Why Can't You Multiply Vectors? - A Mathematical Journey into Vector Multiplication

Embark on a mathematical journey exploring the complexities of vector multiplication in this 51-minute conference talk from Dutch Game Day 2023. Delve into the anatomy of vectors, various types of products, and the intricacies of complex numbers. Witness attempts at multiplying vectors, experience moments of frustration, and discover unexpected leaps of faith. Explore concepts such as basis vectors, dot and cross products, quaternions, and geometric algebra. Gain new perspectives on mathematical constructs used in game development, including bivectors, wedge products, and multivectors. Conclude with a Q&A session addressing practical applications and tools for implementing these concepts in game engines.

Intro
Talk Start
Anatomy of a Vector
Products
Numbers of different kinds
Complex Numbers
Code for complex numbers
Complex multiplication visualized
Multiplying Vectors an attempt
Frustration
A Leap of Faith
A divine axiomatic truth
Squaring Basis Vectors
The Diagonal of Bases
Vector multiplication unraveling
Dot/Cross Byproducts
Complex Byproduct
Quaternionic Byproduct
The Answer
Beyond the Algebra
Basis Bivectors
Conceptualizing Vectors & Bivectors
Wedge Product
Curvature Bivector
Mental Gymnastics
Geometric Algebra & Multivectors
What does the multiplication represent?
Outro
Q: When is this useful?
Q: Does your math lib support geometric algebra?
Q: Do you plan on making tools for other engines?
AV team kicking us out