black_knight
Joined 12 years ago
Joined 12 years ago
No, it is a matter of degree, it is not a binary thing. It is a measure we can put on government. It is not the only thing which matters, but there are differences between governments today. One is not the same as the other, just because none of them are ideal.
With the caveat that “the government” should somehow represent the will of society (I know, basic democracy seems like a big ask today), this seems like how it should be. The land belongs to us humans together, and if someone wants to control it exclusively, there should be something in return for the rest of us.
Fable is good, especially at conceptual stuff, don’t get me wrong, but it has limits. Opus 5.5 is a machine at getting correct code out once the concepts are in place. But I can’t trust either to not make mistakes.
While we should hold AI companies accountable, I feel like this one is on the person making the LLM generate, without also making it come up with sources (which it can do!)
-- An element has at most one two-sided inverse.
inverse-unique : ∀ (M : Monoid) (open Reasoning M)
(x y z : type M)
→ y ⋆ x = unit M
→ x ⋆ z = unit M
→ y = z
inverse-unique M x y z leftInverse rightInverse =
begin
y ⟪ sym (unitᵣAt y) ⟫
y ⋆ unit M ⟪ mapᵣ (sym rightInverse) ⟫
y ⋆ (x ⋆ z) ⟪ sym (associativeAt y x z) ⟫
(y ⋆ x) ⋆ z ⟪ mapₗ leftInverse ⟫
unit M ⋆ z ⟪ unitₗAt z ⟫
z
∎
where open Reasoning M
Not sure if all the unicode characters will render on HN, but the things left of the ⟪ ⟫-brackets is exactly what a text book in mathematics will have. While the things inside the brackets are just a functional-programming way of saying out the argument which would be left for the reader to make in their head for why each step holds.(If you know Agda, I dare you to look carefully at this example!)
Parser combinators alone makes monads (or really applicative functors) worth it. But then there are the all the other spectacular things we can do with monads!
I think the confusion stems from people being exposed to set theory, believing that formalisation is akin to writing those horrible set encodings of everything. Which I would agree would be akin to writing assembly.
But Lean, Rocq and Agda are all based in type theory. Which means it is more like the highest level programming language you can imagine! You have all the powers of abstraction, but you still have to convince the type checker – i.e. no “trust me, bro” casting, or even questionable while loops (“I promise this loop finishes at some point”).
These abstractions along with meta programming techniques (“tactics”) means that you can write readable correct proofs, but it takes effort. Math is extremely deep, and getting formalised all the way to the research frontier in a given subfield is a serious undertaking.
Also, I guess with agents it should be possible to explore new algorithms more efficiently. You may discover something cool! And yes, anyone can copy it, but you will still have first mover advantage. Also, in music tech brands matter a lot. People love getting stuff from small “artisan” companies.
But at the same time, I am happy with my current use of LLMs. I get to do things I only dreamed about before. I would have so many ideas I could never realise. Now I can fire up Claude Code and get cracking. And because of my experience, I can keep up with it, correcting it, suggesting better ways of doing things…
And yes, so glad I have my PhD already. But I am looking forward to all the articles I will be writing based on my collaborations with both humans and LLMs.