'From Geometry to Algebra and Back Again: 4000 Years of Papers' by Jack Rusher

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.

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.

[jgyb]

The clapping for Emacs at 27:09 warmed the cockles of my cold dead heart

[ngideo]

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".

[nosy-cat]

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?"

[evandrofilipe]

That was such a fast pace, high octane talk, truly electrifying and it shows the importance of a hook before a big explanation

[JohnL]

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.

[Comonad]

I watched this a couple of months ago and thought “wow what a good talk”, then last week I was coding up some geometry based on a frustratingly written standard, and realised it was so unintuitive because they were effectively working in higher dimensions with 2D tools and came back to watch this video again, and I’m even more impressed than before.

Currently working on a GA solution, thank you for such an informative and entertaining talk

[AzureFlash]

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.

[jeremiahreilly]

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. ★★★★★

[ArrowofEntropy]

Terrific talk! One of the best GA intro talks to date.

[jimmonroe]

My coworkers are wondering why I am cackling so much. Thank you.

[stokedfool]

"Notation as a tool for thought" and no mention of Ken Iverson or APL?

[SimGunther]

for those curious to look up that last publication

[vscwrgr]

How to do a 3 hour talk in 30 minutes.

[UliTroyo]

I hoped this would be about GA. It had to be! GA is the bee’s knees.

[killymxi]

So, where the links are to be found?
Great talk, btw

[yash]

17:14 the australian univorsity's talk about "the vector algebra war" - the clifford algebra - 2^n types of numbers for n dimensional space.

[christophergame]

Bertrand, Bernard. It seems that it's bERnəd in England, bərnARd in the US. It seems that its bERtrənd in England, and mainly bERtrənd and sometimes bərtrAnd in the US. Capital letters here denote stress (louder).

[tactics]

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.