Since electric charge is comprised of discrete units and and mass is formed by discrete units is it possible that space-time itself is discrete as well?
On a quantum scale the smallest unit is the , which is a discrete measure.  There several question that come to mind:   Does that mean that particles can only live in a discrete grid-like structure,  i.e. have to "magically" jump from one pocket to the next? But where are they in between? Does that even give rise to the old paradox that movement as such is impossible (e.g. )? Does the same hold true  for time (i.e. that it is discrete) - with all the ensuing paradoxes? Mathematically does it mean that you have to use difference equations instead of differential equations? (And sums instead of integrals?) From the point of view of the space metric do you have to use a discrete metric (e.g. the ) instead of good old Pythagoras?   Thank you for giving me some answers and/or references where I can turn to.  Update: I just saw this call for papers - it seems to be quite a topic after all: Is Reality Digital or Analog? FQXi Essay Contest, 2011. , , . One can find some pretty amazing papers over there.
What is the difference between "till" and "until"? What is the difference between till and until?    When to use till or until? Please explain with examples. Java method dispatch with null argument Why does it (apparently) make a difference whether I pass null as an argument directly, or pass an Object that I assigned the value null?  Object testVal = null; test.foo(testVal);    // dispatched to foo(Object) // test.foo(null);    // compilation problem -&gt; "The method foo(String) is ambiguous"     public void foo(String arg) { // More-specific     System.out.println("foo(String)"); }  public void foo(Object arg) { // Generic     System.out.println("foo(Object)"); }   In other words, why is the (commented-out) second call to foo(...) not dispatched to foo(Object)?  Update: I use Java 1.6. I could compile Hemal's code without problems, but mine still doesn't compile. The only difference I see is that Hemal's methods are static while mine are not. But I really don't see why this should make a difference...?  Update 2: Solved. I had another method foo(Runnable) in my class, so the dispatcher couldn't unambiguously select the single most specific method. (See my comment in Hemal's second answer.) Thanks everyone for your help. True or false: {{∅}} ⊂ {∅,{∅}} A ring element with a left inverse but no right inverse? Can I have a hint on how to construct a ring $A$ such that there are $a, b \in A$ for which $ab = 1$ but $ba \neq 1$, please? It seems that square matrices over a field are out of question because of the determinants, and that implies that no faithful finite-dimensional representation must exist, and my imagination seems to have given up on me :) Proof that $1729$ is the smallest taxicab number Why can I see the output of background processes? For example, when I type ping 8.8.8.8 &amp;, why can we see ping process working? And when I type find / -name '*test*' &amp; , it's also seen on monitor.  Why is that? Is it not really in background? File issues after importing Drupal site I recently tried to move my Drupal site to a new server using this page: . But now the style doesn't seem be loaded and more importantly I get this error on every page in the site (even on the frontpage):  Warning: file_put_contents(temporary://filef76T9k): failed to open stream: &quot;DrupalTemporaryStreamWrapper::stream_open&quot; call failed in file_unmanaged_save_data() (line 1900 of /Library/Server/Web/Data/Sites/Default/drupal/includes/file.inc). The file could not be created.  Any ideas what this could be about? The security guard problem Evaluating a PDF to find an unkown constant Evaluate the PDF to find K  $1 = \int_0^{\infty} \frac{k}{(1+x)^4}$  using u substitution I got:  $u=1+x$ and $du= dx$  $\int_0^{\infty} \frac{k}{u^4} \to \frac{k}{\frac{-1}{3} u^3}$   Since $u^4 du = \frac{u^{-4+1}}{-4+1}=$ $\frac{u^{-3}}{-3}$  which evaluating gives:  $1=\frac{k}{\frac{-1}{3(1+x)^3}} \vert_0^{\infty} \to \frac{-3k}{(1+x)^3} \vert_0^{\infty} = 0 -3k$   and $k= \frac{-1}{3}$  somehow though they came up with $\frac{-k}{3} \frac{1}{(1+x)^3}$ after integrating $\int_0^{\infty} \frac{k}{(1+x)^3}$   Was my approach correct to use substitution? Where does my work go wrong? Overall reputation scores are headed nowhere but up.  Pretty soon there will be thousands of mods.  What to do?  Thoughts on possibilities:   Thousands of mods is fine.  Carry on. Adjust the threshold values for high-level SO privileges. Do a straight-up inflation adjustment.  You had x rep, then at the turn of the year we applied the Consumer Rep Index to all scores, now you have (x / inflation) rep. Implement a rep decay mechanism, so that inactivity sheds some of the overall rep that's built up. Which are the safety recommendations for soldering? Assume that $X$ and $Y$ are two random variables such that $Y=E[X|Y]$ almost surely and $X= E[Y|X]$ almost surely. Prove that $X=Y$ almost surely.   The hint I was given is to evaluate: $$E[X-Y;X&gt;a,Y\leq a] + E[X-Y;X\leq a,Y\leq a]$$  which I can write as: $$\int_A(X-Y)dP +\int_B(X-Y)dP$$ where $A=\{X&gt;a, Y\leq a\}$ and $B=\{X\leq a,Y\leq a\}$.  But I need some more hints. Can a non-EU citizen travel freely within the Schengen area without passport? My current situation is that I have residence permit of Germany (as a stamp in passport) and I wish to apply for UK visa in next few days from Germany and won't have my passport anymore during the processing time.  Instead of waiting for the process, I wish to travel to Scandinavian countries immediately on holidays, later receive my passport from visa center after I return back to Germany.   I am wondering if photocopy of passport and residence permit suffice as identity proof to border control (if I face them)? What else are valid documents that I can show as valid identity proof to border control? What are the exact problems I will face if I face the border control, and they are not satisfied with my travel documents? Phrase to give a non-detailed answer/explanation What expression could I use when giving non-detailed answers/explanations about how something works? Let's say I want to explain how a printer works without getting into too much detail, Would it be OK to say:   "At a very superficial level, a printer ...." "At a very high level, a printer ..."   I feel like there are more appropriate expressions to begin such type of sentence. Any help would be greatly appreciated. Filling only when one curve is below the other How can one have a mini table of contents for the current chapter appear just after the chapter name listing all sections of that chapter? Area of intersection between two circles Suppose you have 2 circles that intersect each other in such a way that each circle passes through the other's center. What is the area between the circle(or common area) i.e. area between the centres of the circles? Character reading from file in Python "wait more than" vs. "wait FOR more than" How to integrate $\int_0^{\infty} \frac{e^{ax} - e^{bx}}{(1 + e^{ax})(1+ e^{bx})}dx$ where $a,b > 0$. This  $$\ \int_0^{\infty} \frac{e^{ax} - e^{bx}}{(1 + e^{ax})(1+ e^{bx})}dx \text{ where } a,b &gt; 0. $$ is a problem that showed up on a GRE practice test. I believe you're supposed to use complex contour integration, but I'm not sure which contour to use. I think it's the keyhole contour, but I wasn't able to get anything useful.