What is a manifold? A brief, intuitive explanation:

Wonderful video! I hope you do more brief, intuitive shorts like this!

Thanks Ben! Love your videos.

“Science doesn’t tell us why the Big Bang happened, how the singularity occurred in the first place, or why it exploded when it did. It tells us there is objective scientific evidence that it occurred. So, what exactly was the Big Bang?” – Book III The Enigmatic Mystery

Nice! Thanks. Maybe add an example of a 3d manifold before ending on the general case?

Nice suggestion! And thanks for watching.

So the dimensions what a manifold "looks like locally" defines it's dimensionality? Will the n-dim manifold always appear in the n+1 dimensions? For example the sphere (a 3 d object) is a 2d manifold. Hope that question made sense. Thanks for the video.

Interesting question! So the dimension of the “ambient space” doesn’t always have to be 1 larger than the manifold’s dimension. For example, you can embed a circle (1 dim manifold) inside R^2, but you can also embed it in R^3 in many ways.

Really enjoyed this new style of video! Nice explanation with examples and motivation as well 😊

thank you!!

can i say no manifold has even one singularity.

Intuitively, yes. A smooth manifold should have no “sharp points” or “corners”.