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I can suggest an equation that has the potential to impact the future: 𝐍𝐚𝐭(𝐇𝐨𝐦(−, 𝐶), 𝐹) ≅ 𝐹(𝐶) + AI Given a category 𝒞, a functor 𝐹 : 𝒞ᵒᵖ → 𝐒𝐞𝐭, and an object 𝐶 ∈ 𝒞. This equation combines Yoneda’s famous Yoneda lemma, which relates a category (𝒞) to…
I think this is more like a particular choice of semantics for programs, which makes sense in some contexts but not others. Or maybe I'm missing the point that all programs can be reduced to these somehow?
Bohmian interpretation of quantum mechanics
Mention one scientific opinion that you’d defend like this ✍️
What is pip then?
Sometimes I don't know how else to convince people to try Functional Programming
Projective geometry is when you draw a lot of lines
People just learning that Israel is an authoritarian theocracy are like:
Whoa I just learned that interfaith marriage is illegal in Israel!! What the fuck?? This is insane.
Still getting weirded out about how: Lax functors C -> Span And Lax normal functors C -> Prof are the same thing
For R&D community nucleation, it’s exciting that @ToposInstitute opened a UK office, relocating @u_map_prop and @myers_jaz; while @JadeMasterMath and @tangled_zans used our funding to launch a new nonprofit research institute in Glasgow (GLAIVE: Glasgow Lab for AI VErification).
Cats are invariant under SO(3) transformations! 😼
You, foolishly: a double category has horizontal and vertical morphisms Me, wise, laying flat: no those are vertical and horizontal morphisms
Zariski inventing algebraic varieties was like:
Yes exactly. The trick is to find the right generality where the definitions have canonical choices
A function a -> a only has one sensible implementation, a function Int -> Int has many—polymorphism is recessive. The implementation is constrained/clarified by the generality of the interface. Programmers warn of "premature abstraction," but this is confused w.r.t. foundations
Above
If you were the empty set, where would you want your face to be?
I don't think this is fair. Think about how hard it is for a machine to distinguish "hallucination". There are just endless unknown unknowns.
The fact that LLMs still hallucinate 2 years after the initial release means: 1. Nobody knows how they actually work to fix them 2. Nobody actually cares
it just like me fr
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