My "P" is for Philosophy, but with a door wide open to Psychology ("come share our P").
Accepting my premise, that I'm a P-person, it stands to reason that I get to lecture the Theater-History folks in my wing, which dynamic duo for me includes literature, both fictional and nonfictional. TH is storytelling, whereas "A for Anthropology" anchors those stories to we-the-humans, that "measure of all things" grounding our analogies.
In explaining Category Theory (CT) for example, I might focus on the right brain diagrams first, and the notation second. Circles with dots in them, with pointing arrows in between. Arrows within circles (or ovals), the morphisms, and then arrows between the circles (or ovals), the functors.
They'll tell you those dots are the objects, mere points, and we're proud of their aspectless zero dimension-hood. We care nothing about their content. Their inscrutability is a feature, not a bug.
However, other times, we've zoomed back to see dots as entire categories, objects within still greater containing structures, these containers themselves categories most likely. We like to be recursive. So dots may have structure after all, if we tune them in.
The Computer Science types naturally want those objects to be types. Motion along an arrow might be to the type of what's returned, should an object operate, or be made to function in some way, perhaps permuting into itself, a set of possible orderings. Categories provide the dirt, the growing grounds, for more elaborate structures, like groups and fields, the various algebras.
Astronomers may have less use for CT, until "Category" is temporarily hot-swapped with "Planet" in some lecture. Now think of Urbit if wanting to catch a ride back to Computer Science.
Little Prince goes here. As does Star Trek. As does Sun Ra. We travel the spaceways, from planet to planet, maybe in a board game, or in a simulation game wherein planet creation (terraforming) is a theme. According to which strategies? What is "world game" in this case?
After listening awhile to my lectures, a PATH student is more likely to see CT as a way of talking about metaphors and analogies while avoiding sounding like a literature major. The whole point is to have an elegant notation and minimalist vocabulary. Let astronomers think of categories their way, as 3D, and let computer scientists think this other 2D way. CT is a glue.
Quoting from our M4W archive:
For example, re CT (Category Theory): how mistaken would it be to temporarily jigger the namespace such that "Planet" was hot swapped with "Category" just for kicks. For "arrows" (morphisms) we have the obvious characteristic that locations on a planet (the objects) may be connected any which way, implying rotation and the ability to inspect as one would a globe, by rotation (as well as by looking more closely, and from further away). Then there's looking from the inside-out.
I bring this up in part because the Cardano article in Britannica assures us that Cardano's thought process would have been characteristically "more Islamic" in giving 2D diagrammatic Euclidean constructions for everything, if I read it right. The ratiocination involved was highly geometric in other words... as was John Harland's presentation I hasten to point out (with the fences and boxes), but more in the sense of employing, versus deriving, said cubic equation.
Also w/r to "hot swappable" that's how I think of getting a 3rd powering tetrahedron in the works, as doing something the cube does, but on a different Planet (in a different Category). The unit-edge sugar-cube is not unit-volumed here on Mars, but the sugar-tet surely is. We haven't given up a certain sweetness. The Pythagorean Theorem may be shown with equilateral triangles constructed on both legs, plus hypotenuse. Still works: a^2 + b^2 = c^2 (picture triangles).
Put another way, it's not either / or. I'm leery of any logic which triggers "flight or fight" reflexes just because there's an alternative planet (another logic) in the picture. This feels too insecure. Why do either? Become friends.
