You chose one of the most difficult examples. It would probably be better to choose something that is difficult for others but simple for you.
Another part of the problem, which Arbital especially failed at, was getting others to contribute.
Too late to cry over spilled milk, but one of the reasons I didn’t contribute was that Arbital seemed too serious; I wasn’t sure whether less serious topics were even allowed. Which might also become a problem of the website where Goedel’s Theorems are the canonical example. Probably it would be better to use something simpler, for example prime numbers, or quadratic equations, just to encourage more people to contribute.
Hey, new contributor! Here’s a list of subsections of different articles, where we want X type of examples for concept Y.
One problem with “using a simpler example”, is that there’s a lower bound. Prime numbers are not-too-hard to explain, at some levels of thoroughness.
Like, some part of my subconscious basically thinks (despite evidence to the contrary): “There is Easy Math and Hard Math. All intuitive explanations have been done only about Easy Math. Hard Math is literally impossible to explain if you don’t already understand it.”
Part of the point of Mathopedia, is to explicitly go after hard, advanced, graduate-level and research-level mathematics. To make them intelligible enough that someone can learn them just from browsing the site and maybe doing a few exercises.
Even if they need to go down a TVTropes-style rabbit-hole (still within the site) to find all the background knowledge they’re missing.
Even if we add increasingly-unrealistic constraints like “any non-mentally-disabled teen should be able to do this”.
Even if it requires laborious features like “there should be a toggle switch / separate page-subsection that replaces all the jargon in a page with [parentheses of (increasingly recursive (definitions)]], so the whole page is full of run-on sentences while also in-principle being explainable to an elementary schooler”.
Even if we have to use some incredibly hokey diagrams.
I agree that too easy example does not make a good demo for “how to explain difficult things”.
Maybe Complex Numbers would be a better topic, because you can start from really simple (an 8 years old kid should be able to understand C as a weird way of writing 2D coordinates) and progress towards complicated (exponentiation). Plus there is a great opportunity to use colors for C-to-C functions.
That said, “easy” is relative to the audience. As a challenge, you could take a smart 8 years old kid and try explaining as much about prime numbers as you can, in the time limit of 10 minutes. Do the same for a 10 years old, etc. (This is my pet peeve: There are many simple explanations of simple things which could be further simplified, but no one bothers to do that, because from the perspective of an adult, they seem already easy enough. Or because at some moment, too simple explanations just feel low-status. We need more and better distillation of all human knowledge. People say “you can’t be a polymath anymore, because we already know too much”. Yeah, but an average person could probably know 10x more than they do now, if our educational methods didn’t suck, because we stop at “good enough”.)
choose something that is difficult for others but simple for you.
Yep, a broader life lesson I’m still learning haha.
IIRC Paul Graham recommended such a tactic, framing it as “easier gains from moving around in problem-space than solution-space”.
And your other recommendations definitely make sense here. In my giant bookmarks folder about the “mathopedia” idea, this post and the comments are bookmarked.
You chose one of the most difficult examples. It would probably be better to choose something that is difficult for others but simple for you.
Too late to cry over spilled milk, but one of the reasons I didn’t contribute was that Arbital seemed too serious; I wasn’t sure whether less serious topics were even allowed. Which might also become a problem of the website where Goedel’s Theorems are the canonical example. Probably it would be better to use something simpler, for example prime numbers, or quadratic equations, just to encourage more people to contribute.
Yes, this would definitely work for me.
One problem with “using a simpler example”, is that there’s a lower bound. Prime numbers are not-too-hard to explain, at some levels of thoroughness.
Like, some part of my subconscious basically thinks (despite evidence to the contrary): “There is Easy Math and Hard Math. All intuitive explanations have been done only about Easy Math. Hard Math is literally impossible to explain if you don’t already understand it.”
Part of the point of Mathopedia, is to explicitly go after hard, advanced, graduate-level and research-level mathematics. To make them intelligible enough that someone can learn them just from browsing the site and maybe doing a few exercises.
Even if they need to go down a TVTropes-style rabbit-hole (still within the site) to find all the background knowledge they’re missing.
Even if we add increasingly-unrealistic constraints like “any non-mentally-disabled teen should be able to do this”.
Even if it requires laborious features like “there should be a toggle switch / separate page-subsection that replaces all the jargon in a page with [parentheses of (increasingly recursive (definitions)]], so the whole page is full of run-on sentences while also in-principle being explainable to an elementary schooler”.
Even if we have to use some incredibly hokey diagrams.
I agree that too easy example does not make a good demo for “how to explain difficult things”.
Maybe Complex Numbers would be a better topic, because you can start from really simple (an 8 years old kid should be able to understand C as a weird way of writing 2D coordinates) and progress towards complicated (exponentiation). Plus there is a great opportunity to use colors for C-to-C functions.
That said, “easy” is relative to the audience. As a challenge, you could take a smart 8 years old kid and try explaining as much about prime numbers as you can, in the time limit of 10 minutes. Do the same for a 10 years old, etc. (This is my pet peeve: There are many simple explanations of simple things which could be further simplified, but no one bothers to do that, because from the perspective of an adult, they seem already easy enough. Or because at some moment, too simple explanations just feel low-status. We need more and better distillation of all human knowledge. People say “you can’t be a polymath anymore, because we already know too much”. Yeah, but an average person could probably know 10x more than they do now, if our educational methods didn’t suck, because we stop at “good enough”.)
Yep, a broader life lesson I’m still learning haha.
IIRC Paul Graham recommended such a tactic, framing it as “easier gains from moving around in problem-space than solution-space”.
And your other recommendations definitely make sense here. In my giant bookmarks folder about the “mathopedia” idea, this post and the comments are bookmarked.