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I'm assuming you're referring to: > This entire analysis of Clifford Algebra was based on my own foundational assumption that mathematics is not a human invent

I'm assuming you're referring to: > This entire analysis of Clifford Algebra was based on my own foundational assumption that mathematics is not a human invention, but more of a discovery of the essential principles of computation in the brain. I don't see what the issue with that is. It's an interesting hypothesis, and he's not alone in thinking about it. It's already a common stance that effective/valuable/interesting mathematical structures are direct consequences/reflections of the universe's own structure, and are seen more as discoveries than inventions. The author's proposal is just refining the question: have we come to this conclusion because it's an intrinsic property of the universe, or does it always seem present because we can only contemplate the universe through the human brain, which does its own structuring? As an example of respected thinkers thinking along these lines, Sir Arthur Eddington's The Philosophy of Physical Science works pretty well (Though, to be fair, it's not as if he's never been called 'out there').

j2kun 10y ago
The nonstandard definitions and notation, the lack of proper typesetting, random clip-arty images, the precociousness of "Grand Unified" whatever, and the general pretense that this isn't covered in most intro algebra graduate courses, all of that doesn't help his case. :(
- westoncb 10y ago
  I guess if it were purporting to be a text book rather than a blog post, these would be issues. As it stands, he's just someone on the internet sharing his thoughts. I'm not sure what you mean by 'precociousness' there, since I imagine you're not attempting to compliment the author—but he's hardly alone in considering Geometric Algebra to be a kind of foundation/'unified theory' for large swaths of mathematics. The other critiques seem mostly along the lines of, "he doesn't dress like us", which, while maybe a little off-putting to the in-crowd, shouldn't earn him an automatic dismissal or derogation.
  - j2kun 10y ago
    Of course people can write and wear whatever they like. I am simply explaining why it smells like crackpottery, since it seems you thought it was only due to that one sentence. And, for the record, anything aspiring to be a grand unified theory of mathematics has to go far beyond algebra.
    - westoncb 10y ago
      That's fair. In my initial comment I was using the quote as an exemplar of an idea running throughout the article--but my reply was directed more to the three comments implying the author is a crank than to yours in particular. As for the unified theory bit, I agree (you can see this in my previous comment) that Geometric Algebra wouldn't cover all of mathematics.
    - jacobolus 10y ago
      Here, start with these: (1) http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf (2) http://geocalc.clas.asu.edu/pdf/GrassmannsVision.pdf http://geocalc.clas.asu.edu/pdf/GrassmannsVision.pdf (3) http://geometry.mrao.cam.ac.uk/wp-content/uploads/2015/02/ImagNumbersArentReal.pdf http://geometry.mrao.cam.ac.uk/wp-content/uploads/2015/02/Im... (4) https://arxiv.org/pdf/1205.5935v1.pdf https://arxiv.org/pdf/1205.5935v1.pdf (5) http://www2.montgomerycollege.edu/departments/planet/planet/Numerical_Relativity/bookGA.pdf http://www2.montgomerycollege.edu/departments/planet/planet/... This book is also great if you are interested whatsoever in computer modeling of geometry, e.g. for robotics, computer vision, computer graphics, VR, etc. http://www.geometricalgebra.net http://www.geometricalgebra.net The “conformal geometric algebra” model developed there is a really amazing recent idea. If you don’t want to buy a book see the papers at http://geocalc.clas.asu.edu/html/UAFCG.html http://geocalc.clas.asu.edu/html/UAFCG.html or this Ph.D. thesis http://www2.eng.cam.ac.uk/~rjw57/pdf/r_wareham_pdh_thesis.pdf http://www2.eng.cam.ac.uk/~rjw57/pdf/r_wareham_pdh_thesis.pd...
GFK_of_xmaspast 10y ago
There's a whole bunch of weirdness spread throughout the post, like the section starting "Now we come to the concept of inversion, 1/x, a concept you learned so long ago that you probably can’t even remember learning it, but in all the time since then, nobody ever pointed out to you that it is a conceptual impossibility!" and continuing through the author getting het up about the one-point compactification of the plane. There's something about clifford algebras that brings out the fanatic in people, the first time I heard about them was Pertti Lounesto posting all sorts of rants in sci.math back in the day.

j2kun 10y ago

The nonstandard definitions and notation, the lack of proper typesetting, random clip-arty images, the precociousness of "Grand Unified" whatever, and the general pretense that this isn't covered in most intro algebra graduate courses, all of that doesn't help his case. :(

westoncb 10y ago
I guess if it were purporting to be a text book rather than a blog post, these would be issues. As it stands, he's just someone on the internet sharing his thoughts. I'm not sure what you mean by 'precociousness' there, since I imagine you're not attempting to compliment the author—but he's hardly alone in considering Geometric Algebra to be a kind of foundation/'unified theory' for large swaths of mathematics. The other critiques seem mostly along the lines of, "he doesn't dress like us", which, while maybe a little off-putting to the in-crowd, shouldn't earn him an automatic dismissal or derogation.
- j2kun 10y ago
  Of course people can write and wear whatever they like. I am simply explaining why it smells like crackpottery, since it seems you thought it was only due to that one sentence. And, for the record, anything aspiring to be a grand unified theory of mathematics has to go far beyond algebra.
  - westoncb 10y ago
    That's fair. In my initial comment I was using the quote as an exemplar of an idea running throughout the article--but my reply was directed more to the three comments implying the author is a crank than to yours in particular. As for the unified theory bit, I agree (you can see this in my previous comment) that Geometric Algebra wouldn't cover all of mathematics.
  - jacobolus 10y ago
    Here, start with these: (1) http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf (2) http://geocalc.clas.asu.edu/pdf/GrassmannsVision.pdf http://geocalc.clas.asu.edu/pdf/GrassmannsVision.pdf (3) http://geometry.mrao.cam.ac.uk/wp-content/uploads/2015/02/ImagNumbersArentReal.pdf http://geometry.mrao.cam.ac.uk/wp-content/uploads/2015/02/Im... (4) https://arxiv.org/pdf/1205.5935v1.pdf https://arxiv.org/pdf/1205.5935v1.pdf (5) http://www2.montgomerycollege.edu/departments/planet/planet/Numerical_Relativity/bookGA.pdf http://www2.montgomerycollege.edu/departments/planet/planet/... This book is also great if you are interested whatsoever in computer modeling of geometry, e.g. for robotics, computer vision, computer graphics, VR, etc. http://www.geometricalgebra.net http://www.geometricalgebra.net The “conformal geometric algebra” model developed there is a really amazing recent idea. If you don’t want to buy a book see the papers at http://geocalc.clas.asu.edu/html/UAFCG.html http://geocalc.clas.asu.edu/html/UAFCG.html or this Ph.D. thesis http://www2.eng.cam.ac.uk/~rjw57/pdf/r_wareham_pdh_thesis.pdf http://www2.eng.cam.ac.uk/~rjw57/pdf/r_wareham_pdh_thesis.pd...

GFK_of_xmaspast 10y ago

There's a whole bunch of weirdness spread throughout the post, like the section starting "Now we come to the concept of inversion, 1/x, a concept you learned so long ago that you probably can’t even remember learning it, but in all the time since then, nobody ever pointed out to you that it is a conceptual impossibility!" and continuing through the author getting het up about the one-point compactification of the plane. There's something about clifford algebras that brings out the fanatic in people, the first time I heard about them was Pertti Lounesto posting all sorts of rants in sci.math back in the day.