Palindrome. The word fairly cascades with onomatopoetic resonance. From the simple Bob to the convoluted Napoleonic reprise, word palindromes have always fascinated those of us who are---well, fascinated by words.
What is a palindrome?
A palindrome is a sequence of numbers or letters that read the same backwards and forwards---allowing for punctuation, including slashes, dashes, capitals, and ampersands. Anna, "Step on no pets!" and "Able was I, ere I saw Elba" are word palindromes. Number palindromes are easier to conjure, like 12233221, but palindromic dates are a very special kind of number.
The palindromic date
Using the American system of 2 digits for the month, 2 digits for the day and 4 digits for the year, every day of the year has one (and only one) palindrome. That means there are only 366 of them. We just had one on 11/02/2011. Did anybody notice?
Palindromic dates of the past
The last time before this was 01/02/2010; before that it was 10/02/2001; and the last one before that was---believe it or not---New Year's Eve of the year 1321. Maybe not such a long time ago if your scale is the time it takes for light to reach us from a distant quasar, but a long time as measured by a human life span.
Palindromic birthdays
Everybody has a palindromic birthday---the date on which his/her birthday was or will be a palindrome. Let's begin with Napoleon, because he started all this when he saw Elba. His palindromic birthday is 08/15/5180. Even if his military adventures had been successful, Napoleon's ultimate Waterloo would have come long before his palindromic birthday.
Few people are lucky enough to celebrate their palindromic birthday. Mine is 04/07/7040. However, I have a grandson who will celebrate his 17th birthday on 12/02/2021. A rare day! To calculate just how rare, we note that the average life expectancy is about 80 years, and between the years 0001 and 9999 (all the years to which we assign 4 digits), there are 9999 years. So the odds are 80 out of 9999, or about one chance in 120 that any given individual will live to see his palindromic birthday.
Much rarer still is being born on one's palindromic birthday. The calculation is a little harder, but stick with me. In an average 80 year lifetime, there are 80 times 365 days (plus a few for the leap years). That's about 30,000 days. So the chance of being born on your palindromic birthday is one chance in 120 multiplied by one chance in 30,000, or about one chance in approximately three and a half million.
Palindromic dates the continental way
In Europe, the date is written with the day first and then the month. This doesn't affect our calculations, but it raises the possibility of an extremely rare event: a transcontinental palindromic date; a day which is a palindrome in America and Europe. It's easy to see that there are just 12 of those, one for each month. Basically there's one per millennium, for each month from January to October, plus two extras for November and December. The last two are 12/12/2121, and---clearly the neatest one of all; too bad we missed it---11/11/1111. There's one coming up on 02/02/2020; maybe they'll issue a commemorative coin.
Palindromic odd man in
Finally we deal with that troublesome date, February 29. As it happens, February 29 qualifies as a palindromic date, because 02/29/9220 will be a leap year, at least if no disasters like an asteroid passing nearby interrupt the present rotation rate of the earth. So take heart, you outcasts who get cheated out of 3 of every 4 birthdays---you get the same allotment of one palindromic birthday per person as everybody else.
Jon Plotkin - The author was a math major at Cornell and has a master's degree in meteorology from MIT.
