Premise 1: Physics don't believe in sense "organs" of the human "robot" (more commonly said "common sense deceives us").      Premise 2: Physics believes in logic or mathematics. Background thrust: Quantum mechanics.     Premise 3: Everything which "revolves" around the nucleus might not have identical properties. There might be some property of particles (revolving around the nucleus) which are not the same, because of our sense not detecting it. Then, we might say the particles to be identical only w.r.t our senses, but that is not the spirit of our physics, it must be proved logically. Or else we might define particles of such and such properties to be such and such, but that doesn't define them to be entirely identical.     So, are particles revolving around the nucleus identical in all properties in reality? Or is there any logical or mathematical proof to show that the particles are all identical?    The same argument can be applied to all the particles which we call identical.
Why should two sub-atomic (or elementary particle) - say electrons need to have identical static properties - identical mass, identical charge? Why can't they differ between each other by a very slight degree? Is there a theory which proves that?  Imagine an alien of size of order of Milky-way galaxy examining our solar system with a probe of size of 10's of solar system dimension and concludes that all planets are identical.
How does LIGO remove the effects of environmental noise? Since LIGO is dealing with readings at nanometers, events such as vehicles driving nearby, and constant (but extremely minor) tremors of the earth can cause movement with the mirrors at nanometers.  Such tiny movements are extremely difficult to measure, but can easily cause errors when using such a small scale.  How does LIGO remove these factors, and take precautions to prevent false readings due to noise? How did they dispose old Joe's wife's body in the movie Looper (2012)? The reason given in the movie Looper for sending targets to the past is that it is difficult to dispose bodies.  From ,     Thirty years into the future in 2074, time travel is invented, but is   immediately outlawed. However, because by that point tracking   technology has rendered it nearly impossible to dispose of bodies   secretly, crime bosses turn to time travel to send their targets to   the past to be killed using "loopers": hired guns paid in silver to   kill whoever is sent to them.   When trying to capture old Joe, they kill his wife. So how did they dispose the body of his wife? Or is it difficult to dispose bodies only in US and not in China? And they came for old Joe only because the Rainmaker wanted to close the loops?  Could someone explain? What am I missing? In Chiswell's Mathematical Logic, there is the following problem is posed using the language of propositions (LP):     In some systems of logic (mostly constructive systems where 'true' is taken to mean 'provable') there is a rule      if $(\Gamma\vdash(\phi\,\lor\psi))$ is a correct sequent then at least   one of $(\Gamma\vdash\phi)$ and $(\Gamma\vdash\psi)$ is also correct.      By giving a counterexample to a particular instance, show that this is   unacceptable as a rule for LP. [Start by giving counterexamples for   both the sequents $(\vdash p_0)$ and $(\vdash(\neg p_0))$.]   In my , it was answered that one can let $\Gamma = \{p_0\,\lor\,(\neg p_0)\}$.  From there, one can deduce neither $(\Gamma\vdash p_0)$ nor $(\Gamma\vdash (\neg p_0))$.  But this does not proceed by the counterexample route that the author suggests.  Namely, he seems to imply that we should (1) take an interpretation of propositional variables $p_0,\,p_1,\,\ldots$ (setting each one equal to T or F), and (2) write $\phi$ and $\psi$ as functions of these propositional variables, and (3) pick sentences for $\Gamma$ which are all T, all with the conditions that (A) $(\phi\,\lor\psi)$ is evaluated as T, yet (B) both $\phi$ and $\psi$ are evaluated as F.  This, of course, seems impossible.  What, then, am I missing?  It seems that taking a concrete interpretation of the propositional symbols makes the constructivist's rule irrefutable.  (Note: this is supposed to be a very simple problem set, and I am an elementary logician). Uninstall, Activate, Deactivate a plugin: typical features & how-to I'm making a WordPress plugin. What are typical things I should include in the uninstall feature?  For example, should I delete any tables I created in the install function?  Do I clean up my option entries?  Anything else? arithmetic progression of primes Prove that there is no arithmetic progression that consists only of primes.  A question that I've been set; I'm guessing it makes use of primes being written in the form 4k+1 and 4k+3? Not sure where to start.  Thanks. How do I remove an element from a list by index in Python?  I found the list.remove method, but say I want to remove the last element, how do I do this? It seems like the default remove searches the list, but I don't want any search to be performed. Trim string in JavaScript? Miraak is stealing all my dragon souls Converting from DMS to DD using Python in Field Calculator? I need to convert lat/long that is expressed as degrees, minutes, and seconds in the data into decimal degrees. For example, in the data, they are listed as N335042.06 in the Latitude column, and W86031.04 in the Longitude column. I have done this problem before where I created a script which converted DMS to DD, and vice-versa, so I guess I could use bits from that. But the problem I'm having is how to ignore (for lack of a better word) the 'N' and 'W' in the data? Can I skip them? And DMS are listed all together without any symbols or spaces.  Can I use len(), range(), split() to specify what part to read from the value? For example, can do the following?  N335042.06 where, 33 = degrees 50 = minutes 42.06 = seconds ...?  I came across  ESRI article, but it's in VB. Will probably use it as a reference but some of the terminology/syntax is different from Python.  Final code that works!   # Pre-logic def latDD(x):   D = int(x[1:3])   M = int(x[3:5])   S = float(x[5:])   DD = D + float(M)/60 + float(S)/3600   return DD  # Expression latDD(!Latitude!) How do I load an mp4 video with multiple audio tracks into blender? Make Blender usable on high resolution screen The Blender UI elements are incredibly small by default on high resolution screens on Windows (15" UHD screen).  I found the Preferences -> System -> DPI setting which can be set up to 144.  This makes Blender usable, but still uncomfortable and difficult on the eyes.  Is there a way to make the UI elements even larger? natbib and hyperref create by default two links to the bibentry in the reference section|chapter of the document:   \begin{filecontents}{\jobname.bib} @book{author08, title = {{A Title}}, publisher = {Alpha}, year = {2008}, author = {Author, A}, address = {London} } @book{buthor90, title = {{B Title}}, publisher = {Bravo}, year = {1990}, editor = {Buthor, B}, address = {New York} } \end{filecontents}  \documentclass{article}  \usepackage{natbib} \usepackage{hyperref} \hypersetup{colorlinks,citecolor=red}  \begin{document}  \noindent citet: \citet{author08}, \citet[see][p. 20]{author08} \\ citep: \citep{author08}, \citep[see][p. 20]{author08}  \bibliographystyle{plainnat} \bibliography{\jobname}  \end{document}     In order to avoid two links to the bibliography (one for the [author] and one for the year [year], respectively), I took  to an older question and added it to my preamble.  \usepackage{etoolbox} \makeatletter  \pretocmd{\NAT@citex}{%   \let\NAT@hyper@\NAT@hyper@citex   \def\NAT@postnote{#2}%   \setcounter{NAT@total@cites}{0}%   \setcounter{NAT@count@cites}{0}%   \forcsvlist{\stepcounter{NAT@total@cites}\@gobble}{#3}}{}{} \newcounter{NAT@total@cites} \newcounter{NAT@count@cites} \def\NAT@postnote{}  % include postnote and \citet closing bracket in hyperlink \def\NAT@hyper@citex#1{%   \stepcounter{NAT@count@cites}%   \hyper@natlinkstart{\@citeb\@extra@b@citeb}#1%   \ifnumequal{\value{NAT@count@cites}}{\value{NAT@total@cites}}     {\ifNAT@swa\else\if*\NAT@postnote*\else%      \NAT@cmt\NAT@postnote\global\def\NAT@postnote{}\fi\fi}{}%   \ifNAT@swa\else\if\relax\NAT@date\relax   \else\NAT@@close\global\let\NAT@nm\@empty\fi\fi% avoid compact citations   \hyper@natlinkend} \renewcommand\hyper@natlinkbreak[2]{#1}  % avoid extraneous postnotes, closing brackets \patchcmd{\NAT@citex}   {\ifNAT@swa\else\if*#2*\else\NAT@cmt#2\fi    \if\relax\NAT@date\relax\else\NAT@@close\fi\fi}{}{}{} \patchcmd{\NAT@citex}   {\if\relax\NAT@date\relax\NAT@def@citea\else\NAT@def@citea@close\fi}   {\if\relax\NAT@date\relax\NAT@def@citea\else\NAT@def@citea@space\fi}{}{}  \makeatother     Which gets me almost where I want to be, but leaves me with two issues I would like to be solved:   while \citet includes pre- and postnotes in the link, \citep doesn't. How can \citep be changed to include postnotes? is there a way to color the brackets and commas that are typeset in black in the unmodified first example also in black in the modified second example without removing them from the link? A tank of 425 liters capacity has been filled with water through two pipes, the first pipe having been opened 5 hours longer than the second. If the first pipe were open as long as the second pipe, the first pipe deliver half the amount of water delivered by second pipe; if the two pipes were open simultaneously, the tank would be filled up in 17 hours. How long was the second pipe open?    a. 10 b. 12 c. 15 d. 18 Simple regular expression for a decimal with a precision of 2 How do I choose an element from a non-empty set? Suppose I have a non-empty set $A$.     How do I choose an element $x\in A$?   More precisely, I believe I would like to find a formula $P(x,y)$ of ZF such that for every non-empty set $y$ there is exactly one $x\in y$ such that $P(x,y)$ is true.  I have thought about this for a while without success and I am beginning to doubt such a formula is even possible. But in mathematical proofs it is quite common to "choose a fixed element" from a non-empty set. So how exactly do we achieve such a thing? Am I missing something?  Thank you in advance. How to clear current “read-only” state on a USB flash drive I setup with Rufus? Three weeks ago I used  2.2 to install Windows 10 on my machine, and it has write-protected my flash drive. I’ve tried diskpart:  diskpart att disk clear readonly  clean create partition primary format fs=fat32 quick   And it kinda worked, it removed the image off the USB, but now it’s showing:  Current Read-only State : Yes Read-only  : No Boot Disk  : No Pagefile Disk  : No Hibernation File Disk  : No Crashdump Disk  : No Clustered Disk  : No   And I can’t format it or write on it.    The drive is a a Kingston DataTraveler G4 32GB model, without physical switches. How would I restore it back to normal (rw) state? solving diophantine equations using congruences So, a question in Elementary Number Theory by David M. Burton:     Problems 4.4      2(a) Using congruences, solve the diophantine equation 4x + 51y = 9       Hint: $4x \equiv 9(mod \ 51) $ gives $ x = 15 +51t$, whereas $ \ 51y \equiv 9 (mod \ 4)$ gives $y = 3+4s $. Find the relation between $s$ and $t$ From this hint, I substitute $ x = 15 +51t$ and $y = 3+4s$ in the given equation $4x + 51y = 9$ to get the relation $s = -t-1$ and using which I can get the solutions $ x = 15 + 51t, \ y =-1-4t$ But we know that the solutions of $ax \equiv b (mod \ n)$ is equivatent to the solutions of the diophantine equation $ax -ny = b$, so, solutions of $4x \equiv 9(mod \ 51) $ is equivalent to solutions of the equation $4x-51y=9$ whereas, solutions of $51y \equiv 9(mod \ 4) $ is equivalent to solutions of the equation $-4x+51y=9$ Now, my question is: as, the above equations $4x-51y=9$ and $-4x+51y=9$ are different, then what is the point of substituting $ x = 15 +51t$ (solution of $4x-51y=9$) and $y = 3+4s $ (solution of $-4x+51y=9$) in the given equation $4x+51y=9$ to find a relation between $t$ and $s$ ? Isn't it absurd as $ x = 15 +51t$ and $y = 3+4s $ are solutions of two different equations? Can anyone please explain this? PS: I did it like this $4x \equiv 9(mod \ 51) $ gives $ x = 15 +51t$ and by substituting it in $4x+51y=9$ we get $y=-1-4t$ How to get my software into Ubuntu? Why would I open a low-rate 9 month CD instead of a higher rate savings account? One specific (popular online) bank is offering a 9 month 1.25% CD, while it's savings account is 1.90%.  There's no way I see interest rates tumbling in the next nine months, so why should I -- why should anyone -- get a 1.25% CD when savings accounts are paying 52% more interest?  (This question is not specific to this particular bank at this particular time.  It's about the general practice of buying low-rate CDs when savings accounts have a higher rate.) On the websites, whenever the OP comments on an answer, or on his question, his name is highlighted. This is a handy feature because you can easily tell whether the comment is from the OP or not.   But on the Android mobile app (don't know about iOS),  this feature is not there. Can we have it please!?