### Base Dozen Forum

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Base Dozen Forum

A board for discussion of the number twelve as the base of numeration in mathematics and physics.

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» Pasigraphie of Joseph de Maimieux
Fri Aug 05, 2022 1:57 pm by Phaethon

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» Optimal Analogue Clock
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### Top posters

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Phaethon

Posts : 118
Points : 195
Join date : 2019-08-05
This is an adaptation of the Duodecimal Myriad System nomenclature system proposed by Takeshi, 1st March 2019, http://www.asahi-net.or.jp/~dd6t-sg/univunit-e/revised.pdf.

It copies the multiplicative principle of natural language ordinarily used by the common majority whereby indices or exponents are not stated explicitly while powers are attained as the products of terms for smaller powers of the base. The words dozen and gross already in English for powers of twelve are retained.

Components of new words for powers are derived from Greek. Greek is preferred over Latin because of the greater presence of Greek in mathematical terminology and contributions of Greeks to mathematics.

A new word mylliad is introduced for the fourth power of twelve. It is derived from the Greek word myriad for ten thousand or the fourth power of ten, as well as the word million from English for 1,000,000. Also it evokes the word mile. The fourth power of twelve so happens to be about twice ten thousand.

The my- syllable is back-formed as a multiplicative prefix meaning times one through the first syllable of Greek mono. This is followed by the suffix -lliad, which means a group of four numerical positions. Dozenal numerical characters are grouped in fours, and the number of these groups of four is indicated by a prefix derived from the Greek cardinal or counting numbers. Thus, twelve to the power of twice four has the prefix dy- from the Greek for two.

The eleventh prefix, enkomi-, is invented from contraction of Greek meaning "one yet", where the "komi" part is related etymologically through Indo-European roots to English "to come". This is analogous to the Greek deka for ten meaning "two to come" before the base twelve. Enkomi has three syllables, but so does eleven.

For the twelfth prefix, the translation of dozen into Greek as ntouzina may be used. Alternatively, a highly contracted form giving zilliad may be preferred. This sounds familiar to English from zillion.

Prefixes for powers higher than twelve times four may be obtained by concatenation of the monosyllabic prefixes, so that dyzilliad would mean twelve to the power of a double dozen.

Table of Dozenal Powers

Phaethon

Posts : 118
Points : 195
Join date : 2019-08-05
After the design of the Mylliad system described here, it was noticed through an internet search of the term that the word mylliad had been used before with a different size meaning for a dozenal system of another https://qedscience.wordpress.com/tag/dozenal/.

Later, a visit to the website of the Dozenal Society of Great Britain revealed that the words milliad, billiad, and trilliad have been proposed by Bryan Parry, http://www.dozenalsociety.org.uk/roses/parry.html, though with different meanings than those of mylliad, dylliad, and trilliad here.

These examples show evidence for convergence of independent minds towards a similar set of names for dozenal powers. The -lliad suffix is similar to the -lliard suffix used for powers of the decimal long scale that are used in many languages for such numbers.

wendy.krieger

Posts : 47
Points : 67
Join date : 2019-08-07
Age : 65
The lesson from the million/billion/trillion thing, is to try and flatten the structure out. 10^9 formerly was 'thousand million, you go to 999 thousand 999 million 999 thousand 999. But the thousands column collapsed, ye have 999 billion 999 million 999 thousand 999.

Twelfty used to go this way too, with 1 million E9 hundred and E9 thousand, E9 hundred and E9. But the desire was to keep Million at the same spot (120^4), for much the same reason that Takashi does: it is a natural order. So we simply invented 'cention' for the large hundred position, and get 1 million E9 cention E9 thousand E9 hundred and E9.

There are fancies for going to very large powers of the base, but usually it's the commercial market, rather than science and technology, that drives it. Mount Isa Mines switched from COBOL to Fortran because the latter could handle the larger numbers being demanded by the accounting section.