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Somehow, in your links, there isn't a single explanation anywhere (that's not in the form of a video that I don't have time or inclination to watch) about what

Somehow, in your links, there isn't a single explanation anywhere (that's not in the form of a video that I don't have time or inclination to watch) about what "geometric algebra" is supposed to mean. I'm trying to gather what this is supposed to be from the catchphrases on the front page, and honestly, this just looks like linear algebra. Can you explain what "geometric algebra" is supposed to be? Or just link to written explanations? I'm a mathematician (algebraic topology), so don't be afraid to get technical. How is this different from linear algebra? The only things I can see are some tensor products and exterior products, and a few couple of division algebra structures. Can you enlighten me? Is there any actually new math behind all this?

nyssos 3y ago
Geometric algebras = Clifford algebras over R.
- uxp8u61q 3y ago
  And they made dozens of hour long videos about that? That's insane. And the arrogance of calling it "geometric algebra" like they invented a new field of math?!
  - BenoitP 3y ago
    One could argue it is more about physics than math. GA has simpler expressions for a lot of physical topics.
    - uxp8u61q 3y ago
      Perhaps, but it's not new math (Clifford algebras are almost 200 years old). Shrouding it in a veil of buzzwords and pizzaz makes you look more like con artists than scientists. A sentence like this one is just absurd: > Clifford's Geometric Algebra enables a unified, intuitive and fresh perspective on vector spaces, giving elements of arbitrary dimensionality a natural home.
ngcc_hk 3y ago
My take is a bit different. May I quote but edit myself : 2 points by ngcc_hk 2 days ago | parent | context | prev | next [–] | on: Visualizing quaternions (2018) Once you accept that imaginary number is not about a straight real number but a number about rotation. And you have two number that is not the same, living in different dimensions. One about straight line and one about rotation I.e. X0 ops X1(another number system ) where X0, X1 is real You then have complex number or a+ bi where i^2 = -1 And you can have split complex number a+bj where j^2 = 1 etc The next move is not only the usual quaternions which one can, but to Clifford algebra x0 ops x1n1 ops x2n2 ops … xi is all real but ni is a different number system represent things not on the real number but a different and higher dimension object. For example, the Clifford Geometry define the 2nd not a i or j but a plane, so you have x0 + x1<plane> … and so on with more high dimensional object (especially if one may say x0 is x0<line>). Like complex number it simplify a lot of things. Spinsor would be easier to define this way say.
- ngcc_hk 3y ago
  After seeing the video I was a bit surprise by her two comments. This is after the most understandable introduction to this king of geometry. Shocking last 5 minutes. The first one that it is not that useful just different way of grouping. IaAware of this taking by both physics and computer people. But it is a total different way of looking and should have been taught in high school or at least undergrad. A bad cycle here. It has a lot of use to understand physics for normal people whilst the tensor … Also her struggle with thinking about shift to another game engine. Unreal … too complex and Godot … to engineering … her remark basically said she may have to go back to game programming (to get a living). Both honest comments and reflect hard reality.

nyssos 3y ago

Geometric algebras = Clifford algebras over R.

uxp8u61q 3y ago
And they made dozens of hour long videos about that? That's insane. And the arrogance of calling it "geometric algebra" like they invented a new field of math?!
- BenoitP 3y ago
  One could argue it is more about physics than math. GA has simpler expressions for a lot of physical topics.
  - uxp8u61q 3y ago
    Perhaps, but it's not new math (Clifford algebras are almost 200 years old). Shrouding it in a veil of buzzwords and pizzaz makes you look more like con artists than scientists. A sentence like this one is just absurd: > Clifford's Geometric Algebra enables a unified, intuitive and fresh perspective on vector spaces, giving elements of arbitrary dimensionality a natural home.

ngcc_hk 3y ago

My take is a bit different. May I quote but edit myself : 2 points by ngcc_hk 2 days ago | parent | context | prev | next [–] | on: Visualizing quaternions (2018) Once you accept that imaginary number is not about a straight real number but a number about rotation. And you have two number that is not the same, living in different dimensions. One about straight line and one about rotation I.e. X0 ops X1(another number system ) where X0, X1 is real You then have complex number or a+ bi where i^2 = -1 And you can have split complex number a+bj where j^2 = 1 etc The next move is not only the usual quaternions which one can, but to Clifford algebra x0 ops x1n1 ops x2n2 ops … xi is all real but ni is a different number system represent things not on the real number but a different and higher dimension object. For example, the Clifford Geometry define the 2nd not a i or j but a plane, so you have x0 + x1<plane> … and so on with more high dimensional object (especially if one may say x0 is x0<line>). Like complex number it simplify a lot of things. Spinsor would be easier to define this way say.

ngcc_hk 3y ago
After seeing the video I was a bit surprise by her two comments. This is after the most understandable introduction to this king of geometry. Shocking last 5 minutes. The first one that it is not that useful just different way of grouping. IaAware of this taking by both physics and computer people. But it is a total different way of looking and should have been taught in high school or at least undergrad. A bad cycle here. It has a lot of use to understand physics for normal people whilst the tensor … Also her struggle with thinking about shift to another game engine. Unreal … too complex and Godot … to engineering … her remark basically said she may have to go back to game programming (to get a living). Both honest comments and reflect hard reality.