Expository Mathematics in the Digital Age
Content Versus Presentation
One of the most important principles in writing web documents is the separation of content and presentation. Content refers to the mathematical and expository information that the author wants to convey to her readers. Presentation by contrast refers to the style in which the information will be conveyed. Content is of paramount importance, presentation much less so. The separation of the two is valuable for a number of reasons. First, it allows the author to concentrate on what's most important, the content, and to worry about matters of style later, and separately. Second, the separation leads to documents that are much more accessible. Keep in mind that a web document might be rendered on a standard computer screen, or on a small screen in a hand-held device (a PDA or a small tablet PC), or printed, or rendered aurally for someone with impaired vision. Thus, how a document is presented depends very much on the presentation device.
In the case of articles for JOMA (or other online journals), many issues involving presentation will be decided by the editorial staff (as is the case with print journals). Thus, work by an author on issues that are purely matters of style is wasted effort. Finally, regardless of what the author or editors think is best, a reader (or processing software) may well override style issues at the point that the article is actually rendered. (A user can easily change font sizes in her browser, for example).
On the other hand, it is not always easy to decide whether an issue involves content or presentation. At JOMA, we believe that matters of document structure--the organization of the document into web "pages", whether pages are rendered in full windows or pop-up windows--fall more into the content category, and should be left primarily to the judgement of the author. As we have noted before, one of the goals of JOMA is to promote expository articles with innovative and effective document structures.
I have already argued that HTML should be the basic language for the expository part of an article. So, how does one separate presentation from content? First, to the extent possible, use mark-up tags that give information about content and structure of the document rather than simply specifying style. For example, the <dfn></dfn> tag for a definition, the <cite></cite> tag (for a citation), the <var></var> tag (for a variable), and the <em></em> tag for emphasis all have italics as the default rendering. But these tags give useful information about the words that they enclose, unlike the <i></i> tag for italics.
Conversely, avoid using tags, such as <i></i> (for italics), <b></b> (for bold), <font></font> (for a font specification) that only specify style. Rather than putting a phrase in italics or boldface or a particular font or a particular color, ask yourself why you want to do so, and then use the appropriate content tag: Is the phrase a definition? Is it a citation? Is it to be emphasized?
The presentation of any HTML tag (including style tags) can be specified with an external style sheet. For example, a style sheet might specify that phrases within the <i></i> tag actually be rendered bold and red. Style sheets for HTML documents are ordinarily written in the Cascading Style Sheet (CSS) language, another standard, text-based, open-source markup language.
Finally, do not use content tags to achieve presentation effects. For example, the default rendering of a phrase in the <blockquote></blockquote> tag is to indent the phrase, as in the following example:
The Chebyshev polynomials are everywhere dense in numerical analysis.
But this tag is intended for a quotation, not for indention. It's wrong to mark-up a phrase that is not a quotation with this tag, just so that the phrase will be indented.A program that processes the source file (a reader for the blind, for example) will expect a phrase marked-up by this tag to be quotation.
For more information, see Mathematics with Structure and Style.
It's interesting to note that in proprietary formats (Word and PDF, for example), the separation of content and presentation is difficult, if not impossible. The two are inextricably linked, often by design--it's one of the ways that users are often forced into using proprietary tools. This is another reason to avoid using such tools for basic exposition.