Making mathmode obey spaces

Question

I know this is kind of blasphemic thing to ask, but is there a way to make mathmode obey spaces? Preferably in Plain with XeTeX.

Answer 1

Sure:

{\catcode`\ =\active\global\let =\ }
\everymath{\catcode`\ =\active}

(The space has mathcode "8000, which is supposed to make it active in math mode. But this is not enough for some reason. You do need the \everymath.)

Answer 2

One can use the fact that the space has mathcode "8000, but TeX checks the mathcode only for category 11 or 12 characters:

\def\spacemath{\catcode`\ =12
  \begingroup\lccode`~=` \lowercase{\endgroup\def~}{\ }}

$\spacemath{}a b$

If one wants this in all math, then

\everymath\expandafter{\the\everymath\spacemath}
\everydisplay\expandafter{\the\everydisplay\spacemath}

Answer 3

I actually managed to somehow accidentally make it work by:

\catcode`\ =13 \def {\space}

after which

$$\def\space{ } meow woof$$ % the thing between the braces is U+A0

much to my surprise, worked.