kmill

15 ms·

151.
by kmill 5y ago
Interesting... Original research is not welcome on Wikipedia. The hedge "for some people" is probably not wrong, but how do you know you actually set up the experiment correctly?
152.
by kmill 5y ago
Quoting Wikipedia (emphasis mine): > for some people the brain is tricked into thinking the middle finger is in the warm water It worked for both me and another willing participant, but we found it depended on the orientations of our f
153.
by kmill 5y ago
The article is all over the place, but I think I might be able to summarize: - ZK involves organizing your cards in a tree - This tree is not a taxonomy. It merely reflects the way in which the information was consumed or the ideas were cre
154.
by kmill 5y ago
The source code is all right there in play.js This is a solution to every puzzle: eval(goal_program); draw_checkerboard = draw_checkerboard_goal;
155.
by kmill 5y ago
That's how I like to explain it to people, though there's a small caveat that doesn't really affect the argument, but it's worth considering. The only times a knot-with-hues actually corresponds to a knot in Euclidean 4
156.
by kmill 5y ago
Distance might be rather a symptom of senseless abstraction. Abstraction is throwing away details. If you throw away the right details, solutions are simpler. If you throw away the wrong ones, you miss the point.
157.
by kmill 5y ago
This reminds me how a chauffeur working for Pixar picked up on what they were up to early in production: https://www.npr.org/2021/03/27/981553332/not-my-job-we-quiz-...
158.
by kmill 5y ago
This is probably known somewhere, but something I noticed is that a way to think about Earley parsing is that, when you create an LR(1) shift-reduce parser, rather than having it be an error in the grammar for there to be shift-reduce or re
159.
by kmill 5y ago
I've been getting into formalizing math in computer proof assistants, and it made be realize equality was much more subtle than I had previously thought. Consider the sets {1, 2}, {2, 1}, {1, 2, 2}, and {n in Z | 1 <= n < 3}. T
160.
by kmill 5y ago
The answer to the puzzle is in the comments on that page (Prof. Baez gives your argument in one of them, too). It would be interesting knowing why there are roughly six clusters of defects. The figure seems to technically have seven cluste
161.
by kmill 5y ago
In C, the && and || operators are short-circuiting. This works (in that it doesn't give a compiler error) because printf returns an int. I remember following a really old Python tutorial that suggested the way to write inline
162.
by kmill 5y ago
Don't you think it's a bit odd that the example program uses short-circuiting booleans as conditionals and uses the fabled downto operator?[1] The article's not teaching how to program, it's just showing you how to set
163.
by kmill 5y ago
The fun of writing an interpreter is that you can extend it with new features easily. With `eval $1` you're stuck with whatever it does (unless you want to do string manipulation of code -- it's only usually a bad idea :-) ) Th
164.
by kmill 5y ago
(A mistake above: it should be "we see it's nothing other than (\x, f (x x)) (\x, f (x x))") While we're here, another cool application is that quines exist. I'll give a way that misuses the theorem (though in a cor
165.
by kmill 5y ago
This cool observation is generalized in Lawvere's fixed point theorem[1]. It basically says that whenever you have an "interpreter" I : A -> (A -> B) that takes elements of A and turns them into functions A -> B, th
166.
by kmill 5y ago
It seems to be node-based programming, done textually instead of graphically. In PureData (or Max/MSP) each node has some number of inputs and outputs, and you wire them up. The semantics here are a bit different though. The idea is
167.
by kmill 5y ago
Indeed, computable functions on binary streams have a uniform bound on how much of a stream they'll look at! "Does this stream include a 1" is not computable, since it won't halt on 00000.... The subset of streams that
168.
by kmill 5y ago
There's an interesting branch of math called "synthetic topology" where you study computational questions topologically. https://ncatlab.org/nlab/show/synthetic+topology Given a set X of things that
169.
by kmill 5y ago
For better or for worse, piecing things together using context clues never seems to really end :-) One useful heuristic is the "unambiguous parse rule." You think about different ways something might be read (even if you have no i
170.
by kmill 5y ago
Yeah, my understanding is that second-order arithmetic picks out the usual natural numbers, but it is a much stronger system since you can additionally quantify over subsets of naturals in your formulas. The context of the comment is ZFC
171.
by kmill 5y ago
The word "type" is very overloaded. In the language of type theory, Prolog (and many other languages, usually dynamic) consider a universal type of all terms, and then a "type" is a set on the universal type. This is a
172.
by kmill 5y ago
Ok, but I'm not sure what your point is. Throwing out only the axiom of choice (which is the difference between ZFC and ZF) does not make things constructive. If you're thinking of Diaconescu's theorem, it's that choic
173.
by kmill 5y ago
No: https://en.wikipedia.org/wiki/Axiom_of_countable_choice
174.
by kmill 5y ago
Thanks for sharing that article. My understanding is that this bridge effect is actually what is happening across the entire length of the string; it's just that the boundary condition makes the effects of stiffness clearer. Stiffness
175.
by kmill 5y ago
> non-continuous functions I think the step function doesn't depend on choice. Say f(x) = 0 if x < 0 and f(x) = 1 if x >= 0. Also, suppose we define the reals through Dedekind cuts. We can define f(x) by checking whether 0
176.
by kmill 5y ago
> calculate the points (like in the end of my comment) Oh, I forgot I commented more than once today on HN. I was referring to this one: https://news.ycombinator.com/item?id=27851188
177.
by kmill 5y ago
Those bass notes are noticeably clearer there! The sound of inharmonicity comes from dispersion -- different frequencies travel through the string at different velocities. The lower the frequency, the less the wave notices the stiffness of
178.
by kmill 5y ago
A theoretical use is that it shows that the axioms of the natural numbers (the Peano axioms) aren't enough to pin down what we think the natural numbers should be -- there are these crazy non-standard natural numbers out there! In cont
179.
by kmill 5y ago
There are two main operations for whole numbers: addition and multiplication. A basic question is what are the "atoms". With respect to addition, the atom is 1, since every number can be written as a sum of 1's, and 1 isn&#
180.
by kmill 5y ago
This surprisingly doesn't mean repeatedly adding 1 will exhaust all natural numbers -- there are models for the natural numbers with elements that can't be reached this way! The ultrafilter construction gives one such model. You

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