I've been playing with the designs of glyphs for a duodecimal number system, also known as dozenal, base-12, base twelve, and uncial.

I'm not a font designer, but here are my sketches of the current frontrunners among the tiny baseTwelve community in the Dozenal Societies of Great Britain and America:

These digits represent ten and eleven, respectively.

And here's my sketches of my own design and personal choice:

My sketches are by no means the only suggestions out there. But I happen to be the one posting this post, so I'll naturally put in my favorites.

What I want from you is, well I guess this is sort of an advertisement to make you aware of the need for duodecimal glyphs. Think about it the next time you're designing a set of numerals.

I'd also like to test the waters and see if anyone here has preferences for one symbol over another, and why, or why not.

As for actual use, for now I guess these would go in the personal use area of Unicode, if I knew how to do that. In the ideal future, I'd like to see a small block of Unicode set aside for base-12 numerals, as well as special hexadecimal characters.

I'm more of a sexagesimal type myself ;-)

It looks to me that duodecimal notation lacks historical sources when it comes to possible glyph shapes, so I think there will need some other element other than "they look pretty to me" for an effective design. Constrain is the father of design (creativity's the mother).

So... you're saying it should be A and B?

Aside: sexagesimal, huh? Do you use the Babylonian numerals then, some other source, or have you invented your own?

"Constraint is the father of design."

Does this apply to arbitrary constraints, too? I guess that would be the paternal grandmother of design, making arbitrary constraints for her son to follow. Some of the constraints that I've seen regarding duodecimal:

* It has to be able to translate to a seven-segment display.

* It has to be something a 19th-century printer could dig out of a drawer by rotating or somehow being creative with existing characters.

* It has to look like other numbers.

* It has to be something used by Dozenalists since the 1940s.

* It should be related to the letters that the words ten and eleven begin with. (T and E, or other letters in other languages)

* It has to be something that already appears somewhere on the keyboard, or ideally, on the telephone pad (* and # were used for a while for this reason)

* The single numeral for 10 should look like a 10 to evoke its history and subsequent demotion from a 2-digit number to a 1-digit number (actually my favourite constraint).

I happened to exchange thoughts on that with a certain Thomas Lambert about two years ago. And some more time ago I was in contact with Tilman Piesk about hexagesimal figures.

I’m not a mathematician, I’m a signographer and fontist. It is good that mathematicians and typographers think about this together.

This matter is surely complex. Perhaps it would be most sensible to deal with dodekadic and hexagesimal figures at once. The issue seems to be the same.

I try to answer briefly on this worthwile account of aspects:

It has to be able to translate to a seven-segment display.

– this is a reasonable request, but aonther request would have to come first:

It has to be easily written and easily recognized (by humans).

It has to be something a 19th-century printer could dig out of a drawer by rotating or somehow being creative with existing characters.

No. There is no reason why we should stick to the technical limitations of 19th century letterpress printing. B.t.w., they were often more flexible like we are nowadays when creation of new characters was at stake.

It has to look like other numbers.

No. It has *to fit to the set of the existing figures*

(note: we are typographically talking about figures here, i.e. the graphical representations of the first numbers, not of numbers as such).

It has to be something used by Dozenalists since the 1940s.

Possibly, but not neccessarily. It would be of merit, though.

It should be related to the letters that the words ten and eleven begin with. (T and E, or other letters in other languages)

No. This is a linguacentric bias which there is absolutely no need for. Choose one language and you end up discriminating all others.

It has to be something that already appears somewhere on the keyboard, or ideally, on the telephone pad (* and # were used for a while for this reason)

No, No, and once more NO.

What is needed on the long run is new glyphs and new characters (please inform yourself about this two crucial concepts). Everything else will not overcome the state of a – more or less – poor workaround. You’ll not get sustainable encoding practice for those characters as long as you use £ or # or something else which already exists for other expressions.

The single numeral for 10 should look like a 10 to evoke its history and subsequent demotion from a 2-digit number to a 1-digit number (actually my favourite constraint).

I do not see any need for that constraint. B.t.w., X means also “ten”.

* It should be simple graphs that can get easily written by hand, easily recognized by the eye and easily typographed.

(Your very first line example looks promising, I’d say.)

* The graphs must not get eventually mixed up in recognition with other figures.

Cool project.

Why not go all the way to hexadecimal?

hhp

I did include suggestions for hexadecimal symbols in the original post here, but I buried them in a bunch of other junk, so you might have missed them. My Big Idea with regard to hexadecimal symbols is to make them much like ABCDEF, but thinner and more rounded, analogous to the difference between O and 0.

Good basic idea, but I think they should be only

reminiscentof ABCDEFwhile remaining identifiably distinct - otherwise there's really no point.

hhp

Well, if you're planning to do glyphs for the sedecimal range 10-15 (A-F), why not base them on scripty minuscules? And if duodecimalists want their very own, I would suggest X for ten ('H' on 7-segment) and Saturn for eleven ('h' on 7-segment).

Some random notes.

My relationship with the sexagesimal number system is mostly of fascination,* not of real use, outside of time tracking and such. Hey, we’re divisible by 5 too! ;-)

About constrains, other than what others already said better than I could do, IPA already claimed any shape even vaguely resembling a Latin letter, but it could be a minor issue, lest you need to write a book about the Mahl language of Minicoy Island.

I’m with Té about X for ten. Unfortunately it (and its variations) is already one of the most heavily laden with meanings symbols of the world.

If I were to lay down some research about duodecimal symbols, I would start looking for already used and working systems.

Té’s suggestion about Saturn led me to think about zodiacal symbols and their relationship with the twelve months. And what about the Chinese zodiacal symbols?** Their twelve years cycle is less meaningful, but they’re more related with numbers, with the symbol for “rat” sometimes replaced with the symbol for “first”.

* http://www.newearthtime.net/

** There are also the Twelve Symbols of Imperial power, if one wants.

Is this a Spencer Brown kind of thing or are you trying to devise a set of symbols that would "read" as particular numbers?

Andreas:

What is needed on the long run is new glyphs and new characters (please inform yourself about this two crucial concepts). Everything else will not overcome the state of a – more or less – poor workaround. You’ll not get sustainable encoding practice for those characters as long as you use £ or # or something else which already exists for other expressions.

I'm glad to see you post this. I feel the same way. That's why I posted here.

* It should be simple graphs that can get easily written by hand, easily recognized by the eye and easily typographed.

(Your very first line example looks promising, I’d say.)

If you look around the internet a bit, at duodecimal sites, you'll find better examples of X / E upon which my sketch is based.

hrant:

Good basic idea, but I think they should be only reminiscent of ABCDEF

while remaining identifiably distinct - otherwise there's really no point.

Agreed. I'm by no means any kind of final arbiter, although if I was, I'd work on my rounded glyphs a bit more. I would want computer-people to be able to glance at a string of new hexadecimal numbers and say to themselves "huh, those symbols are obviously hexadecimals, and not alphabet letters." No more confusion between hexadecimal strings and various algebraic expressions you might find in computer programming, plus the fact that now you could use hexadecimal in algebra with actual As and Bs.

I can imagine keyboards being made with an extended set of numbers, although having read various cases for the dozenal system, I think it's more practical to add only two duodecimal numbers to the keyboard, rather than six for hexadecimal.

riccard0:

If I were to lay down some research about duodecimal symbols, I would start looking for already used and working systems.

That's what the first four symbols that I posted are. They are in use by the Dozenal Societies of Great Britain and America. The sketches are my interpretations, but I didn't come up with those shapes.

Té:

Well, if you're planning to do glyphs for the sedecimal range 10-15 (A-F), why not base them on scripty minuscules?

Why not? Because I'd want to create a sense of continuity between the capital letters that everybody uses now, and any new system. I've looked at minuscules in the desired context, and to me they look like algebraic and calculus expressions.

Everybody uses A-F? Reckon that 'everybody' does not include programmers.

I've looked at minuscules in the desired context, and to me they look like algebraic and calculus expressions.

But, since we're talking about "based on", if you create glyphs that are lining with numerals, they should look less algebraic.

[X…] Unfortunately it (and its variations) is already one of the most heavily laden with meanings symbols of the world.

Lets be careful. Let’s try to describe **exactly** what is meant. It is essential not to mix up things here.

As a matter of fact, it is rather natural that the basic cross-shape is materialized in many different signs and characters, and in *some* symbols, too. It may help mentally to distinguish:

• graph • sign • symbol. as well as • glyph and • character.

In extensive fonts you are likely to find many different glyphs or characters based on one and the same graph:

A new figure glyph based on the X-graph could well be done, in the carving adjusted to the existing figures and proportions rather slim, like here the later two (Runic and Ogham).

Everybody uses A-F? Reckon that 'everybody' does not include programmers.

Hmm, I was assuming by everybody to mean mostly programmers, but I'm not one myself, so I might be wrong there. It also depends what language. Writing HTML means you pretty much have to use ABCDEF for hexadecimals.

Writing HTML means you pretty much have to use ABCDEF for hexadecimals

I write all my html in lowercase. And css too,* including colour values.

* my only nitpick is proper capitalisation of font names.

A new figure glyph based on the X-graph could well be done

I think, Andreas, you've demonstrated that it is possible to repurpose the X for ten. My question would be: is it desirable?

I'd like to mention too, that a new character for ten might also need to be written by hand. Subtle distinctions are well and good when creating computer fonts, but if I wrote most of those with my hand, I wouldn't know which was which. Learning algebra for the first time was hard enough for me, and having x as both multiplication and a variable made it harder. Fortunately, the curriculum thought of this, and took out x as multiplication, replacing it with brackets.

But, since we're talking about "based on", if you create glyphs that are lining with numerals, they should look less algebraic.

I think I might be able to imagine this, but I'm not sure. A numerical scripty minuscule B would look like 6, if I understand what you're suggesting. Did you see my butterfly B sketch?

A very quick sketch (not for typophiles faint of heart).

Please keep in mind that a script minuscule b will not resemble a 6: its loop would be on top (I didn’t included the design in my sketch in order to avoid possible confusion with e. I used something akin your “butterfly B”, hopefully less similar to an 8):

Those satisfy me, at this stage being very preliminary sketches (as mine also are), I am convinced they won't be confused for variables. Next step: conquer the world.

Ah, there is a thread on this subject.

The top two symbols, it turns out, were designed by W. A. Dwiggins, of Caledonia fame!

The second two are due to Isaac Pitman, the shorthand innovator.

And even the two you identify as your own invention and personal favorite are similar to one set that dates from the 1500s, designed by Juan Lobkowitz.

Incidentally, I see that there are no duodecimal positions in Unicode at present. I would have thought that at the very least, the "10" and "11" used to print sterling pence amounts would be there, because some computer character codes had them.

We're gonna need a few more: sexagesimal, anyone?

hhp

In fact, someone

diddesign unique digits for sexagesimal.Since hexadecimal can be achieved without additional memorization - one could even go up to base 36, at least if one zig-zagged between upper- and lower- case to use i but also L, rather than I or l...

although one would have to create confusion by omitting too many letters trying to extend the alphabet with Greek or Cyrillic, you well know the

obvioussolution to the problem.Cool stuff.

hhp

This

0123456789

ABCDEF

GHiJKLMNoPQRSTUVWXYZ

ԱԲԳԴԵԶԷԸԹԺԻԼԽԾԿՀՁՂՃՄՅՆՇՈՉՊՋՌ

սՎտՐՑՒՓՔ...Ֆ

gets us up to base-64, before we have to switch to lower-case again.

With a suitable typestyle, a lowercase Օ (here replaced by an ellipsis) wouldn't get confused with the Latin o either, so one could go to base-74, without any additional memorization... except having to learn the Armenian alphabet, of course.

Come to think of it, though, while 4 and 7 are exceptions, most of the digits are rounded in shape, while most upper-case Latin letters are angular - and Greek, Cyrillic, and Armenian capital letters are closely enough related that the same applies to them. Perhaps another alphabet should be chosen, one with rounded shapes that match well with the digits...

Thus, I unveil... New Hexadecimal!

0123456789აბგდევ

Oops; F and 3 will get confused (at least with oldstyle digits) and why is Georgian being aliased differently from everything else in my browser (perhaps resorting to a different font)?

Hmm. I think I've come up with a way to avoid memorization entirely. Use a-z followed by A-Z, and avoid confusion by using a script face for the letters used as digits.

It is not acceptable to merely add two new numeral characters to the ten digits of the decimal Indo-Arabic numeral system in order to make a duodecimal system. It would also then be necessary to write some kind of a note next to any number written with the supplemented numerals to the effect of "this is a base-twelve number", as otherwise the reader would not know what base the numeral system is supposed to be if only the digits of the small counting numbers zero to nine happen to appear in the expression of the number. But it is not convenient to have to write such a note every single time any number is written by an expanded decimal to base-twelve system.

What should be required instead in the design of a duodenary system of numeral notation is creation of a complete set of twelve new numeral digits, such that none of the new digits could be confused with any of the old decimal number characters. The dozenal digits should also preferably look different from alphabetic letters. This I have done (See image "DKdozenalJPEG" of numeral characters adapted for familiar modular display).

I used to complain about the decimal system of notation and advocate a base-twelve system instead as a child. The number ten as base for a numeral system seems quite bizarre in comparison to twelve. Now I have been routinely using a dozenal numeral system privately, and this differs from that which I display here in that only one of its numerals neatly written can be converted to one of the others by adding marks, but it is not so suitable for the monospaced concept.

One person with good judgement can propose better in a single day what many other people in decades or centuries suggest.

John, I hereby nominate you as an honorary Armenian. ;-)

Well, we do re-use the ten decimal digits in non-decimal systems and it still works out OK... Although there are advantages to not overloading a symbol, there's also an advantage to having to learn less redundant stuff; after all the symbol/numeral "1" for example has the same value in binary, decimal, hexadecimal, etc.

Indeed. Or as Galileo said:

"In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual."

hhp

Kepler wrote a letter to Galileo asking for his opinion on his Mysterium Cosmographicum and stated

"I much prefer the sharpest criticism of a single intelligent man to the thoughtless approval of the masses."

In 1931 under Nazi influence in Germany, a publication called "A Hundred Authors Against Einstein" appeared. Einstein remarked: "If I were wrong, one would have been enough."

hrant: "we do re-use the ten decimal digits in non-decimal systems and it still works out OK... [...] the symbol/numeral "1" for example has the same value in binary, decimal, hexadecimal, etc."

People only re-used the same symbols for different numeral bases because they had no other immediate option that could be applied systematically. A make-shift work-around does not rule out supersedence by a surpassing tailor-made fix. Identical decimal numerals used for different bases only barely perform when the different bases are not co-existing in the same application or if there is a notation to explain explicitly what the base of a given number is supposed to be.

A particular digit could hardly be said to have the same meaning in different base notations. Even within a same base numeral system, a character signifies different numbers depending on the context of its position in the place value. For example, in decimal notation a digit 1 followed by just one other digit to its right hand side means ten; but with two or three other digits to its right it would mean a hundred or thousand. But in base sixteen its values would be sixteen, two hundred and fifty-six, or four thousand and ninety-six. If there is no explicit instruction explaining what the place value is, since counting the number of digits to the right hand side is inadequate because it only provides the power or exponent of the base but not the base itself, then the digits themselves by their dedicated design ought to assume the role of informing the reader of the base. Otherwise, the reader would have to try to guess what the base is by watching how many different characters happen to appear in the numbers; although this method is not reliable, because the character signifying the largest number of units for the base might not appear in a given sample.

Insistence on using only pre-existing alphanumeric characters for other bases than decimal is not optimal, has no inherent justification, and prevents the practical simultaneous use of different numeral base systems.

I designed some cursive versions of the characters that I proposed here in my post of 19 Mar 2013 — 12:35pm (See image "DKdodenaryJPEG"). I have not done any further work on this picture since Tuesday 26th March 2013.