From: Jukka K. Korpela <jkorpela_at_cs.tut.fi>

Date: Wed, 11 Jul 2012 20:30:22 +0300

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

Unicode.

* > 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

tensors.

* > 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.

Yucca

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

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