and an external faculty member of the Santa Fe Institute.He applied the “Page 99 Test” to his new book, The Model Thinker: What You Need to Know to Make Data Work for You, and reported the following:
The Model Thinker describes how we use models to be better thinkers. Models are formal abstractions written in mathematics or symbols that can be brought to data. The book has three parts. The first part describe the uses of models - to reason, explain, design, communicate, act, predict, and explore - and advocate the use of many models when confronted with complex phenomena. The middle of the book contains short, self contained chapters on a core set of the most widely used models. Finally, the third part shows how to apply ensembles of these models to real world problems - the opioid epidemic and obesity.Visit Scott E. Page's faculty webpage.
Page 99 puts us near the beginning of the middle. The first half of the page completes the introduction to the concept of concavity. The page begins with a tantalizing notion borrowed from Jim March: concavity can explain why people are often blissful in long distance relationships.
Allow me to explain.
An increasing concave function has a slope that decreases. In economics, ecology, and other fields, such functions capture diminishing marginal value. For example, the marginal value of each additional scoop of ice cream falls as we add scoops: One scoop of ice cream is way better than an empty cone. Way better!! Two scoops of ice cream is better than one, but by less of a margin. And three scoops of ice cream may only be a tiny bit better than two scoops.
Page 99 describe how concavity implies risk aversion: one scoop of ice cream for certain is preferred to a risky bet in which with probability 1/2 you get nothing and with probability 1/2 you get two scoops. It also describes how concavity defined over two arguments -- ice cream and time on the beach -- implies a preference for diversity. Most of us would prefer one scoop of ice cream and four hours on the beach to either two scoops of ice cream and no beach time or no ice cream and eight hours on the beach.
At the bottom of page 99, I start to describe economic growth models -- which assume that the output produced in an economy is a concave function of both labor and physical capital. The logic as to why output is concave in labor parallels the logic for why happiness is concave in scoops of ice cream. One worker at a coffee shop can serve a lot of coffees. The second worker increases output as does the third and so on. But each worker, at the margin, adds less to total output because the area behind the counter becomes crowded. Plus, the workers have to wait in line to use the espresso machine.
Let's go back to those happy long distance relationships. My wife Jenna is, for me, an ideal life partner - brilliant, kind, considerate, conscientious, other focused, and ridiculously good at cribbage. Nevertheless, my happiness is concave in Jenna. At the end of a long day, sitting with her in front of the fire reading or watching a mystery, I feel quiet joy. But, were I only to see Jenna for an hour a month, during that hour I would be ridiculously happy.
That same logic applies in other unexpected cases as well. Page 99 follows up the happy long distance relationships with an observation that concave happiness also explains why condo developers invite us for a free weekend and not for a free month. For a weekend, sitting on a secluded beach can be awesome. After a month, once you've finished reading The Model Thinker and other great new books, you may find the beach a bit dull.
--Marshal Zeringue