By delving into topos theory and sheaves one will eventually discover a "deep connection" between logic and geometry, two fields, which are superficially rather unrelated.
But what if I have not the abilities or capacities of delving deeper into topos theory and sheaves? Does the deep connection between logic and geometry have to remain a mistery for me forever?
At which level of abstraction and sophistication can this connection be recognized for the first time?
And which seemingly superficial analogies have really to do with this "deep connection"?
What's rather easy to grasp is that there is (i) an algebra of logic and (ii) an algebra of geometry. But is this at the heart of the "deep connection"?
What comes to my mind is, that both logic (the realm of linguistic representations) and geometry (the realm of graphical representations) have to do with - representations. Is this of any relevance?