"Algebraic indistinguishability" When people talk about Galois theory they often say that the basic idea behind it is that certain numbers are "algebraicaly indistinguishable".  I never really understood what this means in a way that doesn't make any reference to the concept of field automorphism.   So is there some intuitive way of looking at this?
What is the meaning of "algebraically indistinguishable" I heard the term couple of times (in Field theory class and book), for example: The different roots of $p(x)=x^3-2$ are "algebraically indistinguishable".  I understand the meaning intuitively, but what does it really mean ?
How to set static IP address? How do you make your own agar.io skins? I have noticed recently that people have their own skins. Not like the ones where you type in a specific nickname and it gives you a skin but where the people make their own. How do you do it? Can't access my home directory "Encrypted private directory is not setup properly" Hi I'm trying to access my home directory on my laptop hard drive through a live usb. I cannot boot into the OS on the hard drive and the home and root directory is encrypted. I have the encryption key but when I try to run the tool to gain access it pops up for a second then disappears and when I run the command in Terminal it says "Encrypted private directory is not setup properly". What are my options on getting into the directory? I really need to get the data off my laptop. How can I String.Format a TimeSpan object with a custom format in .NET? How do I assign a value to a whole array of integers? Is there any canon reference to the Mirror Universe Borg that would explain more about them?   I've tried searching on my own and haven't found anything. How do I pass variables and data from PHP to JavaScript? Implementing the decorator pattern in Python I'm a student who uses the laptop all the time and I have a problem with Wifi on the laptop. I don't really know what it is. I can describe the problem tho. For example, i closed my laptop last night, so it goes in suspend mode. I turn it on this morning and my wifi doesn't want to connect until I restart the laptop. It says that it's connecting and in Wifi settings the circle animation is spinning, turning Wifi off and on doesn't do anything. Here's what happens when I check to see my network info: sudo lshw -C network   *-network                         description: Wireless interface        product: Wireless 3160        vendor: Intel Corporation        physical id: 0        bus info: pci@0000:02:00.0        logical name: wlp2s0        version: 83        serial: 00:1e:64:e6:1c:93        width: 64 bits        clock: 33MHz        capabilities: pm msi pciexpress bus_master cap_list ethernet physical wireless        configuration: broadcast=yes driver=iwlwifi driverversion=5.4.0-52-generic firmware=17.3216344376.0 ip=192.168.0.14 latency=0 link=yes multicast=yes wireless=IEEE 802.11        resources: irq:129 memory:df100000-df101fff   *-network        description: Ethernet interface        product: RTL810xE PCI Express Fast Ethernet controller        vendor: Realtek Semiconductor Co., Ltd.        physical id: 0        bus info: pci@0000:03:00.0        logical name: enp3s0        version: 07        serial: f8:ca:b8:52:72:49        capacity: 100Mbit/s        width: 64 bits        clock: 33MHz        capabilities: pm msi pciexpress msix vpd bus_master cap_list ethernet physical tp mii 10bt 10bt-fd 100bt 100bt-fd autonegotiation        configuration: autonegotiation=on broadcast=yes driver=r8169 firmware=rtl8106e-1_0.0.1 06/29/12 latency=0 link=no multicast=yes port=MII        resources: irq:17 ioport:d000(size=256) memory:df000000-df000fff memory:d0000000-d0003fff  Also I have to mention that my Linux is doublebooted alongside Windows 10, but I don't think that makes any difference. Help would be much appreciated, I wouldn't want to miss my classes because of this hahah Thanks! When you tap a row in a UITableView, the row is highlighted and selected. Is it possible to disable this so tapping a row does nothing? What’s the correct URL for placing a call on an iPhone? "As a beginner, I am happy that I learned a new thing."  You will recognize this as your DoReMi-s.( at 4:52)  What is the meaning of the "AS" there and when do we use that?  In depth answers would be appreciated.  Similarly:     Do I have your word as a lawman not to shoot me down like a dog in the street?    Can you explain this sentence?   Can I understand it as a lawman wouldn't shoot down people on the street or wouldn't have his word or what? Obtain screen status using ADB What does the plus sign do in '+new Date' How to stop event propagation with inline onclick attribute? Consider the following:  &lt;div onclick="alert('you clicked the header')" class="header"&gt;   &lt;span onclick="alert('you clicked inside the header');"&gt;something inside the header&lt;/span&gt; &lt;/div&gt;   How can I make it so that when the user clicks the span, it does not fire the div's click event? Which algorithm does the JavaScript Array#sort() function use?  I understand that it can take all manner of arguments and functions to perform different kinds of sorts, I'm simply interested in which algorithm the vanilla sort uses. I am a little bit confused by early stopping and in particular by how it can be inserted inside a CV framework. As far as I understand, I can fix the optimal number of epochs (for NN, or number of trees for XGB) by early stopping, that is:   pick a validation set, train with increasing number of epochs until a predefined metric evaluated on the validation set starts worsening that is the optimal number of epochs to prevent overfitting   and that's fine. But then I would like to insert this early stopping framework inside a CV framework: Suppose I have a model with 10 hyperparameters I want to fix via CV. And suppose that there is an eleventh hyperparameter, the number of epochs. My feeling is that one can do like this:   create the K resampled folds, for each of which you have a training and validation set choose a suitable grid for your 10 hyperparameters for each point on the grid train your model in each fold with early stopping, that is use the validation set of the fold to keep track of the preferred metric and stop when it gets worse take the mean of the K validation metric choose the point of the grid (i.e. the set of hyperparameters) that gives the best metric   Questions:   What number of epochs should I choose as optimal? in each of the K folds I have, in general, a different number of stopping epochs.  seems to suggest they take the mean of the K stopping epochs. Is this right? Is it actually a "fair" practice to use the validation metric coming from the early stopping as a proxy of the out-of-sample metric? As  in section 3.4.5, maybe the best thing to do would be:     ...if you want to do early stopping, then in each fold you should take your training set and split it again, holding out a small early-stopping-set to guide the early stopping, and then evaluate the model on the validation set of that fold.   But this seems to me a really intricate process...   Unfortunately, I wasn't able to find references where this issue is presented in a clear and transparent form. The exchange of photons gives rise to the electromagnetic force Pardon me for my stubborn classical/semiclassical brain. But I bet I am not the only one finding such description confusing.  If EM force is caused by the exchange of photons, does that mean only when there are photons exchanged shall there be a force? To my knowledge, once charged particles are placed, the electromagnetic force is always there, uninterruptedly. According to such logic, there has to be a stream of infinite photons to build EM force, and there has to be no interval between one "exchange event" to another. A free light source from an EM field? The scenario is really hard to imagine.  For nuclei the scenario becomes even odder. The strong interaction between protons is caused by the exchange of massive pions. It sounds like the protons toss a stream of balls to one another to build an attractive force - and the balls should come from nothing.  Please correct me if I am wrong: the excitations of photons and pions all come from nothing. So there should be EM force and strong force everywhere, no matter what type of particles out there. Say, even electrical neutral, dipole-free particles can build EM force in-between. And I find no reason such exchanges of particles cannot happen in vacuum.   Hope there will be some decent firmware to refresh my classical brain with newer field language codes. There's a book I borrowed from my grade 8 teacher's lending shelf (in Ontario, Canada) that I've been trying to identify for years. The main character was a man in a futuristic setting who... I think... had the secret to an improved version of the lifespan-extension serum everyone used. If I remember correctly, the flawed version caused people's skin to turn clear over the course of their extended lives. I think he was revived from some sort of stasis, but I can't be sure of that. I just vaguely remember a &quot;stranger in a strange land&quot; sort of cultural disconnect, him being cared for in some kind of hospital-like setting, and a sense that maybe the formula they want from him was invented by a now-dead family member of his. The most distinctive detail I remember was the love interest, a cloned nurse named &quot;Eliza Tertia&quot; who he encourages to break out of her role. (All the cloned nurses were named Eliza, and I remember &quot;Eliza Duodecima&quot; being the name of another one who is briefly seen.) I also remember the secret eventually being gotten out of him, only for it to be discovered that it's flawed, in that, while it does replenish the compounds that go missing in extended old age, it doesn't moderate their production. I don't remember if it was long enough to be a novel or if it was just a novella. My vague memories of the cover design and material suggest it was a 1970s printing or earlier, which would also fit with what I remember of the story's atmosphere. Is it a good practice to refer to countries, ships etc using the feminine form?