M F Hasler <mhasler@dsi972.fr> wrote:

Keith F. Lynch wrote:

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Dan Asimov wrote:

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Or consider the number 73. Not particularly conducive to symmetry, you might think.

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73 is a palindrome in Morse Code: --... ...--

This Morse code symmetry comes from the base-10 complement palindromic symmetry, ...

Right. It's also interesting to look into Morse Code text palindromes and words that are reversals of other words. The longest single-word Morse palindrome is FOOTSTOOL. Since the commonest letters have the shortest codes, the reverses of common letters tend to be common letters, so there are lots of words that have reversals. Spaces between words are simply pauses, so the reverses of spaces are spaces. It's fun to find sentences whose reverses are sentences. Such searches are hard to automate, since computers aren't good at distinguishing between valid sentences and meaningless word salad. (Or at least they weren't last time I checked.) There are 30 possible Morse characters of one, two, three, or four "elements" (dots and/or dashes), all of which are either assigned to letters or unassigned, so the reverses of letters are usually letters. Unfortunately, the letters C, J, and Z can't be used, since their reverses are unassigned, at least in English. (I think their reverses are assigned to accented letters in various foreign variants of Morse.) Also rich in meaningful reversals and palindromes is the five-bit ITA2 teletype code, often wrongly called Baudot. To minimize wear on mechanical teletypes, it was designed so that the commonest letters have the fewest 1-bits, so once again the reverses of common letters are common letters. The reverses of letters are always letters, and the reverse of a space is a space. The ASCII code isn't very good at this. Most letters don't reverse into letters. It might be fun to design a character code for the sole purpose of making palindromes and reversals as common as possible. There's no need to actually assign bit patterns, but just to choose which letters will be the reverse of which letters. The space will of course remain the space. With 26 letters, there are 25!! (i.e. 25 * 23 * 21 * ... * 5 * 3 * 1) = 7905853580625 such codes, so it's not completely intractable to simply try them all. In addition to making common letters reverse into common letters, you'd probably want to make common digrams (e.g. TH, HE, IN, ER, etc.) reverse into common digrams. For instance TH would be its own reverse if T and H were the reverse of each other. Also see my article on this subject in the November 2005 WSFA Journal, http://www.wsfa.org/journal/j05/b/index.htm#bp