xkcd

Qaanol

Assuming the sampling rate is significantly higher than the frequencies of the signal, there is indeed an approach that uses a relatively small number of calls to the oracle.

Qaanol

Is this for work?

If so, how much is a solution worth to your employer?

Qaanol

CorruptUser wrote:I often go to portland, maine...

Huzzah!

Qaanol

This is a cut-and-paste repost of a thread on this very forum from 2010: link.

Edit: So is the smoking one (albeit with the typo in the subject fixed)

Edit 2: Pretty sure the product/service one is as well: link

Edit 3: And the “intelligent information” one is from 2009: link

Qaanol

I’ve been tinkering with the α·max + β·min approximation to the distance formula. As a quick refresher, if you know the x and y distances to some point and want to estimate the straight-line distance, you can take the dot product of ⟨x, y⟩ with an appropriately chosen vector ⟨α, β⟩. Since the dot pr...

Qaanol

Cauchy wrote:Don't you do that determinant thing that gets you the cross product?

Thank you much!

Qaanol

Given a basis for a hyperplane in ℝⁿ, what’s the best way to obtain a vector orthogonal to it? In particular, given n independent vectors in ℝⁿ, is there an efficient way to calculate a vector orthogonal to the hyperplane containing all of their differences ( v i − v 0 )? The general problem would b...

Qaanol

As another minor thing, you can improve speed a little by looking at distance^2 rather than distance. The square root operation is one of the slowest basic operations a computer can do. Things often go quite a bit faster if you check whether distance^2<R^2 rather than doing the square root to calcu...

Qaanol

I mean, submitting a middling score on someone necessarily means having less impact on that person's chances than giving a 0 or a 5, right? Voters tend to have their preferences decided and want to vote strategically to the advantage of the candidates they prefer and the disadvantage of alternative...

Qaanol

Cueball knows what’s up, approval voting is *way* better than IRV, and Condorcet methods are generally better as well. There’s a new method being proposed in Oregon called “star voting” (aka. score-runoff) where you rate each candidate on a 0–5 scale (like website reviews) and the 2 highest-scoring ...

Qaanol

In either order there is a double plosive from the final consonant of the first word and the initial consonant of the second. This makes is a fairly awkward phrase to say out loud, especially when speaking quickly, so perhaps people avoid it for that reason. I’m not convinced this explains it. Afte...

Qaanol

I was reading about how adjectives in English have a certain order in which they appear (shown in this list ), and it occurred to me that “good big” is a pairing which obeys the ordering rule, yet nonetheless does not naturally appear in English (at least apart from compound-word situations like “bi...

Qaanol

Depending on exactly what you are doing, and how the data are organized, and how many data points there are, the following approaches may be beneficial: • Split the universe into spatial bins (small boxes, like a 3D checkerboard) by coordinates, and keep track of which atoms are in which bins. This ...

Qaanol

I’m a fan of Swift nowadays.

Qaanol

Are you also opposed to sort() returning a sorted array? Will you argue that arrays are an unsorted type, and it's valid for sort() to return an unsorted array, and it's the caller's job to handle that? Well if you’re working with an array of IEEE–754 floating-point values, some of which are NaN, a...

Qaanol

But how can it be that assuming the n = k case proves the n = (k + 1) case? I'm more confused now than before, I'm afraid. Okay, I think we are making progress now. Proof by induction is not magic. The n=k case doesn’t *automatically* prove the n=(k+1) case. There are plenty of statements for which...

Qaanol

I don't understand how we're not assuming both the k case and the (k + 1) case at the same time - isn't that what all of the algebraic manipulations are about? Can you explain what you're getting at using different words? I'm sorry; I'm just not understanding your answer or your question about (k +...

Qaanol

I don't understand why we want "(k + 1)(k + 2)/2" on the right side. What am I missing? What does the statement “(1+2+3+…+n) = n(n+1)/2” say when n=(k+1)? I'm not sure what you're asking, my apologies. In particular, I don't know how we're proving the (k + 1) case by assuming both the (k)...

Qaanol

That's another thing that I don't get - how is it that what I "know about k" is that (1 + 2 + 3 + ... + k) = k(k+1)/2? Am I not just assuming that, as opposed to knowing it? You know that about k because you assume it about k. You are proving something about *every* number k for which (1+...

Qaanol

That's fair. What I'm having trouble making sense of is how the three layers interact, and why three layers are necessary. I only see 2 layers. We have a program “willHalt” which somebody claims can analyze programs to determine whether they halt with given input data. And we concoct a program to t...

Qaanol

But how does "assume A, therefore B" prove anything? It proves that *if* you are on some rung of the ladder, *then* you can step up to the next rung. You are right that it doesn’t say anything about whether you can reach the rung you are assuming to start on, it just says that *if* you st...

Qaanol

I will admit my ignorance. There's something about induction that feels like I'm improperly assuming the truth of what I hope to prove. Great! That is a common feeling for people just learning about induction. One analogy that sometimes helps is to think about climbing a ladder. 1. The base case is...

Qaanol

I think you mean E² = p²c² + m²c⁴.

Qaanol

Please reveal the secret. It should be clear to everyone that I'm struggling, and I see no point in dwelling on my ignorance other than for posters to prove some rhetorical point. I have a vague sense that the combination of a base case (n) and countability (i.e., that integers can be put into orde...

Qaanol

This is my hangup. I can't keep straight how willHalt can be called by the very thing it's supposed to evaluate, and how all of that affects the ultimate result of willHalt (i.e., the second premise that willHalt always gives a correct answer as to whether a particular program and the input to that...

Qaanol

You keep repeating premises (integers are countable) and conclusions (induction works) without providing any line of reasoning to connect the two. You are completely skipping over the “why”, which is what I asked you to explain. Is there a reason you are so reluctant to acknowledge that you do not u...

Qaanol

I am working through your example with pen and paper, and I'm comfortable with treating the willHalt program as a black box that does only the two things you've described (i.e., willHalt always halts and willHalt always correctly tell us whether a given program, with a particular set of input data,...

Qaanol

Why don't you tell me what you're after? As a beginner, I'm not going to be able to create novel examples of things that are provable via mathematical induction. We are not asking for examples. We are asking you to explain, as best you understand it, why mathematical induction works. (Hint: the cor...

Qaanol

MathDoofus wrote:As far as I can tell, mathematical induction is a valid method of proof for those things that depend on countability.

*Why* is it valid?

Qaanol

I'm not exactly certain why the proof works (it does feel like I'm assuming the conclusion, at least in part, which is question-begging) It sounds like you are having trouble with the concept of mathematical induction. The concept, in general terms, I think that I've got down. All that we need to b...

Qaanol

But how does a program containing self-contradictory (or paradoxical) instructions prove that the attachment won't work? In other words, does it matter whether the attachment itself halts or whether it gets the answer right as to whether whatever it's fed will halt? No instructions are paradoxical ...

Qaanol

Are you having a conceptual problem with the idea of induction, or a mechanical problem with applying induction to this particular problem?

Qaanol

All right, how about this: For some reason, your boss sends you a whole bunch of programs and a whole bunch of data files, and wants you to determine which programs will run forever when given which data files as input. At first you just start dragging files onto programs and waiting to see how long...

Qaanol

Shenguin wrote:
Really, the only honest 24-hour stores are the ones in places like Arizona and Hawaii (sic), and many of them are still wrong in certain years

Why Arizona and Hawaii? I am missing something about the alt text.

DST.

Why did OP add “(sic)” though? The spelling is correct.

Qaanol

What happens to all the gas that gets blasted out of Uranus? Assuming there is solid land underneath, to make it habitable will we have to irrigate Uranus? And at that distance from the sun there is hardly any light, so why would anyone want to live on the cold, dark surface of Uranus? Even if it be...

Qaanol

One degree is approximately 1.75 percent

Qaanol

Derek wrote:
Xenomortis wrote:And don't forget about the Fourier Transform.

Now I'm wondering if there is an algorithm to find the fouriest base for a given number that is better than a linear search.

How about base (1 - 4/n)?

Qaanol

Thanks, I ended up using L’Hôpital’s rule with respect to t, and the fact that the limit of a product is the product of the limits.

I’m not quite sure your approach works, since t′(1) = ∞.

Qaanol

The link is http://localpr.ca/details/. I haven’t read it yet though.

Qaanol

Pretty sure it’s one-dimensional, though depending on your universe that 1D path may be embedded in some other topology.

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