What's the difference between ~ and {\mbox{$~$}}

Question

I'm looking at the source code of a book where I found:

D.{\mbox{$~$}}Knuth

What's the purpose of this?

Answer 1

In the \mbox, the space will not be compressed (nor expanded, for that matter) by line-width considerations.

As Manuel points out and egreg emphasizes, the construct \mbox{$~$} "is really useless," as it is functionally indistinguishable from and less efficient than \mbox{ }. Nonetheless, I use it in the MWE below to most directly answer the OP's original question. Were the reader to mimic the technique, please use \mbox{ }.

\documentclass[10pt]{book}

\begin{document}
\noindent\hrulefill

\def\dx{4.2in}

\hspace{\dx}D.{\mbox{$~$}}Knuth

\hspace{\dx}D.~Knuth

\def\dx{0in}

\hspace{\dx}D.{\mbox{$~$}}Knuth

\hspace{\dx}D.~Knuth
\end{document}

To see this on a grand scale, here I use \sloppy to give LaTeX all the rope it needs to hang itself:

\documentclass[10pt]{book}
\sloppy
\begin{document}
\noindent\hrulefill
\def\dx{3.64in}

\hspace{\dx} D.{\mbox{$~$}}Knuth rocks!

\hspace{\dx} D.~Knuth rocks!
\end{document}

Answer 2

You can define a new command that uses the normal interword space with the possibility to shrink it if the line needs shrinking, but not stretching it. It's necessary to add \@ in order to properly set the space factor (the \  command does it implicitly).

In the example I use the low level \hbox spread command in order to show the effect; it typesets the text in a box stretched (or shrinked) by the stated amount.

\documentclass{article}

\DeclareRobustCommand{\nostretchspace}{%
  \nolinebreak\@\hspace{\fontdimen2\font minus \fontdimen4\font}%
}

\begin{document}

\hbox spread 2cm{D.~Knuth wrote \TeX}

\hbox spread 2cm{D.\nostretchspace Knuth wrote \TeX}

\hbox spread -3pt{D.\mbox{ }Knuth wrote \TeX}

\hbox spread -3pt{D.\nostretchspace Knuth wrote \TeX}

\end{document}

Note that \mbox{ } doesn't give a good result in the third line.