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Geometric Algebra is really cool. Unfortunately, people who promote it tend to sound like insufferable crackpots. Why is that? People who explain other cool

Geometric Algebra is really cool. Unfortunately, people who promote it tend to sound like insufferable crackpots. Why is that? People who explain other cool things in math are never like that. Although there are a few honest texts, almost every introduction to geometric algebra sounds as if they are introducing a new "school of thought" that will change mathematics forever. As if there was a worldwide conspiracy of powerful people who promote backwards concepts like exterior algebra, tensors and quaternions, and they want us to take the red pill. This may have sounded slightly funny the first time it was written, but it is an ugly, self-defeating meme right now. To anybody who may be discouraged from learning geometric algebra due to the weird antics of its promoters: please, ignore the stupid rhetoric and study some Clifford algebra. There are a lot of neat ideas in there! (but of course, not only in there; you may still want to learn the other, well-known, equivalent definitions and notations for the same objects).

DreamScatter 6y ago
It is a way of thought which will change mathematics, it is new to 99.9999% of people, isn't part of any curriculum yet. Since GA is such a powerful idea, it will have a big impact on mathematics for a long time to come, when more people find out about it. Once you learn it, you will naturally wonder why such a thing wasn't ever part of what people learn yet.
- deleted 6y ago
  [deleted]
- enriquto 6y ago
  I love this kind of satire! :)
orbots 6y ago
Don't paint us all with the same brush please. Some of us are totally sufferable.
andi999 6y ago
Exactly. I read one of the books a long time ago, and it was like 'we have this surpressed magic here', but somehow there were no hard (math) results. I understand it is easier to calculate the product of two rotations with G.A. is there apart from that anything (substantial) else?
rsj_hn 6y ago
I've noticed that it's not math people who are promoting it but CS people or other engineers. E.g. those who took mostly cookbook classes (no offense intended) rather than theory classes. This tells me there is a large latent desire for deep understanding. When I first encountered the term "geometric algebra" and read some of the articles, I couldn't understand what was new about the content. In college, we learned about tensor products, wedge products, clifford algebras, and duals, and geometric algebra struck me as a subset of this core knowledge applied to three dimensions, where you can do things like take a wedge product of two vectors to get a 2 form and then take the dual to get back to a one form, and now you have a "geometric" (more of a linear algebra) interpretation of the cross product as a dual to an exterior product -- which is how we were taught what a cross product is. But I think a lot of people who don't study this stuff were never taught these relationships, so bundling them up in a marketing name and letting them understand why these standard linear algebra relations behave as they do can really help the working engineer, which seems to be a condemnation of the rote learning approach where you are asked to memorize a bunch of stuff but are never told that what an inner or exterior product really is. Then things like calling two vectors "orthognal" if they have an inner product of zero seems mysterious. By the way, this isn't just linear algebra. There are many deep connections behind well known algorithms in number theory, topology, calculus, algebraic geometry, (co)homology theories, that are ripe for a snazzy name and a presentation of some of the deeper ideas, so that people can start seeing connections between stuff like complex integrals and euler characteristics and winding numbers, holonomy groups and short exact sequences, etc. So in this sense, I applaud the geometric algebra evangelists, even though this is all standard stuff that a math undergrad should learn, and the name "geometric algebra" is a completely made up term for what are well known mathematical structures.

DreamScatter 6y ago

It is a way of thought which will change mathematics, it is new to 99.9999% of people, isn't part of any curriculum yet. Since GA is such a powerful idea, it will have a big impact on mathematics for a long time to come, when more people find out about it. Once you learn it, you will naturally wonder why such a thing wasn't ever part of what people learn yet.

deleted 6y ago
[deleted]
enriquto 6y ago
I love this kind of satire! :)

orbots 6y ago

Don't paint us all with the same brush please. Some of us are totally sufferable.

andi999 6y ago

Exactly. I read one of the books a long time ago, and it was like 'we have this surpressed magic here', but somehow there were no hard (math) results. I understand it is easier to calculate the product of two rotations with G.A. is there apart from that anything (substantial) else?

rsj_hn 6y ago

I've noticed that it's not math people who are promoting it but CS people or other engineers. E.g. those who took mostly cookbook classes (no offense intended) rather than theory classes. This tells me there is a large latent desire for deep understanding. When I first encountered the term "geometric algebra" and read some of the articles, I couldn't understand what was new about the content. In college, we learned about tensor products, wedge products, clifford algebras, and duals, and geometric algebra struck me as a subset of this core knowledge applied to three dimensions, where you can do things like take a wedge product of two vectors to get a 2 form and then take the dual to get back to a one form, and now you have a "geometric" (more of a linear algebra) interpretation of the cross product as a dual to an exterior product -- which is how we were taught what a cross product is. But I think a lot of people who don't study this stuff were never taught these relationships, so bundling them up in a marketing name and letting them understand why these standard linear algebra relations behave as they do can really help the working engineer, which seems to be a condemnation of the rote learning approach where you are asked to memorize a bunch of stuff but are never told that what an inner or exterior product really is. Then things like calling two vectors "orthognal" if they have an inner product of zero seems mysterious. By the way, this isn't just linear algebra. There are many deep connections behind well known algorithms in number theory, topology, calculus, algebraic geometry, (co)homology theories, that are ripe for a snazzy name and a presentation of some of the deeper ideas, so that people can start seeing connections between stuff like complex integrals and euler characteristics and winding numbers, holonomy groups and short exact sequences, etc. So in this sense, I applaud the geometric algebra evangelists, even though this is all standard stuff that a math undergrad should learn, and the name "geometric algebra" is a completely made up term for what are well known mathematical structures.