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Often when distinguishing one variable from another we use different characters or if using the same character different subscripts. For instance we might use x for one variable, and y for another, or we might use x_1 for one variable and x_2 for another. I was wondering if in a paper I could get away with using the same character but with different colors when referring to different variables. So for instance if I was referring to two different objects, then I might refer to variables related to one object using the color red and variables related to the other object using the color blue, and variables related to both objects using the color magenta. So for example the schrodinger equation for a system of particles only interacting with each other would be written in the form

enter image description here

Would writing equations with variables denoted with color make a paper less likely to get published assuming that I explained what the colors meant?

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  • 3
    For accessibility purposes (USA) one must use some other mechanism of distinguishing such as font, style, etc. See answers also. Oct 5 at 13:57
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    So you mean the red $1/m$ is different from the green $1/m$? If I saw this in print, I doubt it would occur to me that the sum of second partial derivatives with respect to the $x,y,z$ of one color is a different thing from the sum of second partial derivatives with respect to the $x,y,z$ of another color. Oct 5 at 18:47
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    Why not use $\green{x_1}$ and $\red{x_2}$? Meaning use both subscripts and color in agreement with each other? Then the color adds to the paper and makes it easier to read, but those with the problems below can still read it.
    – nickalh
    Oct 5 at 21:09
  • 1
    BTW I did something similar when I was a graduate student. I found that using colored pencils could help me understand some difficult equations better. But I never attempted to publish my lecture notes.
    – emory
    Oct 6 at 0:11

12 Answers 12

168

Do not do this. Those of us who prefer to read on paper and have black and white printers will be extremely confused.

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    Also reduces accessibility, e.g. for the colour blind.
    – GoodDeeds
    Oct 3 at 23:33
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    It would also be a pain for a reader with a colour printer or working on screen, who wanted to make notes
    – Chris H
    Oct 4 at 11:28
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    Also I've seen people reading papers on e-ink screens (admittedly back when there was a large-screen kindle)
    – Chris H
    Oct 4 at 11:30
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    Or if you are taking notes/working on this, and you don't have a multi-colored pen on hand with the same colors the paper uses.
    – Kimball
    Oct 4 at 12:13
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    @Evorlor They magically turn what is on you screen into a physical object. Like a replicator.
    – DKNguyen
    Oct 4 at 18:51
64

(Personal opinions, so a fully anecdotal answer, but too long for a comment.)

My immediate thought when seeing that screenshot was "wait, aren't those red and green ones the same variable?" (Obviously, I don't know the Schrödinger equations.)

I automatically expected that of course you meant to use color only for emphasis, while still keeping the "traditional" subscripts or whatever to actually distinguish them. I could see some uses in using color as a helper, while keeping the same equation readable if, no, when it gets turned black-and-white. But color as the only distinguishing feature seems unconventional enough to be surprising.

Even if colors are used only for emphasis, the choice of them can be somewhat problematic. My immediate second thought was about the blue-on-black being almost completely unreadable. Someone with bad eyesight, or color blindness, or such might have different problems. Switching the background from black to white might also require reconsidering the colors.

5
  • exactly. problem isn't for just non-colourblind or black and white prints. even for the regular reading with colour it is confusing like w/c variable is what.
    – BCLC
    Oct 4 at 11:06
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    And of course if you prefer a black background, as I do, the dark blue variables which I assume are in the third parenthesized group are effectively invisible.
    – jamesqf
    Oct 4 at 15:57
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    I did this in a StackExchange answer, once. But I also made sure to include an explanation of the issue in the surrounding text, and to phrase that explanation in such a way that the variables could be identified without needing to see the colors. I also called out the fact that the variable clash was confusing, and renamed the (bound) variable on the next line. IMHO this is OK, but even so I was a little concerned that the color might not be fully accessible to everyone.
    – Kevin
    Oct 4 at 22:57
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    FWIW I do know the Schrödinger equation fairly well and I had the same thought as you did, ilkkachu: the same variable in different colors still looks like the same variable.
    – David Z
    Oct 5 at 0:00
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    FWIW, as I understand the law where I am, it's fine to use colour as an aid, as long as it's not the only way to distinguish things; there must always be some other way that colour-blind folks can use. Now, I doubt any law applies in this case, but I think it's still a good principle — and this answer explains some of the reasons.
    – gidds
    Oct 5 at 18:30
35

The obvious problem, as noted in another answer, is monochrome (black) printers. Yes, you can get a color printer for very little money (not much more than the cost of the ink cartridges), monochrome printers are still far more common for those who need to print a moderate amount (hundreds to thousands of pages per month) because the cheap color printers tend to cost a lot per page (inkjet) and the expensive color printers (laser) have a high upfront cost.

But there are other problems as well:

  • Screen readers for the visually impaired. I'm amazed (my evil twin has told me all about it) how many people rely on screen readers to read email, web pages and everything else on a computer. The colors would either be lost altogether or would add a lot of extra time to the reading ("white a blue x squared").
  • Copying. Even if the journal is published in color, someone might make a photocopy (yes, an actual photocopy, not a print from a PDF!) and that will very often be only (or default) in black and white.
  • Readability. In addition to true color blindness, color text can be harder to read on paper than black text simply because it has lower contrast.
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    Re color printers for "not much more than the cost of the ink cartridges", it's often less. And for many of us, the cartridges dry up long before they run out of ink.
    – jamesqf
    Oct 4 at 15:55
10

If you are trying to publish in a journal which has printed issues, you will (at best) eventually run into the problem that these (even ones which normally have no publication charge, which is pretty much all the ones in my field) typically impose a significant charge for every page which needs to appear in colour. Normally that might just be one page with a particular diagram, but in your case it sounds like it will be most of the pages, and there's no way for you to argue that colour printing isn't really necessary.

However, I very much doubt it will get to that stage, for the excellent reason Alexander Woo gives. I can't print in colour at work, and I doubt that's unusual. That means I wouldn't review your paper, since I always make notes on a printed copy when reviewing. And the editor might veto this idea even before trying to find reviewers, since readers will want to print.

8

Since your profile avatar mentions physics as an interest of you, I assume you either possess, or know someone with working knowledge of LaTeX. (If not yet, learnlatex.org is an entry, and tex.stackexchange worth a subscription.)

If so, you may consider underbraces, e.g.

enter image description here

which define the terms contributing to the global function in mind. In the paper/poster/presentation, you may focus on each of them on a one-by-one basis (minima/maxima/symmetry and other peculiarities). If the equation spans into a second column, you equally may split the equations over multiple lines, too.


The MWE of above was generated on latex2png.com (no affiliation, your TeX editor of choice likely equally offers a .tex to .png/.pdf conversion) with this snippet:

%
% syntax of an underbrace:  \underbrace{content to underbrace}_{underbrace label}
%
i\hbar \frac{\partial \Psi}{\partial t} = - \frac{\hbar^2}{2} \bigg(%
%
\underbrace{\frac{1}{m} \left( \frac{\partial^2 \Psi}{\partial x^2} + \frac{\partial^2 \Psi}{\partial x^2} + \frac{\partial^2 \Psi}{\partial x^2}\right)}_{\text{contribution a}} + %
%
\underbrace{\frac{1}{m} \left( \frac{\partial^2 \Psi}{\partial x^2} + \frac{\partial^2 \Psi}{\partial x^2} + \frac{\partial^2 \Psi}{\partial x^2}\right)}_{\text{contribution b}} + %
%
\underbrace{\frac{1}{m} \left( \frac{\partial^2 \Psi}{\partial x^2} + \frac{\partial^2 \Psi}{\partial x^2} + \frac{\partial^2 \Psi}{\partial x^2}\right)}_{\text{contribution c}}  %
%
\bigg)
%
%
+ V_1\Psi + V_2\Psi + V_3\Psi
5

You should not "get away with" anything while trying to publish your work. You comply with the rules/guidelines, and everyone will be happy. Less headache for everyone (you, the editor, the publisher, the readers) - there's already a lot of headache in publishing a paper.

"Could I use color...", yes you could, in theory, depending on the rules imposed by your publisher. But you probably shouldn't. The guidelines are there for their reasons. In some conferences or journals I sent papers too, they even highlighted that I couldn't/shouldn't use/rely on colors in my charts, let alone for the text content (like the variables). Instead of using red column, blue column, etc. which is discouraged, they suggest using texture patterns to fill the columns. The extensive use of (verbose) description using colors in the Figure captions or in the text body is also frowned upon: e.g. "we can see that the red line diverges significantly lower from the blue and green lines", instead use markers on chart lines, and the legends in the chart should be sufficient enough (a picture is worth a thousand words, no?).

4

If it helps to convey meaning and the advantages outweigh the disadvantages mentioned in the other answers, do it.

The answers make some good points about the usage in your example, but I honestly think that using color in equations is a good idea. Inventing new notation to declutter equations has certainly been done before. I think color could really help make complex equations easier to understand. The common use of color for syntax highlighting for programming languages supports this idea.

Honestly, I can't believe the most highly voted answer makes the argument that people won't be able to distinguish it if they print it out in black and white. Literature from recent years is full of images and graphs that are useless in black and white. For instance, I see a lot of biology papers that include fluorescence microscopy images like this:

Fluorescence microscopy image from Slater et al. (CC BY 1.0) https://doi.org/10.1371/journal.pmed.0040164

Fluorescence microscopy image from Slater et al. (CC BY 1.0) https://doi.org/10.1371/journal.pmed.0040164

You won't get much out of an image like that in monochrome. In the graph below from a recent PLOS ONE paper, color and shape both carry distinct meanings, so you won't be to get all of the information in the plot without color:

Plot with many colors and shapes from Zhao et al. (CC BY 4.0) https://doi.org/10.1371/journal.pcbi.1009345 Zhao et al. (CC BY 4.0) https://doi.org/10.1371/journal.pcbi.1009345

Let me address some criticisms in the other answers.

  1. Not accessible for people with colorblindness. You can avoid ambiguity for people with the most common types of colorblindness by choosing your colors carefully. This Nature Methods paper has some good suggestions. Some will argue that you should never represent information purely with color, but in the era of "big data" you really need all of the tools available to synthesize complex information into a plot. At the end of the day, we have to make some compromises. Most plots are not accessible to people with visual impairments, yet we still rely on them heavily for the enormous benefits they have in imparting information.

  2. The publisher won't let you. You could include the equation as a "figure" or "diagram" rather than a pure equation. If they don't let you do that, then find another journal.

  3. Extra charges for color pages. Many journals used to charge extra for color pages, but, increasingly, journals are all digital and these page charges have gone away. I haven't published in a journal with such charges for 10 years. Journals used to suggest using different patterns for different data rather than colors, but high contrast patterns can be distracting and difficult to distinguish.

As you've seen here, you are likely to experience some backlash when introducing a notational innovation; however, if it truly enhances understanding, others may pick it up and it may become more standard despite initial misgivings.

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  • 4
    Part of the difference here might be differences in working patterns between fields. If you're a biologist, you're probably in your lab when reading a paper, and that means a computer with a good screen is available. As a mathematician, if I'm seriously reading a paper (rather than just looking up a reference), I'm at a coffeeshop (without my laptop), if not on top of a mountain or at the beach. Oct 4 at 19:23
  • 1
    Or I may well be reading it on a tablet, at night, with the screen in dark mode. The examples here work (at least for me) because the background colors of the images are specified. But in the OP's example, the background is not specified, which makes the dark blue basically invisible on my black background. Those of you who prefer light backgrounds would have similar problems seeing my highly visible yellow text.
    – jamesqf
    Oct 5 at 3:34
  • 1
    With regard to those two examples that you chose, the first actually seems separate the images by showing the first of each set of colocalized structures on the left. Further, when the image is converted to grayscale, each set of structures has two distinct brightnesses. Although the image uses color, it does not seem to rely on it as much as you say. Also, note that it is a paper from 2006, so it should perhaps not necessarily be taken as guidance on best practices in the field today.
    – Obie 2.0
    Oct 5 at 16:10
  • 2
    As for the second image, I would have to say that while color certainly adds something to the image in terms of interpretation, it is far from ideal because it is an unreadable mess in grayscale (and undoubtedly for people with some types of color blindness). With the image already being quite busy in color, it would probably be advisable to consider an alternate means of presenting the data.
    – Obie 2.0
    Oct 5 at 16:15
  • 1
    "This is exactly my point. For better or for worse, much current literature includes figures that rely solely on color to convey information." That's the reason slavery lasted so long: it was the state-of-art of cotton picking! Which does not mean it was the most effective way, nor the best way. Especially reg. the second plot, it is quite sloppy visualization, to the point that same data are plotted separated in inserts B-C-D, making the different shapes of marker useless.
    – EarlGrey
    Oct 6 at 8:23
4

The problem with colors in an equation, is suppose I don't believe your calculations and want to re-derive the equations myself with pen and paper. Do I need now need to find a set of color pens to work with? and hope I don't pick up the wrong pen at the wrong time? Just make your readers lives easier and just use different symbols (or subscripts) for different variables. Or if the equation is still too complicated break it up into smaller chunks and use intermediate variables.

3

my opinion in 2 parts:

part1. bad since confusing even for non-colourblind.

besides having to read the thingy as like 'red-x', 'green-x', what's hard is reproducing the equation like when we write the equation in our notes we'll write $(red-x)^2$? (as mentioned in a comment above this is the same with those cases where multiple fonts like mathfrak, mathscr, mathcal are all used in the same thing)

part2. BUT i think a good idea for certain cases, but most probably just informal cases of explaining things directly to students or other colleagues, where you have show certain details in proofs

enter image description here

BUT as much as possible no using different colours for the same letter... here i had to use different colours for the same letter y to show where each y was going. (I forgot the exact context, but I think $y_0$ would've been weird to use. But right now I'm screaming at my past self to use $y_0$ instead somehow. idk.)

3

As others have said, color is fine as an aid (so long as you select more sensible color combinations than dark-blue on black), but it is useless on its own

Something I haven't noticed mentioned yet: if someone wants to quote or discuss your work, whether in speech or writing, they'd be unable to do so without circumlocutions like "the blue m".

No form of OCR would be able to read the expression. MatLab would not understand it.

You could not even ask this question without using an image.

So it's not just about "black and white printing" or "e-readers" or "colorblind people" - it's about people being able to apply the expression you have written.

2

The general consensus is to not use colors. However, this also depends on the field. Some fields, particularly in computer science, have accepted the use of colors for sake of readability. The following does not only hold for papers, but also for presentations, since accessibility at conferences or workshops should also be considered.

If you really want to add colors to your work, some care must be taken. As the other answers have indicated, using colors to convey important information can seriously impede the experience for the color-blind. It really depends on what colors you choose. You can choose colors that any type of colorblind people can still distinguish. To make sure you use the right colors, use a tool like Sim Daltonism.

In order to distinguish on black-white print, it's advisable to add additional emphasis/use different fonts, e.g. the blue one is bold, the other, green one cursive, the next, orange one is underlined. That way, people with monochromatic vision and people who read your work on a black-white printout can still benefit from your highlighting.

That said, depending on how adopted the use of colors is in your field, you might have more trouble than good if researchers, and ultimately referees, are not used to it and strongly oppose to the use of syntax highlighting, despite its benefits and, if done rightly, accessibility. To try to remedy this, you should add a line to your paper that says "This paper uses colors. While still readable as a black-white print, for an enhanced experience, view this paper in colors."

Concluding, yes you do can use colors in your paper. However, do so in a sensible manner that keeps the accessibility. Nevertheless, you should really ponder whether the inclusion of colors+font diversification is actually beneficial to your work after all. As a personal judgement from your screenshot, the current choice of colors and fonts makes it much more difficult to read than without colors. You should abstain from using a hard blue or a hard red on black background.

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  • 1
    "...computer science, have accepted the use of colors..." Not in the way OP is proposing, no. Code terms are distinguished by grammar, naming, capitalization, and enforced uniqueness. Color/font are additional aids by the viewing software, never consciously applied by the developer as they work, and never solely used to distinguish between unique items of the same type, as OP is proposing. Instead, all languages are legible if printed monochrome and monospaced, because we have not accepted color as syntactically meaningful, and would not. The only exceptions are toy langs like Whitespace. Oct 6 at 3:21
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    I do agree with you. Nevertheless, especially with e.g. POPL papers, authors really do seem to consciously choose to use color + font alteration to distinguish between syntax of multiple languages within one development, e.g. true in language A and true in language B. As I've explained, the use of colors + font alteration in such a scenario still renders the work as legible even if printed monochrome or when read by colorblind. Here is an example: ccs.neu.edu/home/amal/papers/fabcc.pdf
    – NaCl
    Oct 6 at 11:01
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    @DewiMorgan: most modern programming languages use reserved words and keywords that are distinguishable without color or font. However, Algol 68 allowed identifiers and keywords to be spelled the same way, distinguished by font bold/nit, or .stropping. This history may indicate that font/color is a bad idea, although it might purely be that color printers and displays were not available back in the old days. Going back to this would avoid the excesses that C++ goes to to avoid breaking old programs as it adds new features.
    – Krazy Glew
    Oct 6 at 21:33
  • @KrazyGlew That's fair comment: I thought that using bold for stropped identifiers was only used in print, not when writing code, but maybe editors/compilers allowed coders to strop ( en.wikipedia.org/wiki/Stropping_(syntax) ) using control characters for bolding rather than, say, apostrophes? Algol was WAY before my time, so if you say they were a thing, that's good enough for me. Plus, those were the days of hand-compiling to punched cards with no IDEs, so I admit the distinction between "code for print" and "code for compiling to punched cards" must've been fuzzier. Oct 8 at 21:53
2

Existing answers make a lot of different points, but there’s an overarching summary point that I think hasn’t been highlighted: You’re approaching the question a bit wrong. Your main question shouldn’t be “Could I do this?” or “Would this reduce the chances of publication?” — it should be “Is this good scientific writing?”

As other answers amply show, the answer to that is “Certainly not, in most people’s judgement” — it has many clear and serious drawbacks, and not much advantage. But what I want to emphasise is that all these reasons aren’t arbitrary rules or conventions of publishing — they’re about making your paper clear and useful to readers. Asking “will publishers be willing or able to accept this?” is only useful when you’re already confident that something is good writing style, and able to make a case for that to people who disagree.

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