Remembering Martin Gardner
Martin Gardner, born on October 21, 1914, was an American popular mathematics and science writer specializing in recreational mathematics, but with interests encompassing micro-magic, literature (especially the writings of Lewis Carroll and G.K. Chesterton), philosophy, scientific skepticism, religion. He published more than 100 books and almost all of his columns have been collected in book form. Martin Gardner died in 2010 at age 95, razor sharp until the end.
The caption to the above picture by Colm Mulcahy, Spelman College, reads: “Martin standing by every word he ever wrote: the six shelves consist entirely of his own publications, dating back to 1930.”
I corresponded with Martin Gardner in my teen years, and I can probably say that he played a greater role in my intellectual development than anyone else (and I am in good company here). I corresponded with him during my school and college days and followed his columns and writings for decades. In 1979 I visited Martin Gardner in his home in Hastings-on-Hudson. He and many others (including myself) had recently founded the skeptical Committee for Investigation of Claims of the Paranormal, which mutated into the Committee of Skeptical Inquiry and became the publisher of the Skeptical Inquirer. It was the first time I met him in person.
Gardner’s uncompromising attitude toward pseudoscience made him one of the foremost anti-pseudoscience polemicists of the 20th century. His book Fads and Fallacies in the Name of Science (1952, revised 1957) is a classic and seminal work of the skeptical movement. It explored myriad dubious outlooks and projects including Fletcherism, creationism, food faddism, Charles Fort, Rudolf Steiner, Scientology, Dianetics, UFOs, dowsing, extra-sensory perception, the Bates method, and psychokinesis. This book and his subsequent efforts earned him a wealth of detractors and antagonists in the fields of “fringe science” and New Age philosophy. With many of them he kept up running dialogs (both public and private) for decades.
Martin Gardner’s column on mathematical puzzles and diversions in Scientific American were my first contact with the work of this extraordinary man. I was still an early teen in school, but I sent letters (handwritten, on paper, with envelopes and stamps) with comments and solutions. He replied to every single one of them — in my boundless stupidity I did not keep his type-written letters, which are lost forever. I have added some of his comments to the following puzzles from memory.
If you want to get an impression of the vintage Martin Gardner get hold, if you can, of a copy of his book “Hexaflexagons and other mathematical diversions”. It is also available as a PDF file here. You can spend a week or two, as I did in my college days, building hexahexaflexagons (or read the article on them here in Scientific American). Or you can try some of the puzzles that have become legendary. Here are a few samples:
A logician vacationing in the South Seas finds himself on an island inhabited by two proverbial tribes — liars and truth tellers. Members of one tribe always tell the truth, members of the other always lie. The traveler comes to a fork in a road, where one path leads to the village and the other into the forest. He meets two natives, one a liar and one a truth teller — but he has no way of telling which is which. The logician thinks a moment, then asks one yes-no question only. From the reply he knows which road to take. What question does he ask?
The solution to the liar/truth teller problem is fairly easy: you ask one of the natives, “What would your friend here say if I asked him if this here is the road to the village?” If the answer is “no” then it is the road to the village, if it “yes” then it leads into the jungle. Got it?
In correspondence, we worked out additional extensions to the problem:
- If there was only one native at the crossing you could still ask him what a member of the other tribe would reply.
- What about only one (very logical) person who sometimes lies and sometimes tells the truth? Well, then the question is “What would you say if I asked you…”
- In a delightful twist some readers noted that if the logician knows that ‘pish’ and ‘tush’ are the native words for ‘yes’ and ‘no’ but has forgotten which is which, he can still determine which road leads to the village. The solution: “If I asked you whether this is the road to the village, would you say ‘pish’?” Work it out: if he replies ‘pish’ do you take that road?
- The final stage of our public discussions defined the “crafty liar” who figures out what you are doing and neutralizes that. Him you ask: “Did you know they are giving out free beer in the village?” After he has said “Yes” you follow him down the path he hurriedly took. However: the “dedicated liar” will say yes and go down the path to the forest, where he and you will be torn to shreds by wild animals. For him a successful lie takes precedence over life and limb.
The following problem is quite incredible, because it seems to lack sufficient data for a solution. A cylindrical hole has been bored straight through the center of a solid sphere. It is exactly six inches long. What is the volume remaining in the sphere?
My most memorable exchange with Martin Gardner was over this problem. At the time I sent him the following solution: “I do not (yet) have the mathematical knowledge to solve the problem. But assuming that the text does not contain a misprint it would appear that it is not necessary to know the diameter of the sphere or the diameter of the drill bit. Just the length of the cylindrical hole through the middle is enough, the remaining volume will be constant. If that is the case then I can drill a hole of zero diameter through a sphere with a diameter of six inches. So the remaining volume will be 4/3 Pi r³ = 113.09733 cubic inches (I can do the volume of a sphere).” Martin wrote back commending my ingenuity, and many years later, when I finally met him, he remembered this exchange and even the fairly silly pseudonym I had used at the time.
A more recent puzzle involved a desk block perpetual calendar (like the one on the left). The day is indicated simply by arranging two cubes so that their front faces give the date. The face of each cube has a single digit, 0 through 9, and one can arrange the cubes so that their front faces indicated any date from 01, 02, 03 … to 31. On the left cube of the calendar you can see two faces whose digits are 1 and 2. On the right cube you can see three faces, 1, 3 and 4. What are the four digits that cannot not be seen on the left cube and the three that cannot be seen on the right cube?
In case you get hooked, there are many other Gardner books with mathematical and logical puzzles. I remember one (of many) he gave me when I visited him in Hastings-on-Hudson: there are three on/off switches on the ground floor of a house. One is connected to a light bulb on the second floor, the other two are unconnected. The switches are all in the off position. You can switch any position and then go upstairs and examine the bulb. Can you tell which switch is connected in a single try? Work out the solution yourself, I will not reveal it here.
Like a good magic trick, a clever puzzle can inspire awe, reveal mathematical truths and prompt important questions. At least that is what Martin Gardner thought. His name is synonymous with the legendary Mathematical Games column he wrote for a quarter of a century in Scientific American. Thanks to his own mathemagical skills, Gardner presented noteworthy problems every month with all the wonder of legerdemain and, in so doing, captivated a huge readership worldwide. Many people — obscure, famous and in between — have cited Mathematical Games as informing their decisions to pursue mathematics or a related field professionally. — From Scientific American October 2014, pp 78–83.
There are countless articles and columns dealing with Martin Gardner and his activities. You can spend days and weeks — or perhaps an entire lifetime — exploring them. Or you can buy some of his 100 or so books he published. Here are a few links I selected for his 100th anniversary report:
- BBC: Martin Gardner, puzzle master extraordinaire
- Guardian: Can you solve Martin Gardner’s best mathematical puzzles?
- A Mind at Play: An Interview with Martin Gardner
- Martin Gardner 1914–2010: an interview by Michael Shermer
- Huffington: Martin Gardner — The Best Friend Mathematics Ever Had
- Remembering Martin Gardner, with Douglas Hofstadter (podcast)
- CSI: Tributes to Martin Gardner
- The Martian Gardner Centennial site