Super-accurate Innumeracy

A.K. Dewdney

Between 1984 and 1991, A.K. Dewdney authored numerous articles in the section on Mathematical Games of Scientific American. He was one of the successors to Martin Gardner, most famous contributor of that section. Dewdney is also the author of an amazing book, The Planiverse (1984), which belongs to the same genre of mathematical fantasy as Edwin Abbott's Flatland, published just a century earlier.

In the previous post I offered a few examples of innumeracy taken from A.K. Dewdney’s book 200% of Nothing. In this book, Dewdney points out, among many others, two very frequent mathematical mistakes. The first consists in giving so few digits of a number that it loses all usefulness (he calls those numbers nums, to indicate that they are not full numbers, as they are not complete). The second mistake is the opposite: giving too many digits of a number, beyond what is necessary or makes sense. He calls unnecessary digits dramadigits, as they only serve to give the particular number a more dramatic look.

Let's look at an example from Dewdney's book:

Innumeracy

Douglas Hofstadter

Douglas Hofstadter, the author of the book Gödel, Escher, Bach, an Eternal Golden Braid, coined the word innumeracy, by analogy to the word illiteracy, to mean the lack of mathematical knowledge affecting a large part of the population.

Let's look at an example of innumeracy proposed by A.K. Dewdney in his book 200% of Nothing:

A man finds a $5 bill, puts it in his pocket and thinks: "As I have a $10 bill in my other pocket, I just won 50%." When he arrives at home, he discovers that he has lost the $5 note he had found. He then thinks: “As I had $15 and have lost $5, I have suffered a 33% loss. As previously I had won 50%, overall I have won 17%.”