In his latest Fermilab video, Dr. Don Lincoln :     (...) even though we shrunk the visible universe down to tiny size, the number line is still infinite. That means that, even when the universe began, it might have already started out to be infinite in size. So that's kind of a mind-blower.   Consider my mind blown.  I always thought that even if beyond the observable[a] is at least 500x bigger (according to the same video), shrinking the universe as a whole would equally shrink the farthest regions to the same point[b] (the farthest out, the bigger the shrink for a given duration).  I presume it's because there's no supporting data (is that correct?), even if it is a logical deduction. But suppose the universe indeed was already infinite before/at/after the Big Bang, then what is our current understanding of what the observable universe had expanded into – space expanding into space?[c]    [a] Is there a better name for it? I couldn't find one. [b] I understand it's not a center, but anywhere can be that point. [c] If the beyond the observable didn't share that point, and it isn't known for sure, then equally it isn't known for sure there was nothing, what implications does that have or what is known about that?
TV documentaries invariably show the Big Bang as an exploding ball of fire expanding outwards. Did the Big Bang really explode outwards from a point like this? If not, what did happen?
Since there is no word "shallowen", is there a good antonym of "deepen"? The meaning of "deepen" that I am referring to here is "to cause to become deeper." It doesn't necessarily refer to digging a hole. For example, a temporary deformation in a soft surface:     Putting the anvil on the mattress deepens the depression in it, but removing the anvil ______ it.   I would also be happy with an antonym of the intransitive version "to become deeper." "Contact us"... and then what? How do I install and manage RPMs? I have a burning desire to install RPMs onto my Ubuntu installation - is this possible? Can I use Yum - or another RPM Package Management tool? What's the main difference between int.Parse() and Convert.ToInt32 What is the main difference between int.Parse() and Convert.ToInt32()? Which one is to be preferred Should the weight of question upvotes be reduced? After thinking about    which I declined for the reasons , and    I have a proposal.  How about if question upvotes were only worth +5 rep instead of +10? And this was applied retroactively? (answer upvotes would be unchanged from the current behavior, so this would be question specific.)  This seems to be a better solution to the particular  problem  without all the rather serious negative repercussions of increasing the punitive value and/or cost of downvotes across the board. How to select multiple files with keyboard only in windows explorer Moderncv package - cventry date width I am writing my CV using moderncv package, everythig is nice but I have a problem with \cventry command. I have something like this:   (it means 2010 - now)  I would want to have this in one line, rather than in two lines. I tried looking into the moderncv style files but with no success. What can I do to achieve the effect I want? I have an android phone to which i have plugged an earphones. So at the top of the phone, I get the headphone symbol which indicates that the earphone is connected (In other words, the circuit at the 3.5 mm jack is closed).   Then I cut the two earphones (transducers) from it, and still the headphone symbol shows. When I later cut this cable, below where it branches out, even then it shows circuit completion.   So my question is this:   How does the phone detect circuit completion at the 3.5 mm jack and thus trigger all sound and music to be directed through the 3.5mm jack? Here I offer a "proof" of why the power set of the natural numbers is countable by creating a supposed bijection. I know that my proof is wrong, but where? If anyone could point it out, that'd be awesome.  Consider the power set of the natural numbers. We can form a bijection $f:\mathbb{N}\to\mathcal{P}(\mathbb{N})$ as follows.  For any $f(x)$ convert $x$ to its binary representation, which is a string of $0$s and $1$s. If the $i$-th digit is $1$, then include $i$ in the output set $S=f(x)$. Otherwise do not include $i$. Note that $i$ is $0$-indexed and starts from the right-most digit.  So in this case $f(5)=\{1,3\}$. Supposedly we can construct any set in $\mathcal{P}(\mathbb{N})$ with an appropriate choice of $x$.  Where does this proof blow up? I just installed a new version of Ubuntu and I want to roll it back to the previous version.  How can I do that? Is that even possible? Continuously invertible operators Are there integer solutions to $9^x - 8^y = 1$? Is there some sort of classification of all minimal non-cyclic groups? Does there exist some sort of classification of all minimal non-cyclic groups (non-cyclic groups, such that all their proper subgroups are cyclic)  I know the following classes of such groups:  1) $C_p × C_p$, where $p$ is a prime  2) $Q_8$  3) $\langle a,b | a^p = b^{q^m} = 1, b^{−1}ab = a^{r}\rangle$, where $p$ and $q$ are distinct primes and $r ≡ 1 \pmod q$, $r^q ≡1 \pmod p$.  (These three classes completely cover the case, when our group is finite: )  4)$C_{p^{\infty}}$, where $p$ is a prime  5)$(\{ \frac{n}{p^m}| m, n \in \mathbb{Z} \}, +)$, where $p$ is a prime  (These two classes completely cover the case, when our group is infinite abelian: )  6)Infinite non-abelian groups, such that all their nontrivial proper subgroups are isomorphic to $C_{p}$ for a fixed prime $p$ (Tarski monster groups)  7)Infinite non-abelian groups, such that all their nontrivial proper subgroups are isomorphic to $C_{\infty}$ ().  However, I do not know, whether there exists anything, that does not fall into these classes. I only know, that if such groups exist, they have to be infinite non-abelian. Blender is rendering an older version my project How do you make a test class for custom controller? My search results involves this but trying to apply it in my test class only create too many error that I don't understand.  public static testMethod void testMyController() {     PageReference pageRef = Page.success;//Observe how we set the Page here     Test.setCurrentPage(pageRef);   . Does my test class need those line of codes when my controller class is only very simple.  public class ClientInfo_VFcontroller{     public Org_Info__c orgInfo {get; set;}     public ClientInfo_VFcontroller(){         orgInfo = new Org_Info__c();     }     public PageReference save(){         insert orgInfo;         orgInfo = null;         ScheduleRetrieve.ScheduleRetrieve();         return null;     } } PCA on correlation or covariance? What are the main differences between performing principal component analysis (PCA) on the correlation matrix and on the covariance matrix? Do they give the same results? Deriving the speed of the propagation of a change in the Electromagnetic Field from Maxwell's Equations I've been told that, from Maxwell's equations, one can find that the propagation of change in the Electromagnetic Field travels at a speed $\frac{1}{\sqrt{\mu_0 \epsilon_0}}$ (the values of which can be empirically found, and, when plugged into the expression, yield the empirically found speed of light)  I'm really not sure how I would go about finding $v = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$ simply from Maxwell's equations in the following form, in SI units --  $$\nabla \cdot \mathbf{E} = \frac {\rho} {\epsilon_0}$$  $$\nabla \cdot \mathbf{B} = 0$$  $$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t}$$  $$\nabla \times \mathbf{B} = \mu_0 \left( \mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}} {\partial t} \right)$$  Is what I believe true? (that the speed of propagation is derivable from Maxwell's Equations)  If not, what else is needed?  If so, can you provide a clear and cogent derivation? I want to write a function that returns the nearest next power of 2 number. For example if my input is 789, the output should be 1024. Is there any way of achieving this without using any loops but just using some bitwise operators? I know that an easy to handle formula for the CDF of a normal distribution is somewhat missing, due to the complicated error function in it.  However, I wonder if there is a a nice formula for $N(c_{-} \leq x &lt; c_{+}| \mu, \sigma^2)$. Or what the "state of the art" approximation for this problem might be. Creating volumetric lighting (crepuscular rays) in Cycles (a.k.a. "god rays" and many other names) can be created in Blender Internal by checking the Halo checkbox in the lamp properties box.  How can I create a similar effect using Cycles?