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Old 07-24-2016, 07:10 AM   #1
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Dozenal numbers! A revolution in counting!

Something on a podcast made me think about base twelve numbers. In some ways, they're very attractive - twelve having prime factors of 2 (twice) and three, meaning it's divisible by 2, 3, 4 and 6, instead of just 2 and five like ten.

I find that there is actually a society promoting it, the Dozenal Society of America. www.dozenal.org

They use the rather dull 'dek' and 'el' for ten and eleven,.

However, I feel that they have erred in thinking that the numbers ten and eleven need new names. They don't. Just use ten and eleven. What we do need are two new symbols for their written representation. I don't think anyone's come up with anything really good for those yet - The Dozenal society seems to use an greek Chi or an upside down 2 for ten and an upside down 3 for eleven.

They also have an article on pronunciation, but that's just dreadful. Lots of poor-sounding words that need to be memorised.

I'd like to propose a different counting system for the dozenal number system:

one, two, three, four, five, six, seven, eight, nine, ten, eleven, dozen
onedeen, twodeen, thirdeen, fourdeen, fifdeen, sixdeen, sevendeen, eighdeen, ninedeen, tendeen, elevendeen, twendy
twendy-one, twendy-two,..... twendy-nine,, twendy-ten, twendy-eleven, thirdy
thirdy....
fordy...
fifdy...
sixdy...
sevendy...
eighdy..
ninedy...
tendy...
elevendy, elevndy-one, ... elevendy-eleven, gross.
one gross and one, one gross and two, ...
two gross...
...
eleven gross...
grousand (= dozen gross = one thousand seven hundred and twenty eight)
one grousand and one...
...
..
dillion (= grousand grousand = 1,000,000 (dozenal) or 2,985,984 (decimal)
...
...
billion (= grousand * dillion)

What, you ask? Isn't billion already used in the decimal system? Well, yes it is, but in two different ways (thousand million or million million). And it's so big no-ones understand ihow big it is anyway.


Go on - see if you can count in dozenal using this scheme. I bet you can after five minutes or less.

And, of course, this have the great advantage that it has the number "elevendy-one" in it.

There are the dozenal numbers to name next (the number to the right of the dozenal point). Perhaps one dozenth, one grossenth, one grousenth

I think I may have spent more time and thought on this than I should have.


Anyone else for a dozenal revolution? When would be good symbols for ten and eleven?
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Old 07-24-2016, 07:18 AM   #2
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Nice idea.

But I don't think twendy, thirdy etc. will work. Spoken, they would be indistinguishable from twenty, thirty etc. for speakers of many varieties of English, I think. Although it might be worth it; I might enjoy hearing the question "Decimal or dozenal?" in the street several times a day.
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Old 07-24-2016, 07:26 AM   #3
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Like the idea too!
But i don't understand how match gross is in decimal?
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Old 07-24-2016, 07:33 AM   #4
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Gross is a dozen dozen = 144, I think.
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Old 07-24-2016, 07:44 AM   #5
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Quote:
Originally Posted by doubleshuffle View Post
Gross is a dozen dozen = 144, I think.
Yes, now i got it.

But ther's no names for 1*10^-(n), like milli or micro in decimal (millimetre, micrometre).

EDIT: the dozenal SIprefix is the same as decimal.

Last edited by oren64; 07-24-2016 at 09:26 AM.
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Old 07-24-2016, 07:53 AM   #6
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I just tried to convert the number of my latest win in that thread which I always win - it's far too complicated anyway, so I don't think we'll have to think about that.

Although, thinking about it, it should be easy: dozenth, grosseth, grouseth etc.

But will 1/2 then be 0.6 or 0.5?
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Old 07-24-2016, 08:46 AM   #7
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one half = 0;6 (Let's use ; for the dozenal point)
one third = 0;4
one quarter = 0;3
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Old 07-24-2016, 08:50 AM   #8
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Originally Posted by oren64 View Post
Yes, now i got it.

But ther's no names for 1*10^-(n), like milli or micro in decimal (millimetre, micrometre).

EDIT: the dozenal SIprefix is the same as decimal.
I'm not sure I like just taking the decimal prefixes. (OK, so I've appropriated billion, trillion, quadrillion, etc) but I think that for SI multipliers we need to distinguish between base 10 multipliers and base 12 multipliers, just like we currently distinguish between base 10 multipliers and the binary multipliers (Kibi, Mebi, Gibi, etc.)

Hmm....
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Old 07-24-2016, 08:51 AM   #9
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In fact the Base-12 systems, duodecimal or dozenal, have been popular in the past because multiplication/division/addition/subtraction are fairly easy. Twelve is a useful base because it has many factors. It is the smallest common multiple of one, two, three, four and six. The standard 12-hour clock and common use of 12 in English units emphasize the utility of the base. Also, before adopting to decimal, the old British currency Pound Sterling (GBP) partially used base-12; there were 12 pence in a shilling, 20 shillings in a pound, and therefore 240 pence in a pound.

The Maya and other civilizations of pre-Columbian Mesoamerica used base-20 (vigesimal), as did several North American tribes. Remnants of a Gaulish base-20 system also exist in French. For example, sixty-five is soixante-cinq (literally, "sixty [and] five"), while seventy-five is soixante-quinze (literally, "sixty [and] fifteen"). In Old French, forty was expressed as two twenties and sixty was three twenties, so that fifty-three was expressed as two twenties [and] thirteen, and so on.

The Babylonian numeral system, base-60, was the first positional system developed, and is still used today to count time and angles.

The Hindu–Arabic numeral system, base-10, is the most commonly used system in the world today for most calculations.
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Old 07-24-2016, 08:56 AM   #10
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Yes, every day has twendy hours in it.
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Old 07-24-2016, 09:25 AM   #11
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Quote:
Originally Posted by pdurrant View Post
I'm not sure I like just taking the decimal prefixes. (OK, so I've appropriated billion, trillion, quadrillion, etc) but I think that for SI multipliers we need to distinguish between base 10 multipliers and base 12 multipliers, just like we currently distinguish between base 10 multipliers and the binary multipliers (Kibi, Mebi, Gibi, etc.)

Hmm....
Dozenal use the optional Power Prefixe.
http://dozenal.wikia.com/wiki/System...l_Nomenclature

Last edited by oren64; 07-24-2016 at 09:30 AM.
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Old 07-24-2016, 10:42 AM   #12
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Originally Posted by oren64 View Post
Dozenal use the optional Power Prefixe.
http://dozenal.wikia.com/wiki/System...l_Nomenclature
There's not bad, as prefixes go. one gross metres == one biquametre.

Hmm... Clearly other people have spent even more time pondering this!
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Old 07-24-2016, 10:44 AM   #13
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I prefer base 9 myself.
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Old 07-24-2016, 10:45 AM   #14
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Octal's fun, but hexadecimal's where all the cool kids hang out.

Last edited by pdurrant; 07-24-2016 at 11:04 AM. Reason: typos
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Old 07-24-2016, 10:58 AM   #15
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Octal's fun, be hexadecimal's where all the cool kids hag out.
Hag = Hang?

I've been at the Hex corner for decades. . .
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