Block universe and quantum mechanics
How can a particle's position be random and uncertain in quantum mechanics if it is already pre-determined in relativity?
If M is a non-orientable closed connected 3 manifold prove H1(M) is an infinite group. What is the command to run System Settings from a terminal? System Settings can be run from the launcher (pinned by default), the Dash, or the power cog. But what command would I enter in a terminal window if I want to run it from there? How to read contacts on Android 2.0 Definition of e I'm very eager to know and understand the definition of $e$. Textbooks define $e$ as follows $$ e = \lim_{p\to\infty} \left[1+\frac1{p}\right]^p \approx 2.71828 $$ Is there an &quot;easy to understand&quot; proof of this? I'm really looking for a derivation of this which is very intuitive and easy to comprehend. By the way I'm watching . How to keep leading zeros in PHP integer Free way to clone HDD to SSD? Is there a free way to clone a full Windows 7 installation from HDD to SSD? (The free part is important, I know I can pay for Acronis True Image.)      SSDs are usually much smaller than HDDs which complicates matters. For instance, I have about 50GB data, my new SSD is 80GB but I still can't use Windows clone/restore system if my HDD is something like 300GB.  Therefore, I'm looking for a third party tool that will be able to:   Create a clone of my C: partition Store it onto an external USB drive Boot from some rescue / restore CD Load the image onto the new SSD   Acronis True Image seems like a tool that should support this but it's a paid-for software and the trial version cannot create clones. Acronis Migrate Easy is a fully functional tria for 15 days but need both the HDD and SSD connected at the same time which is a bit of a problem for me as a laptop user.  P.S. I almost got there combining Windows image backup combined with Acronis True Image restore CD (which can load .vhd's) but was not able to boot as some boot information were probably lost and could not be repaired using the Win7 installation DVD. Where does the extra kinetic energy of the rocket come from? How to Improve Mathematical Thinking and General Problem Solving Skills? I'm a sophomore in university and seriously feel that I'm bad at solving mathematical and algorithmic problems (be it discrete math, calculus or just puzzles). I noticed that I'm only good at solving questions that are similar to the ones that have been taught to us.  Here's how I generally approach it:   What is the problem? What do I need to do here? Does it look like I've encountered this before?  Can I think of a smaller problem to solve instead?   If the answer is no to all the above then I sort of blank out. I stare at it and force my brain to run through a wide variety of stuff, almost like a brute force attempt of solving it. Obviously that leads me to nowhere everytime. I simply can't think "outside the box."   What can I do to improve my situation? How to change camera movement speed on Path during animation Im making a animation in blender that requires the camera to change speeds while moving along a path. I'm using the Curve/Path for the path. I need the camera to move at a certain speed going between 2 places, and then slow down while moving around something its focusing on. Is there an ideal PWM frequency for DC brush motors? Learning Regular Expressions I don't really understand regular expressions.  Can you explain them to me in an easy-to-follow manner?  If there are any online tools or books, could you also link to them? I am in 1.13 Pre-Release 7 trying to make a one command creation and I need an item with a specific name. The command I use is /give @p diamond_sword{display:{Name:"Sword of Power"}} and it gives my a diamond sword, but it doesn't have the name.   This is me running the command.   This is the command not working. Restricting T to string and int? What are "electron holes" in semiconductors? I'm tutoring senior high school students. So far I've explained them the concepts of atomic structure (Bohr's model &amp; Quantum mechanical model) very clearly. Now the next topic to be taught is semiconductors.  I myself am not conviced with the concept of electron holes. If there is no electron then there is no electron. How can it be a hole. We define a hole when there is some thing every where except at a place. But inside an atom how can we define a HOLE.  Kindly explain it with the help of Bohr's model. What was the need of introducing such abstract concept in semi conductors? I have installed Linux Bash on Windows 10 (available from Microsoft), but I've forgotten my password.  I've searched for a solution but I only find suggestions that involve doing something before the system boots, like accessing recovery mode, but that will not work in this case as this Ubuntu is just an application within a Windows system and doesn't have its own boot process.  How can I reset my password? How to avoid perceived circularity when defining a formal language? Suppose we want to define a first-order language to do set theory (so we can formalize mathematics). One such construction can be found . What makes me uneasy about this definition is that words such as "set", "countable", "function", and "number" are used in somewhat non-trivial manners. For instance, behind the word "countable" rests an immense amount of mathematical knowledge: one needs the notion of a bijection, which requires functions and sets. One also needs the set of natural numbers (or something with equal cardinality), in order to say that countable sets have a bijection with the set of natural numbers.  Also, in set theory one uses the relation of belonging "$\in$". But relation seems to require the notion an ordered pair, which requires sets, whose properties are described using belonging...  I found the following in Kevin Klement's,  (pages 2-3).  "You have to use logic to study logic. There’s no getting away from it. However, I’m not going to bother stating all the logical rules that are valid in the metalanguage, since I’d need to do that in the metametalanguage, and that would just get me started on an infinite regress. The rule of thumb is: if it’s OK in the object language, it’s OK in the metalanguage too."  So it seems that, if one proves a fact about the object language, then one can also use it in the metalanguage. In the case of set theory, one may not start out knowing what sets really are, but after one proves some fact about them (e.g., that there are uncountable sets) then one implicitly "adds" this fact also to the metalanguage.  This seems like cheating: one is using the object language to conduct proofs regarding the metalanguage, when it should strictly be the other way round.  To give an example of avoiding circularity, consider the definition of the integers. We can define a binary relation $R\subseteq(\mathbf{N}\times\mathbf{N})\times(\mathbf{N}\times\mathbf{N})$, where for any $a,b,c,d\in\mathbf{N}$, $((a,b),(c,d))\in R$ iff $a+d=b+c$, and then defining $\mathbf{Z}:= \{[(a,b)]:a,b\in\mathbf{N}\}$, where $[a,b]=\{x\in \mathbf{N}\times\mathbf{N}: xR(a,b)\}$, as in  question or  on Wikipedia. In this definition if set theory and natural numbers are assumed, then there is no circularity because one did not depend on the notion of "subtraction" in defining the integers.  So my question is:     Question Is the definition of first-order logic circular?   If not, please explain why.   If the definitions are circular, is there an alternative definition which avoids the circularity?   Some thoughts:   Perhaps there is the distinction between what sets are (anything that obeys the axioms) and how sets are expressed (using a formal language). In other words, the notion of a set may not be circular, but to talk of sets using a formal language requires the notion of a set in a metalanguage. In foundational mathematics there also seems to be the idea of first defining something, and then coming back with better machinery to analyse that thing. For instance, one can define the natural numbers using the Peano axioms, then later come back to say that all structures satisfying the axioms are isomorphic. (I don't know any algebra, but that seems right.) Maybe sets, functions, etc., are too basic? Is it possible to avoid these terms when defining a formal language? Why wouldn't the `which` command work for `cd`? I can't find the executable for `cd` either! I tried which cd and it didn't give a path but instead returned the exit code 1 (checked with echo $?). The coreutil cd itself is working, so the executable should be there, right? I also ran a find for cd, but there was no executable file shown. How is it implemented then?  Update:  I don't know if I should ask this in another post but since I think it is good here, I'm expanding (?) the post... So the answer was actually quite simple, there's no executable for that — because it's a builtin — But I've found some builtins (bash shell in Fedora) have the executable files! So builtin -> no executable isn't right I suppose? Maybe an answer explaining what builtins actually are (builtin commands?), which actually is the matter here, rather than focusing more on cd... Some good links posted previously indicate that builtins are not programs... so what are they? How do they work? Are they just functions or threads of the shell? Trying to find a story about an unborn telepathic baby who can save a spaceship from doom There's a spaceship, nearing the end of its journey. Everybody on board is in cryosleep. For some reason the wake-up system malfunctions, and the ship will fly on indefinitely. The people at the space port realise this, and try to wake someone up. Their last resort is finding someone on board who is telepathic, and wake this person up. They find one, but it turns out to be an unborn baby. Is there a way to change the environment variables of another process in Unix? Is linear algebra more “fully understood” than other maths disciplines? In , it was discussed how LA is a foundation to other branches of mathematics, be they pure or applied. One answer argued that linear problems are fully understood, and hence a natural target to reduce pretty much anything to.   Now, it's evident enough that such a linearisation, if possible, tends to make hard things easier. Find a Hilbert space hidden in your domain, obtain an orthonormal basis, and bam, any point/state can be described as a mere sequence of numbers, any mapping boils down to a matrix; we have some good theorems for existence of inverses / eigenvectors/exponential objects / etc..  So, LA sure is convenient.  OTOH, it seems unlikely that any nontrivial mathematical system could ever be said to be thoroughly understood. Can't we always find new questions within any such framework that haven't been answered yet? I'm not firm enough with G&ouml;del's incompleteness theorems to judge whether they are relevant here. The first incompleteness theorem says that discrete disciplines like number theory can't be both complete and consistent. Surely this is all the more true for e.g. topology.  Is LA for some reason exempt from such arguments, or does it for some other reason deserve to be called the best understood branch of mathematics?