pig and a block of ice in a sealed chamber. The two Frenchmen measured the rate at which the ice melted and collected the carbon dioxide that the guinea pig exhaled. They found that the quantities were closely matched. The principles of calorimetry, as the technique came to be called, have remained unchanged ever since: We measure either the heat radiated by the body, the chemicals exchanged with the environment, or both. The first calorimeter big enough to carry a human was built in Munich in the 1860s by Carl Voit. The subject sat in a chamber surrounded by water, and Voit measured the rise in water temperature caused by the subject’s body heat. Like Lavoisier, Voit was a chemist who became interested in human biology, and his laboratory produced the first generation of biologists interested in metabolism and nutrition.

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In the Beat of a Heart: Life, Energy, and the Unity of Nature One of these early biologists, Max Rubner, did more than anyone to lay the foundations for the modern science of metabolism and diet. He was an ardent measurer—in the 1880s he began a daily record of the number of steps he took, with the intention of recording his physical decline with age. He was also a gifted instrument builder, a talent perhaps passed down from his locksmith father, and took calorimetry to new peaks of precision. (Dr. Costarelli’s machine is descended from Rubner’s calorimeters.) Rubner left Munich at the age of 31, to run his own lab in Marburg. There, in 1889, he conducted probably his greatest experiment. Rubner kept a dog in a calorimeter for 45 days, comparing the food the animal ate with the energy it gave off as body heat and in chemical form via respiration, urine, and feces. The heat measurement came to 17,349 calories, the chemical one to 17,406—near-enough identical. This result showed that animals obeyed the first law of thermodynamics—energy cannot be created or destroyed, only converted from one form to another—and struck a powerful blow against vitalism. Rubner proved that you are what you eat. Rubner’s experimental gifts were matched by the insight needed to turn measurements into theories. In the process he was the first to realize many things that seem obvious to us now. For example, in 1878 he determined that no one foodstuff is the sole source of the body’s energy—protein will do as well as fat or sugar—and calculated the energy values of these different food groups (a gram of protein yields 4.1 calories, one of fat 9.3, and one of carbohydrate 4.1). These measurements were used worldwide in analyzing the diets of populations and making nutritional recommendations. It was Rubner who discovered that the amount of energy released by burning food is identical to the amount released by eating it, an experiment replicated in school science classes to this day (at my school we measured the calories in a burning peanut). He found that measuring gas exchange is as good a gauge of energy consumption as measuring heat output, which is why I had to stick only my head inside the machine that measured my metabolism. He showed that chemical reactions can heat bodies in the same way as physical exercise and that animals in cold environments can exploit this principle by raising their metabolic rate to keep warm.

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In the Beat of a Heart: Life, Energy, and the Unity of Nature He also believed that his science should be practical, and advocated the public benefits of a scientific approach to eating. Rubner came up with some of the first dietary recommendations: After studying laborers and finding that they burned 3,100 calories a day, he recommended that their daily diet contain 127 grams of protein (later shown to be rather high). During the First World War, by which time he was working in Berlin, Rubner tested different types of flour to see whether, in times of shortage, flour bulked with bran could make nutritious loaves. Whenever he went to a restaurant, he would take a copy of the menu to track changing fashions in diet. Rubner’s experimental labors, keen insights, and public spirit were backed up with a forceful personality. Acquaintances described a well-built man with a powerful physical presence. Photographs show that he was strikingly handsome, with clear, confident eyes and smooth, boyish features under his nineteenth-century dress and beard. But Rubner could also be difficult company, prone to long silences punctuated by bursts of sarcastic wit. He gave no quarter in claiming priority for himself, criticizing others’ work, or standing up for his own. A representative sentence from his major book Die Gesetze des Energieverbrauchs bei der Ernährung (The Laws of Energy Conservation in Nutrition) reads: “A number of arguments, which shall be shown to be perfectly meaningless, have been raised against my methods.” (Scientists do not write like this anymore, at least for public consumption, but many will still talk this way with little or no provocation.) He fell out with many colleagues—including Voit, who stymied his work on the energy found in different foods—but was loyal to those he trusted. Rubner’s prickliness didn’t stand in the way of him having a long and distinguished career, but it may have cost him the biggest scientific prize. His obituary quotes a friend as saying: “You should have won the Nobel Prize, you must have stepped on X’s toes.” “I did,” he replied. (X’s identity is not recorded, but may have been Voit.) While in Marburg, Rubner also came up with the first major theory to explain the value of resting metabolic rate.

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In the Beat of a Heart: Life, Energy, and the Unity of Nature Max Rubner’s Big Idea Rubner’s theory was based on body size. The idea that an animal’s size is the best guide to its energy requirements makes intuitive sense. Just as buses need more fuel than cars, and a cottage has a smaller electricity bill than a skyscraper, larger animals are going to have to eat more and so will have a higher metabolic rate. This also means that it becomes harder to lose weight the more weight one loses, as the newly slimline body has a smaller appetite for energy. But although larger animals have larger absolute metabolic rates, when you consider relative metabolic rates, the opposite is true—in animals, small is not necessarily economical. A shrew must eat more than its own body weight every day just to survive. An elephant makes do on food weighing about 3 percent of its weight, and elephants eat indigestible vegetation, not the high-energy insect diet that shrews need. The smallest bats eat like shrews, and hummingbirds rely on sugary nectar. Some hummingbirds and bats also save energy by dropping into a hibernation-like torpor overnight. Why, pound for pound, does a canary need 25 times more energy than a cow? Rubner believed that smaller animals’ relatively greater need was due to their relatively larger surface area. To understand this, put aside all the other jobs that metabolism does for a moment and consider only its heat-generating powers. Think of an animal as a boiler that burns fuel to keep warm. Heat is generated throughout the body’s bulk, in every cell, by the chemical reactions encountered earlier. But it is lost only through those bits of the animal exposed to the outside world. To understand how surface area (skin) changes as a body’s size—and hence its mass and volume—increases, imagine a cubic creature, whose sides are each 1 centimeter long. The animal has a volume of 1 cm × 1 cm × 1 cm = 1 cm3 and will lose heat across each of its six sides, which have a combined area of 1 cm × 1 cm × 6 = 6 cm2. Now imagine the cube grows to double its original size. Its volume will be 23 cm = 8 cm3, and its surface area will be 22 cm × 6 = 24 cm2. For an eightfold increase in volume and mass, assuming the big cube is made of the same stuff as the small one, its skin area has increased only four times. Instead of having 6 cm2 of surface for every cubic centimeter of volume, it has 3.

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In the Beat of a Heart: Life, Energy, and the Unity of Nature Large objects have proportionately less surface area than small ones. Doubling the linear dimensions of this cube increases its volume by eight times but its surface area by only four times. This, thought Rubner, is why a 3-kilogram cat doesn’t need 100 times more calories than a 30-gram mouse. The cat has proportionately much less skin than a mouse. More of the cat’s body is snug and warm away from the outside world, and so it loses heat much more slowly. Nor are mice cooler than cats. The body temperature of mammals and birds, the two groups of animals that burn fuel to keep warm or cool off, does not vary much with size. It follows that small animals must be working harder to heat themselves, and so need proportionately more food. An animal’s size is its defining characteristic. We have such strong impressions of how big animals are that they have entered the language—elephantine, for example, or fleabite. This intuition reflects a profound biological truth. Every aspect of an organism’s life depends on its dimensions. The relationship between surface area and volume is one of the keys to understanding the effects of size. Over 400 years ago Galileo noticed that big animals have proportionately thicker leg bones than small ones. The key area here is bone rather than skin. A bone’s strength depends on its thickness, which, like surface area,

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In the Beat of a Heart: Life, Energy, and the Unity of Nature increases with the square of length. So as an animal gets bigger, if the girth of its bones remains in proportion with the rest of its body—which, remember, is gaining weight at the rate of length cubed—the bones will become too weak to hold up the animal. This is why a rhino’s legs are short and stumpy and a gazelle’s legs are long and slender. Galileo realized that big animals need more support because gravity exerts a stronger pull on them. “A dog,” he wrote, “could probably carry two or three such dogs upon his back; but I believe that a horse could not carry even one of his own size.” Or, as the British biologist J. B. S. Haldane put it 350 years later, in his classic essay On Being the Right Size: “You can drop a mouse down a thousand-yard mineshaft; and, on arriving at the bottom, it gets a slight shock and walks away, provided that the ground is fairly soft. A rat is killed, a man is broken, a horse splashes.” “Comparative anatomy,” Haldane continues, “is largely the story of the struggle to increase surface in proportion to volume.” Relative surface area decreases so quickly with increasing size that the bodies of all but the smallest and flattest animals need to make extra surface. (Haldane and D’Arcy Thompson spoke on the biology of size at the 1926 British Association meeting. “Bobbed-haired girl scientists, unable to find chairs, sat on the floor, and additional chairs had to be brought in,” said one newspaper report of the event. “Roars of laughter from professors as well as from girl scientists punctuated the discussion.”) We interact with the world across surfaces. We take oxygen across the membrane of our lungs, absorb food across our intestines, secrete waste into our kidneys. The surfaces of all these organs are incredibly convoluted, to create the large surface needed to supply a large body. This is why the journeys through the lungs and bloodstream are so complicated. Both are structured to increase the surface area over which cells can absorb chemicals. A pair of human lungs spread out flat would cover a tennis court. This trick is repeated at every scale of life. Mitochondria have convoluted internal surfaces, to give the maximum area for burning oxygen. Combustion outside cells works in the same way, creating a risk of fire or explosion in any place where there are large quantities of dust, such as coal mines, flour mills, and custard-powder factories.

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In the Beat of a Heart: Life, Energy, and the Unity of Nature Of Poles and Penis Bones In the mid-nineteenth century, several biologists independently drew links between a body’s surface area and the rate of its heat loss. The earliest published report dates from 1839; it is by a French multidisciplinary research duo consisting of the mathematician Pierre Sarrus and the biologist Jean-Francois Rameaux. Sarrus and Rameaux were also interested in energy requirements: They were calculating the food needs of employees at the state tobacco factory in their native Strasbourg. Eight years later the German biologist Carl Bergmann realized that the link between size and energy could control how an animal fit its environment, as well as its internal economy. He further deduced that the physical environment could produce patterns in the living world, thus showing that an understanding of how individual organisms work can lead to an understanding of how nature as a whole works. In 1847, Bergmann suggested that, in any group of closely related, warm-blooded animals (also known as endotherms, because they heat themselves from within, or homeotherms, because they maintain a constant temperature), species living in cold climates would be bigger than their relatives from hot places, to help them conserve heat. So animals living near the poles will be bigger than those at the equator. A brief mental tour of the animal world provides plenty of examples to support this notion. Arctic foxes are the smallest animal living on the Arctic island of Spitzbergen; they are considerably larger than the red foxes that live in my London garden. Polar bears in the Canadian arctic are bigger than Californian black bears. Emperor penguins in Antarctica weigh about 30 kilograms, but equatorial Galapagos penguins weigh on average less than 2.5 kilograms. There is support for the rule within species, too—the wolves of Alaska are bigger than those of Arizona. Humans too are bigger away from the equator. Conversely, large animals in hot climates can have a problem losing heat, and so have evolved body structures that help them cool off, such as the high-surface-area radiators attached to either side of an elephant’s head. In the 1870s the American biologist Joel Allen extended Bergmann’s arguments to animal shape, suggesting that animals living in hot

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In the Beat of a Heart: Life, Energy, and the Unity of Nature climates should be longer and thinner, with larger appendages and extremities. Desert jack rabbits have long legs and ears and slender bodies; Arctic hares are squat. Not every appendage shrinks toward the poles. Many mammals have a penis bone, which augments an erection—a feat male humans must accomplish through blood pressure alone. Two Canadian zoologists, Steven Ferguson and Serge Lariviere, measured the penis bones of 122 species of carnivorous mammal and found that the more polar the beast, the bigger the penis bone, relative to body size. Elephant seals living in temperate waters weigh a couple of tonnes and have a penis bone about 30 centimeters long. Male walruses swimming in the Arctic Ocean, on the other hand, weigh in at a comparatively flyweight 1.7 tonnes, but have a penis bone a whopping 60 centimeters long. It’s not swimming in frigid polar waters that leaves the walrus needing a little something extra, the Canadian duo believe. Populations of polar species tend to be more thinly spread than those in more hospitable climates. Elephant seals live in big colonies and use their extreme bulk to win and defend mates. For a male walrus, maintaining such a harem would be a geographical impossibility—so, when he does meet a female, there’s a heavy pressure to perform. Ferguson and Lariviere believe that a long penis bone helps males who mate sporadically perform well in the competition between males to sire offspring. The way that a species changes size through time also seems to show the workings of Bergmann’s rule. A study of the changing sizes of American woodrats over 25,000 years (based on the size of their droppings) showed that the animals got bigger when the climate was cold and smaller when it got warmer. Other studies, using museum specimens collected over the past century, have suggested that several bird species have gotten smaller as the world has warmed—showing that the effects of global warming will be subtle and surprising, as well as potentially Earth-changing. So the logic is simple. Tropical and desert animals should be small and lanky; polar ones should be big and rotund. But Bergmann’s rule is controversial. Ecologists still can’t agree whether it holds or not, despite testing it on everything from robins to moths to kangaroo rats. Some have asserted that the rule fails on the grounds of evidence, and

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In the Beat of a Heart: Life, Energy, and the Unity of Nature that the majority of animals don’t show a tendency to get bigger toward the poles. One 1936 study claiming that the geographical trends in the sizes of American mammals showed support for the rule was later attacked for taking the dubious shortcut of using numbers from field guides, rather than new measurements. Others have taken up conceptual cudgels, arguing that large size is not actually a good way to conserve heat, compared with, say, thicker fur. Some contend that big animals may actually have a harder time keeping warm in cold climates because they need more food overall than small ones. Another camp believes that the patterns in body size noted by Bergmann are genuine but that they are not caused by temperature. Humidity is more important, some claim. Others have asserted that big animals are better placed to cope with a seasonal climate because they can carry larger fat reserves and so survive periodic brushes with starvation. This might explain why some species of reptiles and insects, animals that don’t need to maintain a constant body temperature, also follow Bergmann’s rule. The past century has seen regular to-ing and fro-ing in scientific journals, as researchers have taken potshots at each other’s hypotheses. Recently it has looked as if the debate might be going Bergmann’s way. A 2003 review of the evidence, by Shai Meiri and Tamar Dayan, from studies covering a total of 94 bird and 149 mammal species found that about three-quarters of the birds and about two-thirds of the mammals obey Bergmann’s rule. It looks as if warm-blooded animals are bigger nearer the poles, although why that is so is still open to debate and is probably the consequence of many different evolutionary forces working at once. Two-thirds might seem like not terribly impressive support. The law of gravity would read rather differently if apples fell up, or sideways, one time in three. But biological rules such as Bergmann’s, of which we shall be meeting many, are not the same as physical laws such as gravity, which hold true everywhere and which can be used to make precise predictions. Biological rules are more often trends that, all other things being equal, hold more often than not. One or several exceptions are rarely enough to discredit the whole pattern. For example, the Galapagos penguin lives closer to the equator than any other penguin, but it is only the second smallest of its kind. The smallest, the fairy

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In the Beat of a Heart: Life, Energy, and the Unity of Nature penguin, lives in Australia. Temperature is not the only thing that affects body size; animals have got to do lots of other things besides keep warm. There’s no point being huge if you want to fly, or swing from one tree branch to another, or escape from your predators down a burrow. Meiri and Dayan found that Bergmann’s rule holds less well for migratory birds than sedentary species, perhaps because these species avoid cold climes by traveling. And, they found, rodents are more likely to buck the rule than other mammals such as bats, perhaps because rodents are more likely to live in insulated burrows. This untidiness makes it easy for researchers to disagree about patterns in nature such as that spotted by Carl Bergmann. The gap between the trend and the variation becomes disputed territory between the lumpers who see patterns and the splitters who see diversity. In 1956 the great German evolutionary biologist Ernst Mayr said that patterns such as Bergmann’s rule should be taken as valid if they applied to more than half of all species. This rather unambitious yardstick brings to mind the scientists’ joke on the differing standards of proof demanded by different disciplines. An astronomer, a physicist, and a mathematician are taking a train ride through the Scottish highlands. From the train window the astronomer—being of an observational bent but also prone to sweeping generalizations—spots a black cow standing in a field. “Look,” he points out, “cows in Scotland are black.” The physicist corrects the astronomer: “You can’t assume that,” she argues. “All we can really say is that particular cow is black.” The mathematician, believing only what can be proved beyond any doubt, rolls his eyes: “Really,” he sighs. “All we know is that one side of that cow is black.” If this party of caricatures had included an ecologist, he would probably have asserted that every field in Europe contained a solitary black cow. This isn’t to say that the patterns in nature aren’t real or that the explanations for them are unscientific, just that we can’t expect things to be too neat. The Surface Rule So an animal doesn’t burn energy twice as fast as one half its size or three times faster than one a third of its size. At what rate does relative

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In the Beat of a Heart: Life, Energy, and the Unity of Nature metabolism trail off, and why? One obvious idea is that the decline in relative metabolic rate mirrors the decline in surface area relative to volume. If this were the case, every 1,000-fold increase in body mass would see a 100-fold increase in metabolic rate. In 1883, Rubner, based on measurements of the metabolic rates of seven different-sized dogs, concluded that this was indeed so. He calculated the surface area of his experimental hounds using a formula published four years earlier by another German, Karl Meeh. Meeh encased human experimental subjects in paper cylinders—I imagine them looking like the Tin Man in The Wizard of Oz—and then weighed this paper. Knowing the paper’s thickness, he could work out the area of the people. Meeh concluded that to work out an animal’s surface area you should first weigh it, then take the two-thirds power of this number, and multiply it by a constant (that is, surface area = constant × weight2/3). Meeh’s experimental conclusion matched the predictions of basic geometry. Let’s return to the cubic beast. Its volume—assuming, again, that body mass reflects body volume and that the flesh of different animals is equally dense—is proportional to its length cubed. This is where heat is generated. Its surface area, where heat is lost, is proportional to its length squared. To get from 3 to 2, from a volume to an area, we need to multiply by 2/3 (3 × 2/3 = 2). This is the relation between volume and surface area—so Meeh’s experiments produced the same result expected from mathematical first principles. (Raising mass to the power of two-thirds is the same as squaring it and then taking the cube root of that result. For example, .) The formula also introduces the important concept of similarity. Similar shapes or objects are those with identical proportions, such as the two cubes with sides 1 and 2 centimeters long. To get from one to the other, you multiply every dimension by the same amount. All cubes are similar. If you multiplied the different dimensions of a cube by different amounts, you would get a different solid, such as a cuboid or a trapezoid. A formula that calculates area as the two-thirds power of mass assumes that large animals have the same proportions as small ones, that a cat is a scaled-up version of a mouse. This is obviously false: The proportions of animals change as they get bigger, both within

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In the Beat of a Heart: Life, Energy, and the Unity of Nature and between species. But the assumption of geometric similarity might be accurate enough not to upset experimental results over the relatively small size range shown by Meeh’s humans or Rubner’s dogs. When Rubner applied Meeh’s formula to his dogs, his measurements showed that the animals’ energy output was proportional to—similar to—their surface area. The measurements made good theoretical sense. Rubner collected evidence on his proposed surface law by experimenting on animals ranging in size from a horse to a mouse. On retiring in 1924 he wrote that he considered the law his greatest contribution to science. “There can be no doubt about [its] general validity,” he concluded. Rubner’s surface law is summed up thus: Each square meter of the surface of every mammal produces the same amount of heat. He estimated this heat output at about 1,000 calories per square meter of skin per day. It was in this sense, Rubner believed, that large and small animals were similar. Although the idea is most closely associated with Rubner, the French biologist Charles Richet came to the same conclusion around the same time, based on measurements of rabbits. This is how science proceeds, usually, not by lone geniuses striving toward stunning breakthroughs but by a community inching forward across a broad front. (Richet, incidentally, was probably happy to let Rubner have the credit for the surface law—Richet did win a Nobel Prize, for his discovery of anaphylactic shock, which laid the foundation for our understanding of allergies.) The surface area law soon became widely accepted by biologists. Scientists wishing to understand metabolism at the beginning of the twentieth century were thus faced with measuring two variables: metabolism and body surface area, the former by either heat output or respiratory exchange, the latter by either direct measurement or some approximation formula. Physiologists went about the task with zeal, measuring the surface area of thousands of men, women, children, babies, fat people, thin people, Asians, Westerners, the able bodied, and the handicapped—one study included two people who had each lost both legs in train accidents and “a 36-year-old cretin,” cretinism being the result of an underactive thyroid gland, which also leads to slow metabolism. Measurements of metabolic rates were made for those

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In the Beat of a Heart: Life, Energy, and the Unity of Nature The surface law hypothesized that every square meter of mammal skin produced the same amount of heat. So relative metabolic rate would decline at the same rate as surface area relative to body volume. lying down, sitting down, moving around, diabetics, hyperthyroids, and so on. As this project progressed, researchers taking measurements of skin surface found that Meeh’s formula seemed to overestimate the body’s area. Meeh had evidently demurred from wrapping his subjects too tightly. Later investigators showed no such squeamishness. They stripped their subjects down to their underwear and wrapped them in tin foil or plaster of Paris. Others took photographs from every angle or worked out the skin’s area from its electrical conductance. Despite its inaccuracies, Meeh’s formula was in common use for nearly 40 years—probably because it was mathematically simple and required only one measurement, weight. It eventually crumbled under an assault by Eugene DuBois, a New York–based pathologist, around 1915. At least as far as humans were concerned, DuBois was perhaps the foremost surveyor of skin and measurer of metabolism. Basal metabolic rate is a slippery concept. It’s hard to define what the basal functions of life are and impossible to measure them in a

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In the Beat of a Heart: Life, Energy, and the Unity of Nature living, breathing, fidgeting animal without also measuring the energy used up by lots of other processes and activities. Some researchers now avoid the term basal metabolic rate altogether, while others use it to refer to sleeping energy consumption; the measurement Dr. Costarelli made on me is usually called resting metabolic rate. DuBois helped develop the standards for measuring metabolic rate—the subject should be relaxed and hungry, at a temperature where he or she is neither shivering nor sweating—in an attempt to find some sort of baseline for metabolism. The hope is that the imprecisions even out over many measurements. Indeed, this is a general issue in biology. In a reversal of the earlier joke, a physicist can know the mass of every electron in the universe by weighing one. A biologist weighing a dog knows only the weight of that dog on that day. This variability has made the outlook of some biologists more similar to the mathematician than the astronomer in that joke, stressing the uncertainty in nature, rather than the generality. If scientists could standardize their measurements and comparisons of energy consumption, they could make progress in understanding metabolism. Minimizing metabolic rate before its measurement was an obvious option—it would avoid all the problems of defining what might be “typical” metabolism. But searching for one catch-all measurement casts the validity of the enterprise into doubt. No human, or any other animal, spends all its time in repose. As we have seen, metabolic rate varies hugely depending on where you are and what you are doing. So what can lying down for half an hour really tell us about energy consumption throughout life? Does a standardized laboratory measurement really tell us anything about the real world? Fortunately, it looks like it does. Metabolic rates of active animals measured in the field are, more or less, three times higher than their resting metabolic rate. A wild animal’s maximum metabolic rate is usually about 10 times its resting rate, although highly trained human athletes and racehorses can achieve up to 20 times their resting rate. It seems that comparisons based on resting rates can be useful guides to energy needs in the wild. Eugene DuBois, working with his engineer brother Delafield, tried to nail down human surface area once and for all. Eugene was a man of

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In the Beat of a Heart: Life, Energy, and the Unity of Nature action as well as science. He served in the U.S. Navy Medical Corps in both world wars and was awarded the Navy Cross in the first, for protecting the crew of the submarine he was serving on from chlorine poisoning. DuBois was interested in how the body performed at extremes. He was a leading light in aviation and diving medicine, and in 1928 he conducted an experiment on the arctic explorer Vilhjalmur Stefansson that showed it was possible to live for several weeks on meat and water alone with no apparent ill effects—as the Inuit do and as Stefansson had done on some of his journeys—an experiment often cited by contemporary advocates of low-carbohydrate, high-protein diets. DuBois, who had a penetrating glare and hawklike features, looks like he too might have liked to live on meat and water alone. He does not look like a man who would have let an experimental subject’s dignity get in the way of an accurate measurement. The DuBois brothers began by wrapping their subjects in brown paper, making molds that could then be laid flat on photographic paper. When exposed, the areas covered by the mold could be cut out and weighed, and this weight could be converted into area. In 1915, they published a formula for calculating body area from 19 different measurements—everything from circumference of the knee joint to length of the hand. Medics ignored this method, probably because it took about 10 minutes to do all the measurements and calculations. The DuBois brothers went away to measure more people’s surface area. By now their quest for accuracy had led them to replace the paper wrapping with sticking plaster, and to make their molds by tipping paraffin wax over the mummified victim. Eugene and Delafield returned a year later with a simplified formula that called only for height and weight to be measured. Other researchers developed less sweaty ways to measure surface area—after all, unlike humans, animals can’t be expected to submit meekly to being transformed into a waxwork. A team at the University of Missouri, led by Samuel Brody, came up with a device like a paint roller that they called the surface integrator. Once the animal was covered in stripes, the number of revolutions multiplied by the circumference of the roller gave the body area. In 1926, Brody’s team used the integrator to measure the surfaces of 600 cattle. In 1927, Hannah

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In the Beat of a Heart: Life, Energy, and the Unity of Nature Samuel Brody’s surface integrator being used to measure the area of a cow. Credit: Brody Environmental Center, University of Missouri. Stillman Bradfield, a graduate student at the University of Missouri, published a study describing her use of the surface integrator to measure the areas of 47 naked young women—to see how their areas compared with the men from whom most of the formulas had been derived. (Eugene DuBois was unimpressed: “There still remains some doubt as to whether the integrator is as accurate as the method employing molds,” he sniffed.) The surface law was going strong. Succeeding generations of physicians have tinkered with the numbers in the DuBois formula, but calculations of surface area are still based on height and weight. Many medical quantities, such as drug dosage, intravenous feeding rates, calorie requirements, and heart output are still calculated in terms of body surface area, as calculated by these formulas. As we shall see, there is no good reason for this.