You might be familiar with George Gamow, the mid-20th-century physicist who, with his student Ralph Alpher, came up with the Big Bang Theory long before there was any experimental evidence. Gamow is also the best writer for the layperson on science, and one of the best on math, I’ve ever read. In particular, his book One, Two, Three… Infinity is a masterpiece, jammed with fascinating ideas presented with absolute clarity. (Though much of it — mostly the non-math stuff — is kind of out-of-date now; the revised edition came out in 1961.)
A few years back, my friend Doug Hofstadter sent me a short article of Gamow’s about how the normal distribution was once used to expose a dishonest baker — apparently a true story. But true or not, it’s a fascinating story of mathematical probability in real life, one that I think would interest even a lot of apathetic middle-school and high-school students! A PDF of the story is available at
You’re probably thinking, “Is this some kind of scam, or has this guy lost his mind?” I don’t think so, though I must admit the title is kind of a dramatic way to make my point. (I’d originally intended to call this “Kill your self today! There’s never been a better time!”, but I thought that might be a bit too much.)
I saw an ad on the Google homepage recently: “Fast. Smart. Safe. It’s never been easier to put _Firefox on your Android phone._” This strikes me as yet another example of a kind of statement that’s been annoying me for years. The statement, nearly always in an ad of some sort, exhorts you to do such-and-such now because “there’s never been a better time”. But it’s clear that what they want you to think is that you should do it because “this is the best time ever”! A much stronger statement — and one that (in my experience) really is often justified by the facts. But why would advertisers ever use a weaker argument than is justified? The only reason I can think of is carelessness.
It pisses me off (please excuse my language. I didn’t realize I felt that strongly about this until I wrote that phrase!) that people are so careless about the fact that “less than” and “greater than” aren’t the only possible relationships between two ordinal values. I suggest bringing this up to students to raise their awareness of mathematical thinking in the Real World. A possible assignment: find 20 random examples of statements that “there’s never been a better time” for something and report on how many really mean “this is the best time ever”.
If you’d like to see more examples yourself, there’s never been a better time! At the moment, Googling “there’s never been a better time” (with quotation marks) gets “about 3,360,000 results”.