as you can see Ive conducted the young experiment with these tiny tiny holes you can see in the pics but get no result again. why ? I asked and your answer was about the size of slit but these slits are not big so where is the final problem ?
My Young's slits experiment doesn’t work. I mean I tried to see wave effect of light but I didn’t see any thing expect particles! I’ve sent you a pic of my laser and a short video of the experiment. Is there any problem you think?
Can I use Divine Intervention or Wish to regain Wish? After reading this question on , I started wondering if there are ways for them to regain that ability.  I figured a Divine Intervention is probably strong enough as that is a god's power, as well as a second caster casting wish to undo the first wish (and thereby undoing its effects).  Are these valid ways of regaining the ability to cast wish? How to use Launchctl for schedule application I try to work with Launchctl and have a question:  How can I set up an application to run in a few minutes using Launchctl? (for example, open the program MyApp.app with arguments "hello" "world" Every 10 minutes)  I know that it can easily be done by creating Launch Agent, I looking for a way to do it using Launchctl directly to programmatically. bash: syntax error near unexpected token `}' I tried using this:  $ if [$a == 1] then { echo 'yes'; } fi;   but I get an error:  -bash: syntax error near unexpected token `}'   What is the correct format?  I tried several with no luck. How to justify $\phi(n) \ge \sqrt{n}$ If $\phi(n)$ is the Euler-totient function, how can I show that $\phi(n) \ge \sqrt{n}$? Does the proof of Bolzano-Weierstrass theorem require axiom of choice? When selecting the terms of subsequence from each bisections, I thought axiom of choice might be required. But I'm not so sure whether or not, so please tell me. [edited] I'm sorry for the lack of explanation. I want to prove this statement: Let $a_1, a_2, \ldots \in \mathbf{R}$, and $(a_n)_{n\in\mathbf{N}}$ is bounded, then $(a_n)$ has some convergent subsequence.  The proof is as follows. Since $(a_n)$ is bounded, for all $n\in\mathbf{N}$,   $a_n \in I = [b, c]$.  Now, let $I_0 = I$ and if $I_n = [b_n, c_n]$,  we define $d_n = (b_n+c_n)/2$ and  if infinite terms of $(a_n)$ is included in $[b_n, d_n]$(resp. $[d_n, c_n]$), we will define  $I_{n+1} = [b_n, d_n]$(resp. $[d_n, c_n]$).If both intervals contain infinite terms, let $I_{n+1}$ be $[d_n, c_n]$. For all $n\in \mathbf{N}$, infinite numbers of $m \in \mathbf{N}$ exist such that $a_m \in I_n$ suffices. We take the sequence of natural numbers $(n(k))_{k\in\mathbf{N}}$which suffices $n(0) &lt; n(1) &lt; \cdots &lt; n(k) &lt; \cdots$ following this procedure: Now we have already selected $a_{n(1)}, \ldots, a_{n(k)}$, there are infinite numbers of $m\in \mathbf{N}$ which suffices $n(k)&lt;m, a_m \in I_{k+1}$, so let's take the minimum m out of it. Applying this process recursively, we obtain a infinite convergent subsequence(?). I think intuitively, by only repeating this process we can't obtain countable infinite terms of subsequence because we have to repeat infinite times. Many econometrics textbooks (e.g. Wooldridge, "Econometric analysis...") simply write something similar to: "If the population model is $y = xB + u$ and (1) $\text{Cov}(X,U) = 0$; (2) $X'X$ is full rank, then OLS consistently estimate parameters $B$". I've worked out the math behind consistency but I'm a bit lost in interpreting the meaning.  We're talking about consistent estimation, but estimation of what? Please tell me if the following points are correct:   If we have random sample $X,Y$ and $X'X$ is invertible, then we can always define Best Linear Predictor of $y$ given $x$. And then OLS always consistently estimates coefficients of Best Linear Predictor (because in BLP we have $\text{Cov}(u,x)=0$ from the definition). Bottom line: we can always interpret OLS estimates as coefficients of BLP The only question is whether BLP corresponds to conditional expectation $\text{E}(y|x)$. If it does (for which we need $\text{E}(u|x) = 0$), then we can interpret OLS estimates as partial effects.   What is wrong with this or what am I missing? I don't get the point of stating the assumption of $\text{Cov}(u,x) = 0$, if this assumption is by definition fulfilled in case of Best Linear Predictor. And if we want to give structural interpretation to BLP coefficients (partial effects) we need stronger assumption of $\text{E}(u|x) = 0$ anyway. Is there any other interpretation we may have with zero covariance? Sometimes a suggested edit is  because of a concurrent direct edit that takes precedence.  Since this is no fault of the edit suggestor, such rejections should not count against the suggestor when counting .  Here are some examples where it happened: Tangent lines to ellipse from external point When and where does Attack on Titan take place? Is the setting of "Attack on Titan" (Shingeki no kyojin) supposed to be Earth in the distant future and Titans suddenly appeared out of nowhere and devolved society to medieval level of technology? Or is this just a completely fictional setting? St. Matthew's vs. St. Matthew There are two schools of thought on how to best extend, enhance, and reuse code in an object-oriented system:   Inheritance: extend the functionality of a class by creating a subclass. Override superclass members in the subclasses to provide new functionality. Make methods abstract/virtual to force subclasses to "fill-in-the-blanks" when the superclass wants a particular interface but is agnostic about its implementation. Aggregation: create new functionality by taking other classes and combining them into a new class. Attach an common interface to this new class for interoperability with other code.   What are the benefits, costs, and consequences of each? Are there other alternatives?  I see this debate come up on a regular basis, but I don't think it's been asked on  Stack Overflow yet (though there is some related discussion). There's also a surprising lack of good Google results for it. birthday problem - expected number of collisions There are many descriptions of the "birthday problem" on this site — the problem of finding the probability that in a group of $n$ people there will be any (= at least 2) sharing a birthday.  I am wondering how to find instead the expected number of people sharing a birthday in a group of $n$ people. I remember that expectation means the weighted sum of the probabilities of each outcome:  $$E[X]=\sum_{i=0}^{n-1}x_ip_i$$  And here $x$ must mean the number of collisions involving $i+1$ people, which is $n\choose i$. All $n$ people born on different days means no collisions, $i=0$; two people born on the same day means $n$ collisions, $i=1$; all $n$ people born on the same day means $n$ collisions, $i=n-1$.  Since the probabilities of three or more people with the same birthday are vanishingly small compared to two people with the same birthday, and decreases faster than $x$ increases, is it correct to say that this expectation can be approximated by  $$E[X]\approx {n\choose 0}p_{no\ collisions}+{n\choose 1}p_{one\ collision}$$  This doesn't look right to me and I'd appreciate some guidance.    Sorry - edited to change ${n\choose 1}$ to ${n\choose 0}$ in second equation. Sloppy of me. I have a quick question about buttons that toggle between two states. (Think Play/Pause, or Shuffle/Regular Play.) As the title says, should the toggle show it's current state or the state to which it will transition?  I think people are used to the Play/Pause convention. But the Shuffle/Regular play might be more confusing if you show the transition state instead of current. For example, the built-in music player on the Xbox 360 does it this way: when it's in shuffle mode, it shows the icon for direct play and vice versa and it always confuses me (am I in shuffle mode or straight play).  I see it this way: Play/Pause is more like action as in begin playing or pause playing. Yes behind the scenes it is a state transition but to the user, there is an action. Whereas Shuffle/Straight Play is an option and it's best to show the current state (and possibly have only one icon and change button to show that the option is enabled/disabled). Thoughts? When is mapping $g$ to $g^{-1}$ a group homomorphism? It just means that the map maps the identity to the identity and inverses to inverses. So does that mean it's only a homomorphism if the inverse is itself? What, precisely, is a confidence interval? So, I was just assaulted by a trio of fairly well armed thugs while walking out of Riften. Before attacking me, they informed me that they were 'here to teach me a lesson.'  After dispatching them in due course, I found this on the body of what I can only assume to be the leader, given his vastly superior armaments:   Orgnar is the innkeeper in Riverwood. Now, I admit, I've stolen a fair amount, but I pride myself on having never been caught. My total bounty to date is at zero. So, how did he figure out that I stole something, why is he taking the law into his own hands, and if I go back to Riverwood, am I going to get shanked? Yesterday I read Modern English:A Practical Reference Guide written by Marcella Frank, and she gives a paradigm about tenses on page 50. The page shows tenses in active voice and passive voice; she said these four tenses are exceedingly rare:   shall/will be being offered has/have been being offered had been being offered shall/will have been being offered   Why are these tense so rare? Are they normally replaced by other tenses? If my Schengen visa starts on the day of arrival which is one day ahead of departure, would they let me get into the plane? Choosing variables to include in a multiple linear regression model I am currently working to build a model using a multiple linear regression. After fiddling around with my model, I am unsure how to best determine which variables to keep and which to remove.  My model started with 10 predictors for the DV. When using all 10 predictors, four were considered significant. If I remove only some of the obviously-incorrect predictors, some of my predictors that were not initially significant become significant. Which leads me to my question: How does one go about determining which predictors to include in their model? It seemed to me you should run the model once with all predictors, remove those that are not significant, and then rerun. But if removing only some of those predictors makes others significant, I am left wondering if I am taking the wrong approach to all this.  I believe that  thread is similar to my question, but I am unsure I am interpreting the discussion correctly. Perhaps this is more of an experimental design topic, but maybe someone has some experience they can share. My local hackerspace has a CNC machine.  I can give them my Gerbers and they can print out the PCB.  The machine does not plate VIAs.  I need to do this after the CNC machine is finished.  What is the best process and materials to use?