"From Geometry to Algebra and Back Again: 4000 Years of Papers" by Jack Rusher
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- Опубліковано 10 жов 2023
- A whirlwind tour of the history of our system of vector algebra - including applications from art, science, and programming - leading to a plea that we trade it in for something even better: Geometric Algebra.
Talk info: jackrusher.com/pwl-2023/
Jack Rusher
Applied Science Studio
@jackrusher
Jack Rusher's long career as a computer scientist includes time at Bell Labs/AT&T Research and a number of successful startups. His current work focuses on the deep relationship between art and technology.
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Recorded on Sept 22, 2023 in the PWLConf track at Strange Loop 2023 in St. Louis, MO.
thestrangeloop.com
pwlconf - Наука та технологія
The clapping for Emacs at 27:09 warmed the cockles of my cold dead heart
I discovered GA only earlier this year while working on a hobby project involving geometry. GA blew my mind, and my strongest emotion was "why the hell did they keep it secret from me at uni?"
You may be interested in the LinkedIn group that is the source of the YT channel that I administer. The group is (unsurprisingly!) "Pre-University Geometric Algebra", and was founded as a space where Ga students, teachers, and subject-matter experts can network and collaborate on developing instructional materials.
That was such a fast pace, high octane talk, truly electrifying and it shows the importance of a hook before a big explanation
I'm kind of annoyed that this notation wasn't there in my engineering classes, it looks like it would've made the equations in many topics way more elegant. I also feel like I was shown Lagrangian mechanics way too late in my life, to a point where I couldn't really get it but I could see how insanely powerful it is. It looked almost like a cheat code for dynamic equations.
Wow. What a great talk. I am a mathematically enamoured musician/artist/homemaker and I loved this talk. I write this before reading the papers, but your presentation lit my mind on fire. ★★★★★
I G&%@&n nearly fell out of my chair at 21:35, thank you. I am not even done watching this and you changed my life.
such a great talk
Terrific talk! One of the best GA intro talks to date.
Its wild that Rusher uses the term "Notation as a Tool for Thought", talks about Maths notations, and doesn't mention Ken Iverson's work on APL entitled "Notation as a Tool for Thought".
How to do a 3 hour talk in 30 minutes.
Hahaha
For real, this is dense.
So beautiful! 😭
"Notation as a tool for thought" and no mention of Ken Iverson or APL?
My coworkers are wondering why I am cackling so much. Thank you.
ReformingtheMathematicalLanguageofPhysics for those curious to look up that last publication
Fantastic introduction to GA.
Fancy seeing you here lol
Awesome talk!
I hoped this would be about GA. It had to be! GA is the bee’s knees.
Same
Quite enlightening/enjoyable
wow wow wow wow wow
So, where the links are to be found?
Great talk, btw
Link is in the description of the video. Preceded by "Talk Info"
17:14 the australian univorsity's talk about "the vector algebra war" - the clifford algebra - 2^n types of numbers for n dimensional space.
Good to see the creepy cult of Clifford is still beating that dead horse.
Clifford algebras are quaint, and are surely useful when you want to calculate things by hand. But they conceptually smoosh things together and leave weird degrees of freedom that aren't physical.
It's more important students of physics and engineering understand the difference between points and talent vectors than to know geometric algebra.
Until we no longer risk of adding Chicago and Paris together, these things have only marginal value.
As an engineering student, GA has huge pedagogic potential - mostly because it has intuitive and natural geometric interpretations.
Like the speaker said, every human lives in 3D space and has a brain developed to process spatial information much faster than symbols. It's simply a more efficient channel.
Instead, myself and millions of other students have to memorize rules to shuffle symbols - rarely knowing what we're adding together or why.
It also saves students from learning five different redundant notations, though it's useless to current mathematicians and researchers who are already used to those systems.
Honestly I doubt GA will ever catch on no matter how many benefits it has in education.
In a way it's like the metric system; which is easier to learn, much better for international coordination than a thousand local units... but it's useless to remote villagers who already have their ancient weights and measures.