This is a slightly-edited version of an email reply I actually wrote recently. This is what inevitably happens when math majors are allowed to communicate with normal people.
To: <everyone@xxxx.com>
Subject: Re: a miracle
At 12:24 PM 2/20/2002 -0600, zzzzz wrote:
As the clock ticks over from 8:01PM on Wednesday, February 20th, 2002, time will (for sixty seconds only) read in perfect symmetry. To be more precise: 20:02, 20/02, 2002. It is an event which has only ever happened once before, and is something which will never be repeated. The last occasion that time read in such a symmetrical pattern was long before the days of the digital watch (or the 24-hour clock): 10:01AM, on January 10, 1001. And because the clock only goes up to 23:59, it is something that will never happen again.
It appears the writer is using the European date format, putting the day before the month. If this is the case, he is actually wrong -- the last time this sort of symmetry occurred was not in 1001, but in 1111, when a digital clock (had it existed) would have displayed 11:11, 11/11, 1111 shortly before noon on November 11. And the next time it will occur is just over a century from now, at 21:12, 21/12, 2112 (9:12 PM, December 21, 2112).
However, there are also other symmetries to take into account which are no less interesting. For instance, on March 30 of this year, the "clock" will read 20:02, 30/03, 2002 -- another palindrome made up of three smaller palindromes, albeit two different ones. Similar clock readouts will occur on October 01, November 11 and December 21. In the year 2112 we can look forward to the time of 21:12 on five dates -- January 10, February 20, March 30, October 01, and November 11 -- in addition to the December 21 palindrome already mentioned. The same goes for 22:22 in the year 2222 and 23:32 a decade later.
Abandoning sub-palindromes for the moment, we can look forward to many more interesting dates and times. Some of the more curious ones: If we switch back to the U.S. method of displaying the month before the day, we have 02:02 02/20, 2020 coming in the not-too-distant future, 03:03, 03/30, 3030 a very long time after that, and so forth. The year 2111 graces us with both 11:12, 11/11, 2111 and 11:12, 21/12, 2111 -- a century later, we'll have 11:22, 11/11, 2211 to look at in wonderment. 01:02, 03/30, 2010 lacks the repetition of those times but makes up for it with a progressive sequence. You could even drop the leading zeros (in either the US or Europe) and prepare for 01:23, 4/4 3210 a millennium from now, and 12:34, 5/5, 4321 and 23:45, 6/6, 5432 in the millennia to follow.
But why stick to palindromes at all? The (European) clock showing 20:12, 20/12, 2012 or 21:02, 21/02, 2102 is no less aesthetically pleasing (or fun to say). 20:05, 20/05, 2005 has the added perk of reading the same time when rotated upside-down or reflected in a mirror. And in the far, far future, our descendants can be the first to tell each other it's 01:23 on 4/5 in the year 6789 -- a truly one-of-a-kind occurrence (unless they leave the US for Europe a month later to do it again).
So let's have no more of this sort of numerological prejudice. All years deserve a chance to be in the spotlight, and it's high time we recognized them in their turn!