What is the right way to use of non-breakable space before math expressions?

Question

I have seen LaTeX code that

1. puts a ~ between every math expression and the text preceding it,
2. does not use ~ in this manner at all, and
3. uses a ~ in this way if and only if the math expression is a number (i.e, consists of digits).

I think the first way is not very nice, since it constrains TeX a lot in how it can typeset the rest of the text. I follow the third way, because I vaguely seem to remember reading somewhere that this is how it should be done; but I cannot recollect where, and I don't have any justification for this.

What is the rule to follow here, and what are the typographical/TeX principles behind this rule? It would be great to have references too, to convince obstinate co-authors (if required!).

Similarly, what is the reasoning behind the (almost universally observed) rule that a ~ should precede a \cite{}? Is this documented somewhere?

Answer 1

The physical effect you would get from a line break at some point is a small pause / distraction in reading, so what I do is use a mental trick: imagine how the sentence sounds with a small pause in the trouble spot(s) when read out loud. Some cases are clearer than others, but in general that works fairly well for me.

Occasionally I see something in the typeset output that looks bad visually even though it sounds OK, then I correct the ties in the input to fix that one break.

As the problem is related to the actual language you are using, you could also ask this question on english.stackexchange.com

Answer 2

See chapter~14 of the TeXbook, where Knuth suggests the following ties:

• Chapter~12
• Theorem~1.2
• Appendix~A
• Figure~3
• Table~\hbox{B-8}
• Lemmas 5 and~6
• Donald~E. Knuth
• Luis~I. Trabb~Pardo
• Bartel~Lendert van~der~Waerden
• Charles~XII
• Charles Louis Xavier~Joseph de~la Vall\'ee~Poussin
• dimension~$d$
• width~$w$
• function~$f(x)$
• string~$s$ of length~$l$
• string~$s$ of length $l$~or more
• 1,~2, or~3
• $a$,~$b$, and~$c$.
• 1,~2, \dots,~$n$.
• of~$x$
• from 0 to~1
• increase $z$ by~1
• in common with~$m$
• of $u$~and~$v$.
• equals~$n$
• less than~$\epsilon$
• (given~$X$)
• mod~2
• modulo~$p^e$
• for all large~$n$
• is~15
• is 15~times the height
• (b)~Show that $f(x)$ is (1)~continuous; (2)~bounded

There are even more examples in the exercises, but that covers most cases...