Feanor

Krakow, Poland

Age: 25

1d
awarded Commentator
1d
comment On mutual tactical serial upvotes and unconstructive comments
Just to play the devil's advocate... Suppose that for whatever reason, person A likes looking at person's B answers. I can imagine a number of ways this could happen, e.g. by similarity of tastes, knowing one another in real life, etc. Nothing wrong with that, I guess. Once A reads X's answer (where maybe X=B, but could also be anyone), he should presumably upvote or downvote, probably upvote more often. And so he does. I agree that this does produce very fair distribution of votes, but we have worse biases than that (e.g. over-voting elementary questions).
Sep
13
comment How to check if a sequence is random?
Of course, I do not have such black box, but if I did, I think this would result in the type of algorithm in the question. At least, I would be able to account for all "random" sequences you can think of (as long as they are computable). In more down-to-earth terms, I could also do the same without the black box, instead iterating over all Turing machines corresponding to "simple" mathematical constructions (i.e. ones that are bound to stop for "simple" reasons).
Sep
13
comment How to check if a sequence is random?
I don't actually want to prove a sequence random - I am well aware that this would be impossible. What puzzles me is if I can prove a sequence fails to be random, whenever it fails to be random. Imagine for a moment that I have another black box, which tells me if a given Turing machine produces a 0/1-valued sequence. If I had that, I could devise an algorithm which iterates over all such Turing machines. For each Turing machine I wait until either $a_n$ differs from the output, or I am reasonably sure $a_n$ agrees with the output more than a random sequence would.
Sep
13
comment How to check if a sequence is random?
Well, I can think of one statistical test I might try that discovers this sequence. Namely, just produce the sequence you mentioned, and check if $a_n$ is equal to $n$-th term of your sequence. Of course, this is a rather obscure test, but I can afford to iterate over similarly obscure tests and see what happens.
Sep
12
revised How to check if a sequence is random?
added 146 characters in body
Sep
12
comment How to check if a sequence is random?
When I said "a sequence" I meant "an infinite sequence". They are not deterministic in this sense.
Sep
12
asked How to check if a sequence is random?
Sep
11
awarded Critic
Aug
27
comment Smallest value taken by a quadratic polynomial in two variables.
Thank you! I made an error in the formulation, corrected now. In the context I have in mind the "leading" quadratic form is guaranteed to be indefinite anyway, and I was a bit sloppy at this point as a result.
Aug
27
revised Smallest value taken by a quadratic polynomial in two variables.
added 31 characters in body
Aug
26
revised Smallest value taken by a quadratic polynomial in two variables.
edited title
Aug
26
asked Smallest value taken by a quadratic polynomial in two variables.
Aug
26
comment $L^{\infty} (X, \mu)$ is not separable?
@Shone: In saying that $\lVert f_A - f_B \rVert = 1$. Otherwise, the norm would be $0$ if e.g. $A = \emptyset$ and $B = \{n\}$ where $\mu(X_n) = 0$.
Aug
25
awarded Supporter
Aug
22
awarded Yearling
Aug
22
awarded Yearling
Aug
21
awarded Notable Question
Aug
18
awarded Electorate
Jul
21
comment What is ethics really about? (the goal or the means)
Your claim strikes me as false. Suppose I say that world peace would be a good thing. I can make sense of this statement without first figuring out how to stop all wars, so here is a goal that can be understood with no reference to means. Or I could tell a child (and a god could tell a person, presumably) how to behave, and it would then know the means without knowing the goal. What am I missing?
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