sudgylacmoe | Dimension is Multi-Dimensional - From Zero to Geo 1.10 @sudgylacmoe | Uploaded November 2023 | Updated October 2024, 3 hours ago.
In this video, we explore the concept of the dimension of a linear space. In doing so, we realize that this concept does not always match with our intuitive, geometric understanding of what dimension is, showing that dimension really is a multi-dimensional concept.

This video is a part of "From Zero to Geo", a series where we formulate geometric algebra, an incredibly powerful branch of mathematics, from the ground up. Full playlist here: youtube.com/playlist?list=PLVuwZXwFua-0Ks3rRS4tIkswgUmDLqqRy
Next video here: youtube.com/watch?v=ZzofLQga1_k

Here's the video on the linear space of lines I mentioned partway through: youtube.com/watch?v=T0b8-NJH79s

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Sections:
00:00 Introduction
00:25 Dimension Pattern
01:08 Dimension Exercise
04:34 Definition of Dimension
05:20 4D Space
05:53 Why care about higher dimensions?
06:42 Higher-Dimensional Visualization
07:42 Algebraic Dimension Exercise
08:18 Dimension of Numbers
09:09 Dimension of Lists of Numbers
10:28 Dimension of 2D Lines
11:06 Dimension of Functions
12:27 Dimension is Multi-Dimensional
14:19 Conclusion