A question about terminology

There’s a project that I and collaborators have been working on for a fairly long time now. It is almost finished, at least the first stage of it, and I will have more to say about it once we have posted the paper on the arXiv. In the meantime, though, there is a very important question that we need to consider.

Would it be well received in the community if we referred to a certain class of sets appearing in the paper as “non-parasitic lampreys”?

For all we know, the community does not currently harbour any particular feelings towards such sets. They have come up in a couple of places over the years, but their possible parasitic behaviour has not really been investigated until now. We can prove that certain particular lampreys of interest are indeed non-parasitic, which is good for us. By way of contrast, “eels” are somewhat more straightforward than lampreys. That makes them easy to manage when they’re small, but otherwise they’re still troublemakers.

This would be a radical departure from the naming conventions established in, say, physics or algebraic geometry. While those of course abound in colourful vocabulary, much of it refers to various forms of enchantment, awe, amazement, pleasure and wonder, not necessarily the feelings that lampreys tend to inspire. But… our unofficial terminology fits so nicely, I’d be quite reluctant to part with it.

What do you think?

Author: Izabella Laba

Mathematics professor at UBC. My opinions are, obviously, my own.

22 thoughts on “A question about terminology”

  1. I’m in favour.

    Some mathematical terms are quite lovely botanical metaphors – root, node, kernel, tree, branch, leaf, and fibre spring to mind – so why not branch out to the ichthyological? Especially if it’s a good metaphor.

  2. If you can give nice names to the underlying structures that sort everything out for you, why not give loathsome names to the obstacles you need to get around?

  3. “Read over your compositions, and wherever you meet with a passage which you think is particularly fine, strike it out.” (Samuel Johnson)

    I’d err on the side of conservatism with regard to colourful notation; I’ve succumbed in the past to the temptation of introducing what I thought was a particularly clever choice of notation, only to find that it is faintly embarrassing, and not adopted by other authors. So, if “lampreys” were already existing notation, and “parasitic” was already used in the literature in a reasonably similar context, there would be nothing objectionable with combining the two to form “non-parasitic lampreys”, but if the notation does not naturally derive from existing conventions in the field then it may look a bit idiosyncratic.

  4. Actually, as far as avoiding unpleasant terminology and other unconventional stuff in mathematics is concerned, Edith Wharton might be more relevant than Samuel Johnson; the penultimate chapter of “The Age of Innocence” comes to mind.

  5. I once heard the following, which I agree with: “Never ascribe negative moral connotations to mathematical objects”. From this point of view, there should never be “evil” primes, or “loathsome” spaces, etc (though generic-negatively-neutral terminology, e.g., “bad set”, seems reasonable for convenience within a proof when it’s not meant to be re-used elsewhere.) The reasoning is partly that what might look pathological and bad to a given mathematician may be beneficial to another (history gives many examples, as nowhere-differentiable continuous functions show).

    In your example, I may like “lampreys” by themselves, but I wouldn’t like “parasitic lampreys” (which I assume have to be there, for “non-parasitic” ones to make sense?)…

  6. There should definitely be “evil” primes. We may try to invent them over lunch tomorrow. 🙂

    You’re right, though, that the “parasitic” lampreys are not all that bad. That’s the main point of our work, actually. We could call them “genuine”, maybe, and rename the other kind accordingly.

    “I dare say it is rather hard to be a rat,” she mused. “Nobody likes you. People jump and run away and scream out, ‘Oh, a horrid rat!’ I shouldn’t like people to scream and jump and say, ‘Oh, a horrid Sara!’ the moment they saw me. And set traps for me, and pretend they were dinner. It’s so different to be a sparrow. But nobody asked this rat if he wanted to be a rat when he was made. Nobody said, ‘Wouldn’t you rather be a sparrow?'” (A Little Princess, F.H. Burnett)

    It must be hard to be a lamprey, too.

  7. A grad student from a nearby university used a very colorful term for a certain type of set. I had the pleasure of seeing not just one, but two different talks by this grad student, at two different conferences. In both talks, the colorful term took the lion’s share of the reactions from the audience. That’s good in the sense of making her talk stand out, draw attention to it, etc. It’s bad in the sense of distracting from what her talk was *actually about*.

  8. 2 is the snobbish prime because it must always be considered separately from all the others. It’s not really evil, but it always wants a bowl of red M&Ms in its hotel room or else it refuses to be in your paper.

    Any prime bigger than 169 is evil because I wouldn’t be able to detect it in under a minute.

  9. Anonymous: I guess you have discovered by accident, then, that I’m not Terry Tao and that I don’t always agree with him.

    When I look at my own writing from 10 years ago or more, it’s not the “wittiness” that grates, because there was none at the time. It’s the boring language, the endless repetition of same-old-same-old, starting each paper with “In this paper”, each section with “In this section”, and so on. So, yeah, it is possible to go too far in the other direction, too. So what? I’ve had worse things happen to me.

  10. Izabella,

    I understand your problem with the boring language: there are only so many variations of thus, hence, whence, thence, therefore, if and only if, suppose that, conversely, anticipating a contradiction, etc., and we use these words with repetition that would drive a creative writing teacher mad. The language does tend to sound flat and un-dynamic, and that even adds a little to the exhaustion of the writer writing a very long document. Harpsichords can not be played dynamically like a piano (soft to loud sound levels), and would sound awfully boring if the composer and player did not express dynamics rhythmically.When writing mathematics I sometimes find myself consciously modulating the rhythm of the language and sentence structure in subtle ways. (I can’t explain it any better than that.) It makes the process of writing, and hopefully the reading, less of a tedious task.

  11. Richard – yes, I get what you’re saying. And yes, I can assure you that the morale over here did go up considerably when we started referring to certain objects as lampreys. (They deserve it.) And that it was a much needed boost.

  12. I quoted from Terry’s blog neither because I confuse the two of you and somehow thought you had forgotten writing those words, nor that I take Terry’s opinions as ex cathedra, but merely because I agreed with them in this instance. But perhaps I misread the tone of your post and that you have already decided on your preferred answer? In which case, I will revise my opinion and wholeheartedly support your proposal 🙂 I suppose if the worse thing one is ever called is idiosyncratic, then one is doing ok.

  13. Anonymous -If you have an opinion and would like to argue in its support, you’re welcome, regardless of whether you do or do not agree with me. I just don’t have much appreciation for arguments quoting general-purpose advice pages for beginners, as if I were unaware of such advice. I’m quite capable of writing a research paper according to generally accepted rules. I just get tired of that sometimes. That’s what the post was about.

  14. Then I am confused, because I *thought* you were merely soliciting opinions.
    I apologize that you found the quote condescending, I offered it only to explain what informed my own thinking on the matter, not because I imagined you were unaware of the issues involved. (Similarly, the link to Terry’s blog is there to give proper attribution, not as an imperative to “read this blog for beginners.”)

    At the risk of digging myself a deeper hole, let me offer some further remarks. Presumably a good metaphor is one which brings to mind a precise image which illuminates some underlying feature of the situation. What images will be evoked by use of the term “lamprey”?
    Some readers will have no idea what a lamprey is, while others still will imagine eels and their corresponding connotation of slipperiness (which may well be appropriate here).
    Mathematical tradition mostly eschews colorful language; by all means break free from the shackles of this convention, as long as it is not at the cost of mathematical clarity. (Apologies in advance if you find this, too, a banal remark.)

  15. I’ll just say that the “regular” terminology here, consistent with the previous literature on the subject, involves the acronym LMPR. That acronym will appear in the paper in any case, because the objects in question do need to have a name.

    “Parasitic” is another story. It came up once we started talking about lampreys, but we should be able to replace this by something more conventional, at least in the formal paper. But we might well keep the more colourful unofficial terminology on our blogs.

  16. > Mathematical tradition mostly eschews colorful language;

    Yes, but my personal impression is that this aspect of mathematical tradition is an effect of the pretty complete word-blindness of most mathematicians…

    If one restricts attention to people who have been known to be careful about language, things are not so clear. I am thinking here in particular of the Bourbaki group (the whole terminology surrounding measure theory and topological vector spaces, for instance “tribu”, “tonneau”, or Lie theory, with “buildings”, “apartments”, “chambers”, etc), and of Grothendieck (“nuclear spaces”, “étale maps”, “cristals”, etc.) More recently, even something as strange-looking as “Property (T)” turns out to be a clever notation-game.

    In fact, there is a lot of mathematical terminology which re-uses common words, and much of this terminology (which is in constant use) could have been called colorful when it was first introduced.

  17. Just for fun, I’ve browsed through the titles of the “What Is…?” columns in the Notices of the AMS over the last few years, and found “resplendent structure”, “sandpile”, “perverse sheaf”, “systole”, “tropical curve”, “infinite swindle”, “bad end”, “grope”, “free lunch”, and “amoeba”.

    (See here (PDF file) for a complete list up to November 2007.)

  18. My understanding was that the term “perverse” in “perverse sheaf” originated from the (previously established) notion of a perversity in intersection homology, so I’m not sure whether this can constitute an example of “colorful language” (see this thread; the origin of the word “perversity” there as explained by Mark Goresky seems rather tame).

    I think Grothendieck’s objection to the terminology is awesome, though.

  19. This discussion about “perversity” seems to more or less describe what happened with the three of us – we had a somewhat subjective reaction to some new complication, and the name reflects that. That future authors merely were repeating existing terminology doesn’t change the origin story.

    In our case, it happens that LMPRe is a mathematically descriptive term which is also suggestive of the jawless grip of an insistent parasite. Unlike Goresky, we did not throw it out there hoping to think of something better later.

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