# Using a list to explain symbols used in an equation?

In papers, the symbols explained in an equation are usually explained like this:

δ(t) = tan⁻¹⁡〖ke(t) / vf(t)〗,
where δ(t) is the steering angle, e(t) is the closest point between the path and the vehicle, v(t) is the vehicle’s velocity and k is the gain parameter.

By contrast, textbooks often explain mathematical notation in a list-like format, e.g., like this:

δ(t) = tan⁻¹⁡〖ke(t) / vf(t)〗,
where

• δ(t) = steering angle
• e(t) = closest point between the path and the vehicle
• v(t) = vehicle’s velocity
• k     = gain parameter

I consider this more legible, and I was thinking if I could use this in my scientific papers. Is there any reason not to do this?

• You may have stumbled on the few textbooks that use the list form, or maybe just those of a particular field. I have close to 1000 textbooks on my personal bookshelf, from different disciplines, and I can't recall a single one using the list form. Jun 21, 2020 at 13:16
• Here’s how the real pros do it: tex.stackexchange.com/questions/95838/… Jun 21, 2020 at 14:30
• To me, one difference is whether one wants to emphasize the notation or not. I could imagine a context in which the learned reader would already be guessing the identities of the symbols, in which case the first one might be better as a concise reality check; the second one might be better if all of these symbols are being introduced for the first time. Jun 22, 2020 at 4:04

Unless you get contrary feedback from a reviewer (or advisor for a thesis), I think the format you use is up to you. Your suggestion adds readability and understandability and only loses compactness. To me it seems a positive tradeoff. But an editor might have specific needs.

But write as you think best, and yield to reviewers as necessary.

• I like this answer calling it a trade-off between compactness and readability. Jun 22, 2020 at 4:10

In some journals there are page limits, and so your first example becomes more relevant. But I agree your second example is more readable.

• Regardless of whether there are formal page limits an editor may wish to minimise the number of pages used by one article. Jun 21, 2020 at 13:56
• A lot of journals charge authors a publishing fee. So there is an added incentive for the author to keep the page count as low as possible.
– MaxW
Jun 21, 2020 at 22:26
• Do page limits make sense now that so much is being consumed digitally? Does a sizable proportion of researchers actually still receive and read physical journal copies? Jun 22, 2020 at 16:46
• @MaxW Do those fees go by page count? Physical Review, e.g., charges by words (above a certain limit), which seems to make more sense. Jun 23, 2020 at 12:40
• @JHare ... though of course, often Physical Review Letter papers are just crammed onto four pages, which can make them considerably harder to read than, say, 6-page papers. (Note also that it used to be a page limit.) Jun 23, 2020 at 19:05

Good question! This is perhaps a matter of taste, and I don't know if there's any science about what's supposed to be more readable, but I prefer the former method. I feel it flows better when I read. The same goes with other kinds of lists, such as lists of assumptions.

A few times I have tried to make a bullet point list, only to find that I can control the flow better when I remove the bullets. I can customize the punctuation, and even interject more details on some points without making the list look typographically unbalanced. Here's an example from one of my own publications:

The expression is valid for a plasma that is 1) collisionless, 2) non-drifting Maxwellian, and 3) nonmagnetized. These assumptions are justified in [1] and will not be further investigated here. It is further required that 4) the ion collected current is much smaller than the electron collected current. This is true for typical ionospheric conditions with ions drifting at approximately 7500 m/s, 5) that the object is not affected by other, nearby objects, and 6) eV/kT > 0 or, for cylindrical objects, eV/kT > 2. As for the probe geometry, it is assumed that 7) the probe is very thin (r << λ_D), and for cylindrical probe 8) very long (l >> λ_D). The m-NLPs on CubeSats typically have a radius of 0.255 mm [2], such that r/λ_D < 0.2 for the Debye lengths considered. According to numerical simulations by Laframboise [7], finite-radius effects are not significant even for r/λ_D = 1, so this assumption is valid. The assumptions eV/kT > 2 and l >> λ_D will be discussed further in what follows. The vicinity of other objects is only briefly considered.

Often I avoid lists all together for the sake of flow, but in this case I wanted the assumptions to be clearly and explicitly listed. Having a bullet point list and discussing the items afterwards would only have disrupted my flow. Others may prefer otherwise, of course.

I suspect some would think lesser of a bullet point list, perhaps in particular since it is unusual, and that this may detract from your referee's impression of the paper. For my own part, I would perhaps suggest to change it, but I would not let it decide whether the paper gets accepted or not.

• The downside of the "flow" is that it is much harder to find those definitions if you don't read a paper sequentially. Jun 23, 2020 at 12:41
• I think, it it really a matter of taste. E.g I cannot follow in-line list (as your in example) after 2-3 points, especially if they are sentences themselves.
– aqua
Jun 23, 2020 at 14:35
• @user151413: That is certainly true. If you need it to stand out for someone skimming the paper, whether for first read or not, that may be a reason for using a bullet point list. Jun 24, 2020 at 17:49
• @aqua: Yes, I suppose it is a matter of taste. Jun 24, 2020 at 17:51

My feeling is that the space that something takes on the page should be positively related to its importance. Often equations are given using symbols that are fairly standard in the subfield. Their definitions might be included for people outside the subfield, but for most readers, these definitions will be unnecessary. So in some cases, it would be drawing a lot of the reader's attention to something that is sort of a footnote.

You claim that the longer format is more legible. I do not think it is necessarily the case, let me explain. (Another reason not to use the longer format is to avoid having too many pages in the paper, but others wrote enough about this, I think, so I will disregard this aspect.)

As a general rule, when writing either a book or a paper, I believe you should try to make it as easy as possible for the reader to distinguish which parts he should pay more attention to (because they are especially important, difficult or nonstandard), and which he can more-or-less safely skim.

In your example, the itemized format puts very strong emphasis on the notation used for various parts of the formula. This might be a good idea especially when you are just introducing this notation, and the formula (and its parts) are heavily used later in the paper. Or maybe you want to make sure the reader remembers exactly the factors on which delta depends.

On the other hand, it may be that the meanings of the symbols are standard/established earlier in the paper and you are merely recalling them. Or maybe you are never going to use them again in the paper. Perhaps the formula is just a side remark. In these cases, the longer format will (unduly) draw the reader's focus to it, so you may prefer to avoid it. In other words, while indeed this makes the formula itself more legible, it may make the whole paper overall less readable.

Of course, in practice, what you write may not fall into either of these extremes, and in the end, what should and what should not be emphasised is up to the writer's/editor's judgement and taste.