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Notinole from Babylon to Middle-earth - Page 6

© Michael Martinez

The decision to emphasize the sixes and twelves, and 144, in Elvish culture was a relatively late one with respect to The Lord of the Rings. Some time after writing the first few drafts for the appendix on calendars Tolkien settled on the impportance of sixes and twelves. Several years later he wrote the story of the first Elves and since he had already introduced the concept in The Lord of the Rings he expanded upon it. But just as historians and mathematicians are certain that the Babylonians inherited their base-60 system from the Sumerians, they cannot explain why the Sumerians would have developed such a system. We have certainly inherited many numerical concepts from the Babylonians, the zero not being the least. We measure time much as they did, dividing days into 24 hours of 60 minutes each, and minutes into 60 seconds. So we reckon in 60s on a daily basis, even though we actually use the decimal numeral system. That the Eldar reckoned in sixes and twelves is therefore not an indication that they were using any sort of duodecimal system for their mathematics. It simply means they were preserving an ancient tradition, honoring their ancestors. Helge suggests that, in a duodecimal system, "the Elvish yen or 'long year' of 144 solar years would in a sense be their equivalent of a 'century', as 144 is the first three-digit number in a duodecimal system, like our 100". Yes, that is so. But the etymology of yen offers no numeric connection, as centuria possesses. Originally yen meant simply a "year" (that is the definition provided in "The Etymologies"). Derivations in the entry for yen show that it was clearly intended (prior to publication of The Lord of the Rings) to refer to a solar year, and not the "long year of the Eldar" which was stipulated in The Lord of the Rings. Many things changed during the development of Middle-earth, which Tolkien began in earnest only when he wrote The Lord of the Rings, and yen was one of those things. In the first draft for the appendix on calendars, Tolkien did not use yen. He wrote, however, "that the Eldar...reckoned in centuries". In the second draft, he introduced the yen: "It seems clear that the Eldar...reckoned in centuries, and the Quenya word yen, often translated 'year', really means a hundred of our years, sometimes called quantien or 'full year'." Quantien is later translated as "century", but in the final (published) version of the appendix Tolkien abandons the word in favor of haranye. There is no etymology offered for either quantien (although qantien, "last day of year", is found in the entry for yen) or haranye. Helge guesses that haran means "hundred".

J.R.R. Tolkien's depiction of 6431 in Tengwar.

J.R.R. Tolkien's depiction of 61 in Tengwar

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