Chapter
Thinking Beyond Three-Dimensional Space with Geometry
32:02 - 39:15 (07:12)
The need for a flexible geometry that could talk about multi-dimensional spaces led to the development of 'differential geometry,' which describes mathematically complex curved shapes that are impossible to represent on a flat surface.
Clips
Chaos theory arises when a very small change in initial conditions produces a significantly different long-term behavior of the system.
32:02 - 33:09 (01:07)
Summary
Chaos theory arises when a very small change in initial conditions produces a significantly different long-term behavior of the system. In the case of the three-body problem, chaos theory explains how the stable and unstable solutions are intertwined and how a tiny change in initial conditions can drastically impact the system's outcome.
ChapterThinking Beyond Three-Dimensional Space with Geometry
Episode#190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries
PodcastLex Fridman Podcast
This episode delves into the concept of high-dimensional spaces and why they are necessary to understand what's going on in our physical world.
33:09 - 36:29 (03:20)
Summary
This episode delves into the concept of high-dimensional spaces and why they are necessary to understand what's going on in our physical world.
ChapterThinking Beyond Three-Dimensional Space with Geometry
Episode#190 – Jordan Ellenberg: Mathematics of High-Dimensional Shapes and Geometries
PodcastLex Fridman Podcast
The human perception of space is three dimensional, but the reality is that there are multiple dimensions that we can't see.
36:29 - 39:15 (02:45)
Summary
The human perception of space is three dimensional, but the reality is that there are multiple dimensions that we can't see. Trying to understand the concept of higher dimensions can be challenging since it requires us to think beyond our normal intuition.