> For maps it is important for people to know if their map is
> in e/Å^3 or sigma/Å^3. Both maps are commonly encountered in
> this field and both are called electron density maps. I could
> put a note on my home page stating that whenever I talk about
> a map I give numbers in e/Å^3 but it is more convenient for the
> reader if I just put the convention next to the number.
The problem obviously arises here because of the ambiguity of using the same
name ('electron density') to define two different quantities simultaneously.
You'll recall I pointed out that "Problems with units often stem from an
ambiguous definition"! Let's suppose you were writing equations involving both
of these quantities, and let's say 'electron density' = 'rho'. Then you might
write in a computer program the perfectly valid statement:
rho = rho/sigma
where the 'rho' on each side means different things. However this is certainly
not valid as an algebraic statement as it stands (where sigma may take any
value). Note that it is not the usual practice to carry the units with the
variables in the equations in the way you suggest in order to allow you to
distinguish them (it would make the equations pretty unreadable!), so the units
are actually irrelevant are far as equations are concerned. So you would have
to write something like:
rho' = rho/sigma
then the ambiguity is resolved. Moreover you would now need to define rho and
rho' in a way that the reader would be able to distinguish them, for example
you might say "rho = electron density = number of electrons/Angstroem^3" and
"rho' = electron density Z-score = rho/sigma(rho)". So now you have not only
been forced to distinguish the variable names, you also have had to distinguish
them in their definitions, hence it should no longer be necessary to
distinguish them by labelling their units.
Now of course labelling things in a computer output in order to distinguish
things that might be confused is quite a different issue from distinguishing
things in equations, for one thing you're free to write anything you want in
your own program, but equations have to obey the rules of algebra. I don't
know what was the context that gave rise to the original question but I think
it's quite likely to have been the equation f = f0 + f' + if", in which case
one needs to be careful to avoid ambiguous definitions.
Cheers
-- Ian
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