The most general form of the reversing sequence is the palingram. Palingrams are sequences of letters, syllables or words that read the same backwards as forwards. To make the game more interesting, spaces and punctuation are ignored. Here are some examples with words or syllables as the units of the palingram.
He was, was he? (words)
O boy boy-o (syllables)
Some people prefer a broader definition of the palingram in which the units are syllables (or at least groups of letters, but some permutation within the group is allowed when doing the reversal. Examples include:
mowed a meadow
workmate did teamwork (or, without "did")
The reader is invited to work out the necessary letter groupings in each case.)
Palindromes (with which more people are familiar) are palingrams where the reversing unit is a single character. That is, the individual letters must read the same forward and backward. To be self-descriptive, perhaps one of these things should have been called a palinilap or a reversrerever. (Some suggest the word rotor but that implies an actual rotation, and rotor is not an upside-down word, so I'll pass on that idea.)
Able was I ere I saw Elba.
Madam, I'm Adam.
Madam, in Eden, I'm Adam.
A man, a plan, a canal--Panama.
Sums are not set as a test on Erasmus.
Never odd or even.
Do geese see God?
Dogma: I am God.
God saw I was a dog.
Draw, O coward!
Doc, note, I dissent. A fast never prevents a fatness. I diet on cod.
Was it a bar or a bat I saw? (Michael Burkley, Niagra Falls)
Of course, there are many palindromic numbers, such as 1001.
For instance, besides being international upside down day, 01 11 10 (November 11, 2001) was also international backwards day. There were other international backwards days on 02 11 20 (November 20, 2002) and 03 11 30 (November 30, 2003.) Alas, there will not be another until 10 11 01 (November 1, 2010), and 11 11 11 (November 11, 2011), the next two international upside-down days.
If you don't mind mixing a variety of date and time styles, 20 02 2002 20:02 (i.e. in ddmmyyyytttt, which is neither American nor proper ISO style 802PM on Feb 20, 2002) is a kind of stuttering backwards day (repeated palindrome) that has only happened twice before, a millennium ago (11 11 1111 11:11 and 10 01 1001 10:01). It will happen again 21 12 2112 21:12 and 30 03 3003 03:30 and never again.) In addition, the introduction of leading zeros for the year generates 01 10 0110 01:10. Of course, if the requirement for the groups to stutter is removed and one confines oneself to ordinary palindromes, dates such as 30 12 9999 12:30 (the last four digit one of this style) could also be mentioned. With more than four digits in the year or the use of some of the other date time formats (I believe there are between ten and twenty in common use), the list could be expanded.
(Thanks to F. Hargrove for some corrections, suggestions, and a prod to do more research on this section.)
A propos of nothing, and while we're off the subject, March is an interesting month. It boasted 03 03 03, one of only twelve stuttering days per century. Every year has the ides of March, when Big Julie was bumped off, St. Patrick's Day, the first day of Spring, and of course 03 32, when the tricksters are out in force. 'Course, April 2003 year had 03 04 05, one of only twelve consecutive days per century, which included for 2005 the day 05 06 07.
Finally, for those who have an irrational fear of pages like this one, we have the name of their malady. It is called aibohphobia. Of course, the disease that lovers of palindromes have is ailihphilia.
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