Technology Forecaster; Consulting Associate Professor, Stanford University
Haldane’s Rule of the Right Size

Toss a mouse from a building. It will land, shake itself off and scamper away. But if similarly dropped, “… a rat is killed, a man is broken, a horse splashes.” So wrote J.B.S. Haldane in his 1926 essay "On Being the Right Size." Size matters, but not in the way a city-stomping Godzilla or King Kong might hope.

Every organism has an optimum size and a change in size inevitably leads to a change in form. Tiny lizards dance weightlessly up walls, but grow one to Godzilla size, and the poor creature would promptly collapse into a mush of fractured bones and crushed organs. This principle is not just a matter of extremes: A hummingbird scaled to the size of a blue jay would be left hopelessly earthbound, fluttering its wings in the dust.

If gravity is the enemy of the large, surface tension is the terror of the small. Flies laugh at gravity, but dread water. As Haldane notes, “An insect going for a drink is in as great danger as a man leaning out over a precipice in search of food.” No wonder most insects are either unwettable, or do their drinking at a distance through a straw-like proboscis.

Thermoregulation is an issue for all organisms, which is why arctic beasts tend to be large while tropical critters are small. Consider a sphere: As it grows, the interior volume increases faster than the surface area of its outer skin. Small animals have lots of surface area relative to their volume, an advantage in the Torrid Zone where survival depends on efficient cooling. Back up in the arctic, the same ratio works in reverse: Large beasts rely upon a lower surface area ratio to help stay warm.

The power of Haldane’s rule is that it applies to far more than just organisms. Hidden laws of scale stalk humankind everywhere we turn. Like birds, the minimum power an aircraft requires to stay in flight increases faster than its weight. This is why large birds soar instead of flapping their wings—and Howard Hughes’ Spruce Goose never got more than a few feet off the water.

Size inevitably comes at a cost of ever-greater complexity. In Haldane’s words, “Comparative anatomy is largely the story of the struggle to increase surface in proportion to volume.” Which is why intestines are coiled and human lungs pack in a hundred square yards of surface area. Complexity is a Goldilocks tool for the large, widening the zone of “just right.”

But complexity can expand the envelope of “just right” only so far before bad things happen. Like the engine on an underpowered aircraft, the cost can be catastrophic. Everything from airplanes to institutions has an intrinsic right size, which we ignore at our peril. The 2008 banking crisis taught us that companies and markets are not exempt from Haldane’s rule. But we got the lesson backwards: It wasn’t a case of “too big to fail,” but rather “too big to succeed.” One cannot help but fret that in their globe-spanning success, mega-companies are flirting with the unforgiving limits of right size.

Our political institutions also cannot escape the logic of Haldane’s rule. The Greeks concluded that their type of democracy worked best in a unit no larger than a small city. Haldane adds that the English invention of representative government made possible a scale-up to large stable nation-states. Now it seems that the US and other nations are growing beyond their right size for their political systems. Meanwhile, globalization is stalling in a cloud of conflict and confusion precisely because no workable political structure right-sized for the entire planet exists. The turbulence of 2016 very likely is a mere prologue to more wrenching shifts ahead.

Haldane wrote decades before the advent of globalization and digital media, but his elegant rule of right size hovers behind our biggest challenges today. Can mega-cities be sustained? Have social networks scaled beyond the optimum size for sensible exchange? Has cyberspace become so large and complexly interdependent that it is at risk of catastrophic scale-driven failure? Is our human population outstripping its right size given the state of our planetary systems? As we face these and the myriad other surprises to come, we would do well to remember that mice bounce, horses splash—and size truly matters.