Lee Sallows

Home > Mathematical Wordplay > Palingram

The self-replicating hour-glass sentence below was composed  in response to Douglas Hofstadter's  "Von  Neumann Challenge" that appeared in his regular Metamagical Themas column in Scientific American in   1982. The typesetting of  that original version was only of typewriter quality, but I have Doug to thank for the elegant version that appeared later in his book of same name (p.65), and is here reproduced.              

down ten ‘a’s,
eight ‘c’s, ten ‘d’s,
fifty-two ‘e’s, thirty-eight ‘f’s,
sixteen ‘g’s, thirty ‘h’s, forty-eight ‘i’s,
six ‘l’s, four ‘m’s, thirty-two ‘n’s, forty-four ‘o’s,
four ‘p’s, four ‘q’s, forty-two ‘r’s, eighty-four ‘s’s,
seventy-six ‘t’s, twenty-eight ‘u’s, four ‘v’s, four ‘W’s,
eighteen ‘w’s, fourteen ‘x’s, thirty-two ‘y’s, four ‘:’s,
four ‘*’s, twenty-six ‘-’s, fifty-eight ‘,’s,
sixty ‘‘’s and sixty ‘’’s, in a
palindromic sequence
whose second
half runs
snur flah
dnoces esohw
ecneuqes cimordnilap
a ni ,s’’‘ ytxis dna s’‘‘ ytxis
,s’,’ thgie-ytfif ,s’-’ xis-ytnewt ,s’*’ ruof
,s’:’ ruof ,s’y’ owt-ytriht ,s’x’ neetruof ,s’w’ neethgie
,s’W’ ruof ,s’v’ ruof ,s’u’ thgie-ytnewt ,s’t’ xis-ytneves
,s’s’ ruof-ythgie ,s’r’ owt-ytrof ,s’q’ ruof ,s’p’ ruof
,s’o’ ruof-ytrof ,s’n’ owt-ytriht ,s’m’ ruof ,s’l’ xis
,s’i’ thgie-ytrof ,s’h’ ytriht ,s’g’ neetxis
,s’f’ thgie-ytriht ,s’e’ owt-ytfif
,s’d’ net ,s’c’ thgie
,s’a’ net nwod


Last Updated:
  Copyright © Lee Sallows