Oke, so my mind is blown by Einsteins view on gravity, at least as far as I understand the basics and principles he based his views on.  One of the first things that struck me was that most of his equations were based on the fact the photons had no mass, something which is virtually impossible to verify experimentally and something I can not convince myself of.  Now he states that mass bends spacetime: in other words, objects can only move in straight paths, but because the "surface" of a path can be bent, the trajectory relative to the mass is bent. So as a reaction, I did the following thought experiment that would separate Newton from Einstein:  Image in space (completely empty) and two objects with mass M and m (whatever the values) placed from a distance R apart completely at rest. According to my interpretation of Einstein, nothing will happen because even if spacetime is bent they have no motion themselves. Our earth orbits the sun because it initially had a motion and is now travelling in an infinite straight line, which becomes an ellipse due to curvature. Newtons would of course state that in my thought experiment, the two masses would collide.  After I realized this, I started to question Einstein's view. Is my basic interpretation correct about Einstein, and how would you (expert/physics professor/lover) respond to this thought? I personally find it pretty confronting...  BTW I'm just a high school student, potentially going to Cambridge to study physical sciences...
It is fine to say that for an object flying past a massive object, the spacetime is curved by the massive object, and so the object flying past follows the curved path of the geodesic, so it "appears" to be experiencing gravitational acceleration. Do we also say along with it, that the object flying past in reality exeriences NO attraction force towards the massive object? Is it just following the spacetime geodesic curve while experiencing NO attractive force?  Now come to the other issue: Supposing two objects are at rest relative to each other, ie they are not following any spacetime geodesic. Then why will they experience gravitational attraction towards each other? E.g. why will an apple fall to earth? Why won't it sit there in its original position high above the earth? How does the curvature of spacetime cause it to experience an attraction force towards the earth, and why would we need to exert a force in reverse direction to prevent it from falling? How does the curvature of spacetime cause this?  When the apple was detatched from the branch of the tree, it was stationary, so it did not have to follow any geodesic curve. So we cannot just say that it fell to earth because its geodesic curve passed through the earth. Why did the spacetime curvature cause it to start moving in the first place?
My disk already has 4 primary partitions, how can I install Ubuntu? I would like to install Ubuntu alongside Windows 7 on a HP G62 Notebook. Although I have installed  Ubuntu in a dual-boot many times before, I found out that this model has already four partitions.    Partitions:   SYSTEM (NTFS, 199MB, used 66.59MB) Partition without any tag: NTFS (579GM, used 129GB)  RECOVERY (NTFS 16.74 GB, used 2.42GB)  HP_TOOLS (FAT32, 103.34 MB, used 13.23MB)   Since I am not an expert with partitions I would like to get advice on how to do this.  My first idea is this one:   Free some space from /dev/sda2 (I don't know if could also free some other space) delete the HP_Tools partition (I have already created a backup) create an extended partition with the free space in #1 containing three parititions: swap (1gb); / (EXT4, 30GB);  /home (EXT4, 120GB)   Another option is to use wubi instead.  What do you think? Is there any other way to achieve this?  PS: I really think this HP policy of using 4 partitions is not a coincidence  PS: I tried using gparted from the live CD and I got a warning message saying that if I freed some space from /dev/sda2 I could create serious issues in the system A more specific question about a tricky redirect case What is the best way to tokenize/split a NSString in Objective-C? I'm setting up an online ordering system but I'm in Australia and for international customers I'd like to show prices in US dollars or Euros so they don't have to make the mental effort to convert from Australian dollars.  Does anyone know if I can pull up to date exchange rates off the net somewhere in an easy-to-parse format I can access from my PHP script ?    UPDATE: I have now written a PHP class which implements this. . Why is charge of the electron negative? There is this puzzling thing that is called : paradoxically, warm (35°C) water freezes faster than cold (5°C) water.  As a physisist, I've been asked about it several times already. And I have no definite answer to that, apart from the standard: "there are many things that can influence it".  So, does anyone knows about the status or progress on that effect? Any recent reviews, publications or other references? Numbering a set of horizontally distributed equations Selecting a Textbox Item in a Listbox does not change the selected item of the listbox Bottom to top explanation of the Mahalanobis distance? Is it possible in Ruby to get a reference to methods of an object ( I would like to know if this can be done without procs/lambdas ) , for example , consider the following code :   class X   def initialize     @map = {}     setup_map   end    private   def setup_map     # @map["a"] = get reference to a method     # @map["b"] = get reference to b method     # @map["c"] = get referebce to c method   end    public   def call(a)     @map["a"](a) if a > 10     @map["b"](a) if a > 20     @map["c"](a) if a > 30   end    def a(arg)      puts "a was called with #{arg}"   end    def b(arg)      puts "b was called with #{arg}"   end    def c(arg)     puts "c was called with #{arg}"   end end   Is it possible to do such thing ? I would like to avoid procs/lambdas because I want to be able to change the behaviour of A,B,C by subclassing . Multiple Inheritance in C# How to convert standard IP address format string to hex and long? Does anyone know how to get the IP address in decimal or hex from standard IP address format string ("xxx.xxx.xxx.xxx")?  I've tried to use the inet_addr() function but didn't get the right result.  I tested it on "84.52.184.224"  the function returned 3770168404 which is not correct (the correct result is 1412741344).  Thanks! How to determine whether the direction of rotating a 2D vector to another one is counter-clockwise or clockwise using the cross product? Vec2 a, b; // some random vector Vec2 cross = a.Cross(b); RelativeDirection(a,b,cross); // return true if the direction of                               // rotating a to b is counter-clockwise   How do I implement the function RelativeDirection()?  I got some suedo code from the textbook:  if a.Cross(b) &gt; 0 then ... else ...   but the cross product is a vector right? how do you compare it with an integer? Convert particle system to animated meshes How to set the close-laptop-lid-action? biblatex: multiple bibliographies categorised by different .bib files biblatex supports multiple bibliographies by looking up the 1) entry type, 2) keyword, or 3) category.  This is all fine, but in the use case of primary sources and secondary sources: 1) the 'type' method doesn't work, 2) it is quite tedious to key in the 'primary' and 'secondary' keywords for each .bib entry, and 3) declaring the sorting by category would entail typing all the primary keys in the document.  So, if I'm storing all my primary bib entries in one .bib file, and secondary one in another, is there a bit to tell biblatex to assign a keyword or category automatically to all the entries from that bib file as it imports them?  Done this way, entries can be easily swapped to and from the primary and secondary .bib files without fiddling individual keywords, and I don't have to type out all the primary and/or secondary entries into categories in each document. Did regular Americans speak the way actors in the 30s and 1940s did? I watch a lot of old movies, and I've noticed that American actors of the 1930s and 1940s often spoke in a quasi-generic-posh-British accent.  Katherine Hepburn's accent would be the perfect example. It seems exaggerated, and I imagine it was not common off the stage and screen. What was that? Was it just an accent or was it a dialect? Did real people actually speak that way? When I'm sneaking around, I can move more slowly and quietly by holding shift.   But walking this way is really slow. I would like to move a little bit faster, but not full speed.    On a console I imagine you have much finer control over how fast you move with the joysticks. Is there any way to accomplish this on the PC (without an external joystick)?  Perhaps there is a console command or config file setting that will change the % speed modifier that holding down shift uses? What is the meaning of "algebraically indistinguishable" I heard the term couple of times (in Field theory class and book), for example: The different roots of $p(x)=x^3-2$ are "algebraically indistinguishable".  I understand the meaning intuitively, but what does it really mean ? Sobolev inequality If $f\in H^2(\mathbb R^2)$, I want to show that    $||f||_{L^\infty}\le c||f||_{H^2}$ $||f||_{L^\infty}\le c||f||_{H^1} [1+\ln(1+||f||_{H^2})]$   For 1, I use $||f||_{L^\infty}\le \sup_{x\in \mathbb R^2} |f|\le\int_{\mathbb R^2} |\hat f(\xi)|d\xi = \int(1+|\xi|^2)^{-1}(1+|\xi|^2)|\hat f(\xi)|d\xi \le (\int (1+|\xi|^2)^{-2}d\xi)^2(\text {which is integrable in this case})||f||_{H^2}\to \text{is this correct?}$   But for 2, I am stucked. How can I get the "ln"? and how can I make it into a product of $H^1$ and $H^2$ norm?