-: Twelfty for Decimal-Users :-


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History

Base 120 is the largest of the historically attested bases: it was in common use in pre-Christian Germanic countries. There are references to a long or twelftywise count vs a short or teenty-wise count in all of the early Germanic writings, including Gothic.

In the Germanic system we have the first three places of an alternating system reckoned as:
      10 = ten.
      120 = hundred, later long hundred
      1200 = thousand, later long thousand

Historically, alternating systems are quite easy to form. All one needs is two counting cycles, where one alternates into the other. Such quite easily happen from the abacus or reckoning table.


          | thou| ten |     twelve-count      |hund | unit|
     -----+-----+-----+----   |    ^      ----+-----+-----+---    
          | hund| unit|       v    |          | doz |     |
                            ten-count
          ten-count                             twelve-count

There appears to be no written form of these numbers in early germanic numbers: the only written ones are the decimal forms.

The Early indo-europeans were decimal counters, using a number form of the type one hund six ty seven. They had no word for thousand. Thousands came later: the Germanic/Slavic form is different to the Latin or Greek forms.

When people absorb other cultures, bits of the absorbed cultures are preserved. So we see the 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 that the germanics were some form of IE that subsumed a pre-existing twelfty-using culture, responsible for a great slice of the germanic vocabulary. In any case, a pre-existing twelfty-base is common to all of the germanic people at the time of the arrival of Christianity.

The Practical Base

The decision to use base 120 was based on practical needs. What i needed was some base that allows all sorts of vulgar fractions to be added together and easily recognised.

I considered many different approaches to the problem of how to express numbers in a readily identifiable way. In the end, twelfty won, not just because of its divisors, but also because it has a preferred interval.

The two-place period of twelfty is a product of small primes: 7, 11 and 17. Even though decimal, base 21, base 99 also have preferred intervals, the twelfty-system is better equiped for the 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

What makes the periods reckonisable is that the periods of say 17/63 is in twelfty and sixty, the same as a seventh. So we see that the number is something of the form 2^x 3^y 5^z 7.


© 2003-2009 Wendy Krieger