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> very real toxicity within the geometric algebra community. I can’t do much about I was hoping the article would be about this instead. OP wondering if you ha

> very real toxicity within the geometric algebra community. I can’t do much about I was hoping the article would be about this instead. OP wondering if you have any elaborations for us to hear.

deleted 2y ago
[deleted]
nicf 2y ago
I'm not the OP, I'm not a part of this community, and I don't know if the thing I'm about to complain about is what the author was thinking of with this comment, but as someone who was trained as a mathematician and who has read some of the popularizations of geometric algebra that sometimes get posted to HN, there is a tone that some (though probably a minority) of them take that I find pretty obnoxious. These pieces are the ones that take the position that geometric algebra is this super secret anti-establishment mathematical samizdat that *they* don't want you to know about. They'll pit themselves against "mainstream mathematics" and say things like, "in differential geometry you do X, but you shouldn't do differential geometry; you should do geometric algebra where we do Y, which is so much better than X." My reaction is always, "My friend, you are doing differential geometry!" Clifford algebras --- the objects that the geometric algebra people study --- are firmly within the "mainstream" of mathematics; there's simply no conflict here, at least not of the sort that these writers often seem to be imagining. It's great that people are enjoying learning about Clifford algebras. I think Clifford algebras are really fun! But we can all just come together and enjoy them together, and I think this "join me in taking down the cabal of gatekeepers who are suppressing the truth" attitude is unnecessary and turns off a lot of people who might otherwise be fun to engage with. If you're into this stuff and feel like this doesn't describe you or the people you know, then that's great, keep doing what you're doing! But it does exist and I wish it didn't.
- gowld 2y ago
  It goes both ways. Mathematicians will take a moment denigrate Geometric Algebra as "linear algebra with a uselessly nonstandard notation", ignoring that we should prefer a less awkward way of structuring linear algebra than "pseudoscalars" and "pseudovectors".
  - aleph_minus_one 2y ago
    > Mathematicians will take a moment denigrate Geometric Algebra as "linear algebra with a uselessly nonstandard notation", ignoring that we should prefer a less awkward way of structuring linear algebra than "pseudoscalars" and "pseudovectors". I have never heard a mathematician using the terms "pseudoscalar" and "pseudovector". These rather seem to be common terms among physicists.
  - prof-dr-ir 2y ago
    > "linear algebra with a uselessly nonstandard notation" Let me chime in that as a physicist (who does use the "pseudo" stuff occasionally) I very much share this opinion. The notation may be really cool and compact, but I just do not see the benefit - for example, d*F = j and dF = 0 is compact enough for me. It is all fine if people use this language to learn linear algebra or differential geometry. And maybe it has a use for numerics or computer science. But I am quite sure that the geometric algebra formalism will not be widely adopted in physics any time soon. Sorry.
    - gugagore 2y ago
      What other way is there around avoiding polar vs axial vectors looking the same but behaving differently? Or normal vs tangent vectors transforming differently?
      - ajkjk 2y ago
        Those concepts are from exterior algebra which GA is built on. You do not need GA (the geometric product, etc) for them.
        gugagore 2y ago
        That's fine. That's still a step beyond just "linear algebra".
        ajkjk 2y ago
- thechao 2y ago
  I used GA as a way to bootstrap into 'real' Clifford algebras, and a way to get over a "reader's block" when it came to Lie algebras, tensors, and (finally) algebraic geometry. I'm not sure GA is great math, but it was really great way to learn "advanced math concepts" for "basic..ish math". Personally, I like Alan MacDonald's GA books — they're a great way to learn more complicated concepts, but couched in a very approachable geometry/visual learning style.
  - nicf 2y ago
    That sounds like a fun and satisfying process! I realize my comment could be taken as denigrating all the people who write about this stuff, but that's certainly not my intention; I've also enjoyed a lot of the visualizations and geometric explanations that people writing under this heading have come up with. My complaint is really just about the ones who take this oppositional attitude, and a big part of why I think it's such a shame when that happens is that there really are some very cool ideas here, so it's sad to see walls being raised for no good reason.

> very real toxicity within the geometric algebra community. I can’t do much about I was hoping the article would be about this instead. OP wondering if you have any elaborations for us to hear.

deleted 2y ago

[deleted]

nicf 2y ago

I'm not the OP, I'm not a part of this community, and I don't know if the thing I'm about to complain about is what the author was thinking of with this comment, but as someone who was trained as a mathematician and who has read some of the popularizations of geometric algebra that sometimes get posted to HN, there is a tone that some (though probably a minority) of them take that I find pretty obnoxious. These pieces are the ones that take the position that geometric algebra is this super secret anti-establishment mathematical samizdat that *they* don't want you to know about. They'll pit themselves against "mainstream mathematics" and say things like, "in differential geometry you do X, but you shouldn't do differential geometry; you should do geometric algebra where we do Y, which is so much better than X." My reaction is always, "My friend, you are doing differential geometry!" Clifford algebras --- the objects that the geometric algebra people study --- are firmly within the "mainstream" of mathematics; there's simply no conflict here, at least not of the sort that these writers often seem to be imagining. It's great that people are enjoying learning about Clifford algebras. I think Clifford algebras are really fun! But we can all just come together and enjoy them together, and I think this "join me in taking down the cabal of gatekeepers who are suppressing the truth" attitude is unnecessary and turns off a lot of people who might otherwise be fun to engage with. If you're into this stuff and feel like this doesn't describe you or the people you know, then that's great, keep doing what you're doing! But it does exist and I wish it didn't.

gowld 2y ago
It goes both ways. Mathematicians will take a moment denigrate Geometric Algebra as "linear algebra with a uselessly nonstandard notation", ignoring that we should prefer a less awkward way of structuring linear algebra than "pseudoscalars" and "pseudovectors".
- aleph_minus_one 2y ago
  > Mathematicians will take a moment denigrate Geometric Algebra as "linear algebra with a uselessly nonstandard notation", ignoring that we should prefer a less awkward way of structuring linear algebra than "pseudoscalars" and "pseudovectors". I have never heard a mathematician using the terms "pseudoscalar" and "pseudovector". These rather seem to be common terms among physicists.
- prof-dr-ir 2y ago
  > "linear algebra with a uselessly nonstandard notation" Let me chime in that as a physicist (who does use the "pseudo" stuff occasionally) I very much share this opinion. The notation may be really cool and compact, but I just do not see the benefit - for example, d*F = j and dF = 0 is compact enough for me. It is all fine if people use this language to learn linear algebra or differential geometry. And maybe it has a use for numerics or computer science. But I am quite sure that the geometric algebra formalism will not be widely adopted in physics any time soon. Sorry.
  - gugagore 2y ago
    What other way is there around avoiding polar vs axial vectors looking the same but behaving differently? Or normal vs tangent vectors transforming differently?
    - ajkjk 2y ago
      Those concepts are from exterior algebra which GA is built on. You do not need GA (the geometric product, etc) for them.
      - gugagore 2y ago
        That's fine. That's still a step beyond just "linear algebra".
        ajkjk 2y ago
thechao 2y ago
I used GA as a way to bootstrap into 'real' Clifford algebras, and a way to get over a "reader's block" when it came to Lie algebras, tensors, and (finally) algebraic geometry. I'm not sure GA is great math, but it was really great way to learn "advanced math concepts" for "basic..ish math". Personally, I like Alan MacDonald's GA books — they're a great way to learn more complicated concepts, but couched in a very approachable geometry/visual learning style.
- nicf 2y ago
  That sounds like a fun and satisfying process! I realize my comment could be taken as denigrating all the people who write about this stuff, but that's certainly not my intention; I've also enjoyed a lot of the visualizations and geometric explanations that people writing under this heading have come up with. My complaint is really just about the ones who take this oppositional attitude, and a big part of why I think it's such a shame when that happens is that there really are some very cool ideas here, so it's sad to see walls being raised for no good reason.