Egg-cellent hidden nuggets This week we continue talking about Easter eggs – not the colourful edible variety, but those little nuggets carefully hidden in books, movies and the like for serendipitous discovery. Lewis Carroll was an author whose genius as a mathematician was evident in his most famous literary work. On about the third page of chapter two in Alice’s Adventures inWonderland Alice starts speaking out some bizarre equations:
“Let me see: four times five is twelve, and four times six is thirteen, and four times seven is – oh dear! I shall never get to twenty at that rate!”
Alice is correct! 4x5=12 when expressed in base 18, bases being different standards by which numbers are measured. For instance we commonly count in base 10 (decimal), computers count in base 2 (binary), and HTML colours are in base 16. Following this pattern: 4x5=12 (b18) 4x6=13 (b21) 4x7=14 (b24) 4x8=15 (b27) 4x9=16 (b30) 4x10=17 (b33) 4x11=18 (b36) 4x12=19 (b39) 4x13=1A (b42) (or about 32(b10) short of 20). The equation falls apart here. Alice will never get to 20 at this rate! Martin Gardner’s Annotated Alice gives us a simpler explanation, while retaining the base 18 premise: like all schoolchildren Alice simply didn’t know her multiplication table beyond ‘twelve times’, so could never reach 20 either.
The dozens of languages that are spoken in Middle Earth in JRR Tolkien’s The Lord of the Rings are all carefully constructed ones by the author! Novices might assume that the names of people and places that populate Middle Earth are just fun little nonsense sounds. Even die-hard The Lord of the Rings fans who know that those are fully formed languages probably assume that they were invented for the novel. But according to Tolkien, the languages came first. He invented 20 different languages over the course of his career, and Middle Earth was just a fictional sandbox where he allowed those languages to play ball.
Still more next week.