Can You Play 4 Dimensional Tic-Tac-Toe?

What happens if we push Tic-Tac-Toe into 4 dimensions? Turns out, the game might be more familiar than you think! In this video, we explore vector spaces, coordinate systems, and how a simple childhood game transforms when you add more axes.

FOR COLOR BLIND VIEWERS: This video relies heavily on color to represent dimensions. Please turn on Closed Captions for text descriptions of the visual data!

Timestamps
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00:00 Intro
01:36 What is a Dimension?
02:50 The "Trick" with Dimensions
03:45 Colors as Dimensions
04:24 Aside 1: Human Vision
05:46 Aside 2: Vision Comparisons
06:38 Vectors and Coordinates in Tic-Tac-Toe
08:25 Coordinates without Numbers
09:19 Aside 3: Skyrim and Character Creators
10:06 4D Tic-Tac-Toe Looks a Lot Like...
11:26 Game-to-Game Mapping Review
12:16 Caveats and 5+ Dimensions
13:47 Acknowledgements and Outro

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Acknowledgements:

Illustrations: Thank you to my wife, Claire (  / authorclaireelizabeth  ) for illustrating Hubert the Goldfish.

Inspiration: Shout out to @marcevanstein, whose great videos on Tic-Tac-Toe likely had something to do with me coming up with the idea for this video.

Music: Original music by Mert 'Hüsrev' Salha.

Animation: Created using a fork of ManimCE with a few modifications.
The Manim Community Developers. (2025). Manim – Mathematical Animation Framework (Version v0.19.0) [Computer software]. https://www.manim.community/

Sources:

Human Vision Data: CIE cone-fundamental-based spectral tristimulus values for 2° field size, International Commission on Illumination (CIE)

Metamerism Explained: https://www.en.silicann.com/blog/post...

Deer Vision Data: "Electrophysiological measurements of spectral mechanisms in the retinas of two cervids..." (Jacobs et al., 1994)

Goldfish Vision Data: "Spectral sensitivity of cones in the goldfish, Carassius auratus" (Palacios et al., 1998)

Curve Calculations: Deer and Goldfish curve calculations were done using "Govardovskii Nomograms" - Compute normalized absorbance according to the nomogram (Govardovskii et al., 2000)

Mantis Shrimp Vision: "Multimodal signals: Ultraviolet reflectance and chemical cues in stomatopod agonistic encounters" (Franklin, Marshall, and Lewis, 2016)

Game Background: https://en.wikipedia.org/wiki/Set_(ca...)

#math #tictactoe #dimensions #manim #setgame