A Comprehensive Dozenal Counting System: 

How to count in duodecimal - number names, scientific notation, prefixes, and abbreviations

Originated: 25 November 2004  Revised: 10 March 2006

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Counting in Dozenal:

For ordinary purposes, counting in dozenal is not difficult at all.  The English language accommodates this quite easily.  The terms 'dozen' and 'gross' represent number sets of 12 and 144 respectively.  This makes counting in numbers less than 1 728 (which we do most often) very convenient.  Beyond that, however, it gets a little troublesome. For example, 1 728 - the dozenal notation equivalent of 1 000 - was traditionally called a 'great gross' - in my opinion, a cumbersome name.  However, since very few people have even heard of a 'great gross', I feel comfortable renaming that particular unit to make conform to the pattern dozenal counting system outlined below.  Most dozenists I have conversed with advocate for a system of number names with the basic numbers having no more than one syllable  (thus, 'twelve' is preferred to 'one dozen' in most dozenal systems I have seen proposed).  I, however, prefer the term 'dozen' to be retained.  The reason is that I want to make counting as easy as possible for people used to thinking in base ten.  My thinking is that, though more cumbersome than 'thirteen, fourteen, fifteen.', 'one dozen one, one dozen two, one dozen three.' is not unlike the hundred sets that people are used to counting in.  Familiarity is important.  If you are going to try to get people to use something new for an important thing like counting, you want them to be able to conceptualize it as quickly and easily as possible.  Despite my preference for the 'dozen' I would like to see 'twelve' also kept as it is a useful term in some circumstances - for example, one dozen o' clock is just a tad more cumbersome than twelve o' clock. 

The chart below lists the numbers of the dozenal counting system I am proposing.  Many of them look similar, but many of them look different.  The far left column shows what the number would look like in dozenal notation (I have substituted the characters X and E for '10' and '11' since the standard keyboard does not accommodate my preferred characters for these).  The far right column shows what the number expressed looks like in our current decimal notation.  The center column gives the proposed names for the numbers in this new dozenal system.  Before we get to the chart, allow me to explain how I decided on these particular names.

I have renamed 'zero' for the sake of efficiency.  The word I use, 'neen', is a transliteration of an Old English word meaning 'none'.  My reasoning should be self-explanatory: try saying 'point zero, zero, zero, zero, zero, one'.  Not that easy, is it?  Americans get around this trouble by substituting 'oh' for 'zero', and the British do it by substituting 'naught' - notice that both substitutions are one-syllable words.  In my system, 'zero' would still be an acceptable name, but 'neen' would be preferred. 

The next oddity is 'seof' instead of 'seven'.  As with most other dozenists, I prefer a basic set of one-syllable numbers - it is more efficient.  'Seof' is derived from an Old English word for 'seven'. 

For the same reason as 'seven', I have replaced 'eleven' with an Old English derivative: 'eolf'.  This term is actually only loosely based on its Old English counterpart.

I have already explained 'dozen' in the first paragraph; however, I did not go into great detail concerning the proper form.  You probably have noticed in certain formal documents that the term 'and' is used to describe numbers between sets of one hundred (for example, the Constitution of the United States of America describes the date as "the Year of our Lord one thousand seven hundred and Eighty seven").  I would like to preserve this construction for formal speech and in certain other circumstances (where it just sounds right - for example: 'I am two dozen and two years old' - as opposed to being asked 'How old are you?' and responding with  'two dozen two.'). For ordinary counting, the 'and' is just an extra syllable.  Therefore constructions like 'three dozen five, three dozen six.' are to be preferred. 

Twelve times twelve in one gross.  While retaining the term 'gross', I have changed the official term to 'grosan'.  The reason being relates to the way it sounds.  In English, I have heard 'I'll take a gross of these' and, in response to 'How many?', 'a gross'.  Try saying 'I drove 144 miles' in that terminology.  'I drove a gross miles' doesn't sound like a proper use of the term 'gross'.  Likewise, 'I drove a gross of miles' doesn't sound quite right, either.  To solve this usage problem, I have added the term 'grosan'.  'I drove a grosan miles' sounds more natural (not to mention that it matches my other set names in sound). 

Now, the next pattern of set names requires a little bit of explanation.  In our current decimal system, one hundred hundreds is called 'one thousand'.  I'm not sure why.  One thousand thousands is called 'one million' after the Latin term 'mil' meaning 'one thousand'.  'Billion' is one thousand multiplied by one thousand to the second power ('bi' meaning 'two').  'Trillion', in turn, is one thousand multiplied by one thousand to the third power ('tri' meaning 'three').   I went in a different direction with my number sets - more visual-based as well as having a rational mathematics base.  In our decimal notation, 'one billion', as I said above, is one thousand times one thousand to the second power.  While making sense in this context, a simplification of this process leaves you with 'one thousand to the third power' - this reduction strips away the rational basis for the name 'billion'. What I have done is similar, but more rational.  We currently like to deal with very big numbers by demarcating them with three-digit sets.  Thus, one million, two hundred and four thousand, seven hundred and three looks like '1 204 703'.  Likewise, 1 billion is '1 000 000 000'.  So when I first started formulating my system, I wanted the name to relate to the number of full three-digit sets following the first one to three digits.  Thus, the number that looks like '1 000' would be named for the one set of three following the first digit.  Likewise, the number that looks like '1 000 000' would be named for the two sets of three following the first digit.  The number scheme I use was borrowed from several sources including Modern English, Old English, and Latin.  For the number '1 000' (1 728 in decimal), I used the Old English word for 'one' - mon - to create the word 'monan'.  For the second set (1 000 000), I use the term 'bi' meaning 'two' to create the word 'bian'.  And so it goes: 'thrian' (1 000 000 000) is derived from the word for 'three', 'fouran' from 'four', 'fifan' from the Old English word for 'five', and 'sixan' from 'six'.  'Septan', 'octan', and 'novan' are from the Latin for 'seven', 'eight', and 'nine'.  'Tennan' is derived from 'ten', 'eolfan' is based on the 'eleven' that I use for my single-digit numbers, and 'donan' is loosely based on the dozen.

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Okay, now we have numbers that we can use.  But what about all those nifty prefixes we have in our decimal system such as 'kilo-' for 1 000 and 'milli-' for 1/1 000?  Decimalists are always lauding their prefixes, talking about how convenient they are, etc.  Well, it just so happens that I have devised a list of such prefixes.  I follow the same pattern that we do in base ten - the only difference being that we are working with one dozen as the base and multiplying by positive or negative powers of twelve. 

All of the prefixes are derived from the number names I assigned in the chart above.  The exception is 'septan' and 'septanth'.  I assigned the prefixes 'petta-' and 'pecco-' to those because there is a 'p' in 'sept' and I wanted a rational explanation for the abbreviation I used.  (The same explanation applies for 'zona-' and 'zoco-' which are the abbreviations for 'donan' and 'donanth' respectively.) 

The abbreviations for the prefixes are simple to explain.  Abbreviations are always one letter.  For powers of twelve, the abbreviation is always capitalized.  For negative powers of twelve, the abbreviation is lower case.  The rule is that the abbreviation shall be the first letter of the prefix.   The exceptions are when a first letter repeats.  Some, I had to alter the prefix so it did not closely resemble the word it was originally supposed to represent (see previous paragraph).  Others had a convenient Roman numeral (five and ten), so I just used that. 

The following chart lists the names for the prefixes in the dozenal system that I propose.

*Remember: '10' is one dozen; also called 'twelve'.