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
