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I am wondering if some peer reviewers may nitpick about the choice of variables in a math-heavy paper, namely whether they follow alphabetical order throughout the succession of the presentation of concepts. For example, variable N may be defined, variable K may be subsequently defined in a way that depends on N, and finally variable A may represent a final result based on an operation. Could a very particular peer reviewer suggest a revision or rejection simply based on the naming of variables in this way? has anyone ever experienced this or similar?

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    I've never seen it done. The main complains are usually related to consistency in the styling of variables. Dec 27 '20 at 4:15
  • Near duplicate of academia.stackexchange.com/questions/148027/… Dec 27 '20 at 10:51
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    @AnonymousPhysicist that question ("what's involved in reviewing an article") seems very remotely connected to this one. Did you cut-and-paste the wrong link ... ? Or am I missing your reasoning?
    – Ben Bolker
    Dec 27 '20 at 18:36
  • @BenBolker The other question is "How do you peer review?" This question is "How do you peer review the alphtabetical order of variables?" The answers to the other question say the answer to this question is "Don't." Dec 28 '20 at 0:18
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    @AnonymousPhysicist: I'm not convinced. The answers to the other question don't even mention "notation" anywhere. (Yes, you could answer that question with some stuff about what to pay attention to [or not] as far as notation in mathematical papers, but no-one did (e.g. is notation coherent? If there's a lot of notation, is there a table summarizing it? I sometimes comment as an editor about whether displayed equations should be inline or vice versa, although that belongs at most in the "minor/stylistic comments" section of a review)
    – Ben Bolker
    Dec 28 '20 at 0:55
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Let a be the number of math-heavy papers I have read that use an alphabetical order to introduce all their variables. Let b be the total number of math-heavy papers I have read. Let c = b - a be the number of math-heavy papers I have read that did not use said ordering. Then c = b.

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    Hmmm, having trouble with the math here. Either you didn't read your own post (a math heavy paper) or you have a counterexample. ;-)
    – Buffy
    Dec 27 '20 at 12:55
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    Not sure I'd call those three lines a math-heavy paper! You think I can get away with adding it to my publication list? ;-)
    – Ben
    Dec 27 '20 at 13:26
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    Works for me. But I'm so old I can't do simple arithmetic anymore. So, best check with your department head.
    – Buffy
    Dec 27 '20 at 13:34
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    My a is probably zero just like yours, but I"m not sure. If I read a paper in which the variables were introduced in alphabetical order, I might not have noticed that peculiarity. Dec 27 '20 at 19:59
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    Good one! Seems like going with an alphabetical ordering instead of trying to use the most memorable letters available (initial letters where applicable) requires significant backtracking on the reader's side, even when only 3 variables are involved in 3 lines of text.
    – natiiix
    Dec 28 '20 at 0:39
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Such rejection is very unlikely to happen and [if happens] would certainly be due to field-specific established conventions and not particularly because of the [non]alphabetic order.

To avoid that, try using the common variable conventions for the field. For example: i vs j for complex unity (square root of -1), or use i, j, k primarily for indices in programming-related fields, or use calligraphic R and C for the field of real and complex numbers, respectively, etc. Reading well-received papers from your field and asking for feedback from your advisor and\or more mature co-authors would allow learning about such conventions.

With all that said, a common reviewer's argument for revision\rejection that "the paper uses unnecessarily unusual, unjustified, uncommon, and cumbersome notation" is a totally valid one. Again, the case of a simply non-alphabetical order does not apply here. Therefore, this potential review response is not applicable to the situation as it is described in the question.

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  • This is unclear. Are you claiming there is a field where the answer is "yes?" Dec 27 '20 at 10:47
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    @AnonymousPhysicist, no. I don't believe I ever wrote such a thing. Which part of the answer hinted at that in your opinion? Dec 27 '20 at 16:51
  • I'm confused. Where does your quote here ("the paper uses [bad] notation") come from? I don't see it in the question, nor do I see any indication that the question has been edited. Are you suggesting this as an argument that a reviewer might make?
    – Ben Bolker
    Dec 27 '20 at 18:39
  • @BenBolker added a bit of clarification on that matter. Dec 27 '20 at 18:52
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    @AnonymousPhysicist I am sorry to hear that. I tried my best. Dec 28 '20 at 2:07
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It is certainly not that a reviewer will suggest a revision based on the non-alphabetical order of introduced variables. However, if you have a long list of dependencies between your variables and no particular naming scheme that allows the reader to see that there are no vicious cycles in the definitions, it may become extremely hard to check the proof and the reviewer may indicate it together with a suggestion to introduce some explicit logic in naming that would guarantee that we do not define $A$ in terms of $B$, $B$ in terms of $C$,..., $Z$ in terms of $A$.

There is also another way to convince the reader that everything is OK even if you have piled up the inequalities between the randomly named parameters in some crazy order in various technical lemmas. It is to make an explicit assignment in the end (say, as functions of a single large parameter $L$: $A=L^{10}$, $B=L^{-3}\log^2L$, etc.) and leave it to the reader to check that all the conditions are met for this choice (it should be a trivial exercise; otherwise you need to do it yourself). I personally prefer it whenever possible. Otherwise I try to introduce some naming convention or just list the order of dependencies in the beginning explicitly so that the reader can easily refer to it any time.

The general principle is that "everything that simplifies the work and spares the time of the reader is good even if it increases the time and complicates the work of the author" (because the hope is that your paper will be read by more than one person; otherwise what's the point of going public with it?).

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Let a force a act on a particle of mass b, giving rise to an acceleration c. These are related by Newton's second law, a = bc. By special relativity, the particle's rest mass is associated with an energy d, a relation involving the speed of light e. This relation is given by Einstein's famous formula d = be2. Etc.

Accept or reject?

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