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The best popular science essay ever
I became a "math popularizer" almost by accident. In 1983 I had an idea for an April Fools spoof in a national daily newspaper, where I would write a mathematics story that was so counter-intuitive that everyone would think it was a spoof, but the real spoof would be that the story was in fact true. (The story was based on the fact that an engineering company had manufactured a rotary drill that would drill a square hole. To see the mathematics behind this feat, see http://mathworld.wolfram.com/ ReuleauxTriangle.html.) I wrote it up and sent it in to the science page editor at The Guardian newspaper in my then home country of Britain. A couple of days later the editor telephoned me. He explained to me why my piece would not work in a national newspaper, but went on to say that he liked my writing style, and would be interested in seeing other contributions from me. A few months later an engineer at Cray Research discovered a new record Mersenne prime number, and I wrote a 700 word piece describing the discovery. The editor published it, the reader response was good, and within a short while I found myself a newspaper "math columnist", with a twice monthly column in the science section.
It wasn't long before book publishers started to approach me with requests for popular expositions of mathematics. Quite unplanned, I had a second career. Over the years, I have found myself spending more of my time on what has come to be called "public education", but it remains a very small part of my regular activities. Nevertheless, I have taken it seriously. I read as many popular science books and newspaper and magazine articles about science I can, and I study closely the way the different successful science writers and journalists go about their job.

An essential device in trying to convey mathematics or science to a lay audience is metaphor. The more basic and familiar the metaphor, the greater the audience...