random example: take a look at the Wikipedia article for "currying". [0] while quite accessible to someone with a math/cs background, this would be pretty much unintelligible to someone who wasn't familiar with the notion of a mathematical function. perhaps it could be rewritten to be even more accessible, but what would be the point of explaining currying to someone who doesn't know about functions and arguments in the first place? brittannica doesn't even cover this topic.
I know Wikipedia isn't supposed to be a textbook, but I'd argue that having a more accessible first paragraph or summary section on every topic could help all uses:
- Specialists would more easily be able to refresh their memories of topics they use infrequently before diving into the details.
- People in neighboring specialties can more easily branch out.
- Informed laypeople (e.g. experts in other industries) could more easily find new ideas for cross-pollination into their own field.
As one random example I have recently found application for an algorithm mainly reserved for use in geophysics and cartography to audio signal processing, but learning and applying it took way more research than it really should have.
I'm curious how you would rewrite that first paragraph then:
"In mathematics and computer science, currying is the technique of translating the evaluation of a function that takes multiple arguments into evaluating a sequence of functions, each with a single argument. For example, a function that takes two arguments, one from X and one from Y, and produces outputs in Z, by currying is translated into a function that takes a single argument from X and produces as outputs functions from Y to Z. Currying is related to, but not the same as, partial application."
BTW I don't like that paragraph, it looks to me that it completely "misses the point" because as far as I understand currying is not about the sets but about the arguments. If it would be about the sets it would be just "a rewrite to a function that accepts the subset of the previous input set" and it's not about that.
simple wikipedia does take your approach though:
> Currying is a technique used in mathematics and computer science that consists of changing a function that takes several arguments into a number of functions that each take one argument. Mathematicians Moses Schönfinkel and Gottlob Frege laid the groundwork for this technique, which is named after Haskell Brooks Curry. Currying is used in Lambda calculus. Some programming languages, such as ML and Haskell say that functions can only have one argument. [0]
that's actually the entire article. not sure how useful it is, but at least they tried.
I like Wikipedia as it is, let's not make it into IdiocracyPedia for the sake of accessibility... if you're not lazy and you're willing to put some focus and time into your research you'll be able to understand quite unfamiliar subjects from Wikipedia, there's nothing blocking you, as opposed to eg. lots of academic articles that may contain un-google-able jargon and unexplained/unmentioned domain specific assumptions.
If you're not convinced, even professional scientists themselves regularly publish and read "review papers" which are pretty much papers doing no research other than summariing and simplifying the current state of the research in their field.
I don't see this as being always true. For example, scientific papers are written in such a way that normally you need a great deal of understanding in a field to read them. Making them accessible would mean either removing or explaining all domain specific knowledge in each paper. Expecting the reader to acquire the knowledge elsewhere and then read the paper with the knowledge makes a group of papers more accessible than if each paper did either of the options making them simple.
In the same way, the wikipedia page on integration by parts does a better job of explaining what it means than if it took the time to explain what a function is, what a variable is, what an integral is, what a product is, what an antiderivative is, or what the common notation it uses. I bring these up because these are all assumptions made before you even get to the table of contents of the article. If the article was simple enough that someone who didn't know any of those concepts could understand the same information presented in the first paragraph, you would have a significant introduction to mathematics that would slow down those who have some basic calculus knowledge seeking to refresh or get a summary of what integration by parts is.
It quickly helps forging an intuition of the new concept, using phrases like "Thus integration by parts may be thought of as deriving the area of the blue region from the area of rectangles and that of the red region." which are not very mathematicallish.
All the while, it's a good article for maths people.
Once again, in a great article, what should be simple and explained is not prior knowledge, but the new concept introduced.
