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The mathematical beauty of life that Geoffrey West refers to in his book “Scale” is something that we are not really taught in schools and colleges.

Stories are at the heart of all good books, and not just works of fiction. And the story that sets the tone for Geoffrey West’s Scale appears on page 52 of the book and is about an elephant, a few scientists and the world gone wrong because of lack of knowledge.

Here is how the story goes. The year is 1962, and three scientists, Louis West (no relation to the author), Chester Pierce and Warren Thomas have proposed to study the impact of the hallucinogen LSD on elephants (yes, you read that right).

The broader idea was to study the potentially therapeutic effects of LSD on humans. The scientists decided to test LSD on an Asiatic elephant because these elephants move from being placid obedient animals to highly aggressive and dangerous ones for periods as long as two weeks.

The scientists speculated that this destructive behaviour was on account of autoproduction of LSD in the elephants’ brains. The idea was to inject LSD into an elephant and see if that would induce the aggressive and dangerous condition. This would help gain insight into studying the effect of LSD on humans.

An elephant named Tusko was chosen. Now the question was how much LSD should be injected into Tusko, given that he weighed a massive 3,000 kg. A safe dosage for a cat was around one-tenth of a milligram per kg of body weight. Hence, the safe dose for Tusco would be 300 miligrams, or so the scientists concluded, given its weight.

A shot of 297 milligrams was finally injected into the elephant. Tusko died one hour and 45 minutes later. The dosage turned out to be fatal. The scientists basically made the mistake of assuming that the dosage for an elephant would follow a linear scale, which it clearly did not.

As West writes: “The calculation of how big a dosage should be used on Tusko was based on the implicit assumption that effective and safe dosages scale linearly with body weight so that the dosage per kilogram was presumed to be the same for all mammals.” But that, as we saw, did not turn out to be the case.

West uses the example of Tusko to tell us that most scaling in life does not happen linearly but non-linearly. Just because elephants weigh X times more than a cat, that does not mean that they require X times more dosage of LSD than a cat. And what is true for mammals is also true for other animals, cities and companies, explains West.

Scaling basically refers to how a system changes when its size changes. If the population of a city doubles, does it also lead to doubling of roads, crime, etc? If an animal’s weight is halved, does it require half as much food?

An animal that is twice the size of another and hence, has twice as many cells, requires only 75 per cent more food and energy every day, rather than 100 per cent more. West writes: “A profound consequence of this rule is that on a per gram basis, the large animal is actually more efficient than the smaller one because less energy is required to support each gram of her tissue.”

How does scaling work in the case of cities? If a city is twice the size of another in the same country, then its wages, wealth, number of patents, AIDS cases as well as violent crime, all increase by 15 per cent above mere doubling. At the same time, a similar saving is made in case of infrastructure. Hence, the total length of pipes, roads, or electrical wires, is only about 85 per cent more, with every doubling of city size.

West writes: “Thus a city of 10 million typically needs 15 per cent less of the same infrastructure compared with two cities of 5 million each, leading to significant savings in materials and energy use. The savings lead to a significant decrease in the production of emissions and pollution. Consequently, the greater efficiency that comes with size has the non-intuitive but very important consequence that on average, the bigger the city, the greener it is and the smaller its per capita carbon footprint.” And these gains are largely unplanned.

But there is a dark side too. While the doubling of city size increases wealth, wages and innovation, it also increases the amount of crime, pollution and diseases to the same degree.

The mathematical beauty of life that West talks about all through the book is something that we are not really taught in schools and colleges. What we are taught instead is Euclidean geometry. Over and above this, these connections are easy to make, given the amount of data that is generated in the United States and other Western economies. But what about countries like India? How do things stack up here? Take the case of Delhi, which has a population of around 1.11 crore, as per the 2011 census. Thus, Delhi’s population is nearly double that of Ahmedabad which is at around 56 lakh.

Does that mean that Delhi has only 85 per cent more physical infrastructure than Ahmedabad has? Are crime and pollution in Delhi, 15 per cent more than double that in Ahmedabad? Sadly, given the weak data collection mechanisms in India, such research hasn’t really been done.

West does refer to this. In fact, a similar sort of comparison can be made between Bengaluru of 2001 which had a population of around 43 lakh, and the Bengaluru of 2011, which had a population of around 84 lakh. Hence, the population has doubled in a period of 10 years.

Another question that crops up here is, the mathematical beauty of this research notwithstanding, how does it help? Having researched and written about these patterns, West is not really sure about what to do with them. But then that’s how most research evolves, from intellectual curiosity to being useful for the public at large.

To conclude, the book is an entertaining read for people looking for something a little more involving than normal non-fiction. Though, it is slightly longer than most books tend to be these days and in the hands of a good editor could easily have had 75-100 pages fewer. But this weakness doesn’t make the book any lesser. West summarises the book best when he writes: “Underlying the daunting complexity of the natural world lies a surprising simplicity, regularity and unity when viewed through the coarse-grained lens of scale.”