People are nitpicking you, but you’re right that the presentations do tend to omit or underemphasize concrete computation. Part of this is lineage, in that it’s

People are nitpicking you, but you’re right that the presentations do tend to omit or underemphasize concrete computation. Part of this is lineage, in that it’s related to differential geometry where much of the point is that you are abstracting away computational aspects like coordinates. But to do much of the fun stuff, you need coordinates, which the community would do well to connect better with the abstractions.