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.

Essays collected in printed or electronic books:


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Middle-earth seen by the barbarians: A compilation of Tolkien's references to the Middle Men of Eriador and Gondor: the pre-Númenóreans and the Dunlendings; the concealed history of Dorwinion, the fate of king Bladorthin and the origin of the Lossoth, the culture and history of the peoples in the east and far south of Middle-earth, with special consideration of the Wainriders, the Black Númenóreans and the Corsairs of Umbar. The appendix discusses the name Bladorthin and gives a new interpretation of this enigmatic king, shows how to apply a grid of latitudes and longitudes to the map of Middle-earth and in a previously unpublished essay discusses various comments by Tolkien on Pauline Baynes' recently recovered LotR map. This volume includes updated versions of “The Indigenous Peoples of Eriador and Gondor”, “The Lossoth and the Forodwaith”, “The Men of Darkness”, “The Third Realm in Exile”, “The mysterious King Bladorthin” and “A meridional grid on the map of Middle-earth” from these Science Pages.

The Moon in ‘The Hobbit’: A discussion and digital simulation of the lunar phases stated in ‘The Hobbit’ and ‘The History of The Hobbit’ and their astronomical background, with special regard to the identification of Durin's Day and the threshold of winter; including an analysis of the various calendar systems in ‘The Lord of the Rings’. Many hints are given on how to use the moon and the seasons as plot elements in your own stories. This book has updated versions of the essays “The Moon and Durin’s Day, 2941 TA”, “Midsummer’s eve and the Moon-letters“, “The Reckoning of Time”, “An ephemeris for Bilbo Baggins” and “(Flawed) Astronomy in the History of the Hobbit” from these Science Pages.

Words of Westernesse: A light-hearted introduction into the grammar of Adûnaic, based on Arthur Lowdham's spiritual research in HoMe IX, and (tentative) etymologies of Adûnaic and Westron as far as the corpus of vocabulary has been established. This volumes includes updated versions of the essays “Lalaith’s Guide to Adûnaic grammar” and “Etymologies of the Atani Languages” from these Science Pages.

Dynasties of Middle-earth: Genealogical tables and comments on the lines of the kings of Númenor, Arnor, Gondor, Rohan, Dale and the Princes of Dol Amroth. A shorter version of this volume had been previously presented here as “Genealogies of the noble Mannish houses”.