Re: Too narrowly defined: DIVISION SIGN & COLON

From: Asmus Freytag <>
Date: Tue, 10 Jul 2012 13:28:14 -0700

On 7/9/2012 11:04 PM, Jukka K. Korpela wrote:
> 2012-07-10 5:32, Asmus Freytag wrote:
>> There are many characters that are used in professional mathematical
>> typesetting (division slash being one of them) that need to be narrowly
>> distinguished from other, roughly similar characters.
> Typographic differences can be made at glyph selection level, too, or
> even in font design and choice of font. Typesetting systems like TeX
> and derivatives have been very successful along such lines.

TeX and similar systems can get the correct appearance, but they do not
have the same benefit of a universal encoding of the semantic
distinction that underlies these variations in appearance.
>> Such narrowly defined characters are not aimed at the general user, and
>> it's totally irrelevant whether or not such a character ever becomes
>> "popular".
> Popularity is relative to a population. When I wrote that “narrow
> semantics does not make characters popular”, relating to the case of
> DIVISION SLASH, I referred to popularity among people who could
> conceivably have use for the characters. I don’t think there’s much
> actual use of DIVISION SLASH in the wild. And this was about a case
> where the distinction is not only semantic (actually the Unicode
> standard does not describe the semantic side of the matter except
> implicitly via things like Unicode name and General Category of the
> character) but also has, or may have, direct impact on rendering.

I don't know, I would ask mathematical publishers whether they use
ordinary or division slash.

>> Very early in the design cycle for Unicode there
>> was a request for encoding of a decimal period, in distinction to a full
>> stop. The problem here is that there is no visual distinction
> This is more or less a vicious circle, and the starting point isn’t
> even true. In British usage, the decimal point is often a somewhat
> raised dot, above the baseline. But even if we assume that no
> distinction *had been made* before the decision, the decision itself
> implied that no distinction *can be made* by choice of character.

Encoding the same appearance (shape) as two separate characters is
something that the Unicode standard reserves to well-motivated
exceptions, such as the multiple encoding of the shape "E" for the
Latin, Greek and Cyrillic scripts. You don't need to look further that
the issues raised with spoofing of internet identifiers to see that
there are strong downsides to duplicate encoding. This is particularly
true, when the distinctions in usage are mere notational conventions and
not as fundamental as script membership.
> If a different decision had been made, people could choose to use a
> decimal point character, or they could keep using just the ambiguous
> FULL STOP character. Font designers could make them identical, or they
> could make them different. But most probably, most people would not
> even be aware of the matter: they would keep pressing the keyboard key
> labeled with “.” – that is, the decimal point character would not have
> much popularity. In British typesetting, people would probably still
> use whatever methods they now use to produce raised dots.

A nice argument can be made for encoding a *raised* decimal dot (if it's
not representable by any number of other raised dots already encoded).
Clearly, in the days of lead typography, a British style decimal dot
would have been something that was a distinct piece of lead from a
period. In the end, no such request was made.
>> Unicode has relatively consistently refused to duplicate encodings in
>> such circumstances, because the point about Unicode is not that one
>> should be able to encode information about the intent that goes beyond
>> what can be made visible by rendering the text. Instead, the point about
>> Unicode is to provide a way to unambiguously define enough of the text
>> so that it becomes "legible". How legible text is then "understood" is
>> another issue.
> That’s a nice compact description of the principle, but perhaps the
> real reasons also include the desire to avoid endless debates over
> “semantics”. Some semantic differences, like the use of a character as
> a punctuation symbol vs. as a mathematical symbol, are relatively
> clear. Most semantics differences that can be made are not that clear
> at all.

Being able to encode an intent that is not directly visible to a reader
of a rendered text has issues that go beyond the niceties of debating
semantics. There are some cases where the downsides of that are (nearly)
unavoidable, and duplicate encoding is - in the end - the better answer.
But notational conventions usually don't qualify, because it's the
sharing of that convention between reader and writer that makes the
notation what it is.
>> Because of that, there was never any discussion whether the ! would have
>> to be re-encoded as "factorial". It was not.
> This implies that if anyone thinks that the factorial symbol should
> look different from a normal exclamation mark, to avoid ambiguity (as
> in the sentence “The result is n!”), he cannot do that at the
> character level.

He can do so on a stylistic level, or a notational level (using a
different convention, perhaps adopting the convention of ending that
statement with a sentence ending period, as in "The result is n!.").
> A large number of mathematical and other symbols have originated as
> other characters used for special purposes, then styled to have
> distinctive shapes, later identified as separate symbols. For example,
> N-ARY SUMMATION ∑ is now mostly visually different from GREEK CAPITAL
> LETTER SIGMA Σ, though it was originally just the Greek letter used in
> a specific meaning and context.

Correct, and at some point, such notational advances lead to new symbols
and new characters. There is a (very short) pipeline of mathematical
symbols that have been recently introduced and might get encoded when
they gain critical acceptance.
> A principle that refuses to “re-encode” characters for semantic
> distinctions seems to put a stop on such development. But of course
> new characters are still being developed from old characters for
> various purposes and can be encoded. They just need to have some
> visual identity different from the old characters from the very start,
> to have a chance of getting encoded.

Correct, the point of differentiation requires not only a different
interpretation, but a distinct appearance as well. Not to recognize that
is an often practiced fallacy based on taking too literally the mantra
that "Unicode encodes the semantics".
>> The proper thing to do would be to add these usages to the list of
>> examples of known contextually defined usages of punctuation characters,
>> they are common enough that it's worth pointing them out in order to
>> overcome a bit of the inherent bias from Anglo-Saxon usage.
> So what would be needed for this? I previously suggested annotations like
> : also used to denote division
> and
> ÷ also used to denote subtraction
> But perhaps the former should be a little longer:
> : also used to denote division and ratio
> (especially since the use for ratio is more official and probably more
> common).


Received on Tue Jul 10 2012 - 15:29:20 CDT

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