# Notations for integer in thesis

I am creating a list of notations for my thesis and I have difficulties trying to avoid overlapping notations. The main problem comes from indexes notations, for example:

• e_{i}, e_{j} with i,j = 1,2,3 when j is already the current density
• d_{lambda,mu} where lambda is already the wavelength

Can I leave these overlaps or not? Would there be a way to mark them as integers without over-complicatiing the notations? Should I include these integers in the table of notations?

EDIT

The document Quantities, Units and Symbols in Physical Chemistry from the IUPAC seems to write the notations with the indexes included without describing the indexes themselves (see page 57, resistivity and conductivity tensors).

• Have you looked at some standard advanced level physics texts to see how this is handled? – Dave L Renfro May 9 at 14:58
• I just looked several physics texts and most of them do not have a table of notations. One of them lists "Symbols with the same meaning in all chapters (unless the text makes clear an alternative meaning)" but there are no indexes in the list. – JuCa May 9 at 15:27
• If you use LaTeX, you should use macros which will permit you to play around with index notation. In physics, you can distinguish a j as index from a j as vectorial quantity by boldfacing or choosing some other font. – Captain Emacs May 9 at 15:44
• @CaptainEmacs The bolfacing for vectors is already done. I started with more than 250 notations, that is where the overlaps come from... The main question is whether or not indexes are a notation of their own. – JuCa May 9 at 15:48
• Unfortunately, not in physics. In math, every theorem/example/definition have their own "variable declaration", not so in physics. You can add an explanation that indices are treated separately - but there is a reason why Misner et al.'s famous Gravitation book uses a larger number (7?) of fonts. – Captain Emacs May 9 at 15:52

It is okay to reuse or “recycle” symbols - I sometimes joke that this is actually good practice since it is “environmentally friendly” and saves mental overhead. However, you must make sure that you do not use the same symbol to denote two different quantities within the same proof or calculation. That is a mistake and invites potential confusion or misunderstanding, even if in some cases the reader can perform disambiguation of the symbol based on context and figure out the correct interpretation.

A way to think about this is that each notation has a scope: it is created, used, and then discarded, often within the space of a single proof or even a couple of paragraphs. Some notations are local and live for a short time; others are global and retain the same meaning throughout the paper or thesis. Overlapping notations are fine if the scopes of the notations do not overlap. This is analogous to the use of variable names in a computer program. (Or to use a physics metaphor, notations can overlap in alphabet space, but not in spacetime - their world lines should not intersect...)

Finally, a list of notations should only contain notations that exist for a significant length of time (say for a whole chapter of the thesis), not “temporary” or ad hoc notations that are used in a short argument. That’s what matters, not whether the quantity represented by the notation is integer-valued. The main consideration is whether the notation is used long enough that a reader might encounter it far from where it is defined and have difficulty figuring out its definition.

It is also a good idea for the notation table to include columns to specify the page number where each notation is defined and which chapters or sections it is used for, to make lookup easier.

• +1 for overall good advice, and the last paragraph especially. Although I do not like recycled notations in physics books, sometimes it's the best compromise between writer's and reader's efforts. – Captain Emacs May 9 at 15:55
• In physics and engineering it's generally better to avoid reusing symbols as much as possible, to avoid confusion and reduce the reading burden. It's true, though, that sometimes that is unavoidable for lack of symbols. – Massimo Ortolano May 9 at 15:59
• @CaptainEmacs thanks, but to clarify, this isn’t about a compromise between the writer’s and reader’s effort. This is about not distracting readers with weird symbols like \Xi to denote a coordinate index just because of some stubborn insistence that i or j can only be used once throughout the thesis. It’s common sense that symbols can be recycled (except for important ones you want to keep with a fixed meaning throughout the document) at benefit to the reader and no extra effort to the writer. – Dan Romik May 9 at 16:47