4 ms·
This article is really well-written and has an excellent description of differential manifolds. Worth a read just for that part (not implying that the rest isn
by ur-whale 3y ago
This article is really well-written and has an excellent description of differential manifolds.
Worth a read just for that part (not implying that the rest isn't good as well).
[Edit]: and the rest is really good as well. In particular if you ever wanted to understand how space-time (4D) can be intrinsically "curved" without it being embedded in a larger dimensional space (5D), this explains it very well.
- jackthetab 3y agoGlad to hear it. I agree it's well written. I was doing okay up until the co(ntra)variant tensor part. My brain is going to get a helluva workout trying to follow this. :-)
- smitty1e 3y agoTechnically correct reading tends toward the dense. It takes several readings to tease out a clear understanding of each of the points in the formulae. The terseness of the expressions is daunting. Several more readings are needed to internalize it to the point of teaching it to someone else, which is when the real grasp arrives. Or maybe I'm just slow.
- jackthetab 3y ago> It takes several readings to tease out a clear understanding of each of the points in the formulae. The terseness of the expressions is daunting. I was quite pleased with the writing/my understanding of the first section. As you say, it is dense but quite readable IMO. Math tensors (as opposed to computer/ML tensors) are new to me so that will take more time. > Several more readings are needed to internalize it to the point of teaching it to someone else, which is when the real grasp arrives. That's part of my study process, can I explain the topic to my imaginary students. Works well for me. > Or maybe I'm just slow. Nothing wrong with savoring things at a leisurely pace.