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Mathematicians should stop naming things after each other
- lixtra 6y agoSome profiling would show that names increase the difficulty of math by 0.001%. I don’t see an issue here.
- colah3 6y agoI'm curious if you feel the same way about programming -- do bad variable and function names only increase the difficult of understanding someone else's code or library by 0.001%?
- mehrdadn 6y agoThis isn't about variable names and functions though. Math has those too, but the proposal isn't to change those. In programming we don't call a C compiler a Ritchie Hopper (or whatever).
- kosievdmerwe 6y agoLike it's not the names that scare me, it's the definition they represent. The fact that the name isn't descriptive doesn't seem like a big problem when the definition has oodles of nuance. Granted I only have an undergrad in math so I can't quite speak to the experience of academics, but then the article is cherry picked too. All the examples given are of trivial things. Isoceles triangles and Fermat's last theorem. Both things you can explain in a sentence. Let's look at something with "mnemonic names": groups, rings and fields. Quickly by just looking at the name which one is the most generic and which most specific. Maths already involves a ludicrous amount of rote memorization, I'm not sure that using some guy's name is the hard problem. Internalizing all its nuance is.
- will4274 6y ago> 0.001% How did you come up with this number? You took 100,000 samples and 99,999 of them agreed? I don't personally know 100,000 mathematicians.
- lixtra 6y agoI first estimated 1% but decided that that is much too high. But let’s make an experiment. Let an average high school student memorize these names: A Calabi-Yau manifold is a compact, complex Kähler manifold with a trivial first Chern class. And now let her explain what the above definition is about.
- pessimizer 6y agoIf anything, naming them after people (especially people with uncommon names) makes them easier to google.
- davorak 6y agoDo you have a suggestion for how you would make a measurement like that? It seems like the experimental procedure would require definitions at least several layers deep, the control based on real names and experimental group based another metric. Maybe the experimental groups names would be more closely tied to the structure of the math they were naming though that seems challenging.
- lixtra 6y agoI studied math in foreign languages, sometimes names are different (French, Russian) and it never caused a problem (except for the first encounter).
- ampdepolymerase 6y agoCompensation in academia is already bad enough. Take away the boosts to the ego and you are going to make the politics even more toxic, and potentially cripple an entire generation.
- gxs 6y agoThis is the nature of mathematics. Statements and theorems are extremely dense with information, where every word might have a it's own area of study. Of a problem may begin with something benign like, the following function is blah blah, but even then, the term function is well defined, and you may need to know the intricacies of functions to be able to solve the problem.
- bengale 6y agoDo the work and you can name it whatever you want.
- evanpw 6y agoI fear the alternative would be all the good names becoming heavily overloaded: https://en.wikipedia.org/wiki/Normal https://en.wikipedia.org/wiki/Normal.
- aaron-santos 6y agoThe lack of eponymous names used in category theory, for example, do nothing to aid in learning it. The term functor is no more descriptive than Carnap mapping.
- gnodar 6y agoNo more descriptive, but IMO more memorable.
- magicalhippo 6y agoIf it's not descriptive, then memorable is a good substitute. Been many years since I went to uni and haven't used much of the math since, but I still recall the Cauchy-Schwarz inequality, what the Kronecker product is and how to do Taylor expansion.
- mycl 6y agoThe Yoneda Lemma is really some kind of "fundamental theorem" of elementary category theory. Then there are Freyd's Adjoint Functor Theorem, Kan extensions and probably others I'm forgetting...
- seles 6y agoThere's an equally annoying problem in software engineering at large corporations (aka Google), where hundreds of services you need to know about are named with some cute name that gives you no idea what the thing actually is.
- tryauuum 6y agoSo how would you solve it?
- notduncansmith 6y agoI imagine they work around the direct reference issue by having good search algorithms.
- tryauuum 6y agoI guess. I wanted to know what kind of corporate wiki / database is a good choice for storing / retrieving human-readable, verbose information about servers or services. My current employer uses atlassian confluence for that. So if you don't know what is this server "potato1" with 7 docker containers for, you can type "potato1" in confluence and hopefully get an answer. Maybe in big companies they use homebrew solutions for this
- wenc 6y agoFor AWS, there's a website called "AWS in Plain English" that explain what each service does. For instance, it's pretty hard to guess what AWS Route53 does unless you've come across it elsewhere. https://expeditedsecurity.com/aws-in-plain-english/ https://expeditedsecurity.com/aws-in-plain-english/ Azure naming is comparatively more pedestrian.
- matthewfelgate 6y agoThanks for sharing. That's actually really useful.
- b855f1d0ea394ac 6y ago
- anu7df 6y agoif you think maths is bad you should take a look at geology. At least mathematicians stick to their names or names of other mathematicians.
- Octoth0rpe 6y agoSounds reasonable. Let's call this new policy "Ball's Law".
- pbhjpbhj 6y agoMathematicians like it when _others_ attach their names to their seminal works; such pride must be stopped argues author who (I am assuming) attaches their own name to their work. #ironic It must be called the "mathematicians should stop naming things after each other" law!
- abnry 6y agoThis is not a fair criticism. The author attributes herself as the author to her piece because that is relevant information. But nowhere does she try to name the idea she raises after herself.
- mehrdadn 6y agoNot sure how feasible or necessary this is in general, but there are certainly some places for improvement. Some more modern examples than "isosceles": - Heaviside function → step function (edit: though maybe this one is, amusingly, already descriptive by accident?) - Fourier domain → frequency domain While I'm here, just a couple suggestions from me: - Markov chain → memoryless chain - Lebesgue integral → horizontal integral
- tomcam 6y agoWas prepared to dislike these suggestions but I think they're all solid. Good thinking.
- mehrdadn 6y agoThank you! :) Though I'd assume I'm not the first to think of them haha.
- joshuamorton 6y agoI'd be concerned that memoryless is misleading for markovian. A markov chain can be used to represent a fixed, nonzero memory, since if you have an n-state dfa D you can take the set of pairs of the states of D (or specifically D + null) and reweight them. The markov chain over D^2 has no memory over D^2, but does have memory over D, and this is often a useful property (bigrams). You repeat this operation to get more and more (but always a fixed constant maximum) history.
- mehrdadn 6y agoMemoryless isn't even something I came up with, it's practically in the first sentence of everyone's description of the Markov property, e.g.: https://en.wikipedia.org/wiki/Markov_chain#Definition https://en.wikipedia.org/wiki/Markov_chain#Definition Also see: https://en.wikipedia.org/wiki/Memorylessness https://en.wikipedia.org/wiki/Memorylessness ("memorylessness refers to the Markov property") All I'm doing is suggesting just using the existing description as the name itself. Even if there were some cases where it wouldn't apply, though, it wouldn't really matter. Fourier domain also applies to things other than time but that doesn't make frequency domain a bad term. It's just a name meant to carry some intuition; that's all. It's not meant to serve as the formal definition.
- archgoon 6y agoYep; check out how the programming community does it! We have descriptive names for things like "Apache", "React", "nginx", "Rust", and "Java"!
- neutronicus 6y agoThat's because "easy to google" is much more important in the short, medium, and long runs than "easy to guess what it does"
- archgoon 6y agoIndeed, and in a previous era, "to google" was "Who wrote the main papers on this, who should I look up?". Honestly; that's true still today.
- sorenjan 6y agoRust, Go, C, D, R, Flask, Rocket.
- YetAnotherNick 6y agoAppend programming language to the query for searching. Imagine C++ would be named as "Object oriented, generic, general purpose programming language with C compatibility"(of course C won't be named C then).
- elondaits 6y agoIt could be called Stroustrupilian ... or "The one with Turing complete templates".
- xxs 6y ago> "The one with Turing complete templates" Java has Turing complete generics as well
- Mindless2112 6y ago
- asperous 6y agoI think the reason is that the concepts are so abstract, no concrete word makes sense. So in the face of an arbitrary choice people use names. The situation isn't much better in computer science, where now when you look up half the simple nouns in the dictionary, you get some language, tool, or javascript library claiming it.
- didibus 6y agoExactly, if you pick a name that kinda sorta describes the concept, but not really because it's a very precise abstract technical concept and actually has no real parallel with day to day mondaine life, it doesn't actually help people understand the concept. Often time it actually gives them the wrong impression. I think beginners are looking for shortcuts, can I reduce this complicated thing into something I already know? And the truth is, you can't, if you could, it would be a trivial concept and there'd probably be nothing interesting about it to learn in the first place.
- aeternum 6y agoIt seems like very few concepts are truly unique. At the very least, they have some relation to other concepts so it would be advantageous to make up a name/word that is similar to an existing concept.
- didibus 6y agoWhy? It's not the same concept, just vaguely similar to some other thing. But all of the interesting aspects are in the difference, otherwise we wouldn't bother mathematically with the concept in the first place. Similar != Same And treating similar things as same is the source of a lot of error and confusion and misinterpretation. If its just to help a beginner at first with a little bit of understanding, you can just say X is a bit like Y, but also very different in really important ways so forget most of what you assume about X, because Y does not work like X, even though it has relations to it.
- 6y ago
- superhuzza 6y agoI actually agree with the author's premise, I think she makes a good case that some of these concepts would be both more approachable, and more memorable, with simpler names. However, coming up with simple names is incredibly difficult. It's easy to write a 10,000 word on a complicated topic, but incredibly difficult to squish it into a few letters.
- pbhjpbhj 6y agoYes, agreed with the second part. >"Why do mathematicians continue to proffer and accept this courtesy, when it increases their own mental load and makes their own work more opaque?" (the OP) // I imagine because it doesn't increase their mental load? It might even reduce it; abstraction is a principle component of the field after all. Using descriptive names sounds like it requires a half-arsed disabstraction, a series of munged verbose partial truths? Naming for authors is partially self-documenting too, though practically that's probably not often useful.
- YetAnotherNick 6y agoAnd bad naming might even make things worse as the reader might get the wrong idea.
- dorchadas 6y agoOr you end up with things like 'clopen' sets, which are both closed and open!
- abnry 6y agoThis is exactly how I feel. What I do think you can criticize, however, is the lack of imagination mathematicians have in naming theorems. If only there were more Ham Sandwich Theorems [1]. [1] https://en.wikipedia.org/wiki/Ham_sandwich_theorem https://en.wikipedia.org/wiki/Ham_sandwich_theorem
- d2v 6y ago> The two-dimensional variant of the theorem (also known as the pancake theorem) can be proved by an argument which appears in the fair cake-cutting literature This is the first time that reading about math has made me hungry.
- mikewarot 6y agoThe alternative is common words meaning different things, depending on field or specialty. Case in point: Entropy
- davidivadavid 6y agoWhich is actually helpful because it potentially helps build bridges and analogies between fields by recognizing similar constructs?
- gridlockd 6y agoMeh. Shaka, when the walls fell.
- woopwoop 6y agoI don't think descriptive names per se would be especially helpful. The challenge of understanding a concept typically dwarfs the challenge of remembering a name. Some people, though, have so many things named after them that Googling for concepts can become challenging. In my thesis, I needed to use something called the Steiner point, which is sometimes also called the Steiner curvature centroid, although I didn't know about this name at first. For a convex set K, this is the limit, as R goes to infinity, of Bar(K + B(0,R)), where Bar(L) denotes the barycenter of L. This is the unique continuous map S on convex sets with the two properties (i) S(K) is in K for all K (ii) S(aK + bL) = a S(K) + b S(L). It is also the map on convex sets satisfying (i) which has the smallest possible Lipschitz constant when the space of compact convex sets is endowed with the Hausdorff metric. It took me a while to get a thorough enough grasp on the literature to learn these things, though, because when you Google "Steiner point", you mostly get stuff about a triangle center, also named after Steiner, which is a totally different concept. It's not that I thought this other triangle center was the Steiner curvature centroid, it was that I literally didn't know what to search for in order to get results on the Steiner point I was interested in.
- abnry 6y agoI don't see how your example proves your point. It is not plausible to think about curvature when discussing triangles (you may discuss curvature of constructed circles, but that's tautological to the size of the circles...) so searching for "Steiner Curvature Point" should help find what you need faster.
- woopwoop 6y agoBut at the time I didn't know the phrase "Steiner curvature centroid", I just knew "Steiner point". The definition I knew was not in terms of the curvature, or in the terms I gave above, but as a certain integral of the support function. As an aside, the Steiner curvature centroid has a perfectly reasonable interpretation in terms of the "curvature" of a triangle. For a convex set in the plane with smooth boundary, the Steiner curvature centroid is equal to the barycenter of the probability measure on the boundary weighted proportionally to the curvature. Given a triangle, take a sequence of smooth convex sets converging in Hausdorff metric to the triangle, and the limit of the Steiner points of these will converge to the following thing: the average of the vertices of the triangle weighted proportionally to pi - the angle. This is the analogue of the barycenter of the curvature-weighted perimeter for triangles.
- petermcneeley 6y agoWe all know what this article is really about. It is disappointing to see these kinds of articles on hn. (posted multiple times as well) ref: http://www.paulgraham.com/say.html http://www.paulgraham.com/say.html
- klyrs 6y agoSpeaking as a mathematician, I have zero idea what you think this article is "really about." So (a) your statement has at least one counterexample, and (b) would you be so kind as to explain what it's really about? Edit: you added a link to a pg essay about self-censorship. Pretty droll excuse to not say what you mean.
- dqpb 6y ago> We all know what this article is really about I don’t. What is this article really about?
- detaro 6y agoUh, nope?
- jmeister 6y agoI came here to make the same comment so I’ll be the explainer: It’s about erasing white male names/dominance/influence/privilege/?? from math history.
- klyrs 6y agoThis is a classical example of attacking the very weakest form of one's arguments. Not even addressing the content in the article, but fabricating a strawman instead. I mean, good on ya for speaking up, your parent just spoke in vague terms about the possible existence of a strawman. And let's look at that pg article. Is discussing the ergonomics of naming things in math taboo? Is it taboo for everybody, or just people of certain demographics?
- Nesco 6y agoEven if it were the hidden objective, the arguments given are still pretty convincing
- dheera 6y agoMy biggest gripe with mathematical naming isn't what the author wrote, but by the inconsistency of noun/adjective endings. For example, Hermitian and Brownian are adjectives, much like Ethiopian or Libertarian or anything else ending in -ian. But Hamiltonian, Jacobian, and Lagrangian are nouns. I'd much prefer they be called the Hamilton, the Jacob, and the Lagrange, for consistency in syntax in parsing. It always trips up my mental English parser when someone says "the Hamiltonian" and I'm always like "the Hamiltonian what? what is or isn't Hamiltonian?"
- 2038AD 6y ago'Ethiopian' and 'Libertarian' are both also nouns
- dragonwriter 6y ago> For example, Hermitian and Brownian are adjectives, much like Ethiopian or Libertarian or anything else ending in -ian As noted in a sibling comment, Ethiopian and Libertarian are both also nouns. As are lots of things ending in -ian, some also adjectives, some not (mathematician, statistician, magician, parliamentarian, crossopterygian, historian, librarian, fruitarian,...)
- mattkrause 6y agoYou could just write out “Hamiltonian {operator, path, system, etc}, but it’s not uncommon for adjective+nouns to be shortened to just the adjective when it’s obvious from context. If you want good Italian [food], you might ask an Italian [person] to translate some Italian [text] you saw in a restaurant review.
- drichel 6y ago> "In the last decade, the field of algebraic geometry was set on fire by “perfectoid spaces” rather than “Scholze spaces” because Peter Scholze kept on calling them that in his talks and papers." Skip to 5:10 to see Peter Scholze apologize for the name: https://youtu.be/J0QdTYZIfIM https://youtu.be/J0QdTYZIfIM
- kazinator 6y ago> Imagine how much steeper the learning curve would be in medicine or law if they used the same naming conventions, with the same number of layers to peel back: I she kidding? Off the top of my head: diseases named after people. Parkinson's disease. McArdle's disease. Bell's Palsy, Hodgkin's Lymphoma, ... https://en.wikipedia.org/wiki/List_of_human_anatomical_parts_named_after_people https://en.wikipedia.org/wiki/List_of_human_anatomical_parts... In Law, precedents are referred to by plaintiff and defendant names: Smith vs. Klein. There are laws named after people, e.g. in the US. Kirsten's Law; Mann Act; Wetterling Act; Sonny Bono Copyright Extension; ...
- TylerE 6y agoIn medicine they are often named after the first (documented) patient, not the discoverer.
- stan_rogers 6y ago"Often", here, should be read as "quite rarely".
- hcs 6y agoA lot of medical and legal terms are literal in some way, but Greek or Latin, so I don't know how much that helps.
- fortran77 6y agoI always wanted to propose my own "Reuben's Law" (named for me) -- no more laws shall be named after dead children.
- gnusty_gnurc 6y agoI guess historians have an impossible job! Having not read the article, is it possible she’s arguing the similar notion of erasing history because it’s psychologically unbearable for some people?
- kgonza 6y ago
- parsimo2010 6y agoThis falls a little flat with me. Let's consider an example from the article- a Kähler manifold. I'm not a geometer, so I looked it up on Wikipedia, and it says that a "Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a Riemannian structure, and a symplectic structure." https://en.wikipedia.org/wiki/K%C3%A4hler_manifold https://en.wikipedia.org/wiki/K%C3%A4hler_manifold Two of those things are not named after a person, and none of them are understandable without special training. Naming something after a person doesn't make it any harder to understand unless there are multiple things named after that person and you can't figure out which they mean from the context. In case you're wondering about those structures, here is what Wikipedia has to say about them: - A Riemannian manifold "is a real, smooth manifold, M, equipped with a positive-definite inner product g_p on the tangent space T_p M at each point p." - "A complex manifold is a manifold with an atlas of charts to the open unit disk in C^n, such that the transition maps are holomorphic." - "A symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2-form ω, called the symplectic form." The only thing in the above descriptions accessible to non-specialists is probably that the Riemannian manifold is probably named after that guy that they heard of in calculus class. Let's not get rid of our ability to honor people in a failed attempt to make the communication more effective. You can call a Riemannian manifold or a Kähler manifold whatever you want, but it's not going to prevent someone from having to spend years before they are able to understand them.
- abnry 6y ago> Let's not get rid of our ability to honor people in a failed attempt to make the communication more effective. I think we should honor mathematicians less with eponymous theorems (prestige culture is toxic), but I agree it shouldn't be done at the expense of worse communication.
- chongli 6y agoWhat's so toxic about honouring a long-dead mathematician? The article praises the Ancient Greeks and how they named things after their teachers. That, to me, is far more problematic. The history and the effort that went into developing the theorems of geometry presented by Euclid's Elements are all lost. Now we only know about Euclid, Pythagoras, Archimedes, and maybe a few others. On the other hand, we know far more about the lives of Fermat, Euler, Gauss, Riemann, and Newton. While we can't owe all of the work of historians to eponymous topics, the use of their names in everyday mathematics helps to keep their memory alive so that new generations of people may be interested in learning about the history of mathematics.
- saithound 6y agoThis 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.
- timkam 6y agoHumans are social beings. An abstract concept that is named after its human creator establishes an immediate link to this person. My guess is that many people like this, because it adds a social dimension to otherwise "dry", technical papers.
- crazygringo 6y agoHard disagree. Once you get to the advanced levels of any field, terminology being "accessible" doesn't really matter, but being precise does. Areas like philosophy and law actually suffer in my opinion when they overload common words with uncommon meanings, or descend into weird disambiguations that depend on suffixes. For example, in philosophy there's "contractarianism" and "contractualism", and trying to remember which is the general term and which refers to a specific theory drives me nuts. (If "contractualism" were just known as "Scanlon's theory" it would be a lot easier.) Naming things after their creator is actually super-helpful because it's really easy to disambiguate, helps situate things historically, and once you're at that level there often isn't a single unique word or phrase that can easily encapsulate the idea anyways and isn't easily confused with something else.
- didibus 6y agoCompletely agree. And when using common terms, people also make all kind of assumptions from it, and that comes with a bias, before even getting a grasp of the concept it describes in a given field.
- dvt 6y agoGoing to pile on to the agreement here -- for example, much confusion can be had when discussing things like "intentionality" with laypeople. Philosophy is riddled with regular words that take non-regular meanings. It might make philosophers feel smart, but it's a detriment to the field imo.
- boomboomsubban 6y agoMuch, though not all, of this is due to philosophers discussing ideas from the past three thousand years originally in a multitude of languages. How should one discuss a "Platonic Idea" without confusion of a general idea?
- nabla9 6y agoYet another example: International relations theory overloads "Liberalism", "Realism" and "Idealism". It's too easy to project meaning for already overloaded words like these. Long articles and opinion pieces are written by people who saw something with these words and it never occurred for them that they should check out what these words mean in the context.
- YetAnotherNick 6y agoI disagree. There are only few cases in which you can describe a mathematical concept with few meaningful words. Like this is the list of number types I could think of. If you don't know it, there is no benefit of knowing what it is called in English. Are rational numbers rational, and are imaginary numbers imaginary? Can the author come up with better name than this, I doubt so. Rational numbers Real numbers Imaginary numbers Complex numbers(including imaginary numbers) Hypercomplex numbers Hyper real numbers Surreal numbers
- davidivadavid 6y agoRational numbers are ratios.
- mdonahoe 6y agoMaybe I misinterpreted what the author is trying to say by using Conway as an example, but I don’t think Conway discovered the Monster group. He credits Fischer and Griess. Conway just referred to it as a monster while corresponding with Fischer and the name stuck.
- hprotagonist 6y agomeanwhile, fields that do feel at liberty to come up with “common word names” usually wind up reinventing 18 names for the same goddamn thing. ML/data science/statistics is notoriously bad at this. It took me about 3 months to realize that i’d known what “ReLu activation” was for a decade by another established name.
- markgall 6y agoI agree that this article is basically preposterous. But there is a grain of truth in it. The foundations of algebraic geometry were basically rewritten in the 1960s by Alexander Grothendieck, perhaps the greatest mathematician of the 20th century. He found names to be extremely important, and many of the basic objects that he developed have very carefully conceived and suggestive names: schemes, stacks, topoi, etale morphisms, dessins d'enfant,... none of which will I attempt to define here. But all of these have stuck. On the other hand, things other than the foundations of the subject? Sure, name it after who did it. Suggestive names aren't really possible for most stuff.
- atrettel 6y agoI have often found eponyms confusing and I try to avoid them when a good alternative exists. Take "Gibbs free energy" as an example. I had trouble remembering what it is compared to "Helmholtz free energy", but then I learned that "Gibbs free energy" is actually "free enthalpy", at which point I could remember it more easily. Perhaps my point isn't that eponyms are bad, per se, but that it is much better to have descriptive names if possible, and better yet to have self-discoverable and structured names. Stigler's law [1] also exists, and I have found far too many eponyms to be named after people who had nothing to do with the concept (and sometimes they did not want their name attached to it even). Eponyms have the advantage of being short and simple. Descriptive names can be pretty wordy. Take "Mach number" as an example. Surely I can call it the "ratio of the velocity to the speed of sound", but that's pretty much the definition at that point. "Mach number" saves a lot of space. Terms like "sonic number" or "sonic ratio" could also work, but everyone already knows what the "Mach number" is, so there is no point in introducing a new word needlessly and sowing confusion (in my opinion). [1] https://en.wikipedia.org/wiki/Stigler%27s_law_of_eponymy https://en.wikipedia.org/wiki/Stigler%27s_law_of_eponymy
- kaetemi 6y agoAnd more descriptive variable names would be handy too. The whole field seems optimized towards obfuscation.
- Waterluvian 6y agoI have no opinion on naming stuff at advanced levels. But in high school and university I felt a palpable frustration on a very regular basis for randomly named stuff. I couldn’t and still can’t get my brain to remember things with unrelated names. So when I learn about and need to recall “isostatic rebound” and not “the Chip Dipson Effect” it just eliminates an entire layer of key lookup and parsing I have to do.
- chromatin 6y agoThis article really betrays a lack of deep understanding of the concepts involved.
- glennon 6y agoTangential--I used to work with a lot of caves as a hydrogeologist: Seven favorite cave names: Abisso "Queen Mama", Big Cave with Bats, Cave of the Swords, Eisriesenwelt (world of the ice giants), Hell Below, Lemon Drop, Mad As A Wet Hen Pit Nice caves, but seven names that could use some help: Carroll Cave, Ellison's Cave, Fitton Cave, Kartchner Caverns, Lehman Cave, Lilburn Cave, Russell Cave
- yongjik 6y agoMeh, that's like saying it's so hard to remember San Francisco from San Jose from Mountain View from Palo Alto, why can't we just name them as Big Sea City, Big South City, Middle Town, and Expensive Town. I.e., it's a fake problem that only sounds plausible to outsiders - if you live in the Bay Area, then Mountain View being called Mountain View is the least of your problems in driving to Mountain View.
- ehmmmmmmmm 6y agoAgree, although as a Mountain View resident I'm pretty disgruntled that there is neither mountain nor view here. A town like Mammoth Lakes, CA would be a better candidate to deserve the name "Mountain View". Jokes aside there are places in the world that name themselves much more intuitively like you described. Beijing = northern capital Nanjing = southern capital Shanghai = on the sea Hong Kong = fragrant harbor Xi'an = western peace Tokyo = eastern capital Taipei = north Tai Tainan = south Tai Taichung = middle Tai Taitung = east Tai Shandong = east mountains Shanxi = west mountains etc.
- ajmurmann 6y agoMany places, even in the West, were named after unique characteristics. Language changed though. I studied in a German town called Paderborn (we lovingly called it "Paderboring" though). A river called Pader originates there and the word "born" is old German for source or spring. Many other German towns have similar names that make sense in old German or are derived from Latin names that were more descriptive but nobody understands anymore. In the USA there are many places like that as well and it's more obvious, since language hasn't changed since they were named. Ironically the landscape has due to human doing in many cases. Think Thousand Oaks, Walnut Creek, Mill Valley A sibling post makes the argument that descriptive names would eventually lose the descriptively as language changes. This is very much validated by the German names. However, that took hundreds if not over a thousand years in some cases.
- srtjstjsj 6y agoDon't forget Lone Pine Mall! https://backtothefuture.fandom.com/wiki/Twin_Pines_Mall https://backtothefuture.fandom.com/wiki/Twin_Pines_Mall
- gourlaysama 6y agoThis seems to misrepresent why people bother naming things. It's not like mathematicians are spending their time randomly naming every object/property/structure/... they encounter just for the sake of it. A "Kähler manifold" exists, as a name, because there is no way to fully describe what it is (and bring forward in the reader all the corresponding context) in two or three words. Using a long sentence (full of things that could themselves be artificial labels, recursively) instead would be a waste of everyone's time. If one can use a short descriptive name for something, then it's not a name, it's just the thing, and everyone refer to it directly. And when you can't, or when you want to indicate its importance, or you want to neatly package all the relevant context about it, all the mathematical baggage that should come with it in something short, then the pretty obvious thing to do it to abstract it away and stick a label on top. It doesn't really matter whether they use mathematicians, flower names or characters from The Lord of The Rings, as long as it's unique enough, in context, then it's fine. The names become part of the vocabulary of the field, just as much as supposed "descriptive" names. All those "descriptive" names have to be precisely defined too anyway, because they carry natural-language connotations, assumptions, and so on, that just don't apply.
- davidivadavid 6y agoUniqueness of names is definitely important — the question is can we do better? If all we want is uniqueness, we could just number theorems and concepts using GUIDs. Might as well abdicate and embrace the fact math is going to be automated, and all mathematical objects are just abstract constructs devoid of meaning that can be referred to by arbitrary labels. But it seems like there's more to it. The names of mathematicians are interesting for the genealogy of theorems... but they're also completely opaque about their semantics. Is it not possible to think a system could make math more intuitive by relying on a more structured nomenclature?
- acd 6y agoStrongly Disagree! You name things after who discovered it. In these case you name it after mathematicians like Newton, Euler, Turing, Gödel. For me its some sort of ignorance if you do not honor the one who discovered it. Other sciences has it too named after persons Fahrenheit, Celsius, Pascal etc.
- davidivadavid 6y agoWere tables invented by Mr/Mrs Table? Bottles by Mr/Mrs Bottle?
- photonemitter 6y agoWere they not?
- alpple 6y agoI think the optimal or universal language is more difficult in practice than in idealism. Reading is the art of sorting through the mess in any field, and acquiring context. I think a lot of this underestimates the complexity and nuance of language for any field.
- moomin 6y agoIf you think plain English words help with this, try either explaining what a compact space is or a normal subgroup. Or, if you don’t know, figure it out from the descriptions on the internet. And these are not hard concepts as far as maths goes.
- bmurray7jhu 6y agoDavid Hilbert was so prolific that one of his eponymous theorems was also numbered: Hilbert's Theorem 90.
- davidivadavid 6y agoJean-Pierre Serre has a fun talk where he says that to write mathematics badly, you can write papers called "A proof of a theorem of Euler", the idea being that there are so many that the title gives 0 information. https://www.youtube.com/watch?v=ECQyFzzBHlo https://www.youtube.com/watch?v=ECQyFzzBHlo
- j45 6y agoThe focus on mathematicians naming things (possibly for legacy) seems similar to the politicians venerating each others with statues. And of course... naming remains one of the hardest things to do in any field.
- prvc 6y agoSee also: https://news.ycombinator.com/item?id=24382438 https://news.ycombinator.com/item?id=24382438
- IshKebab 6y ago> Imagine how much steeper the learning curve would be in medicine or law if they used the same naming conventions, with the same number of layers to peel back: I don't think medicine or law are the best examples to use here unless you think Sarbanes-Oxley or the anterior medial malleolar artery are well named.
- firebaze 6y agoComplex things cannot be explained easily. As such, from this perspective, it doesn't matter if a complex topic is named by a person or by some abstract, ridiculously compressed word describing an aspect of it. But on the other hand, names are simply irrelevant. Anything is better than a name of a person, even if that person was brilliant. The person may be remembered as an aspect of some discovery (say, Einstein), but the concept as such should have some distinct name, not tainted by history, or mere human lifetimes. It should transcend existence as experienced by a human.
- lambdatronics 6y agoWe've got at least one physicist in our corner: "Hestenes is adamant about calling this mathematical approach “geometric algebra” and its extension “geometric calculus,” rather than referring to it as “Clifford algebra”." https://en.wikipedia.org/wiki/David_Hestenes#Geometric_algebra_and_calculus https://en.wikipedia.org/wiki/David_Hestenes#Geometric_algeb... Unfortunately, this should really be called algebraic geometry, but that name is already taken by another field...
- DreamScatter 6y agoCome on, switching geometric algebra and algebraic geometry makes no difference.
- WoahNoun 6y agoThe name Teichmüller needs to be deleted from modern mathematics. I don't care about slippery slope arguments. He was an adamant Nazi and the fact that his name represents a large portion of modern mathematics is abhorrent. Especially with prisoner of war Jean-Leray being far more influential with his idea of sheaves that was conceived while he was a POW. Yet we don't hear his name nearly as often as the war criminal whose name is infused modern topology.
- krick 6y agoWell, unless Hairy Ball Theorem is called after her, I don't think it's up to her to decide, what mathematicians "should" do. Jeez, these journalists researching "computational morality"... To be fair, I do actually think some math jargon is unnecessarily complex and we could do better, and that it is something that actually matters. And I do think, for instance, that "commutative group" is better than "abelian group", since it is descriptive, unlike the latter. But this rarely is the culprit. Kähler manifold is called after Kähler, because he is the one who introduced such a thing, and we don't really have any better name to describe it. (And it wasn't Kähler who named it after himself too.) Can she propose a better name? I'm curious to hear it, but she conveniently skips that issue in her musings. If not, this whole argument of hers is just silly, as is thinking that "monster group" is a "cool name". It is not cool, it's rather awful, it's called that precisely because we don't have a clue WTF this thing is, and I sincerely hope that some 300 years later we'll have a much better understanding of group theory to rewrite all that stuff and to see that "monster group" is not such a "monster" after all, but quite a natural thing, that can be described conveniently and assigned some proper name. So if we want to improve the landscape, let's rather start small, by abandoning π in favor of ½τ. Let's see how many centuries that will take.
- WoahNoun 6y agoA Kahler manifold is just a complex manifold with both a Riemann metric and a sympletic (Hamiltonian) form. It's not a rare class of manifolds and while the "adjective" Kahler has come to mean those properties. Why not call it a Reimann-Hamilton manifold if we care so much about the "history"?
- krick 6y ago> Kähler manifold is a bad name, stop naming things after each other! > Why not call it a Reimann-Hamilton manifold I'm not sure if this is top-notch sarcasm or not, but I'll upvote just to be safe.
- WoahNoun 6y agoI'm not suggesting that name. I'd prefer it was called a symplectic smooth inner product manifold. I'm merely pointing out the hypocrisy of the "name it after the discoverer argument"
- 8note 6y agoAn important thing for name sis that you want them to be immutable because it's hard to refactor both all the writing using that name, and everyone's memory to change the concept of a spheroid from one definition to another. This makes it hard to choose generic names from the get-go since the first person to use name might not attach it to the best concept for it, making it unavailable for the best concept for the name to describe. ----- I've always imagined people's names in concept names to be a shorthand for the papers that defined them. Eg. "Calabi-yau manifold" is just another way to write "manifolds as described by calabi and Yau in <well known paper>" and importing all the detailed definitions from that paper. To get the same from properties from a generic name, you need to get a canonical definition that everyone agrees with
- lambdatronics 6y agoYeah, arguably geometric algebra and algebraic geometry should switch labels. Algebraic geometry is geometric techniques for solving polynomials (algebra) so it should really be geometric algebra. OTOH, geometric algebra is an algebraic formulation of geometry -- so that should be algebraic geometry. shrugs
- DreamScatter 6y agoI work with geometric algebra (I'm the developer of Grassmann.jl) and I disagree, I don't think it matters whether the two topics change their name.
- karxxm 6y agoPlease give me only one example how one can come up with a single name for a complex mathematical concept. There are so many details, that the naming can never be precise enough to be useful. But they need to be named. So why not by their inventors?
- Grustaf 6y agoThe fact that mathematics honors the people that built it is one of the things I love the most about it. But speaking practically, it’s by far the beat option in many cases. There might be a small number of basic concepts (like dodecahedron or inverse) that can be given actually descriptive names, but for anything even slightly complex it’s impossible, so we end up with a mixture of almost nonsensical and often confusing “descriptive” names, and concepts named after people. Is it harder to remember and distinguish “Hamiltonian”, “Dirac delta” or “Lagranian” than “cohomology”, “homomorphic” and “homeomorphic”? Having said that, in many cases the names are quite evocative, like “fibre-bundle”.
- palae 6y ago> Is it harder to remember and distinguish “Hamiltonian”, “Dirac delta” or “Lagranian” than “cohomology”, “homomorphic” and “homeomorphic”? While I agree with your overall point, I must note that you did write Lagranian instead of Lagrangian ;)
- Grustaf 6y agoAh you got me. Although those Greek and Latin names aren’t always trivial to spell either!
- rajbiswas125 6y agoNaming this is things is hard. Also many of the people who are doing their PhD dream of one day having a theorm named after them.
- Grustaf 6y agoI’d suggest that people that prefer “descriptive” names should come up with clever descriptive names the next time they invent a new mathematical concept or prove a new theorem. I’m quite sure nobody will try to stop you.
- matthewmorgan 6y agoYeah let's stop reminding people that it was mostly white men who invented everything
- xg15 6y agoIT equivalent: Obscure shell commands with one-letter flags and a manpage that really wanted to be a novel.
- ezoe 6y agoIf it's unique name, it's fine. What I don't like it is math notations. Many math notations requires complex typesetting and layout which cannot be expressed in the plain text. It may be not much of a problem when math notations were written by hand, but not anymore in the age of computer. The mathematicians should have invented and standardise the notation that can be expressed as the plaintext decades ago.
- footballnate29 6y agoWhy. They spend all that time dedicating their life to their research. They deserve to name shit after themselves?
- Xlurker 6y agoHumans are vain, it's just how it is.
- NashHallucinate 6y ago>Polish Mathematicians never getting things named after them because their names were too hard to spell
- dmckeon 6y agoThe pattern of using eponyms instead of descriptives is also recognized in medicine: https://scopeblog.stanford.edu/2020/01/30/eponym-debate-the-case-for-biologically-descriptive-names/ https://scopeblog.stanford.edu/2020/01/30/eponym-debate-the-...
- rosywoozlechan 6y agoYou know, why don't you discover some new ridiculously hard thing and then you get to decide to not name it after yourself? This level of entitlement is beyond the pale.
- kepler1 6y agoOh thank god. I thought the point was going to be that naming things after people was discriminatory to women and minorities.
- valw 6y agoHere we see the classic tension between synthetic names and natural names. The best discussion I've seen of this topic is in the 1st chapter (which is fortunately freely accessible and concise) of this excellent programming book: https://leanpub.com/elementsofclojure/read_sample https://leanpub.com/elementsofclojure/read_sample Relevant excerpt: > Most natural names have a rich, varied collection of senses.3 To avoid ambiguity we must use synthetic names, which have no intuitive sense in the context of our code. > Category theory is a rich source of synthetic names. ‘Monad’, to most readers, means nothing. As a result, we can define it to mean anything. Synthetic names turn comprehension into a binary proposition: either you understand it or you don’t. Between experts, synthetic names can be used to communicate without ambiguity. Novices are forced to either learn or walk away. > Conversely, a natural name is at first understood as one of its many senses. Everyone understands, more or less, what an id is. In a large group, however, these understandings might have small but important differences. These understandings are refined, and gradually converge, through examination of the documentation and code. At the cost of some ambiguity, novices are able to participate right away. > Natural names allow every reader, novice or expert, to reason by analogy. Reasoning by analogy is a powerful tool, especially when our software models and interacts with the real world. Synthetic names defy analogies,4 and prevent novices from understanding even the basic intent behind your code. Choose accordingly.
- muzani 6y agoI think good naming convention is something like Chesterton's Fence. "Fence" describes the idea well, and "Chesterton's" makes it unique. Something like "Djikstra's Algorithm" is too vague. Maybe if it were something like "Djikstra's Path", it would be easier to understand.
- tazedsoul 6y agoI’m not opposed to naming things after people. That said, I often suspect that the naming conventions and rituals of mathematicians (and sometimes physicists) serve as gatekeeping mechanisms that make life extra difficult for newcomers to a field while preserving the authority of current experts in a field by turning their history and duration of involvement into a more powerful resource than it probably deserves.
- ineedasername 6y agoThis is not a naming problem. In fact the naming is consistent: There's a base-case "manifold". Another one build on top of it; another one build on top of that second one, etc. This is precisely how knowledge is built, one thing on top of another. Naming would not have solved this "manifold" issue, in fact in would have obscured the root of that bit of knowledge. In short, the author's real problem isn't names, is that they don't fully appreciate the way knowledge is built with ever more complex layers of abstraction.
- tazedsoul 6y agoAlso, naming things is hard. If the things you are naming are specific concepts, and the conclusions reachable by reasoning about such concepts are highly sensitive; that is highly dependent upon such specificity, then the problem of naming things is even harder. I think this may be because what is hard about mathematics is the degree to which specificity matters. The names are just pointers to ideas, and these ideas are often unique but similar to one another, with differences that matter. It’s as if in naming a mathematical concept we are performing a compression algorithm on an object of great detail. A loss of information is expected. Of course, this process is an art form. Are some names easier to remember than others? Are there good names? Bad names? Of course. But I do think generalizing that “naming ideas based off people is bad” to all cases is a bad idea — rather a mixed approach is fruitful.
- vertbhrtn 6y agoThis is some mediocre people came up with idea that they could easily understand what Calabi-Yau manifold is, if only mathematicians defined it with simple plain words. They don't like the idea that such a full definition would be 1000 pages long, full of complex concepts.
- valand 6y agoName is like a pointer to an information for people to access. I think when people name things, unless they are very narcistic, should be having that sole purpose in mind. This comment by xamuel relatably describes what people usually do when naming things https://news.ycombinator.com/item?id=24386695 https://news.ycombinator.com/item?id=24386695 > Rather, what really happens is that mathematicians are a community, and they refer to things in whatever way is convenient. Davis's colleague refers to such-and-such theorem as "Davis's Theorem" not because of some committee on naming, but rather because they were there at the conference where Davis announced the theorem, and everyone at said conference excitedly talked about "Davis's Theorem" for the whole rest of the conference because it was so exciting. The arguments that say names should be self descriptive is only a part of the discussion. There's the name overloading problem, where we only have a limited set of existing descriptor which can cause two object name to conflict. There's the memorability aspect. There's the homophonic / homographic problem where multiple names could be perceived differently. There's the complexity aspect. The more complex an information, the harder it is to write an accurate name. There's context aspect. There's the extreme connotation aspect. Some words triggers extreme emotional response to someone. There's the dependency aspect where people have been using a name for years. All in all, naming things are hard problem. But the important thing is naming things should be done for the sake of naming things in mind. If naming things is done primarily for other agenda, like someone's glory, the result might be questionable. Assuming that people are naming things for the right cause, problems that arise from names should not be attributed to naming process. For example the article author's problem might be simply caused by the complexity of the information referred by the name. Edit: grammar and formatting
- bikenaga 6y agoI recall Paul Halmos (https://en.wikipedia.org/wiki/Paul_Halmos https://en.wikipedia.org/wiki/Paul_Halmos) once advocated for naming things in mathematics descriptively rather than honorifically. I recall his argument was that it aids in recall and understanding to name descriptively, and that there are better ways to honor discoverers. I found this statement in "How to Write Mathematics" (https://bookstore.ams.org/hwm https://bookstore.ams.org/hwm): "... surely I cannot stop without a discourse on the proper naming of concepts (why 'commutator' is good and 'set of the first category' is bad) and the proper way to baptize theorems (why 'the closed graph theorem' is good and 'the Cauchy-Buniakowksy-Schwarz theorem' is bad)." I thought he'd said more in "I Want to be a Mathematician" (https://www.springer.com/gp/book/9780387960784 https://www.springer.com/gp/book/9780387960784), but I just looked through the book and couldn't find anything. (Halmos was a particularist, and thought very highly of examples, and "I Want to be a Mathematician" has examples/opinions of how to do nearly everything in the profession, from teaching to writing to being a department chair to giving talks to doing research ... He was very opinionated, but also specific and absolutely clear, so at least if you disagree with him you know what you're disagreeing about.)