Dienstag, 30. Mai 2017

Tuesday, 30 May: An arithmetic trap

The first two editions of "The Hobbit" scheduled the encounter with the trolls on the last day of May, which was originally meant to be 31 May according to the Gregorian calendar but shifted to 30 May when Tolkien decided that the Shire Reckoning had to be retconned into the book (where May, like all months, has 30 days). Next, he went at stakes to align the lunar phases, i. e. a "waning" moon described on 30 May and "a broad silver crescent" on midsummer's eve. 

Bilbo put his little hand into William's huge pocket:
Illustration by Évelyne Drouhin, 1969
John Rateliff, in "The History of the Hobbit", has published several sets of notes in which we witness Tolkien repeatedly pondering how to reconcile these two observations. He has not interpreted them thoroughly from an astronomical point of view, that's why I have done it in "The Moon in 'The Hobbit'". The entire discussion takes up a whole chapter in the book but briefly, the result is as follows

In the whole discussion, Tolkien consistently committed two errors, one minor, the other significant: (1) He assumed the "broad silver crescent" to be 3 or 4 days old. Check it out tonight, the moon is currently 4 days old. You will see that there is still some way to go until the crescent is really broad, say, to the 6th day. (2) Inexplicably, he assigned to the period of a lunation (full moon to full moon) the rather biblical value of 28 days instead of correct 29.5 days. This value, as unfounded as it is, seems to be a zombie of English folklore - even the BBC perpetuates it till today: http://www.bbc.co.uk/bitesize/ks3/science/environment_earth_universe/astronomy_space/revision/6/

Unfortunately, both his errors added up to a calamity from which Tolkien found no escape: his "arithmetic trap", as I have called it in my analysis. Whenever he tried to calculate backwards from Midsummer Eve to the encounter with the trolls, he got a new moon for this very night - irreconcilable with the waning moon he had described!

We have seen as we went through the 1960 timetable that his problem would have been solved if only he had applied the astronomically correct values. Even when he decided in 1966 to retain 30 May as the day of the troll encounter, it would have been enough to exchange one character: substitute "waning" with "waxing". But since it never occurred to him to check his aberrant premises, his ultimate emergency escape - as published in the 1966 Hobbit and ever since - was to simply camouflage the problem and hope it would remain unnoticed: The "waning" became a "wandering" moon, "tomorrow will be June" mutated into "soon it will be June", and from then on, the troll encounter had no specific date any more. 

Of course, this was of no help when it came to that other discrepancy: from 30 May or whatever other day in late May on, the Company would still have two sloppy weeks ahead to crawl to the Ford of Bruinen that is otherwise a mere three day-trips away.