The Helmholtz decomposition is one of the fundamental results of vector calculus. It says any well-behaved vector field can be split into two parts, one capturing sources and sinks through divergence, and one capturing rotation through curl. Video

Reasoning unmoored from reflection is delusion.

Mix logic with ontology? You're doing metaphysics. Abstract it away? Still metaphysics? Ignore representative function completely. Metaphysics. Write a grocery note. Believe it or not, still metaphysics.

doing some light katabasis

That's it. I'm reifying myself.

this is how actual philosophy looks like in the wild

You're X, your enemy is Y. You start calling Y a non-X, but this unites all your enemies with Y. Why would anyone do this? And why is it happening so often?

there is no transformation problem if you don't care

writing black/purple prose