Mathematicians should stop naming things after each other • Hacker News Board

Re: Mathematicians should stop naming things after each other

#61

Post by mehrdadn » Sat, Sep 05, 2020, 6:41 PM UTC

OskarS wrote: post #53

mehrdadn wrote: post #11

Not 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…

Another example is Abelian groups, which should just be called commutative groups. Though that example brings up a decent counterargument to the thesis: ”groups”, ”rings” and ”fields” all have descriptive names, but that doesn’t help a bit, they’re still mad confusing. They’d almost be easier to pick apart if they were named after people.

+1 for commutative groups.

Interesting point! So like we'd rename group theory to Galois theory? :)

Re: Mathematicians should stop naming things after each other

#62

Post by hprotagonist » Sat, Sep 05, 2020, 6:41 PM UTC

meanwhile, 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.

Re: Mathematicians should stop naming things after each other

#63

Post by mycl » Sat, Sep 05, 2020, 6:41 PM UTC

aaron-santos wrote: post #7

The 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.

The 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...

Re: Mathematicians should stop naming things after each other

#64

Post by lixtra » Sat, Sep 05, 2020, 6:41 PM UTC

will4274 wrote: post #25

lixtra wrote: post #2

Some profiling would show that names increase the difficulty of math by 0.001%. I don’t see an issue here.

> 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.

I 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.

Re: Mathematicians should stop naming things after each other

#65

Post by didibus » Sat, Sep 05, 2020, 6:44 PM UTC

crazygringo wrote: post #55

Hard 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 remembe…

Completely 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.

Re: Mathematicians should stop naming things after each other

#66

Post by markgall » Sat, Sep 05, 2020, 6:45 PM UTC

I 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.

Re: Mathematicians should stop naming things after each other

#67

Post by hcs » Sat, Sep 05, 2020, 6:46 PM UTC

saagarjha wrote: post #18

archgoon wrote: post #13

Yep; check out how the programming community does it! We have descriptive names for things like "Apache", "React", "nginx", "Rust", and "Java"!

Also check out "Duff's device" or "Dijkstra's algorithm" ;)

or "bool" (Boole)

Re: Mathematicians should stop naming things after each other

#68

Post by TylerE » Sat, Sep 05, 2020, 6:47 PM UTC

kazinator wrote: post #41

> 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... In Law, precedents are referred to by plaintiff a…

In medicine they are often named after the first (documented) patient, not the discoverer.

Re: Mathematicians should stop naming things after each other

#69

Post by atrettel » Sat, Sep 05, 2020, 6:47 PM UTC

I 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

Re: Mathematicians should stop naming things after each other

#70

Post by didibus » Sat, Sep 05, 2020, 6:47 PM UTC

asperous wrote: post #15

I 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.

Exactly, 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.