George G. Szpiro's "Perplexing Paradoxes"

George G. Szpiro is an author and journalist who was a longtime correspondent for the Swiss daily Neue Zürcher Zeitung. His many books include Numbers Rule: The Vexing Mathematics of Democracy, from Plato to the Present (2010) and Risk, Choice, and Uncertainty: Three Centuries of Economic Decision-Making (2020). Szpiro was on the faculty at the Wharton School, University of Pennsylvania, and the Hebrew University in Jerusalem.

He applied the “Page 99 Test” to his new book, Perplexing Paradoxes: Unraveling Enigmas in the World Around Us, and reported the following:

On page 99 you will see nothing but a picture of 10,000 dots randomly scattered within a square that contains an inscribed circle. The caption says “Simulating the number Pi.”

The graph is an illustration of the paradox – and the power -- of random numbers. The paradox is that if someone shows you a sequence of numbers, claiming that they are random, there is no way of verifying that they are, in fact, random. Because if you ‘recognize’ the sequence as random, it is, by definition, not random.

The power of random numbers, on the other hand, is that one can use them for many kinds of simulations. For example -- and this is what is shown on page 99 -- by counting the randomly generated dots that fall within the inscribed circle, and dividing that number by the total of all the points in the square (10,000 in our case), one actually simulates the number Pi (3.14159…). This technique of using random numbers is called Monte Carlo simulation, after the famous casino in France.

Page 99 on its own would be an unfortunate choice for casual browsing because browsers may erroneously believe that this is a book about mathematics. Unless they are open to learning about mathematical ideas, they may be discouraged from exploring the book further. And they would miss out because, firstly, the paradox of random numbers is not very mathematical, and, secondly, it is only one paradox out of sixty that I describe in the book. There are many more paradoxes about subjects like economics, linguistics, religion, law, philosophy, logic … and yes, also about mathematics, physics and statistics.

Visit George G. Szpiro's website.

--Marshal Zeringue