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First off, there's nothing wrong with including information that's not
primarily "meaningful to the user," as long as it doesn't get in the user's
way. You include information that is meaningful primarily to manufacturing,
for example, like the book's part number and probably a barcode, so why not
something like an unobtrusive figure code that's useful to the writing
group?
I'd keep the number, make it smaller (6 point), and put it into a font
different from the labels in the figure. Here's why.
My previous company did this, and it made life simpler for both the writers
and the artists. If we wanted a figure that was a lot like a previous one,
all we had to do was mark up a copy of the original the way we wanted it to
be. The artists just pulled the original from their files, made the changes,
assigned a new number, and made the .eps file available to us. This meant
they didn't have to do a new drawing, and we got quicker turnaround.
The company I'm now with doesn't do that. When I want a figure, I have to
print a copy and do a markup, then send it to the artists. They have to
either search through all their art files to find the original or do a whole
new drawing.
Within the last month, we've finally convinced them to add figure numbers
and set up a database so that they can more readily reuse/adapt artwork. The
big hangup for them was what numbers to assign. The writers didn't care, but
the administrators wanted a great long number that included a multi-digit
part/revision number. They finally hired a new editor who simply said,
"Look, do it this way." And we all lived happily ever after... at least for
the last few weeks.