Specifically, why would some say that the time experienced for those on Earth would be far greater than the time for light to travel to the destination and back. Example, I have heard it said that if you travel to Alpha Centauri and back at the speed of light, far more than 10 years will have passed on Earth than what it takes for light to travel there and back. Here is my thinking on this when considering the speed of light time dilation versus actual distance traveled. The speed at which I am traveling at means that I experience time far slower. So if I were to adjust my space ship's experienced travel time to compensate for this time dilation, then I could experience travel to say Alpha Centauri in seconds for me. Even though the actual time it took, relative to Earth, would be about 4.5 years. If that is the case, then all of these concerns about travelling at relativistic speeds should theoretically be moot. Yes, that means in a round trip to and from Alpha Centauri for the study of the stellar system it would take almost 10 years to those on Earth. But for those on the flight, it should take what I would think is seconds plus time spent in the system doing the study. All the arguments I see center around the idea of traveling those distances over the duration of time as experienced by the traveler. Thus, when I hear people such as Neal DeGrasse Tyson talking about traveling 4.5 light-years, it always sounds like he is saying that the traveler experiences the passage of time as 4.5 years while moving at relativistic speeds. Thus the problem for the traveler is that going there and coming back while experiencing those years means far more time has passed here on Earth. But if you are traveling at those speeds and those speeds slow the passage of time from your perspective, then you shouldn't be traveling for 4.5 years from your perspective because you would severely overshoot your target. Instead, you should calculate how much time would pass from your perspective in order to travel 4.5 light-years, which I imagine would be experienced in seconds or possibly minutes. Then travel for that long from your perspective to reach your target area. Is that correct or am I fundamentally missing something about time dilation and traveling at relativistic speeds?
Suppose I wanted to travel to one of the recently discovered potentially Earth-like planets such as Kepler 186f that is 490 light years away. Assuming I had a powerful rocket and enough fuel, how long would it take me?
Counting the number of surjections. What is the CVE-2014-6271 bash vulnerability (Shellshock) and how do I fix it? Recently, there have been news going around regarding "CVE-2014-6271" (See ), which is a vulnerability in Bash. How do I know if I am affected by this, how can I fix it, and why should I care?  This is designed as a canonical answer for this vulnerability, due to its scope and severity. "If $1/a + 1/b = 1 /c$ where $a, b, c$ are positive integers with no common factor, $(a + b)$ is the square of an integer" If $1/a  +  1/b  =  1 /c$   where $a, b, c$ are positive integers with no common factor, $(a + b)$ is the square of an integer.  I found this question in RMO 1992 paper !  Can anyone help me to prove this ?  May be it's too easy and simple . But , I'm just novice in number theory ! I just browsed through this wonderful book: . The irony is, I am still not able to understand the motivation for using multivariate (regression) models instead of separate univariate (regression) models. I went through stats.statexchange posts  and  that explain (a) difference between multiple and multivariate regression and (b) interpretation of multivariate regression results, but I am not able to tweak out the use of multivariate statistical models from all the information I get online about them.   My questions are:   Why do we need multivariate regression? What is the advantage of considering outcomes simultaneously rather than individually, in order to draw inferences. When to use multivariate models and when to use multiple univariate models (for multiple outcomes).  Take an example given in the  with three outcomes: locus of control, self-concept, and motivation. With respect to 1. and 2., can we compare the analysis when we do three univariate multiple regression versus one multivariate multiple regression? How to justify one over another? I haven't come across many scholarly papers that utilize multivariate statistical models. Is this because of the multivariate normality assumption, the complexity of model fitting/interpretation or any other specific reason? Questions with no close votes appearing in the close vote queue? I've just been offered the wonderful opportunity to review .        ... but on closer inspection ?        Is this  (e.g I'm assuming this post did previous have a close vote, but has now aged away in ways I don't understand), or should questions with no active close votes be removed from the queue.  p.s. If it's , please expect my  asking for this not to be the case ;). Write this equation I want to write this equation in this way down but I have been unsuccessful. How can I improve this codes in order to get the equation below?  \[ DeltaC{t} = \left\{ \begin{array}{ll}  -1.40- 0.588w_{t-1} - 0.5351\DeltaC_{t-1}+ 0.169\DeltaBC_{t-1} &amp; \mbox{ if $w_{t-1}&lt;- 0.62$} \\ -1.40 - 0.588w_{t-1} - 0.5351\DeltaC_{t-1} + 0.169\DeltaBC_{t-1} &amp; \mbox{$w_{t-1}&gt;0.62$} \end{array} \right. \] What do you call someone that believes he is the only living being? What do you call someone that believes he is actually the only living being and that everyone and everything that exist (besides him self) is a state of his own mind? I am not referring to a What is the difference between "meet" and "meet with"?  For example, which of these should I say?        I met my boss yesterday    I met with my boss yesterday   I'm meeting my friends tonight    I'm meeting with my friends tonight Evaluating $\lim\limits_{n\to\infty}(a_1^n+\dots+a_k^n)^{1\over n}$ where $a_1 \ge \cdots\ge a_k \ge 0$ Need to find $\lim\limits_{n\to\infty}(a_1^n+\dots+a_k^n)^{1\over n}$ Where $a_1\ge\dots\ge a_k\ge 0$  I thought about Cauchy Theorem on limit $\lim\limits_{n\to\infty}\dfrac{a_1+\dots+a_n}{n}=\lim a_n$ and something like what happen if all $a_i=0$ or $a_1=\dots=a_k$, but may be something I am thinking wrong?  Maybe it is too simple but I am not getting it; please help. Formula between wire size and current Is there a mathematical formula between wire size, current, temperature and wire type(Or resistance)? Is there a word to describe indecisiveness between two things? Possible Duplicate:          Is there a word to describe indecisiveness, specifically between two things? I tried online dictionaries, but did not find anything. apt-get update, unlinking Characterizing all mobius transformations from unit disk to itself. All answers to this problem involve the following process:   Pick a point $a$ in the unit disk such that $T(a)=0$. Then, $T(a^*)=\infty$ if $a^*$ is the symmetric point $a^*=\frac{1}{\bar{a}}$ of a. Clearly, such a transformation is of the form $T(z)=\frac{z-a}{1-z\bar{a}}$. We might as well place a constant C in there: $T(z)=C\frac{z-a}{1-z\bar{a}}$. Then, most answers magically jump to replacing $C=e^{i\theta}$ in the formula and claiming the job is done.  Why does a function built so that it sends a point inside the unit disk to zero, and its symmetric point to $\infty$, be the one that preserves the unit disk? What's the motivation behind approaching this problem in that manner? Could one proceed bruteforce: with $|\frac{az+b}{cz+d}|&lt;1$ and arrive at the same function? For some reason this seems to me like somebody pulled a rabbit out of a hat. Once given the formula, I understand why it does the job, but why would somebody think that choosing a point inside the disk and building a function that sends it to zero create a mobius transformation that does the job? Where did the "Magic Blood" of the Harry Potter Universe Originate From? Are the Night's Watch still required? Triangular Numbers Modulo $k$ - Hit All Values? How to select faces by area I found this documentation:   Under "Face Selection Mode" it says:     Face Selection Mode:      ...        Area   Selects all faces that have a similar area as those already selected.   But I can't figure out where in blender this option is hiding? What is the difference between $* and $@? Is there a good way to determine the value of magic items in 5e? In 5e, magic items aren't as common or as varied as in older editions, but that also means it is hard to place prices on them.  As DM, NPC's can't really sell a magic item because we don't know the prices for these items. While it is stated that they are rare and usually unpurchasable and unsellable, but I still have to have some basis on what to price them.  So is there a way to find buying and selling prices for magic items in 5e? $\mathbb R$ has the same cardinality of any interval