The early Wikipedia was much better with this sort of thing. Gradually those educational level articles were replaced by articles written to show off the author's sophisticated theoretical knowledge.
Happily, the old versions of Wikipedia are still readily accessible. But few people know that.
"Impedance extends the concept of resistance to alternating current (AC) circuits, and possesses both magnitude and phase, unlike resistance, which has only magnitude."
It's the first result for "impedance" on Kagi, and second result for "impedance" on Google, and the first result is decent too.
I think this article overlooks how different platform work. While Wikipedia isn't really useful for these, one can easily find more educative videos on youtube.
Which is why reading books is so important - they are a specific format that hopefully covers an area of scope as advertised. This is underemphasised. Also why people like videos - to be engaging they need to be accessible
Wikipedia is an encyclopedia, though -- not a textbook. Were dead-tree encyclopedias much better at this use case? I remember them as being too terse and vague to be used as a first introduction.
What we are missing are curated collections of textbooks, as college or school libraries would often provide. I am aware of one attempt to create one for mathematics ( https://aimath.org/textbooks/approved-textbooks/ ), but it is far from complete and missing some of my favorite texts such as https://courses.csail.mit.edu/6.042/spring18/mcs.pdf or Samir Siksek's notes https://homepages.warwick.ac.uk/staff/S.Siksek/ . More would obviously be helpful, but there are no incentives for it anywhere, and the most ambitious book critics are writing their own instead. And I have no idea where to find similar collections for the sciences.
Conceptually, sure, but I don't think they're useful right now and I wouldn't be sending people there. Wikiversity looks just kinda weird / half-baked, e.g.:
Well, that's why I note it's not necessarily a Wikipedia problem - it's the "using Wikipedia as a default destination" problem of the internet era.
That said, while paper encyclopedias weren't textbooks, they were generally written to be comprehensible and avoid circular definitions: they were a reasonable starting point for many things - they were just terse out of necessity. Wikipedia doesn't have that constraint, and if you take the Fourier transform article as an example, it is 30+ print pages long (!). In many fields, the editors make it their mission to explain concepts - it's just not an editorial policy.
I also think think it's a bit of a cop-out, because if you're not making hard sciences at least *somewhat* accessible, your mission shrinks to "jogging the memory of forgetful graduates" - and I don't remember seeing that in their fundraising pleas.
Strong agree with lcamtuf. There is a *wide* margin between where a lot of the Wikipedia math writing is and a textbook. And just saying "it's an encyclopedia" ignores that there is a spectrum in that category. I've actually written entries in a specialist encyclopedia targeted narrowly at practitioners in a particular field. Wikipedia should be about as far from that as you can get: something that any educated person can learn something from.
As a non-mathematician who worked closely with academic mathematicians for a while, something curious about their culture struck me. They seem to love to start with the highly refined, abstract expression of an idea, then elaborate on it. But for people who don't already understand, it's almost always better to start with something concrete and then work towards the more abstract version.
Couldn't agree more. Every so often, I realise quite how simple a topic really is, and how the Internet makes a meal of things, usually by insistence on being exactly "correct". We need layers of simplified models to understand and interact usefully with knowledge.
Physics and hard sciences in particular demonstrate the need for this. There are too many details to pay attention to them all. We have to say things like "For now let's pretend solid objects exist".
With those deficiencies in the mainstream education experience in mind I undertook to give my 5 children a STEM based education at home and build a learning lab for the purpose. They currently have no direct internet access, but love their Ollama AI installations. It has some distinct uses in combination with Kiwix Offline and other Open Source software such as Golden Dictionary. First they chat with the AI to ask which words mean <the thing they are describing> then they check that those words really do match a formal description in the dictionary, which I have also set up with an AI voice to give them translation and pronunciation help. With their vocabulary thus enhanced they go back to the AI and explore a topic, periodically stopping to check against the online copy of Wikipedia and other sources, using Kiwix Offline. They have been shown this specific method and told exactly why it is advantageous in that it allows naive entry into a topic, divergent exploration, then finally verification of facts and concepts in a convergent process.
It is like having a 1 to 1 teacher ratio with the students leading the learning experience, but with me as the head teacher should extra tutoring be required. The next step is using Llamaindex against a large ebook library to add a final layer whereby they have direct links from the AI into the exact parts of formal texts that contain relevant information.
This education method sets the student up to be an autonomous life long learner, who can still team up with others, as there is a lot of constant interaction and collaboration in the learning lab compared to formal classes, because everyone is also connected to a Mumble server. Each workstation has a large 4K screen, custom Debian machines running on AMD Ryzen 7 5700G CPUs (very good power for cost ratio), and they have graphics tablets for use in Inkscape, Krita, and Blender 3D. Where the average kids may manage to squeeze 2 or 3 hours of real learning into a day, a home lab easily doubles that, with the advantage that they get 3 home cooked meals a day and opportunity to interact with the entire family and discuss things at the same time.
The bottom line, take from the internet what you need, then build the knowledge engine you really need from those parts and use that so that you can focus on learning and ignore the pests and weirdos who just want to waste your time and mess with your mind. STEM based home education, done right, is empowering, and VPNs such as ZeroTier mean that you can take that AI with you wherever you go which is great for field excursions where you may want to ID flora or fauna etc.
I've long been mystified by the style of much of the math writing on Wikipedia. It's like the authors are trying to impress each other with their concision, rather than trying to explain something to someone who doesn't already understand it.
I can confirm that reading the "Exceptional inverse image functor" wiki entry aloud in a refined voice is one of the most exhilarating experiences I have ever undertaken.
What I've observed is that teaching is a talent and almost an art form which few have mastered. Many of these "complex" concepts are quite simple if explained in terms understandable to the student. It's this "translation" from domain-speak to common-speak which is generally missing in these wikis.
I agree largely, but there are some really amazing visual resources for learning math and science now they are worlds better then when I learned the same concepts 30 years ago. In my experience, Google search results often put videos from these educators near or at the top (maybe I pick the "right" search terms).
We need to emphasize those resources more. And your own substack 😀
Yeah, and it's not necessarily a uniform phenomenon to begin with. For example, chemistry articles on Wikipedia tend to be on average far easier to parse.
The early Wikipedia was much better with this sort of thing. Gradually those educational level articles were replaced by articles written to show off the author's sophisticated theoretical knowledge.
Happily, the old versions of Wikipedia are still readily accessible. But few people know that.
my trick:
ELI12 concept of impedance
(ELI12 = Explain Like I am 12 years old)
https://www.perplexity.ai/search/eli12-concept-of-impedance-dDic4oteRO605wZkuBJHww
To be fair, the https://en.wikipedia.org/wiki/Electrical_impedance article seems easy to understand for someone who has a vague notion of what impedance is.
"Impedance extends the concept of resistance to alternating current (AC) circuits, and possesses both magnitude and phase, unlike resistance, which has only magnitude."
It's the first result for "impedance" on Kagi, and second result for "impedance" on Google, and the first result is decent too.
These days the default resource for math problems for Polish kids is YouTube.
I think this article overlooks how different platform work. While Wikipedia isn't really useful for these, one can easily find more educative videos on youtube.
Which is why reading books is so important - they are a specific format that hopefully covers an area of scope as advertised. This is underemphasised. Also why people like videos - to be engaging they need to be accessible
Wikipedia is an encyclopedia, though -- not a textbook. Were dead-tree encyclopedias much better at this use case? I remember them as being too terse and vague to be used as a first introduction.
What we are missing are curated collections of textbooks, as college or school libraries would often provide. I am aware of one attempt to create one for mathematics ( https://aimath.org/textbooks/approved-textbooks/ ), but it is far from complete and missing some of my favorite texts such as https://courses.csail.mit.edu/6.042/spring18/mcs.pdf or Samir Siksek's notes https://homepages.warwick.ac.uk/staff/S.Siksek/ . More would obviously be helpful, but there are no incentives for it anywhere, and the most ambitious book critics are writing their own instead. And I have no idea where to find similar collections for the sciences.
What about Wikiversity or Wikibooks?
Conceptually, sure, but I don't think they're useful right now and I wouldn't be sending people there. Wikiversity looks just kinda weird / half-baked, e.g.:
https://en.wikiversity.org/wiki/Water
https://en.wikiversity.org/wiki/Introduction_to_the_Planets/Introduction
https://en.wikiversity.org/wiki/Topology/Lesson_1
Well, that's why I note it's not necessarily a Wikipedia problem - it's the "using Wikipedia as a default destination" problem of the internet era.
That said, while paper encyclopedias weren't textbooks, they were generally written to be comprehensible and avoid circular definitions: they were a reasonable starting point for many things - they were just terse out of necessity. Wikipedia doesn't have that constraint, and if you take the Fourier transform article as an example, it is 30+ print pages long (!). In many fields, the editors make it their mission to explain concepts - it's just not an editorial policy.
I also think think it's a bit of a cop-out, because if you're not making hard sciences at least *somewhat* accessible, your mission shrinks to "jogging the memory of forgetful graduates" - and I don't remember seeing that in their fundraising pleas.
Strong agree with lcamtuf. There is a *wide* margin between where a lot of the Wikipedia math writing is and a textbook. And just saying "it's an encyclopedia" ignores that there is a spectrum in that category. I've actually written entries in a specialist encyclopedia targeted narrowly at practitioners in a particular field. Wikipedia should be about as far from that as you can get: something that any educated person can learn something from.
As a non-mathematician who worked closely with academic mathematicians for a while, something curious about their culture struck me. They seem to love to start with the highly refined, abstract expression of an idea, then elaborate on it. But for people who don't already understand, it's almost always better to start with something concrete and then work towards the more abstract version.
Couldn't agree more. Every so often, I realise quite how simple a topic really is, and how the Internet makes a meal of things, usually by insistence on being exactly "correct". We need layers of simplified models to understand and interact usefully with knowledge.
Physics and hard sciences in particular demonstrate the need for this. There are too many details to pay attention to them all. We have to say things like "For now let's pretend solid objects exist".
With those deficiencies in the mainstream education experience in mind I undertook to give my 5 children a STEM based education at home and build a learning lab for the purpose. They currently have no direct internet access, but love their Ollama AI installations. It has some distinct uses in combination with Kiwix Offline and other Open Source software such as Golden Dictionary. First they chat with the AI to ask which words mean <the thing they are describing> then they check that those words really do match a formal description in the dictionary, which I have also set up with an AI voice to give them translation and pronunciation help. With their vocabulary thus enhanced they go back to the AI and explore a topic, periodically stopping to check against the online copy of Wikipedia and other sources, using Kiwix Offline. They have been shown this specific method and told exactly why it is advantageous in that it allows naive entry into a topic, divergent exploration, then finally verification of facts and concepts in a convergent process.
It is like having a 1 to 1 teacher ratio with the students leading the learning experience, but with me as the head teacher should extra tutoring be required. The next step is using Llamaindex against a large ebook library to add a final layer whereby they have direct links from the AI into the exact parts of formal texts that contain relevant information.
This education method sets the student up to be an autonomous life long learner, who can still team up with others, as there is a lot of constant interaction and collaboration in the learning lab compared to formal classes, because everyone is also connected to a Mumble server. Each workstation has a large 4K screen, custom Debian machines running on AMD Ryzen 7 5700G CPUs (very good power for cost ratio), and they have graphics tablets for use in Inkscape, Krita, and Blender 3D. Where the average kids may manage to squeeze 2 or 3 hours of real learning into a day, a home lab easily doubles that, with the advantage that they get 3 home cooked meals a day and opportunity to interact with the entire family and discuss things at the same time.
The bottom line, take from the internet what you need, then build the knowledge engine you really need from those parts and use that so that you can focus on learning and ignore the pests and weirdos who just want to waste your time and mess with your mind. STEM based home education, done right, is empowering, and VPNs such as ZeroTier mean that you can take that AI with you wherever you go which is great for field excursions where you may want to ID flora or fauna etc.
I've long been mystified by the style of much of the math writing on Wikipedia. It's like the authors are trying to impress each other with their concision, rather than trying to explain something to someone who doesn't already understand it.
I can confirm that reading the "Exceptional inverse image functor" wiki entry aloud in a refined voice is one of the most exhilarating experiences I have ever undertaken.
What I've observed is that teaching is a talent and almost an art form which few have mastered. Many of these "complex" concepts are quite simple if explained in terms understandable to the student. It's this "translation" from domain-speak to common-speak which is generally missing in these wikis.
I agree largely, but there are some really amazing visual resources for learning math and science now they are worlds better then when I learned the same concepts 30 years ago. In my experience, Google search results often put videos from these educators near or at the top (maybe I pick the "right" search terms).
We need to emphasize those resources more. And your own substack 😀
Yeah, and it's not necessarily a uniform phenomenon to begin with. For example, chemistry articles on Wikipedia tend to be on average far easier to parse.