Why are \showboxbreadth and \showboxdepth set to 2^{30}-1 in \loggingall?

Question

The plain TeX format defines

\def\loggingall{\tracingcommands\tw@\tracingstats\tw@
  \tracingpages\@ne\tracingoutput\@ne\tracinglostchars\@ne
  \tracingmacros\tw@\tracingparagraphs\@ne\tracingrestores\@ne
  \showboxbreadth\maxdimen\showboxdepth\maxdimen}

This sets \showboxbreadth and \showboxdepth to \maxdimen, which is effectively 2³⁰−1 = 1,073,741,823.

But \showboxbreadth and \showboxdepth are “integer parameters”, so aren’t they supposed to be set to 2³¹−1 = 2,147,483,647? Consider, say, an hbox containing 2³⁰−1 pairs of \kern1sp\kern-1sp (2³¹−2 kern items).

Answer 1

Arguably, but latex follows plain tex here, \maxdimen is just standing for "something big" If you really have a box with more than 2^30 nodes the chance that you want to do \showbox output is... slim, so it makes little difference in practice, and back then saved using up tokens for another "big number".