@quinnswm@Gabri272l Like, sure we might call something a vector bundle because it has vector-like properties, but is it meaningfully the same thing as a vector space?
And at the point where you have to get weird about definitions to find counterexamples, I'm happy saying vectors are derivatives.
@quinnswm@Gabri272l I've never heard anyone use the term geometric topology and I learned this in a class on topological geometry.
Yeah you're right that you can make vector bundles over non-smooth manifolds this doesn't apply to, but at that point I think you can start debating what "vectors" are.
@JetStreamSham Long story short, once you start doing a serious rigorous description of vector fields, they're isomorphic to derivatives. This has some rather important implications for topological geometry.
@JetStreamSham Get deep enough into topological geometry and a vector field assigns a tangent vector to each point in a subset of Rn, which is described as a derivation. Then the set of all vector fields on an Rn subset is isomorphic to the derivations of the algebra of functions on that subset
@Stuckinthebunk1 immediately adjacent to defensible fortresses, relatively fertile fields, and creature comforts, which are defended only by household guards and slow mustering non-standing armies. With a volatile political situation and the standing army having nothing to lose. It's a powderkeg.
@Stuckinthebunk1 we're presented with in the story isn't an unstable institution. It's an explicitly ultra stable institution capable of lasting centuries with us single hiccup in the Night King more than half a millennia ago.
And that's what doesn't make sense. A moderate standing army
@SydneyFreedberg@BretDevereaux Like the whole thing about food storage for long winters doesn't have to be explained, it's a symbol. Until the details of food transport and supply trains are (poorly) made fundamental to the narrative. Then it's a technical problem and the symbol is looking rather shaky.
@SydneyFreedberg@BretDevereaux Yeah ASOIAF has this weird dichotomy. It's got this strong symbolic theming which stands strong on its own ... but then it tries to prop up and justify that with historical realism and metanarrative claims to such, which fall apart under scrutiny and undermines the symbolism.
@jeffhurtsjeff@BretDevereaux That's true, but also most fantasy writers don't try to build a brand off of how historically grounded their stories are, nor end up making the politics of such an organization a centerpiece of their story.
To ask for acclaim is to also receive critique.
I’ve worked in agriculture for 27 years. I put that experience to work helping other people succeed. And it works. Because unlike certain other people, I actually know what I’m doing.
Now, I’m running in the US’s only competitive statewide Agriculture race this year.
By the way, something that a lot of the reporting misses:
Their greenhouses routinely hit 120-125°F. And at that point, it’s a hellhole for workers. But also, let’s not forget, YOU CAN’T GROW A VIABLE CROP AT 125°.
You’re failing at the ONE thing a farm is supposed to do!