Find a tall straight glass whose height exceeds its circumference; a paper ribbon will assist with estimating. It’s not so easy, and reflects our human failure to appreciate the fact that the glass needs to be more than three times as tall as it is wide. This was one of the favorite geometrical observations of Martin Gardner, the best friend mathematics ever had.
Today, fans of mathematics, wordplay, magic, and cerebral and mechanical puzzles are gathering in Atlanta and more than 65 cities around the world (from Buenos Aires to Tehran), for a Celebration of Mind, to mark what would have been Gardner’s 96th birthday. It’s been said that he brought more mathematics to more millions than anyone. When he died last May, a light was extinguished that may never be relit.
Gardner and Atlanta were no strangers: Every two years the city hosts a by-invitation-only Gathering for Gardner conference, attracting the likes of physicist Roger Penrose, magicians Teller and David Blaine, and New York Times crossword puzzle maestro Will Shortz. By contrast, the Celebration of Mind events this week are open to all, and free.
A wide-ranging journalist and distinguished man of letters, as well as numbers, Gardner wrote more than 80 non-fiction books in the eight decades since publishing his first magic trick as a teenager in 1930. He was a consummate magic inventor, as well as a deep-thinking philosopher of science, and an expert on the works of Lewis Carroll (his most popular book is his “Annotated Alice”).
Gardner was a passionate and articulate ambassador for a much-maligned, misunderstood and feared subject, which is also one of the great triumphs of the human mind over the millennia: the field of mathematics. He set the gold standard for exposition of recreational mathematics. He wrote engagingly about ideas both simple and profound, in language the educated layperson could understand, first in a hugely popular monthly column called “Mathematical Games” in Scientific American, and then in a series of books that are a terrific resource for anyone wishing to teach or learn how to think clearly.
He was also a firm believer that mathematics is more about thinking clearly, and less about number crunching, than the popular perception.
A good illustration of this is one of the many brain teasers Gardner popularized over the years that the guys at NPR’s “Car Talk” used as one of their “puzzlers.”
It can be solved in one’s head — under no circumstances should a calculator be used! — once one realizes what the core of the problem is: “Two missiles speed directly toward each other, one at 9,000 mph and the other at 21,000 mph. They start 1,317 miles apart. Without using pencil and paper, calculate how far apart they are one minute before they collide.”
Here’s one involving a curious letter/number coincidence. Write out the alphabet starting with J, and wrapping around, namely:
Erase all letters that have left-right symmetry (such as A) and count the letters in each of the five groups that remain.
Ironically, Gardner never took a college-level mathematics course. His interests were very broad, and he wrote about many diverse things. He played a major role in introducing origami to a wider audience, and he also knew Salvador Dali and M.C. Escher personally, helping to popularize the latter’s mind-boggling art in the U.S.
To his dying day, Gardner was passionate about debunking medical quackery and pseudo-science. His first book “Fads & Fallacies in the Name of Science,” from the early 1950s, lead to the founding (alongside Carl Sagan, Isaac Asimov and James Randi) of CSICOP, the Committee for the Scientific Investigation of Claims of the Paranormal. One of the last things he published was a respectful and carefully reasoned piece for their flagship journal the Skeptical Enquirer, called “Oprah Winfrey: Bright (but Gullible) Billionaire.”
Still stuck on the puzzles above? For the first one, remember that, as in real life, there is more information than you really need. The key lies in distinguishing what to ignore (the 1,317 miles) and what to focus on (the rest). For the second one, recall that Pi was implicit in our glassy-eyed opener in the first paragraph.