From e03ce0f90e420cc36beb820519c6ce023a47bf1b Mon Sep 17 00:00:00 2001
From: Ed_ <edwardgz@gmail.com>
Date: Thu, 27 Aug 2026 18:20:36 -0400
Subject: [PATCH] 2093065798399176704

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 .../index.md                                  | 42 +++++++++++++++++++
 archive/threads/HostOfMeta/index.md           | 12 ++++++
 archive/threads/index.md                      |  1 +
 3 files changed, 55 insertions(+)
 create mode 100644 archive/threads/HostOfMeta/2026-08-27-after-2-decades-of-using-it-naively-i-have/index.md
 create mode 100644 archive/threads/HostOfMeta/index.md

diff --git a/archive/threads/HostOfMeta/2026-08-27-after-2-decades-of-using-it-naively-i-have/index.md b/archive/threads/HostOfMeta/2026-08-27-after-2-decades-of-using-it-naively-i-have/index.md
new file mode 100644
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--- /dev/null
+++ b/archive/threads/HostOfMeta/2026-08-27-after-2-decades-of-using-it-naively-i-have/index.md
@@ -0,0 +1,42 @@
+---
+title: "After 2 decades of using it naively, I have deconstructed the (×) cross product."
+type: archive
+source: twitter
+source_url: "https://x.com/HostOfMeta/status/2093065798399176704"
+author: "Jeremie Pelletier"
+handle: HostOfMeta
+post_id: "2093065798399176704"
+date: 2026-08-27
+archived: 2026-08-27
+draft: false
+tags:
+  - archive
+  - twitter
+  - HostOfMeta
+description: "After 2 decades of using it naively, I have deconstructed the (×) cross product."
+in_reply_to: ""
+---
+
+## Source
+
+- URL: https://x.com/HostOfMeta/status/2093065798399176704
+- Author: Jeremie Pelletier (@HostOfMeta)
+- Posted: 2026-08-27 19:59:08
+
+## Thread
+
+**1/** **@HostOfMeta** ^2093065798399176704
+
+After 2 decades of using it naively, I have deconstructed the (×) cross product. Only took learning geometric algebra. Goes like this:
+
+u×v = ⋆(u∧v) = w
+
+As in, it combines two operations: a lift and a drop. First the wedge creates a bivector out of (u) and (v), which turns the two vectors into an oriented plane. Then the dual multiplies by the antiscalar, which cancels out (u) and (v) while leaving an orthogonal (w) vector in place.
+
+And explains why it only works in 3D (7D uses a different contraction, because this formula yields a 5D blade.)
+
+**2/** **@HostOfMeta** ^2093066969188622765
+
+Quick precision: the "cancels out" part only applies when (u) and (v) are the basis vectors e1 and e2, meaning their coefficients stay unitary as (1).
+
+When these input vectors have non-unit coefficients, then the dual makes more of a selection operation because they play a role.
diff --git a/archive/threads/HostOfMeta/index.md b/archive/threads/HostOfMeta/index.md
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+++ b/archive/threads/HostOfMeta/index.md
@@ -0,0 +1,12 @@
+---
+title: HostOfMeta
+type: note
+draft: false
+description: Archived threads by HostOfMeta.
+tags:
+  - archive
+  - twitter
+  - HostOfMeta
+---
+
+- [[archive/threads/HostOfMeta/2026-08-27-after-2-decades-of-using-it-naively-i-have]]
diff --git a/archive/threads/index.md b/archive/threads/index.md
index fb5d52f..9de0180 100644
--- a/archive/threads/index.md
+++ b/archive/threads/index.md
@@ -22,6 +22,7 @@ Example of the note shape (single spine, no branches): [[archive/threads/How to
 - [[archive/threads/Dispatch_Graph]]
 - [[archive/threads/EricLengyel]]
 - [[archive/threads/FFmpeg]]
+- [[archive/threads/HostOfMeta]]
 - [[archive/threads/hsn8086]]
 - [[archive/threads/ID_AA_Carmack]]
 - [[archive/threads/iquilezles]]