Decoys, Neuromarketing, and Behavioral Economics

Richard Feynman, one of the best mathematical physicists of the last century, thought that a particularly important virtue of scientists was not to fool people. To this Feynman, with his keen sense of irony, added that the easiest person to fool is oneself. Feynman, here, was speaking to the confirmation bias that infects so much of […]

Vaccines and Autism — What Might the Numbers Be Saying?

While autism rates in the United States have exploded over the last 50 years, autism’s prevalence is still small enough that in most nuclear families children are not affected by this disorder. Still, the prevalence is now sufficiently high that most people know some family affected by this disorder. This was not the case even […]

What are you going to believe, me or the numbers?

In the classic Marx Brothers comedy DUCK SOUP, Groucho finds Chico with Groucho’s girlfriend in a bedroom. Chico tries to deny any hanky-panky by asking “What are you going to believe, me or your own eyes?” Obviously, Groucho should believe his own eyes and not Chico’s baldfaced lies. And yet, in many circumstances of life, […]

Hurricane Sandy, Rising Oceans, and Global Warming — What Are the Numbers Really Saying?

Debates in our culture are increasingly polarized. This is especially evident in the debate over global warming. Thus, those who think man-made or anthropogenic global warming is real and destructive take one side. On the other side are the global warming skeptics, who think that humanity’s contribution to global warming is negligible and that our […]

The Amazing History of Information Storage: How Small Has Become Beautiful

People have been storing information since the stone ages, ever since they’ve been writing or putting art on tablets and walls. With the invention of paper and ink, the “density of information” increased significantly, packing a lot more information into a tighter space (such scrolls and eventually bound books, as we still use today). The […]

Goedel’s Theorem for Dummies

When people refer to “Goedel’s Theorem” (singular, not plural), they mean the incompleteness theorem that he proved and published in 1931. Kurt Goedel, the Austrian mathematician, actually proved quite a few other theorems, including a completeness theorem for first-order logic. But the incompleteness theorem is the one for which he is most famous. To get […]

The Mathematics of Hell

(Or Jonathan Edwards Meets Leonhard Euler) Visions of hell abound, not just in Christian literature but also in mythology. The Greeks, for instance, had Sisyphus, who was condemned to an eternity of futility, constantly rolling a rock up a hill, only to have it come tumbling back once he was almost at the crest. Or […]

Potential Infinity vs. Actual Infinity

What is infinity and does it even exist? In our everyday experience, we find only finite things. A basket of eggs contains only a fixed number of eggs and no more. Our bodies are composed of particles (molecules, atoms, protons, quarks, etc.). But whatever particles describe our make up, we find only a finite number. […]

Lesson of the Monty Hall Problem

On the television game show Let’s Make a Deal, Monty Hall, the show’s best known host, used to present contestants with the following situation: the contestant would be presented with three doors behind one of which was a big prize (say a brand new car). Behind the other two doors was a small prize (say […]

The Bare Bones of Bayes’ Theorem

Thomas Bayes died over 200 years ago, but his legacy is still with us and provides some very useful insights into probability. What is his legacy? It is a probability formula that tells us how to update probabilities in light of new information. Suppose, for instance, you learn that Fred is a physical fitness fanatic […]