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This is one of those articles that might sound convincing to non-mathematicians (because it is annoying to learn names for difficult concepts, and many people c
by saithound 6y ago
This is one of those articles that might sound convincing to non-mathematicians (because it is annoying to learn names for difficult concepts, and many people can relate to that experience), but will not sound all that convincing to domain experts.
It'd be hard to deny that descriptive terms are easier to memorize. Sometimes a piece of natural and/or physical intuition allows such terminology to arise.
Scientist and mathematicians do tend to think about terminology quite frequently: communicating with other scientist and mathematicians is a major part of doing science, and "the reviewers couldn't follow your argument" is a valid, and not especially rare reason for rejected articles in mathematics. Given the amount of thought put into it, "intuitive" names do tend to come about when possible (as it happened with what we now call the Ham Sandwich theorem, the concept of Fibration, the Squeeze Lemma, and countless others).
Given that mathematicians do put thought into terminology, there's often a good reason for not having more intuitive names: maybe no good common-sense intuition was available (e.g. Chu constructions are too general for this sort of thing), or the thing comes up only in highly specialized contexts where it's not worth bothering with it (e.g. Girard's paradox), or there are too many different metaphors that one would have to invoke to describe the situation appropriately, so that it's more efficient to derive a completely new term from an associated name (e.g. Abelian became such an adjective, which now has its own associations).
It's telling that the author criticizes terms like "Calabi-Yau manifold", but doesn't suggest any alternative: coming up with an insightful name that communicates the key properties of such an object, and is easier to use and remember than "Calabi-Yau" is, let's just say, very very hard.
The same phenomenon is not limited to mathematics. Would Dijkstra's algorithm, the Haber–Bosch process or the Otto cycle be easier to learn and remember if they had snappy, insightful names? Probably. But the same concerns apply. It's hard to come up with genuinely better, more descriptive names for these processes. And even if we were successful in popularizing newer, better names, we would find that the names were not the real bottlenecks that made computer science, chemistry or mechanical engineering difficult to master.
- i_cannot_hack 6y agoAt first I agreed with you, but I think your analogy to algorithms actually somewhat counters your point. The Wikipedia article for Dijkstra's algorithm gives an alternative name of "Shortest Path First", or "SPF algorithm", which I do think is a much better and more descriptive name. It also made me think of sorting algorithms, which all have wonderfully snappy and descriptive names. I think the world would be a sadder place if – instead of quicksort, mergesort, and heapsort – we had to struggle with opaque names like Hoare sort, Neumann sort, and Williams sort.
- gjulianm 6y agoThe issue is that some concepts can't have descriptive names, unless you just explain the whole concept. For example. Lipschitz or Holder continuous function, or Riemanninan manifold... Whenever concepts can be described with a good name, those names tend to be used, but unfortunately a lot of times we just can't.
- dragonwriter 6y ago> It also made me think of sorting algorithms, which all have wonderfully snappy and descriptive names.@@ Well, bubble, shell, insertion and merge, sure. Quick less so. And then there is Tim...
- taeric 6y agoYou do know that Shell is a name, right?
- thaumasiotes 6y agoWhat? Shell sort isn't a descriptive name. The algorithm is named after Donald Shell, and has nothing to do with shells.
- xdavidliu 6y agokind of reminds me of the Heaviside function, which is a step function. When I first learned about it in school, I thought it was named after the "heavy side" on the right, as opposed to the "light side" on the left. Turns out that Oliver Heaviside was an actual person.
- dllthomas 6y agoNagle's Algorithm is named after a person. It helps make sure more data is sent together, rather than split across unnecessarily many packets. I recently learned that in Polish, "nagle" can mean "all at once" - not pronounced the same, but still a cute coincidence!
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- kxyvr 6y agoAs a counterpoint, I've a Ph.D in math and I largely agree with the article. Frankly, it's difficult enough to keep track of the names in my own field much less interact with people in other fields who would greatly benefit from these results if they were comprehensible. While I agree that precision is necessary, is it really that hard to say something like a complete inner product space vs a Hilbert space? Should we have an argument about whether we should call the triangle inequality the Cauchy-Schwarz or the Kantorovich inequality? How many years did it take to recognize Karush for providing algebraic optimality conditions long before Kuhn and Tucker? Anyway, outside of general griping about names, very specifically, I have to regularly interact with technical people in other fields and memorizing names is one additional, often superfluous, barrier to their understanding. Even if it's important for someone credit the (supposed) originator outside of a citation, giving an intuitive name for the context would go a long way in improving understanding. For example, the triangle inequality from Cauchy and Schwarz or the algebraic optimality conditions from Karush, Kuhn, and Tucker. By the way, I'll also mention that the majority of other mathematicians that I know don't feel this way and prefer using names after people. I understand; I just disagree.
- Davidzheng 6y agoIf you have to write complete inner product space a hundred times in an article that's pretty annoying tbh
- kergonath 6y agoIn a Physics article, we'd just call it CIPS after the first instance. It does get a bit unwieldy if there are too many acronyms or initialisms in a sentence.
- xigency 6y agoTerrible excuse. Things are read much more than they are written. That’s like using short variable names rather than descriptive ones as they are easier to type. With current IDEs that isn’t even the case and I’m sure word processors could use the same autocomplete. Every writing shortcut adds cognitive load for the reader to remember.
- mjw1007 6y agoIf you summarise the article as "John Conway was good at thinking of names. Try to be more like John Conway.", then I think many mathematicians will think it's a reasonable suggestion.
- yellowapple 6y agoReally, "Try to be more like John Conway" is good advice all around.
- montjoy 6y agoI think that even an arbitrary name (e.g. quark colors blue, green, red) is easier to digest/process/memorize over a person’s name that may be from a language you are not familiar with. However that also points to another problem. How do you translate? Do you force the word from the discover’s language on all other languages or do you translate it? If you translate then you are introducing drift but if you don’t translate then the word is just as effective as a foreign name. It’s almost like you would have to come up with a table for the concept in all common languages. So while names suck I don’t know what would be better.
- livre 6y agoI think you make a great argument with the translation problem. English is a second language for me, and many of the people that studied with me at university didn't speak it at all so clases were as much in Spanish as it was possible. Things like "bubble sort" where translated to things like "ordenamiento de burbuja," etc. There were two problems with that: one is that not all authors used the same translation and second is that information in non English languages tends to be more outdated or not even exist at all on the web so many times I had to try and guess the right name in English when I wanted to understand something better. Now that I have a job a similar problem appeared with translations, Microsoft has this annoying habit of translating useful technical error messages and many times the error in Spanish doesn't yield any useful information on Google searches (if at all) so I'm again having to guess-translate terms into their original form.
- WoahNoun 6y agoWe should strive to remove all references to Teichmüller. It is abhorrent that the name of a prominent Nazi is so deeply embedded in modern mathematics.
- srtjstjsj 6y agoYou can start calling them Alfhors spaces instead. But I think it's important to keep Teichmuller around as a reminder of the important lesson (especially around here) that mathematical genius does mean that everything one says on all topics is logically or morally correct. As Teichmuller wrote: > I am not concerned with making difficulties for you as a Jew, but only with protecting – above all – German students of the second semester from being taught differential and integral calculus by a teacher of a race quite foreign to them. I, like everyone else, do not doubt your ability to instruct suitable students of whatever origin in the purely abstract aspects of mathematics. But I know that many academic courses, especially the differential and integral calculus, have at the same time educative value, inducting the pupil not only to a conceptual world but also to a different frame of mind. But since the latter depends very substantially on the racial composition of the individual, it follows that a German student should not be allowed to be trained by a Jewish teacher.[8]
- Grustaf 6y agoIs learning the names of the concepts the problem for non-math undergraduates? I’d say that’s the only part that doesn’t give them headaches. Remembering peoples’ names is something we practice every day, understanding abstract mathematical concepts on the underhand is very painful for most people.
- yellowapple 6y ago> Chu constructions Star-autonomous category constructions? > Girard's paradox Provability paradox? > Calabi-Yau manifold Smooth n-dimensional complex manifold? > Dijkstra's algorithm Shortest-path-first algorithm? (I'm cheating here because this is literally an already-common alternative name for it) > Haber–Bosch process Ammonia synthesis loop? (Also cheating here, since the "Ammonia production" Wikipedia article uses this exact terminology) > Otto cycle Four-stroke cycle? (Cheating yet again, since Wikipedia states: "This is why the four-stroke principle today is commonly known as the Otto cycle and four-stroke engines using spark plugs often are called Otto engines.")
- saithound 6y agoThe names you suggest are generic terms that already exist in the respective jargons with different, more generic (and in fact more intuitive) meanings. It's like noticing that the name "Jonathan" has no mnemonic function in the term "Jonathan apple", then suggesting the term "fruit" as a better replacement. This would not solve, but exacerbate the issues raised in article, in that this would make all of learning, teaching and expert communication harder (compare your suggestions with the ham sandwich theorem, a snappy name which serves as an exceptionally good mnemonic device for both the theorem and its usual proof, despite not mentioning Lebesgue measure, Euclidean space, exact division, or really any specific objects involved in the statement of the theorem). Non-Otto four-stroke cycles abound (cf. Diesel cycle); new industrial methods for ammonia synthesis come into existence every few years and there's not much point in singling one out and calling it _the_ ammonia synthesis loop. The case of shortest-path algorithms has been thoroughly discussed upthread. Your suggestion for Calabi-Yau and Girard's paradox are not coherent with the meanings of these terms. No big deal: giving a purer meaning to the words of the tribe is not easy, and requires deep domain expertise. And those with deep domain expertise do think about this task, have some strong incentives to think about it (teaching evaluations factor into promotion and tenure) and generally do fairly well at it. (Startup idea: your-jargon-reform-is-bad as a service, backed by GPT-3?)
- yellowapple 6y ago> The names you suggest are generic terms that already exist in the respective jargons with different, more generic (and in fact more intuitive) meanings. The last three, like I mentioned, were pretty much direct from Wikipedia. But yeah, I'm under no pretense that these are necessarily correct. My only point is that we can surely do better than "$person $thing" for nomenclature. The Otto cycle is a perfect example; sure, "four stroke cycle" might be too broad, but "spark-ignited four stroke cycle" (maybe abbreviated to SI4C) doesn't seem to be (there are technically other such cycles, but the vast majority of the time people talk about a spark -ignited four-stroke cycle they're talking about an Otto cycle or some evolution thereof).