ihm

25 ms·

211.
by ihm 11y ago
> These are generally called axioms, but these are totally distinct from axioms in the sense of ZFC's axioms. I wouldn't really say they're "totally distinct". For example, one could say that general group theory
212.
by ihm 11y ago
I got 1/3, but with a "different" distribution. (I took symmetrized pairs rather than pairs. But I realized after I wrote this comment that folding a square in half preserves relative area so symmetrizing makes no difference.
213.
by ihm 11y ago
I would take a look at Andrej Bauer's excellent talk "Stages of Accepting Constructive Mathematics"[0]. Essentially, constructive mathematics is mathematics done without the law of excluded middle ("for all propositions
214.
by ihm 11y ago
The reals one defines thee reals constructively in essentially the same way as one does classically. When the parent commenter says the reals in constructive mathematics are uncountable, he means that inside of a constructive system one can
215.
by ihm 11y ago
I actually think it's very possible to have an "intuitive understanding" of Banach Tarski (I would say I have one, but perhaps we disagree on what is mean by such an understanding). My "intuitive understanding" of t
216.
by ihm 11y ago
I would suggest making all the text visible instead of fading in and out. It's very distracting and makes the page a lot less readable (especially since I don't want to have to scroll constantly or read things only when they'
217.
by ihm 11y ago
A friend of mind suggested the very good idea of solving the diffeq for the constantly turning curve and using this when the user is simultaneously turning and going forward instead of doing one or the other first.
218.
by ihm 11y ago
Hm. Do you have any other info about your setup? I can't reproduce the behavior.
219.
by ihm 11y ago
Yes yes, just wanted to keep things simple for those without much mathematical background (and for a small infobox. I didn't want to try to explain that they locally minimize distance, or that the vector field given by the derivative h
220.
by ihm 11y ago
Added the Klein model! WRT your question, I'm not sure.
221.
by ihm 11y ago
Movement is implemented by using approximate numerical solutions to the geodesic equations (a system a differential equations whose solutions give geodesics in a Riemannian manifold). As such, there are some numerical inaccuracies due both
222.
by ihm 11y ago
Jeff Weeks has done some excellent stuff. His Curved Spaces[0], lets you fly around funny 3 manifolds. [0]: http://www.geometrygames.org/CurvedSpaces/index.html
223.
Show HN: Walk around unusual geometries(parametricity.com)
149 points by ihm 11y ago|34 comments
224.
by ihm 11y ago
Was this inspired by the last 2 episodes of Silicon Valley?
225.
by ihm 11y ago
> In other sub-fields (e.g. OO, logic programming and concurrency), category theory has not so far proven terribly useful. I wouldn't say that. I don't know about OO and logic programming, but there's a good amount of cate
226.
by ihm 11y ago
OCaml's module system (and conventions associated with it) give a few advantages over Haskell. - There are good conventions for naming and argument order (and named arguments!) so I don't have to memorize a bunch of different APIs
227.
by ihm 11y ago
Python in CPython is executed after being compiled to the lower-level Python bytecode. Is this not sufficient to consider CPython to involve a virtual machine?
228.
by ihm 11y ago
Yes, program is a term of art. It means a "term" in the type theory under consideration. A type theory is essentially a programming language with a fancy type system, and there are many type theories, just as there are many progra
229.
by ihm 11y ago
Well, the set theoretic attempt to describe functions isn't a very nice one. Type theory gives a formal definition closer to the intuitive notion: a function from A to B is a program of type A -> B. I.e., a rule for turning things o
230.
by ihm 11y ago
It's locally R and connected but not path connected.
231.
by ihm 11y ago
Interestingly enough the "mental software" used to handle the crisis of the atom bomb came from mathematics (von Neumann's game theory, in particular the idea of mutually assured destruction) rather than moral philosophy or s
232.
by ihm 11y ago
The Elm compiler is written in Haskell, and as others have mentioned, I use xmonad and pandoc.
233.
by ihm 11y ago
> As others pointed out, the way Haskell uses the term "functor" is related to the way mathematicians had been using it for at least a decade before cfront. Rather a bit more than that. Eilenberg and Maclane's original pa
234.
by ihm 11y ago
I think Itai Benjamini is at MSR. http://www.wisdom.weizmann.ac.il/~itai/
235.
by ihm 11y ago
I beat it. http://imgur.com/9D6144h
236.
by ihm 11y ago
"Closed manifold" typically means a compact manifold without boundary (see e.g., http://en.wikipedia.org/wiki/Closed_manifold ).
237.
by ihm 12y ago
> Some of the computer scientists, however, instinctively interpreted the statement “Let x be such that P(x)” as a variable declaration. This led them to give an “incorrect” answer to a question "Let x be such that P(x)" is som
238.
by ihm 12y ago
Certainly physics is not a branch of mathematics, but it isn't uncommon for papers in theoretical physics to essentially be math papers with an eye toward applications to some physical notions, and physicists do come up with new math
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ShowHN: Short Words – A new game of geometry and groups(parametricity.com)
1 points by ihm 12y ago|0 comments
240.
Animating Abstractly(parametricity.com)
11 points by ihm 12y ago|0 comments

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