I'm just a layman with no real science background  (a) I'm not really sure what a shadow is. Some people are saying that it's the absence of something (a photon?) and therefore it is not subject to laws of physics. But I know when I'm in a shadow and when in sunlight... that's "information", and I thought that information flow can't break the speed of light limit.  (b) Some others use the laser pointer/flicking wrist example to talk about laser dots moving faster than light speed. But that can't be right, can it? The photons from the laser point have to travel from A to B and (after wrist flick) from A to C ... but the photons are all moving at the speed of light - there's no law-breaking in moving the laser dot from point B to point C because the photons are moving either from A to B or A to C ... the distance from B to C is not material (is it?).  (c) Also, can a shadow be thought of as a gap in a photon flow? E.g. if I interrupt a beam of single photons then can I think of it as e.g. PPPSSSPPPSSSPPPSSSPPP, etc where P = photons and S(shadow) = no photon &amp;, if so, the "SSS" is effectively travelling at the speed of light ... no faster.
I have seen many folks doing this  concluding that shadow from point A on the Moon can travel to point B on the Moon faster than light.  What I fail to understand here (and I am sure I am wrong), is nothing can travel faster than light. I also read about Relativity where Einstein stated that every event happening for you depends on how fast the light gets from where the event is happening to you.  This is my particular problem with this Moon shadow experiment. You cannot make a shadow travel faster than light, because in order for the "disappearance" of light to get to the Moon, it has to travel at light speed.  Here is one way to understand my point. Consider we shine a flashlight on Moon, like the guy in the linked video did, we move the finger across the face of the flashlight, before we moved the finger it was casting the shadow at Point A on Moon, after we finish moving our finger, the shadow is at Point B on the Moon.  When the finger reaches the end of it's moving length, the light waves that have left the flashlight before the finger reached there will have to hit Point B and it will take them a second and a half to get there, and another second and half for us to see that shadow on point B, which makes it 3 seconds + finger moving time for us to actually see the shadow at point B. That means shadow traveled (say) across the diameter of the Moon in 3 seconds.   So. about 3000 Km in ~3 seconds make it 1000 Km per seconds which is very tiny compared to the speed of light. How can these experiments conclude that Shadow could be made to travel faster than light? What is the obvious clue that I am missing here?
The problem statement is: for $a,b$ coprime, prove that there exists positive integers $x,y$ such that $ax-by=1$.  The question is form Arthur Egnels' problem solving text, and from the chapter on the pigeonhole principle.    My question: His proof begins by generating a list $a,\ldots,a(b-1)$, where he then points out that each element in this list(which proceeds sequentially) doesn't have remainder $0\pmod{b}$.  He then shows that we arrive at a contradiction if we assume that we also don't get remainder $1$ in this list $\bmod b$.  To show the contradiction in this last statement, he first states that we would have positive integers $p,q $ where $ 0&lt;p&lt;q&lt;b$ so that $pa\equiv qa \pmod{b}$.  He then goes on to point out that since we $a$ and $b$ are coprime, we then have that $b| q-p$.  I understand the last part here, but don't see why we get $pa\equiv qa \pmod{b}$.  Thanks in advance When can you build up all representations from the fundamental and antifundamental ones? Under what conditions can you determine all representations of a Lie algebra from the fundamental and antifundamental ones using just the tensor product, direct sum and Clebsch-Gordan decomposition? I think this is true for $\mathfrak{su}(2)$ and $\mathfrak{sl}(2,\mathbb{C})$, or at least that's what physics books lead me to believe!   Is it true in general for semisimple Lie algebras? If I would show someone a yellow object and ask them, "is this object yellow?" That person would say "yes".  But I could never know if my perception of the color yellow is the same as that other person's. Because he or she could actually be seeing, what I know to be the color green. But then tells me that its the color yellow because that has been taught to him or her from young age.  So how can you test if people are really seeing the same color?  Question closed and can now be found @ How to compute PCA scores from eigendecomposition of the covariance matrix? Given a data matrix $\mathbf X$ of $12 \times 7$ size with samples in rows and variables in columns, I have calculated centered data $\mathbf X_c$ by subtracting column means, and then computed covariance matrix as $\frac{1}{N-1} \mathbf X_c^\top \mathbf X_c$.  The dimensions of this covariance matrix are $7 \times 7$. After that I have calculated the eigenvalue decomposition, obtaining eigenvector matrix $\mathbf V$ with eigenvectors in columns.  Now I want to know about projections (i.e. principal component scores in PCA): is it $\mathbf{V}^\top \mathbf{X}_c$ or $\mathbf{X}_c \mathbf{V}$?  mean_matrix = X - repmat(mean(X),size(X,1),1); covariance = (transpose(mean_matrix) * mean_matrix)/(12-1);  [V,D] = eig(covariance); [e,i] = sort(diag(D), 'descend'); V_sorted = V(:,i); Suppose your git history looks like this:  1 2 3 4 5  1–5 are separate revisions. You need to remove 3 while still keeping 1, 2, 4 and 5. How can this be done?  Is there an efficient method when there are hundreds of revisions after the one to be deleted? This is a  about how Unix operating systems report memory usage.   Similar Questions:                    I have production server that is running Debian 6.0.6 Squeeze  #uname -a  Linux debsrv 2.6.32-5-xen-amd64 #1 SMP Sun Sep 23 13:49:30 UTC 2012 x86_64 GNU/Linux   Every day cron executes backup script as root:  #crontab -e  0 5 * * * /root/sites_backup.sh &gt; /dev/null 2&gt;&amp;1   #nano /root/sites_backup.sh  #!/bin/bash str=`date +%Y-%m-%d-%H-%M-%S` tar pzcf /home/backups/sites/mysite-$str.tar.gz /var/sites/mysite/public_html/www mysqldump -u mysite -pmypass mysite | gzip -9 &gt; /home/backups/sites/mysite-$str.sql.gz cd /home/backups/sites/ sha512sum mysite-$str* &gt; /home/backups/sites/mysite-$str.tar.gz.DIGESTS cd ~   Everything works perfectly, but I notice that Munin's memory graph shows increase of cache and buffers after backup.  Then I just download backup files and delete them. After deletion Munin's memory graph returns cache and buffers to the state that was before backup.  Here's Munin graph:  Externally hosted image was a dead link. How do I fix the GPG error "NO_PUBKEY"? I added some extra repositories with the Software Sources program. But when I reload the package database, I get an error like the following:     W: GPG error:  trusty InRelease: The following signatures couldn't be verified because the public key is not available: NO_PUBKEY 8BAF9A6F   I know I can fix it using apt-key in a terminal, according to the official Ubuntu documentation. But I would have liked to do it graphically. Is there a way to do this without using a terminal? How do I add a Pokestop to an area that has none? It is an area where there are tons of businesses but unless I drive about a mile from my work area there are no Pokestops.   I want to add one since we have 1000's of people in the work area, a lot of them play Pokemon Go, and we all can't leave work to drive a mile away to get to a Pokestop area.   Plus it would be nice to be able to capture Pokemon on our breaks. Prospective PhD contacts potential supervisor but receives no answer after 2-3 emails, what to do? Say a prospective PhD has a high reply rate (90-95%) to first contact emails with potential superviors. He/She has a well thought out e-mail, but a particular professor (here: USA) that is in the top preferences does not reply after two to three e-mails that were sent within a time frame of three months. I also followed the instructions on the professor personal website in the section "prospective PhD students". The student has already contacted some of the advisor students and has received positive feedback about the professor.  Should the student just give up and move on? Should the student keep trying?  Aside from the obvious "I have too many incoming e-mails to answer" or "I am out in the field", what could create a no response behavior from the professor?  I have seen the simplistic answer "move on, bad advisor, doesn't have time, etc". But this seems a contradiction in this case. The PhD students like the professor and say he/she is personable and no e-mail response after a few well written emails. My reputation suddenly raised by 10k! How do you pass a function as a parameter in C? I want to create a function that performs a function passed by parameter on a set of data. How do you pass a function as a parameter in C? I am working to build a reinforcement agent with DQN. The agent would be able to place buy and sell orders for a day trading purpose. I am facing a little problem with that project. The question is "how to tell the agent to maximize the profit and avoid the transaction where the profit is less than 100$".  I want to maximize the profit inside a trading day and avoid to place the pair (limit buy order, limit sell order) if the profit on that transaction is less than 100$. The idea here is to avoid the little noisy movements. Instead, I prefer long beautiful profitable movements. Be aware that I thought using the "Profit &amp; Loss" as the reward.  "I want the minimal profit per transaction to be 100$" ==> It seems this is not something that is enforceable. I can train the agent to maximize profit per transaction, but how that profit is cannot be ensured.  At the beginning, I wanted to tell the agent, if the profit of a transaction is 50 dollars, I will remove 100 dollars, then It becomes a penalty of 50 dollars for the agent. I thought it was a great way to tell the agent to not place a limit buy order if you are not sure it will give us a minimal profit of 100$. It seems that all I would be doing there is simply shifting the value of the reward. The agent only cares about maximizing the sum of rewards and not taking care of individual transactions.   How to tell the agent to maximize the profit and avoid the transaction where the profit is less than 100$? With that strategy, what guarantee that the agent will never make a buy/sell decision that results in less than 100 dollars profit? Does the sum of reward - # transaction * 100 can be a solution? Is there a difference in disenchanting strong items vs. weak ones? Possible Duplicate:           states that the strength of the enchantment doesn't matter when disenchanting items to learn new enchantments.  Am I reading that right? If I have novice robes with 50% faster regen and disenchant it and my enchantment skill is at 5/5, when I enchant that item will it be the same result as disenchanting master robes with 150% faster regen? Because if you do the math, 5/5 enchanting will give you 100% better enchantment.   Therefore wouldn't it be better to disenchant more powerful items than weaker ones? I have a particular situation here, In March of 1997 I travelled to the US as a tourist and lived there illegally for almost 9 years. I was never arrested, or had any trouble with the law, I was never deported. I paid my taxed (had a TFN) had a job, bank account bought a house, etc. About 9 years ago I decided to leave as I was tired of living like that, not able to be legal, in fear of deportation and loosing everything. I also got married (to a person in the exact situation as me) we were able to legally migrate to Australia and now we are Australian citizens. We never returned our I-94s and in 2005 left through Mexico (walked through the border) so there are no records of us ever leaving. We have lived here in Australia for over 9 years.  OK so my question is... We have been thinking we would like to visit our friends and family back in the US now that we have a little girl. Is there any chance they won't let us in because they know we overstayed? We would be travelling with our Australian passports. A few years ago I saw a scifi movie about a group of travelers stranded at what I believe might have been a bus station (I don't remember that detail with any certainty).  There were 2 children (a boy and a girl) who were running around and everyone thought they belonged to someone else there.  As it turned out, the children were aliens that reverted to their true form and began hunting down the travelers.  I've been searching all over the internet but can't come up with the name of the movie.  Does anyone know the name of it? Should I put myself last? "me and my friends" vs. "my friends and me" or "my friends and I" How many nonnegative integer solutions are there to the pair of equations  \begin{align}x_1+x_2+\dots +x_6&amp;=20  \\ x_1+x_2+x_3&amp;=7\end{align}  How do you find  non-negative integer solutions? Inequality: $x^2+y^2+xy\ge 0$ I want to prove that $x^2+y^2+xy\ge 0$ for all $x,y\in \mathbb{R}$.  My "proof":  Suppose wlog that $x\ge y$, so $x^2\cdot x\ge x^2\cdot y\ge y^2\cdot y=y^3$ (because $x^2\ge 0$ so we can multiply both sides by it without changing the inequality sign) giving $x^3\ge y^3$. Substracting we have $x^3-y^3\ge 0$ or $(x-y)(x^2+xy+y^2)\ge 0$. Since $x\ge y$ we can divide by $x-y$ to get $x^2+xy+y^2\ge 0$.  Is it right?  Thanks for your help! Given 4 integers, $a, b, c, d > 0$, does $\frac{a}{b} < \frac{c}{d}$ imply $\frac{a}{b} < \frac{a+c}{b+d} < \frac{c}{d}$? We were trying to come up with an easy way to generate a rational number in between two existing rational numbers with a fairly low numerator and denominator (the way we were doing this earlier was to find the average of the two rationals, but that results in a denominator of up to $c * d$. Does this inequality hold for all values of $a, b, c, d$? Comparing currency values as floats does not work