I have heard various definitions of the .  Yet I cannot quite comprehend how it is true. Nevertheless, something tells me, it is a consequence of the wave nature of light/electron which gives the intrinsic nature of uncertainty even if we don't measure it.  Is it true that this principle is a consequence of wave nature of particle, that the uncertainty pops up due the fact that particle acts as a wave(I find no answer which stated the exact implication of the wave characteristics which should give the uncertainty principle)?  Will it be true to assume that, if an electron acts only like a particle and not as a wave, the uncertainty principle will not be necessary(this part of the question is not asked anywhere)?   Can you please tell me without much mathematics why this is so?  Like we understood the photoelectric effect contradicts the wave nature of light,  Could you please guide me the intuitive explanation with formal reason why we cannot absolutely know simultaneously the position and momentum of a particle?
I have heard several pseudoscientific explanations about the  and find them hard to believe.  As a mathematician mainly focusing on functional analysis, I have a considerable interest in this matter. Although I still have no idea about it, I aim to truly understand it one day. For now, the question is:  Can the Heisenberg Uncertainty Principle be explained so that a non-scientist can at least get a correct idea of what it says and what not?  One of the most heard explanations is the one that says naïvely that while trying to determine the position of a particle you send energy (light) so you modify its speed, therefore making it impossible to determine the speed. If I understand well this should only be a some sort of metaphor to explain it, right?
Why does my grep expression need to use $'string' to match tab characters? I have seen a few  here on Meta&nbsp;Stack&nbsp;Exchange that cover parts of this, but they are often too local, and none of them seem to cover all the relevant scenarios.  I will break it up into multiple parts in order to make this more specific:     When should I vote on a question:   What are the qualifications for a question to be deserving of being up-voted? When shouldn't I vote up on a question? What are the things that would cause a question to need to be down-voted?   How should I go about down-voting the question (do I wait a little while to give the OP a chance to change it, or do I down-vote it immediately)?  When shouldn't I vote down on a question?  When should I vote on an answer:   What are the qualifications for an answer to be deserving of being up-voted? When shouldn't I vote up on an answer? What are the thing that would cause an answer to need to be down-voted?   How should I go about down-voting the answer (do I wait a little while to give the OP a chance to change it, or do I down-vote it immediately)?  When shouldn't I vote down on an answer?  When should I vote on a comment:   While votes on comments do not affect reputation points, it might be useful to new users to know when to up-vote them.    It seems that a full, comprehensive list of these would be invaluable to new users looking to figure out how the voting system works, but this list seems to be missing from the meta site. How do you detect support for VML or SVG in a browser I'm writing a bit of javascript and need to choose between SVG or VML (or both, or something else, it's a weird world). Whilst I know that for now that only IE supports VML, I'd much rather detect functionality than platform.  SVG appears to have a few properties which you can go for: window.SVGAngle for example.  Is this the best way to check for SVG support?  Is there any equivalent for VML?  Unfortuntaly - in firefox I can quite happily do all the rendering in VML without error - just nothing happens on screen. It's quite hard to detect that situation from script. What is the difference between shell, console, and terminal? To friend vs. to befriend mysql select from n last rows I have a table with index (autoincrement) and integer value. The table is millions of rows long.  How can I search if a certain number appear in the last n rows of the table most efficiently? $ KC $ spaces imply $ US $ spaces , but vise versa is false. In many courses, say Linear Algebra, Group Theory, Topology, instructors often say that knowing that certaing objects are isomorphic, sometimes makes life easier because we can work with more friendly objects.  Is there any example of using isomorphism concept to solve a non trivial concrete problem?   I must say, I'm not looking on important or famous isomorphic objects, but on non trivial application of the concept of isomorphism used in order to solve another kind of problem. Save site as template using client object model The age of the universe I needed to create a list of lists in Python, so I typed the following: my_list = [[1] * 4] * 3  The list looked like this: [[1, 1, 1, 1], [1, 1, 1, 1], [1, 1, 1, 1]]    Then I changed one of the innermost values: my_list[0][0] = 5  Now my list looks like this: [[5, 1, 1, 1], [5, 1, 1, 1], [5, 1, 1, 1]]    which is not what I wanted or expected. Can someone please explain what's going on, and how to get around it? How to boot from a USB drive in VirtualBox? The question is simple and straight forward:  How to boot from an USB drive in VirtualBox?  EDIT:  I have attached usb to VirtualBox as shown in the screenshot.    But it is not possible to boot from an USB drive even when attached  .  So I would like to know if there is any other possiblity to boot from an USB drive? Created user can access all databases in PostgreSQL without any grants Proving an identity relating to the complex modulus: $z\bar{a}+\bar{z}a \leq 2|a||z|$ Show that $z\bar{a}+\bar{z}a \leq 2|a||z|$  I was able to check this using some examples which is not ideal for a mathematician way of proving a problem/case/theorem. I couldn't generalize it (prove it). I will be glad if I can be given the hint/proof for this problem. Thank you. How do I generate a random int value in a specific range? I have tried the following, but those do not work: Attempt 1: randomNum = minimum + (int)(Math.random() * maximum);  Bug: randomNum can be bigger than maximum. Attempt 2: Random rn = new Random(); int n = maximum - minimum + 1; int i = rn.nextInt() % n; randomNum =  minimum + i;  Bug: randomNum can be smaller than minimum. Configure mouse speed (not pointer acceleration!) Is there way to increase the mouse speed in KDE4? I don't want any pointer acceleration, it's just the mouse speed that I want to change.  Edit: Unfortunately, editing the xorg.conf is not an option for me, because I want the users to be able to configure the mouse speed themselves and it is company policy do deny users permission to change the xorg.conf. Related:   I know I must describe my past and current research in my personal/research statement or statement of purpose. But do I use technical terms?  I was given the advice that since the people reading my statement are mathematicians (I am applying to US for applied mathematics), they should know what I am talking about.  Although I am applying to applied mathematics, it would also be nice to hear from other fields (biology, computer science, engineering etc) about this. "does not contain a static 'main' method suitable for an entry point" Making some tests in Windows XP for customizing a user interface in QGIS 1.8 (see ), I have unchecked, among other options, the Settings Menu. This means that, after restarting QGIS, there's no way of recovering the older settings because there is not already a Setting Menu. So, I cannot reload any ini file.  For your information, as a precaution, previously I have saved in a folder both the original ini file, with all the options, and the customized ini file with only some options (of course, not included here the necessary Settings Menu).  Before reinstalling QGIS (version 1,8), I would like to try other smarter options if there's any. Where and what does QGIS look at where this applications starts? I am a British citizen and US permanent resident. I rarely need visas. However, I am considering a Mediterranean cruise in the spring or summer of 2019.  Unlike British politicians, I like to plan ahead and be prepared. If I am going to need a Schengen visa, I want to assemble the documentation early next year, so I can apply to the appropriate country as soon as I have an itinerary and it is at most 90 days before travel. Given how things are going, I am preparing for a hard, no-agreement, Brexit.  For trade, that would mean WTO rules. For personal travel, is there a similar fall-back that would allow me visa-free visits to the Schengen countries?