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In scientific writing, we are often in a situation where we need to think about whether we should write down the full sentence that defines a concept, or we can be more concise without raising any ambiguity. For example,

"There are two broad approaches to problem X. The first is ...". Here, ...describes and assesses this approach, which may take 20 words. Then I start describing and assessing the 2nd approach. I can be more concise and say "The second approach is ~~~", or the opposite, "The second approach to problem X is ~~~".

If I want to be more concise, ... should not be too long, otherwise readers may lose track and need to recall what "approach" refers to.

What's the recommended length of ... if I want to be more concise?

Is there a rule of thumb for dealing with such a dilemma?

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    Frame challenge, "In scientific writing, we are often in a situation where we need to think about whether we should write down the full sentence that defines a concept, or we can be more concise without raising any ambiguity" followed by "... should not be too long, otherwise readers may lose track...?" In scientific writing, who is the reader? Surely either, scientists, or, general readers with an interest in science. Surely both of these will read through a long sentence or paragraph before (worst case!) giving up? So - you should be clear at expense of length? ... Feb 20 at 21:59
  • ... If your reader is likely to give up on a single sentence or paragraph that is too long, it suggests they are very busy, or very unavailable, and really you need to find another strategy to get their attention, since "short first sentence/paragraph" might not cut it. Feb 20 at 22:00
  • Isn't the rule of thumb to seek clarity, not 'word distance'? Did you never watch The Dead Poets' Society? Why would it be hard to rephrase the Question to avoid any dilemma? Why would you not first write a shortened version, then attach a longer explanation, leaving it up to your audience how much to read? Mar 2 at 22:43

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I think the best option here is to name the two approaches. For example:

There are two ways problem "X" has been solved in the past. For the purpose of comparison we will call the first the "gradient descent approach", and the second the "genetic search approach."

The gradient descent approach consists of [fairly long text].

The genetic search approach, on the other hand, takes more time but is gradient free, thus making it more generally applicable. This consists of [fairly long text].

The broader applicability of the genetic search approach makes it the most commonly used method, because it is widely applicable; but obviously it can take much more computing resources and time, up to 20 times as long, to converge on a solution.

This paper proposes a hybrid option we will call the "Implied Gradient Genetic Search", that recovers much of the efficiency of the gradient descent approach.

[source: Amadeus making stuff up.]

Something like that.

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There is no rule of thumb, but it is unlikely that your readers will forget what problem X is because:

  • The whole preceding passage (i.e. "The first is...") has put problem X in relation to the first approach.

    To spell this out clearly: When you describe your first approach to problem X you will constantly repeat the name of problem X, otherwise you aren't properly describing how your solution relates to problem X

    Example: If you are writing about how to open a door, and your first approach is to use a key, your description of what to do with a key will contain the words door and open, otherwise a reader who has never used a key will not understand that the lock is part of the door and turning the key in the lock will open the door. When you get to your second approach (breaking in with a ram), your readers will then still be aware that everything they read is about how to open doors.

  • Problem X is the overarching topic of this section or chapter of your writing or even the topic of your whole paper. You will have written some introductory remarks about problem X and probably this part of your writing or the whole paper will have problem X in its title. Learning about problem X will be the reason why your readers read (that part of) your writing, and it is unlikely they will forget why they are reading it.

    For example, your section about how to open doors with have the heading "How to Open Doors" and the beginning of that section will explain what doors are and where we may encounter them (to explain why knowing how to open them is of interest to us at all).

That said, I would nevertheless repeat the name of problem X every time that the sub-topic of a passage changes.

For example:

How to Open Doors [problem X is named in the heading]

Doors are a common part of everyday life. And many doors are closed, so we may need to open them. [Introduction: Why should your reader care about how to open doors?] ...

There are different kinds of doors, those that open by themselves – such as automatic doors – or are opened by someone else and those that need to be opened by the person that wants to pass through them. [Definition of problem X]

There are two main approaches to opening doors. The first is ...

The second approach to opening doors is ...

Other options include ringing the door bell or ignoring the door altogehter and entering through a window ... but ...

Opening doors is not only a technical problems but has legal implications as well. ...

As you see, I am repeating problem X (or a significant part of problem X) in different ways in every section of my writing. The reason for this is twofold:

  • it adds clarity

    Scientific writing is all about being clear. Spelling things out adds clarity and helps an inattentive or cursory reader understand what they are reading more quickly.

  • it makes a passage comprehensible even if you haven't read the preceding passages

    Much of scientific writing is not read but scanned quickly, because most scientists have to process a large volume of papers every day, so make it as easy as possible for them to orient themselves and to always understand what they are reading, no matter where in a text they happen to look.

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