Notinole from Babylon to Middle-earth - Page 5
© Michael Martinez
Tolkien also acknowledged that the Numenoreans resembled the Egyptians in many ways (Letter 211). Their numeral system appears to be one of those resemblances, even though it must ultimately be attributed to the Eldar. The tengwar system is, in fact, a very elegant and flexible system. We could, for example, extend the digits easily. "Ten" could be represented by adding another luva to "nine". And now we have a base-eleven numeral system. If we also add a luva to "six" we can create a duo-decimal numeral system. Of course, these higher-base systems require that the values in the tengwar table be shifted: "six" remains a six, but "seven" becomes eight, "eight" becomes nine, "nine" becomes ten, and the new symbols become seven and eleven.
And that brings us back to Helge's discussion of Elvish numerals. Helge points out that The War of the Jewels says that after all 144 of the first Elves had come together, they "ever after reckoned in twelves, and ... 144 was for long their highest number, so that in none of their later languages was there any common name for a greater number." The problem is that, if the Elves were really using a duodecimal system, then Aragorn's numbers wouldn't use the tengwar we are given: "six", "four", "three", "one". It could be assumed, without any rationale, that the Dunedain had simply abandoned the duodecimal system in favor of the decimal system. But the decimal system offers advantages over the duodecimal system (such as the ease of counting fingers and toes) that makes it inherently easier for children to learn.
If the Elves could devise the extremly flexible and powerful tengwar numeral system, then why would they overlook the advantages of the decimal system? That makes no sense. On the other hand, the English system of measurements uses 12 inches to the foot, 3 feet to the yard, 220 yards for the furlong, etc. Where is the indication in that system of a decimal numeral system? There is none.
The Elves may have reckoned in sixes and twelves, but they would not have settled upon a duodecimal system without actually using it. And had they used it, they would have conveyed that system to the Dunedain. And then Tolkien would have had to explain why the Dunedain abandoned the Elvish system, or simplified it. The Dunedain were smart and innovative, but they were better at preserving Elvish traditions than the Elves ("The Dunedain alone of all races of Men knew and spoke an Elvish tonguel for their forefathers had learned the Sindarin tongue, and this they handed on to their children as a matter of lore, changing little with the passing of the years", Appendix F, The Lord of the Rings).
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