2014810110493884650

2026-08-26 23:38:03 -04:00
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+---
+title: "One thing I like about GA is that it is so systemic and makes so much sense when it comes to linear stuff."
+type: archive
+source: twitter
+source_url: "https://x.com/Jonathan_Blow/status/2014821856772292614"
+author: "Jonathan Blow"
+handle: Jonathan_Blow
+post_id: "2014821856772292614"
+date: 2026-01-23
+archived: 2026-08-26
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "One thing I like about GA is that it is so systemic and makes so much sense when it comes to linear stuff."
+in_reply_to: ""
+parent_post_id: "2014810110493884650"
+---
+
+## Source
+
+- URL: https://x.com/Jonathan_Blow/status/2014821856772292614
+- Author: Jonathan Blow (@Jonathan_Blow)
+- Posted: 2026-01-23 22:05:38
+
+## Branch
+
+**1/** **@Jonathan_Blow** ^2014821856772292614
+
+One thing I like about GA is that it is so systemic and makes so much sense when it comes to linear stuff. The conformal stuff just kind of loses me though, at first glance it always looks like a lot of added complexity for small gain. What should I look at to convince myself I am wrong here?
+
+**2/** **@EricLengyel** ^2014843525083627609
+
+You're not wrong about the conformal stuff. While I find it convenient for expressing a small set of geometric calculations, I don't think it's very useful in general, and it certainly isn't a monument to efficiency. My book is very candid about this, going as far as calling parts of it "computationally absurd". (I also think just about all traditional presentations of CGA are quite poor and fail to convey any intuition whatsoever, which does contribute something to its lack of practical utility.)
+
+What I find most useful in GA is not the conformal stuff but the 4D projective algebra that encompasses homogeneous coordinates, planes, Plücker coordinates, quaternions, and dual quaternions all in one nice neat framework.
+
+The projective algebra is fully contained inside the conformal algebra, so it doesn't hurt to just have the extra conformal tools available in case you want to use them here and there. This does not require any changes to geometric representations for things not in the conformal algebra, so you wouldn't have to do anything stupid like storing five components for every point.
+
+**3/** **@Oktahedro** ^2014971292714140079
+
+**@EricLengyel** **@Jonathan_Blow**
+
+wow, you are wrong on this point. PGA is fine but CGA is ultrafine. Our Universe is eminently conformal. Take a deep breath and look at the quantum level for instance.
+
+**4/** **@EricLengyel** ^2014989505061958101
+
+**@Oktahedro** **@Jonathan_Blow**
+
+I’m aware. Jon and I work in the same industry, and as such, I think there is an implicit understanding between us that we’re talking about practical utility in computer graphics, collision detection, etc., and not theoretical physics. My comment does not apply universally.
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel 👏👏👏👏👏👏👏👏👏🚀🚀"
+type: archive
+source: twitter
+source_url: "https://x.com/gvi1herme/status/2014848338563064267"
+author: "Guilherme 🔭"
+handle: gvi1herme
+post_id: "2014848338563064267"
+date: 2026-01-23
+archived: 2026-08-26
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel 👏👏👏👏👏👏👏👏👏🚀🚀"
+in_reply_to: ""
+parent_post_id: "2014810110493884650"
+---
+
+## Source
+
+- URL: https://x.com/gvi1herme/status/2014848338563064267
+- Author: Guilherme 🔭 (@gvi1herme)
+- Posted: 2026-01-23 23:50:52
+
+## Branch
+
+**1/** **@gvi1herme** ^2014848338563064267
+
+**@EricLengyel**
+
+👏👏👏👏👏👏👏👏👏🚀🚀
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel Seems like this could be introduced much earlier like in high school"
+type: archive
+source: twitter
+source_url: "https://x.com/intspg/status/2014829949073686695"
+author: "Intrepid Sponge 𐇐𐇑𐇒𐇓𐇔𐇕𐇖𐇗𐇘𐇙𐇚"
+handle: intspg
+post_id: "2014829949073686695"
+date: 2026-01-23
+archived: 2026-08-26
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel Seems like this could be introduced much earlier like in high school"
+in_reply_to: ""
+parent_post_id: "2014810110493884650"
+---
+
+## Source
+
+- URL: https://x.com/intspg/status/2014829949073686695
+- Author: Intrepid Sponge 𐇐𐇑𐇒𐇓𐇔𐇕𐇖𐇗𐇘𐇙𐇚 (@intspg)
+- Posted: 2026-01-23 22:37:48
+
+## Branch
+
+**1/** **@intspg** ^2014829949073686695
+
+**@EricLengyel**
+
+Seems like this could be introduced much earlier like in high school
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a]]
@@ -0,0 +1,55 @@
+---
+title: "@EricLengyel can you provide a link to reference [3] ?"
+type: archive
+source: twitter
+source_url: "https://x.com/rlucas7/status/2014828024286306807"
+author: "Lucas Roberts"
+handle: rlucas7
+post_id: "2014828024286306807"
+date: 2026-01-23
+archived: 2026-08-26
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel can you provide a link to reference [3] ?"
+in_reply_to: ""
+parent_post_id: "2014810110493884650"
+---
+
+## Source
+
+- URL: https://x.com/rlucas7/status/2014828024286306807
+- Author: Lucas Roberts (@rlucas7)
+- Posted: 2026-01-23 22:30:09
+
+## Branch
+
+**1/** **@rlucas7** ^2014828024286306807
+
+**@EricLengyel**
+
+can you provide a link to reference [3] ?
+
+**2/** **@EricLengyel** ^2014844956796756215
+
+Lengyel, E. Projective Geometric Algebra Illuminated, 2024. ISBN 979-8985358254.
+
+https://www.amazon.com/dp/B0CXY8C72T/?tag=terathon-20
+
+**3/** **@OpenNetBattle** ^2014855981436428438
+
+**@EricLengyel** **@rlucas7**
+
+I purchased this when it came out on Amazon. It was an enlightening read. Do you know if the page thickness or material can be upgraded? I found that my quality highlighters bled through the pages and had to switch to red pen to make notes.
+
+**4/** **@EricLengyel** ^2014862120735904083
+
+**@OpenNetBattle** **@rlucas7**
+
+I've already selected the highest-quality paper that's available through Amazon's KDP (which prints the books). I have found it to be pretty good, but it's possible that the paper differs in quality depending on where in the world the actual printing took place.
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel This chip on your shoulder thing screams crank"
+type: archive
+source: twitter
+source_url: "https://x.com/BBobbity16/status/2014877514481500193"
+author: "BibbityBobbity16"
+handle: BBobbity16
+post_id: "2014877514481500193"
+date: 2026-01-24
+archived: 2026-08-26
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel This chip on your shoulder thing screams crank"
+in_reply_to: ""
+parent_post_id: "2014810110493884650"
+---
+
+## Source
+
+- URL: https://x.com/BBobbity16/status/2014877514481500193
+- Author: BibbityBobbity16 (@BBobbity16)
+- Posted: 2026-01-24 01:46:48
+
+## Branch
+
+**1/** **@BBobbity16** ^2014877514481500193
+
+**@EricLengyel**
+
+This chip on your shoulder thing screams crank
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel Awesome."
+type: archive
+source: twitter
+source_url: "https://x.com/DanielWhiteson/status/2014854858956996983"
+author: "Daniel Whiteson"
+handle: DanielWhiteson
+post_id: "2014854858956996983"
+date: 2026-01-24
+archived: 2026-08-26
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel Awesome."
+in_reply_to: ""
+parent_post_id: "2014810110493884650"
+---
+
+## Source
+
+- URL: https://x.com/DanielWhiteson/status/2014854858956996983
+- Author: Daniel Whiteson (@DanielWhiteson)
+- Posted: 2026-01-24 00:16:47
+
+## Branch
+
+**1/** **@DanielWhiteson** ^2014854858956996983
+
+**@EricLengyel**
+
+Awesome. The diversity of curiosity that leads to people doing deep dives to build out these ideas is super enriching to the whole intellectual enterprise.
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel I like GA way of explaining spinors and double cover for quantum mechanics"
+type: archive
+source: twitter
+source_url: "https://x.com/Yoloslide/status/2014906372631179452"
+author: "Slider"
+handle: Yoloslide
+post_id: "2014906372631179452"
+date: 2026-01-24
+archived: 2026-08-26
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel I like GA way of explaining spinors and double cover for quantum mechanics"
+in_reply_to: ""
+parent_post_id: "2014810110493884650"
+---
+
+## Source
+
+- URL: https://x.com/Yoloslide/status/2014906372631179452
+- Author: Slider (@Yoloslide)
+- Posted: 2026-01-24 03:41:29
+
+## Branch
+
+**1/** **@Yoloslide** ^2014906372631179452
+
+**@EricLengyel**
+
+I like GA way of explaining spinors and double cover for quantum mechanics
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel I've bounced off GA a few times after approaching it eagerly, so I get what is tantalizing and frustrating about it."
+type: archive
+source: twitter
+source_url: "https://x.com/alexisgallagher/status/2014894502436339780"
+author: "Alexis Gallagher"
+handle: alexisgallagher
+post_id: "2014894502436339780"
+date: 2026-01-24
+archived: 2026-08-26
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel I've bounced off GA a few times after approaching it eagerly, so I get what is tantalizing and frustrating about it."
+in_reply_to: ""
+parent_post_id: "2014810110493884650"
+---
+
+## Source
+
+- URL: https://x.com/alexisgallagher/status/2014894502436339780
+- Author: Alexis Gallagher (@alexisgallagher)
+- Posted: 2026-01-24 02:54:18
+
+## Branch
+
+**1/** **@alexisgallagher** ^2014894502436339780
+
+**@EricLengyel**
+
+I've bounced off GA a few times after approaching it eagerly, so I get what is tantalizing and frustrating about it. So I salute the effort the make it clear; and if you've succeeded so well that others are adopting your formulation, then double congratulations!
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a]]
@@ -0,0 +1,39 @@
+---
+title: "@EricLengyel GA is the most underappreciated advance in human knowledge in the past couple hundred years."
+type: archive
+source: twitter
+source_url: "https://x.com/dynamic_linker/status/2014881464530198962"
+author: "Jason Wilkes"
+handle: dynamic_linker
+post_id: "2014881464530198962"
+date: 2026-01-24
+archived: 2026-08-26
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel GA is the most underappreciated advance in human knowledge in the past couple hundred years."
+in_reply_to: ""
+parent_post_id: "2014810110493884650"
+---
+
+## Source
+
+- URL: https://x.com/dynamic_linker/status/2014881464530198962
+- Author: Jason Wilkes (@dynamic_linker)
+- Posted: 2026-01-24 02:02:30
+
+## Branch
+
+**1/** **@dynamic_linker** ^2014881464530198962
+
+**@EricLengyel**
+
+GA is the most underappreciated advance in human knowledge in the past couple hundred years. 
+
+Language of god just silently dropped and nobody noticed.
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a]]
@@ -0,0 +1,38 @@
+---
+title: "@EricLengyel Great, then this is for you too!"
+type: archive
+source: twitter
+source_url: "https://x.com/ehsanxpin/status/2015098963959992726"
+author: "Ehsan Azari"
+handle: ehsanxpin
+post_id: "2015098963959992726"
+date: 2026-01-24
+archived: 2026-08-26
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel Great, then this is for you too!"
+in_reply_to: ""
+parent_post_id: "2014810110493884650"
+---
+
+## Source
+
+- URL: https://x.com/ehsanxpin/status/2015098963959992726
+- Author: Ehsan Azari (@ehsanxpin)
+- Posted: 2026-01-24 16:26:46
+
+## Branch
+
+**1/** **@ehsanxpin** ^2015098963959992726
+
+**@EricLengyel**
+
+Great, then this is for you too!
+https://x.com/ehsanxpin/status/2014822751840706615?s=20
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel I've been following your work for a few years & I implemented in Python earlier stuff from your website & new stuff from the book, even the transwedge product."
+type: archive
+source: twitter
+source_url: "https://x.com/vinjovanovic/status/2014904274476581245"
+author: "V. Jovanovic"
+handle: vinjovanovic
+post_id: "2014904274476581245"
+date: 2026-01-24
+archived: 2026-08-26
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel I've been following your work for a few years & I implemented in Python earlier stuff from your website & new stuff from the book, even the transwedge product."
+in_reply_to: ""
+parent_post_id: "2014810110493884650"
+---
+
+## Source
+
+- URL: https://x.com/vinjovanovic/status/2014904274476581245
+- Author: V. Jovanovic (@vinjovanovic)
+- Posted: 2026-01-24 03:33:08
+
+## Branch
+
+**1/** **@vinjovanovic** ^2014904274476581245
+
+**@EricLengyel**
+
+I've been following your work for a few years & I implemented in Python earlier stuff from your website & new stuff from the book, even the transwedge product.  That's all at the frontier of GA so much that all other effort by others looks pale in comparison.  You restarted GA!
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a]]
@@ -0,0 +1,35 @@
+---
+title: "I've worked very hard over many years to develop a complete and correct picture of Grassmann and geometric algebras, often in the face of extreme antagonism."
+type: archive
+source: twitter
+source_url: "https://x.com/EricLengyel/status/2014810110493884650"
+author: "Eric Lengyel"
+handle: EricLengyel
+post_id: "2014810110493884650"
+date: 2026-01-23
+archived: 2026-08-26
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "I've worked very hard over many years to develop a complete and correct picture of Grassmann and geometric algebras, often in the face of extreme antagonism."
+in_reply_to: ""
+---
+
+## Source
+
+- URL: https://x.com/EricLengyel/status/2014810110493884650
+- Author: Eric Lengyel (@EricLengyel)
+- Posted: 2026-01-23 21:18:58
+
+## Thread
+
+**1/** **@EricLengyel** ^2014810110493884650
+
+I've worked very hard over many years to develop a complete and correct picture of Grassmann and geometric algebras, often in the face of extreme antagonism. The results of my efforts are now being adopted by prominent scientists and engineers in various fields. I feel very honored, and you can imagine the deep sense of satisfaction and justification this provides for me. The images below are from a recent NASA paper and a new textbook in aerospace engineering.
+
+![](https://pbs.twimg.com/media/G_YGqgpWgAAq0Fr?format=jpg&name=orig)
+![](https://pbs.twimg.com/media/G_YGtKqXAAAsJC8?format=jpg&name=orig)
+
+Branches: [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a/2026-01-23-gvi1herme-thread]], [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a/2026-01-23-intspg-seems-like-this-could-be-introduced-much-earlier]], [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a/2026-01-23-Jonathan_Blow-one-thing-i-like-about-ga-is-that-it-is-so]], [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a/2026-01-23-rlucas7-can-you-provide-a-link-to-reference-3]], [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a/2026-01-24-alexisgallagher-ive-bounced-off-ga-a-few-times-after-approaching]], [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a/2026-01-24-BBobbity16-this-chip-on-your-shoulder-thing-screams-crank]], [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a/2026-01-24-DanielWhiteson-awesome-the-diversity-of-curiosity-that-leads-to]], [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a/2026-01-24-dynamic_linker-ga-is-the-most-underappreciated-advance-in-human]], [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a/2026-01-24-ehsanxpin-great-then-this-is-for-you-too-https-x-com]], [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a/2026-01-24-vinjovanovic-ive-been-following-your-work-for-a-few-years-i]], [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a/2026-01-24-Yoloslide-i-like-ga-way-of-explaining-spinors-and-double]]
@@ -0,0 +1,12 @@
+---
+title: EricLengyel
+type: note
+draft: false
+description: Archived threads by EricLengyel.
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+---
+
+- [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a]]