Something that frustrates me, and maybe I’m just confessing my stupidity, is the extra layer of indirection in any discipline when things are named after people and not the thing’s characteristics.
My doctor once told me “if you learn enough Latin, a lot of names in medicine will hint at what they are, so you have less to memorize.”
I find that these names often lend a sense of complexity to concepts that turn out to be rather simple. In high school this really contributed to my struggles.
Edit: apparently Eigen isn’t a person’s name so I sure picked an embarrassing moment to bring this up.
> is the extra layer of indirection in any discipline when things are named after people and not the thing’s characteristics.
"Eigen" in German has same English root as "own": "Eigenvalue" is Germanglish for "Own/inherent value", so meets your spec of naming a thing after its characteristics, as long as "naming" is allowed to be in multiple languages.
How I learnt/taught myself when I first studied this subject, was characteristic or character. People change when they come into money, or rather their character changes (in my head I called them characterless). People with character don't change. Characteristic vector/Eigen vector is something which doesn't change.
I recently embarked on a journey to come up with a math vocabulary for Toki Pona, a lovely little artistic conlang which deserves better than what I'm doing to it. In Toki Pona, words are build up from simpler ones to describe a thing as it is. A friend is 'jan pona', a person who is good (to me, the speaker). So I've had to come up with names which describe math topics.
It's awful.
You know how many same-xs there are?! Eigenvalue, eigenvector, homomorphism, isomorphism, homeomorphism, homotopic. Which one gets to actually be "same shape"? Worse are when well meaning mathematicians use descriptive names anyway. Open and closed are not mutually exclusive, giving rise to the awful clopen (and don't pretend like ajar helps. an ajar door is an open door!). Groups, rings, and fields all sort of bring to mind the objects they describe, but only after you know the archetypal examples. Math is the study of giving the same name to different things, and that gives rise to more names than there are short descriptions.
So do you know what I did? Whenever I could, I used a real person's name. It freed up a limited vocabulary, and gave enough wiggle room to translate most undergrad math without too much loss. I suspect a similar thing is in play with math. Maybe the category theory people have abstractions to usefully describe "same-functions" without confusion. But in general, things are named poorly because it's genuinely a hard task.
It is sometimes very hard to name things well.
The name either becomes so unspecific that it is just as useless, or it gets so long that nobody will use it.
This gets worse the "deeper" the math goes, but for me it never was a real problem, as you usually learn the definition together with the name.
For really simple compounds, names are more or less settled and consistent (with some exceptions).
But as soon as your compound starts to get more complex (think organic chemistry) all the sudden, it becomes nigh impossible to consistently name things. There are tons of compounds with the same chemical formula that are regionally named differently. Even worse, there are tons of compounds with the same chemical formula that are actually different things due to how the compound is arranged. (Good ole carbon chains).
A common language fosters research and common understanding.
In IT, that language is English. In diplomacy, before interpreters were plentiful, that language was French. And in many classical, medieval-era sciences, that language was Latin (as a commonly-understood language that came from it's ease of being learned by romance-language speakers and being rather relevant in the (then church-run) universities).
So, there's no indirection intended. It's just an artefact of the past - an artefact that helps Chinese, Spanish and American doctors communicate (in broad strokes) even today.
My favorite is the "Lemma that is not Burnside's". Also known as the orbit-counting theorem, the Pólya-Burnside lemma, the Cauchy-Frobenius lemma, and of course Burnside's lemma.
My doctor once told me “if you learn enough Latin, a lot of names in medicine will hint at what they are, so you have less to memorize.”
I find that these names often lend a sense of complexity to concepts that turn out to be rather simple. In high school this really contributed to my struggles.
Edit: apparently Eigen isn’t a person’s name so I sure picked an embarrassing moment to bring this up.