I read in a book today ( the computer music tutorial by curtis roads), that humans are not capable of imagining any long series of truly random numbers. Apparently, the only way to generate a series of truly random numbers is to use either a Geiger counter or some type of cellular automata algorithm. Is it true that a computer would be able to detect a pattern and accurately guess the nth number in a series of random numbers thought up by a person?
Let's say you tell me to produce randomly a number from 1-100, and I choose the number 47. Can it be said that there is a specific reason I chose the number 47, and that it is not completely random? By random I mean that there is absolutely no reason this number in particular was chosen.    It seems odd to me, since it seems like since I have applied conscious effort to produce or choose a number within that range, or even without range, that it can't be truly random, but there might be a reason why I chose that number amongst the many others I could have chosen.  I guess the general question, which I'm interested to know if any philosophers in the past have discussed, is whether our thoughts are necessarily based on prior thoughts, or if thoughts can be truly spontaneous and random?
Lighter in CPU/Memory Usage: Lubuntu or Xubuntu I am looking for an Ubuntu version that consumes less Memory and CPU. I have read both Lubuntu and Xubuntu (The homepages, wikipedia, phoronix and other sites comparing both). But from experience, which one uses less memory and is less CPU intensive. I need to install them in very old hardware and want to persuade the owner of the hardware of the benefits of Ubuntu.  in this case I want to install 11.10 or 12.04 when it comes out. How are each behaving in those versions?  The 2 PCs I will be installing either Xubuntu or Lubuntu are:  Granpa PC:  CPU - Pentium 2 450Mhz RAM - 64MB DIMM Video - 16MB Used for - Documents and Internet. No listening to music, no looking at videos. Just using it for document writing.  The other old meat:  CPU - Pentium 3 550Mhz RAM - 128MB DIMM Video - 16MB Used for - Documents and Internet also but they want.. or maybe they are wishing for it to use it to see movies and listen to music. This one has internet. The other one does not.  UPDATE  Wanted to update this question with the test results for over 8 months worth of using Lubuntu and Xubuntu. When it comes to very old hardware, am talking about 64 MB, 128 MB or even 256 MB of RAM computers, Lubuntu is better than Xubuntu when comparing Memory usage. When it comes to CPU usage, both are the same.  This will not improve I/O Disk performance which will be the bottleneck for old computers. Also the difference in performance between Xubuntu and Lubuntu is about 10% to 20% percent in memory usage. Again, CPU usage is the same.  Now, when it comes to how responsive the Desktop is, LXDE (Lubuntu) has a much better response time than XFCE (Xubuntu). I would say about 50% or just simply noticeable to the eye. Lubuntu is similar to how Windows XP looks while Xubuntu is more like how Gnome 2 looked.  The computers (The old ones mentioned here) and 2 more are still working in excellent conditions thanks to the Ubuntu family. I also want to add I am using 13.10 for both distros. Discouraged by simple Bayesian Question My university is testing an intro Machine Learning (ML) course for us undergrads, and having been interested in ML since the beginning to understand what it was, I jumped at the chance to take it. But being someone who has not been back in school for a long time and much busier than I was in my first years long ago, I am finding that I need more info and examples than the class in its current form has.  I am struggling to figure out what the attached question is asking. I am searching online for help with this particular topic, but I am also finding that everyone seems to have their own way of phrasing similar questions in such a way that I am finding it hard to link the info.   My understanding from stats way back when is that $p(x|\omega_1)$ is stating the probability of $x$ given $\omega_1$ for $0\le x \le 2$ and zero other wise. Same obviously if given $\omega_2$. If I understand, the priors are the probability of $\omega_1$ and $\omega_2$ which are somehow obtained. And honestly that is as far as I am really comprehending. I am not sure what (a) and (b) are truly asking for or how to get them. If anyone is able to help me with some pointed info on the topic it would be greatly appreciated. Significance of the second focus in elliptical orbits The following C++ code uses a ifstream object to read integers from a text file (which has one number per line) until it hits EOF. Why does it read the integer on the last line twice? How to fix this?  Code:  #include &lt;iostream&gt; #include &lt;fstream&gt; using namespace std;  int main() {     ifstream iFile("input.txt");    // input.txt has integers, one per line      while (!iFile.eof())     {         int x;         iFile &gt;&gt; x;         cerr &lt;&lt; x &lt;&lt; endl;     }      return 0; }   input.txt:  10   20   30   Output:  10   20   30   30   Note: I've skipped all error checking code to keep the code snippet small. The above behaviour is seen on Windows (Visual C++), cygwin (gcc) and Linux (gcc). How do you document your databases? Sometimes, others just inform us about things without us asking them, other times they do not do that even if we ask them. I want a verb for when others do not give us information — whether because they do not like to or they just don't give it, but we cannot directly ask them to — but we actively extract the information from them sometimes without them being aware of it.   So the word I am looking for shouldn't be only for cases where we coerce or force others to give us information, and it shouldn't be only for cases where others do not like to give us information.  Example:     I needed that information. But I couldn't ask her for it, or most   probably she would not give to me even if I asked her. So, I ....   the information I wanted.   It could be a phrasal verb and so not just a single word, but I couldn't devise a  blank suitable for all possibilities!   Two verbs I've already had but I think are not suitable:  to give someone the third degree   To prize something from/out of somebody How to remove the lines which appear on file B from another file A? IPv4 vs IPv6 priority in Windows 7 I have IPv6 connectivity through Hurricane Electric tunnel. Since IPv6 day this year, many services (google.com, facebook.com, etc.) enabled IPv6 on their main domains. On my Windows machine, IPv6 is preferred over IPv4. This means that whenever I visit Google, all traffic goes through my tunnel to Hurricane Electric, which raises the latency by more than 100%:  C:\&gt; ping www.google.com  Pinging www.l.google.com [2001:4860:8005::68] with 32 bytes of data: Reply from 2001:4860:8005::68: time=85ms Reply from 2001:4860:8005::68: time=84ms Reply from 2001:4860:8005::68: time=112ms Reply from 2001:4860:8005::68: time=86ms  Ping statistics for 2001:4860:8005::68:     Packets: Sent = 4, Received = 4, Lost = 0 (0% loss), Approximate round trip times in milli-seconds:     Minimum = 84ms, Maximum = 112ms, Average = 91ms   C:\&gt; ping -4 www.google.com  Pinging www.l.google.com [173.194.79.103] with 32 bytes of data: Reply from 173.194.79.103: bytes=32 time=28ms TTL=48 Reply from 173.194.79.103: bytes=32 time=28ms TTL=48 Reply from 173.194.79.103: bytes=32 time=55ms TTL=46 Reply from 173.194.79.103: bytes=32 time=29ms TTL=46  Ping statistics for 173.194.79.103:     Packets: Sent = 4, Received = 4, Lost = 0 (0% loss), Approximate round trip times in milli-seconds:     Minimum = 28ms, Maximum = 55ms, Average = 35ms   Question: How can I make Windows 7 to always prefer IPv4, when both IPv4 and IPv6 records are available for a specific domain name? I've been having trouble defeating this monster. Even with lots of buff potions, health potions, high tier armor (Molten), and ranged weapons with plenty of ammo (Minishark), I can't seem to kill this boss.  Worse, when I get it down to about 2000 hp, even if I'm fairly far away, it'll suck me in and continually rise towards the skybox, which doesn't allow me to do anything for some reason.  How do I defeat the Wall of Flesh? What gear should I be using and what kind of potions do I need? Showing that $f$ is identically $0$ on $\mathbb{D}$ Here is the question: Let $f:\mathbb{D}\rightarrow\mathbb{C}$ be an analytic function.  Suppose that there exists $\epsilon&gt;0$ such that for every $\theta$, $|\theta|&lt;\epsilon$, and $\lim_{z\rightarrow e^{i\theta}}f(z)=0$.  Prove that $f$ is identically $0$ on $\mathbb{D}$. My thoughts:  Well, honestly, I am quite stumped here.  I was thinking I could let $f$ be analytic in some other region (can I even do this?), say the lower half plane and suppose $\lim_{z\rightarrow x}f(z)=0$ whenever $-1\leq x\leq1$, by assumption.  Maybe then I could show that $f$ is identically $0$ on the bigger region, and then consider $f$ on the intersection of those two regions, and then ultimately making my way towards using the uniqueness theorem to show what I want... but I am quite stuck on how to do that... any thoughts, suggestions, etc. are greatly appreciated!  Thank you. I'm about to travel to the US, where iPods / AirPods / iPhone are much cheaper than in my country.   I wonder if Apple's warranty is international, and/or what warranty coverage exists when I return to my country.  Where can I understand what Apple Warranty covers in the US when products leave the US? As I prefer outer parentheses to grow larger in nested expressions, I happen to insert \bigl and \bigr and its larger cousins a lot. I have always wondered whether there is a way to do this automagically.  Inserting \left and \right prophylacticly before all opening and closing parentheses and hoping that it sorts things out doesn't do the trick in all cases as seen below.  The left column is without any size changing commands. The middle column as a \left \right pair at every parentheses/brace/bracket and the rightmost column shows my preferred version.    As seen in the middle column of the second and third line the \left and \right pair sometimes makes the outer parentheses larger, on the cost of an extra horizontal space between \Pr and (. The extra space is fine in case of really big opening parentheses but here I'd prefer the regular spacing.  \documentclass{scrartcl} \usepackage{amsmath} \usepackage{amsfonts} \begin{document} \begin{align*} &amp;1-(1-F(x))^n&amp;&amp;1-\left(1-F(x)\right)^n&amp;&amp;1-\bigl(1-F(x)\bigr)^n\\ &amp;\Pr(X_{(1)}\le x)&amp;&amp;\Pr\left(X_{(1)}\le x\right)&amp;&amp;\Pr\bigl(X_{(1)}\le x\bigr)\\ &amp;\mathbb{E}[\min\{X_1,X_2\}]&amp;&amp;\mathbb{E}\left[\min\left\{X_1,X_2\right\}\right]&amp;&amp;\mathbb{E}\bigl[\min\left\{X_1,X_2\right\}\bigr]\\ &amp;\left(\pi-\arccos(\frac{y}{r})\right)&amp;&amp;(\pi-\arccos\left(\frac{y}{r}\right))&amp;&amp;\left(\pi-\arccos \left(\frac{y}{r}\right)\right) \end{align*} \end{document}   As mathematical expressions can be arbitrarly complex there is probably no general way to do this. But I’m not asking for a solution of the general case. A partial solution that works in the simple cases shown above would be a big help. The simple rule could be, that parentheses never shrink below the size of an inner pair. Of course you can immediately think of extensions like a \mid in a conditional expectation that grows with the size of the expectation’s brackets.  What is your preference regarding the size of nested parentheses? Is there a better way to archieve your preferred style despite inserting \bigl \bigr manually?    EDIT:  A colleague pointed me to section 8.3 of Herbert Voß’  document where size problems with parentheses are solved by playing with two TeX parameters within a group around the expression in question. This led naturally to appendix G of the TeXbook where the mechanics of \delimitershortfall and \delimiterfactor are explained.  \delimitershortfall specifies the maximum space not covered by a delimiter (default 5pt) and \delimiterfactor is the ratio for variable delimiters, times 1000 (default 901).  I used them to implement the never shrink below a subformular size idea from above by setting the shortfall to 0pt and the ratio to 1.0.    While it works nicely in line one and three, in line two and four the parentheses now grow too much, and still there is the extra horizontal space introduced by \left. Error Message:      "A reboot is pending. Please restart before starting Visual Studio".    I installed Visual Studio (Visual Basic 2015 and SQL 2015) and after what looked like a successful install I then got the "Reboot" window.   Not expecting it I had a bunch of things open. So I closed a bunch a bunch of things, and did the reboot myself.   Now I cannot run Visual Basic because it ONLY gives me the above error message in the pop-up window. It won't even let me do a re-install.   All it does is keep giving me the above error message.   If you have any advice that's better than a complete uninstall/reinstall I'm sure everyone in my situation would benefit from it.  How can I resolve this issue? Right so seeing as the new Deadpool movie shows the origins of Deadpool: specifically, he got cancer... blah blah had to get him the healing factor from Wolverine.  But that makes no sense — they used the same actor, so I'm assuming there must be some connection, right... right? Repeated squaring method How do I use the repeated squaring method to calcualte 2^176 (mod 177)? I'm not sure, but is there something about the fact that 177 is 1 greater than 176 that makes this a problem? In general, in most places, it is said that using TeX defaults is the best. However, TeX does provide things like \, and \quad etc. When one should use them? Both in general and in math mode in particular. Can I manually put an external hard disk to sleep? Convert UTC/GMT time to local time Changing affiliation on publication I am moving from one job to another (postdoc to tenure track) this summer and I have papers in several stages of being written, these go from handwritten notes with all the necessary arguments to under revision at a journal. All the papers will have my new contact information put on them but where is the line for changing affiliation? It seems obvious to me that the one that is still in the handwritten notes stage will get the new affiliation and that the ones under revision won't. So somewhere in between is a line.   Where is it?  There are some similar questions so far (see  and  but they do not seem to be quite the same situation since I am not changing fields and the appointments are not concurrent. Show that no application $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, of $C^k$ class, $k \geq 1$ can be injective How can I proof this:     Show that no application $f: \mathbb{R}^2 \rightarrow \mathbb{R}$, of $C^k$ class, $k \geq 1$ can be injective, i.e., there are $A,B \in \mathbb{R}^2$ such that $A \neq B$ and $f(A) = f(B)$ (Hint: show that given $(a,b) \in \mathbb{R}^2$ in every open neighbourhood of $(a,b)$ there are points $(c,d),(c_1,d_1)$ where ${\partial}_1f(c,d) \neq 0$ or ${\partial}_1f(c_1,d_1) \neq 0$).   The problem is that I have no idea how to use the hint.  Thanks for all your comments.