Nov 6, 2025 12:23 AM
(This post was last modified: Nov 6, 2025 02:39 PM by C C.)
How to understand Einstein’s relativity without math
https://bigthink.com/starts-with-a-bang/...ivity-math
KEY POINTS: It’s been 120 full years since Einstein first put forth his special theory of relativity into the world, dictating how neither space nor time were absolute, but rather the speed of light was. Near the speed of light, durations of time dilate and lengths appear to contract along the direction of motion in a velocity-dependent way, with each unique observer seeing different values. This doesn’t reflect an inconsistency in physics, however, merely a new, deeper way of looking at and successfully understanding our world. Einstein was the first, but now we can all get there... (MORE - details)
What is a manifold?
https://www.quantamagazine.org/what-is-a...d-20251103
INTRO: Standing in the middle of a field, we can easily forget that we live on a round planet. We’re so small in comparison to the Earth that from our point of view, it looks flat.
The world is full of such shapes — ones that look flat to an ant living on them, even though they might have a more complicated global structure. Mathematicians call these shapes manifolds. Introduced by Bernhard Riemann in the mid-19th century, manifolds transformed how mathematicians think about space. It was no longer just a physical setting for other mathematical objects, but rather an abstract, well-defined object worth studying in its own right.
This new perspective allowed mathematicians to rigorously explore higher-dimensional spaces — leading to the birth of modern topology, a field dedicated to the study of mathematical spaces like manifolds. Manifolds have also come to occupy a central role in fields such as geometry, dynamical systems, data analysis and physics.
Today, they give mathematicians a common vocabulary for solving all sorts of problems. They’re as fundamental to mathematics as the alphabet is to language. “If I know Cyrillic, do I know Russian?” said Fabrizio Bianchi(opens a new tab), a mathematician at the University of Pisa in Italy. “No. But try to learn Russian without learning Cyrillic.”
So what are manifolds, and what kind of vocabulary do they provide? (MORE - details)
https://youtu.be/ABQ0w08nTBQ
https://www.youtube-nocookie.com/embed/ABQ0w08nTBQ
https://bigthink.com/starts-with-a-bang/...ivity-math
KEY POINTS: It’s been 120 full years since Einstein first put forth his special theory of relativity into the world, dictating how neither space nor time were absolute, but rather the speed of light was. Near the speed of light, durations of time dilate and lengths appear to contract along the direction of motion in a velocity-dependent way, with each unique observer seeing different values. This doesn’t reflect an inconsistency in physics, however, merely a new, deeper way of looking at and successfully understanding our world. Einstein was the first, but now we can all get there... (MORE - details)
What is a manifold?
https://www.quantamagazine.org/what-is-a...d-20251103
INTRO: Standing in the middle of a field, we can easily forget that we live on a round planet. We’re so small in comparison to the Earth that from our point of view, it looks flat.
The world is full of such shapes — ones that look flat to an ant living on them, even though they might have a more complicated global structure. Mathematicians call these shapes manifolds. Introduced by Bernhard Riemann in the mid-19th century, manifolds transformed how mathematicians think about space. It was no longer just a physical setting for other mathematical objects, but rather an abstract, well-defined object worth studying in its own right.
This new perspective allowed mathematicians to rigorously explore higher-dimensional spaces — leading to the birth of modern topology, a field dedicated to the study of mathematical spaces like manifolds. Manifolds have also come to occupy a central role in fields such as geometry, dynamical systems, data analysis and physics.
Today, they give mathematicians a common vocabulary for solving all sorts of problems. They’re as fundamental to mathematics as the alphabet is to language. “If I know Cyrillic, do I know Russian?” said Fabrizio Bianchi(opens a new tab), a mathematician at the University of Pisa in Italy. “No. But try to learn Russian without learning Cyrillic.”
So what are manifolds, and what kind of vocabulary do they provide? (MORE - details)
https://youtu.be/ABQ0w08nTBQ
