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Oreoracle
Guest
Certainly more fundamental notions are more general in a way. But what I meant by saying that ellipsoids are more general is that the set of spheres is a subset of the set of ellipsoids. Likewise, the conic sections are generalizations of these, and the quadric surfaces are generalizations of those, and so on.I would say that because the concept of sphere predates ellipsoid that the concept of sphere is the generalization, and the ellipisoid is the particular encompassed in the generalization.
I’m currently debating with myself on whether my explanation is satisfactory, though. Is it enough to say that our senses can get us “in the ballpark” as far as the ideals are concerned, and then we whittle down the possibilities using logic until an ideal agrees with experimental results?
I agree. We should be able to test whether a surface conforms to a sphere to a certain degree of accuracy, however.In the material world there is no perfect circle, it exists in the conceptual world.