I would also answer, although I am not familiar with group theory, that a sphere is more symmetrical…But there is from another point of view an infinite number of points in a circle as in a sphere…so maybe with Cantor (?) one could say that one infinite set can be greater than another infinite set, although this is counterintuitive…

Entirely agree…having had a long career teaching media studies and communication, often did I create a course to learn and understand a topic that seemed important to me…for example, early in my teaching years, I wanted to understand system’s theory and cybernetics, two subject matters that stimulated my curiosity…so I created two courses on these topics and it sure worked…My motto…I remember reading somewhere this sentence: We teach best what we most need to learn. Indeed.

The problem here seems related, as far as I can think or grasp, since I’m not a mathematician, to the question: what do we mean by the word ‘nature’? Is there something else? Above? Different? As a materialist, I’m inclined to say that nature is all there is…wether it be ‘things’, minds, and so of course ‘human constructs’, products of our brains or neuronal organization…of a very high complexity, I agree, but nonetheless a ‘material’ complexity…so maths, or whatever, cannot exist ‘without nature’ because I don’t see how anything could exist without nature…It’s obvious to me that the physics community can use maths discovered long before physics…but mathematical human constructs belong intrinsically to nature just as physics does, and also the physics community and also any ‘human’ construct…Spinoza: Deus sive Natura…if you endorse a flat ontology, it’s not surprising then that maths has such effectiveness when it comes to describing or explaining the world in terms of physical laws…

Very fascinating…I always thought of earth as the ‘blue’ planet, the ‘water planet’…quite instructive…thank you!