A man looking at a hippopotamus may sometimes be tempted to regard a hippopotamus as an enormous mistake; but he is also bound to confess that a fortunate inferiority prevents him personally from making such mistakes. -- GK Chesterton

After reading JBS Haldane's On Being the Right Size, I wondered why I never asked a question during my visits to the zoo. How come a rhinoceros with such a huge body rests on so lean legs? Wouldn't it collapse due to its weight?

Haldane answers: "legs [would be] short and thick, like the rhinoceros, so that every pound of weight has still about the same area of bone to support it."

He has more wonderful things to say about humans. Why mythical giants are pictured sitting? "These monsters were not only ten times as high...but ten times as wide and ten times as thick, so that their total weight was a thousand times or about eighty to ninety tons. Unfortunately the cross sections of their bones were only a hundred times... so that every square inch of giant bone had to support ten times the weight borne by a square inch of human bone. As the human thigh-bone breaks under about ten times the human weight, Pope and Pagan would have broken their thighs every time they took a step."

Haldane is also notorious of saying that the Creator seems to have an inordinate fondness for bees -- as they make up 25% of all insect species. And as such, insects it seems are hardly bugged by gravity as mammals do.

"For the resistance presented to movement by the air is proportional to the surface of the moving object. Divide an animal’s length, breadth, and height each by ten; its weight is reduced to a thousandth, but its surface only to a hundredth. So the resistance to falling in the case of the small animal is relatively ten times greater than the driving force."

"But there is a force which is as formidable to an insect as gravitation to a mammal. This is surface tension. A man coming out of a bath carries with him a film of water of about one-fiftieth of an inch in thickness. This weighs roughly a pound."

In fact, such scaling problems abound in science. Galileo, the contrarian barely in his 20s, gave a lecture on Dante's Divine Comedy -- demolishing the very structure of the inferno geometrically.

"Ironically, it was a lecture on literature that would turn Galileo's fortunes. The Academy of Florence had been arguing over a 100-year-old controversy: What were the location, shape, and dimensions of Dante's Inferno? Galileo Galilei wanted to seriously answer the question from the point of view of a scientist. Extrapolating from Dante's line that "[the giant Nimrod's] face was about as long/And just as wide as St. Peter's cone in Rome," Galileo deduced that Lucifer himself was 2,000 armlengths long. The audience was impressed, and within the year, Galileo had received a three-year appointment to the University of Pisa, the same university that never granted him a degree!"


"What Galileo said, put simply, is that many commonly accepted dimensions did not stand up to mathematical scrutiny. Using complex geometrical analysis, he attacked a leading scholar’s version of the Inferno’s structure, pointing out that his description of the infernal architecture — such as the massive cylinders descending to the center of the Earth — would, in real life, collapse under their own weight."

"The insights Galileo gleaned from analyzing Dante’s measurements in fact anticipated a vital principle of structural engineering. By asserting that you cannot create a giant Lucifer by super-sizing the model of a man — that increasing an object’s magnitude would create a whole new set of structural and material imperatives — Galileo was paving the way for the construction of everything from ocean liners to skyscrapers..."

As someone who's at least got a degree in literature, I wondered if this eliminated all the beauty that many claim Dante's poetry had. But Galileo,an admirer of Arts he was, used its imagination as much in ushering a Scientific Revolution as he did to understand the poetry in its true dimension.

Here is another insight into scaling.

"In the early 1930s, Max Kleiber was a biologist working in the animal-husbandry department at the University of California, Davis. He noticed that the sprawlingly diverse animal kingdom could be characterized by a simple mathematical relationship, in which the metabolic rate of a creature is equal to its mass taken to the three-fourths power. This ubiquitous principle had some significant implications, because it showed that larger species need less energy per pound of flesh than smaller ones. For instance, while an elephant is 10,000 times the size of a guinea pig, it needs only 1,000 times as much energy. Other scientists soon found more than 70 such related laws, defined by what are known as “sublinear” equations. It doesn’t matter what the animal looks like or where it lives or how it evolved — the math almost always works.

"...[Using Kleiber's insight, Geoffrey West of Santa Fe Institute and another researcher, Bettencourt] concluded that cities looked a lot like elephants. In city after city, the indicators of urban “metabolism,” like the number of gas stations or the total surface area of roads, showed that when a city doubles in size, it requires an increase in resources of only 85 percent.

This straightforward observation has some surprising implications. It suggests, for instance, that modern cities are the real centers of sustainability. According to the data, people who live in densely populated places require less heat in the winter and need fewer miles of asphalt per capita. (A recent analysis by economists at Harvard and U.C.L.A. demonstrated that the average Manhattanite emits 14,127 fewer pounds of carbon dioxide annually than someone living in the New York suburbs.) Small communities might look green, but they consume a disproportionate amount of everything. As a result, West argues, creating a more sustainable society will require our big cities to get even bigger. We need more megalopolises.

But a city is not just a frugal elephant; biological equations can’t entirely explain the growth of urban areas. While the first settlements in Mesopotamia might have helped people conserve scarce resources — irrigation networks meant more water for everyone — the concept of the city spread for an entirely different reason. “In retrospect, I was quite stupid,” West says. He was so excited by the parallels between cities and living things that he “didn’t pay enough attention to the ways in which urban areas and organisms are completely different.”

What Bettencourt and West failed to appreciate, at least at first, was that the value of modern cities has little to do with energy efficiency. As West puts it, “Nobody moves to New York to save money on their gas bill.” Why, then, do we put up with the indignities of the city? Why do we accept the failing schools and overpriced apartments, the bedbugs and the traffic?

In essence, they arrive at the sensible conclusion that cities are valuable because they facilitate human interactions, as people crammed into a few square miles exchange ideas and start collaborations...Cities are all about the people, not the infrastructure.”


"Recently, West and Bettencourt...began exploring yet another subject: the corporation. At first glance, cities and companies look very similar. They’re both large agglomerations of people, interacting in a well-defined physical space. They contain infrastructure and human capital; the mayor is like a C.E.O.

But it turns out that cities and companies differ in a very fundamental regard: cities almost never die, while companies are extremely ephemeral. As West notes, Hurricane Katrina couldn’t wipe out New Orleans, and a nuclear bomb did not erase Hiroshima from the map. In contrast, where are Pan Am and Enron today? The modern corporation has an average life span of 40 to 50 years.

This raises the obvious question: Why are corporations so fleeting? After buying data on more than 23,000 publicly traded companies, Bettencourt and West discovered that corporate productivity, unlike urban productivity, was entirely sublinear. As the number of employees grows, the amount of profit per employee shrinks. West gets giddy when he shows me the linear regression charts. “Look at this bloody plot,” he says. “It’s ridiculous how well the points line up.” The graph reflects the bleak reality of corporate growth, in which efficiencies of scale are almost always outweighed by the burdens of bureaucracy. “When a company starts out, it’s all about the new idea,” West says. “And then, if the company gets lucky, the idea takes off. Everybody is happy and rich. But then management starts worrying about the bottom line, and so all these people are hired to keep track of the paper clips. This is the beginning of the end.”

The danger, West says, is that the inevitable decline in profit per employee makes large companies increasingly vulnerable to market volatility. Since the company now has to support an expensive staff — overhead costs increase with size — even a minor disturbance can lead to significant losses. As West puts it, “Companies are killed by their need to keep on getting bigger.”