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

by Geoffrey West

One final note: Mandelbrot showed surprisingly little interest in understanding the mechanistic origins of fractals. Having revealed to the world their extraordinary universality, his passion remained more with their mathematical description than with their physical origins. His attitude seemed to be that they were a fascinating property of nature and we should delight in their ubiquity, simplicity, complexity, and beauty. We should develop a mathematics to describe and use them, but we should not be too concerned about the underlying principles for how they are generated. In a word, he approached them more as a mathematician than as a physicist. This may have been one of the reasons that his great discovery did not receive quite the appreciation in the physics community and scientific establishment that it perhaps deserved and, as a result, he did not receive the Nobel Prize, despite broad recognition in many quarters and a litany of prestigious awards and prizes.

Despite being based on the same set of principles, the actual mathematics and dynamics are typically quite different in each case, reflecting the different physical structures of the networks. I will not belabor how these various systems exploit the same set of principles, but in all cases the results are very similar and quarter-power scaling emerges.

A general argument to address this can be made by recognizing that, in addition to minimizing energy loss, natural selection has also led to a maximization of metabolic capacity because metabolism produces the energy and materials required to sustain and reproduce life.

In other words, the total effective area of two-dimensional sheets filling three-dimensional washing machines scales like a volume rather than an area, so in this sense, we have turned an area into a volume.

surfaces. This additional dimension, which arises from optimizing network performance, leads to organisms’ functioning as if they are operating in four dimensions. This is the geometric origin of the quarter power. Thus, instead of scaling with classic 1⁄3 exponents, as would be the case if they were smooth nonfractal Euclidean objects, they scale with 1⁄4 exponents.

Although living things occupy a three-dimensional space, their internal physiology and anatomy operate as if they were four-dimensional.

In marked contrast to this, almost none of our man-made engineered artifacts and systems, whether automobiles, houses, washing machines, or television sets, invoke the power of fractals to optimize performance. To a very limited extent, electronic equipment such as computers and smart phones does, but compared with how you work they are extraordinarily primitive.

the whale needs only one hundredth the amount of energy needed by a shrew to supply blood to one of its cells.

There is, however, one human invention that has evolved via this process which is comparable to what traditional natural selection has thus far produced, and that is the city. Cities clearly have an organic nature and share much in common with traditional organisms. They metabolize, they grow, they evolve, they sleep, they age, they contract disease, suffer damage and repair themselves, and so on. On the other hand, they rarely reproduce nor do they easily die. Furthermore, their size is enormously greater than even a mythical Godzilla.

The onto part of this word is derived from the Greek word for “being,” while genesis means “origins,” so ontogenesis, or ontogeny, connotes the idea of the study of how we came to be.