knappa

7 ms·

31.
by knappa 4y ago
There are different sum- and product-like operations for different types of things: For sets (and topological spaces), the sum operation is the disjoint union and the product is the Cartesian product. For vector spaces, the sum operation is
32.
by knappa 4y ago
It's the unique thing that makes the commutative diagram from the wikipedia article work. As in: You want V⊕W to be a vector space that contains the vector spaces V and W. You want that for any linear maps V → U and W → U, you get a li
33.
by knappa 4y ago
> It is unfortunate coincidence, but Haskell sum types don't correspond to sums of spaces. It depends on the perspective. Both are a form of coproduct https://en.wikipedia.org/wiki/Coproduct which forms a disjo
34.
by knappa 4y ago
Yes, this looks like an error. You don't want unordered pairs, which do not form a vector space, but an isomorphism of under order permutation of the terms. Roughly speaking, V⊕W is not the same as W⊕V, but if you swap the order everyw
35.
by knappa 4y ago
Eventually your (for example) great*N paternal grandfather is going to show up on your mother's side, forming a loop. That's just due to bounds on the human population and how the number of labels for previous generations grows ex
36.
by knappa 5y ago
In [1]: length = 10_000 In [2]: %%timeit ...: pre = [None] * length ...: ...: 38.7 µs ± 128 ns per loop (mean ± std. dev. of 7 runs, 10,000 loops each) In [3]: %%timeit ...: pre = np.empty(length, dtype=
37.
by knappa 5y ago
Beware the Green Decorative mug!
38.
by knappa 6y ago
Let me show you some things: https://en.wikipedia.org/wiki/Multiplication_algorithm#Fouri... https://en.wikipedia.org/wiki/Sch%C3%B6nhage%E2%80%93Strasse...
39.
by knappa 6y ago
I'm always confused by people complaining about knowing 'advanced' mathematical notation. The thing that requires effort to understand is the actual mathematics, not the notation.
40.
by knappa 6y ago
From a 'not currently in front of the class' perspective, it's pretty clear what the student meant by 1/3 + 1/3 = 2/6. They were taking + to mean something like a general 'and' or combining action, no
41.
by knappa 7y ago
Sagemath includes a lot more math, esp. number theoretic stuff, and is a quite large. (~1.6G compressed) Sympy is _much_ smaller and integrates more easily into python code that isn't solely mathematical.
42.
by knappa 7y ago
Thank you, the corresponding Washington Post article (which I have access to) does not seem to have that information.
43.
by knappa 7y ago
A more interesting statistic would be the (percentage) change in the number of students whose scores indicate that they are college-ready. Increasing that number is, presumably, what these get-more-kids-to-take-the-SAT programs are about.
44.
by knappa 7y ago
"Cobordism" is actually more descriptive than he thinks, but it is French derived. "bord" means edge or boundary and a cobordism is something which connects two boundaries.
45.
by knappa 8y ago
It was my first exposure to linux; the 1994 version.
46.
by knappa 8y ago
The sex-discrimination lawsuit against UC Berkley seems to be a kind of academic urban myth; the administration was apparently afraid of such a lawsuit and the study was done in response to those administrative fears.
47.
by knappa 8y ago
Is there a story behind why the version numbers went from 4.4 to 5.1?
48.
by knappa 8y ago
I don't think you mean to use a term as strong as diffeomorphism. A diffeomorphism is differentiable, sure, but it is also invertable with a differentiable inverse. They have a lot of properties that machine learning honestly does not
49.
by knappa 8y ago
That's a lot of overlap of those confidence intervals in Table 3.
50.
by knappa 8y ago
Well, x mod 1 is just x minus a series of Heaviside step functions, each of which are non-constructive. The core problem is determining if your real number x is equal to an integer. You might be able to prove that x is close to a particular
51.
by knappa 8y ago
Unfortunately, tee's are backed by a queue and upon each read of a "fresh" value from one of the branches of the tee, the shared queue is appended to. There is no opportunity to remove an element from the queue until all bran
52.
by knappa 8y ago
A lot of this seems ridiculous: > Mental health issues are rife: approximately one-third of PhD students are at risk of having or developing a psychiatric disorder like depression. The baseline percentage of the population which experien
53.
by knappa 8y ago
I like it, despite the infeasibility. Here are a few more things missing from the plan: 1) The main door should be by the admin offices, for security reasons. 2) The gym has to be rectangular for the basketball court, or large enough that i
54.
by knappa 8y ago
No it isn't unsound, it is an application of the pigeonhole principle. A finite memory and finite set of states implies that there are some finite number of configurations (call it N) that the computer can be in. Once you let the compu
55.
by knappa 8y ago
I haven't thought it through yet, but Pick's theorem ( https://en.wikipedia.org/wiki/Pick%27s_theorem ) might be useful for the current puzzle.
56.
by knappa 8y ago
I would think that the virii that have that kind of prevalence are mostly bacteriophages.
57.
by knappa 8y ago
https://imgur.com/a/czq93
58.
by knappa 9y ago
Not according to the article. (Well, they compare different time scales. So...maybe?) > While New York City's murder rate has gone down - decreasing by around 87 per cent since the 1990's - the Big Smoke’s has simultaneously su
59.
by knappa 9y ago
Having watched a few rounds of CS faculty searches, I'm certain the shortage will still be there. (At least at my university.) The reasons are more or less what you mention, but objectively, it really isn't a particularly difficul
60.
by knappa 9y ago
Mathematician here: It isn't exactly that proof assistants are looked down upon. Rather, most of us don't do 1st order logic and it isn't on anybodies radar. Even if it were, it is often new proof techniques that lead to new

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