When LIGO said one merging black hole was thirty or so solar masses, the other twenty, and that they were one billion light years away;   how do they know that?
The  was observed, giving us the frequency and amplitude of the event. Because LIGO has two detectors a  could be derived.  But how do these three factors allow for the mass of the black holes and their distance to be calculcated? If the wave strengths are in a square relationship to distance, then couldn't there be an infinite number of other masses and distances which would give the same signals?
We have a few cases of chat accounts remaining without valid parent account:  and  for example. What should mods do when that happens:  delete the chat account notify the SE team so they can reattach or clean it up leave it as is: it's a normal situation $$\sqrt{x + \sqrt{x + \sqrt{x + \cdots}}}= 5$$ What sources of randomness can be made with commands in Minecraft? I want to make a mini game in Minecraft were I need a random command generator for 9 commands. I need a random command to give the player a random item. I can't do the command block in the dispenser any more because it will just drop out instead of being placed. What different ways are there for generating randomness in commands, and which one would be best for my use? This question is similar to the one about , but I am specifically attempting to get randomness when using commands - the redstone solutions do not apply here. If $m_1 , m_2, \cdots m_n$ are natural numbers where at least one of them is not a perfect square, then how do I prove that the sum $$\sqrt{m_1}+\sqrt{m_2}+ \cdots + \sqrt{m_n}$$ is irrational? I'm hoping to prove this using methods from pre-calculus level algebra. Dell R730xd - Best way to configure storage for simultaneous use with ZFS & Hardware RAID I recently purchased a Dell R730xd that came with an H730 RAID card. I would like to bring an existing 6 disk ZFS pool to this server as well as create an additional 6 disk hardware RAID.   Is it possible to configure an H730 RAID card to operate in both HBA and RAID mode simultaneously? And then only manage 6 of the disks in a hardware RAID and allow the OS to manage the remaining 6 disks in a software RAID?  If not, can a Dell R730xd use both an H730 RAID card and an LSI 9207-8i HBA card simultaneously? Would you simply plug one SAS cable from each card into each part of the Backplane? Will I need to purchase any new cables to connect the LSI 9207-8i to the backplane in my R730xd?  Is there a better card to use for ZFS in an R730xd using spinning disks than the LSI 9207-8i? Dismiss flags on the same posts with different validities Sometimes a post has both valid flags and invalid flags. As far as I can tell, all the flags on the same post have to be dismissed with the same validity.  The scenario I encountered (on ):   A low-quality question is closed. The asker improves the question and flags for reopening. A moderator reopens the question, but doesn't dismiss the flag yet. Someone else flags the question as “off topic”.   Since I agree with the reopening, and I don't consider the question off-topic, I would like to dismiss the first flag as valid and the second flag as invalid. But there's only one set of buttons for both flags.  And just now, two flags on a closed question: one that says “delete it”, the other one that says “reopen it”. The correct course of action is neither (the ideal outcome would be for the question to be edited then reopened). I should provide different feedback to the two flaggers, but I can't.  Unless I've missed something, please allow multiple flags on the same post to be dismissed separately. When lecturing about conservation of energy in the 1960s, Richard Feynman remarked:     It is important to realize that in physics today, we have no knowledge of what energy is. We do not have a picture that energy comes in little blobs of a definite amount. It is not that way. However, there are formulas for calculating some numerical quantity, and when we add it all together it gives “28” —always the same number. It is an abstract thing in that it does not tell us the mechanism or the reasons for the various formulas.    50 some years later, have we made any progress in terms of understanding the fundamental nature of what energy is? Subdivision Surface not making things smooth as they are in the tutorial I am following The game  has a very unique intro that I would like to show my friend again for the first time. I'm not sure how to reset all my progress on this game to achieve this though. Any thoughts? How do you handle "that that"? The double "that" problem I just received a PhD invitation letter from a German University which mentions that my remuneration will be 2/3 of full TV-L 13 position. I do not know what a TV-L 13 position is (Google is of no help here), and didn't want to be rude, so I am asking here first. Is this a common position or specific to Germany? If anyone knows, currently how much remuneration corresponds to a TV-L position? PHP considers null is equal to zero Intuitive Understanding of the constant "$e$" True or False: there is a space $X$ such that $S^1$ is homeomorphic to $X\times X$ I had an exam this morning, one of the questions asked about the truth of the statement      There is a space $X$ such that $S^1$ is homeomorphic to $X\times X$.   I said that this was false and this was my reasoning... was I correct? (Note, an earlier part of the question asked me to prove $\pi_1(Y\times Z)=\pi_1(Y)\times\pi_1(Z)$, I took this as a hint.)  Suppose for the sake of contradiction that such an $X$ exists. Then $\Bbb{Z}\cong G\times G$ where $G\cong\pi_1(X)$. Let $\Phi$ be the isomorphism.  Let $\Phi(1)=(g_1,g_2)\in G\times G$. Then at least one of $g_1,g_2$ is nonzero, since $\Phi(0)=(0,0)$ (the identity on $G\times G$, and $\Phi$ is injective). Without loss of generality $g_1\ne 0$. Then which element $n\in\Bbb{Z}$ has $\Phi(n)=(kg_1,0)$? Since $$kg_1=\underbrace{g_1+\dots +g_1}_k\in G,$$ and $\Phi$ is surjective, such an $n$ should exist. But this is not possible since $\Phi(n)=(kg_1,0)$ implies (since $\Phi$ is a homomorphism) that $kg_1=ng_1$ and $ng_2=0$, and since $k$ was arbitrary and this need not hold if $k\ne 0$. Why is James Bond less tech savvy in the Daniel Craig movies? Why use foreign keys if cascade action is not need? Much as I loathe Microsquish's Word, it does allow you to insert into a header or footer the automated text "Page X of Y."   When using InDesign, it's easy to set up the "Page X" part on a master page. But is there any placeholder character for the Y? That is, it will count the number of pages in the document, either in an absolute or a relative-to-the-section fashion? Every now and again I narrowly miss sending out something with a footer which reads "Page 4 of 3," and I would love to know if there's some way around that. Assign points within 150 meter buffer of each other the same unique identifier? I have a bunch of points on a QGIS map. Each point is a unique sampling event. However, some of these points have been sampled multiple times but there is no common identifier in the attribute data to determine this. The only way we can see this is by looking at the map and seeing points very close to each other.   I am wondering if anyone has a method to assign points within a 150 meters of each other a common identifier? I consider the co-finite topology on $\mathbb{R}$ that is $$\{G\subset \mathbb{R}, card(\mathbb{R}\setminus G)&lt;+\infty\}\cup \{\emptyset\}$$  What are the convergent sequences in this space .  thank you Add an image directly from the clipboard I've tried to find other questions covering this, but (surprisingly) I did not find any.  When I want to add a screenshot to a post, as far I know the only way to do it is to save it as a file and then upload the file, using Stack Overflow's image hosting. OK, much better than finding a hosting site yourself, but sometimes I wish I could just paste the image from the clipboard.  It's not as straightforward as it may seem, I know. , and it needs a Java applet to get it done.