On Tuesday, November 11, 2025 at 6:37:20 PM UTC-7 Russell Standish wrote:
As promised below, my student article on differentiable manifolds can now be found at https://www.hpcoders.com.au/docs/differentiableManifolds.pdf Apologies for the difficult to read font - this was done on Wordstar and a dot matrix printer, before laser printers (and LaTeX) became a thing. Cheers *Thank you. It's readable by enlarging the font. Tell me if you agree with this* *statement; a manifold is a topological space on which a coordinate system* *is defined, but to actually define a coordinate system one needs additional* *information, namely, that the topological space is also a metric space. But the* *problem is that a metric space requires points to have labels, and I don't see* *how points can have labels unless there's a pre-existing coordinate system.* *IOW, there's a circularity here that I want to avoid, but I'm not sure how to do* *so. **AG* On Mon, Nov 10, 2025 at 05:15:53PM +1100, Russell Standish wrote: > On Sun, Nov 09, 2025 at 09:55:15PM -0800, Alan Grayson wrote: > > > > > > Someday I might find a teacher who can really define tensors, but that day has > > yet to arrive. Standish seems to come close, but does every linear multivariate > > function define a tensor? I'm waiting to see his reply. AG > > Well I did say multilinear function, but the answer is yes, every > multilinear function on a vector space is a tensor, and vice-versa. > > I did write an 8 page article appearing in our student rag "The > Occasional Quark" when I was a physics student, which was my attempt > at explaining General Relativity when I was disgusted by the hash job > done by our professor. I haven't really thought about it much since > that time, though. I can also recommend the heavy tome by Misner, > Thorne and Wheeler. > > I could scan the article and post it to this list, but not today - I > have a few other things on my plate before finishing up. > ---------------------------------------------------------------------------- > Dr Russell Standish Phone 0425 253119 (mobile) > Principal, High Performance Coders [email protected] > http://www.hpcoders.com.au > ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/0ac93a9d-2e3b-4713-b0f9-5923cfb811acn%40googlegroups.com.
