I’m going to make a few comments as I read through this, but first I’d like to thank you for taking the time to write this down, since it gives me an opportunity to think through your arguments in a way I wouldn’t have done otherwise.
Thank you for the detailed responses! I very much enjoy discussing these topics :)
My impression is that you tend to see this as a statement about flatness, holding over macroscopic regions of parameter space
My intuitions around the RLCT are very much geometrically informed, and I do think of it as being a kind of flatness measure. However, I don’t think of it as being a “macroscopic” quantity, but rather, a local quantity.
I think the rest of what you say coheres with my current picture, but I will have to think about it for a bit, and come back later!
Thank you for the detailed responses! I very much enjoy discussing these topics :)
My intuitions around the RLCT are very much geometrically informed, and I do think of it as being a kind of flatness measure. However, I don’t think of it as being a “macroscopic” quantity, but rather, a local quantity.
I think the rest of what you say coheres with my current picture, but I will have to think about it for a bit, and come back later!