What's particularly neat about this is I can construct a pyramid of interests so the foundation is fairly broad ... and narrows to the specialization I'm interested in as you go up.
James, may we risk saying that cosmology generates one of your principal ideals?
Well, the irony is ring theory isn't part of the constructed background of interests for cosmology :-)
Actually, I'm wrong, my constructed background does include the course "Groups, Rings and Modules" at Cambridge.
BTW, huge points to Dave for suggesting the light-cone as a more useful analogy in the context of cosmology.
if speaking in terms of Principal Ideals is inconsistent, we could always press the cosmological background-cone into service.
Consider the interval between, eg cosmology, and any other concept: we can classify these intervals according to the following schema:
consequential: one background cone contains the other.
inconsequential: the background cones fail to intersect, or do so only partially.
tangential: one concept occurs on the boundary of the other's background cone.
I hope a trichotomous classification of intervals is consequential with regard to cosmology? :-)
I love the idea of saying that, for example, "Vector Calculus is in the past light-cone of cosmology".
To more precisely relate his trichotomy to light-cones, I think you have:
I'd intended the trichotomy to be:
consequential / timelike
tangential / lightlike
but it's been decades since I've dealt with the molluscs of space-time.