I have never seen a *good* base 12 number system. Thus, I created this one (which hopefully is). Decimal numbers are on the left hand side of the slash, dozenal on the right. I have adopted a variant of the symbols for nine plus one and nine plus two as supported by the dozenal society of Great Britain.
Where I have deviated from normal numbers where you might not expect me to (eg. Nine = “en”) I have done so for practical reasons only.
I have tried to create reasonable and distinct sounding names, that are easy to say.
The “teens” are accommodated by the suffix –twe, and the dozens beyond that by the suffix –do. Occasionally, you may note “blips” in the spelling such as ad + twe = addwe. This is a simple matter of assimilation, that which occurs so that adjoining consonants move to the same point of articulation etc (for ease of speech). Thus, sometimes “-do” becomes –to.
Occasionally, some vowels may also be missed (eg. One + twe = ontwe). This, too, is for pronounciation and language reasons. Sometimes, though, I have not done this when by pattern I should have- this is so as to indicate pronounciation.
1/1 = One
2/2 = Two
3/3 = Three
4/4 = Four
5/5 = Five
6/6 = Six
7/7 = Sept (pronounced “set”, like the French number for seven)
8/8 = Ad
9/9 = En
10/Í = Dene (pr. “deen”)
11/Ú = Elf (German for eleven)
12/10 = Twelve
13/11 = Ontwe
14/12 = Tutwe (pr. Tut-wee or too-tway)
15/13 = Thretwe (pr. Thret-wee, thret-way)
16/14 = Fortwe
17/15 = Fiftwe (sometimes I pronounce this “fye-wee”)
18/16 = Sixtwe (I have come to pronounce this as “sight-wee”)
19/17 = Septwe (set-wee, set-way)
20/18 = Addwe
21/19 = Entwe
22/1Í = Dentwe (sometimes denetwe - “den-et-way”)
23/2Ú = Elftwe (I usually do not pronounce the t here)
24/20 = Tudo (pr. “too-doh”)
25/21 = Tudo one
26/22 = Tudo two
27/23 = Tudo three
…
36/30 = Thredo (I often pronounce this as “thray-doh”)
48/40 = Fordo
60/50 = Fifto
72/60 = Sixto
84/70 = Septto/Seddo (Pr. “Sept-toh” or “set-toh” or “see-doh”)
96/80 = Addo
108/90 = Endo
120/Í0 = Denedo
132/Ú0 = Elfto
144/100 = Gross
1728/1000 = Grand
2,985,984/1,000,000 = Milliad
The present year, 2003ad/11ÍÚad = Ontwe Denedo elf (or) One grand, One gross and denedo-elf
As far as higher powers go, it depends really on whether you are using the one thousand million = 1 billion system, or the one million million = 1 billion system. I will not impose, but will say that the higher names are:
I hope you got that. I shall rephrase, in case you did not:
One dozenal million = 1 milliad
One dozenal billion = 1 billiad
One dozenal trillion = 1 trilliad
One trilliad times by one trilliad = 1 hexiad
One hexiad times one hexiad = 1 uniad.
The values are different, obviously, due to the two different number systems used worldwide.
Even higher numbers are formed in the usual way. That is, the numbers + iad (illion in decimal). So, Grossiad, for instance.
Afterwords/notes:
I reject the often-heard “dek”, amongst others, as I view them as aesthetically displeasing. If a number has to be changed, the goal is to make it easy to say, distinct, possibly vaguely English, and aesthetically pleasing (at least not distasteful).
The symbols for dene and elf are borrowed from Arabic, hence their strange style. These are as close as word can come to the *actual* dozenal symbols for these. Though, these symbols are almost exactly right, just move them up onto the line, and Romanise their curves. Dene is like a cursive t, and elf is a back-to-front *rounded* three.
I believe this to be a full and useful system of dozenal numeration. Obviously it is not “final”, in as much as pronounciation changes, new ways are found to distinguish things, etc. Thus, if anyone has any comments or points to make on this system, or has used it etc, please contact me.
Question
December 10 2003, 9:24 PM
Does anyone have any information regarding dozenal calculators?
martin
Re: Fascinating Essay...
December 10 2003, 11:24 PM
THe cost of making one calculator is huge. The cost of making subsequent calculators is very small. This means that unless there is a good market for a particular calculator, that model will not be made.
I do not believe that there is much of a market for dozenal calculators (unless somebody has an arbitrary calculator that has a variable base).
If however you would sponsor me for a week for a normal professional fee, I could write you a software dozenal calculator program (four functions) - writing computer software is my business and I would find it quite interesting, even if, in my opinion, it is compltely useless - however, if a customer is prepared to pay me to do the job I see no harm in takig his money and doing a professional job.
Re: Fascinating Essay...
December 11 2003, 1:08 AM
Well, I would pay you man, but I am brassic
Re: Fascinating Essay...
December 11 2003, 10:59 PM
<<
Does anyone have any information regarding dozenal calculators?
>>
Several of the Texas Instruments graphing calculators in the TI-85, 86 and 89 series can perform arithmetic in binary, octal, and hexadecimal. I'm sure dozenal wouldn't be much of a challenge to make.
martin
Re: Fascinating Essay...
December 12 2003, 8:37 AM
The first one would probably cost $1,000,000 and each subsequent calculator 50c. Thus, if there was a market for 10 such calculators, the cost would be $100,000.50 each, if there was a market for 1,000,000 such calculators, the cost would be £1.50 each.
Maybe my figures are not quite correct, but I think that the economic argument comes across.
Evil Engineer
Re: Fascinating Essay...
December 16 2003, 8:10 PM
Why do you need a special calculator ?
I was under the impression that everyone who uses imperial had wonderful mental arithmetic skills.
The same skills that have sadly been lost my those poor souls versed only in the metric system!
PaulEOS
Re: Fascinating Essay...
December 17 2003, 3:11 PM
And those who use metric exclusively never resort to using an electronic calculator or slide rule?
Evil Engineer
Re: Fascinating Essay...
December 19 2003, 8:09 PM
What's a slide rule ?
PaulEOS
Re: Fascinating Essay...
December 20 2003, 11:27 AM
You are joking, right?
Evil Engineer
Re: Fascinating Essay...
December 20 2003, 1:31 PM
Yes, I am joking.
Perhaps you've spent too much time in the states if you can't spot "tongue in cheek" without a smiley.
I'm vaguely aware of what a slide rule is for but I've never used one and haven't got a clue how they work.
We did get taught how to use log tables at school but I could never see the point when you had a calculator sat on the corner of the desk.
It must have been character building, or something.