On Being The Right Size — J.B.S Haldane on Size, Structure, Nature and Institutions

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On Being the Right Size — J.B.S Haldane on size, structure, nature and institutions

Galileo and Godzilla

In On Being the Right Size, biologist JBS Haldane writes that each animal, as a product of chance mutation and natural selection over geologic time, “has a most convenient size”. We don’t expect, for example, to see cheetah-like elephants or elephant-like eagles in the wild, do we?

As Haldane writes:  

“Suppose that a gazelle, a graceful little creature with long thin legs, is to become large, it will break its bones unless it does one of two things. It may make its legs short and thick, like the rhinoceros, so that every pound of weight has still about the same area of bone to support it. Or it can compress its body and stretch out its legs obliquely to gain stability, like the giraffe.”

JBS Haldane. (1927). On Being the Right Size.

Scaling ideas are not new. Galileo observed long ago in the Two New Sciences that a proportionate increase in dimensions will see its volume (a cubic multiplier) increase faster than its surface area (a square multiplier). It follows that a thousandfold increase in some poor lizard’s dimensions would produce a Godzilla that collapses under its own weight. The cross-sections of its limbs cannot cope with all that extra stress.

“Who does not know that a horse falling from a height of three or four cubits will break his bones, while a dog falling from the same height or a cat from a height of eight or ten cubits will suffer no injury?  …  Nature cannot produce a horse as large as twenty ordinary horses or a giant ten times taller than an ordinary man unless by miracle or by greatly altering the proportions of his limbs and especially of his bones, … Likewise, the current belief that, in the case of artificial machines, the very large and the very small are equally feasible and lasting is a manifest error.”

Galileo Galilei. (1638). Dialogues Concerning Two New Sciences.

Size and design

Indeed, there seems to be peculiar design and scaling principles at work. If you increase an animal’s dimensions tenfold isometrically, then its volume and weight will jump one thousand times over (assuming no changes in structure). The animal would require a thousand times more oxygen and nutrients to sustain its cells and livelihood.

Such a creature, you can imagine, might struggle under simple scaling rules. Small organisms like the microscopic worm, for example, can make do with a simple respiratory system, absorbing oxygen through its skin. Larger beasts, whose oxygen requirements grow manifold, depend on complex evolutionary technologies like gills and lungs.

The story is similar for plants too. Haldane contrasts the “mere round cells” of simple, green algae with the roots and leaves of higher plants (where the increased surface area helps with oxygen intake). Many evolutionary strategies exist to help larger creatures with resource and nutrient absorption.

“The higher animals are not larger than the lower because they are more complicated. They are more complicated because they are larger.”

JBS Haldane. (1927). On Being the Right Size.

Of mice and elephants

Evolution is a masterful, blind watchmaker. An elephant is not simply an oversized mouse. It has proportionately stouter bones to support its weight. This is also, in part, why we find grander lifeforms in our oceans. Water buoyancy helps to counteract the ‘weight’ of gravity. Whales do not need the musculoskeletal technologies that Godzilla might on land.

Scaling operates on many more dimensions. In Of Mice and Elephants, George Johnson reports that animals average around one billion heartbeats in their lifetime. But the pulse rates of larger animals “slow down”, and their “life spans stretch out longer”. Elephants use their heartbeats more slowly than mouses do.1

Evolution, it seems, has generated nutrient supplying networks in larger organisms with greater economies of scale. While scale may impose constraints on design, it also confers efficiencies and survival traits to the organism. Darwinism, as always, is a game of trade-offs.

“The overarching lesson, … is that as organisms grow in size they become more efficient. That is why nature has evolved large animals[.]… It’s a much better way of utilizing energy. This might also explain the drive for corporations to merge. Small may be beautiful, but it is more efficient to be big.”

Geoffrey West in Of Mice and Elephants: A Matter of Scale (1999) by George Johnson.

1 Note, however, that this isn’t a universal law. We know, for instance, that the life expectancy of dogs tends to fall with size. Nature is full of quirks and outliers. 

Size and institutions

Engineers are also well aware of scaling challenges. Simple increases in proportions are unlikely to bring about longer bridges, larger vessels, and taller skyscrapers. Can you imagine ferrying a thousand souls on supersized canoes? As the history of engineering shows, new designs, materials, and innovations are necessary to meet our insatiable appetite for more with less.

Haldane believes that such scaling principles apply to society as well. The citizens of Ancient Greece, for example, “could listen to [their] orators and vote directly on questions of legislation”. But such a model, in its exactitude, would fail in the United States. Such practices cannot handle a populace that is many times larger and multidimensional. Advances in organization and communications were necessary to facilitate the larger political institutions of modern times.

Companies exhibit similar patterns too. How often do we see large corporations preserve the start-up cultures that birthed their success? Processes, structures, and hierarchies help businesses to cope with newfound size. The preferred model of organization and culture, of course, is open to heated debate and endless Harvard Business Review articles.

“And just as there is a best size for every animal, so the same is true for every human institution”.

JBS Haldane. (1927). On Being the Right Size.

We cannot do the topic of scaling justice with only a thousand words. But I leave it here at that as food-for-thought. Just know that, whether in nature, engineering or business, scaling principles are busy at work. Indeed, as physicist Mitchell Feigenbaum reminds:

“One has to look for different ways… One has to look for scaling structures – how do big details relate to little details. You look at fluid disturbances, complicated structures in which the complexity has come about by a persistent process. At some level, they don’t care very much what the size of the process is – it could be the size of a pea or the size of a basketball. The process doesn’t care where it is, and moreover, it doesn’t care how long it’s been going. The only things that can ever be universal, in a sense, are scaling things.”

Mitchell Feigenbaum. In James Gleick. (1984). Solving the Mathematical Riddle of Chaos.

Sources

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