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My personal annoyance with Wikipedia articles on advanced math is that often it's "monoid in the category of endofunctors" on steroids. A lot of those articles

by xg15 4y ago

My personal annoyance with Wikipedia articles on advanced math is that often it's "monoid in the category of endofunctors" on steroids. A lot of those articles seem to follow a pattern of: "An A is a B that also does C". If you click on the link to understand what a B is, you get "B is a D in the space of Es with properties F and G". and so on... I can understand that this appears logically consistent and very satisfying for people who have already understood the concepts, but it doesn't help at all if you're trying to gain an understanding. A good textbook has a sense of order in which dependent concepts are introduced. With Wikipedia, the task of discovering that order is outsourced to the reader. Maybe you could develop some kind of path finding algorithm to figure out the optimal reading order for understanding a given concept, but to my knowledge, that doesn't exist yet. The other problem is that no shortcuts are offered. Even if you figure out the order yourself, Wikipedia gives you no hints how much of B, C, D, E and F you have to understand to get the idea of A. The expectation seems to be to read the entire articles on the dependent concepts, which can be long, rambling and full of obscure special cases.

Nimitz14 4y ago
Wikipedia is by definition a reference. If you want to learn something use different material. Trying to make wikipedia articles tutorials is out of scope (not that it isn't nice to get practical examples for concepts, which ime there often are!)
GTP 4y ago
But I think that this is a core difference between an encyclopaedia and a textbook. If you need the topics presented in an order that takes you from a certain level of understanding to the next, you need a textbook.
- Dylan16807 4y ago
  Well that's the problem. An encyclopedia should neither provide nor need such an ordering. But Wikipedia often does need it, while also not providing it, the worst of both worlds.
  - threatofrain 4y ago
    Wikipedia math has competition and they are generally much harsher than Wikipedia, which indicates the direction which communities of volunteers wish to go when they disagree with Wikipedia's execution. https://ncatlab.org/ https://ncatlab.org/ https://kerodon.net/ https://kerodon.net/ https://stacks.math.columbia.edu/ https://stacks.math.columbia.edu/ The people who are looking up references to advanced math concepts are likely students who are already on a mainstream pedagogical pathway and are looking to fill in holes to a concept map they're already building. The use case of someone who (1) does not wish to consult the vast and well-discussed pedagogy of math and (2) is not an advanced math student and thus wishes to have stand-alone math definitions is a Very special case.
    - Dylan16807 4y ago
      > Wikipedia math has competition and they are generally much harsher than Wikipedia, which indicates the direction which communities of volunteers wish to go when they disagree with Wikipedia's execution. Okay, but I don't think those communities are relevant to this conversation. > The use case of someone who (1) does not wish to consult the vast and well-discussed pedagogy of math and (2) is not an advanced math student and thus wishes to have stand-alone math definitions is a Very special case. Number 1 is a weird assumption! Unless by "consult" you mean spend weeks studying a textbook, the problem is that consulting is too difficult! And if I understand "harsher" correctly you just said the other sites are harder to use, didn't you? So then it's just "not an advanced math student", which may or may not be a majority of people on these pages but it's a very significant amount and it's the more important target for a general encyclopedia.
threatofrain 4y ago
There are alternative wikis for math and they’re way harsher.¹² Wikipedia is the middle ground between math wikis written by current students and professionals vs pedagogues.³ But I’d argue that if you want pedagogy or step by step proofs, then why not simply buy a well vetted textbook, of which math has many? Also, Wikipedia tried a wiki textbook project and no doubt people were very unsatisfied because they couldn’t compete with textbooks, which often have a singular pedagogical vision behind it. It’s hard to compete with famous well discussed texts. I’m happy with Wikipedia as a reference which supplements those students who are already studying the material; in other words, those students looking up topics in Linear Algebra are taking or have taken the course already. [1]: https://ncatlab.org/nlab/show/linear+algebra https://ncatlab.org/nlab/show/linear+algebra [2]: https://plato.stanford.edu/entries/algebra/#Lin https://plato.stanford.edu/entries/algebra/#Lin [3]: https://en.wikipedia.org/wiki/Linear_algebra https://en.wikipedia.org/wiki/Linear_algebra
- xg15 4y ago
  That's certainly true, buy I think it also makes it quite unsuited as a reference (except for people who are already familiar with the concepts and just need a quick reminder). Wikipedia math articles are not useful to get a shallow understanding of a topic. On the contrary, it pulls you into a rabbit hole of dependent concepts just for you just to be able to understand the words in the article's summary. From an actual reference, I'd expect that it gives a brief, self-contained description of the basic idea of a concept, without going too deep into specifics, possibly with a "see also". That's not what Wikipedia does.
random314 4y ago
Have you tried Simple wikipedia? Also, wikipedia is a reference, not a textbook.

by xg15 4y ago

Nimitz14 4y ago

Wikipedia is by definition a reference. If you want to learn something use different material. Trying to make wikipedia articles tutorials is out of scope (not that it isn't nice to get practical examples for concepts, which ime there often are!)

GTP 4y ago

But I think that this is a core difference between an encyclopaedia and a textbook. If you need the topics presented in an order that takes you from a certain level of understanding to the next, you need a textbook.

Dylan16807 4y ago
Well that's the problem. An encyclopedia should neither provide nor need such an ordering. But Wikipedia often does need it, while also not providing it, the worst of both worlds.
- threatofrain 4y ago
  Wikipedia math has competition and they are generally much harsher than Wikipedia, which indicates the direction which communities of volunteers wish to go when they disagree with Wikipedia's execution. https://ncatlab.org/ https://ncatlab.org/ https://kerodon.net/ https://kerodon.net/ https://stacks.math.columbia.edu/ https://stacks.math.columbia.edu/ The people who are looking up references to advanced math concepts are likely students who are already on a mainstream pedagogical pathway and are looking to fill in holes to a concept map they're already building. The use case of someone who (1) does not wish to consult the vast and well-discussed pedagogy of math and (2) is not an advanced math student and thus wishes to have stand-alone math definitions is a Very special case.
  - Dylan16807 4y ago
    > Wikipedia math has competition and they are generally much harsher than Wikipedia, which indicates the direction which communities of volunteers wish to go when they disagree with Wikipedia's execution. Okay, but I don't think those communities are relevant to this conversation. > The use case of someone who (1) does not wish to consult the vast and well-discussed pedagogy of math and (2) is not an advanced math student and thus wishes to have stand-alone math definitions is a Very special case. Number 1 is a weird assumption! Unless by "consult" you mean spend weeks studying a textbook, the problem is that consulting is too difficult! And if I understand "harsher" correctly you just said the other sites are harder to use, didn't you? So then it's just "not an advanced math student", which may or may not be a majority of people on these pages but it's a very significant amount and it's the more important target for a general encyclopedia.

threatofrain 4y ago

There are alternative wikis for math and they’re way harsher.¹² Wikipedia is the middle ground between math wikis written by current students and professionals vs pedagogues.³ But I’d argue that if you want pedagogy or step by step proofs, then why not simply buy a well vetted textbook, of which math has many? Also, Wikipedia tried a wiki textbook project and no doubt people were very unsatisfied because they couldn’t compete with textbooks, which often have a singular pedagogical vision behind it. It’s hard to compete with famous well discussed texts. I’m happy with Wikipedia as a reference which supplements those students who are already studying the material; in other words, those students looking up topics in Linear Algebra are taking or have taken the course already. [1]: https://ncatlab.org/nlab/show/linear+algebra https://ncatlab.org/nlab/show/linear+algebra [2]: https://plato.stanford.edu/entries/algebra/#Lin https://plato.stanford.edu/entries/algebra/#Lin [3]: https://en.wikipedia.org/wiki/Linear_algebra https://en.wikipedia.org/wiki/Linear_algebra

xg15 4y ago
That's certainly true, buy I think it also makes it quite unsuited as a reference (except for people who are already familiar with the concepts and just need a quick reminder). Wikipedia math articles are not useful to get a shallow understanding of a topic. On the contrary, it pulls you into a rabbit hole of dependent concepts just for you just to be able to understand the words in the article's summary. From an actual reference, I'd expect that it gives a brief, self-contained description of the basic idea of a concept, without going too deep into specifics, possibly with a "see also". That's not what Wikipedia does.

random314 4y ago

Have you tried Simple wikipedia? Also, wikipedia is a reference, not a textbook.