Here's an idea for an extended set of Hindu-Arabic digits covering up to hexadecimal. I started with Pitman's set, because of:

- Its antiquity. I'm unsure if it was in fact the first ever proposal for dozenal digits, but in any case it dates back to the 19th century, predating both the DSA and the DSGB, and the fact that it is still used and talked about by dozenalists up to this day testifies to its having withstood the test of time, even if of course not everyone agrees with it.

- The renowned status of its proposer, well-known for his work on shorthand writing, which gives this proposal a certain halo of venerability and fame that raises it above parochial disputes and matters of personal taste.

- Because of the above, Pitman's is the only proposal anywhere near the status of an existing standard for dozenal digits. Certainly the only one that might have a chance to be included into Unicode.

- The choices can be justified on the ages-old principle of acrophony, which is a likely origin for most of the other Hindu-Arabic numerals. In the case of 4, 5, 6, 7, 8 and 9, their acrophonic origin would lie in the Kharosthi script spelling of the words for the corresponding numbers in Sanskrit: chatur, panca, shat, sapta, nava, and in the case of :A and :B, they can be related to the Latin script spelling both of English ten and eleven and of German zehn and elf (and maybe for the words in other languages). And even if they could be related only to the English words, after all most of the efforts to spread and keep alive the dozenal idea, and maybe even the dozenal idea itself, have come from English-speaking countries, so entitling English to be the source for the dozenal digits would be similar to entitling the discoverer of a chemical element to name it (and note that I'm not saying this precisely out of chauvinism, because I come from outside the Anglosphere and neither English is my native tongue nor my native country has had what could be called the most amicable historical relations with Britain and the United States).

- They can be further justified on the fact that they are modified forms of the first two existing digits from which a distinct shape can be obtained.

- Since their shape is based on that of existing Hindu-Arabic digits, they do look something like digits (unlike the * and # used by the DSA).

So my idea is to further extend this set up to hexadecimal, going by the same principle of modifying existing digits. By rotating and/or mirroring the 0 to 9 digit set we get the following possibilities:




Continued in the next post, to avoid the unnecessarily restrictive (and what's worse, ten-based!) limit on the number of images one can include in one post. <_<

The rotated and mirrored versions of 0, 1 and 8 are an obvious no go. The rotated versions of 6 and 9 generate each other, and their mirrored versions unfortunately happen to be very similar to two symbols very common in mathematics: the letter e used for Euler's number, and the modified cursive form of d used for partial derivatives. So I think we'd better discard them, even though in my opinion they could have made fine digits. The only distinct modified form of 3 is already in use in Pitman's set. So we're left with the modified versions of 2, 4, 5 and 7 to choose from. The inverted versions of 4, 5 and 7 are in my opinion the shapes that happen to look the least like digits of all the set. So in the end my selection has been:













Note that every extended digit in this set (including Pitman's) is related to the digit with a value of the corresponding digit minus 8, except for the one that would be based on 6 because of the above stated reason, for which a replacement is substituted by restarting the cycle with another variation of the first digit that admits further variations, that is, 2.

In case someone is wondering how they could fit into the very limited possibilities of 7-segment displays, here's one option:

Sure the adaptations are somewhat arbitrary, and maybe a more adequate and consistent scheme would be preferrable, reassigning the current 7-seg shape of 2 to mean the mirrored 5, and using mutually related shapes for 2 and its rotated and flipped versions, possibly alternative shapes where the top and bottom segments correspond to the straight lines in the typographical form instead of to the round parts, that is:

Were it not for the fact that the choices for the digits 0 to 9 are already fixed and cannot be reassigned to another value, so we have to make do with what was left unused. But just think of the degree of variation among the various typographical and cursive variants of some letters like a, f, g, r or z, not to mention the differences between uppercase and lowercase glyphs, let alone the adaptations of some of the alphabetic letters like M to the limitations of seven-segment displays. So the deviation from the original typographic form of some of the new digits and their proposed form adapted to 7-segs isn't really radical.

The adaptations would be mostly trivial (except maybe for the mirrored 5) in the case of fourteen- or sixteen-segment displays, which do not impose the extreme limitations of 7-segs, not to mention the adaptations to dot-matrix displays, which nowadays have largely superseded and replaced the others because of their far greater versatility.

The problem I have with these suggestions is that i read the all the digits underlined in red as "2" and the ones underlined in cyan as "5" - which leaves me with the two with double underlines as choices for ten and eleven (or just ten if the E symbol is used for eleven).

I agree with uaxuctum that digits 0, 1, 8, 6, and 9 in any flipped or mirrored versions are unusable. I also agree with Shaun regarding the proposed versions of 2 and 5 and their alternative forms in that they would result in ambiguous forms that could easily be mistaken.

I disagree with the discarding of inverted and mirrored versions of 4 and 7 on the sole grounds of aesthetics which I feel is a unsatisfactory argument for their elimination. However, of the four different arrangements of 4, only three have possible acceptable analogues in a seven segment display. These are the existing symbol, the flipped version and the mirrored version, while the flipped and mirrored version on a 7 segment display looks like a lower case letter "h".

The alternate versions of the digit 7 can be displayed in 4 different arangements. These are shown the diagram below along with the variations of the digit 4. Below these is a diagram showing the possible 7 segment versions of each of these alternatives. Of these, the flipped 7 with the tail on the seven segment version looks like a capital letter "J". The flipped and mirrored 7 witha seven sgment display without a tail looks like a capital letter "L". Of the four different printed versions of 7, the first two shown have a vertical line sloping to the right from top to bottom and as such these do not fit well with the other existing digits. This leaves only the last two amended versions of the 7 and to avoid possible misidentification with the letter "L", I suggest the last version is the better choice.

Thus there are two additional possible versions of the digit 4 and one additional version of the digit 7 that would fit the looks of the existing digits and are capable of being displayed unambiguously on a 7 segment display.

uaxuctom also makes a claim that there is no great need to allow for representations on a 7 segment display as there are many other displays that could be used. However, if there is any possibility of introducing any extended number system it should at least allow for the minimum of disruption. That there are so many 7 segment displays in current use is easily demonstrated. Go out in the world and see what ratio of displays are 7 segment versus all others. Start with the gas pumps at your local gas station and multiply that for all the pumps in existance as the majority will still be using the humble 7 segment version for reasons of cost.

A final argument in favour of these alternatives is that all three, both new versions of 4 and the one new version of the 7 can be easily written by hand without lifting the pen and they also have the advantage of familiarity thus easing the learning curve.
It just remains to decide what to which numbers each of these symbols should be assigned.

Comments?

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