Why can't you multiply vectors?

Video Description

..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 💖 Patreon ❱ https://www.patreon.com/acegikmo 🐦 Twitter ❱ https://twitter.com/FreyaHolmer 📺 Twitch ❱ https://www.twitch.tv/acegikmo 💬 Discord ❱ https://discord.gg/v5VWuga 📧 Mailing list ❱ https://acegikmo.substack.com/ 🌸 Instagram ❱ https://instagram.com/freya_holmer