Let’s play the number game Mathematics and word puzzles have never been distinct from each other. A prime illustration of this would be the extensive output of Martin Gardner, who wrote on mathematical puzzles for decades but was equally fascinated by words and word puzzles. Gardner wrote the Mathematical Games column in the Scientific American from 1956 to 1981, which was then taken over by Douglas Hofstadter who gave it the clever anagrammatic spin Metamagical Themas.
In one series of now-anthologised articles originally appearing in that column, Hofstadter discusses many varieties of self-referential sentences. These range from the elementary (“This sentence no verb”) to the more head-scratching (“This sentence contains exactly threee erors”). Others are just plain fun: “This sentence is a !!!! premature punctuator”, and “You have, of course, just begun reading the sentence that you have just finished reading”. A longer submission to the
Scientific American had Hofstadter himself (as editor) in a snit in trying to verify it: “Only the fool would take trouble to verify that this sentence was composed of ten a’s, three b’s, four c’s, four d’s, forty-six e’s, sixteen f’s, four g’s, thirteen h’s, fifteen i’s, two k’s, nine l’s, four m’s, twenty-five n’s, twenty-four o’s, five p’s, sixteen r’s, forty-one s’s, thirty-seven t’s, ten u’s, eight v’s, eight w’s, four x’s, eleven y’s, twenty-seven commas, twenty-three apostrophes, seven hyphens, and, last but not least, a single!”
Dutch mathematician Hans Freudenthal sent Hofstadter a story narrated by 18th-century German poet Christian Fürchtegott Gellert, which combines self-referential sentences and a moral lesson about honesty. It tells of a father and son taking a walk during which the son tells a big lie. His father issues a dire warning to him about the “Liars’ Bridge”, which they are approaching, saying this bridge always collapses when a liar walks across it (there is an actual bridge so named in Sibiu, Romania, with such a legend attached). After hearing this warning, the boy admits his lie.
When Freudenthal told a boy this story, the lad asked him what happened when they came to the bridge. Freudenthal replied, “It collapsed under the father, who had lied, since in fact the Bridge doesn’t do that”! We’ll leave you pondering on that Catch-22 until next week.