Information as a conserved quantity A physics friend of mine asserted today that within the field of information theory, information can be thought of as a conserved quantity. this put me in mind of Noether's theorem and motivated the following question; if it is ill-posed or meaningless, please let me know before you downvote and I will delete it so it doth not offend:  If information within a defined dynamical system is a conserved quantity, can Noether's theorem be used to tell us anything about the lagrangian of that system, and what the symmetry is which is responsible for that conserved quantity?
Is there a symmetry associated to the conservation of information? Conservation of information seems to be a deep physical principle. For instance, Unitarity is a key concept in Quantum Mechanics and Quantum Field Theory.  We may wonder if there is an underlying symmetry, in some space, which may explain this conservation of information.
How to make UV loft like 3ds Max in Blender using curves? I am try to make a car Body using the technique like UV loft in 3ds Max.  How to apply this technique in  Blender using curves or closer to this technique? I have seen this technique in a Blender tutorial, but I forgot about it. Please allow using nested expressions when filtering with tags Please support the use of nested expressions like  and (or ) when searching.  Looking here, on meta, at questions tagged   and at questions found with +search +tag +boolean I didn't see any information on this topic. Computers on board Starfleet vessels are quite primitive compared to on board computers such as . At their best, they can decipher requests such as "Computer, delete that last sentence" and utter things such as "That crewman is no longer on board this vessel". Even real life computers will be capable of this within a decade or so (by some estimates). Even computers such as HAL 9000 are likely to be available within a few decades.  So, in a genre where intelligent computers are abound, why this strange absence? Did the Federation run into some Battlestar-Galactica-like problem with AI in the past and decide to keep on board computers decentralized?  But if that is the case, how can one explain Data and highly intelligent holographic characters? The technology and programming constructs clearly exist, yet Starfleet vessels continue to be manned by hundreds of people standing in front of consoles. How to type \sim above another symbol x? I want to put a "~" above x, just like \hat x but replacing \hat with \sim.   How to do that? How to pass an argument to event handler in tkinter? Associativity of symmetric difference of sets By $A\oplus B$ we denote the symmectric difference of two sets. The definition is $A\oplus B =(A\setminus B) \cup (B\setminus A)$. Now I hope to show that $A\oplus (B\oplus C) = (A\oplus B)\oplus C$. I remember that there's an elegant proof, but I forget its detail. (The first step is to show $A\oplus (A\oplus B) = B$, and maybe applying this formula, we can obtain associativity.) C#: How to create an attribute on a method triggering an event when it is invoked? $ is not a function in drupal 7 theme What does "$$" mean in the shell? What does the output of the command below mean? (result is positive integer)  echo $$ How to make X.org listen to remote connections on port 6000? This is on Ubuntu 10.10 (Maverick Meerkat) 64-bit desktop.  I want to make my X server listen to remote connections from clients in other machines on the local network. I know about ssh -X and that is not what I want. I vaguely remember changing something like TCPListen from no to yes, but I don't remember where this change should be applied.  I'm interested in either a GUI method or a CLI one.  PS editing /etc/X11/xinit/xserverrc to remove the -nolisten tcp option and rebooting does not work. Why are values in Entites obtained directly and sometimes by using getters? For example  Drupal\Core\Entity\Entity::id() returns $this-&gt;id(or NULL) Drupal\Core\Entity\ContentEntityBase::id() returns $this-&gt;id-&gt;value Drupal\Core\Entity\ContentEntityBase::uuid() returns $this-&gt;get('uuid')-&gt;value Drupal\node\Entity\Node::id() returns $this-&gt;get('nid')-&gt;value  Also in some methods there are setValue() and getValue() utilised but sometimes there are just $this-&gt;field-&gt;value. So what is the reason for this inconsistent behavior? From my understanding all the &quot;fields&quot; are TypedData fields hence the setValue() and getValue() methods should be used instead of directly access $this-&gt;field-&gt;value. Besides it's strange because $value is private. Color the edges of $K_6$ red or blue. Prove that there is a cycle of length 4 with monochromatic edges. Color the edges of $K_6$ red or blue. Prove that there is a cycle of length 4 with monochromatic edges.  Attempt: I know that i have to...  prove that there must be TWO vertices with “red-degree” at least 3, or two with "blue-degree" at least 3. Call these U and V. (We'll assume we're in the red case; the blue case is similar.) Now, ask if they’re connected by a red edge, and how many red-adjacent neighbors they share. If you analyze this, there should be only a few cases to consider – and each should be relatively straightforward. For each case, you’ll show either that that case can’t actually happen in $K_6$, or that it gives rise to a monochromatic 4-cycle. What does {0} mean when found in a string in C#? In a dictionary like this:  Dictionary&lt;string, string&gt; openWith = new Dictionary&lt;string, string&gt;();  openWith.Add("txt", "notepad.exe"); openWith.Add("bmp", "paint.exe"); openWith.Add("dib", "paint.exe"); openWith.Add("rtf", "wordpad.exe");  Console.WriteLine("For key = \"rtf\", value = {0}.", openWith["rtf"]);   The output is:     For Key = "rtf" value = wordpad.exe   What does the {0} mean? How to install tzdata on a ubuntu docker image? I have the following line in the Dockerfile.  RUN apt-get install -y tzdata   When I run it, it asks for my input. After I provided my input, it hung there. Does anybody know how to solve this problem?  Step 25/25 : RUN apt-get install -y tzdata  ---&gt; Running in ee47a1beff84 Reading package lists... Building dependency tree... Reading state information... The following NEW packages will be installed:   tzdata 0 upgraded, 1 newly installed, 0 to remove and 0 not upgraded. Need to get 189 kB of archives. After this operation, 3104 kB of additional disk space will be used. Get:1 http://archive.ubuntu.com/ubuntu bionic-updates/main amd64 tzdata all 2018i-0ubuntu0.18.04 [189 kB] debconf: unable to initialize frontend: Dialog debconf: (TERM is not set, so the dialog frontend is not usable.) debconf: falling back to frontend: Readline debconf: unable to initialize frontend: Readline debconf: (This frontend requires a controlling tty.) debconf: falling back to frontend: Teletype dpkg-preconfigure: unable to re-open stdin:  Fetched 189 kB in 1s (219 kB/s) Selecting previously unselected package tzdata. (Reading database ... 25194 files and directories currently installed.) Preparing to unpack .../tzdata_2018i-0ubuntu0.18.04_all.deb ... Unpacking tzdata (2018i-0ubuntu0.18.04) ... Setting up tzdata (2018i-0ubuntu0.18.04) ... debconf: unable to initialize frontend: Dialog debconf: (TERM is not set, so the dialog frontend is not usable.) debconf: falling back to frontend: Readline Configuring tzdata ------------------  Please select the geographic area in which you live. Subsequent configuration questions will narrow this down by presenting a list of cities, representing the time zones in which they are located.    1. Africa      4. Australia  7. Atlantic  10. Pacific  13. Etc   2. America     5. Arctic     8. Europe    11. SystemV   3. Antarctica  6. Asia       9. Indian    12. US Geographic area: `` Manually change filetype icons in Windows 7 I'm trying to find the dialog tab in Windows 7 that allows a user to change the icon used for a particular file type.  In Windows XP it would be under the Folder Options properties dialog.    Where is it on Windows 7?  I only want to change the icon of a specific filetype, to anything I want but this tab is no longer present in Folder Options of Windows 7. Coauthoring with a reviewer possible? I recently submitted an article to a math journal and got a response from a reviewer, with an attachment. In it, I have found some good  advice that could improve my article tremendously.  I am a bit suspicious of its accuracy since it could resolve what I have been working with for some months in a few  sentences.   But anyway, it was enough for me to ask the reviewer for coauthoring with me.   My question would be, does it often happen that an author asks a referee for coauthoring during the review process? Or could it even be possible?  I was given a month to revise my article, but the chance that I could revise successfully by myself seems to be fat.  I would be looking forward to any advice.  Thanks in advance. Software was blocked from opening because it is not from an identified developer I went to run LibreOffice on my OS X 10.9 and it would not let me install it. It said it was from an unidentified developer. I'm aware of the security features of the Mac and went to System Preferences to allow the software to run.   When I opened this setting I saw a button that said, '"LibreOffice" was blocked from opening because it is not from an identified developer.' and there was a button next to it that said "Open Anyway". I clicked this button and nothing happened. I clicked it multiple times, like a hundred, out of frustration. Is there something else I need to do? Could someone verify this is not a bug?   UPDATE: I've included the photo below of what my System Preferences screen looked like and the button I pushed that didn't work.  UPDATE II: So I tried opening the application again and went into the system preferences and pressed the "Open Anyway" button again and nothing happened at first but a few minutes later while I was typing an email something flashed across my screen, possibly another dialog (or more likely a chewpacabra), but it quickly disappeared and the next thing I know LibreOffice launched! What does "off of" mean? I have read a sentence from “Diary of a Wimpy Kid 4”:     The teachers have really been cracking down on kids copying off of each other this year.   How to understand "off of"? Please parse it. Measure of Image of Linear Map I am trying to work my way through the proof of the change of variables theorem for Lebesgue integrals. A key lemma in this context is as follows:  If $T:\mathbb{R}^n \rightarrow \mathbb{R}^n$ is a linear map and $A \subset \mathbb{R}^n$ is Lebesgue measurable then $\lambda(T(A)) = |\det T \  | \cdot \lambda (A)$, where $\lambda(X)$ denotes the Lebesgue measure of $X$.  Can anyone provide a reference for a proof of this lemma that clearly references the facts from linear algebra that are necessary to effect the proof? The source I have for this lemma refers to German texts that I am incapable of reading and I have been unsuccessful at finding an alternate proof.  Added For the Benefit of Future Readers: In addition to the excellent references I received in response to this question, I have managed to find an additional reference that also provides a good proof of this fact: Aliprantis and Burkinshaw's Principles of Real Analysis, Third Edition, Lemma 40.4 pp 389-390. Do two beams of light attract each other in general theory of relativity? In general relativity, light is subject to gravitational pull.  Does light generate gravitational pull, and do two beams of light attract each other?