Some theories propose that there are .   In one of them it is said that there are parallel universes, due to inflations after the big bang that created them.  But in the two-slit experiment is also known the multiverses theorie. The probability wave is not collapsing but each possibility is creating a universe on his own.  So they both speak about other universes. But is there a link between them? Or are that just completely different things/theories?
Are  and the  really the same thing?  Not too long ago, Susskind and Bousso uploaded the article "" with the thesis that the many-worlds interpretation and the multiverse of eternal inflation are one and the same thing. The parallel worlds of one are exactly the same thing as the parallel worlds of the other.   First, they claim decoherence can't happen over a complete description of the future light-cone of the measurement. Then, they apply that principle to eternal inflation. Without decoherence, superpositions of nucleating bubbles and metastable vacua can't decohere. According to the anthropic principle, most bubbles have no conscious observers, but an exponentially small minority do. Apply black hole complementarity to causal horizons.  Then, somehow, in a way I can't follow, they combine causal diamond worlds into a global multiverse.  Then they claim decoherence is reversible.  My head is spinning. What are your opinions on this paper?
Show that, if $a$ and $h$ are positive numbers, $h &lt; a^2$, then $$\sqrt{a^2 + h}-a &lt; \frac{h}{2a} &lt; a - \sqrt{a^2 - h}$$  I've been working on this problem for about 2 hours now, but I've made no progress. I'm not looking for an answer, but I just need some help to get me started since we didn't practice inequalities this complex in highschool. Thanks.   All I can tell is that we're supposed to take the square root of an expression at some point since one inequality ( h &lt; a^2 ) becomes two.   Edit : Thank you guys for the replies, but I'd appreciate only hints in the future (like Robert Israel) so that I can learn. Regardless, I found a different way to do it, so it's cool :) On the bash command-line, ↑ gives me the previous command. On the command-lines in ipython or matlab, when I type a few characters, ↑ gives me the previously entered command starting with those characters. How can I enable exactly this behaviour in bash? I am aware of more advanced ways of searching through the command-line history, but sometimes a simple way is more convenient. Prove that $\frac{1}{f'(a)} = \frac{1}{2\pi i} \int_C \frac{1}{f(z)-f(a)} dz$ Let $f$ be analytic on an open set $U$, let $a \in U$, and $f'(a)\neq 0$.  Show that  \begin{align*} \frac{1}{f'(a)} = \frac{1}{2\pi i} \int_C \frac{1}{f(z)-f(a)} dz \end{align*} where $C$ is a small circle centered at a.  I thought that this is very similar with Cauchy's integral formula. But, I can't apply the Cauchy's integral formula. How to apply that?   Any help is appreciated..   Thank you! How to uninstall Windows from a Dual Boot system? Finder search doesn't work properly after Yosemite update Ever since I upgraded to Yosemite, search no longer works properly in Finder. Spotlight works fine but Finder search just gives me a blank window with a spinning ball.  I've tried reindexing and I've also tried deleting Spotlight's .plist file. I restart my MacBook Pro after doing either. Finder search will work for one or two queries and stop again. I don't know what else I can do. How is canon determined for the works set in the world of ASOIAF? Integrating the inverse of a function. $f(x)$ is a strictly increasing, and continuous, function on $[0,+\infty)$. Consider the integral,  $$\int_0^a f^{-1}(x) dx.$$  Reasoning  The interval $[0,a]$ is "reflected" across the line $y=x$ onto the interval $0 \leq y \leq a.$  $f(x)$ and $f^{-1}(x)$ are symmetric across the line $y=x$. So, the integral is equivalent to the area bounded by $y = 0$, $y=a$, and $f(x)$.  So, "integrating $f$ along an interval on the $y$-axis" is the same as integrating $f^{-1}$ along the same interval on the $x$-axis?  Question  Is my reasoning correct? Initial connection to SQL Server Connection Is Slow. Why? How to analyze lightly varying senses of adjective *very* Use of very as an adjective is (in my experience) most frequently attested in phrases like     ...the very person I was looking for.   To use adjective very with the indefinite article sounds quite bizarre in this case:     ?...a very person I was looking for.   But consider this sentence, where indefinite a is used:     Visualizing a very transformation of the master-slave relation, Thomas presses further: the slave is brother to the master, even doubly a brother.   OED treats the two uses as separate senses of the word, with the following definitions:           (first use):&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;With limitation (usually expressed by the or a possessive) to particular instances      (second use): Really or truly entitled to the name or designation   Here are two respective examples quoted in OED:     What would you say to me now, and I were your verie, verie Rosalind? (1616)   Thence we went into Queen Mary's room, and saw that beautiful portrait—that very queen and very woman. (1857)   Clearly, the difference in meaning between the two senses is quite light, and it seems to me like a kind of difference which is recurrent enough to have its own term. What is the proper term? Are there other English words having similarly related pairs of senses? And lastly, is OED jumping the gun in treating these as two senses? Could the difference in meaning instead be due to the choice of determiner? I have secured a visa for the US, be it an ESTA or another visa requiring me to go for an interview. My understanding is that obtaining a visa for the US does not guarantee me entry into the country. Rather, :  Entering the United States A visa allows a foreign citizen to travel to a U.S. port-of-entry (generally an airport) and request permission to enter the United States. A visa does not guarantee entry into the United States. The Department of Homeland Security (DHS), U.S. Customs and Border Protection (CBP) officials at the port-of-entry have authority to permit or deny admission to the United States. If you are allowed to enter the United States, the CBP official will provide an admission stamp or a paper Form I-94, Arrival/Departure Record.  What happens once I arrive in one such port-of-entry? Will I have to go through customs checks? Will I have to talk to an immigration officer explaining my reasons for visiting the US? What documentation, if any, should I bring? Is the documentation I brought for the interview enough? What if I did not attend an interview since it was not required (for example if I obtained an ESTA online)? Failed a Reopen Question audit — sure looks like "Not a real question" to me I just failed , which was shown as being closed as "Not a real question".  Seeing as the vote count was positive, I figured it was an audit, but I selected "Leave Closed" anyways because to me     It's difficult to tell what is being asked here.  This question is ambiguous, vague...   There's no code examples, and the phrasing is clunky at best.  This is my second failed audit in two days for difficult questions (first failed audit is , also now closed), so if I get temporarily suspended, it won't be the end of the world (I'll think of it as a forced vacation).    That said, is there a way to dispute these audits?  Or is posting the audit here sufficient? How did this character come to be in the Nethersphere? How is it that       The Master   Came to be in the Nethersphere?  The last time we saw him      He died and refused to regenerate.  The Doctor even cremated his body.   So, given what previously happened to him, how was he now able to      Regenerate as Missy and take over the Nethersphere? General relativity is expressed in terms of differential geometry, which allows you to do interesting things with the coordinates: multiple coordinates may refer to a single point, eg. the  has whole lines at the top and the bottom that correspond to the North and South poles, respectively; or a single coordinate may refer to multiple points, for example by using inverse geometry the origin refers to all the points infinitely far away.  So, is the singularity just a single point in the curved spacetime, or can it be a more extended object, described by a single coordinate? Show that$\displaystyle\sum_{n=1}^\infty\frac{\sin( nz)}{n}$ diverges if $\mathfrak{Im} \,(z)\neq0$ We have to show that$\displaystyle\sum_{n=1}^\infty\frac{sin( nz)}{n}$ diverges if $Im\,(z)\neq0$  My try:$$\sin (nz) = \mathfrak{Im}(e^{nzi})$$  $$\sum_{n=1}^{\infty} \frac{\sin nz}{n} = \mathfrak{Im} \sum_{n=1}^{\infty} \frac{(e^{zi})^n}{n} = - \mathfrak{Im} \ln\left(1-e^{zi}\right). $$ Then how to proceed? Consolidate tag wiki excerpt and body contents with regards to suggested edits At the moment, in major part because they are two separate post objects in the system, the excerpt and the body of a tag wiki count as two separate posts with regards to suggested edits in the queue. Mechanically, this is sane, but when it comes to handling the actual queue, it can be confusing. A body edit might consist of little more than a bed of links, which looks bad. But then an excerpt is shown that includes the rest of the data, and since excerpts can be included on the actual wiki page, it makes a lot more sense when they're taken in the same space.  And this is how they are composed, too. The actual edit interface for working on tag wikis has both the excerpt and the body on the same page. In a sense, the excerpt behaves a lot like the "title" of the wiki, if we make a parallel to normal post edits.  Thus, my suggestion (which is to say a suggestion that I repossessed from Robert Cartaino) is that when suggested edits are reviewed for tag wikis, that they be presented in a single unit, treating the excerpt the same as how a title is treated in a question edit. This way, relevant information that is crossed between the two isn't lost because they are reviewed separately. Quotient ring of a localization of a ring Let $A$ be a commutative ring. Let $P$ be a prime ideal of $A$. Let $I$ be an ideal of $A$ such that $I \subset P$. Let $\bar A = A/I$. Let $\bar P = P/I$. Is $\bar A_{\bar P}$ isomorphic to $A_P/IA_P$? Override parent theme translation on child theme I have a parent theme that uses correctly load_theme_textdomain() to load all the translated strings in many languages.  Then I created a child theme that uses load_child_theme_textdomain() to achieve the same thing for its strings.  There are certain translated strings for a particular language on the parent theme that I'd like to replace/override in the child theme.  I know if they were on a template file I could replace the file and simply change the textdomain for those strings, but unfortunately the ones I'm talking about are used in many places and also in the dashboard (so inside some filter/action functions).  So my question is: is there a way to replace those translated strings inside the child theme without having to replace parent template files or functions?  I don't know, maybe adding a parent-theme.mo file inside the languages folder of the child theme with only those strings translated, or something like that. Create an instance of a class from a string Is there a way to create an instance of a class based on the fact I know the name of the class at runtime. Basically I would have the name of the class in a string. Number of subrings of a Field "The following packages have been kept back:" Why and how do I solve it? I just added a PPA repository for the development version of the GIMP, but I get this error:  $ apt-get update &amp;&amp; apt-get upgrade ... The following packages have been kept back:   gimp gimp-data libgegl-0.0-0 libgimp2.0   Why and how can I solve it so that I can use the latest version instead of the one I have now?