## Wow, 2015 Is a Palindromic Year, Equals 11111011111 in Binary

By John Allen Paulos

This is a turning point in human history, in part because the year 2015 is a palindrome that encourages us to take stock by simultaneously viewing the future and the past.

Let me explain a bit. Numbers can be expressed in decimal notation as we normally do, but they can also be expressed in the binary notation of 0's and 1's. For example, the number 13 can be expressed as 1101 in binary notation since it equals 1 eight, 1 four, 0 twos and 1 one. Another example 22 can be expressed as 10110 since it equals 1 sixteen, 0 eights, 1 four, 1 two, and 0 ones. In general, the 1's and 0's represent the successive powers of two - 1, 2, 4, 8, 16, 32, 64, ... - that contribute to the value of the given number.

This brings us to the present, year 2015. In binary notation it is 11111011111 and thus is a palindrome reading the same way forwards and backwards, like the verbal palindromes "A man, a plan, a canal Panama" or "Able was I ere I saw Elba."

There is also a sense in which 2015 is a palindrome in decimal notation. If we break it down into its prime number constituents (numbers that cannot be further broken down), we find that 2015 can be written as 13*5*31, a palindrome of sorts if we arrange the prime numbers in this order.

Evidence for the even more special nature of this particular month in 2015 is that January is often said to derive from the Roman god Janus. Two-faced, Janus was the god of beginnings, endings, and transitions, who faced both the future and the past. And Zeus knows, January has been a pivotal month in many ways.

Thus it is that we live at an historical hinge, a turning point, both a beginning and an ending. We can only wonder at what epiphany will occur in 32 years as we transition from 2047 (11111111111) to 2048 (100000000000).

Yes, and there's a bridge in Brooklyn I'd like to sell you. It also goes in both directions. All of this, of course, is numerological nonsense, fatuous flapdoodle, a mere artifact of our conventions for representing numbers. It means nothing. Likewise for people's belief in astrology and other calendrical schemes, which are not in the least any more compelling.

Let's forget the dates and the baseless predictions. All we can do is take things a day at a time.

Or, more palindromically put: Anne, I stay a day at Sienna.