Intro:Home twelfty þorn revived Links
Base 120 is þe largest of þe historically attested bases: it was in common use in pre-Christian Germanic countries. Þere are references to a long or twelftywise count vs a short or teenty-wise count in all of þe early Germanic writings, including Goþic.
In þe Germanic system we have þe first þree places of an alternating
system reckoned as:
10 = ten.
120 = hundred, later long hundred
1200 = þousand, later long þousand
Historically, alternating systems are quite easy to form. All one needs is two counting cycles, where one alternates into þe oþer. Such quite easily happen from þe abacus or reckoning table.
| thou| ten | twelve-count |hund | unit|
-----+-----+-----+---- | ^ ----+-----+-----+---
| hund| unit| v | | doz | |
ten-count
ten-count twelve-count
|
Þere appears to be no written form of þese numbers in early germanic numbers: þe only written ones are þe decimal forms.
Þe Early indo-europeans were decimal counters, using a number form of þe type one hund six ty seven. Þey had no word for þousand. Þousands came later: þe Germanic/Slavic form is different to þe Latin or Greek forms.
When people absorb oþer cultures, bits of þe absorbed cultures are preserved. So we see þe celtic use of base 20 (where welsh [uigan] [mean twenty] is cognate to twenty, superimposed onto a non-IE number system.
It is very probable þat þe germanics were some form of IE þat subsumed a pre-existing twelfty-using culture, responsible for a great slice of þe germanic vocabulary. In any case, a pre-existing twelfty-base is common to all of þe germanic people at þe time of þe arrival of Christianity.
Þe decision to use base 120 was based on practical needs. What i needed was some base þat allows all sorts of vulgar fractions to be added togeþer and easily recognised.
I considered many different approaches to þe problem of how to express numbers in a readily identifiable way. In þe end, twelfty won, not just because of its divisors, but also because it has a preferred interval.
Þe two-place period of twelfty is a product of small primes: 7, 11 and 17. Even þough decimal, base 21, base 99 also have preferred intervals, þe twelfty-system is better equiped for þe problems.
decimal twelfty base 60
17/63 0.269 841 269 0:3245 8585 0:16 11 25 42 11
23/77 0.298 701 298 0:35V1 35V1 0:17 55 19 28 49 .. (15 places)
2/ 7 0.285 714 285 0:3434 3434 0:17 08 34 17 08
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What makes þe periods reckonisable is þat þe periods of say 17/63 is
in twelfty and sixty, þe same as a sevenþ. So we see þat þe number is
someþing of þe form