I have not watched this video yet, but I'm book marking it to watch later. I really appreciate your channel, I've learned a lot already and it seems you're always doing the topic I'm interested in at the moment. I think you deserve an even bigger following than you have! Thanks for putting in the time and effort!
Great Job in your explanations. I recently purchased Sean Carroll’s book, Spacetime & Geometry , only to find that I needed to learn topology, manifolds, tensors, etc. just so I can through his very rigorous formalisms in the first three chapters. Luckily I came across your videos and I watched them all. Thanks 🙏. Looking forward to your videos in Differential Geometry at some future time. Btw. Don’t worry about those comments regarding your excessive hand waving . You just do you😎
I really don't understand intrinsic curvature... I understand that you can have intrinsically GAINED knowledge of some curved space. Or you can have extrinsically GAINED knowledge of that curvature. But for the curvature ITSELF being intrinsic or extrinsic that i really don't understand the meaning of it. You can have a 2D plane. That 2D plane can either be flat, or embedded on the surface of a 3D sphere so it's now still 2D but curved. If we deduce that curvature from living on the surface of the sphere then our knowledge about the curvature is intrinsic. If the opposite happened, then it's extrinsic. But no matter what, the 2D surface DID REQUIRED a 3D sphere to be mapped on its surface... Here as well. We have a 4D flat space. That we have to embed into the surface of a 5D object in order for the resulting 4D surface to be curved, either by intrinsic or extrinsic observers.
I have not watched this video yet, but I'm book marking it to watch later. I really appreciate your channel, I've learned a lot already and it seems you're always doing the topic I'm interested in at the moment. I think you deserve an even bigger following than you have! Thanks for putting in the time and effort!
Great Job in your explanations. I recently purchased Sean Carroll’s book, Spacetime & Geometry , only to find that I needed to learn topology, manifolds, tensors, etc. just so I can through his very rigorous formalisms in the first three chapters. Luckily I came across your videos and I watched them all. Thanks 🙏. Looking forward to your videos in Differential Geometry at some future time.
Btw. Don’t worry about those comments regarding your excessive hand waving . You just do you😎
I would like to point out that torsion is also a part of the Einstein - Cartan theory. Great job on explaining intrinsic and extrinsic curvature.
Great video, thankyou, and love your pumpkin dog!!!!!!
(awesome)
I really don't understand intrinsic curvature...
I understand that you can have intrinsically GAINED knowledge of some curved space. Or you can have extrinsically GAINED knowledge of that curvature. But for the curvature ITSELF being intrinsic or extrinsic that i really don't understand the meaning of it.
You can have a 2D plane. That 2D plane can either be flat, or embedded on the surface of a 3D sphere so it's now still 2D but curved. If we deduce that curvature from living on the surface of the sphere then our knowledge about the curvature is intrinsic. If the opposite happened, then it's extrinsic. But no matter what, the 2D surface DID REQUIRED a 3D sphere to be mapped on its surface...
Here as well. We have a 4D flat space. That we have to embed into the surface of a 5D object in order for the resulting 4D surface to be curved, either by intrinsic or extrinsic observers.
You didnt talk about Einstein-Cartan theory at all, this is just pure GR.
Cartan theory has torsion.
Bro literally said at the beginning of the video he is going to work up to it