Movie series show that Dr. Emmett Brown can adjust time machine to go a somewhat selectable/quantized time in future or past.  Especially "today but exactly N years ago" quote seems to be showing a calculation of earth orbit around sun so it doesn't pop out in space after the journey.  Question: what is giving that car, the power of computing of N years of earth orbit to make it "land" in the same XYZ space(and surface) coordinates, within just the time of acceleration from 0 to 88 mph (1 minute?)?    Earth is not only moving around sun, but its rotating too! Same XYZ coordinate may not be same after exact N years! I mean 1 year is not exact multiple of 1 day. And in N years, even earth rotation could change some milimeters per second. Add the gravity effect of unknown celectial bodies orbiting sun, it would be a lot harder to compute.   Even if its possible, what about people? Very lucky that not a single human was harmed after time travel landing. They could have killed some people with delorean car.  Maybe flux-capacitor is a super computing neural network that computes time-space travel trajectory such that it always lands on asphalt(or desert sands) at the same height?
Every time the DeLorean travels in time, it appears in the same place as the place it left. But that's the same place relative to the Earth's surface. In space-time terms, that point is constantly moving: the Earth rotates on its axis at a speed of one revolution per day, and moves around the Sun at a speed of one revolution per year (a roughly circular orbit with a radius of 93 million miles). The Sun is orbiting around the centre of our galaxy, pulling its planets with it, and our galaxy is moving relative to all other galaxies.  So if the DeLorean does not move in space in absolute terms, then a time-jump of even a few minutes would place it outside the Earth's atmosphere as the planet would have moved a few miles in that time. Therefore, to prevent this, the car's computer has to calculate the precise movement of the Earth (and Hill Valley) over the required interval travelled.  Two questions:   A computer powerful enough to do that kind of calculation probably couldn't have fitted into a car in 1985. So where did Doc get it from? If he could calculate the spatial displacement to remain in the same place on the Earth's surface that accurately, why couldn't he adjust those calculations to make the DeLorean appear wherever he wanted?
out file with multiple criteria in python? In WPF, what are the differences between the x:Name and Name attributes? I have an android phone to which i have plugged an earphones. So at the top of the phone, I get the headphone symbol which indicates that the earphone is connected (In other words, the circuit at the 3.5 mm jack is closed).   Then I cut the two earphones (transducers) from it, and still the headphone symbol shows. When I later cut this cable, below where it branches out, even then it shows circuit completion.   So my question is this:   How does the phone detect circuit completion at the 3.5 mm jack and thus trigger all sound and music to be directed through the 3.5mm jack? Fast way to find period-n points of a tent map? I need to find a period-3 orbit for a tent map defined by $$T(x)=\begin{cases}2x &amp; 0\le x\le0.5 \\[2ex] 2-2x &amp;0.5 &lt; x \le 1 \end{cases}$$  So, what is a fast and efficient way of finding it? I only know how to do it by guessing-and-checking. For example, I picked a random point, $x = \frac{2}{7}$ and found that $$T\left(\frac{2}{7}\right)=\frac{4}{7}\\[4ex]T\left(\frac{4}{7}\right)=\frac{6}{7}\\[4ex]T\left(\frac{6}{7}\right)=\frac{2}{7}$$ which is a period-3 orbit. Is there any better way of finding a period-3 orbit , more specifically, a period-3 point? How can I check if a directory exists in a Bash shell script? What command can be used to check if a directory exists or not, within a Bash shell script? Why does an overridden function in the derived class hide other overloads of the base class? Solving 4 Quadratic Simultaneous Equations Consider the equations:   $$\begin{cases} ab+c+d=3\\ bc+d+a=5\\ cd+a+b=2\\ da+c+b=6 \end{cases}$$   Where $a,b,c,d \in \mathbb{R}$. How can we find $a,b,c,d$?   The furthest I've got is by adding the first two equations and the last two equations together to get: $ab+bc+c+d+d+a=(b+1)(a+c)+2d=8$ and $(d+1)(a+c)+2b=8$ We can rearrange these (assuming $b,d \neq -1$) to get $$\frac{8-2d}{b+1}=\frac{8-2b}{d+1} \implies -d^{2}+3d+4=-b^{2}+3b+4$$ Which leads us further to $$b^{2}-d^{2}-3(b-d)=0 \implies (b-d)(b+d-3)=0$$ Now since $b=d$ gives us an absurdity (equations 1 and 4 reduce to 3=6), we must have $b+d=3$. This is as far as I can get unfortunately, since trying the same approach with the other pairs doesn't work in the same way.  Help would be much appreciated; the problem is from the BMO1 2004 paper. How can I maintain open ssh connection and use it from shell scripts? Currently i invoke the following:  $ ssh me@host.com my_cmd   This is slow and not easy to automate safely. I would like to establish ssh connection once and have some script that will forward my commands to host.com and print output.  Is that possible ?  Adding my machine to authorized_keys is not an option for me and it wouldn't solve slowness issue. Schadenfreude is the joy or pleasure derived from the misfortunes of others. What is the word for joy or pleasure derived from the happiness of others? I've installed reCAPTCHA module but spam still bypass my security and leave nasty comments. What should I do? How to block them? Is it possible to to take a screenshot of a webpage with JavaScript and then submit that back to the server?  I'm not so concerned with browser security issues. etc. as the implementation would be for . But is it possible? I read it in English in the United States, somewhere in the 1990s. I got it off of the big bookshelf in our family room, which means it could be a good bit older; some of the books were my Dad's. At the beginning, a young boy (maybe an early teen?) leaves his house, where he lives with his parent or parents, and takes a test to become a spaceship pilot for the military. Part of the test judges reaction speed, and he fails the test. He later learns (I think when he's approached by an agent of the government) that he "failed" because he has some sort of enhanced fortune that meant that he was actually giving the results before they could be displayed on the screen. At the time, I remember thinking that the book felt a bit like a Star Wars rip-off.  Years later, I read that one of the Star Wars books (probably now Legends) had Luke similarly failing the Imperial Academy test because he gave his answers too quickly, and it amused me that I was uncertain as to which had come first.  I don't remember anything concrete about the cover, although I have a general impression that it was white. Definitely futuristic. My impression was that the boy was wearing a white uniform for the testing and that the government agent who spoke to him had a grey beard, but I might be mixing bits of Star Wars in there. Intuition behind logistic regression Recently I began studying machine learning, however I failed to grasp the intuition behind .   The following are the facts about logistic regression that I understand.   As the basis for hypothesis we use . I do understand why it's a correct choice, however why it's the only choice I don't understand. Hypothesis represents the probability that the appropriate output is $1$, therefore the domain of our function should be $[0,1]$, this is the only property of sigmoid function I found useful and appropriate here, however many functions satisfy this property. In addition, sigmoid function has a derivative in this form $f(x)(1-f(x))$, but I don't see the utility of this special form in logistic regression.   Question: what so special about sigmoid function, and why we cannot use any other function with domain $[0,1]$? The cost function consists of two parameters ${\rm Cost}(h_{\theta}(x),y)=-\log(h_{\theta}(x))$ if $y=1, {\rm Cost}(h_{\theta}(x),y)=-\log(1-h_{\theta}(x))$ if $y=0$. In the same was as above, I do understand why it's correct, however why is it the only form? For example, why couldn't $|h_{\theta(x)}-y|$ be a good choice for the cost function?  Question: what is so special about the above form of cost function; why cannot we use another form?   I would appreciate if you could share your understanding of logistic regression. Could the change from an edit be displayed in a side-by-side display What tool do you use to monitor your servers? Should I mention my Canadian visa refusal in my UK visa application? How to access object properties containing special characters? book recommendation on functional analysis Find the subgroups of A4 I had a question I was hoping for some help on:     Find all of the subgroups of $A_4$   Here is what I know:  $A_4$ is the alternating group on 4 letters. That is it is the set of all even permutations. The elements are:  $(1), (12)(34), (13)(24), (14)(23), (123), (132), (124), (142), (134), (143), (234), (243)$   which totals to 12 elements. Which means, the subgroups should have order 1,2,3,4,6 and 12. The groups of order 1 and order 12 are trivial. I also know the groups of order 2 which are:  $[1,(12)(34)], [1, (13)(24)], [1, (14)(23)]$  but would someone be able to help me find the subgroups of order 3, 4 and 6 and be able to provide a good, easy explanation of how you got to them for me? I'm pretty sure there is no such groups of order 6, but I don't know how to explain why.  Thank you so much for your help in advance, I really appreciate it! How do I test a nonlinear association? For plot 1, I can test the association between x and y by doing a simple correlation.   For plot 2, where the relationship is nonlinear yet there is a clear relation between x and y, how can I test the association and label its nature?