- The Geometry -

  A **flat torus** is a theoretical mathematical concept that cannot be fully embedded in 3D space, but it can be visualized in different ways. Here are some helpful resources to understand its structure: ### 1. **Wikipedia - Flat Torus**      [ https://en.wikipedia.org/wiki/Flat_torus ]( https://en.wikipedia.org/wiki/Flat_torus )      - Explains the mathematical definition and properties. ### 2. **Video Visualization (YouTube)**      - **"Flat Torus in 3D"** (by 3Blue1Brown) – Explains how a flat torus relates to video game topology:        [ https://www.youtube.com/watch?v=4sylflOkY9M ]( https://www.youtube.com/watch?v=4sylflOkY9M )      - **"Torus Games"** (by Numberphile) – Discusses how a flat torus behaves in geometry:        [ https://www.youtube.com/watch?v=0H3_hQ8KZQk ]( https://www.youtube.com/watch?v=0H3_hQ8KZQk )   ### 3. **Interact...

26 Sept 2024 What is the deepest level of reality? In this Quanta explainer, Vijay Balasubramanian, a physicist at the University of Pennsylvania, takes us on a journey through space-time to investigate what it’s made of, why it’s failing us, and where physics can go next. Explore black holes, holograms, “alien algebra,” and more space-time geometry: https://www.quantamagazine.org/the-un... 00:00 - The Planck length, an intro to space-time 1:23 - Descartes and Newton investigate space and time 2:04 - Einstein's special relativity 2:32 - The geometry of space-time and the manifold 3:16 - Einstein's general relativity: space-time in four dimensions 3:35 - The mathematical curvature of space-time 4:57 - Einstein's field equation 6:04 - Singularities: where general relativity fails 6:50 - Quantum mechanics (amplitudes, entanglement, Schrödinger equation) 8:32 - The problem of quantum gravity 9:38 - Applying quantum mechanics to our manifold 10:36 - Why particle a...