geography-geometry
If you look at the map of the US it’s for the most part a box with clearly defined boundaries on all four sides. Canada is also a box but with only three sides, the top boundary line essentially does not exist. This is not a liability. Once understood it allows for great clarity of thought. It ultimately avoids the inherent claustrophobia of a completely four sided model. The Mediterranean Sea functioned in the same way to form thinking in the early archaic culture of the Greek islands in the Aegean.
The US is also situated mid way between the Far East and Europe and has benefitted from proximity to the former to produce great artists like Ad Reinhardt and Agnes Martin.
and behind geography is geometry
.... “Grothendieck found the right way to define abstract notions of space, new ways of thinking about spaces.” He recognized that “the way you probe the geometry of a space is not by looking at the points, but by studying other things.”
Grothendieck's schemes let you study geometric spaces through algebraic structure rather than points directly
Grothendieck 1954 / 2013
pg 38 :
In our probing of things in the Universe (mathematical or otherwise), we dispose of a crucial rehabilitating power: innocence. By this I mean the original innocence which we have all received at birth and which rests within us, often the target of our scorn and of our deepest fears. It alone unites the humility and audacity which allow us to penetrate into the heart of things, while also allowing these things to penetrate into us and impregnate us with their meaning. This power does not only come as a privilege for the extraordinarily “gifted” - (say) with an exceptional intellectual power allowing them to absorb and manipulate, with ease and dexterity, an impressing quantity of known facts, ideas, and techniques. Such gifts are admittedly precious, and susceptible to generate the envy of those (like myself) who were not so gifted at birth, “beyond all measure”. Yet, it is not those gifts, nor even the most burning of ambitions, accompanied with a relentless will, which allow us to cross the “invisible and imperious circles” which enclose our Universe. Only innocence can cross them, without noticing or even caring to, during the times where we find ourselves alone and listening to the voice of things, intensely absorbed in child’s play...