I already proposed a similar idea in another thread, but I wasn't sure if that was the right place for it. Plus, I fleshed out the idea a little bit more.

Basically it's the following:



It works for any number base, and it could even theoretically be extended to base-100 before it got unwieldy.

See, my thing is, we have a perfectly good system in base-10, it's got a lot of good things going for it. It's just not as good as base 12. That's not to say we should throw all the babies out with the bathwater. Let's salvage what we can from the decimal system and apply it to the duodecimal system. Anyways, that's what I say.

Also, I've given some thought to a "duodecimal point" since I don't find the semicolon satisfying. Here's what I came up with:



I don't actually know if there is an existing character that looks like this. Well there oughtta be. It could be represented slightly differently in different fonts, but the idea is that it's half of this: |

so the bottom extends slightly below the baseline, and the top is never higher than the midline.

Yes, it looks like a lowercase undotted "i", but that is actually more helpful to me than a semicolon, because when I read a number out loud or even in my head, in decimal it's

"one point two five seven . . . "

so in duodecimal it could be

"one eye two five seven . . . "

rather than

"one semi-colon, gee I like the semi-colon, I wonder who invented the semi-colon, two five seven . . ."

I see a problem there with handwriting. One would be to very, very careful to distinguish these ligatures from normal digits. Thus, I don't think this system is useful for everyday dozenal usage.

Secondly, the seperator sign you propose is quite similar to the comma, which is already used in many countries (including mine, Germany) as decimal seperator. Frankly, I don't see the need for a distinguished dozenal seperator at all; why not simply use the same as in decimal?

Having said that, your ligatures do look nice, especially the 13.

Which is a bit similar to the double-s symbol in German.

The separator - I have never been keen on the semi-colon - and if we're going to use a "point" as now then there will have to be some other marker to show dozenal, like, for example, the asterisk. One-half would be *0.6, for example.
I still write the decimal point as we have always done in Britain, half-way up and not on the line. A point on the line meant multiplication over here - e.g. 2.6 = 12, but two point six would be 2·6.
(Though I expect our younger generations follow the US usage with the point on the line for the separator.)

I like using the semicolon; it clearly notes that a number is dozenal, and it's just as easily pronunciable as the decimal point if you follow Pendlebury's usage and simply say it "dit":

11 :A 5;6---onezen one elvzen five dit six---the current year and the current month.

That's interesting. I follow British usage in some things---I slash my sevens, for example, as did my father and grandfather before me, though I'm not sure how they got the habit which they taught to me---but I've never really understood this one.

In America, of course, a period *on* the line is a fractional separator, while a period *above* the line indicates multiplication, the exact opposite of the system you just described. Odd how a standard would develop in precisely the opposite way.

I would think the handwriting problem would be nearly insurmountable. I don't write a 1 with an introductory serif, yet such a serif is the only thing connecting the two ones in your symbol for :B. And when I'm doing lots of figures, my numbers often touch each other, which would result in great confusion for me in this system.

No question, though, that they are visibly attractive and well-done.

For a dozenal point, I see three main points of view that I generally sympathize with:

1.) Just use the same symbol, whatever it might be in your area.
2.) Use the semicolon, because it appears to be the most established usage among dozenalists.
3.) Use the apostrophe ('), because we already use it for feet and inches.

I order these, in my own preference, as 2, 3, 1. They all have the advantage of being in general use already within restricted fields. I don't really see the benefit of inventing an entirely new symbol for this, personally, though naturally I'm hopeful to hear one if anyone cares to tell me.

Fair enough, of course, do what's most easy for you. The thing is, when handwriting, I don't use an introductory serif on my 1s either. This is what makes the ligatures work for me when handwriting. It actually helps to distinguish plain old unconnected 1s and 0s from my connected versions of 10 and 11. But, if you prefer to avoid serifs altogether, my symbol for :A / X / T can also be essentially a capital letter thorn:



and the symbol for :B / E / can be this letter, whose name I forget:



The others follow in a similar manner. my 13 looks kind of like a "B", and so on.


Now, Ebbe said this:

You do have a point about it being rather similar to the comma. In print and on a computer screen, it should be fairly easy to distinguish the two. My separator is supposed to be at least twice as tall as your typical comma. That might not be distinct enough, as you could easily argue. I happen to think it's sufficiently different. The reason I choose a symbol that's similar to both the comma and the period is that I do want it to be recognized as having a very similar yet distinct meaning from both of those symbols in multiple countries in Europe and the Americas.

In handwriting, again you have a problem in that not everyone writes their commas the same way. I'm not familiar with how everyone writes their commas, but as for me, my commas are always slanted, while this new symbol is supposed to be written straight up-and-down. And as with the print version, the written version should go up to halfway up the line.

Maybe this conversation has been had already on these boards, but I think it is very necessary to have a distinguished duodecimal separator, especially in the transition stage between decimal and duodecimal systems. This way, you can start using a different separator right away, in order to distinguish the two notation styles, and then when duodecimal supplants decimal in any field, there's no reason to transition back.

This is my problem with the asterisk. ie. *10 = 12

With asterisk notation, the idea is that the asterisk will eventually be phased out. So it's a temporary and admittedly imperfect solution. However, a brand new dozenal separator can always be used, and it need never be phased out, in the same way that we can pretty much always understand what a decimal point after a number means. Ie. 12. = 12

So in a way you do phase it out, but the phasing out remains optional for an indefinite period of time, just as it is now with the decimal point.

The problem I have with using "." and "," is that when you intersperse numbers with text, it can lead to confusion, like for example when you end a sentence with a number. Or maybe you don't want to end a sentence. I say, wouldn't it be nice if there was a symbol that wasn't also used in language punctuation.

I don't like the idea of using the radix point to distinguish the base. Because it means that we'd need to use one even for integers. In handwriting, this is a mere aesthetic concern. But to my eyes as a computer programmer, "12." is a very different thing from "12". While they have the same numeric value, the former has type [DoHTML]<code>float</code> (or <code>double</code>) while the latter has type <code>int</code>[/DoHTML].

On the other hand, I don't like the * prefix either, because it suggests multiplication.

I agree with you about the "*"; once the basic concept has been explained, it seems to me that we ought to assume dozenal rather than decimal, unless otherwise stated. An explicit statement in this regard would normally be called for. On the other hand, "*" has been used for a long period, and I normally only use it to indicate multiplication when there are two operands, and even then I use a space before and after it.

As for using the radix point to distinguish the base, I'm a programmer as well, though an amateur, and I don't find it confusing. While you're right that it means "float", it only means that in an actual program, in which you're always going to be inputting decimal anyway. (At least until we get some good programming languages that expect dozenal numbers.) When you're *not* programming, there's really no confusion, is there?

I haven't used * for multiplication (or ** for powers) since the days when I used to program in Fortran. Would the ordinary person think that *10 meant "multiply by 10" when there's nothing to multiply the 10 by?
Also it's only needed when a text contains bases other than twelve.

Well put by Shaun. That's what I was getting at with the "two operands" statement. In other words,

is clearly multiplication, while

is clearly not. Furthermore, I think that

is clearly different from the first, even if one were to require such an odd notation (why not just say something along the lines of, "The following equation is in dozenal"?).

Finally, the "*" is only necessary to clarify possible confusion, and it's not necessary at all if there's a fractional part and you're using a distinct separator for it. So all in all, the custom of marking dozenal numbers with "*" when confusion is possible seems reasonable, at least to me.

I use "*" for multiplication in Excel. But since I'm not aware of duodecimal support for Excel, it doesn't really make a difference. I do input duodecimal figures in Excel, but only as text. In Excel, my convention lately has been to color duodecimal figures purple.

Really, I could adapt to any system, as I'm not attached to any particular figure, but if someone was to ask me which figures to use, I would naturally gravitate to figures that I hadn't already assigned a specific meaning to, in my mind. I could adapt, I'd just rather not, unless I had a good reason.

It should be relatively trivial to write a VBA loop for Excel to translate numbers into dozenal from decimal, or into decimal from dozenal. This could then be used for your calculations. I'd write it, but I never use Microsoft Office, rarely use WYSIWYG office software of any variety, and strongly dislike Visual Basic in general, so it's got rapidly diminishing returns for me. However, if you're a dedicated Excel user, I'd encourage you to look up a tutorial on visual basic and just write in the algorithms you use to convert by hand. It'll probably take a few solid hours of work, but it'll be worth the investment in the time it saves you in the long run.

I think that's a wise way of looking at it, and I feel the same way. While I genuinely like the Pitman characters and the semicolon, I'd probably be using them even if I didn't simply because they seem to be a widely recognized standard. I consider the existence of such a standard sufficient reason to "adapt," as you put it, as far as my purposes in using dozenal go.

FWIW, OpenOffice.org Calc has [DoHTML]<code>BASE</code> and <code>DECIMAL</code>[/DoHTML] functions for converting between bases. Unfortunately, it only works for integers.

This topic has led me to attempt to program a dozenal converter into an old TI-83 I had laying around, which uses a species of Basic. It should be relatively easy to port this to Office. I've got a number of other projects going, but when I get through this one, I'll post it up.

I wrote a base converter for the TI-89 once.

I don't suppose you could post it for us?

http://www.ticalc.org/pub/89/basic/math/nu.../baseconv89.zip

Thanks! I'd started one but had become overwhelmed with other projects. I'm glad this exists; thanks for doing it.

You are welcome to look at the code for my base converter in Javascript. It converts floats , not just integers. To see it in action go here http://www.footrule.com/1/conversn/convjvs...ac=1&jt=1.2.3.2
You can also use basic math operations in the decimal input.

Thanks for that, too, Ruthe. I've written my own in C, which runs great on Unix-like systems (it could probably be compiled for Win32, as well, but I've never tried since I (almost) never use it), and of course GNU bc will do not only conversions but also arbitrary precision calculations in any base at all. So I don't really need one for my own use on a general-purpose computer.

A Javascript converter would be great for a website, though. Is the code free for that sort of use?

I reserve the right of using that format for my own website. As you can find out for yourself, there are numerous examples of number base converters on the web, but I haven't found another that handles fractional values other than mine.

Using the Javascript code to develop the same facilities in another application I would allow.