782682929151381504, 1229229674397437954, 1389106103179378689, 1444787589320298499, 1467579488498159619, 1601902349601058816, 1436788358768828417

2026-08-27 21:50:29 -04:00
1 parent f10f7cbfec
commit 2e10386c44
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel smells a little bit like the world I live in lol"
+type: archive
+source: twitter
+source_url: "https://x.com/bmcnett/status/782706023261806592"
+author: "bmcnett"
+handle: bmcnett
+post_id: "782706023261806592"
+date: 2016-10-02
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel smells a little bit like the world I live in lol"
+in_reply_to: ""
+parent_post_id: "782682929151381504"
+---
+
+## Source
+
+- URL: https://x.com/bmcnett/status/782706023261806592
+- Author: bmcnett (@bmcnett)
+- Posted: 2016-10-02 22:17:12
+
+## Branch
+
+**1/** **@bmcnett** ^782706023261806592
+
+**@EricLengyel**
+
+smells a little bit like the world I live in lol
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2016-10-02-i-love-wasting-time-over-driver-bugs-that-clearly]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel It was tested and worked, but later changes in other bits broke it, and they didn't have automated test coverage."
+type: archive
+source: twitter
+source_url: "https://x.com/jwatte/status/782683922924576768"
+author: "Very Human Robot"
+handle: jwatte
+post_id: "782683922924576768"
+date: 2016-10-02
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel It was tested and worked, but later changes in other bits broke it, and they didn't have automated test coverage."
+in_reply_to: ""
+parent_post_id: "782682929151381504"
+---
+
+## Source
+
+- URL: https://x.com/jwatte/status/782683922924576768
+- Author: Very Human Robot (@jwatte)
+- Posted: 2016-10-02 20:49:23
+
+## Branch
+
+**1/** **@jwatte** ^782683922924576768
+
+**@EricLengyel**
+
+It was tested and worked, but later changes in other bits broke it, and they didn't have automated test coverage.
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2016-10-02-i-love-wasting-time-over-driver-bugs-that-clearly]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel yuuup"
+type: archive
+source: twitter
+source_url: "https://x.com/rygorous/status/782683567067312128"
+author: "Fabian Giesen"
+handle: rygorous
+post_id: "782683567067312128"
+date: 2016-10-02
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel yuuup"
+in_reply_to: ""
+parent_post_id: "782682929151381504"
+---
+
+## Source
+
+- URL: https://x.com/rygorous/status/782683567067312128
+- Author: Fabian Giesen (@rygorous)
+- Posted: 2016-10-02 20:47:58
+
+## Branch
+
+**1/** **@rygorous** ^782683567067312128
+
+**@EricLengyel**
+
+yuuup
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2016-10-02-i-love-wasting-time-over-driver-bugs-that-clearly]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel the story of my life lately."
+type: archive
+source: twitter
+source_url: "https://x.com/esmolikowski/status/782795598361534464"
+author: "Eric Smolikowski"
+handle: esmolikowski
+post_id: "782795598361534464"
+date: 2016-10-03
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel the story of my life lately."
+in_reply_to: ""
+parent_post_id: "782682929151381504"
+---
+
+## Source
+
+- URL: https://x.com/esmolikowski/status/782795598361534464
+- Author: Eric Smolikowski (@esmolikowski)
+- Posted: 2016-10-03 04:13:08
+
+## Branch
+
+**1/** **@esmolikowski** ^782795598361534464
+
+**@EricLengyel**
+
+the story of my life lately.
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2016-10-02-i-love-wasting-time-over-driver-bugs-that-clearly]]
@@ -0,0 +1,32 @@
+---
+title: "I love wasting time over driver bugs that clearly indicate that the functionality I'm trying to use was never tested even one time."
+type: archive
+source: twitter
+source_url: "https://x.com/EricLengyel/status/782682929151381504"
+author: "Eric Lengyel"
+handle: EricLengyel
+post_id: "782682929151381504"
+date: 2016-10-02
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "I love wasting time over driver bugs that clearly indicate that the functionality I'm trying to use was never tested even one time."
+in_reply_to: ""
+---
+
+## Source
+
+- URL: https://x.com/EricLengyel/status/782682929151381504
+- Author: Eric Lengyel (@EricLengyel)
+- Posted: 2016-10-02 20:45:26
+
+## Thread
+
+**1/** **@EricLengyel** ^782682929151381504
+
+I love wasting time over driver bugs that clearly indicate that the functionality I'm trying to use was never tested even one time.
+
+Branches: [[archive/threads/EricLengyel/2016-10-02-i-love-wasting-time-over-driver-bugs-that-clearly/2016-10-02-rygorous-yuuup]], [[archive/threads/EricLengyel/2016-10-02-i-love-wasting-time-over-driver-bugs-that-clearly/2016-10-02-jwatte-it-was-tested-and-worked-but-later-changes-in]], [[archive/threads/EricLengyel/2016-10-02-i-love-wasting-time-over-driver-bugs-that-clearly/2016-10-02-bmcnett-smells-a-little-bit-like-the-world-i-live-in-lol]], [[archive/threads/EricLengyel/2016-10-02-i-love-wasting-time-over-driver-bugs-that-clearly/2016-10-03-esmolikowski-the-story-of-my-life-lately]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel When I was young my dad taught me to read multiplication as “of”."
+type: archive
+source: twitter
+source_url: "https://x.com/82unpluggd/status/1229337343234015233"
+author: "Jacob Foshee"
+handle: 82unpluggd
+post_id: "1229337343234015233"
+date: 2020-02-17
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel When I was young my dad taught me to read multiplication as “of”."
+in_reply_to: ""
+parent_post_id: "1229229674397437954"
+---
+
+## Source
+
+- URL: https://x.com/82unpluggd/status/1229337343234015233
+- Author: Jacob Foshee (@82unpluggd)
+- Posted: 2020-02-17 09:30:37
+
+## Branch
+
+**1/** **@82unpluggd** ^1229337343234015233
+
+**@EricLengyel**
+
+When I was young my dad taught me to read multiplication as “of”. When I teach the Lin Alg basics for graphics math it all starts there. “Of” is a projection.
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel While I can't say I ever looked into into, introductory physics taught me that just about any formula complex enough can be derived"
+type: archive
+source: twitter
+source_url: "https://x.com/Antypurus/status/1229251848147787776"
+author: "Tiago Magalhães"
+handle: Antypurus
+post_id: "1229251848147787776"
+date: 2020-02-17
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel While I can't say I ever looked into into, introductory physics taught me that just about any formula complex enough can be derived"
+in_reply_to: ""
+parent_post_id: "1229229674397437954"
+---
+
+## Source
+
+- URL: https://x.com/Antypurus/status/1229251848147787776
+- Author: Tiago Magalhães (@Antypurus)
+- Posted: 2020-02-17 03:50:53
+
+## Branch
+
+**1/** **@Antypurus** ^1229251848147787776
+
+**@EricLengyel**
+
+While I can't say I ever looked into into, introductory physics taught me that just about any formula complex enough can be derived
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel I hope this a prelude for a tweetorial!"
+type: archive
+source: twitter
+source_url: "https://x.com/CShamone/status/1229230851872870401"
+author: "One propylcyclobutane 🌲🍀🌿🌷🐸"
+handle: CShamone
+post_id: "1229230851872870401"
+date: 2020-02-17
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel I hope this a prelude for a tweetorial!"
+in_reply_to: ""
+parent_post_id: "1229229674397437954"
+---
+
+## Source
+
+- URL: https://x.com/CShamone/status/1229230851872870401
+- Author: One propylcyclobutane 🌲🍀🌿🌷🐸 (@CShamone)
+- Posted: 2020-02-17 02:27:27
+
+## Branch
+
+**1/** **@CShamone** ^1229230851872870401
+
+**@EricLengyel**
+
+I hope this a prelude for a tweetorial!
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for]]
@@ -0,0 +1,43 @@
+---
+title: "@EricLengyel @Atrix256 I learned the inner product in university but I had to wait another 10 years for me to deep dive into outer products on my own."
+type: archive
+source: twitter
+source_url: "https://x.com/GuillaumeCL/status/1229242900988547072"
+author: "Guillaume Couture-Levesque 🍟🤰"
+handle: GuillaumeCL
+post_id: "1229242900988547072"
+date: 2020-02-17
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel @Atrix256 I learned the inner product in university but I had to wait another 10 years for me to deep dive into outer products on my own."
+in_reply_to: ""
+parent_post_id: "1229229674397437954"
+---
+
+## Source
+
+- URL: https://x.com/GuillaumeCL/status/1229242900988547072
+- Author: Guillaume Couture-Levesque 🍟🤰 (@GuillaumeCL)
+- Posted: 2020-02-17 03:15:20
+
+## Branch
+
+**1/** **@GuillaumeCL** ^1229242900988547072
+
+**@EricLengyel** **@Atrix256**
+
+I learned the inner product in university but I had to wait another 10 years for me to deep dive into outer products on my own. This is probably my own fault for not taking more higher math courses.
+
+**2/** **@EricLengyel** ^1229254926624124929
+
+**@GuillaumeCL** **@Atrix256**
+
+Based on what I've seen, most universities don't even offer the higher math courses that would teach the right concepts for a complete understanding. I'd like to see that change.
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel Had to look up Grassman, but I remember the parallelogram-area as one of the key elements in the buildup towards Vector algebra."
+type: archive
+source: twitter
+source_url: "https://x.com/ISaenen/status/1229393847005982721"
+author: "@skjaero.bsky.so + @Skjaero@mastodon.gamedev.place"
+handle: ISaenen
+post_id: "1229393847005982721"
+date: 2020-02-17
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel Had to look up Grassman, but I remember the parallelogram-area as one of the key elements in the buildup towards Vector algebra."
+in_reply_to: ""
+parent_post_id: "1229229674397437954"
+---
+
+## Source
+
+- URL: https://x.com/ISaenen/status/1229393847005982721
+- Author: @skjaero.bsky.so + @Skjaero@mastodon.gamedev.place (@ISaenen)
+- Posted: 2020-02-17 13:15:08
+
+## Branch
+
+**1/** **@ISaenen** ^1229393847005982721
+
+**@EricLengyel**
+
+Had to look up Grassman, but I remember the parallelogram-area as one of the key elements in the buildup towards Vector algebra. It would have been strange to talk about spaces and operations in 2+ dimensions for high-school grade(d?) math, no..
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for]]
@@ -0,0 +1,43 @@
+---
+title: "@EricLengyel Derived in high school (higher level maths only)."
+type: archive
+source: twitter
+source_url: "https://x.com/Peter_Blackburn/status/1229240719241445376"
+author: "Peter Blackburn"
+handle: Peter_Blackburn
+post_id: "1229240719241445376"
+date: 2020-02-17
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel Derived in high school (higher level maths only)."
+in_reply_to: ""
+parent_post_id: "1229229674397437954"
+---
+
+## Source
+
+- URL: https://x.com/Peter_Blackburn/status/1229240719241445376
+- Author: Peter Blackburn (@Peter_Blackburn)
+- Posted: 2020-02-17 03:06:40
+
+## Branch
+
+**1/** **@Peter_Blackburn** ^1229240719241445376
+
+**@EricLengyel**
+
+Derived in high school (higher level maths only). Ignored in university, only calculus covered:(
+
+**2/** **@EricLengyel** ^1229252171855581184
+
+**@Peter_Blackburn**
+
+What was the gist of the derivation you saw in high school?
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel I was tought rather this way: dot product is linear."
+type: archive
+source: twitter
+source_url: "https://x.com/czerenkow/status/1229329050725949441"
+author: "Piotr Wołoszkiewicz"
+handle: czerenkow
+post_id: "1229329050725949441"
+date: 2020-02-17
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel I was tought rather this way: dot product is linear."
+in_reply_to: ""
+parent_post_id: "1229229674397437954"
+---
+
+## Source
+
+- URL: https://x.com/czerenkow/status/1229329050725949441
+- Author: Piotr Wołoszkiewicz (@czerenkow)
+- Posted: 2020-02-17 08:57:40
+
+## Branch
+
+**1/** **@czerenkow** ^1229329050725949441
+
+**@EricLengyel**
+
+I was tought rather this way: dot product is linear. If we have basis e_i, and assume that dot(e_i, e_j)=kroneker_delta(i,j), then we can derive your formula easly. So this is like "Equivalence of the definitions" in wiki https://en.wikipedia.org/wiki/Dot_product
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for]]
@@ -0,0 +1,39 @@
+---
+title: "@EricLengyel I saw them in a CS cursus, so we obviously didn't saw algebra behind it, but I remember a few way to retrieve them with some math, I'm not sure how it relates to other stuff."
+type: archive
+source: twitter
+source_url: "https://x.com/edhebi/status/1229293662426800130"
+author: "Léo 🦋"
+handle: edhebi
+post_id: "1229293662426800130"
+date: 2020-02-17
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel I saw them in a CS cursus, so we obviously didn't saw algebra behind it, but I remember a few way to retrieve them with some math, I'm not sure how it relates to other stuff."
+in_reply_to: ""
+parent_post_id: "1229229674397437954"
+---
+
+## Source
+
+- URL: https://x.com/edhebi/status/1229293662426800130
+- Author: Léo 🦋 (@edhebi)
+- Posted: 2020-02-17 06:37:02
+
+## Branch
+
+**1/** **@edhebi** ^1229293662426800130
+
+**@EricLengyel**
+
+I saw them in a CS cursus, so we obviously didn't saw algebra behind it, but I remember a few way to retrieve them with some math, I'm not sure how it relates to other stuff.
+
+Dot product is multiplying a raw vector with a column on, and some matric multiplication for the cross)
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for]]
@@ -0,0 +1,73 @@
+---
+title: "@EricLengyel What's this supposed to mean - these _are_ basic definitions."
+type: archive
+source: twitter
+source_url: "https://x.com/ggerganov/status/1229262137488314368"
+author: "Georgi Gerganov"
+handle: ggerganov
+post_id: "1229262137488314368"
+date: 2020-02-17
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel What's this supposed to mean - these _are_ basic definitions."
+in_reply_to: ""
+parent_post_id: "1229229674397437954"
+---
+
+## Source
+
+- URL: https://x.com/ggerganov/status/1229262137488314368
+- Author: Georgi Gerganov (@ggerganov)
+- Posted: 2020-02-17 04:31:46
+
+## Branch
+
+**1/** **@ggerganov** ^1229262137488314368
+
+**@EricLengyel**
+
+What's this supposed to mean - these _are_ basic definitions. Everybody was taught that in school
+
+**2/** **@EricLengyel** ^1229264293234765824
+
+**@ggerganov**
+
+That's my point. Everybody was taught that those are the basic definitions, but it's not true. Those formulas naturally (and easily) arise from more fundamental principles in Grassmann algebra. But since *that* is not taught to the teachers, they simply don't know any better.
+
+**3/** **@ggerganov** ^1229267361959751680
+
+**@EricLengyel**
+
+I wouldn't call this a "derivation". It's a generalisation of the operations
+
+**4/** **@EricLengyel** ^1229269409748750337
+
+**@ggerganov**
+
+I didn’t state the derivation, yet. Both the dot product and cross product can be derived by starting with nothing more than the wedge product of something with itself is zero.
+
+**5/** **@prathyvsh** ^1229340464974725120
+
+**@EricLengyel** **@ggerganov**
+
+But then how can that be derived?
+
+**6/** **@elijahlape** ^1229538734200295425
+
+**@prathyvsh**
+
+It's covered here https://youtu.be/WZApQkDBr5o
+
+**7/** **@prathyvsh** ^1229553290142072833
+
+**@elijahlape**
+
+This looks lovely. Let me take a look. But I think it’s an axiomatic first principle foundation that can’t be “derived”.
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for]]
@@ -0,0 +1,43 @@
+---
+title: "@EricLengyel In the absence of exterior algebra, you can also have students discuss why symmetry, bilinearity, and positivity are natural geometric properties for any inner product."
+type: archive
+source: twitter
+source_url: "https://x.com/keenanisalive/status/1229351518614249472"
+author: "Keenan Crane"
+handle: keenanisalive
+post_id: "1229351518614249472"
+date: 2020-02-17
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel In the absence of exterior algebra, you can also have students discuss why symmetry, bilinearity, and positivity are natural geometric properties for any inner product."
+in_reply_to: ""
+parent_post_id: "1229229674397437954"
+---
+
+## Source
+
+- URL: https://x.com/keenanisalive/status/1229351518614249472
+- Author: Keenan Crane (@keenanisalive)
+- Posted: 2020-02-17 10:26:56
+
+## Branch
+
+**1/** **@keenanisalive** ^1229351518614249472
+
+**@EricLengyel**
+
+In the absence of exterior algebra, you can also have students discuss why symmetry, bilinearity, and positivity are natural geometric properties for any inner product. Then show that the Euclidean dot product is the only one invariant to (Euclidean) rigid motions, up to scale.
+
+**2/** **@AntoPatriarca** ^1229392878893510656
+
+**@keenanisalive** **@EricLengyel**
+
+This was shown to me in my first linear algebra course at college. I would argue GA does not make any of this easier, it just change what is considered as a basic definition and what is instead derived from them.
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for]]
@@ -0,0 +1,43 @@
+---
+title: "@EricLengyel We were taught these in geometric terms."
+type: archive
+source: twitter
+source_url: "https://x.com/kernelfusion_/status/1229254999810592769"
+author: "ap 🦖"
+handle: kernelfusion_
+post_id: "1229254999810592769"
+date: 2020-02-17
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel We were taught these in geometric terms."
+in_reply_to: ""
+parent_post_id: "1229229674397437954"
+---
+
+## Source
+
+- URL: https://x.com/kernelfusion_/status/1229254999810592769
+- Author: ap 🦖 (@kernelfusion_)
+- Posted: 2020-02-17 04:03:25
+
+## Branch
+
+**1/** **@kernelfusion_** ^1229254999810592769
+
+**@EricLengyel**
+
+We were taught these in geometric terms. Dot product is a product with a vector projection, and cross product is a scaled normal.
+
+**2/** **@EricLengyel** ^1229257472604397568
+
+**@killerooo**
+
+This view of the cross product is what stops a lot of people from generalizing to other numbers of dimensions. The cross product is better viewed as a parallelogram in the plane determined by the two vectors being multiplied.
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for]]
@@ -0,0 +1,43 @@
+---
+title: "@EricLengyel Yup, in high school and college."
+type: archive
+source: twitter
+source_url: "https://x.com/masonremaley/status/1229277671625936896"
+author: "Mason Remaley"
+handle: masonremaley
+post_id: "1229277671625936896"
+date: 2020-02-17
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel Yup, in high school and college."
+in_reply_to: ""
+parent_post_id: "1229229674397437954"
+---
+
+## Source
+
+- URL: https://x.com/masonremaley/status/1229277671625936896
+- Author: Mason Remaley (@masonremaley)
+- Posted: 2020-02-17 05:33:30
+
+## Branch
+
+**1/** **@masonremaley** ^1229277671625936896
+
+**@EricLengyel**
+
+Yup, in high school and college. I stopped taking math in college after a professor told me I shouldn’t worry about how cross products work—I figured if that’s the level of insight I’d get from the classes I was better off self studying
+
+**2/** **@masonremaley** ^1229278098731831296
+
+**@EricLengyel**
+
+(5 years later I’m pretty sure that, for me, this was absolutely the right call)
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for]]
@@ -0,0 +1,55 @@
+---
+title: "@EricLengyel I don’t even know how to answer a question like this."
+type: archive
+source: twitter
+source_url: "https://x.com/maxliani/status/1229246838860959744"
+author: "Max Liani"
+handle: maxliani
+post_id: "1229246838860959744"
+date: 2020-02-17
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel I don’t even know how to answer a question like this."
+in_reply_to: ""
+parent_post_id: "1229229674397437954"
+---
+
+## Source
+
+- URL: https://x.com/maxliani/status/1229246838860959744
+- Author: Max Liani (@maxliani)
+- Posted: 2020-02-17 03:30:59
+
+## Branch
+
+**1/** **@maxliani** ^1229246838860959744
+
+**@EricLengyel**
+
+I don’t even know how to answer a question like this. Very little of what I know was actually taught to me. Most of what I do I had to search for or figure out in my own...
+
+**2/** **@maxliani** ^1229247127001264129
+
+**@EricLengyel**
+
+... that’s probably why I know so little.
+
+**3/** **@EricLengyel** ^1229254113210204161
+
+**@maxliani**
+
+I would consider reading something in a book to be a form of teaching. But I can relate to having to figure out a lot of stuff on your own. Much of the teaching is horribly inadequate.
+
+**4/** **@maxliani** ^1229255742256865280
+
+**@EricLengyel**
+
+In which case I’d say I saw the formulas in some book and thy were good enough for me. Although I am a visual thinker and I tend not to remember the formulas... often re-deriving them using visual or geometric interpretations. Still not sure where that places me :)
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel Unfortunately, I was."
+type: archive
+source: twitter
+source_url: "https://x.com/pikuma/status/1229232718061473793"
+author: "pikuma.com"
+handle: pikuma
+post_id: "1229232718061473793"
+date: 2020-02-17
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel Unfortunately, I was."
+in_reply_to: ""
+parent_post_id: "1229229674397437954"
+---
+
+## Source
+
+- URL: https://x.com/pikuma/status/1229232718061473793
+- Author: pikuma.com (@pikuma)
+- Posted: 2020-02-17 02:34:52
+
+## Branch
+
+**1/** **@pikuma** ^1229232718061473793
+
+**@EricLengyel**
+
+Unfortunately, I was. I had to go out of my way to find a satisfying answer to this... years later.
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel People were taught things like this in secondary/high school??"
+type: archive
+source: twitter
+source_url: "https://x.com/soylentgraham/status/1229324845260967937"
+author: "graham (parody)"
+handle: soylentgraham
+post_id: "1229324845260967937"
+date: 2020-02-17
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel People were taught things like this in secondary/high school??"
+in_reply_to: ""
+parent_post_id: "1229229674397437954"
+---
+
+## Source
+
+- URL: https://x.com/soylentgraham/status/1229324845260967937
+- Author: graham (parody) (@soylentgraham)
+- Posted: 2020-02-17 08:40:57
+
+## Branch
+
+**1/** **@soylentgraham** ^1229324845260967937
+
+**@EricLengyel**
+
+People were taught things like this in secondary/high school??
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for]]
@@ -0,0 +1,32 @@
+---
+title: "How many people were taught that the formulas for the dot product (x₁x₂ + y₁y₂ + z₁z₂) and cross product (y₁z₂ − y₂z₁, z₁x₂ − z₂x₁, x₁y₂ − x₂y₁) are simply definitions and cannot be derived?"
+type: archive
+source: twitter
+source_url: "https://x.com/EricLengyel/status/1229229674397437954"
+author: "Eric Lengyel"
+handle: EricLengyel
+post_id: "1229229674397437954"
+date: 2020-02-17
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "How many people were taught that the formulas for the dot product (x₁x₂ + y₁y₂ + z₁z₂) and cross product (y₁z₂ − y₂z₁, z₁x₂ − z₂x₁, x₁y₂ − x₂y₁) are simply definitions and cannot be derived?"
+in_reply_to: ""
+---
+
+## Source
+
+- URL: https://x.com/EricLengyel/status/1229229674397437954
+- Author: Eric Lengyel (@EricLengyel)
+- Posted: 2020-02-17 02:22:47
+
+## Thread
+
+**1/** **@EricLengyel** ^1229229674397437954
+
+How many people were taught that the formulas for the dot product (x₁x₂ + y₁y₂ + z₁z₂) and cross product (y₁z₂ − y₂z₁, z₁x₂ − z₂x₁, x₁y₂ − x₂y₁) are simply definitions and cannot be derived?
+
+Branches: [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for/2020-02-17-CShamone-i-hope-this-a-prelude-for-a-tweetorial]], [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for/2020-02-17-pikuma-unfortunately-i-was-i-had-to-go-out-of-my-way-to]], [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for/2020-02-17-Peter_Blackburn-derived-in-high-school-higher-level-maths-only]], [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for/2020-02-17-GuillaumeCL-i-learned-the-inner-product-in-university-but-i]], [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for/2020-02-17-maxliani-i-dont-even-know-how-to-answer-a-question-like]], [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for/2020-02-17-Antypurus-while-i-cant-say-i-ever-looked-into-into]], [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for/2020-02-17-kernelfusion_-we-were-taught-these-in-geometric-terms-dot]], [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for/2020-02-17-ggerganov-whats-this-supposed-to-mean-these-are-basic]], [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for/2020-02-17-masonremaley-yup-in-high-school-and-college-i-stopped-taking]], [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for/2020-02-17-edhebi-i-saw-them-in-a-cs-cursus-so-we-obviously-didnt]], [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for/2020-02-17-soylentgraham-people-were-taught-things-like-this-in-secondary]], [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for/2020-02-17-czerenkow-i-was-tought-rather-this-way-dot-product-is]], [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for/2020-02-17-82unpluggd-when-i-was-young-my-dad-taught-me-to-read]], [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for/2020-02-17-keenanisalive-in-the-absence-of-exterior-algebra-you-can-also]], [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for/2020-02-17-ISaenen-had-to-look-up-grassman-but-i-remember-the]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel awesome!"
+type: archive
+source: twitter
+source_url: "https://x.com/JEdwardPrice1/status/1389571619429961728"
+author: "J Edward Price"
+handle: JEdwardPrice1
+post_id: "1389571619429961728"
+date: 2021-05-04
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel awesome!"
+in_reply_to: ""
+parent_post_id: "1389106114583678980"
+---
+
+## Source
+
+- URL: https://x.com/JEdwardPrice1/status/1389571619429961728
+- Author: J Edward Price (@JEdwardPrice1)
+- Posted: 2021-05-04 13:24:25
+
+## Branch
+
+**1/** **@JEdwardPrice1** ^1389571619429961728
+
+**@EricLengyel**
+
+awesome!
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2021-05-03-back-in-1993-i-was-taking-a-number-theory-class]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel You sir are my hero"
+type: archive
+source: twitter
+source_url: "https://x.com/JonathanShafter/status/1389377790395527169"
+author: "Jonathan Shafter"
+handle: JonathanShafter
+post_id: "1389377790395527169"
+date: 2021-05-04
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel You sir are my hero"
+in_reply_to: ""
+parent_post_id: "1389106114583678980"
+---
+
+## Source
+
+- URL: https://x.com/JonathanShafter/status/1389377790395527169
+- Author: Jonathan Shafter (@JonathanShafter)
+- Posted: 2021-05-04 00:34:13
+
+## Branch
+
+**1/** **@JonathanShafter** ^1389377790395527169
+
+**@EricLengyel**
+
+You sir are my hero
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2021-05-03-back-in-1993-i-was-taking-a-number-theory-class]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel"
+type: archive
+source: twitter
+source_url: "https://x.com/StevenB337/status/1389433710047637504"
+author: "Steve Brady🏛️SteveBrady.eth"
+handle: StevenB337
+post_id: "1389433710047637504"
+date: 2021-05-04
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel"
+in_reply_to: ""
+parent_post_id: "1389106114583678980"
+---
+
+## Source
+
+- URL: https://x.com/StevenB337/status/1389433710047637504
+- Author: Steve Brady🏛️SteveBrady.eth (@StevenB337)
+- Posted: 2021-05-04 04:16:25
+
+## Branch
+
+**1/** **@StevenB337** ^1389433710047637504
+
+**@EricLengyel**
+
+<video controls src="https://video.twimg.com/tweet_video/E0hClw1WUAACsNY.mp4"></video>
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2021-05-03-back-in-1993-i-was-taking-a-number-theory-class]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel @threadreaderapp please unroll"
+type: archive
+source: twitter
+source_url: "https://x.com/otaria123/status/1389620691654303745"
+author: "otaria123"
+handle: otaria123
+post_id: "1389620691654303745"
+date: 2021-05-04
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel @threadreaderapp please unroll"
+in_reply_to: ""
+parent_post_id: "1389106114583678980"
+---
+
+## Source
+
+- URL: https://x.com/otaria123/status/1389620691654303745
+- Author: otaria123 (@otaria123)
+- Posted: 2021-05-04 16:39:25
+
+## Branch
+
+**1/** **@otaria123** ^1389620691654303745
+
+**@EricLengyel** **@threadreaderapp**
+
+please unroll
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2021-05-03-back-in-1993-i-was-taking-a-number-theory-class]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel Did the computer lab catch on?"
+type: archive
+source: twitter
+source_url: "https://x.com/riptusk331/status/1389729041863921677"
+author: "riptusk"
+handle: riptusk331
+post_id: "1389729041863921677"
+date: 2021-05-04
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel Did the computer lab catch on?"
+in_reply_to: ""
+parent_post_id: "1389106114583678980"
+---
+
+## Source
+
+- URL: https://x.com/riptusk331/status/1389729041863921677
+- Author: riptusk (@riptusk331)
+- Posted: 2021-05-04 23:49:58
+
+## Branch
+
+**1/** **@riptusk331** ^1389729041863921677
+
+**@EricLengyel**
+
+Did the computer lab catch on?
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2021-05-03-back-in-1993-i-was-taking-a-number-theory-class]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel Macsbug was freaking work of genius imho @jdeamattson"
+type: archive
+source: twitter
+source_url: "https://x.com/thinkx/status/1389598107105701888"
+author: "think(x)"
+handle: thinkx
+post_id: "1389598107105701888"
+date: 2021-05-04
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel Macsbug was freaking work of genius imho @jdeamattson"
+in_reply_to: ""
+parent_post_id: "1389106114583678980"
+---
+
+## Source
+
+- URL: https://x.com/thinkx/status/1389598107105701888
+- Author: think(x) (@thinkx)
+- Posted: 2021-05-04 15:09:40
+
+## Branch
+
+**1/** **@thinkx** ^1389598107105701888
+
+**@EricLengyel**
+
+Macsbug was freaking work of genius imho @jdeamattson
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2021-05-03-back-in-1993-i-was-taking-a-number-theory-class]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel they let you win the contest cuz they felt sry 4 u staying in a computer lab all night instead of with friends"
+type: archive
+source: twitter
+source_url: "https://x.com/vapejuicepen/status/1389617536753414149"
+author: "BcupEmoWin"
+handle: vapejuicepen
+post_id: "1389617536753414149"
+date: 2021-05-04
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel they let you win the contest cuz they felt sry 4 u staying in a computer lab all night instead of with friends"
+in_reply_to: ""
+parent_post_id: "1389106114583678980"
+---
+
+## Source
+
+- URL: https://x.com/vapejuicepen/status/1389617536753414149
+- Author: BcupEmoWin (@vapejuicepen)
+- Posted: 2021-05-04 16:26:53
+
+## Branch
+
+**1/** **@vapejuicepen** ^1389617536753414149
+
+**@EricLengyel**
+
+they let you win the contest cuz they felt sry 4 u staying in a computer lab all night instead of with friends
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2021-05-03-back-in-1993-i-was-taking-a-number-theory-class]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel Serious applause and kudos!"
+type: archive
+source: twitter
+source_url: "https://x.com/udsd007/status/1390790449816915973"
+author: "Mike Andrews, woodbutcher, σισαδμιν, microscopist"
+handle: udsd007
+post_id: "1390790449816915973"
+date: 2021-05-07
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel Serious applause and kudos!"
+in_reply_to: ""
+parent_post_id: "1389106114583678980"
+---
+
+## Source
+
+- URL: https://x.com/udsd007/status/1390790449816915973
+- Author: Mike Andrews, woodbutcher, σισαδμιν, microscopist (@udsd007)
+- Posted: 2021-05-07 22:07:37
+
+## Branch
+
+**1/** **@udsd007** ^1390790449816915973
+
+**@EricLengyel**
+
+Serious applause and kudos!
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2021-05-03-back-in-1993-i-was-taking-a-number-theory-class]]
@@ -0,0 +1,66 @@
+---
+title: "Back in 1993, I was taking a number theory class, and there was a semester-long factorization contest that we could participate in."
+type: archive
+source: twitter
+source_url: "https://x.com/EricLengyel/status/1389106103179378689"
+author: "Eric Lengyel"
+handle: EricLengyel
+post_id: "1389106103179378689"
+date: 2021-05-03
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "Back in 1993, I was taking a number theory class, and there was a semester-long factorization contest that we could participate in."
+in_reply_to: ""
+---
+
+## Source
+
+- URL: https://x.com/EricLengyel/status/1389106103179378689
+- Author: Eric Lengyel (@EricLengyel)
+- Posted: 2021-05-03 06:34:37
+
+## Thread
+
+**1/** **@EricLengyel** ^1389106103179378689
+
+Back in 1993, I was taking a number theory class, and there was a semester-long factorization contest that we could participate in. I implemented a distributed multiple polynomial quadratic sieve (MPQS) for the Mac, and I needed a cluster of computers to run it on.
+
+**2/** **@EricLengyel** ^1389106104240525319
+
+The computer lab in the math building had a bunch of Mac Centris 650s on an AppleTalk network. But they were running some kind of secure software that didn't give you access to the Finder, only specific software, so I couldn't pop in a disk and run my own programs.
+
+**3/** **@EricLengyel** ^1389106107696631808
+
+You can see in this picture that the Centris had two little buttons on the front. One was a reset button, and the other generated a non-maskable interrupt (NMI). If Macsbug was installed, the NMI button froze everything and dropped you into the system debugger.
+
+![](https://pbs.twimg.com/media/E0cP-6yVgAERsOJ?format=jpg&name=orig)
+
+**4/** **@EricLengyel** ^1389106109265235970
+
+If no debugger was installed, then the NMI button brought up a small system monitor window. It was extremely basic and didn't do much more than let you look at raw memory and, importantly, let you poke new byte values into memory at arbitrary addresses.
+
+**5/** **@EricLengyel** ^1389106110389391362
+
+On my own computer, I wrote a tiny program that would display the system file picker and execute whatever file was chosen. I printed out the machine code for that program and brought it with me to the lab. It was only a few dozen 8-bit hex values.
+
+**6/** **@EricLengyel** ^1389106111450468352
+
+I could enter that program in the system monitor, but I needed a way to run it. The Mac had several hooks (function pointers) at fixed low-memory addresses, and one of them was a callback that would be repeatedly invoked as the user was dragging something in the GUI.
+
+**7/** **@EricLengyel** ^1389106112436195330
+
+So I put my program's address into that hook, exited the monitor, and dragged a scroll bar indicator somewhere. Bam! The system file picker appears. I navigate to the Finder program, select it, and click Open. The Finder launches, and I have full access to the computer.
+
+**8/** **@EricLengyel** ^1389106113618989057
+
+I repeated this on about 15 computers and loaded my MPQS program on each of them. About half the lab was now running a distributed factorization algorithm controlled by a central host over the network, and the whole thing actually got results!
+
+**9/** **@EricLengyel** ^1389106114583678980
+
+On these computers, I could factor a general number with around 70 decimal digits in a reasonable amount of time (like overnight). And yes, I won the contest.
+
+Branches: [[archive/threads/EricLengyel/2021-05-03-back-in-1993-i-was-taking-a-number-theory-class/2021-05-04-JonathanShafter-you-sir-are-my-hero]], [[archive/threads/EricLengyel/2021-05-03-back-in-1993-i-was-taking-a-number-theory-class/2021-05-04-StevenB337-thread]], [[archive/threads/EricLengyel/2021-05-03-back-in-1993-i-was-taking-a-number-theory-class/2021-05-04-JEdwardPrice1-awesome]], [[archive/threads/EricLengyel/2021-05-03-back-in-1993-i-was-taking-a-number-theory-class/2021-05-04-thinkx-macsbug-was-freaking-work-of-genius-imho]], [[archive/threads/EricLengyel/2021-05-03-back-in-1993-i-was-taking-a-number-theory-class/2021-05-04-vapejuicepen-they-let-you-win-the-contest-cuz-they-felt-sry-4]], [[archive/threads/EricLengyel/2021-05-03-back-in-1993-i-was-taking-a-number-theory-class/2021-05-04-otaria123-please-unroll]], [[archive/threads/EricLengyel/2021-05-03-back-in-1993-i-was-taking-a-number-theory-class/2021-05-04-riptusk331-did-the-computer-lab-catch-on]], [[archive/threads/EricLengyel/2021-05-03-back-in-1993-i-was-taking-a-number-theory-class/2021-05-07-udsd007-serious-applause-and-kudos]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel Okay, I'm super curious - what _was_ Photoshop doing?"
+type: archive
+source: twitter
+source_url: "https://x.com/SheriefFYI/status/1444788762945286144"
+author: "Sherief, FYI"
+handle: SheriefFYI
+post_id: "1444788762945286144"
+date: 2021-10-03
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel Okay, I'm super curious - what _was_ Photoshop doing?"
+in_reply_to: ""
+parent_post_id: "1444787589320298499"
+---
+
+## Source
+
+- URL: https://x.com/SheriefFYI/status/1444788762945286144
+- Author: Sherief, FYI (@SheriefFYI)
+- Posted: 2021-10-03 22:17:38
+
+## Branch
+
+**1/** **@SheriefFYI** ^1444788762945286144
+
+**@EricLengyel**
+
+Okay, I'm super curious - what _was_ Photoshop doing?
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2021-10-03-so-i-was-seeing-inexplicable-100-200-ms-frame]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel I would’ve put money on Chrome"
+type: archive
+source: twitter
+source_url: "https://x.com/rompa69/status/1445001652503650304"
+author: "Mark Wayland"
+handle: rompa69
+post_id: "1445001652503650304"
+date: 2021-10-04
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel I would’ve put money on Chrome"
+in_reply_to: ""
+parent_post_id: "1444787589320298499"
+---
+
+## Source
+
+- URL: https://x.com/rompa69/status/1445001652503650304
+- Author: Mark Wayland (@rompa69)
+- Posted: 2021-10-04 12:23:35
+
+## Branch
+
+**1/** **@rompa69** ^1445001652503650304
+
+**@EricLengyel**
+
+I would’ve put money on Chrome
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2021-10-03-so-i-was-seeing-inexplicable-100-200-ms-frame]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel Not enuf GPUs"
+type: archive
+source: twitter
+source_url: "https://x.com/s0lly/status/1444992737779015686"
+author: "s0lly"
+handle: s0lly
+post_id: "1444992737779015686"
+date: 2021-10-04
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel Not enuf GPUs"
+in_reply_to: ""
+parent_post_id: "1444787589320298499"
+---
+
+## Source
+
+- URL: https://x.com/s0lly/status/1444992737779015686
+- Author: s0lly (@s0lly)
+- Posted: 2021-10-04 11:48:10
+
+## Branch
+
+**1/** **@s0lly** ^1444992737779015686
+
+**@EricLengyel**
+
+Not enuf GPUs
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2021-10-03-so-i-was-seeing-inexplicable-100-200-ms-frame]]
@@ -0,0 +1,32 @@
+---
+title: "So I was seeing inexplicable 100-200 ms frame times in my game, and I couldn't figure out what was going on."
+type: archive
+source: twitter
+source_url: "https://x.com/EricLengyel/status/1444787589320298499"
+author: "Eric Lengyel"
+handle: EricLengyel
+post_id: "1444787589320298499"
+date: 2021-10-03
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "So I was seeing inexplicable 100-200 ms frame times in my game, and I couldn't figure out what was going on."
+in_reply_to: ""
+---
+
+## Source
+
+- URL: https://x.com/EricLengyel/status/1444787589320298499
+- Author: Eric Lengyel (@EricLengyel)
+- Posted: 2021-10-03 22:12:58
+
+## Thread
+
+**1/** **@EricLengyel** ^1444787589320298499
+
+So I was seeing inexplicable 100-200 ms frame times in my game, and I couldn't figure out what was going on. Turns out that it was caused by Photoshop running in the background with no documents open.
+
+Branches: [[archive/threads/EricLengyel/2021-10-03-so-i-was-seeing-inexplicable-100-200-ms-frame/2021-10-03-SheriefFYI-okay-im-super-curious-what-was-photoshop-doing]], [[archive/threads/EricLengyel/2021-10-03-so-i-was-seeing-inexplicable-100-200-ms-frame/2021-10-04-s0lly-not-enuf-gpus]], [[archive/threads/EricLengyel/2021-10-03-so-i-was-seeing-inexplicable-100-200-ms-frame/2021-10-04-rompa69-i-wouldve-put-money-on-chrome]]
@@ -0,0 +1,40 @@
+---
+title: "@FlohOfWoe @xgalaxy @CasualEffects @soylentgraham @MGDev91 The original glTF 2.0 spec did have the 4-influence limit."
+type: archive
+source: twitter
+source_url: "https://x.com/EricLengyel/status/1467579488498159619"
+author: "Eric Lengyel"
+handle: EricLengyel
+post_id: "1467579488498159619"
+date: 2021-12-05
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@FlohOfWoe @xgalaxy @CasualEffects @soylentgraham @MGDev91 The original glTF 2.0 spec did have the 4-influence limit."
+in_reply_to: ""
+---
+
+## Source
+
+- URL: https://x.com/EricLengyel/status/1467579488498159619
+- Author: Eric Lengyel (@EricLengyel)
+- Posted: 2021-12-05 19:39:51
+
+## Thread
+
+**1/** **@EricLengyel** ^1467579488498159619
+
+**@FlohOfWoe** **@xgalaxy** **@CasualEffects** **@soylentgraham** **@MGDev91**
+
+The original glTF 2.0 spec did have the 4-influence limit. Later, they bolted on the hacky extra components to fix this, but they never changed the version number. This is one of many ways in which glTF was terribly designed and delivered poorly.
+
+https://opengex.org/comparison.html
+
+**2/** **@EricLengyel** ^1467580446636576770
+
+**@FlohOfWoe** **@xgalaxy** **@CasualEffects** **@soylentgraham** **@MGDev91**
+
+The president of Khronos himself admitted to me that they failed to get the proper expert input on glTF. But they just crammed it down everyone's throat anyway, and somehow they now have a community of fanboys who can't take criticism of something they weren't involved in making.
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel @fatlimey ‘Complexity’ seems to work, sticking with the real/imaginary naming"
+type: archive
+source: twitter
+source_url: "https://x.com/9eronimo/status/1602223075210182656"
+author: "Jeroen Krebbers"
+handle: 9eronimo
+post_id: "1602223075210182656"
+date: 2022-12-12
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel @fatlimey ‘Complexity’ seems to work, sticking with the real/imaginary naming"
+in_reply_to: ""
+parent_post_id: "1602171519832317952"
+---
+
+## Source
+
+- URL: https://x.com/9eronimo/status/1602223075210182656
+- Author: Jeroen Krebbers (@9eronimo)
+- Posted: 2022-12-12 08:45:23
+
+## Branch
+
+**1/** **@9eronimo** ^1602223075210182656
+
+**@EricLengyel** **@fatlimey**
+
+‘Complexity’ seems to work, sticking with the real/imaginary naming
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2022-12-11-objects-in-conformal-ga-can-have-a-real-or]]
@@ -0,0 +1,39 @@
+---
+title: "@EricLengyel @fatlimey Imaginarity."
+type: archive
+source: twitter
+source_url: "https://x.com/crertel/status/1602362051954970631"
+author: "crertel ᐛ"
+handle: crertel
+post_id: "1602362051954970631"
+date: 2022-12-12
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel @fatlimey Imaginarity."
+in_reply_to: ""
+parent_post_id: "1602171519832317952"
+---
+
+## Source
+
+- URL: https://x.com/crertel/status/1602362051954970631
+- Author: crertel ᐛ (@crertel)
+- Posted: 2022-12-12 17:57:38
+
+## Branch
+
+**1/** **@crertel** ^1602362051954970631
+
+**@EricLengyel** **@fatlimey**
+
+Imaginarity.
+
+(comedy answer: quantum names like spin, charm, strange, etc.)
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2022-12-11-objects-in-conformal-ga-can-have-a-real-or]]
@@ -0,0 +1,37 @@
+---
+title: "@EricLengyel @fatlimey Intuition tempts me to call it phase."
+type: archive
+source: twitter
+source_url: "https://x.com/m_zandvliet/status/1602229547109433346"
+author: "Mar"
+handle: m_zandvliet
+post_id: "1602229547109433346"
+date: 2022-12-12
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "@EricLengyel @fatlimey Intuition tempts me to call it phase."
+in_reply_to: ""
+parent_post_id: "1602171519832317952"
+---
+
+## Source
+
+- URL: https://x.com/m_zandvliet/status/1602229547109433346
+- Author: Mar (@m_zandvliet)
+- Posted: 2022-12-12 09:11:06
+
+## Branch
+
+**1/** **@m_zandvliet** ^1602229547109433346
+
+**@EricLengyel** **@fatlimey**
+
+Intuition tempts me to call it phase. It's already appropriate when talking about oscillators, and in physics we speak about phases of matter. I'm comfortable reading it in the examples above, possibly because I'm in my imaginary phase.
+
+## Related
+
+- Spine: [[archive/threads/EricLengyel/2022-12-11-objects-in-conformal-ga-can-have-a-real-or]]
@@ -0,0 +1,61 @@
+---
+title: "Objects in conformal GA can have a real or imaginary radius."
+type: archive
+source: twitter
+source_url: "https://x.com/EricLengyel/status/1601902349601058816"
+author: "Eric Lengyel"
+handle: EricLengyel
+post_id: "1601902349601058816"
+date: 2022-12-11
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - EricLengyel
+description: "Objects in conformal GA can have a real or imaginary radius."
+in_reply_to: ""
+---
+
+## Source
+
+- URL: https://x.com/EricLengyel/status/1601902349601058816
+- Author: Eric Lengyel (@EricLengyel)
+- Posted: 2022-12-11 11:30:56
+
+## Thread
+
+**1/** **@EricLengyel** ^1601902349601058816
+
+Objects in conformal GA can have a real or imaginary radius. I need a term that describes the property of being real or imaginary without regard for size.
+One could ask "What is the _____ of X?", and the answer would be either "real" or "imaginary". What should go in the blank?
+
+**2/** **@EricLengyel** ^1601902893791006720
+
+We usually only see the square of the radius, which is positive in the real case and negative in the imaginary case. A fitting term could reflect this positive or negative property instead of the realness or imaginariness of the radius.
+
+**3/** **@fatlimey** ^1602124968133038081
+
+**@EricLengyel**
+
+Make up your own terminology, e.g."Is the value a 'forward' or 'backward' vector?". Implying general directionality without explicitly talking about sign or basis.
+
+**4/** **@EricLengyel** ^1602170950971105280
+
+**@fatlimey**
+
+The terms "real" and "imaginary" are already established for the value of the property, but the property itself doesn't have a convenient name. I'm seeing more and more cases when I want to talk about this property by name without specifying an exact value. 1/2
+
+**5/** **@EricLengyel** ^1602171519832317952
+
+**@fatlimey**
+
+For example,
+
+• An object's container has the same ____ as the object itself.
+• The dual of an object has the opposite ____.
+• This function flips the object's ____.
+
+In each of these, ____ would be the name of the property that can have the value "real" or "imaginary".
+
+Branches: [[archive/threads/EricLengyel/2022-12-11-objects-in-conformal-ga-can-have-a-real-or/2022-12-12-9eronimo-complexity-seems-to-work-sticking-with-the-real]], [[archive/threads/EricLengyel/2022-12-11-objects-in-conformal-ga-can-have-a-real-or/2022-12-12-m_zandvliet-intuition-tempts-me-to-call-it-phase-its-already]], [[archive/threads/EricLengyel/2022-12-11-objects-in-conformal-ga-can-have-a-real-or/2022-12-12-crertel-imaginarity-comedy-answer-quantum-names-like-spin]]
@@ -16,6 +16,7 @@ tags:
 - [[archive/threads/EricLengyel/2014-04-05-id-like-a-code-editor-that-can-recognize-some]]
 - [[archive/threads/EricLengyel/2014-12-20-remember-that-integer-range-checks-can-always-be]]
 - [[archive/threads/EricLengyel/2015-02-01-textedit-just-took-20-sec-to-open-a-1-kb-plain]]
+- [[archive/threads/EricLengyel/2016-10-02-i-love-wasting-time-over-driver-bugs-that-clearly]]
 - [[archive/threads/EricLengyel/2016-12-15-that-would-be-taking-the-antiwedge-product-of-two]]
 - [[archive/threads/EricLengyel/2017-04-13-the-more-i-talk-to-people-about-other-engines]]
 - [[archive/threads/EricLengyel/2017-05-26-needs-repeating-you-can-always-perform-a-signed]]
@@ -35,4 +36,9 @@ tags:
 - [[archive/threads/EricLengyel/2019-12-05-im-not-convinced-that-casting-to-force-disjoint]]
 - [[archive/threads/EricLengyel/2019-12-21-the-term-g-buffer-was-already-in-use-by-the-mid]]
 - [[archive/threads/EricLengyel/2019-12-24-1-8-every-operation-in-grassmann-geometric]]
+- [[archive/threads/EricLengyel/2020-02-17-how-many-people-were-taught-that-the-formulas-for]]
+- [[archive/threads/EricLengyel/2021-05-03-back-in-1993-i-was-taking-a-number-theory-class]]
+- [[archive/threads/EricLengyel/2021-10-03-so-i-was-seeing-inexplicable-100-200-ms-frame]]
+- [[archive/threads/EricLengyel/2021-12-05-the-original-gltf-2-0-spec-did-have-the-4]]
+- [[archive/threads/EricLengyel/2022-12-11-objects-in-conformal-ga-can-have-a-real-or]]
 - [[archive/threads/EricLengyel/2026-01-23-ive-worked-very-hard-over-many-years-to-develop-a]]
@@ -48,6 +48,7 @@ Example of the note shape (single spine, no branches): [[archive/threads/How to
 - [[archive/threads/pikuma]]
 - [[archive/threads/rfleury]]
 - [[archive/threads/rianflo]]
+- [[archive/threads/rygorous]]
 - [[archive/threads/SebAaltonen]]
 - [[archive/threads/SheriefFYI]]
 - [[archive/threads/simplex_fx]]
@@ -0,0 +1,168 @@
+---
+title: "@ladyaeva They're 2D vectors with a major extra feature: you can multiply two vectors to get a third, and this multiplication is just like multiplication in the reals: it's commutative (a*b=b*a), invertible unless you're multiplying by 0, and also has a nice geometric interpretation."
+type: archive
+source: twitter
+source_url: "https://x.com/rygorous/status/1436788358768828417"
+author: "Fabian Giesen"
+handle: rygorous
+post_id: "1436788358768828417"
+date: 2021-09-11
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - rygorous
+description: "@ladyaeva They're 2D vectors with a major extra feature: you can multiply two vectors to get a third, and this multiplication is just like multiplication in the reals: it's commutative (a*b=b*a), invertible unless you're multiplying by 0, and also has a nice geometric interpretation."
+in_reply_to: "1436618444477190148"
+---
+
+## Source
+
+- URL: https://x.com/rygorous/status/1436788358768828417
+- Author: Fabian Giesen (@rygorous)
+- Posted: 2021-09-11 20:26:53
+
+## Thread
+
+**1/** **@rygorous** ^1436788358768828417
+
+**@ladyaeva**
+
+They're 2D vectors with a major extra feature: you can multiply two vectors to get a third, and this multiplication is just like multiplication in the reals: it's commutative (a*b=b*a), invertible unless you're multiplying by 0, and also has a nice geometric interpretation.
+
+**2/** **@rygorous** ^1436789164813402113
+
+**@ladyaeva**
+
+This is the part that makes them special; you can get real vector spaces in any dimension, but spaces where you can also define a nice product are hard to come by.
+
+**3/** **@rygorous** ^1436789973630390274
+
+**@ladyaeva**
+
+There's nothing nice for 3D, for example. You can take  the cross product, which is vector*vector -> vector (so right "types" at least), but a x b =- b x a so it's anti-commutative, and in particular a x a = 0 for any a so it's also not invertible.
+
+**4/** **@EricLengyel** ^1437160350961438723
+
+**@rygorous** **@ladyaeva**
+
+The incorrect belief that vector × vector -> vector, that the result of a cross product has the same type as its operands, is the source of over a century of misunderstanding and incomplete mathematics.
+
+**5/** **@EricLengyel** ^1437160587016892416
+
+**@rygorous** **@ladyaeva**
+
+You can try to stuff its three components into the same type as a vector, but you can't escape the fact that the result of a cross product has different properties.
+
+**6/** **@rygorous** ^1437173844716834820
+
+**@EricLengyel** **@ladyaeva**
+
+_This_ of all places is the thread (see https://x.com/ladyaeva/status/1436763466619097099) where you decide to parachute in with your pet peeve about how cross products are wrong, actually? Come on.
+
+**7/** **@rygorous** ^1437174450911285248
+
+**@EricLengyel** **@ladyaeva**
+
+Yes, bivectors are a better way to understand this, but cross products are everywhere, be it textbooks, tutorials, papers or classes, and "um actually you're doing it wrong" is not the way to rectify that situation.
+
+**8/** **@ZPostFacto** ^1437186294400962560
+
+**@rygorous** **@EricLengyel** **@ladyaeva**
+
+"Wrong" seems to me to be drastically overstating the case.  "Incomplete" maybe.
+
+I feel the same way on this stuff as I do about Hamiltonian mechanics.  It's more elegant in a certain sense, perhaps it is accessing some deeper truth (?).  And yet is is undeniably less intuitive.
+
+**9/** **@ZPostFacto** ^1437187241265164293
+
+**@rygorous** **@EricLengyel** **@ladyaeva**
+
+Intuitiveness has real value; it's not clear to me that teaching things in a more elegant but less intuitive manner is the correct tradeoff, for most people.
+
+Even though I think the Deeper Ways are interesting & valuable.
+
+There are only so many hours in the day to learn stuff.
+
+**10/** **@EricLengyel** ^1437223683089518592
+
+**@ZPostFacto** **@rygorous** **@ladyaeva**
+
+So a question on my mind is whether someone who was never taught that vector × vector = vector would still find it less intuitive to learn that more things than just scalars and vectors exist, and vector × vector = bivector. (That's what you're getting at, right?)
+
+**11/** **@EricLengyel** ^1437224384360431617
+
+**@ZPostFacto** **@rygorous** **@ladyaeva**
+
+Would somebody who was taught the graded exterior algebra with wedge and antiwedge products from the beginning, only later being exposed to the cross product, find the cross product to be an unintuitive hack?
+
+**12/** **@ZPostFacto** ^1437231042734137349
+
+**@EricLengyel** **@rygorous** **@ladyaeva**
+
+I think I has to do with how concrete the concepts are.
+
+E.g. in both Lagrangian and Hamiltonian dynamics, energy plays a central role.  It's just a much more abstract quantity than force.
+
+"Vector perpendicular to the argument vectors" is a very concrete thing.
+
+**13/** **@ZPostFacto** ^1437231332170428416
+
+**@EricLengyel** **@rygorous** **@ladyaeva**
+
+And I think good pedagogy always goes from concrete to abstract, and from specific to general.
+
+**14/** **@ZPostFacto** ^1437232576322629637
+
+**@EricLengyel** **@rygorous** **@ladyaeva**
+
+So if somebody had always been taught the more abstract way from the beginning, yeah they might find it intuitive.  But imo that's basically just a bad way to teach.  It asks people to leap across a big conceptual chasm.  Many won't make it.  And most don't need it.
+
+**15/** **@rygorous** ^1437237573995282435
+
+**@ZPostFacto** **@EricLengyel**
+
+The way I view it is that certainly in programming and engineering, most people are consumers not producers of math. When they have a problem, they look up a formula (or go on StackOverflow), maybe massage it a bit with some algebra, and plug their numbers in. That's it.
+
+**16/** **@rygorous** ^1437238342026809345
+
+**@ZPostFacto** **@EricLengyel**
+
+"I don't actually know how this really works under the hood and I don't care as long as it does" is totally valid. E.g. there's lots of people who learn the Z-transform by rote, know how to work with, know nothing about formal power series or complex analysis, and don't ned to.
+
+**17/** **@rygorous** ^1437238864498757633
+
+**@ZPostFacto** **@EricLengyel**
+
+"You're not understanding this right" is less than useless when you're in that position. Indeed I don't understand this right, I don't understand it at all, but I should still be able to function within it.
+
+**18/** **@rygorous** ^1437239562615463939
+
+**@ZPostFacto** **@EricLengyel**
+
+For better or for worse, and for all the conceptual baggage they come with, cross products are everywhere, and they're treated as vectors. You're going to find them in textbooks, formula collections, as ∇ ×, in the code you got from SO to set up a look-at matrix, everywhere.
+
+**19/** **@rygorous** ^1437239917600395267
+
+**@ZPostFacto** **@EricLengyel**
+
+The world you live in doesn't have everything stated as blades. You don't get around knowing what × is or how it works, even when you don't agree with it.
+
+**20/** **@rygorous** ^1437240600604991488
+
+**@ZPostFacto** **@EricLengyel**
+
+If you don't particularly care about the theory, couldn't care less about whether it's beautiful or elegant or not, but do want to just grab code or formulas and have them work, GA does very little for you and mostly places extra barriers between you and getting what you want.
+
+**21/** **@EricLengyel** ^1437260942908092416
+
+**@rygorous** **@ZPostFacto**
+
+I disagree, mostly. In my experience, specific parts of GA are extremely practical in 3D apps. I use them like crazy for common calculations that would otherwise be more complex / obfuscated. However, I agree that some other parts gain you very little and could even hurt.
+
+**22/** **@EricLengyel** ^1437261490155753477
+
+**@rygorous** **@ZPostFacto**
+
+In my opinion, *almost all* of the existing learning resources for GA are terrible, focus on the wrong things, and are written by people who don't have a full grasp of it. I'm in the midst of trying to change this by providing the big picture and approaching GA with pragmatism.
@@ -0,0 +1,12 @@
+---
+title: rygorous
+type: note
+draft: false
+description: Archived threads by rygorous.
+tags:
+  - archive
+  - twitter
+  - rygorous
+---
+
+- [[archive/threads/rygorous/2021-09-11-theyre-2d-vectors-with-a-major-extra-feature-you]]