Scale (2017) is a glimpse into the hidden and fascinating world of the mathematical relationships that tie the world together. The blinks describe how such laws connect everything from microscopic organisms to international metropolises, and what they can tell us about the behavior of complex systems.
Earth is home to over 8 million different species, from microscopic bacteria to enormous blue whales, as well as an incredible diversity of social life, cultures, cities and traditions.
It can be quite overwhelming to think about. But the truth is that there are some surprising systematic patterns behind the complexity of biological and socioeconomic life. For instance, if you plot a graph of the metabolic rate of animals – that is, the amount of energy they spend per unit of time – against the body mass of those animals, you’ll see a perfectly straight line.
That’s right; the metabolic rate of any animal from a mouse to an elephant is perfectly fixed relative to its body mass. Not only that, but if in the same equation you substitute the metabolic rate for the total number of heartbeats in an animal’s life, you’ll get another straight line!
There is, however, one trick at play. To get this result, the scales need to be logarithmic, meaning the units on each axis need to increase by factors of ten, so from one to ten to 100, and so on.
Take an example from the world of economics: if you plot out the number of patents registered in a city against that city’s population, you’ll find that the number of patents will increase 15 percent faster than the population, also producing a straight line.
Are these incredible correlations mere coincidences?
Hardly. What you’re actually observing are called scaling relationships. The examples above are just a peek into the ways organisms and cities scale with size, and understanding this phenomenon can illuminate much about the world.
For instance, new drugs are often tested on mice to model the way they’ll impact the human body. However, mice are of course much smaller than people – so how can scientists draw conclusions about humans from tests on rodents? Well, scaling can explain the answer. In the following blinks, you’ll learn about other incredible ways scaling can explain organisms, cities and even companies.