Okay, so here's a question I've been thinking about lately.

In base twelve, should "10" remain "ten", or should it be "twelve/dozen/zen/whatever" as we usually imagine? I mean, perhaps the connection between "10" and "ten" is just too strong, and it might be better to say eight, nine, dek, elv, ten, or whatever.


Thoughts?

The word "ten" means nine and one, just like the word "dozen" means a group of eleven and one. In the mind of the speakers they are not linked to written representations such as "10" until after they have been taught to make that association at school. Illiterate English-speakers understand words like "ten", "twenty", "dozen", "pair", "score" or "hundred" even though they do not know anything about representing those numbers in written form using Hindu-Arabic digits.

What I mean is that one thing is the written numeric labels such as "10", which are language-independent and whose meaning is dependent on what radix one is using because that is the essence of a positional system, whereas a very different thing is the linguistic labels, whose meaning does not depend on a non-linguistic variable called "radix" and they already had a meaning previously and independently of the written system of numeration. Trying to change the meaning of the word "ten" would be like trying to change the meaning of words like "thousand" or "fifty" or "six" or "dozen". "Ten" means nine and one whether represented numerically as "10", "X", "0xA", etc., just like "a dozen" means eleven and one whether represented "12", "XII", "*10", "0xC", etc.

Note also that numerals in English do not use a positional system (you do not say "two-zero-three-one" to mean 2031, unless you're reading a phone number), and the word "ten" is no more linked to the Hindu-Arabic decimal place-value representation "10" than to the Roman numeral sign-value representation "X". The numeral system of English is actually akin to the system of Chinese written numbers, where the quantity is decomposed into multiples of powers of ten (units, tens, hundreds, etc.) in a fashion similar to a decimal positional system, and the order is conventionally fixed, but unlike in a digital positional system this default order can be altered without affecting meaning because the exact value of each element is expressed in words (which power of ten the "digit" multiplies is explicit) instead of left implicit by its relative position in the string (you usually say "two thousand and thirty-one" but might as well say "one, thirty and two thousand", while this is not possible in digital representation where 2031 and 1302 are not synonymous), and English doesn't require that you include intermediate zeroes for the meaning to be clear (one doesn't normally say "two thousand, zero hundred and thirty-one", while the digit sequences 2031 and 231 mean markedly different things). Moreover, nothing prevents one from "mixing radices" when saying a number in English; you can perfectly say "two thousand, three dozen and one" and the meaning is clear to every speaker (and it certainly doesn't mean neither decimal 2031 nor dozenal *2031, but could be expressed in extended Roman numerals as MMZZZI or in Chinese numerals as 二千三打一).

My opinion, "ten" means a quantity equal to the radix in use; one full grouping. So "ten" in dozenal is 1 dozen and zero ones. It is the "first rank" designator. Same goes for "hundred". In base twelve, the digit representing 2*5 should have a different name (the American Dozenal society calls it "dek".) I don't think there is anything wrong with appropriating the present rank nomenclature for dozenal or any other base. If "confused" about which base you're dealing with, say "dozenal" after your number.

This is my point; I think as you. When someone says "ten" to me, I tend to think "10", not *** *** *** *. I understand the linguistic point, but none of us here are illiterate, frankly. Are we actually aiming our propsals at converting the fraction of a percent in this country who are actually illiterate?

Anyway, I made this thread cos I realised when I work in base eight, I tend to say "...six, seven, ten..."



My theory is we should probably rename all numbers from 10 | *T upwards, or else keeps as many of the present names as possible. By my above logic, "ten" and "eleven" should probably be renamed, as they call to mind "10" and "11". So maybe something like "...eight, nine, dek, elf, ten, ten-one, two-one..." But I understand how this might be confusing to some. "elf, ten, eleven, twelve" wouldn't probably work for fairly obvious reasons,.

Neither of you has so far addressed any of my points showing that English numerals are not a positional system and thus the concept of radix does not apply to them. Claiming that the primary meaning of the English word "ten" is "the first power of the radix", instead of the number of fingers and thumbs in both hands, is akin to claiming such a thing for other collective numerals like "dozen" or "score"; a very particular interpretation that you have chosen yourselves but that is not supported by the actual linguistic usage of that word. You yourselves admit that such a thing as saying "[dozenal] ten-one" to mean "a dozen and one" would be "confusing to some" (I'd say "confusing to most"). Why would it be confusing if the word "ten" actually meant what you claim it means? Precisely because the linguistic meaning of the word "ten" is fixed and clear and is not dependent on what radix one uses to represent numbers positionally in ideographic written form, its association with the particular non-linguistic representation "10" being a completely a posteriori thing.

Moreover, it's precisely this pernicious association that people get ingrained in their brains at school what poses the greatest hurdle for them to later understand other radices (even though they can perfectly understand counting by the dozen or by the score in linguistic terms such as saying "two dozen and one" or "three-score and four"). Since, when they are taught to write numbers at school, what they do in their minds is to link the representation "10" with the meaning of the word "ten" (that is, with the quantity * * * * * * * * * *, so that they have great difficulty in understanding "10" to mean "one dozen" or "one score"), and what they (or the great majority of them, anyway) don't actually do is, viceversa, to dissociate the word "ten" from its pre-existing linguistic meaning and make it dependent on what the radix makes "10" mean, so that if you said "duodecimal twenty-five" they would immediately understand what quantity it refers to (most people would be puzzled and wonder what the hell "duodecimal twenty-five" means other than five times five or a quarter of a hundred, whereas they would immediately understand "two dozen and five"). Just look up the definition of the word "ten" in the dictionary (AHD: "The cardinal number equal to 9 + 1", OED: "one more than nine; 10. (Roman numeral: x or X.)"), where no reference is made to its meaning being dependent on the concept of radix, which is an non-linguistic construct and has little to do with the way English numerals work.

Ten is ten.
If you're counting, whether or not you see the numerals in your mind, ten comes before eleven and not after it.
"10" is whatever the base requires it to be. Which in turn implies that we can't use "twenty" for *20 and so on.

uax, Shaun: touche ;D

There appear to be three methods of assigning names to numbers.

Method A | The community of mathematicians (from high school experience, perhaps) simply calls out the digits of any nondecimal notation, followed by "base x". So 736 base eight is "seven three six base eight", and *49a54 is "four nine <ten> five four base twelve", with <ten> maybe pronounced eigh, alfa, ten, etc. This is perhaps acceptable analytically and while in airspace (fower niner ten fife fower) but not very sweet if one is going to use dozenal each day. In giving a speech about base 60, I will be using "digit twenty seven digit forty six digit forty" to refer to the fourth power of 2*5. Pretty lengthy for a three digit figure.

The other two methods aren't satisfied with Method A's robot speech.

Method B | There's another (perhaps admittedly naive) camp that retains the present rank nomenclature (whether or not linguistically it exists in English). This is the ten(radix)/-teen(digit+radix)/-ty(radix*digit), and hundred, etc. The only nomenclature required would be for transdecimal digits and some means to distinguish the notation from decimal. This method is convenient for bases smaller than decimal. So octal 736 may be called seven hundred thirty six octal. Ten wouldn't come after eleven, but always before it. the fifth prime would have another name. Actually, maybe "eleven" might not play a role. Radix plus one would be called oneteen; radix plus two "twenteen" or "two-teen". I read somewhere on the internet, in a paper about the conversion of an African tribe using dozenal to decimal, that they simply collapsed out the two transdecimal names and retained the "first rank" nomenclature, etc. So it is viable if it isn't as linguistically chic.

Method C | There's a more creative camp that would use one, two, three, ... nine, ten, eleven, twelve, maybe new digit names, ... then some "first rank" radix word that would have to be concocted. For bases who possess an extant word, like dozen and score, well those bases would have convenient first rank words that are fortunately familiar. This camp would need to use their creativity and devise a set of rank nomenclature in addition to nomenclature for transdecimal digits (if radix is greater than 2*5). The rank nomenclature will then introduce a layer of some unfamiliarity and "confusion". cf. *38 = "thirdy eight", "threezen eight", "three do eight". Then there's the conservative approach: the use of the existing english dozen words, that's fine if we have four digits or less: "six great gross eleven gross four dozen one". Above that, we're back to inventing rank nomenclature. Sorry about this word "rank", it comes from Menninger.

Absent any dozenal contacts, I generally resorted to using the second method, simply inventing two digit names (for 2*5 and the fifth prime), and employing the decimal nomenclature. When writing out the date in dozenal days I use the first method. Today is, for example, either seven great gross ten gross one dozen ten, or the seven dozen tenth period of 144 days (I called shurga or xrga), and the one dozen tenth day of that period.

So we're back, given Uax & Shaun's stipulations, to inventing nomenclature, which leads to discussions of proposals for dozenal nomenclature. We can be more "authentic" and research old english and indoeuropean to justify concocted names, or we can be whimsical. In the meantime while we are discussing all this I would like to use dozenal. I wish I spoke better espanol because Uax's scheme for dozenal in spanish is sublime.

Hello all. I'm new here (both to the forum and to the broader dozenal movement), and one of the main reasons I joined was to ask about the nomenclature. I'd hoped -- and this is also the case with the symbols -- that everyone would be united behind a consensus, but it seems there's a situation comparable to that which is found in the International Language Movement. Oh well...

I'm in the "principle of least change" camp, so would support something like this (where the numerals are dozenal):

1 = one
2 = two
:
9 = nine
:A = ten
:B = eleven
10 = twelve
11 = oneteen
12 = twoteen
13 = thirteen
:
1 :A = tenteen
1 :B = eleventeen
20 = twenty
:
2 :A = twenty ten
2 :B = twenty eleven
30 = thirty
:
:A0 = tenty
:
:B0 = eleventy
:

Failing this, I'd want a wholly new system.

Are there others here who support this proposal (which I won't label as "mine" because it's so simply derived)? And is it possible to get closer to the existing system?

I use "ten" for :A and "eleven" for :B, since these are already words. For higher numbers, I use the form:
(gross digit) gross (dozens digit)-dy or dozen (ones digit)
example 1 :A :B=one gross ten dozen eleven (or one gross tendy eleven)

The exception is programmers. I've heard 4096 called a "hex thousand". But it still took me a while to realize what it meant.

I like that possibilty of using "-dy", Imp. I reckon we could do something similar for the gross multiples, using the ending "-gre" (pronounced as in "meagre"), i.e.

One gross
Twogre
Threegre
Fourgre
Figre (rhymes with "eiger")
Sisgre
Sevengre, or sengre
Eightgre
Ninegre
Tengre
Elevengre, or elengre

-gre ...
What about a word to mirror "century'? (Obviously "grocery" won't do!)

My initial best idea for that one is "grossure".