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Whenever this kind of topic arises there is always someone that has worked a bit on 3D geometry, that comes to school mathematicians and physicists on what they

by pa7x1 3y ago

Whenever this kind of topic arises there is always someone that has worked a bit on 3D geometry, that comes to school mathematicians and physicists on what they are missing out for not using geometric algebra. Usually with a weird tinge of conspiracy theory and cultish behavior mixed in. They are not missing out, they are aware of geometric algebras and the work of David Hestenes. They instead prefer to use exterior algebra and Clifford algebras as a generalization. There is no conspiracy theory or large-spread ignorance by the physics/mathematics community. Geometric algebra feels like introducing a quirky notation to talk about the same concepts, with no clear added conceptual or computational benefit. So most people ignore this approach. As I'm not particularly well-versed in the historical elements of this affair, nor I have much interest on them, I googled quickly and found this pertinent answer by John Baez: https://www.physicsoverflow.org/42912/geometric-algebra-geometric-calculus-all-that-its-hyped-be https://www.physicsoverflow.org/42912/geometric-algebra-geom...

msla 3y ago
“Symmetrical equations are good in their place, but ‘vector’ is a useless survival, or offshoot from quaternions, and has never been of the slightest use to any creature.” — William Thompson, 1st Baron Kelvin (better known as Lord Kelvin) Letter to G. F. FitzGerald (1896) as quoted in A History of Vector Analysis: The Evolution of the Idea of a Vectorial System (1994) by Michael J. Crowe, p. 120
jiggawatts 3y ago
Wait till I start telling you about how we should be using tau as a replacement for 2 pi! In all seriousness, we wouldn't accept this kind of thing in the standard library of a programming language. Imagine if due to a historical mistake, all arrays reported their length as 2x the number of items in them, and indices would similarly be multiplied by two. So the first item would be a[0], and then a[2], a[4], etc... Now imagine the entire software development world making excuses and justifications. "Oh, it's isomorphic, and shift-left-by-one is cheap!", or "sure, you can only use half of the system memory for any single array, but do you really need more than 2GB of data? 64-bit is common now anyway!" Physics is in a dire need of refactoring, but it has never had it happen. My opinion of studying it was that I didn't expect it to be the "history of physics". I expected to be studying the current state of the art, not the three-hundred-year journey of comedic errors getting there. Imagine starting Chemistry by studying alchemy for years and only then being told -- oh -- there's these things called atoms! Or trying to understand Linux by reading the commit history from day one. Etc...

by pa7x1 3y ago

msla 3y ago

“Symmetrical equations are good in their place, but ‘vector’ is a useless survival, or offshoot from quaternions, and has never been of the slightest use to any creature.” — William Thompson, 1st Baron Kelvin (better known as Lord Kelvin) Letter to G. F. FitzGerald (1896) as quoted in A History of Vector Analysis: The Evolution of the Idea of a Vectorial System (1994) by Michael J. Crowe, p. 120

jiggawatts 3y ago

Wait till I start telling you about how we should be using tau as a replacement for 2 pi! In all seriousness, we wouldn't accept this kind of thing in the standard library of a programming language. Imagine if due to a historical mistake, all arrays reported their length as 2x the number of items in them, and indices would similarly be multiplied by two. So the first item would be a[0], and then a[2], a[4], etc... Now imagine the entire software development world making excuses and justifications. "Oh, it's isomorphic, and shift-left-by-one is cheap!", or "sure, you can only use half of the system memory for any single array, but do you really need more than 2GB of data? 64-bit is common now anyway!" Physics is in a dire need of refactoring, but it has never had it happen. My opinion of studying it was that I didn't expect it to be the "history of physics". I expected to be studying the current state of the art, not the three-hundred-year journey of comedic errors getting there. Imagine starting Chemistry by studying alchemy for years and only then being told -- oh -- there's these things called atoms! Or trying to understand Linux by reading the commit history from day one. Etc...