4 ms·

Math wiki pages are so bad. Would it kill them to use concrete examples? Why does it have to be written so that only mathematicians can understand it? It’s actu

Math wiki pages are so bad. Would it kill them to use concrete examples? Why does it have to be written so that only mathematicians can understand it? It’s actually not that complicated once you know what they’re talking about, but the entry does nothing to explain it to a layman.

jiggawatts 3y ago
It’s a “thing” in certain mathematical circles to reduce everything to the purest possible definition and then refuse to sully that purity with pedestrian nonsense like practical examples. Any attempt at requesting clarification is met with: “This is the only fully general definition” or some such. It inevitably leads to articles that can’t be understood even in principle without understanding everything else already, because simple concepts are rephrased in terms of the most general (most abstracted) concepts. My favourite is that they never miss an opportunity to rephrase alternation like 0,1,0,1 in terms of exponentials raised to complex powers. Or computer algorithms that couldn’t have existed before the nineteen hundreds using symbols from Ancient Greek and maybe two other character sets just to make it more spicy if you want to “translate” it back into mere code.
svat 3y ago
The page does have concrete examples in the very first section after the lead? https://en.wikipedia.org/w/index.php?title=Untouchable_number&oldid=1145359635 https://en.wikipedia.org/w/index.php?title=Untouchable_numbe... (avoiding edits from today) — it gives the example of how 4 is not untouchable and why 5 is, and the example it gives of 5 is what the GP is asking about. How would you suggest improving it?
- earthboundkid 3y ago
  Neither example explains what a proper divisor is.
  - svat 3y ago
    It seems the root comment here had confusion/difficulty not with “proper divisor”, but with “the sum of all the” proper divisors. In any case, if your problem is that this page doesn't explain "proper divisor", then note that the phrase "proper divisor" in the first sentence is a link that goes to the relevant section of the [[divisor]] article, which has lots of examples. If the complaint behind “Math wiki pages are so bad” is simply that not every page explains everything from scratch but relies on the reader having to follow links, then this is an inherent property of a random-access reference work like an encyclopedia (rather than a careful linear presentation like a textbook), and the fact that mathematics is a subject with quite some depth (where understanding a topic requires understanding several others first). This is not unique to mathematics articles, e.g. if you go to the Wikipedia article on "init", it says: > In Unix-based computer operating systems, init (short for initialization) is the first process started during booting of the operating system. where "Unix", "operating system", "process" and "booting" are wiki links: you need to follow the links if necessary and understand them first, as this page won't start by explaining what a computer is, what operating systems are, etc. This is true for basically all topics: clicking on https://en.wikipedia.org/wiki/Special:Random https://en.wikipedia.org/wiki/Special:Random a few times, I find: > Ustilaginoidea is a [[genus]] of [[fungi]] in the family [[Clavicipitaceae]]. where you need to understand "genus" and "fungi" first, or > Masaumi Shimizu is a Japanese former professional baseball Catcher,and current the fourth squad battery coach for the Fukuoka SoftBank Hawks of Nippon Professional Baseball (NPB). where "catcher", "battery" etc are links that need to be followed (this page won't start from first principles and explain sport, baseball, catcher, etc). I think it may be instructive to compare Wikipedia math pages to something professionally published and edited like, say, The Princeton Companion to Mathematics. I just did that for a few random topics, and Wikipedia was in some cases easier to read and in some cases harder: it was not consistently better or worse. But doing this for more pages may be instructive — or simply pick some random math pages and show how they can be improved, while still remembering that in an encyclopedia much of the information necessary to understand a certain page will inevitably be at other pages.
    - earthboundkid 3y ago
      Yes, I clicked the link and read that. It wasn’t actually very relevant and did not help me understand the original article. I eventually figured it out on my own by, yes, examining the two examples they gave and proving to myself how it works. The article has a bad explanation. Untouchable numbers are a very simple idea. Any elementary school student who knows about divisors and prime numbers can have it explained to them in about ten minutes. The Wikipedia page for the article should be pitched so that a layman can understand it. I understand that if you’re writing a cookbook, you have to decide if you’re pitching it first time chefs who need “how to boil water” explained to them or professional chefs who just need references for some ratios. What serves one audience wastes the time of the other. If you want to know how init works, you probably already know what Unix is. If you’re looking up a particular species of mushrooms, you probably know how genii and species work. Untouchable numbers is a simple concept. It should not be pitched at professionals first. It should start with an explanation that a middle schooler can understand and then move on to advanced explanations in later sections.

jiggawatts 3y ago

It’s a “thing” in certain mathematical circles to reduce everything to the purest possible definition and then refuse to sully that purity with pedestrian nonsense like practical examples. Any attempt at requesting clarification is met with: “This is the only fully general definition” or some such. It inevitably leads to articles that can’t be understood even in principle without understanding everything else already, because simple concepts are rephrased in terms of the most general (most abstracted) concepts. My favourite is that they never miss an opportunity to rephrase alternation like 0,1,0,1 in terms of exponentials raised to complex powers. Or computer algorithms that couldn’t have existed before the nineteen hundreds using symbols from Ancient Greek and maybe two other character sets just to make it more spicy if you want to “translate” it back into mere code.

svat 3y ago

The page does have concrete examples in the very first section after the lead? https://en.wikipedia.org/w/index.php?title=Untouchable_number&oldid=1145359635 https://en.wikipedia.org/w/index.php?title=Untouchable_numbe... (avoiding edits from today) — it gives the example of how 4 is not untouchable and why 5 is, and the example it gives of 5 is what the GP is asking about. How would you suggest improving it?

earthboundkid 3y ago
Neither example explains what a proper divisor is.
- svat 3y ago
  It seems the root comment here had confusion/difficulty not with “proper divisor”, but with “the sum of all the” proper divisors. In any case, if your problem is that this page doesn't explain "proper divisor", then note that the phrase "proper divisor" in the first sentence is a link that goes to the relevant section of the [[divisor]] article, which has lots of examples. If the complaint behind “Math wiki pages are so bad” is simply that not every page explains everything from scratch but relies on the reader having to follow links, then this is an inherent property of a random-access reference work like an encyclopedia (rather than a careful linear presentation like a textbook), and the fact that mathematics is a subject with quite some depth (where understanding a topic requires understanding several others first). This is not unique to mathematics articles, e.g. if you go to the Wikipedia article on "init", it says: > In Unix-based computer operating systems, init (short for initialization) is the first process started during booting of the operating system. where "Unix", "operating system", "process" and "booting" are wiki links: you need to follow the links if necessary and understand them first, as this page won't start by explaining what a computer is, what operating systems are, etc. This is true for basically all topics: clicking on https://en.wikipedia.org/wiki/Special:Random https://en.wikipedia.org/wiki/Special:Random a few times, I find: > Ustilaginoidea is a [[genus]] of [[fungi]] in the family [[Clavicipitaceae]]. where you need to understand "genus" and "fungi" first, or > Masaumi Shimizu is a Japanese former professional baseball Catcher,and current the fourth squad battery coach for the Fukuoka SoftBank Hawks of Nippon Professional Baseball (NPB). where "catcher", "battery" etc are links that need to be followed (this page won't start from first principles and explain sport, baseball, catcher, etc). I think it may be instructive to compare Wikipedia math pages to something professionally published and edited like, say, The Princeton Companion to Mathematics. I just did that for a few random topics, and Wikipedia was in some cases easier to read and in some cases harder: it was not consistently better or worse. But doing this for more pages may be instructive — or simply pick some random math pages and show how they can be improved, while still remembering that in an encyclopedia much of the information necessary to understand a certain page will inevitably be at other pages.
  - earthboundkid 3y ago
    Yes, I clicked the link and read that. It wasn’t actually very relevant and did not help me understand the original article. I eventually figured it out on my own by, yes, examining the two examples they gave and proving to myself how it works. The article has a bad explanation. Untouchable numbers are a very simple idea. Any elementary school student who knows about divisors and prime numbers can have it explained to them in about ten minutes. The Wikipedia page for the article should be pitched so that a layman can understand it. I understand that if you’re writing a cookbook, you have to decide if you’re pitching it first time chefs who need “how to boil water” explained to them or professional chefs who just need references for some ratios. What serves one audience wastes the time of the other. If you want to know how init works, you probably already know what Unix is. If you’re looking up a particular species of mushrooms, you probably know how genii and species work. Untouchable numbers is a simple concept. It should not be pitched at professionals first. It should start with an explanation that a middle schooler can understand and then move on to advanced explanations in later sections.