A confusion between geocentric and heliocentric model
What made us think that Earth moves around the Sun?
Break a previous commit into multiple commits Creating your own Tinyurl style uid I'm writing a small article on humanly readable alternatives to Guids/UIDs, for example those used on TinyURL for the url hashes (which are often printed in magazines, so need to be short).  The simple uid I'm generating is - 6 characters: either a lowercase letter (a-z) or 0-9.   "According to my calculations captain", that's 6 mutually exclusive events, although calculating the probability of a clash gets a little harder than P(A or B) = P(A) + P(B), as obviously it includes numbers and from the code below, you can see it works out whether to use a number or letter using 50/50.  I'm interested in the clash rate and if the code below is a realistic simulation of anticipated clash rate you'd get from generating a hash. On average I get 40-50 clashes per million, however bare in mind the uid wouldn't be generated a million times at once, but probably only around 10-1000 times a minute.  What is the probability of a clash each time, and can anyone suggest a better way of doing it?  static Random _random = new Random();  public static void main() {     // Size of the key, 6     HashSet&lt;string&gt; set = new HashSet&lt;string&gt;();     int clashes = 0;     for (int n=0;n &lt; 1000000;n++)     {         StringBuilder builder = new StringBuilder();          for (int i =0;i &lt; 7;i++)         {             if (_random.NextDouble() &gt; 0.5)             {                 builder.Append((char)_random.Next(97,123));             }             else             {                 builder.Append(_random.Next(0,9).ToString());             }         }          if (set.Contains(builder.ToString()))         {             clashes++;             Console.WriteLine("clash: (" +n+ ")" +builder.ToString());         }          set.Add(builder.ToString());         _random.Next();         //Console.Write(builder.ToString());     }      Console.WriteLine("Clashes: " +clashes);     Console.ReadLine(); }   UPDATE:   from this question  I really asked two questions here so I was cheating. The answer I was after was rcar's, however Sklivvz's is also the answer to the 2nd part (an alternative). Is it possible to make a custom unique id generator in a database, or would it be client side (which would be 2 possible reads first)?  The general idea I was after was using Ids in databases or other stores that can be used by phone or printed material, not a giant 16 byte guid.  UPDATE 2: I put the formula for two mutually exclusive events above instead of 2 independent ones (as getting an 'a' the first time doesn't mean you can't get an 'a' the second time). Should've been P(A and B) = P(A) x P(B) Android App sometimes loses answer drafts Hill Cipher known plaintext attack I know a plaintext - ciphertext couple of length 6 for a hill cipher where its key is a [3x3] matrix.  Based on what I've read and learned, to attack and crack keys of [n x n], if we know a plaintext - ciphertext duo of length $n^2$ then we have our set of n equations with n variables, and this is generally solvable. However in my case there is only length of $6$ instead of $n^2 = 9$ .   My question is, how will I solve this problem and find the key? Or, since this is an obvious homework question, what should be my way of thinking? I cannot think of anything else but matrix multiplications and inverses but they do not help me at all. Objects vs arrays in Javascript for key/value pairs Say I have this file:  hello world hello world   This program  #!/bin/bash  for i in $(cat $1); do     echo "tester: $i" done   outputs  tester: hello tester: world tester: hello tester: world   I'd like to have the for iterate over each line individually ignoring whitespaces though, i.e. the last two lines should be replaced by  tester: hello world   Using quotes for i in "$(cat $1)"; results in i being assigned the whole file at once. What should I change? What is the simplest way (least error-prone, least lines of code, however you want to interpret it) to open a file in C and read its contents into a string (char*, char[], whatever)? Prepositional Phrase - confused - at or in This question is essentially the same as one of my , except the only difference is that I am using "only" to change the text at the same location (i.e., ). In other words, I am destroying my earlier text as I go, and not adding new ones underneath the previous ones.   Since the text for the first "only" is shorter than the second "only", therefore the image will shift location. I would like for the image to remain at its location.   Here is an example     it may not be obvious but the second image is higher up than the first.  The code is here, can someone find a solution?  \documentclass{beamer}  \usepackage{graphicx}  \title[Title]{Presentation} \author{Sandro Botticelli} \institute{Italy} \date{1484}  \begin{document}   \begin{frame} \begin{figure} \includegraphics[scale = 0.8]{Venus}     \caption{Nascita di Venere} \end{figure}  \only&lt;1&gt;{In the centre the newly-born goddess Venus stands nude in a giant scallop shell. Its size is purely imaginary, and is also found in classical depictions of the subject. }    \only&lt;2&gt;{Alternative identifications for the two secondary female figures involve those also found in the Primavera; the nymph held by Zephyr may be Chloris, a flower nymph he married in some versions of her story, and the figure on land may be Flora. Flora is generally the Roman equivalent of the Greek Chloris; in the Primavera Chloris is transformed into the figure of Flora next to her, following Ovid's Fasti, but it is hard to see that such a transformation is envisaged here.} \end{frame}   \end{document} I am planning to visit Moscow this winter as a solo tourist. I am a Hungarian citizen. I booked airplane tickets myself. I was informed that I will need an invitation letter, and I think I will go this way: (), but now the tourist visa application online form asks:    the options are: None, Travel company. I think I will need to select travel company because the description says:     In the case of a tourist visa select "Travel company" from the list and give the name and address of the travel company. In the case of   business visa select "Organization" from the list and enter in the   "Name of organization" name of the host organization, enter the   address of the organization and TIN in the appropriate fields. In   the case of private visa select “Individual” from the list and enter   the name, birth date and home address of the host. In the case of   transit, select "None" from the list.  Reference number: printed on   the bottom line of approval of a foreign tourist "Референс №». It is   necessary to introduce whole number with leading zeros.       Confirmation number: printed on the top line of confirmation of a   foreign tourist. The number can contain only numbers or numbers with   letters. You should only enter the numbers.   However I do not have a travel company.   What do I do?   Select "None" from the drop down so that I don't have to fill in travel company(this seems to be against the description that says select travel company for tourist visa) Select Travel company and the Invitation letter company will be my travel company and they will provide appropriate details? as in () Apply at some additional travel company, because there is no other way?  Some other option?   I didn't expect the visa application to be this complicated. I hope I get there. Why is Facebook missing from the list of ways to share a page in Safari?  That option used to exist before the latest update.  When I'm directed to the extensions box Facebook is not there. I lost the source code from one project I did on the company I'm working for and haven't been able to find a Visual Basic 6 decompiler; does that even exists?  I only have the EXE that I've rescued from a user's machine. Before, the concept of imaginary numbers, the number $i = \sqrt{-1}$ was shown to have no solution among the numbers that we had. So we declared $i$ to be a new type of number. How come we don't do the same for other "impossible" equations, such as $x = x + 1$, or $x = 1/0$?  Edit: OK, a lot of people have said that a number $x$ such that $x = x + 1$ would break the rule that $0 \neq 1$. However, let's look at the extension from whole numbers to include negative numbers (yes, I said that I wasn't going to include this) by defining $-1$ to be the number such that $-1 + 1 = 0$. Note that this breaks the "rule" that "if $x \leq y$, then $ax \leq ay$", which was true for all $a, x, y$ before the introduction of negative numbers. So I'm not convinced that "That would break some obvious truth about all numbers" is necessarily an argument against this sort of thing. Fibonacci numbers and proof by induction Consider the Fibonacci numbers $F(0) = 0; F(1)=1; F(n) = F(n-1) + F(n-2)$.  Prove by induction that for all $n&gt;0$,  $$F(n-1)\cdot F(n+1)- F(n)^2 = (-1)^n$$  I assume $P(n)$ is true and try to show $P(n+1)$ is true, but I got stuck with the algebra. How do we reach $P(n+1)$ from $P(n)$? Also, strong induction may be used instead. Efficient way to check collision with potentially hundreds of objects I am trying to make a top down shooter that could potentially have hundreds of objects at once at one point. I need to check collision with projectiles, walls, and enemies. I am currently using ArrayLists which probably won't suffice later on and was wondering if someone had a good method or knows a good method for checking all of those objects at once. This is going to be a game for smartphones and is built in java. Any ideas would be great or if you could point me in some direction that would be fantastic.  Thanks in advance! Ubuntu 16.04 Jan 3 2018 update causing screen/access issues Yesterday (Jan. 3, 2018), I installed an OS update (Ubuntu 16.04), using the Software Center. My system isn't working correctly now. When my mouse rolls over the Launch bar, it disappears, then any open window disappears, leaving me with only the desktop screensaver showing. I can't even shut the computer off using the settings button on the top.  I went into the Terminal and attempted to fix it using the following commands:  sudo apt-get dist-upgrade sudo apt-get autoremove   But I'm still having the same problem.  I have reinstalled Ubuntu 16.04 and when I accepted the update on install had the same problem.  I have reinstalled it a second time but have not done an OS update and everything seems to be working fine.    Found another user with the same problem:    Is it possible that the Meltdown security update is at fault?  I've read the update has been issued for 64-bit x86 architecture ();  I'm running a 32 bit i386 architecture.  Could that be an issue and is there a way to correct it? I have a statement,     Either p or q   and I have to write it in terms of logical connectives but I don't get which logical connector should I be using? Here is what I did (I think there could have been a better way to do this)     $(p \lor q ) \land (\neg((p \Rightarrow q) \land (q \Rightarrow p)))$ If a two vectors $\bf u$ and $\bf v$ in linearly independent, can their images be linearly dependent given they were transformed by a linear transformation $T$? I think not. My reasoning If the images are linearly dependent, then $c_1T({\bf u})+c_2T({\bf v})={\bf 0}$ for scalars $c_1$ and $c_2$, not both $0$. Then $c_1T({\bf u})+c_2T({\bf v})={\bf 0}$ $T(c_1{\bf u}+c_2{\bf v})=T({\bf 0})$ $c_1{\bf u}+c_2{\bf v}={\bf 0}$ Therefore, ${\bf u}$ and $\bf v$ are linearly dependent. My reservation A homework problem seems to contradict the above. Here's the problem: Let $\mathbb R^n\rightarrow\mathbb R^m$ be a linear transformation. Suppose $\{{\bf u},{\bf v}\}$ is a linearly independent set, but $\{T({\bf u}),T({\bf v}\})$ is a linearly dependent set. Show that $T({\bf x})={\bf 0}$ has a nontrivial solution. Are ideal hashes possible to create? Difference between spin and polarization of a photon I understand how one associates the spin of a quantum particle, e.g. of a photon, with intrinsic angular momentum. And in electromagnetism I have always understood the polarization of an EM wave as the oscillations of the E and M field, not necessarily being  aligned with the direction of propagation of the wave.     Questions:   But when one talks about the polarization of a photon in Quantum Mechanics, how does it really differ from its spin?  Are they somehow related and what's the physical idea behind photon polarization in contrast to photon-spin? Feel free to use mathematical reasonings as well if you see it fit!