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Yes, I agree completely. It communicates information very cheaply and in-band to very few people who are intimately familiar with the mathematics involved. And

by 127 5y ago

Yes, I agree completely. It communicates information very cheaply and in-band to very few people who are intimately familiar with the mathematics involved. And nobody else. Calling this mathematical education makes me doubt your implicit claim of pedagogical ability. I think a lot of math could be taught with a lot less overhead and in more understandable fashion. It's just that the natural incentives seem to drive people to unnecessary overhead and barriers for those who actually want to learn. Lot of the language and symbols involved could be streamlined. But like QWERTY keyboard and C++, you would first have to turn this huge hulking ship of legacy cruft into that direction.

gspr 5y ago
> I think a lot of math could be taught with a lot less overhead and in more understandable fashion. It's just that the natural incentives seem to drive people to unnecessary overhead and barriers for those who actually want to learn. Ok. Have at it, I guess. > Lot of the language and symbols involved could be streamlined. But like QWERTY keyboard and C++, you would first have to turn this huge hulking ship of legacy cruft into that direction. This screams a fundamental misunderstanding of mathematics. The symbols need context to make any sense whatsoever. To a reader with intimate knowledge of the context, the symbols convey lots of information very efficiently. That doesn't mean that the symbols are understandable without context, or even that they could be made understandable without context.
- 127 5y ago
  For example, using greek instead of latin letters is completely unnecessary. Just to point out completely meaningless overhead. Using in-group context-sensitive symbols is by definition exclusive. Using descriptive well thought out names is inclusive. Math as a language seems very needlessly compressed. Imagine a world where programmers invented a new symbol for every function and you would have to look up what they mean, but when you look up what they mean, you would have to look up 10 other symbols. Most of those symbols refer back to symbols where you came from in the first place. It's a detriment for learning. Simple as that. Not everybody wants to be a mathematician. Some people just want to get work done and read through a bunch of research papers.
  - gspr 5y ago
    > For example, using greek instead of latin letters is completely unnecessary. Just to point out completely meaningless overhead. Are you saying the whole field of mathematics (and physics) is wrong, and we're doing something "meaningless"? > Using in-group context-sensitive symbols is by definition exclusive. Using descriptive well thought out names is inclusive. Not when the group is open to anyone who wants to join. Math is probably the most "open source" field out there. Barring the very cutting edge front of research, everything can be learned from free sources or ones that can be borrowed for free from libraries, or had through very very cheap second hand material. That there is a high barrier to entry when it comes to effort isn't some malicious gatekeeping design. It's just because some things are hard. > Math as a language seems very needlessly compressed. Imagine a world where programmers invented a new symbol for every function and you would have to look up what they mean, but when you look up what they mean, you would have to look up 10 other symbols. You clearly have never done math! The way it works requires intimate familiarity with the definitions of the symbols. Once you actually manage to internalize that (it can be a lot of work), remembering what the symbols stand for comes for free. > Not everybody wants to be a mathematician. Some people just want to get work done and read through a bunch of research papers. "Not everyone wants to be a surgeon, some people just wanna read medical research papers." "Not everyone wants to be an astrophysicist, some people just wanna read astrophysics papers." Do you not see how ridiculous this is? Nobody is gatekeeping for the sake of gatekeeping. You're conflating gatekeeping with something just being hard, and the practitioners of the hard thing not wanting to change the way we work to accommodate non-practitioners (to our own detriment!)
    - 127 5y ago
      Symbols and math are two completely different things. Symbols are just something you attach concepts and ideas to. I believe that with words and labels instead of obscure symbols and surnames of mathematicians, teaching math could be more efficient. Even with set theory being a branch of mathematics, categorizing things seems to be very shooting from the hip. All I'm seeking here is how to improve communicating math without having to go through the credentialism of higher education. edit: Why you didn't understand my comment on reading papers: some computer science papers require heavy math background. A lot of math is actually applied math.

by 127 5y ago

gspr 5y ago

> I think a lot of math could be taught with a lot less overhead and in more understandable fashion. It's just that the natural incentives seem to drive people to unnecessary overhead and barriers for those who actually want to learn. Ok. Have at it, I guess. > Lot of the language and symbols involved could be streamlined. But like QWERTY keyboard and C++, you would first have to turn this huge hulking ship of legacy cruft into that direction. This screams a fundamental misunderstanding of mathematics. The symbols need context to make any sense whatsoever. To a reader with intimate knowledge of the context, the symbols convey lots of information very efficiently. That doesn't mean that the symbols are understandable without context, or even that they could be made understandable without context.

127 5y ago
For example, using greek instead of latin letters is completely unnecessary. Just to point out completely meaningless overhead. Using in-group context-sensitive symbols is by definition exclusive. Using descriptive well thought out names is inclusive. Math as a language seems very needlessly compressed. Imagine a world where programmers invented a new symbol for every function and you would have to look up what they mean, but when you look up what they mean, you would have to look up 10 other symbols. Most of those symbols refer back to symbols where you came from in the first place. It's a detriment for learning. Simple as that. Not everybody wants to be a mathematician. Some people just want to get work done and read through a bunch of research papers.
- gspr 5y ago
  > For example, using greek instead of latin letters is completely unnecessary. Just to point out completely meaningless overhead. Are you saying the whole field of mathematics (and physics) is wrong, and we're doing something "meaningless"? > Using in-group context-sensitive symbols is by definition exclusive. Using descriptive well thought out names is inclusive. Not when the group is open to anyone who wants to join. Math is probably the most "open source" field out there. Barring the very cutting edge front of research, everything can be learned from free sources or ones that can be borrowed for free from libraries, or had through very very cheap second hand material. That there is a high barrier to entry when it comes to effort isn't some malicious gatekeeping design. It's just because some things are hard. > Math as a language seems very needlessly compressed. Imagine a world where programmers invented a new symbol for every function and you would have to look up what they mean, but when you look up what they mean, you would have to look up 10 other symbols. You clearly have never done math! The way it works requires intimate familiarity with the definitions of the symbols. Once you actually manage to internalize that (it can be a lot of work), remembering what the symbols stand for comes for free. > Not everybody wants to be a mathematician. Some people just want to get work done and read through a bunch of research papers. "Not everyone wants to be a surgeon, some people just wanna read medical research papers." "Not everyone wants to be an astrophysicist, some people just wanna read astrophysics papers." Do you not see how ridiculous this is? Nobody is gatekeeping for the sake of gatekeeping. You're conflating gatekeeping with something just being hard, and the practitioners of the hard thing not wanting to change the way we work to accommodate non-practitioners (to our own detriment!)
  - 127 5y ago
    Symbols and math are two completely different things. Symbols are just something you attach concepts and ideas to. I believe that with words and labels instead of obscure symbols and surnames of mathematicians, teaching math could be more efficient. Even with set theory being a branch of mathematics, categorizing things seems to be very shooting from the hip. All I'm seeking here is how to improve communicating math without having to go through the credentialism of higher education. edit: Why you didn't understand my comment on reading papers: some computer science papers require heavy math background. A lot of math is actually applied math.