The Geometry of Thought

Barbara Tversky at Edge: “…So far, we have categories and themes, in our minds and in the world. Your mind might have jumped back to lines: we arrange towels and dishes and toys in lines on shelves. That seems by necessity—after all, there’s gravity. But we line up windows in rows in apartment and office buildings; surely, gravity doesn’t require that. Buildings are lined up on streets. Streets are traditionally lined up in grids, not just in the west but also in the east. Also not required by gravity, more likely by our desire to organize. I did say lines are not necessarily straight, though there are huge advantages to straight lines, but you might be thinking: what about the curved streets and paths common in US suburbs and Chinese gardens? Answers: first, almost nothing is always (note the hedge, I added “almost”). Second, the curved streets aren’t so much designed to disorient you, though they do that, but to give a feeling of mystery and discovery. And perhaps to slow down traffic. There’s aesthetics too. Some people like curves, others like lines.

Our arrangements in space go far beyond lines and categories. We create hierarchies of categories, plates on one shelf, bowls on another, arranged by size. Books arranged by topic, then ordered alphabetically by author. Table settings arranged in 1-1 correspondences, everyone gets a plate and a glass and a napkin and cutlery. There are also symmetries and repetitions and recursions in both the outsides and insides of buildings. There are orderly arrangements in time as well as space. It’s beginning to sound like programming.

We’ve begun an answer to the question: how do we structure our thoughts and our world? Many ways, not just one, and they mirror each other. We put our minds in the world. The mind in the world creates common ground for our collective thoughts. It informs us, tells us what it is, it directs our thoughts and it directs our actions. Think how different our world looks, where nearly everything is designed, from the world of our hunter-gatherer ancestors. Think of what that organization, an organization by abstractions, does to our minds and to our bodies, even tiny minds and bodies….(More)”.