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”.)
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”.)