kmill

10 ms·

61.
by kmill 3y ago
Higher homotopy groups of spheres goes way back to the 30s. This isn't lazy writing. https://en.m.wikipedia.org/wiki/Homotopy_groups_of_spheres Looking at all the continuous functions from all dimensions of sphere
62.
by kmill 3y ago
I'm now remembering a couple hundred slides I saw scattered on the sidewalk and street on Cesar Chavez near Sanchez in early 2020. I picked up a couple to take a look, but I can't recall what they were of anymore...
63.
by kmill 3y ago
That's the first I'd heard that Rust-oleum was named for one of its original pigments rather than its rust-protection capabilities. I can't find anything to substantiate your story, but I did learn that the inventor pursued f
64.
by kmill 3y ago
Interestingly, when people speak slowly it comes out as "je swee zanglais". The terminal sound is deposited onto the following word!
65.
by kmill 3y ago
"Set-theoretic type theory" is working with the lattice of all subsets of possible values, where a "type" is one of these subsets. This lattice has plenty of structure, but sure individual subsets do not. The category of
66.
by kmill 3y ago
I once wrote a final exam for a linear algebra course with a section "all the following are false, explain why." I did it to make it easier than a T/F, but it was unintentionally devious. So many students said some of them we
67.
by kmill 3y ago
Just to clarify, continuations don't have a snapshot of the whole heap, and they can be thought of as being a snapshot of just the interpreter state for a particular execution thread (roughly the call stack and source position). If hea
68.
by kmill 3y ago
The paper is about trying to statically analyze this. As I understand it, fip-annotated functions are ones that are checked to neither allocate nor deallocate.
69.
by kmill 3y ago
Lean 4 uses FBIP, but it looks like this paper is about something called FIP, which is related but about guaranteeing there are no allocations or deallocations. FBIP as I understand it is more about being able write functional code in a n
70.
by kmill 3y ago
The verb/noun stuff I understand was the UI for the astronauts (the DSKY). There was also the native instruction set for the CPU as well as an interpreter with a richer instruction set built on top of that, and they used this to more e
71.
by kmill 3y ago
You might also like the fact that the Apollo Guidance Computer (which ran at a similar speed) was also programmed using something like bytecodes. It didn't have to drive a graphical display though, only a spaceship.
72.
by kmill 3y ago
Yep. Still, it turns out there's a lot you can do with non-Turing-complete languages, and it's nice knowing that a program will definitely finish.
73.
by kmill 3y ago
Here's an equivalent-ish problem: Given a programming language, what's the smallest program that's an infinite loop? Some languages are designed to never let you write infinite loops (every program halts in them), but maybe t
74.
by kmill 3y ago
I've seen interleaved lexing and parsing, where the recursive descent parser asks for the next token, which is computed on demand. They're still separate modules. You just don't have to run lexing to completion ahead of time
75.
by kmill 3y ago
A handwavy argument for this is that if you continuously deform your picture, you can bring an upright and an inverted image toward each other until they cancel out (if you've ever played around with curved mirrors you probably can ima
76.
by kmill 4y ago
It's also the origin of the integral sign! (Mentioned on the Wikipedia article.) There's a nice accidental parallel between sigma notation (the discrete, "angular" summation) and integral notation (the continuous, "
77.
by kmill 4y ago
I think it's the same 'from' as 'far from home', but I'm not British so take that with a grain of salt. Even 'work from home' is weird. The only way I can read it if I really think about it is your wo
78.
by kmill 4y ago
Ah, but they didn't say they used nearest-neighbor when scaling it back down. This gives a (theoretically) better result when you want to scale up by a non-integer factor. (If it ends up just being an integer factor then there's n
79.
by kmill 4y ago
It's amusing that parsing theory was already at least 1-2 decades old by the time they made this mistake (consider that ALGOL 60 had a complicated grammar, introducing BNF too). I'd chalk it up to this being a shell language that
80.
by kmill 4y ago
My wife once purchased a ticket over the phone for the Acela line from the Penn Station in New York, but they misheard it as the one in Newark. So it's even hard for Amtrak! Something we learned out of all this was that each train comp
81.
by kmill 4y ago
I've been using ChatGPT/GPT-3 as a French tutor, to answer questions about different ways to say things, formally or informally. It's not always accurate, but still I learn from it. Amusingly, there's a mildly rude expre
82.
by kmill 4y ago
Another number system, which I learned about recently on HN, are the Kaktovik numerals, which are even closer to D'ni. Interestingly, they were developed just a couple of years before Riven was released. https://en.wikipedia
83.
by kmill 4y ago
This sort of rotation-and-superposition number system also appears (in base 5 too!) in the game Riven: https://dni.fandom.com/wiki/D%27ni_Numerals It's sort of funny how both Kaktovik and the D'ni numerals we
84.
by kmill 4y ago
Sure, I'm a mathematician, but what point are you making beyond a potential ad hominem? I myself include code in my own papers when it's useful. As the author of this paper mentioned (and it's something I'm a bit embaras
85.
by kmill 4y ago
Are you familiar with the different stages of research? This is "basic research" -- they found a new determinant formula and analyzed it. Others can pick up their work and continue, for example creating implementations and compari
86.
by kmill 4y ago
Here's the website where they kept track of the status of the Sphere Eversion Project: https://leanprover-community.github.io/sphere-eversion/ They have a dependency graph that shows the general structure of the a
87.
by kmill 4y ago
I can't really compare non-standard analysis with filters due to not knowing much about NSA, but filters are a natural sort of completion of the poset of subsets, the pro-completion. Every subset can be naturally regarded as a filter (
88.
by kmill 4y ago
Thanks for confirming -- I didn't trust my own ears for such a strange fragment of a sentence! It turns out it comes from a book called "The Foolish Dictionary: An exhausting work of reference to un-certain english words, their or
89.
by kmill 4y ago
Ah, thanks for the report -- it seems not to work on mobile Chrome. One of our Equestrians will take care of it on the next sprint.
90.
by kmill 4y ago
A surprising recent bit of news is that we learned that there's a phishing website out there somewhere that mysteriously redirects to endless.horse. We tried adding endless.horse to a database of non-phishing urls (after all, it's

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