Sunday, August 15, 2010

Constant Gardner

As I power up the blog machine, I would like to begin by saying a few words about Martin Gardner, who died earlier this year (at age 95). That name may or may not sound familiar to you. To help jog your memory I could try a number of directions. Gardner was well known for his 25 years of writing the Mathematical Games column for Scientific American. But he also authored over 70 books on a range of topics: recreational mathematics, magic, and Alice in Wonderland to name a few. He was a prominent critic of pseudoscience. His book Fads and Fallacies in the Name of Science is often credited with helping to launch the scientific skepticism movement, and he wrote regularly for Skeptical Inquirer after resigning from Scientific American in 1981.

Despite having no formal training in mathematics, Gardner is said to have done more to promote interest in the subject in the U.S. than any other single figure in the 20th Century. I can offer anecdotal evidence of this from my own life. I encountered my first Gardner book while visiting a friend’s childhood home shortly after graduating from college. The book, aha! Gotcha, featured paradoxes of mathematic as well as logical and philosophical origins. I liked it so much that I largely ignored my hosts for the remainder of the weekend. The book revived my interest in numbers and equations, after a very humanities-centered stint in college, beginning a path that would eventually lead me back to the study of science and the writing of this blog (I know, lucky you, right?)

Mathematical Games began in 1956 when Scientific American invited Gardner to write a regular column based on an article he had shown to them on the subject of hexaflexagons. In interviews, Gardner stated that he was unprepared to produce monthly math puzzles and often had to teach himself the concepts he was to present to his readers. Yet he wrote so effortlessly on the subject that it was easy to assume (as I did) that he was a mathematician by trade. In paying tribute to Gardner’s memory, many friends, fans, and colleagues cited his lack of specialization as a strength rather than a hindrance. His writings on math culled analogies from his diverse interests, rendering his explanations both vivid and easy to grasp, even for us non-mathematicians.

If I accomplish nothing else with this blog, I would at least like to introduce a few more people to the world of Martin Gardner. Do yourself a favor and seek out one of his many books. In the meantime here is my humble paraphrase (with illustrations from the book) of a favorite item that Mr. Gardner explained to me: Newcomb’s Paradox…

In this thought experiment, you play a game set up by a “predictor”, in Gardner’s version this is an omniscient extraterrestrial superbeing named Omega. The rules are simple. You are presented with 2 boxes, box A and box B. Box A is transparent and contains 1 thousand dollars. Box B is opaque and contains either 1 million dollars or nothing at all. You are offered 2 choices, either take both boxes or take only box B, whose contents are hidden from you. You are given one additional piece of information. Omega has filled (or not filled) box B based on his prediction of what choice you will make. If he predicted that you will choose both boxes, then he has left box B empty and you will emerge with the modest $1000 amount contained in Box A. However, if Omega predicted that you will choose only box B, then he has filled that box with a million dollars, which will be yours to keep. Tax-free. You are not told what Omega has predicted about your decision, just that he has made his prediction. He now leaves you alone with the 2 boxes to make your choice. Keep in mind that Omega has conducted this experiment countless times and his record of accurate predictions is un-besmirched by even a single error. What now, dear earthling? Take both boxes or take only box B?

Gardner describes the paradox as a, “…litmus paper test of whether a person does or does not believe in free will” Those who believe that a choice is really theirs to make take both boxes, while determinists decline box A and opt for the hidden contents of box B. I’ll leave you to work out the arguments for each strategy on your own.

No comments:

Post a Comment