It's unclear from "A Song of Ice and Fire" (AKA Game of Thrones), at least from what I remember, if the world is flat or round. Westeros is at the west of the "known world" - but if you kept going west, what would you find? Would you end up at the other side, like in our world?
For quite some time now I have been asking myself how the world of Game of Thrones is shaped and if the people living in that world know the shape.   In questions here on SciFi.Stackexchange concerning the unnatural seasons or the definition of a year in Westeros, it is often  that the Westerosi can measure the duration of a revolution of their planet around the sun. But that only works if they know that they actually live on a planet.   In  answer it was said that people have been travelling in ships around the world. However, I cannot remember any passage in the books supporting this. Actually I only remember evidence for the opposite:    During the  on the Iron Islands, there is a man called  who promises the Ironborn treasures from lands far to the west, if they elect him as king. However, the POV character of that chapter (I think it was Victarion Greyjoy) does not believe him and sees the madness in Gylbert's eyes - as if speaking of travelling west is crazy.  Later when he leads the attack against the Shield Islands, the Iron Fleet travels out of sight of the coast line. This manoeuvre is considered very dangerous and risky. If this is already dangerous, traveling even further west appears close to suicide.   In addition, there was a  who sailed to the far west and never returned.   establishes that the world is not a hollow world, but is not conclusive as to whether it is a planet.  Is there any evidence in the books that the World of Ice and Fire is a planet? Was it established that the Westerosi know the nature of their world?
Proof concerning Stirling numbers of the first kind How do I show that   $${ n\brack 2} = \frac{n!}{2} \sum_{m=1}^{n-1} \frac{1}{m(n-m)}$$  using a combinatorial argument?  My definition of ${n \brack 2}$ is "the number of elements of $S_n$ which can be decomposed as the product of exactly $2$ disjoint cycles". Where does gravitational waves' energy go? I was naively validating my binomial logit models by testing on a test dataset. I had randomly divided the available data (~2000 rows) into training (~1500) and validation (~500) datasets.   I now read a post in another thread ( Frank Harrell) that causes me to question my approach:     Data splitting is not very reliable unless you have more than 15,000   observations. In other words, if you split the data again, accuracy   indexes will vary too much from what you obtained with the first   split.   How serious is this worry and what are ways around it? The OP speaks of "resampling" but not sure how that works here for validation.   Edit: Adding context as per @Bernhard's comment below: Where can I ask a question about finding general software that meets certain requirements? I have a list of requirements for a program, but I don't know what program meets these criteria. That's about general-purpose software, for example, not a programming IDE or statistical workbench, questions about which would certainly go to respective sites.  Is this question appropriate on Stack Overflow? Where should I ask about it? On Super User or elsewhere? How to open a serial port by friendly name? What is mirror lockup and what is its primary function? My SLR is equipped with the mirror lockup function. What does it do, and when would I employ such a feature? Lucia is gone. Just gone Skyrim problem here. I've finally found a house mod that will support a family (as in allow them to move there). I'm excited to install it, but it says that a new save game is highly recommended unless you haven't adopted any kids yet.   I recently adopted Lucia. I have two saves in my game, a quick and a full. I know that the full save has Lucia as adopted, but I'm not sure if the quick does. If it does not, then my reasoning is that I can install the mod and load that save, rather than having to work all the way back through eighteen levels.   And here's the problem. I loaded the quick save and searched for Lucia, in an attempt to see if she was adopted or not. She is nowhere to be found. She is not sitting under the tree in the middle of Whiterun, she is not in Breezehome, and she is not in the inn.   I tried to use console commands. both the moveto and placeatme commands do not work. I used both the refid and the baseid. Neither worked. I used help Lucia, thinking maybe the wiki was wrong on her ID. it gave me a different ID, which also didn't work. Every time, the console says either that it can't find the objectbaseid, or that the id is invalid.   This has led me to the conclusion that Lucia has been entirely erased from the game's memory, and I KNOW that hasn't happened. Can someone tell me what is going on?   Additional details: I am using a Breezehome overhaul mod. When I adopted Lucia, she moved in perfectly with no trouble though, so I can't really see how that would be the problem. Scattering, Perturbation and asymptotic states in LSZ reduction formula I was following Schwarz's book on quantum field theory. There he defines the asymptotic momentum eigenstates $|i\rangle\equiv |k_1 k_2\rangle$ and $|f\rangle\equiv |k_3 k_4\rangle$ in the S-matrix element $\langle f|S|i\rangle$ as the eigenstates of the full Hamiltonian i.e., $H=H_0+H_{int}$. Therefore, the states $|i\rangle=|k_1 k_2\rangle$ is defined as $$|k_1 k_2\rangle=a_{k_1}^{\dagger}(-\infty) a_{k_2}^{\dagger}(-\infty)|\Omega\rangle$$ where $|\Omega\rangle$ is the vacuum of the full interacting theory. Then the LSZ reduction formula connects the S-matrix element $\langle f|S|i\rangle$ to the Green' functions of the interaction theory defined as $$G^{(n)}(x_1,x_2,...x_n)=\langle \Omega|T[\phi(x_1)\phi(x_2)...\phi(x_n)]|\Omega\rangle.$$ Here are a few doubts. Doubt 1 When the particles are far away, the interaction can be considered to be adiabatically switched off. Therefore, at $t=\pm\infty$ the states are really free particle states and should have been written as $$|k_1 k_2\rangle=a_{k_1}^{\dagger}(-\infty) a_{k_2}^{\dagger}(-\infty)|0\rangle$$ and $$|k_3 k_4\rangle=a_{k_3}^{\dagger}(+\infty) a_{k_4}^{\dagger}(+\infty)|0\rangle$$ where $|0\rangle$ is the vacuum of the free theory.  I do not understand why these the states $|i\rangle$ and $|f\rangle$ are derived from $|\Omega\rangle$ instead of $|0\rangle$. Doubt 2 The initial and final states were derived from the vacuum of the interacting theory $|\Omega\rangle$. According to my understanding, this suggests that the states $|i\rangle\equiv |k_1 k_2\rangle$ and $|f\rangle\equiv |k_3 k_4\rangle$  are eigenstates of the full Hamiltonian $H$. Since then there is no perturbation, there should not be any scattering or transition at all.  More references Even Peskin &amp; Schroeder, Bjorken &amp; Drell, Srednicki take the same approach as Schwartz; they too define the external momentum eigenstates to the eigenstate of the full Hamiltonian $H$. However, if the system was initially in a stationary state why should it undergo a transition in absence of any perturbation? What is the plural form of "Software"? Is it correct to use softwares, as in the following sentence?  There are various video conversion softwares in the market. What is model identifiability? I know that with a model that is not identifiable the data can be said to be generated by multiple different assignments to the model parameters. I know that sometimes it's possible to constrain parameters so that all are identifiable, as in the example in Cassella &amp; Berger 2nd ed, section 11.2.  Given a particular model, how can I evaluate whether or not it's identifiable? How to parse a query string into a NameValueCollection in .NET I would like to parse a string such as p1=6&amp;p2=7&amp;p3=8 into a NameValueCollection.  What is the most elegant way of doing this when you don't have access to the Page.Request object? Completion of rational numbers via Cauchy sequences Can anyone recommend a good self-contained reference for completion of rationals to get reals using Cauchy sequences? How can I improve framerate of Minecraft client? Is it possible to induce Mathematica to chop off parts of Graphics objects that exist outside of a Frame? Why do we need to use:  extern "C" { #include &lt;foo.h&gt; }   Specifically:     When should we use it? What is happening at the compiler/linker level that requires us to use it?   How in terms of compilation/linking does this solve the problems which require us to use it? How can I remove excess fat from stews or soups without refrigerating? Due to my ignorance, I find that most of the references for mathematical analysis (real analysis or advanced calculus) I have read do not talk much about the "multivariate calculus". After dealing with the single variable calculus theoretically, it usually directly goes to the topic of measure theory.    After reading the wiki article "", I'd like to find the rigorous proof for this test. The first book comes to my mind is Courant's Introduction to Calculus and Analysis which includes the multivariate case in the second volume.   Motivated by this, I'd like to put the question here:     What are the usual references for the   theoretical treatment for   ? Writing basic systemd service files I would like to revise the default new user registration form in Drupal 7. Rather than to requst "username", I want to request "full name" with helper instructions to enter the text "username is your full name as you would normally use it."  There may be some other minor formatting changes I would like to make as well.  I cannot find an admin menu item to access anything relating to this question. And I am unable to locate a file within any director that has any text that would indicate it is the source for the new user registration form.  I realize this is a bit unconventional, however it is useful for our needs. I am aware of a module that allows the input of First Name / Last Name, but in processing it changes the input to first initial/lastname, ie Tom Thumb = username of "tthumb". The module "Realname Registration" would be just what I am looking for if it would only translate the username the same as the input.   That wouldn't necessarily solve the other formatting edits, but I would be very happy just to be able to manually edit the registration form help text under the username field, instructing the new user to register using thier real name.  Thanks for any help that you can provide.  J.M. How to export and import mysql database with its data using php script?