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I'm currently writing a paper on analysing miRNA targeting in animals. It's principally a statistical analysis involving many graphs.

However, to explain the creation of one of the graphs, I've resorted to using set theory notation, as this, to me, seemed the most efficient way of explaining how the graph was produced.

However, this may potentially have some issues:

1) Will the use of terminology that is outside the theme of papers in this field detract from the description? Such that few people who read this paper will understand set theory and therefore many will not understand the mathematical notation? The description, I hasten to add, will be a tenth of the length when using set theory notation.

2) Evidently, concepts should always be written as clearly as possible, but where is the line formed between explaining concepts in words, as opposed to mathematical notation? Why would one choose one way over another?

3) Should you make assumption of the mathematical understanding of a person reading the paper?

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Is this within scope for this site ? maybe on Mathematics or even the new Mathematics Educators site ? –  Suresh Apr 21 at 0:31
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'concepts should always be written as clearly as possible', this is a decision you have to make. If it takes many paragraphs to explain in words your concept, vs 2 lines of math that is clear to anyone who understands your notation, i would go with the math –  user1938107 Apr 21 at 1:25
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@Suresh: This question is relevant across many academic disciplines, and is therefore very much on-topic. –  aeismail Apr 21 at 5:26
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@Federico: I don't think MO is the right place since the question is about writing a biology paper, not a math paper. Anyway, if you ask it on MO, the answer will surely be "Yes, use set theory notation. Why not? Everyone knows it." :-) –  Nate Eldredge Apr 21 at 12:58

3 Answers 3

up vote 16 down vote accepted

An author should always be careful when using mathematical notation that is "outside the theme of papers in this field," especially if the papers typically have little math notation. I have personally found that running into a cryptic (at first glance) equation makes me put the brakes on and engage some deeper thought to decipher what's trying to be said. Oftentimes, the notation is required, or at least useful, but when I end up thinking, "Couldn't they have just said 'such-and-such' in plain English'", I get a bit cranky.

Sometimes, though, you do need the space savings to stay within page limits, so if you really will shave off 90% of the space, and you need that space to fit in something else that is key to the paper, AND in your best judgement that the audience won't be derailed by the notation, you might be OK. Otherwise, because you have stated that you can describe it clearly in words, you should consider perhaps rewriting that description to be more concise and precise, rather than potentially obfuscating the details of your graph production.

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+1 for 'I get a bit cranky' (and for the content of your answer). –  xLeitix Apr 21 at 7:52

By and large, I would say avoid using non-standard presentation techniques in your paper. This includes using non-trivial mathematical notation in a field that generally does not use maths.

Consider that simply by choosing your way of presenting your techniques / results you (a) already lose most casual readers of your paper (i.e., those that don't have to study your paper for some reason, but were just interested in its content), and (b) presumably significantly increase the chance of your paper being falsely rejected by a reviewer who was inexperienced in the used notation, and hence misunderstood some details. Of course, this is not supposed to happen in an ideal world, but we don't necessarily live in such a world.

That being said, I should add that (especially for lower-ranked venues), the opposite of (b) may also happen - you may get a reviewer who does not fully understand your notation, but decides that it looks "sciency" enough and hence accepts the paper (even though, maybe, the content was actually weak). I have certainly seen paper submissions that tried to ride the train of camouflaging weak content with complex notation.

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+1 for "paper submissions that tried to ride the train of camouflaging weak content with complex notation" –  Alexandros Apr 21 at 16:32

So far, I'm missing the option of giving the 110% version of set notation plus explanation in plain English. That way, readers familiar with the set notation can skip the written explanation, and others can either skip the formula or learn what it means from your explanation.

(As you think whether you should give the long explanation, I assume that there are no particular length restrictions.)

I may add that I (chemist/chemometrician) was actually taught that a formula should preferrably be accompanied by a plain text explanation of the idea behind this formula.

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Is that not overkill, saying the same thing twice in two different ways? –  Mark Ramotowski Apr 21 at 13:54
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@MarkRamotowski: IMHO no, at least not unless the topic of the paper (and journal) is not deep inside stats but rather explaining the statistical methods used for a particular application problem. A supervisor once told me: Part of the art of writing good scientific papers is making it easy for the reader to understand what is going on. That would be in favor of the plain English version for an application paper. I'd like to add: I think it equally important to report what exactly was calculated. That is often more easily done by giving the formula (text explanation often leaves ambiguity). –  cbeleites Apr 21 at 15:24
    
@cbeleites well said, both the answer and the comment. –  Faheem Mitha Apr 21 at 15:52
    
How about presenting the Set Theory notation after "This is best explained with Set Theory. If you are not comfortable with Set Theory, an alternate explanation is available in Appendix C." Do you have room to do it that way? The appendix entry could be prefaced with "Not everyone in this field is familiar, or comfortable with, Set Theory notation, so I will explain it here in prose:" –  Phil Perry Apr 21 at 17:22
    
@PhilPerry: Sure, why not. But if going for an appendix (or supplementary) I'd put the mathematical details there, not the generally expressed explanation: the appendix is for more specialized stuff, the main paper for the general which I'd here suspect to be the explanation. –  cbeleites Apr 21 at 20:58

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