Spaces in TeX, part II

Finally back. A while back, I covered spaces in TeX and why they don't always appear. Today's much shorter post will cover a few additional places spaces do not appear. The most obvious place one might expect a space—a vertical one this time—comes from consecutive new lines. The thought goes, if one blank line produces a newline, then surely two blank lines will produce two newlines. This reasoning is incorrect. From before, recall that TeX produces \par tokens when it sees end of line characters in state N. What TeX does with a \par token depends on its mode. There are six different modes, vertical, internal vertical, horizontal, restricted horizontal, math, and display math, but to simplify matters, let's only consider vertical and horizontal. (The internal vertical and restricted horizontal are similar enough to vertical and horizontal for our purpose.) TeX starts in vertical mode and then transitions to horizontal mode (and does things like indentation) to typeset a paragraph. When it sees a \par token, it transitions back to vertical mode. While in vertical mode, \par tokens are ignored. Thus, while two blank lines produce two \par tokens, the first causes TeX to return to vertical mode and the second is ignored. The TeX primitive \vskip or the LaTeX macro \vspace can be used in vertical mode to get additional space, as desired. There are a few other places where TeX ignores spaces, but those are fairly rarely encounted, so I'll only briefly mention them. When TeX expects to see a number, the number can be given as a sequence of digits followed by an optional space. There's actually one place where the optional space is fairly important and that is changing the category code of a character and then using that character immediately. Even less frequently encountered, at least by me, is starting a paragraph with an \hbox causes the paragraph to not be indented. Use of the LaTeX macro \mbox solves this problem, as does starting the paragraph with \indent or \noindent, as desired. And I think that wraps up all I have to say about spaces in TeX.