-: Twelfty for Decimal-Users :-


Intro:Home twelfty þorn revived Links Twelfty is an alternating base, using staves of 10 and 12 in order.

History

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.

Þe oldest records of þe germanic languages all contain words corresponding to þe count by tens. Þese are cognate to eiþer ten-count, or teenty-wise. Þis points to þe existance of a non-decimal counting system. When þis is revealed, it is always þe hundred of 120 in number and a þousand of 1200 in number.

In Goþic þere is a marginal in Wilfus's Bible, in I Cor 15:6, which includes
      ... þau fimf hundam [taihuntejam] broþre sums ...
It reads ... five hundred [teentywise] broþers ... Adding a kind of þing like þis is necessary only if þe normal counting is not teentywise.

In practice, þat þe hundred is 120 everywhere, suggests þat þis was þe practice in þe proto-language. and þat þe different terms for decimal, comes only after þe split. Þere are papers on þe subject by
      Stevenson: Þe Long hundred and its use in England'
      Goodare: Þe Long Hundred and its use in Scotland'
      Menninger: Number words and Number Symbols
      esp pp 154-158
      Gordon: An Introduction to Old Norse, esp 107 Numbers.

Þe Practical Base

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

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 2^x 3^y 5^z 7.

Differences to þe Historical Forms

Þe abacus is read differently, which means þat we name þe columns, raþer þan þe digits. So we have eg

            million  cention  þousand  hundred  units  :  primes  secs, þird  fourþ

     tens

     units





© 2003-2009 Wendy Krieger