Friday - - Wanted -

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.

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