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Recently I had my paper reviewed for potential publishing. With no big surprise I need to make some adjustments to my paper. One of the criticisms was that my work lacks "textbook explanations" (e.g. what is BETA, alpha).

To further clarify, this is the first ever work I ever plan to get published (academic context is finance). But I am surprised I should be required to explain basic concepts.

Would you have any recommendations as to what is the best way to incorporate these explanations in a work (e.g. footnotes) and what should be explained (of this really basic stuff/how to identify it) and what not?

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    a VERY concise resume of basic concepts is generally present before going further on. – Blue_Elephant Jun 6 '16 at 9:01
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    First of all, you should define all the symbols that you use. – Massimo Ortolano Jun 6 '16 at 9:03
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    What is beta? Could be anything. It is a good practice to give the reader at least a hook at which they can read up things in detail in the literature. – Captain Emacs Jun 6 '16 at 9:14
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    Ironically, when I read "alpha" and "beta", I though A/B testing, not symbolic notation. – Laurel Jun 6 '16 at 18:48
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    It's easy for students who spend a long time focusing on a single problem to think that something is obvious to you is obvious to everyone else. It's often not to someone who doesn't work on this things. See academia.stackexchange.com/a/66329/19607 for some thoughts along these lines, though your situation is different. – Kimball Jun 6 '16 at 19:51
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Symbolic notation must always be defined in a paper. The reason is that there are not that many symbols and lots of things they can be used to represent. Thus, even if every class you ever took used v to represent voltage, other people are using it to represent velocity, vertices, values, etc. See, for example, this far-from-complete Wikipedia list of how Greek letters are used.

At a minimum, each symbol should be defined the first time that it is used. It is also helpful to your readers to provide a table of important symbols and to refresh their memory on definitions of critical symbols from time to time. This can often be done quite simply and efficiently within the sentence where the symbol is used, e.g.:

we consider a particle traveling at velocity v through a magnetic field of strength B(x), where x is the position of the particle in space.

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    This is the question, but it is important to really stretch: That wikipedia article is far-from-complete, because it has about 5% of possible uses of the letter, not because it lack a couple! – Ander Biguri Jun 6 '16 at 12:44
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    Uh... no. Yes, people may use $V$ to represent voltage in physics or a vertex set in graph theory, but if a paper says "let $G=(V, E)$ denote a graph", then anyone with passing familiarity with graph theory knows what $V$ is, especially if this appears in The Journal of Graph Obfuscation. Same if a statistical paper uses $\beta$ or $p$. I shudder to think how papers would read that "always" defined their notation. – Stephan Kolassa Jun 6 '16 at 12:52
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    @StephanKolassa Actually, I would consider "let $G=(V, E)$ denote a graph" to be a reasonable definition, though "let $G=(V, E)$ denote a graph of vertices $V$ and edges $E$" is better and little less compact. – jakebeal Jun 6 '16 at 12:56
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    @StephanKolassa You're talking about the values from statistical tests, right? Those aren't quite as monolithic as you seem to think. There are multiple ways of computing those statistics, each with its different applications and cautions: $t$ from a one-sample t-test is not necessarily the same as $t$ from a two-sample t-test. Thus, I still think those should be explicitly stated, e.g., "For this experiment, a one-sample t-test finds $t = 0.4$" and not just "For this experiment $t = 0.4$." Doing otherwise invites sloppiness and error. – jakebeal Jun 6 '16 at 13:23
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    Probably also worth adding that conventional use of symbols can change with time. Will someone reading your article in 20 years have the same conventions, especially if you're working with theories that are still being developed and standardized? – jpmc26 Jun 7 '16 at 1:04
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A rule of thumb is: The article (including its references) should be self contained. Of course "self contained" is pretty hard to pin down exactly but as an example: If you use some β, then either define it or (at minimal) write something like "we follow the notation of X" with some standard book X. Also note that this usually does not cost you too much space because either something is very simple to define (e.g. writing the "c is the speed of light" is enough) or there is a good reference.

Another rule is that if the notion is uniquely defined in your field and taught to every undergraduate than you don't need to define it. From above: c can be something different from the speed of light, even within Physics, but a continuous function does always mean the same thing (once the topologies are fixed which should be from the context) as also "electric field" always means the same.

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  • notion that was taught to every undergraduate 100 years ago may not be in use anymore, likewise we don't know what will be in use in a 100 years time. – Ian Jun 6 '16 at 14:30
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    @Ian True. But I am not sure if one should plan with a time scale of 100 years in mind when writing scientific texts. If you look at 100 year old papers today you realize that you can read them with some effort (depending a lot on the specific paper) but in general you need quite some historic background to go 100 years back in science. I am pretty sure, that this will be the same in 100 years from now. – Dirk Jun 6 '16 at 15:05
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What is too obvious to explain in a scientific paper?

It all depends on your audience.

In The Structure of Scientific Revolutions, p. 20, Kuhn laments how scientists pick up where textbooks leave off and specialize their writing into "brief articles addressed only to professional colleagues," those "whose knowledge of a shared paradigm can be assumed, and who prove to be the only ones able to read the papers addressed to them."

In general, it is better to broaden one's audience by simple explanations and definitions that do not individually require significant expansion of the paper length (including by citation to longer explanations that would significantly lengthen things), than to limit oneself to a smaller audience whose actual knowledge matches your assumptions.

Here, you're getting clear feedback from the editor/reviewers about things that need to be clarified, so definitely do those things. The editor knows your audience better than you do, and the request is quite reasonable (even much more light than requests for changes often are).

Symbols should almost always be defined, and acronyms should be spelled out on first use, even if well known. This can be done within a sentence (e.g. ", where c is the speed of light in a vacuum") or parenthetical (e.g. "the New York Stock Exchange (NYSE)").

For other terms with specific meanings, it is helpful to define those specific meanings, to make it clear in your paper and help readers distinguish your specific meaning from all the other misuses of the term they've heard. Where specific definitions vary (and they do, a lot more often than you'd expect), it's helpful to cite a source for that definition just as you'd cite a source for any other fact you've included from the literature.

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The other answers here address some general principles in useful ways. My thought in answer to your question is "it depends". You need to think about your prospective audience and what you expect your typical (perhaps casual) reader to know.

It might help to look at other papers in the journal you're submitting to, to see what authors do there. Match their style and level of exposition.

Finally, thank your editor and reviewers for their help, and do what they ask.

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