Scale: The Universal Laws of Life and Death

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Scale: The Universal Laws of Life and Death in Organisms, Cities and Companies, by Geoffrey West

Fascinating book, though probably somewhat in thrall to the financialisation of everything, in that it seeks to extract mathematical rules that explain sociological, as well as biological, phenomena. No great surprise: West is a theoretical physicist from the Santa Fe Institute. These people are prone to hardcore reductionism and simplified mathematical truths — Steven Weinberg’s Lake Views was similar — but on the other hand you can see social scientists being a bit sniffy about this outsider traducing their sacred turf and calling it all a simple case of maths.

There are some dimensional constants between organisations of different sizes.

There seems to be something about the factor of four: scale factors are all expressed in “fourths” — five-fourths, halves, three-quarters and so on — though West doesn’t offer a theory for what it is, and in any case, isn’t clear anything turns on it. Lots of numbers are expressible in fractions denominated by four.

Sublinear versus superlinear scaling

Scaling rates of a given phenomenon can be sublinear — where with growth the effect is progressively diluted — and superlinear — where the effect is amplified. Bounded organisms scale sublinearly as “research and development” across the “enterprise” is diluted; distributed networks that are not bounded or delimited, and which may be composed of bounded organisms — scale superlinearly. Here “research and development” is distributed at the edges and nodes, and the more edges and nodes there are the more research and development.

Human lifespans are bounded

The maximum human lifespan is around 120 years: while we have greatly improved the weighted average of human life expectancy over the last century — it was around 50 years, it is now nealy 80 — the maximum human lifespan, of about 120 years, has not shifted. We are moving towards an asymptotic maximum, apparently. (This view is not, if Google is anything to go by, universally shared).

Companies versus cities

There is an interesting comparison between cities — which scale at a superlinear rate, are more or less immortal — and companies, which scale at a sublinear rate have a definitive lifespan that seems as determinate as does a human one. The early superlinear growth of companies plateaus and then becomes sublinear as the internal costs of organisation grow and the marginal return from growth tails off, and expenditure switches from research and development — innovation — to management and control — administration.

This does not happen in cities, where the degree of innovation scales superlinearly with growth of the city. A huge city manages more innovation per capita than a small city; a huge multinational manages less innovation per capita than a small firm.