Re: Too narrowly defined: DIVISION SIGN & COLON

From: Jukka K. Korpela <>
Date: Wed, 11 Jul 2012 20:30:22 +0300

2012-07-11 19:33, Hans Aberg wrote:

> As for the ISO standards mentioned in section 5.2 "Bold style",

I’m sorry, I’ve lost the context: section 5.2 of what?

> I think they call for the use of sans-serif fonts.

The ISO standard on mathematical notations, ISO 80000-2, is very vague
about fonts: “It is customary to use different sorts of letters for
different sorts of entities. This makes formulas more readable and helps
in setting up an appropriate context. There are no strict rules for the
use of letter fonts which should, however, be explained if necessary.”
(clause 3)

The standard itself uses a sans-serif font throughout, as ISO standards
in general. This is unfortunate for many reason. Sans-serif fonts are
generally unsuitable for mathematical texts. Moreover, if your overall
font is sans-serif, some essential distinctions are lost, since tensors
and symbols for dimensions are conventionally rendered in sans-serif
font as opposite to the tradition of using serif fonts for mathematics.
This is one of the reasons for “mathematical sans-serif” characters in

> In pure math, one uses serif fonts, also for tensors, which do not
have any fixed notation.

Pure math, applied math, and physics partly use conflicting conventions
for some notations. Standards are supposed to remove unnecessary and
disturbing differences, at least in the long run. And ISO 80000-2 says:
“Two arrows above the letter symbol can be used instead of bold face
sans serif type to indicate a tensor of the second order.” (2-17.19)
This implies that the normal, basic notation uses bold sans-serif for

> Also, it is traditional to typeset variables in italics and constants
in upright,

There is considerable variation here. By ISO 80000-2, *mathematical*
constants such as i, e, π, and γ are denoted by upright symbols, whereas
*physical* constants such as c (speed of light in vacuum) are treated as
denoting *quantities* and therefore italicized. It is however very
common in mathematics (but not that much in physics) to italicize
mathematical constants

> but this has not been strictly adhered to, perhaps due to the lack of fonts.

I think the diversity is mostly due to traditions. Mathematicians tend
to be very conservative in notational issues.

> Unicode adds all variations: serif/sans serif, upright/italics.
> In principle, one could use all styles side-by-side indicating semantically different objects.

Yes, you could, but I think it’s not *normal* to make the distinctions
at the character level. Rather, higher-level protocols are used to
indicate italics, bolding, and font family. One obvious reason is that
it is rather clumsy to *type* the mathematical italic, mathematical
sans-serif, etc., characters and usually very easy to use font or style
settings, markup, or style sheets for italics etc.

I was surprised at realizing that MS Word 2007 and newer, when
processing formulas, internally converts normal characters to
mathematical italic and relative. For example, in formula mode, when you
type “x”, Word by default changes it to mathematical italic x. It does
*not* used a normal “x” of the font it uses in formulas (Cambria
Math)—that font lacks italic, and if you “italicize” it, you get fake
italic, algorithmically slanted normal letter, which is very different
from mathematical italic letters of the font.

It’s interesting to see such usage—it’s probably the most common use of
non-BMP characters that people encounter, even thought we are usually
ignorant of what’s really happening here, and it *looks* like play with
fonts only.

Received on Wed Jul 11 2012 - 12:32:37 CDT

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