and so what function if applied twice results in total annihilation? well, probably lots of things, but most notably d^2 = 0 suggests d is potentially a boundary operator

i think in order to make the most sense of this it's best to not think of the zero map as a contraction but more like total annihilation. you don't get sucked into a vortex, you get vaporized on the spot.

i sometimes have the 5mg gummies, maybe 2-6 at a time. they don't do much for me, though. i prefer to smoke.

so one can lean in either direction and reap benefits, so long as one doesn't lose balance

what's notable, though, is that low concept high intuition and low intuition high concept both seem to be desirable places to be. the latter is about endurance, whereas the former reminds me of something Romanovsky said: "concreteness of thought is characterized by its dynamism."

or maybe a basis is a basis is a basis and that's just about all we can say

i guess by observing the space in a certain way (setting a coordinate system), we've effectively specified some sort of motion: the stretching and shearing of the standard basis vectors under this change of basis transformation

furthermore, a vector space with a linear map is the same thing as an F[x] module

conversely, any invertible linear map can be thought of as a change of basis and hence simply as the image of the standard basis under this map

in the comments of my previous post i basically said "0 is for observer." what's a basis, then? well, each basis B can be matched with a change of basis map from the standard basis to B itself

i guess positing the void is akin to accepting an axiom that says "there is an observer." it can be viewed either as specifying an ambient space or as setting an origin, and furthermore, either one implies the other. cogito ergo sum.

i describe the absolute as having a timed and timeless component, an observation that presumes the void. the idea about the void being generated by confusion is from G. Spencer Brown; i liked it so i stole it.

the bravery of dualism is kinda like that NGE quote about how "mankind fears the darkness, so he scrapes at the edges of it with fire." the void is effable, and so we work with it, by which i mean we compare things sometimes.

the honesty of monism is rooted in a belief that most of us share, which is that anything exists at all. this seems like a sound axiom; it kinda reminds me of that "proof" that the empty set exists (if otherwise, the set of all empty sets would be empty).

so this is classic monism vs. dualism, except i wanted to try and see both sides of the argument. monism feels honest to me while dualism feels brave.