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How do I know my results are significant enough to be published?

I am a physicist and I have found a very common mistake that appears in every paper in my area of interest. I thought it would be nice to let the people know it should be corrected. However, it is a very simple mistake, very basic math. I thought at first I could publish that as a short letter, but then I realized that I am unsure what actions the significance of the error(s) warrant.

How do I know whether an error is important enough to write a letter to the publication's journal?

recursion.ninja
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AAA
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  • of possible interest http://academia.stackexchange.com/questions/18911/what-should-you-do-if-you-spotted-a-non-trivial-error-in-a-highly-cited-paper – gman Jul 22 '14 at 14:15
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    If you do decide to publish (and have the time), you should do an analysis of exactly what the significance is. Work out the worst case and average error. Maybe do some simulations. Look at a few famous results based on the technique, and redo the work to show how the results differ. Think kind of thing can help you build a simple insight into a more substantial publication. However, be sure to make the page count proportional to the heart of the paper. If it's a simple mistake 2-4 pages should suffice. – Peter Bloem Jul 22 '14 at 23:36
  • Out of interest, could you update the answer with what mistake it was, or publish in comments, once you have figured out what to do. – Viktor Mellgren Jul 23 '14 at 07:52
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    I'm sure you'll agree physicists frequently make minor errors, or rather have different interpretations of certain concepts in mathematics. I see this in differential geometry and representation theory for example. Sometimes it's simply a matter of language. I would check with someone else whether this 'mistake' is actually worth addressing, and whether physicists are aware of it and ignore it as a very minor technicality, e.g. in the exact definition of the tangent bundle. – JNS Aug 18 '15 at 17:11
  • Does it affect experimental/simulative results? Are there cases where it would, but which haven't been explored (in which case you could propose an experimentum crucis)? – Captain Emacs Feb 05 '16 at 17:43

3 Answers3

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You should talk to colleagues from that area of interest to check whether it actually is a mistake or maybe a common generalization that, although not perfectly correct, is still 'good' in the systems that were discussed in the papers. Also writing a mail to the authors of said papers is a better idea before writing to the journals without any cross-check.

BPND
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Many journals have special formats for such remarks, usually called comments. Though these are usually directed at single papers, there might be journals out there which do not impose such a requirement. Also, as such requirements are not carved in stone, you might just contact the journals which published most of the papers making the mistake whether they would consider such a comment for publication.

That being said, you should ensure that the presumed mistake is really a mistake and not just notational sloppiness or a standard approximation (see BPND’s anwer), which nobody wastes words about anymore.

Finally, you might consider to not only mention the mistake but perform and report about some research and demonstrate or estimate the negative effect of that mistake and thus increase the impact of your publication. Also, to address one of your questions: The existence of such negative effects is a good criterion for the relevance of a mistake.

Community
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Wrzlprmft
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This is where you define yourself. There isn't a right and wrong answer to be suggested. You're helping improve the wisdom contained within the Academic Establishment itself.

Otherwise, I'd say you don't have to know. That's what the peer review process is for. But it might save you some time to use this radical tool of the Internet, whereby you can be in informal dialog with peers across the world.

Marxos
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    True, however, estimating whether it’s worth one’s time to invest a considerable amount of time to prepare a manuscript is quite something. – Wrzlprmft Jul 22 '14 at 15:31
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    I find it remarkable that you should take such a condescending tone, as if to say "Oh, everybody knows you should discuss it with your peers on the internet." Well, everybody except you, apparently, since you only included that part of your answer after somebody suggested it to you! – David Richerby Jul 22 '14 at 22:51
  • @David, well I knew of the internet, and I assume the OP does also. For example, he could ask his question on physics.stackexchange.com instead of here couldn't he? I think a little condescension can be appropriate if used in a corraling manner. – Marxos Jul 23 '14 at 00:50
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    Condescension is never an appropriate response to someone who is legitimately asking for help. It only serves to alienate people and push them away from ever returning to contribute here. – Chris Hayes Jul 23 '14 at 04:15
  • Funnily, this was not even what I was aiming at in my comment. Rather I wanted to comment that letting the peer-review process decide about the relevance may be quite uneconomical. – Wrzlprmft Jul 23 '14 at 12:15