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The neglect of the exterior algebra is the mathematical tragedy of our century. Why has it been neglected?
by unao 9y ago
The neglect of the exterior algebra is the
mathematical tragedy of our century.
Why has it been neglected?
- xyzzyz 9y agoI don't know what the quotation author meant. Exterior algebra has definitely been well understood and frequently used tool in 20th century.
- unao 9y agoYou are most likely right, but it is still kind of a niche. If you take a look at curriculum of Computer Science studies it is pretty non-present. From what I know Exterior / Geometric Algebra is superior in many ways to Linear Algebra: first it is backwards compatible and second (apparently) it is much more intuitive. But still Linear Algebra is pretty standard.
- xyzzyz 9y agoExterior algebra is not particularly useful in Computer Science, and that's probably it's non-present. There are other things competing for place in curriculum, and they probably deserve it more. Exterior algebra is not any more superior to linear algebra than multiplication is superior to addition. Both are important, there are important connections between the two, and you definitely need to understand addition first before you understand multiplication.
- auggierose 9y agoIf you look at the paper you will see that it uses a relatively advanced mathematical language. Did you understand the significance and meaning of exterior and geometric algebra from that? If not, then there you have a partial explanation for it. It is much easier to just understand vectors and matrices and maybe tensors for practical and applied work.
- yiyus 9y agoI do not agree with this. The simplest mathematical concepts can look very complicated when presented in a formal way. Learning the geometric product in high school wouldn't be more difficult than learning the dot and cross products, and would make obvious difficult to grasp concepts as complex numbers and even quaternions. There are historical reasons for which we do not learn this from another point of view, and in my opinion it is, indeed, a great tragedy. A tragedy that I hope will be remedied some day. Disclaimer: I deal everyday with 3D rotations. Euler angles have been traditionally used in my field, but they present many problems. Everybody knows we could do better with quaternions, but very few people understand them. I have shown many people how to interpret what quaternions are from geometric algebra concepts and I have not yet found anybody who doesn't think it is much more approachable that way.
- auggierose 9y agoI do not disagree with you! For example the book http://faculty.luther.edu/~macdonal/laga/ http://faculty.luther.edu/~macdonal/laga/ gives an elementary introduction to the subject. I have learnt about geometric algebra just this year, and applied it to compute the graphics in an app I wrote for a customer. It was a real eye opener, concepts that I struggled with before were really simplified by using geometric algebra. BUT: I would never have guessed the usefulness of it for me from this paper.
- zardo 9y agoSecond recommendation for laga.
- unao 9y agoThe formalism is pretty hard to grasp indeed, but I guess it concerns any mathematical theory. From what I know Exterior / Geometric Algebra is much simpler and more intuitive than let say Linear Algebra.
- auggierose 9y ago