Contexts and Seas

https://www.quantamagazine.org/emily-riehl-conducts-the-mathematical-orchestra-from-the-middle-20200902/

I wonder if chaos theory, or mathematics in general, had anything to do with how the dinosaurs got out. Did Dr. Malcolm know what he was talking about? Was he showboating? Both?

But then again, when does "mathematics in general" not have anything to do with anything? I wonder if mathematicians who work in dynamical systems sort of see the world differently, and they can just "see" certain things which seem magical to us.

Must be. Sometimes, knowledge global structure and dynamics yields really valuable insight about local patterns. Even things that seem chaotic locally often seem to admit some global pattern, right?  History gives us perspective into law and modern-day politics, evolutionary theory yields insights for psychology, sociology. 

It's sort of a Grothendieck-esque thing, I feel. One of my favorite analogies by Grothendieck is the following: 

"If you think of a theorem to be proved as a nut to be opened, so as to reach “the nourishing flesh protected by the shell”, then the hammer and chisel principle is: “put the cutting edge of the chisel against the shell and strike hard. If needed, begin again at many different points until the shell cracks—and you are satisfied”. He says: I can illustrate the second approach with the same image of a nut to be opened. The first analogy that came to my mind is of immersing the nut in some softening liquid, and why not simply water? From time to time you rub so the liquid penetrates better, and otherwise you let time pass. The shell becomes more flexible through weeks and months—when the time is ripe, hand pressure is enough, the shell opens like a perfectly ripened avocado!"

He imagined that a problem could be "submerged and dissolved by some more or less vast theory, going well beyond the results originally to be established". I think this is particularly striking, because that's how I imagine it -- a structure made of something loose, porous, and then some sea comes along which basically surrounds, marinates, penetrates, and incorporates this structure so that it's not literally the same, but rather the same thing viewed in a lager context. Something that is more "filled in" but at the same time more general, global, reaching beyond your initial world (the porous structure). 

Or maybe it's like never seeing a car before, and looking at a particular portion of it, perhaps the gearbox. You study the thing to death and do some really cool things with it, and then you are shown the whole car, the whole damn thing and you realize why the components are arranged the way they are, and why they HAVE to be like that. But I imagine that cars are not the only thing that use gearboxes, so there are even more ways to expand your concept of gearboxes. 

So I imagine that there are actually multiple "seas" that might encapsulate the same "structure" in different ways. 

Lately I've been wondering exactly how much I know, and judging by my "learning velocity" I know basically nothing. There's so many mind-opening things to be known, so many seas to immerse my models into.