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I am trying to find some insight into editorial rejection due to "not easy to access due to style."

I understand that it probably basically means that the paper was hard to read, or the notation was confusing, or the overall structure didn't flow well or something like that. But what I am looking for is insight from folks who are more experienced in terms of what they think the likely cause is.

  1. Has anyone ever had similar comments from an editor or reviewer, and if so, what did you do to change your paper?
  2. Does anyone here have editor or referee experience where they said something like that to the author, and if so, what did you mean by it?

As far as I can tell, I didn't have any undefined notation, and none of it was strange or obscure. The paper just flowed linearly building as it went, referencing past steps along the way. None of it was multipage proofs using extremely complex theorems. Any complicated theorems used were just standard results from textbooks and always referenced. There was only one proof that took a full page, and most are just 10-20 lines long or less. The paper is normal length, 20 pages in standard latex article document class 11pt font.

Things I can think of that might be the cause are notation being defined in-line instead of as a standalone definition, but this was only done a couple of times, and it isn't anything complicated, just something like vector x multiplied by matrix M is denoted x_M. That's not exactly it, but pretend such notation made a certain formula really easy to write out and derive (rather than writing x^t M over and over).

Another possible cause is that to understand the statement of the main results, you really do need to have some understanding of the underlying concepts.

Obviously, without taking the time to read the manuscript, nobody can give direct feedback, but there has to be somebody here who has helpful thoughts/comments.

I am in a situation where I don't have colleagues capable of commenting on the paper, nor a good research network, so that's kind of out.

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    What is your level of experience in publishing papers more generally? What stage of career are you at?
    – Bryan Krause
    Apr 26, 2023 at 22:07
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    "Another possible cause is that to understand the statement of the main results, you really do need to have some understanding of the underlying concepts." Well, do you provide an explanation that would enable the reader to understand the statement of your results or do you just start from the assumption that they already have this understanding? Apr 26, 2023 at 23:28
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    @BryanKrause mid-career, employed at teaching institution with a very small number of publications, really only one in this particular subfield. Part of the problem is going for top journals since this is actually a good result.
    – jdods
    Apr 26, 2023 at 23:48
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    Why not just ask the editor to expand on their comment? Presumably they have something to say about the matter that everyone else could only speculate about. Apr 27, 2023 at 19:49
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    @jdods I mean, yes, it is annoying from anyone -- it's more work. My personal take is that it is an editor's responsibility to also explain their decisions, and a single sentence is just not an explanation. We could read tea leaves over it all day long. But it's also clear to me that my personal opinion is not shared by all my colleagues. Apr 27, 2023 at 20:59

5 Answers 5

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You put yourself in a bind here:

  • The editor and the reviewer could not understand your paper.

  • You think that your paper is understandable and you do not understand why the editor / reviewer came to this conclusion.

  • You need some more immediate feedback, but you ruled that out.

Somehow you have to break this bind.

Now, there is a hint in your question. You seem to write the product of a vector and a matrix using a subscript. This is quite unusual if true. Let's assume that I read your question correctly. Then you have invented your own notation different from the standard notation. Presumably, you have good reasons to like your notation. However, the effect on a more casual reader is a bit disastrous as they need to spend energy to learn your notation and at least in the beginning translate it to standard notation. Unfortunately for you, people that do not use standard notation and prefer their own instead tend to be amateurs and often cranks of the circle-squaring variety. Additionally, you say that all of your theorems use standard textbook results and are short. Frankly, this might mean that you are not using the armory developed in a Mathematical field.

So I speculate that you wrote a paper that uses unusual notation and does not seem to be aware of other people's work. Reviewers and editors will not spend a lot of time reading your paper and come up with cryptic reasons for rejection such as the one that you received. There is a chance that you made a real contribution, but you will not get editors and reviewers to read it unless you change the way you write. I assume that you are not working in academia since there are no people that you ask to help you. There are certainly amateur Mathematicians who make valid contribution to the science. They usually write in a more accessible manner.

Now, I am basing my advise on interpreting your question and I might be completely wrong in this. In this case, disregard it.


Added after reading the clarifying comments:

You need someone you trust to read your paper. There is no way around this.

Reviewers and editors are not infallible. I would still bet some money on that you have made it more difficult to understand your result by not using standard notation or at least prejudice the reviewer against you.

As a published author, I can assure you that I frequently suffer from author's blindness, meaning I cannot see the problems with my papers. The only good way (other than waiting for a year before rereading the paper) to overcome this is to ask someone else take a look.

I also stand by my diagnosis (as the most likely) that the reviewer / editor did not think you were a serious contributor. This could be because you are not at a research active institution. So, they fed you a cryptic line. Unfortunately, Mathematics paper are very terse, which makes explaining results difficult. But it is on the author to make themselves understood.

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    The notation thing is more justified than the example I gave, but it's hard to explain without going into full mathematical details, which I like to avoid. Maybe I'll try to take out the "special notation" before the next submission even at the expense of making the formulas way more bulky. Awareness of existing literature shouldn't be an issue here, but of course there could always be papers that I missed.
    – jdods
    Apr 26, 2023 at 23:45
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    Thanks for the edits. My worry is that your last paragraph is the actual issue and that it’s hard to convince an editor to actually give the paper an honest read. I understand the crank worry too as I have come across my fair share. It is indeed very unusual for someone at my career stage to have a new result at this level of theoretical depth —it is a modest result at best, compared to what’s out there, but highly unusual for a teacher, say, as opposed to a professional researcher. I think my real hope is for someone here to chime in: “I do probability theory, send it to me!” Ha!
    – jdods
    Apr 27, 2023 at 13:04
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    @jdods People have lots of things to do, nobody will ask for extra work. You need to find out what people work in the subfield your paper is in, and perhaps to go to workshops or follow discussion groups or something like that to get an impression how things operate there. And yes: do not use private notation unless absolutely unavoidable. People have a hard enough job working through the paper without learning a new language. I got a request to privately check a paper in the periphery of my interests. The author used private vocabulary/notation/concepts, I had to decline. Apr 27, 2023 at 16:08
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    @jdods In short: In an attention economy It's the job of the author to make the reader's job easy, not the other way round. Apr 27, 2023 at 16:09
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    @jdods There's not much to go on in your question, so people are grabbing on to the scant details you do give in attempt to "read the tea leaves" as best they can. Which brings us back to the main point that can't be overemphasized You need someone you trust to read your paper. There is no way around this. (I'll add that that person should be objective and familiar with the publishing standards in your field.)
    – R.M.
    Apr 27, 2023 at 16:20
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This is an easy one. You show it to colleagues and ask them if it's actually hard to read. If you don't have "colleagues capable of commenting on the paper, nor a good research network", then that's now at the top of your list of things to do.

When you find such a network, and they agree with you that it's not hard to read, then it's just a lazy editor.

I once received a rejection with the note "full of spelling and grammar mistakes", but it did not have any. I had a professional editor look at it, and she agreed. It was a lazy editor. I sent it to another journal and it was accepted.

In conclusion, the answer really depends on the actual quality of the writing, and you need an honest opinion about it.

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    It's a big ask. Unknown people asking me to read their unpublished manuscripts are, in my experience, all cranks.
    – Cheery
    Apr 26, 2023 at 23:51
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    I am assuming you ( @jdods ) had a cohort of peers in your PhD program. Could you not email it to one of them? I can't imagine a scenario where I would decline to give feedback on a paper sent to me by someone I attended a PhD program with. I note that none of these people is "in my field" exactly, but I am competent to read a paper and give them feedback on notation, etc.
    – Dawn
    Apr 27, 2023 at 0:10
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    But the journal comments were not about the math, but the writing and notation, correct? Wouldn't someone in a related field be able to help?
    – Cheery
    Apr 27, 2023 at 0:31
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    @jdods You've not had any contact with anyone in your field in 15 years? No one you went to school with or collaborated with or had dinner with at a conference?
    – Bryan Krause
    Apr 27, 2023 at 2:13
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    @jdods did your work build on anyone else's work? You could try asking one of the people you cited to read the paper.
    – Allure
    Apr 27, 2023 at 9:00
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Native vs. non-native speaker?

The OP doesn't state whether he/she is a native speaker of English. In my experience, many non-native English speakers speak and write a hybrid of English and their native language in English words. I mean this in no way derogatory, as I am guilty of this as well, and I fully understand the difficulty of mastering a second language.

In my example, I observe many native German speakers simply transferring the German way of formulating things into an English vocabulary, resulting in long, nested sentences. This is especially the case in writing. Again, no offense to anyone; and also, I am guilty of this too.

Get a second pair of eyes

In the German language, there's the wonderful word Betriebsblind; which approximately describes a blindness towards the things you regularly do. This also applies to writing papers. When writing a paper about a topic we are very familiar with, we may fall victim to our own Betriebsblindheit by e.g., starting to explain concepts halfway down the logical order of things, because we consider the fundamental concepts as obvious.

Here, I found it beneficial to let someone unrelated to a topic read and comment on the text. Someone completely outside of the topic of the paper will immediately spot gaps in the logical reasoning simply because they know nothing about it, while oneself unconsciously "bridges" these gaps with all one's knowledge.

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    Native English speaker. I'm not saying I am the best writer ever... you can look through my posts here to see that I'm not completely unintelligible. Even though this got a downvote, I think this is an important point of consideration, say for the casual non-native-English reader. I've reviewed papers where I thought the poor English was a major barrier, but I tend to be more forgiving than others probably.
    – jdods
    Apr 28, 2023 at 12:23
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To add another point to other great answers.

I'm just speculating because I haven't seen the paper, but this paragraph hints about another possible problem:

As far as I can tell, I didn't have any undefined notation, and none of it was strange or obscure. The paper just flowed linearly building as it went, referencing past steps along the way. [...] The paper is normal length, 20 pages in standard latex article document class 11pt font.

Researchers don't actually usually read papers from beginning to end. Most go through a lot of papers and just skim through to find the interesting parts. Only if the paper seems interesting, they may want to read the full paper, to understand the full derivation in order to find insights (or even to check correctness when in doubt). But this usually happens only after figuring out what the main results are.

This presents a challenge of balancing different objectives when writing a paper:

  • You obviously need to write your article so that the derivation is logically correct.
  • You need to give enough background so that readers unfamiliar to the particular topic can understand the result without too much extra trouble. For that, the way you present stuff is important: Using standard notation removes some boundaries, but sometimes introducing new notation might assist reading.
  • But you also need to make it clear enough so that experts already familiar with the topic can spot the important parts quickly.

Just from the way you wrote your question, it looks like you might have only focused on the first two items.

Could it be that even experts familiar with the area can't understand your main result without carefully reading through all your definitions? In that case, perhaps you could reformulate the paper so that the main result is more obvious to those who already have the necessary background.

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  • Experts can understand the statement of the main theorems without trouble, that is for certain. There is no unusual notation in there at all. The problem set up is basic. I mean, they'd need to read about a page fully grasp the theorem statement, say. That's not unusual though. The important things are set apart with display equations in that page to help quickly spot them so that the theorem statement can be digested quickly. I use descriptive section and subsection titles, for example, and follow standard norms on display vs inline equations, etc.
    – jdods
    Apr 28, 2023 at 12:18
  • To understand the results though does require a mix of linear algebra and stochastic processes though, and the cross-expertise required is probably more rare. My real worry is that that is the actual issue, and that it will be an issue for every possible journal. The linear algebra theory is what actually solves the problem though, so it's unavoidable I feel. So your last paragraph could be part of the issue.
    – jdods
    Apr 28, 2023 at 12:19
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    @jdods I notice that you are focusing on details, like whether you use section titles, and counting how many times you use unconventional notation. I will have to echo the advice of other answerers: get someone who is like the people you want to read the paper, to read the paper, and see what they think of it. They probably won't count the number of section titles or whether they have the same font size. You want to know how understandable they feel the paper is and, if possible, improve that.
    – user253751
    Apr 28, 2023 at 17:50
  • @jdods By the way I think linear algebra is quite common all over mathematics, and for example, a Markov chain is a reasonably well known thing that is a crossover of linear algebra and stochastic processes, so it's not an unusual combination.
    – user253751
    Apr 28, 2023 at 17:51
  • @user253751 true, but I'm using it in a way never seen before. It's very much like standard Markov chain usage, but not with an actual stochastic matrix.
    – jdods
    Apr 28, 2023 at 17:54
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Publishing in journals is a form of socializing. (It's a peculiar kind of socializing, but still.) Journals may claim that they exist in order to publish new and interesting results, but that's only a small part of it. They mainly exist in order to get read. Therefore, the articles can't just be fascinating and enlightening - they also have to be popular with the people who might read that journal. The fact that you have ended up somewhat professionally isolated takes away your ability to gauge how much your colleagues LIKE the paper. The real way forward is to change the final sentence of your original post: "I am in a situation where I don't have colleagues capable of commenting on the paper, nor a good research network, so that's where I'm going to focus 99% of my future effort if I expect to publish."

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  • I think this is an important point. And once you become an outsider, it's very hard to get back in!
    – jdods
    Apr 30, 2023 at 13:39
  • There are many reasons for becoming an outsider. Some of those reasons can create more difficulty than others.
    – David R
    May 2, 2023 at 3:26
  • The difficulty in my case is just a gap in research and low productivity. But I've always been in academia.
    – jdods
    May 2, 2023 at 3:32

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