Frank Morgan's Math Chat


January 17, 2002

Palindromic Years

Last week over four thousand mathematicians gathered in San Diego for the annual joint mathematics meetings. Dave Bayer talked about his work as mathematical consultant to Ron Howard's brilliant new movie "A Beautiful Mind," about the schizophrenic Nobel Laureate John Nash. The movie is based on Sylvia Nasar's biography "A Beautiful Mind," previously recommended here in Math Chat. A new book, "The Essential John Nash," contains fascinating autobiographical and mathematical material by Nash, as well as commentary by Harold Kuhn and Nasar.

OLD CHALLENGE. The new year 2002 is a palindrome, the same backwards as forwards. How common are palindrome years?

ANSWER. (Joseph DeVincentis, Toby Gottfried, Sonny Kunnakkat). Currently palindrome years occur at 110-year intervals. The next one after 2002 occurs in 2112. At the end of each millennium, there is an exceptionally short 11-year interval, as we just had from 1991 to 2002 and will have from 2992 to 3003. Long ago, during the two- and three-digit years, there was a palindrome year every 10 or 11 years, as from 989 to 999 or from 88 to 99, with some exceptionally short 2-year intervals, as from 999 to 1001 or from 99 to 101. In the distant future, when we move into the five-digit years, they will generally occur at 100-year intervals, as from 10001 to 10101.

Although the Christian-era calendar has long been the standard throughout the Western world, there are other calendars in use in other parts of the world, most of them also in their four-digit years now. If you consider these years as well, the total frequency of palindrome years is generally multiplied by the number of calendars used--two or three or more per century.

John M. Sullivan writes: I like to look for palindromes on my car odometer. Of course, the first month or two I owned the car, they were quite frequent, but since then I've gotten used to seeing about one every couple of hours on a long drive. (To increase the fun, I ignore any leading or trailing zeros in the number.) Two weeks ago, during a single four-hour drive, I saw no less than seven plaindromes (including three consecutive ones)! But then last week, I went for a trip twice as long without seeing any. PS: Last October, some noted the palindromic date 10/02/2001). Europeans (who put the month first) might note 20/02/2002 next month.

QUESTIONABLE MATHEMATICS. Eric Brahinsky found the following account in an article, "Noise Meter Doesn't Lie," by Bonnie Walker in the San Antonio Express-News (28 December 2001):

"After borrowing the [Digital Sound Level] meter..., which measures noise in decibels,... we headed out to a few restaurants to listen.... The numbers on this listening device, we were told, rise logarithmically, not numerically. I have no idea what this means, except that a rating of 80 is not just 10 percent more than a rating of 70. It's actually way higher."

Brahinsky comments: Ms. Walker is at least honest about her ignorance of logarithms (though her ploy, familiar among mainstream journalists, of currying readers' favor by proudly proclaiming her lack of mathematical prowess is a bit tiresome). She needn't have stopped there, however, since she seems also to have little idea what percentages mean! Of course, on an absolute linear ("numerical") scale, 80 is some 14 percent higher than 70, not 10 percent higher. Admittedly, decibels are a bit complicated. A sound of 80 decibels has 10 times the physical intensity of one of 70 decibels (that's 900% louder), but since the human ear itself seems to respond logarithmically, a person would judge the former sound to be about twice as loud (or 100% louder). Well, I guess either 900% or 100% would be "way higher" than either 10% or 14%, so she's right about that....

Readers are invited to submit more examples of questionable mathematics.

NEW CHALLENGE. What is the loudest sound ever made on earth? the softest?

Copyright 2002, Frank Morgan.

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