Why can't you multiply vectors?

..or can you? A deceptively simple question with a complex answer – come join a mathematical journey into madness and wonder, in search of answers that might just give you a new perspective on the mathematical constructs we use in our games

Recorded at Dutch Game Day 2023, October 4th

Timestamps:
00:00 Intro
04:34 Talk Start
05:17 Anatomy of a Vector
06:09 Products
09:14 Numbers of different kinds
13:32 Complex Numbers
18:10 Code for complex numbers
19:10 Complex multiplication visualized
20:22 Multiplying Vectors (an attempt)
24:08 Frustration
24:36 A Leap of Faith
25:36 A divine axiomatic truth
26:40 Squaring Basis Vectors
27:46 The Diagonal of Bases
29:09 Vector multiplication unraveling
29:36 Dot/Cross Byproducts
30:32 Complex Byproduct
31:17 Quaternionic Byproduct
31:52 The Answer
32:52 Beyond the Algebra
33:29 Basis Bivectors
35:06 Conceptualizing Vectors & Bivectors
37:08 Wedge Product
38:46 Curvature Bivector
40:59 Mental Gymnastics
41:56 Geometric Algebra & Multivectors
43:19 What does the multiplication represent?
44:10 Outro
45:53 Q: When is this useful?
48:11 Q: Does your math lib support geometric algebra?
49:22 Q: Do you plan on making tools for other engines?
50:53 AV team kicking us out

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