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

by Geoffrey West

Scaling up from the small to the large is often accompanied by an evolution from simplicity to complexity while maintaining basic elements or building blocks of the system unchanged or conserved.

skyscraper in a large city is a significantly more complex object than a modest family dwelling in a small town, but the underlying principles of construction and design, including questions of mechanics, energy and information distribution, the size of electrical outlets, water faucets, telephones, laptops, doors, et cetera, all remain approximately the same independent of the size of the building.

organisms have evolved to have an enormous range of sizes and an extraordinary diversity of morphologies and interactions, which often reflect increasing complexity, yet fundamental building blocks like cells, mitochondria, capillaries,

that “metabolic rate scales as a power law whose exponent is very

close to the number 3⁄4.”

elephants are roughly 10,000 times (four orders of magnitude, 104) heavier than rats; consequently, they have roughly 10,000 times as many cells. The 3⁄4 power scaling law says that, despite having 10,000 times as many cells to support, the metabolic rate of an elephant (that is, the amount of energy needed to keep it alive) is only 1,000 times (three orders of magnitude, 103) larger than a rat’s; note the ratio of 3:4 in the powers of ten.

This represents an extraordinary economy of scale as size increases, implying that the cells of elephants operate at a rate that is about a tenth that of rat cells.

The scaling law, however, is nonlinear and says that metabolic rates don’t double but, in fact, increase by only about 75 percent, representing a whopping 25 percent savings with every doubling of size.12

This scaling law for metabolic rate, known as Kleiber’s law after the biologist who first articulated it, is valid across almost all taxonomic groups, including mammals,

example, if the size of a mammal is doubled, its heart rate decreases by about 25 percent.

Highly complex, self-sustaining structures, whether cells, organisms, ecosystems, cities, or corporations, require the close integration of enormous numbers of their constituent units that need efficient servicing at all scales.

This has been accomplished in living systems by evolving fractal-like, hierarchical branching network systems presumed optimized by the continuous “competitive” feedback mechanisms implicit in natural selection.

prevalence of the one-quarter exponent. As an example, Kleiber’s law follows from requiring that the energy needed to pump blood through mammalian circulatory systems, including ours, is minimized so that the energy we devote to reproduction is maximized.

mature organism is essentially a nonlinearly scaled-up version of the infant—just compare the various proportions of your body with those of a baby.

Growth at any stage of development is accomplished by apportioning the metabolic energy being delivered through networks to existing cells to the production of new cells that build up new tissue.

why we eventually stop growing even though we continue to eat. This turns out to be a consequence of the sublinear scaling of metabolic rate and the economies of scale embodied in the network design.

Because networks determine the rates at which energy and resources are delivered to cells, they set the pace of all physiological processes. Because cells are constrained to operate systematically slower in larger organisms relative to smaller ones, the pace of life systematically decreases with increasing size. Thus, large mammals live longer, take longer to mature, have slower heart rates, and cells that don’t work as hard as those of small mammals, all to the same predictable degree. Small creatures live life in the fast lane while large ones move ponderously, though more efficiently, through life; think of a scurrying mouse relative to a sauntering elephant.

Like organisms, cities are indeed approximately scaled versions of one another, despite their different histories, geographies, and cultures, at least as far as their physical infrastructure is concerned.

Despite their amazing diversity and complexity across the globe, and despite localized urban planning, cities manifest a surprising coarse-grained simplicity, regularity, and predictability.

scaling implies that if a city is twice the size of another city in the same country (whether 40,000 vs. 20,000 or 4 million vs. 2 million), then its wages, wealth, number of patents, AIDS cases, violent crime, and educational institutions all increase by approximately the same degree (by about 15 percent above mere doubling), with similar savings in all of its infrastructure.

The bigger the city, the more the average individual systematically owns, produces, and consumes, whether goods, resources, or ideas.

planet. With the invention of language and the consequent exchange of information in social network space we discovered how to innovate and create wealth and ideas, ultimately manifested in superlinear scaling.

biology, network dynamics constrains the pace of life to decrease systematically with increasing size following the 1⁄4 power scaling laws.

In contrast, the dynamics of social networks underlying wealth creation and innovation leads to the opposite behavior, namely, the systematically increasing pace of life as city size increases: diseases spread faster, businesses are born and die more often, commerce is transacted more rapidly...

In biology, growth is driven by metabolism whose sublinear scaling leads to a predictable, approximately stable size at maturity.

Just as bounded growth in biology follows from the sublinear scaling of metabolic rate, the superlinear scaling of wealth creation and innovation (as measured by patent production, for example) leads to unbounded, often faster-than-exponential growth consistent with open-ended economies.

finite time singularity. In a nutshell, the problem is that the theory also predicts that unbounded growth cannot be sustained without having either infinite resources or inducing major paradigm shifts that “reset” the clock before potential collapse occurs.

We have sustained open-ended growth and avoided collapse by invoking continuous cycles of paradigm-shifting innovations such as those associated on the big scale of human history with discoveries of iron, steam, coal, computation, and, most recently, digital information technology.

Theory dictates that such discoveries must occur at an increasingly accelerating pace; the time between successive innovations must systematically and inextricably get shorter and shorter.

the time between the “Computer Age” and the “Information and Digital Age” was perhaps twenty years, in contrast to the thousands of years between the Stone, Bronze, and Iron ages.

If we therefore insist on continuous open-ended growth, not only does the pace of life inevitably quicken, but we must in...

Innovation and wealth creation that fuel social systems, if

left unchecked, potentially sow the seeds of their inevitable collapse.

this sense, companies are much more like organisms than cities. The scaling exponent for companies is around 0.9, to be compared

with 0.85 for the infrastructure of cities and 0.75 for organisms.

despite their broad diversity and apparent individuality, companies grow and function under general constraints and principles that transcend their size and business sector.

the sublinear scaling of metabolic rate underlies their cessation of growth and a size at maturity that remains approximately stable until death.

In their youth, many are dominated by a spectrum of innovative ideas as they seek to optimize their place in the market. However, as they grow and become more established, the spectrum of their product space inevitably narrows

at the same time, they need to build a significant administration and bureaucracy.

Relatively quickly, economies of scale and sublinear scaling, reflecting the challenge of efficiently administering a large and complex organization, dominate innovation and ideas encapsulated in superlinear sc...

they grow companies tend to become more and more unidimensional, driven partially by market forces but also by the inevitable ossification of the top-down administrative and bureaucratic needs perceived as necessary for operating a traditional company in the modern era.

Change, adaptation, and reinvention become increasingly difficult to effect, especially as the external socioeconomic clock is continually accelerating and conditions change at a faster and faster rate.

nor can nature produce trees of extraordinary size because the branches would break down under their own weight; so also it would be impossible to build up the bony structures of men, horses,

or other animals so as to hold together and perform their normal functions if these animals were to be increased enormously in height . . . for if his height be increased inordinately he will fall and be crushed under his own weight.

how areas and volumes associated with any object scale as its size increases

that the strength of pillars holding up buildings, limbs supporting animals, or trunks supporting trees is proportional to their cross-sectional areas (Figure 6).

Thus, when an object is scaled up in size, its volumes increase at a much faster rate than its areas.

most heating, cooling, and lighting is proportional to the corresponding surface areas of the heaters, air conditioners, and windows. Their effectiveness therefore increases much more slowly than the volume of living space needed to be heated, cooled, or lit, so these need to be disproportionately increased in size when a building is scaled up.

large animals, the need to dissipate heat generated by their metabolism and physical activity can become problematic because the surface area through which it is dissipated is proportionately much smaller relative to their volume than for smaller ones.

Elephants, for example, have solved this challenge by evolving disproportionately large ears to significantly increase their surfa...