In Einstein's General Relativity, do the space-time dimensions curve?

Question: In Einstein's General Relativity, do the space-time dimensions curve according to the positions of stars, planets, and masses?
Comment: The curvature is an effect that is ascribed to the spacetime as a whole - not to any one particular dimension of it. But yes, generically speaking, all the dimensions behave differently as compared to how they would behave in flat spacetime.
Comment: As I mentioned in my previous comment, there is nothing like the curvature in one particular dimension. We only talk about the curvature of the whole of spacetime at a particular point. So, it seems meaningless to ask whether all the dimensions curve in the same way or not. I am not an expert at differential geometry but at least in General Relativity, that is not how the things work. Maybe looking up something on Reimann Curvature might help you. That is the concept of curvature that we use in General Relativity.
Comment: According to GR, space-time does curve because of the massive objects (and because of energy and momenta, in general). Not sure what you mean by space-time 'dimensions' getting curved.
Comment: We have three spatial dimensions x1, x2, x3 and a fourth dimension x4.  Can all these dimensions curve in GR?
Comment: In the presence of mass, can the x dimension curve differently from the y or z dimension?  Or do all space time dimensions always curve in the exact same dimension?
Comment: So are you saying that close to a black hole, space time is equally curved in the x, y, and z dimensions?  So are you saying that the space time dimensions always curve in the exact same manner?
Comment: You write, "As I mentioned in my previous comment, there is nothing like the curvature in one particular dimension. " so are you saying that there are no distinct dimensions in general relativity?  Is this what Einstein stated?
Comment: I think its important for you to realize two things: 1) We don't think of spacetime as embedded in anything. I imagine the picture you have in your mind is of an elastic sheet of some sort with coordinate lines drawn on it being deformed by a mass sitting somewhere on it. If this were how GR was actually treated we would need to observe spacetime from outside of itself to actually say anything about it. This is not the case; all notions of "curvature" in GR are "intrinsic," meaning they can be deduced from making measurements from inside spacetime.
Comment: 2) Your choice of coordinate system is arbitrary. You're talking about a Cartesian coordinate system, which can be translated, rotated, and stretched along any of its axes while remaining a Cartesian coordinate system. But you need not even use Cartesian coordinates, its often profitable to use spherical coordinates. There also exist cylindrical, toroidal, and barycentric coordinates, for example. Whatever you choose, the only requirement is that you have 4 parameters in total. As has been mentioned, its never really relevant to ask how much an individual coordinate line is curving.
Answer: No, the dimensions do not curve. It's the metric that changes, and induces curves and bends in the spacetime geometry, and consequently the geodesics as well.
The Einstein's equation is $G_{\mu \nu} = 8 \pi G \ T_{\mu \nu}$. When you add mass/energy in an otherwise empty space, you are basically adding a nonzero energy momentum tensor $T_{\mu \nu}$. This nonzero $T_{\mu \nu}$ then dictates what $G_{\mu \nu}$ will be so that it solves the Einstein's equations. $G_{\mu \nu}$ is made up entirely of the metric tensor $g_{\mu \nu}$, so you get a solution for the metric tensor $g_{\mu \nu}$ in the presence of some $T_{\mu \nu}$.
$g_{\mu \nu}$ encodes the information on how distances are calculated in a general spacetime (flat or curved). In the presence of some nonzero $T_{\mu \nu}$, the resultant $g_{\mu \nu}$ will be different from the metric tensor in flat spacetime $\eta_{\mu \nu}$. As a result, the spacetime geometry gets distorted into some (non flat) shape.
Comment: @girlphysicsmajor Since the metric tensor $g_{\mu \nu}$ describes spacetime geometry, yes, spacetime 'curves'. The dimensions do not. What is your definition of spacetime dimensions 'curving'? Dimensions, quantified by coordinates, are just labels in a classical field theory like general relativity that pinpoint the location of events in spacetime. I don't understand what it means for dimensions to bend.
Comment: The Guardian is a newspaper. Newspapers and other similar forms of media typically 'explain' physics in very crude, misleading and probably even incorrect ways. If you want to learn physics, learn from a textbook. Misner T W's book is a classic and I suppose it's very good, though I've never studied from it. And no, coordinates don't change in the presence of mass. Why would they?
Comment: So are you saying that while the spacetime geometry curves, the spacetime dimensions do not? Are you saying that the x axis, representing the x axis, is always the exact same entity in GR, and that the coordinates never stretch nor curve?
Comment: You say that the dimensions do not curve?  Does spacetime curve?  Do the spacetime dimensions curve?  Does only space time curve, while the spacetime dimensions remain flat?
Comment: Are you saying that the spacetime dimensions provide a fixed background which can never bend nor curve?
Comment: So are you saying that the coordinates of the space time dimensions are fixed in an absolute manner and mass has no effect on them?
Comment: So are you saying that the space time dimensions curve, but the coordinates do not, and that all axis defining the space time dimensions are completely unaffected by mass?
Comment: As I said, I don't understand what you mean when you say that dimensions curve. Also, are you reading a textbook on relativity at the moment?
Comment: You write, "Dimensions, quantified by coordinates, are just labels in a classical field theory like general relativity that pinpoint the location of events in spacetime." So are you saying that the "labels" of the "coordinates" of an event are completely independent of all masses?  Are you saying that a black hole would have no effeect whatsoever on the "labels" of the "coordinates" of an event, and that said even would have the exact same "labels" of "coordinates" in the absence of a black hole?  Yes I am using Misner/Wheeler's book GRAVITATION.
Comment: This article states, "Einstein was right: space and time bend" https://www.theguardian.com/science/2007/apr/15/spaceexploration.universe  Are you saying that the space and time dimensions do not bend, and that Einstein was wrong?
Comment: The article "Epic study confirms Einstein on space-time vortex around Earth" states, "Einstein was right: There is a four-dimensional space-time vortex around Earth, and the spin of Earth does twist space-time.  In other words, according to Einstein, mass causes space-time to curve."  Are you saying that the space-time dimensions do not curve?  Are you saying that Einstein was wrong?
Comment: Dear @user4150, are you aware that mass bends the spacetime dimensions?  https://books.google.com/books?id=Iqg3BQAAQBAJ&pg=PA21&lpg=PA21&dq=coordinates+change+presence+of+mass&source=bl&ots=3Tb3QzZJ-e&sig=nBq--pUSzo8KwiM5WUqYkFIR83k&hl=en&sa=X&ved=0ahUKEwjCs_Pdl8_TAhXIi1QKHdXJDk8Q6AEIRzAG#v=onepage&q=coordinates%20change%20presence%20of%20mass&f=false
Comment: Ah. See, first I want to make it clear that coordinates are NOT absolute in general relativity. What that means is that you should get the same physical result irrespective of which coordinate system you use. Sure, you can change your coordinates by moving from one coordinate system to another. But this MUST follow the tensor transformation rule in the underlying tensor equation. Although I still don't understand what you mean by 'change in coordinates in the presence of mass', the book's paragraph reminds me of an interesting discussion in Carroll's book (pg 74-75). See if you understand that
Answer: Space is curved if you don't come back to your starting point when you walk around a square. Or equivalently, you wind up at different points if you walk east-then-north vs north-then-east.
The surface of the Earth is curved in this sense. It doesn't show for a small square. But try a really large square. Start on the equator.

Walk 1/4 of the way around the world to the east. Turn left and walk 1/4 of the way around the world to the north. You are at the north pole.
Walk 1/4 of the way around the world to the north. Turn right, and walk 1/4 of the way around the world. (OK, it isn't east because coordinates are weird at the north pole.) But you are on the equator.

In GR, a mass causes distortions of distance and time. If you are in orbit, the distance to the center of a star is deeper than you would expect from dividing the circumference traced out by the orbit by $2\pi$. Time runs slower at the surface than in orbit.
Space-time is 4 dimensional, so you get an extra direction you can walk around the block. You can also wait a while.
So trace out this "square" where one side is distance, and the other time. Start at a point above the star.

Have a person at the top wait a bit, then find the point/time a distance X below him at that time.
Find the point/time a distance X below the top person right now. Have someone at that bottom point wait a bit.

Time is slower at the bottom. In his travel through time, the bottom person passes through the the point/time the top person picks out. But when he does, he isn't done waiting yet.
Comment: So do the 4 space-time dimensions actually move when they curve?
Comment: Consider that each point in 4-D spacetime has its own coordinate system.  And, to make use of this coordinate system in terms of multiple points separated by some distance you need to compute how coordinates at one point change to become useful at another point.  This is a coordinate transformation and the key idea of working with general relativity.
Answer: Your question, strictly speaking, doesn't make much sense, but I think I understand your confusion, so I'll try to make an according answer.
What is dimension?
Since your account name is "girlphysicsmajor", I assume you are a physics major, so you probably know some linear algebra. You know, then, that given a vector space $V$, the dimension of $V$ is the natural number that gives the cardinality of a maximal set of linearly independent vectors.
So the dimension of a space = the amount of independent directions you can go in.
There are more sophisticated notions of dimension (Lebesgue covering dimension, Hausdorff dimension for example), but these are useful mainly when the space in question is very unstructured. The curved spacetime of general relativity is what mathematicians call a differentiable manifold. This structure is more general than a vector space structure, but the vector space notion of dimension can be used here as well (I don't want to detail how).
So even for GR, the number of dimensions = the number of linearly independent directions. Curvature has nothing to do with this.
What you mistake for dimension (I think):
Coordinate systems. In special relativity you describe physics using pseudo-Cartesian coordinates, a quartett of numbers $(ct,x,y,z)$, for which the $(x,y,z)$ are cartesian coordinates, and the $t$ time coordinate is also "cartesian" related to the other three in the sense that the line element can be written as $$ ds^2=-c^2dt^2+dx^2+dy^2+dz^2. $$ If the pesky minus sign wasn't there, then this would be a cartesian coordinate system. With the minus sign involved, we often call this a "pseudo-cartesian" coordinate system.
There are 4 coordinates, because spacetime is 4 dimensional, but the coordinates themselves are not "dimensions".
In particular, nothing stops you from using noncartesian coordinate systems even in special relativity. For example, you can transform the spatial coordinates to spherical polar coordinates, then you have the line element $$ ds^2=-dt^2+dr^2+r^2(d\vartheta^2+\sin^2\vartheta d\varphi^2), $$ but this STILL describes the same spacetime.
What I think your question is:
I think you are asking that if spacetime is curved does that mean that the $t,x,y,z$ "coordinate lines" are curved lines then?
This question is not well posed, because in a general curved spacetime, there is no analogue of cartesian coordinates.
It is true, that curved spacetimes will always be described by coordinate systems whose coordinate lines are curved lines, but a general curved spacetime will never ever distinguish any particular coordinate system from any other.
What is curvature, then?
Consider flat spacetime with cartesian coordinates, let $(ct,x,y,z)=(x^0,x^1,x^2,x^3)=(x^\mu)_{\mu=0}^3$. The line element is $$ds^2=-c^2dt^2+dx^2+dy^2+dz^2=\eta_{\mu\nu}dx^\mu dx^\nu,$$ where summation on the repeated indices is assumed, and $\eta_{\mu\nu}$ is 0 if $\mu\neq\nu$, 1 if $\mu=\nu=1,2,3$ and -1 if $\mu=\nu=0$.
Now, we make a general coordinate transformation $$x^\mu=x^\mu(u^0,u^1,u^2,u^3).$$
The differentials are then $$ dx^\mu=\frac{\partial x^\mu}{\partial u^\nu}du^\nu, $$ (repeated indices summed!), so $$ ds^2=\eta_{\mu\nu}dx^\mu dx^\nu=\eta_{\mu\nu}\frac{\partial x^\mu}{\partial u^\sigma}\frac{\partial x^\nu}{\partial u^\kappa}du^\sigma du^\kappa=g_{\sigma\kappa}(u)du^\sigma du^\kappa, $$ where $$ g_{\sigma\kappa}(u)=\eta_{\mu\nu}\frac{\partial x^\mu}{\partial u^\sigma}\frac{\partial x^\nu}{\partial u^\kappa}, $$ and I have indicated that these "$g$" coefficients now depend on the new coordinates $u=(u^0,u^1,u^2,u^3)$.
This new line element describes the same flat spacetime too, though. But you can ask the question that if you are given some totally unknown coordinate system $(u^0,u^1,u^2,u^3)$, and a line element as $$ ds^2=g_{\mu\nu}(u)du^\mu du^\nu, $$ is it possible to find a coordinate system $(x^0,x^1,x^2,x^3)$ such that in that coordinate system, the line element is in standard form $ds^2=\eta_{\mu\nu}dx^\mu dx^\nu$?
In general, this is not possible. When it is not possible, we say that spacetime is curved. How not possible this is, is measured by an object called the Riemann curvature tensor. If the curvature tensor is zero, spacetime is flat, and can be described with cartesian coordinates. If the curvature tensor is nonzero, then spacetime is curved and there is simply no such coordinate transform that would bring the line element to its standard form! This is what we call curvature.
Is it possible for a coordinate to be curved?
The answer is no, not really. For the purposes of curvature, you cannot decompose a manifold as some sort of "direct product" $\mathbb{R}\times \mathbb{R}\times \mathbb{R}\times \mathbb{R}$ and "measure the curvature of each coordinate" separately or anything like that.
In fact, one dimensional manifolds have no curvature and the curvature of two dimensional manifolds can be described by a single function. By contrast, the curvature tensor in four dimensions has 20 independent components. From this alone it is clear that you cannot simply decompose a manifold to a "sum" or "product" of lower dimensional manifolds and calculate the curvature separately (after all $2+2=4$ for dimensions but $1+1\neq 20$ for curvature components).
In some cases, it is possible to have metrics, for which "some parts of it are flat". For example, the "spatially flat FLRW metric" used often in cosmology, is given by $$ ds^2=-d\tau^2+a^2(\tau)(dx^2+dy^2+dz^2) $$. As you can see, the "constant time" spatial slices have a spatial metric of $ds^2_{\text{space}}=a^2(\tau_0)(dx^2+dy^2+dz^2)$. Performing the coordinate transform $x\mapsto x/(a^2(\tau_0))$, $y\mapsto y/(a^2(\tau_0))$ etc. will give $ds^2_{\text{space}}=dx^2+dy^2+dz^2$ and from this we can see that the spatial slices are flat three dimensional manifolds.
But you cannot perform this procedure for the entirety of spacetime to obtain a "flat spacetime", despite the fact that all spatial slices are flat. And the reason you cannot perform this procedure is because for a single $\tau=\tau_0$ constant time slice, the coefficient $a^2(\tau_0)$ is a constant. But if you consider all of spacetime, $a(\tau)$ is a function of $\tau$, so if you defined $x'=x/a^2(\tau)$, you'd have $dx'=dx/a^2(\tau)-(2x/a^3(\tau))d\tau$, and you wouldn't get a flat metric anymore.
Comment: You write: "Is it possible for a coordinate to be curved? The answer is no, not really."  So is the answer no? No not, not really, but kind of?  Is it possible for the geometry of the spacetime dimensions to be curved?  Can it be curved differently in the x, y,  z, and x4 dimensions?
Answer: A (somewhat crude) analogy may help- Consider you have 2 blank papers. On one you draw straight margins along the edges(call this sheet A). On the other, you draw curved( in any way whatsoever) margins(call this sheet B). Then, roll up A( or crumple it if you like). Now look at both the sheets. The margins of both look similar, of course. But which one is curved? Certainly not both, even though the margins look alike. Only A is actually curved!
The point is; the "margins" are akin to "dimensions". And (what should now be obvious) this suggests that the dimensions themselves are not guaranteed signposts to check for curvature.
As a side note, you may like to know that just by changing your coordinate systems you could fool yourself that space is 'curved' even though it is not.( the margins may fool you when you compare the crumpled and flat sheet; a 'good' crumple would mean they may look exactly similar!). A subtle interplay of cartesian and curvilinear coordinates is involved, which I will skip. You may want to read up on Christoffel symbols though.
Note- General relativity is much more complicated. You don't have one sheet; you have a sheet at every point of the body you are looking at. This is only a 2 dimensional analogy to try to explain a 4 dimensional phenomenon. Please keep that in mind.
Hope this helps.


Difference between "lieu" and "endroit"

Question: What is the difference between "lieu" and "endroit"? I know both of them mean place, so what exactly is the difference? Please use examples in your answers.
Comment: Please make sure to read the help pages ([on topic questions and how to ask](http://french.stackexchange.com/help/on-topic), and [how to answer](http://french.stackexchange.com/help/how-to-answer)). What research have you done, what dictionary have you looked at (Larousse: [endroit](http://larousse.fr/dictionnaires/francais/endroit/29395), [lieu](http://larousse.fr/dictionnaires/francais/lieu/47076?q=lieu#47003); you may also try _Collins_, and _TLFi_) and what did you not understand? Thank you!
Answer: Usually when I say 'lieu', it is like the english 'location', and 'endroit' is like 'spot'. so:
Le lieu est les Caraïbes.
Vas-tu me rencontrer à cet endroit?
I would say 'lieu' is more broad, it's not very specific. I also think it's more formal, I hear it more on the news, than I hear people saying it in real life.
Endroit is like 'spot', or area.
I would say the BIGGEST difference is that lieu is not very commonly used in speech, and endroit is more familiar language.
Answer: Lieu as a spot is not used a lot in speech, sometimes in formal situations (news, speeches, ...)
Lieu is rather well-known because used in many expressions:

en lieu sûr
cela n'a pas lieu (cela n'arrive pas)
cela donne lieu (cela entraîne)
il y a lieu de faire cela (il faut faire cela)
au lieu de faire cela (à la place de faire cela)
en dernier lieu (comme dernière solution)

et lieu-dit, non-lieu, lieu commun
à ne pas confondre avec lieue (distance)

à dix lieues de là, ou à des lieues de là (très loin)
des bottes de 7 lieues (le petit poucet)
Answer: In many cases, when talking about a place, the difference is really a matter of usage, both words can be used and nobody will see anything wrong:

J'ai visité l'endroit, j'ai visité les lieux.
Ce n'est pas le lieu, ce n'est pas l'endroit (meaning it's not the appropriate place to do something).
Repérer l'endroit, repérer les lieux (with a view to doing something).

However there is a small difference: J'ai visité l'endroit, refers to the place we are talking about, while j'ai visité le lieu implies we are talking about a location where some action took or will take place.
Avoir lieu means to take place, and le lieu de l'action is where it takes place, shortened into le lieu, sometimes les lieux.

Un endroit is a part of something larger, not necessarily a place:

Un endroit agréable: A nice place.
Il était au mauvais endroit: He was at the wrong place.
On voit du sable par endroits: We can see sand in some places. (Lieu wouldn't be correct in this sentence.)
À quel endroit mettre la chaise? Where to place the chair?  (Lieu wouldn't be correct in this sentence.)
Elle a été touchée à plusieurs endroits du corps: She was hurt at several parts of her body. (Lieu wouldn't be correct in this sentence.)

Lieu is used to denote where some action takes place:

Le lieu de naissance: The place of birth.
Un lieu de vacances: A place used for vacations.
Au lieu de vente: At point of sale.
Le lieu de tournage: The film location.
Dresser l'état des lieux: To perform an assessment, conduct a joint verification. Endroit wouldn't be correct in this sentence.)

Maybe a good sentence to see the difference is about the place where a murder is committed:

L'endroit idéal pour un crime: The best place for a crime (in general).
Le lieu du crime: The crime scene (the place where the crime took place).

In some cases, lieu doesn't refer to any place, but indirectly to the action, and it cannot be replaced by endroit:

En premier lieu: In the first place.
Au lieu de: Instead of, as a replacement.
Tenir lieu de: Acting as, replacing.
Il n'y a pas lieu de s'inquiéter: There is no reason to worry about.

Lieu comes from latin locus, still used in English in math. For example a circle is the locus for points at an equal distance of its center. French equivalent is lieu.
Answer: un lieu", "une place" and "un endroit" design all a location and in most occasion you can use the one you want without disctinction.
However, they are mostly used for different scale :
"lieu" will mostly be used for larger location like a village, a valley .... It is not so much used in oral modern French.
"place" will be use for the location of the size of one man or one object, a location where an object/a man is/has to be : "This is my spot!" => "C'est ma place!" or "The phone is not where it should" => "Le téléphone n'est pas à sa place". It's also use to design your seat in a plane/train/bus "This is my seat" => "C'est ma place".
But "place" is also the French word for "Plaza", like a big open place without building in a city.
"endroit" will be used for a location at the dimension of a room. Most "place" in English will be translated by endroit : "This is a nice place" => "C'est un endroit agréable". In modern oral French, it case be used for larger location like village/valley.
Source :
https://www.reddit.com/r/French/comments/3bgaaf/whats_the_difference_between_lieu_place_and/
See also the other answers therein.
Comment: Link-only answers are useless if the linked site is not accessible. Please summarise the relevant content in your answer and only provide links as references.

Difference between “lieu” and “endroit”


Can I save bodies?

Question: I found a guy in my house, the elf from river wood I walked in with Sven then realised that I'm marred to Camila (awkward...three men in a room with a woman they're in love with) I heard the elf guy say that he loved her so I drew my sword and killed him. His body has stayed on the table as a souvenir, will I be able to keep him?
Comment: must be fun telling that story to guests when you invite them over for dinner.
Comment: I would try to Freeze the poor guy - do you have proper shout? From what I saw, the target stay frozen until being hit though never tried it on a corpse (yet)
Answer: Bodies are removed when the "cell" (in this case, the house's interior) resets.  The trick, then, is to prevent it from resetting by visiting it at least once every ten in-game days (some reports on cell resets go as high as thirty days, but as you're trying to avoid a reset, you ought to play it safe).
If this house is your primary base of operations, that isn't likely to be an issue for you, but be careful when waiting for shop inventory resets and the like; you don't want to stay away for too long!

Can I save bodies?


Novel/Story with wireheads?

Question: I remember reading a long time ago a novel where some people who, through a surgical operation had a wire connected to the pleasure center of their brains. They could just plug themselves in, it became an addiction. The were called wireheads. Does anyone recall what novel that was ?
Comment: Wireheads appear in several Larry Niven stories, but they are hardly a unique there. More detail would help.
Comment: I believe it first showed up in Niven's [Death by Ecstasy](http://en.wikipedia.org/wiki/Death_by_Ecstasy).
Abuse (for pleasure) of a brain implant meant for something else occurs in a slightly earlier novel [The Terminal Man](http://en.wikipedia.org/wiki/The_Terminal_Man) by Michael Crichton. Incidentally, it also shows up in Spider Robinson's [Mindkiller](http://en.wikipedia.org/wiki/Mindkiller) and the related books in that series.  It's a pretty major plot element, although used in various ways.
Comment: Thanks, that could be it, is there any story in particular where they are introduced ? Sadly, I cannot remember any more details.
Comment: [Related](https://scifi.stackexchange.com/questions/94578/novel-where-a-man-is-paid-to-travel-to-a-planet-inside-a-metallic-sphere/)
Answer: Per wikipedia:

In Larry Niven's Known Space stories, a wirehead is someone who has
been fitted with an electronic brain implant (called a "droud" in the
stories) to stimulate the pleasure centres of their brain. In the
Known Space universe, wireheading is the most addictive habit known
(Louis Wu is the only given example of a recovered addict), and
wireheads usually die from neglecting themselves in favour of the
ceaseless pleasure. Wireheading is so powerful and easy that it
becomes an evolutionary pressure, selecting against that portion of
Known Space humanity without self-control. Wireheading need not use an
actual brain implant; the pleasure centre can be remotely activated by
a small device called a "tasp" (important in the Ringworld novels)

"Wireheading" appears in several Niven works, notably Flatlander and the Ringworld Engineers

She reminded me of a wirehead. You can't get a wirehead's attention, either, when house current is trickling down a fine wire from the top of his skull into the pleasure center of his brain. But no, the pure egocentric joy of a wirehead hardly matched Charlotte's egocentric misery. Flatlander - Larry Niven

and

Times change. Generations later, these same cultures usually see
current addiction as a mixed lessing. Older sins—alcoholism and drug
addiction and compulsive gambling—cannot compete. People who can be
hooked by drugs are happier with the wire. They take longer to die,
and they tend not to have children.
It costs almost nothing. An ecstasy peddler can raise the price of the
operation, but for what? The user isn't a wirehead until the wire has
been embedded in the pleasure center of his brain. Then the peddler
has no hold over him, for the user gets his kicks from house current.
And the joy comes pure, with no overtones and no hangover. Ringworld Engineers - Larry Niven
Comment: A wirehead / wireheads appear in our own space and time in Spider Robinson's 1977 novella "God is an Iron" which was expanded into the 1979 novel  _Mindkiller_.
Comment: There's a line in John Steakley's  Armor about looking like "K Dick wireheads", which led me to believe it was a reference that went further back, to Philip K. Dick.  There's some speculation [here](http://www.network54.com/Forum/97413/thread/996361480/997113193/wireheads) to that effect.  I haven't read enough pkd to know myself, though.
Comment: According to the linked Wikipedia article, (this) *Flatlander* is not a novel but a collection of stories including "Death by Ecstasy".

Novel/Story with wireheads?


Initial velocity of stone

Question: If we drop a stone from a balloon rising at $4\text{m/s}$ , magnitude of initial velocity of stone is taken to be $4$ but why it is so?  Please explain by giving more examples.
Answer: I think its because the stone is initially travelling along with the baloon with a velocity of 4m/s(with respect to the ground) in the upward direction.So the initial velocity of the stone with respect to the ground is 4m/s.While trying to get off a running bus,  you should run along the bus for a small distance.If you try to stand firm (without running), you will fall down.This is because your initial velocity with respect to the ground is not zero.So the ground will try to decelerate you by friction(try to topple you).To prevent such high deceleration, you should run along and gradually come to rest.
Comment: run along the bus in the direction opposite to the direction of the bus
Comment: No.In the same direction as the bus moves(w.r.t ground).Running in the opposite direction will make things worse.
Comment: Are we on the bus trying to get off?  In the bus is 10km/hr and you run on the bus 10km/hr is the same direction, total velocity to the ground is 20!
Comment: This is similar to the case of a threadmill.The only difference is that in case of threadmill, the surface wiil be in motion and here you(on the bus) will be initialy in motion.The relative mostion is the same(the threadmill moving back is equivalent to your motion forward).If you are initialy standing over the edge(on the stationary part) of the thread mill and suddenly jump on the moving thread mill, to gain balance you should run in the forward direction.If you stand or run backward, you will fall.Because after jumping, the threadmill will pull the bottom of your leg backward.
Comment: If you want balance, your legs and centre of mass should be in line.So run along the centre of mass(in the ddirection of initial motion of centre of mass) get balance.and slowly come to rest.
Comment: So jump off the bus and start to run in the air before hitting the ground,  Ok I see what you are saying now.

Initial velocity of stone


Is there an inflatable pillow that can be inflated by hand : a piston, hand pump or a rotating handle?

Question: Is there an inflatable pillow, preferably ultra-light material, and inflatable by hand, not by blowing with the mouth. May be with a small hand piston or hand pump. There are these torch lights that charge by rotating a handle, somewhat like that. To be used in (Indian non-AC) trains. I am not good at blowing through little nozzles. Or the pillow I end up buying are too unfriendly to blow, require pressing the nozzle too tightly to see a tiny opening and  have to blow till eyes pop out, like a lung exercise!
Comment: Edited the question to be more on gear than shopping.
Comment: Most pillows I have seen use the same kind of nozzles as small airbeds and balls. You can buy a pump for those and carry it as a separate item.
Comment: Is there a pump that is buyable separately ?
Comment: Yes, almost shops that sell airbeds, balls to be used on the beach and so on have them.
Comment: @WhirlMind good edit, I have retracted my close vote and +1 to the Q.
Answer: I have never seen pillows that have a build in pump but I have seen many pumps that can be used for pillows, inflatable balls, small airbeds and so on.
Most of them are foot operated but the smaller ones can mostly be hand operated as well.
And besides dedicated pumps, many small bike pumps can be used for pillows as well, as long as you have the right attachment or adapter.

Like the red one in this picture (Picture taken from a shop catalog.)
Shops that are likely to sell pumps:
Out-of-doors sports shops.
Camping equipment shops.
Toy shops near bodies of water, where they sell blow up balls and use on the water airbeds.
Bike shops and shops selling bikes and parts will most likely have a wide range of bike pumps, often with the needed attachment as part of the set or separate. Just a bike pump will not do, as you can not connect it.
Answer: Yes there is

google for "self-inflating pillow"
google for "foot pump" or "inflator" etc.
google for "bicycle pump" and "pump adapter"

Substitute your favourite search enging for google.
Answer: There are self-inflating pillows, which work in the same manner as self-inflating sleeping mats, no blowing required, just open the valve and air is drawn into the internal foam structure. To deflate they need rolling tightly with the valve open and then close the valve to keep the pillow compressed.
The one's I've seen are quite lightweight but they are definitely bulkier than ones you have to blow into.
Comment: The self inflating one I have is useful for something to sit on, but not for something under your head to sleep, unless you fold it. Can do for a person camping, but not a replacement for a normal pillow for most.


Can the output layer be connected to multiple layers?

Question: Normaly, the output layer is only connected to the second last layer.
Is there any model that the output layer is connected to multiple layers (For example, the second last layer AND the layer before it.)
Comment: Residual networks have connections that skip layers, the obviously called _skip connections_. I don't know if skip connections also happen for that specific case you're mentioning, but you should look into ResNets because they may be one answer to your question.
Comment: Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer.
Answer:
Normaly, the output layer is only connected to the second last layer.

This is only normal for standard MLPs. As soon as you look into slightly more sophisticated neural networks, you'll find a variety of different schemes to connect the layers within a neural network.

Is there any model that the output layer is connected to multiple layers

There are many examples of such a case, like WaveNet, U-Net, HRNet, to name a just few. The first two networks use skip-connections. Mostly summation or concatenation is applied to combine the multilayer results.
And like @nbro mentioned in his comment, ResNet is also comparable which uses residual connections to bypass layers.
There are a lot more examples than that because this practice has a very beneficial aspect to it: It shortcuts the backward pass and thus mitigates the vanishing gradient problem.
A more general answer to your question is that you can wire up your layers however you want as long as the network stays differentiable. It should somehow make sense though: In the case of Wavenet these skip-connections help to capture temporal features from different granularities (short-term temporal features detected in the early layers / long-term temporal features detected in later layers).


dnf install self-signed package Error: GPG check FAILED

Question: I have a repository and a package and want to install it from that repository on Fedora 39.
The repository is here for (testing purposes, ignore the bucket name ubuntu, it contains rpm repo) https://storage.googleapis.com/repotestubuntu2204 created via createrepo
The package sample_project-1.3.5-1.fc39.x86_64.rpm is just C hello world signed via rpm --addsign, the keys generated via gpg --gen-key (RSA 4096 bits, no passphrase, no expire)
Adding this repository
dnf config-manager --add-repo https://storage.googleapis.com/repotestubuntu2204/sample_project.repo
Adding repo from: https://storage.googleapis.com/repotestubuntu2204/sample_project.repo

Seems to be ok. Now trying to install the package
dnf install -yv sample_project
  ...
Using rpmkeys executable at /usr/bin/rpmkeys to verify signatures
Package sample_project-1.3.5-1.fc39.x86_64.rpm is not signed
The downloaded packages were saved in cache until the next successful transaction.
You can remove cached packages by executing 'dnf clean packages'.
Error: GPG check FAILED

So it is telling me that the package is unsigned and that it's using rpmkeys to verify this. Ok, downloading the rpm itself ang checking the signature
wget https://storage.googleapis.com/repotestubuntu2204/sample_project-1.3.5-1.fc39.x86_64.rpm

rpmkeys -Kv sample_project-1.3.5-1.fc39.x86_64.rpm
sample_project-1.3.5-1.fc39.x86_64.rpm:
    Header SHA256 digest: OK
    Header SHA1 digest: OK
    Payload SHA256 digest: OK
    MD5 digest: OK

I tried gpg import and rpm --import - nothing helps, and afaik it shouldn't b/c there's link to gpgkey in .repo file which seems to be imported successfully upon adding the repository.
The rpm built for openSUSE with the exact same procedure works, zypper adds repository, asks to trust the public key, and that's it. Fedora does not ask trust or not the key, however, which is a bit suspicios. But manually downloading the key file and importing it doesn't help either.
yum install gives the same error. rpm -i works without any issues. What's wrong with the signature?
Answer: Figured out. While debugging rpm signatures for Fedora I've added --showrc option, so the sign command was rpm --showrc --verbose --addsign *.rpm and turns out this didn't sign the package header. rpm --addsign *.rpm works


Hot Tank Solution for Aluminium?

Question: My aluminium cylinder head is caked with oil and carbon. I'm going to be cleaning that along with other steel/iron parts. I'm planning to make a DIY hot tank to boil the parts in but what can put in the water that won't damage the metal that would also clean effectively? Would Clean Green be fine? What about washing power, easily available, would that damage the metal?
Comment: Here in the USA, all cleaning of engine parts is done in ovens now, they literally cook off the carbon, then they shot peen or sand blast the parts to bring back the metal luster. Carbon is hard to remove using chemicals, the ones that do an excellent job also attack the aluminum unfortunately. They make carburetor cleaner in a 5 gallon pails, in the past I have bought several of these to fill a cold tank to soak aluminum heads, works well without damaging the aluminum finish but it is expensive these days.
Answer: I tried many normal household products to clean engines and parts...
And for 1 off then petrol, thinners etc may work, but the best solution by far was to take my disassembled engine block, heads, crank etc to the local machine shop and then put it in their washing machine.
The parts come out like new except now you can see the wear marks and scoring etc. Cost was so cheap, but that was probably because I got all my crank grinding and machine work done there. Also, I always gave them plenty of time for my work - never "I need this done in 2 hours..." makes a big price difference :)

Hot Tank Solution for Aluminium?


Frames in Selenium

Question: I have never had to test an application that had frames.
When does it make sense to divide a window into frames?
How do I refer to (target) objects within a frame?
Comment: If your main question is how to handle frames and iFrames in Selenium, could you please edit your question to make this clear? Otherwise this question is likely to be closed as off-topic.
Answer: Frames are an older way of maintaining a sub-widget/page inside of a bigger page.  With html5, css3, and javascript there is no longer any need for iframes/frames even though they are still supported and some sites still utilize them.  The main goal is to split the screen into content areas and each area pulls in seperate functionality that has a different window scope based on the frame instead of the whole window.  iframes are floating vs. static locations of frames.
The underlying functionality refers to the frame like it is the window, however, the browser itself does not, but segments based on that.  So the view part of the window gets divided by the frames.  Within each frame the elements work normally with Selenium like it's a window, but from the browser level the elements get abstracted into the frames and are not as easily identifiable.
As html5 and css3 handle all of the above without having to create extra constructs it obsoletes the frame/iframe idea...I personally hate frames as they disrupt the webpage in general.
Selenium drives off the html view of the browser.  Since the frames fragment the view you have to get the focus into each frame and then select instead of going from the browser window level down like normal web pages.  I usually do this by mousemove by a certain amount of pixels to get in the frame, so find a parent container for the frame and move focus there and then offset and then look again for the element.  You will need to play around with the specific rendering and figure out what works best.  If you want specific help there you need to post your html code.

Frames in Selenium


Why can mass not be considered concentrated at CM (center of mass) for rotational motion?

Question: Could anyone explain the following expression: Why can mass not be considered concentrated at CM (center of mass) for rotational motion?
Answer: The total linear momentum of a system of particle labeled with $i \in {1\dots n}$ can be found in the microscopic view just by summing the linear momentum of the constituents:
$$ \vec{P} = \sum \vec{p} = \sum m_i \vec{v}_i $$
Now, writing $M = \sum m_i$ for the total mass, $\vec{X}$ as the position of the center of mass, and $V$ as the velocity of the center of mass, we can express the total linear momentum in the macroscopic view as
$$
\vec{P}_{CM}
  = M \vec{V}
  = M \frac{\mathrm{d}}{\mathrm{d}t} \vec{X}
  = M \frac{\mathrm{d}}{\mathrm{d}t} \left( \frac{1}{M} \sum m_i \vec{x}_i \right)
  = \sum m_i \frac{\mathrm{d}}{\mathrm{d}t} \vec{x}_i
  = \sum m_i v_i
  = \vec{P} $$
That a system where it is OK to treat the mass as if it were concentrated at the CM.

Next consider angular momentum, and I'm going to proceed a little differently.
I will define $\Delta \vec{x}_i = \vec{x}_i  - \vec{X}$ and the displacement of the $i$th particle from the center of mass, and note the consequence that $\Delta \vec{v}_i = \vec{v}_i - \vec{V}$.
Now write the microscopic angular momentum as
$$
L = \sum m_i \vec{x}_i \times \vec{v}_i
  = \sum m_i \left( \Delta \vec{x}_i + \vec{X} \right) \times \left( \Delta \vec{v}_i + \vec{V} \right)
$$
Computing all four partial products we get
$$
L = \sum m_i \left(
      \Delta \vec{x}_i \times \Delta \vec{v}_i +
      \Delta \vec{x}_i \times \vec{V} +
      \vec{X} \times \Delta \vec{v}_i +
      \vec{X} \times \vec{V}
    \right)
$$
and from the definition of the center of mass quantities you should be able to show that the two center terms are identically equal to zero [1]. That leaves us with
$$
L = \left (\sum m_i \Delta \vec{x}_i \times \Delta \vec{v}_i \right)
    + \left( M \vec{X} \times \vec{V} \right)
  = L_{INT} + L_{CM}
$$
where $L_{INT}$ is the "internal" angular momentum.
The result is that you can not compute the angular momentum of the system from the macroscopic properties of the system without including an additional term that describes the rotation and mass distribution around the center of mass.

[1] As in
$$
\sum m_i \Delta \vec{x}_i
  = \sum m_i \left( \vec{x}_i - \vec{X} \right)
  = \left( \sum m_i \vec{x}_i \right) - \left( \vec{X} \sum m_i \right)
  = \left( M \vec{X} \right) - \left( M \vec{X} \right)
  = 0
$$
Answer: If it was, then the object would spin around its center of mass at infinite speed with 0 force. Clearly this does not happen in reality.
Comment: Is the expression mean that as the car's wheel; there is no mass at the CM ??
Comment: There is negligible mass *at any one point*, since a point is a 0-dimensional construct. The mass is distributed across the full volume of the wheel.
Answer: This expression means that when considering rotational motion one cannot make the simplification of assuming that the rotating body in consideration is a point mass. In other words: shape and mass distribution matters.
This is due to the fact that spatial distribution of mass of the body around its rotation axis is a very important factor determining the rotational motion. The quantity which describes the distribution of mass relative to the rotation axis is called the tensor of inertia.
In practice, while calculating quantities describing the rotational motion one almost always uses moment of inertia with respect to the current rotation axis. Now, since this depends on the distribution of mass (and not only on the amount of mass), one ends up with very different results for different shapes and mass distributions.
Example: let's calculate rotational kinetic energy of two bodies of the same mass m, but with different moment of inertia. First, take a thin rod of length L rotating around one of its ends with angular velocity ω:
\begin{equation}
E_k = \frac{I \omega^2}{2}= \frac{mL^2}{3}\frac{\omega^2}{2}=\frac{mL^2\omega^2}{6}
\end{equation}
Then, replace the rod with a point mass positioned at the center of mass of the rod, i.e. point mass m placed L/2 away from the rotation axis:
\begin{equation}
E_k = \frac{I\omega^2}{2}=\frac{mL^2}{4}\frac{\omega^2}{2}=\frac{mL^2\omega^2}{8}
\end{equation}
Answer: Because rotational inertia depends on the distance (radius) of mass from the center of rotation.  That's one simple reason.
Answer: Consider rotating ball. It's center of mass can be at rest, but it still has rotational kinetic energy. Given the angular velocity, this energy is dependent on mass distribution inside the ball. If all the mass will be concentrated in the center of the ball, the rotational kinetic energy will be zero.
Please note that this very simple argument is totally ignored when elementary particles are considered :).
Answer: The total angular momentum of a rigid body about an arbitrary point A can be thought of as the sum of 2 parts: 1) the angular momentum about A of the total mass concentrated at the center of mass (point G), and 2) the angular momentum of the body with respect to G.
If you want to calculate the angular momentum, you can only treat the body as a point mass when the angular momentum about its mass center is small compared to the total angular momentum of the body about A.
For example, if you were to treat a large body which is rotating rapidly about its center of mass as a point mass, and then calculate the angular momentum about its center of mass, you would get 0, even though the angular momentum should obviously be high!
Now if you calculate the angular momentum of a slow-spinning yoyo that is swinging at the end of its string about your finger, you could treat it as a point mass and still observe almost the exact dynamics as if you were to do all of the extra math to include the angular momentum of the yoyo spinning about its bearing.


pxe-e61 media test failure Ubuntu Dual boot Win

Question: So I had win 8.1 and Ubuntu 14.04 in dual boot and it was all working fine, but after I enabled the Intel Rapid feature on win this error "pxe-e61 media test failure check cable" started showing up and I can't boot anymore. When I go to the boot menu on the BIOS none of the boot loaders appears anymore. I ran the Boot-repair program and this was the output. http://paste.ubuntu.com/9207990/
Answer: That message means there is no network cable connected. It also means it's trying to boot from the Network, so either -

The network card is listed before the hard drive in the boot order in the BIOS (Check boot order)
The hard drive is dead/has a bad cable. (Replace the cable and/or hard drive and try again)
The hard drive is disabled in the BIOS. (Enable it)


Can I import a ZFS data pool from FreeNAS without losing the data?

Question: I'm switching to Ubuntu server from FreeNAS and I don't have a hard drive to back the data up to. Is is possible to import it into Ubuntu even though the data pool is split between two different HDD?
Answer: As Bruno Pereira has said, the zfs version number from FreeNAS needs to be equal or smaller than the zfs version number ubuntu supports. After zfs v28, this switched over to the need for support of the enabled zfs options.
For 16.04, the versions of zfs and FreeNAS 9.10 or even FreeNAS 10 are equal and a FreeNAS pool can be converted. I just converted a FreeNAS 10 trial installation myself for use under 16.04.
Answer: No.
The version of the ZFS on Linux is not compatible with the version you used for your FreeNAS system, you will not be able to import it using ZFS on Ubuntu.
The other way around is possible (importing older versions of ZFS using FreeNAS).
There is no downgrade option for ZFS.
The issues is not the way ZFS is set (pools over different disks, raid setup etc), it has to do with options - mainly datasets - that are present in the FreeBSD release of ZFS, that are not present in the ZFS on Linux release.
Comment: A delete and an upvote!  (on my answer and yours respectively!)


Are facts objects of some kind?

Question: What is a fact, exactly? A table, for instance, is an object located within a particular region of space. But what about facts? Are they one kind of object, and if so, what kind of objects are they?
Comment: Does this answer your question? [What are facts as considered independently of any thinking being?](https://philosophy.stackexchange.com/questions/37635/what-are-facts-as-considered-independently-of-any-thinking-being)
Comment: This is a much involved question. What is the context of your questioning? Do you have any hypotheisis or reflection to present? What is at stake for you here, and why does it look necessary to answer this question?
Comment: I'm voting to close this question because can be answered by dictionary.
Comment: If a table is an object, the statement asserting that the table has four legs corresponds to a *fact* "involving" the table.
Comment: Depends on your definition of '[object](https://plato.stanford.edu/entries/object/)', which is a very ontological question. Read SEP's article on what 'object' means before making up your mind. Your question goes to the nature of the classic issues of [naive realism](https://en.wikipedia.org/wiki/Na%C3%AFve_realism) and [Cartesian duality](https://en.wikipedia.org/wiki/Mind%E2%80%93body_dualism). You're getting into questions of ontology and metaontology and men such as Carnap, Quine, and Meinong.
Comment: @SwamiVishwananda Just because a question can be answered with a dictionary doesn't exclude it as a philosophical problem. 'What is the mind?' certainly can be [answered by a dictionary](https://www.merriam-webster.com/dictionary/mind). It would be ludicrous to not consider it a philosophical question on that account.
Comment: Facts as objects enjoy a "sufficiently cheap" existence, which is roughly the point made in @Dcleve's answer.
Answer: (1) History tells facts, novels do not.
Here, fact means true event.
(2) Scientific facts differ from historical facts.
The fact that water freezes at 0° C is a fact but not an event; it is, at best, an event type of which each freezing of water at 0° C is a token. Sometimes scientific facts are called "phenomenon".
(3) Science does not study facts but consequences; only history (natural or civil) studies facts (Hobbes, Leviathan).
A fact corresponds to a categorical sentence ("The Earth rotates about its N - S axis"); a consequence corresponds to a conditional statement ("if no net force acts on a movng body, then this body will continue its movement in a straight line at a constant speed").
(4) A fact is whatever denotes a true proposition. Truth is adequation of a sentence to a fact.
But in that case, a false sentence denotes nothing; in such a way that there is no meaningful false sentence? (Russell's critique in Problems of Philosophy).
(5) A fact is nothing else than a true proposition, the fregean "sense" (of a true sentence).
(6) A fact is an obtaining state of affairs, a fact is "what is the case".
A state of affairs is a complex entity involving a particular and a universal (property or relation) . Some states of affairs do not obtain; only those which obtain are facts.
A fact is not an event: that the Earth is (roughly) round is a fact, but it is not something that  "happens" in whatever way. That mother Theresa never married is a fact; again, no assiciated event.
"The world is the totality of facts, not of things". (Wittgenstein, Tractatus, 1.1)
(7) A fact is a contingent obtaining state of affairs. (Hume)
That 2+2 = 4 is not a fact, but a "relation of ideas".
Comment: Your entries 1,4,5, & 6 express the same idea or concept. This is the basis of what propositions are. How the sentence is worded is irrelevant. How the concept or idea is literally expressed is irrelevant.  Furthermore none of the entries Express that FACTS never expire & can never be false which are essential. If a fact can be falsified the term fact is meaningless. How is one supposed to know if the fact is true or false in that scenario? By definition a fact must be true & forever be true. The state of affairs would not change. Changing a quantifier to SOME takes away importance of a fact.
Comment: Historical novels contain many facts. Any many factual accounts are assuredly fiction.
Answer: The philosophical notion of facts is "sentence-like slices of reality" (Quine). Basically, when we look at things, like a red sky, do we only directly think "a red sky" or do we think, "The sky here is red right now"? If we think the latter, do we think it into the sky, or from it?
This is sort of obscure but it underwrites the classical notion of substance. An object was said to be a substance if it was a sort of "subject that can't be a predicate" objectively. Of course we could invert the orders of words so that any subject becomes a predicate,  so here, substances are things themselves conforming to the notion of facts.
This is what Wittgenstein is claiming about the world itself, then: that if the world is like a book, the book isn't a list of noun phrases but of full sentences.
Answer: Karl Popper holds that facts are the hypotheses that we have sufficient confidence in to build other hypotheses upon.  IE -- the things we know about the world are all inferences, and none are certain or objective.  "Facts" are just the most reliable of those inferences.
As hypotheses are abstract objects, inhabiting world 3, so are all facts.  They are abstract objects.

Are facts objects of some kind?


ZFS pool broken after upgrading to 14.04 LTS

Question: Well, I have been putting off upgrading to 14.04 for fear that I would break something.  Actually for fear that it would break zfs (or I would break it).   I am bascially slightly better than novice at linux.
Spent the last couple of hours trying to get the pool back.  Now I am at the stage where I don't think I have a complete failure, but I am worried that I may break it.  So if could help me not break it, and recover it,  I would be thankful.
My zfs is file storage and not boot.
It was working fine for a year and was working perfectly before the upgrade (scrub and everything was fine).  I was confident that the upgrade would work (or at least I could fix it) because I had upgraded once in the past, the pool went missing, but I was able to get it back.
I have reinstalled zfs, zfs utilities, and some dependencies (after searching this forum)
I think what happened is 14.04 deleted some config file, or specified disk names differntly, but I could be wrong.  When I set the pool up originally, I was using specific device Ids as I recall (because I did not want to break things if they got reassigned at boot)
So see if this helps.
I can confirm that old mountpoint folders  are there but empty.
no talloc stackframe at ../source3/param/loadparm.c:4864, leaking memory

pool: naspool1
 state: UNAVAIL
status: One or more devices could not be used because the label is missing
    or invalid.  There are insufficient replicas for the pool to continue
    functioning.
action: Destroy and re-create the pool from
    a backup source.
   see: http://zfsonlinux.org/msg/ZFS-8000-5E
  scan: none requested
config:
NAME                                           STATE     READ WRITE CKSUM
naspool1                                       UNAVAIL      0     0     0  insufficient replicas
  raidz1-0                                     UNAVAIL      0     0     0  insufficient replicas
    scsi-SATA_WDC_WD1001FALS-_WD-WMATV0990825  UNAVAIL      0     0     0
    scsi-SATA_WDC_WD1001FALS-_WD-WMATV2995365  UNAVAIL      0     0     0
    scsi-SATA_WDC_WD10EARS-00_WD-WMAV51894349  UNAVAIL      0     0     0

___@ourserver:~$ sudo zpool import naspool1
cannot import 'naspool1': a pool with that name is already created/imported,
and no additional pools with that name were found

___@ourserver:~$ sudo zfs list
 no datasets available

What other output can I post to help?  I'm thinking the update deleted some zfs config files.  It seems like the pool exists and certainly 3 perfectly working disks did not fail at once.  I am worried that I may break something without a little bit of guideance.
Thanks.
Answer: The problem is that after the upgrade zfs thinks that this is a different server. You should be able to fix it by simply exporting and then importing the pool.
sudo zpool export naspool1
sudo zpool import naspool1

Most likely the import will complain that the "pool may be in use by another system, use -f to import it anyway". Use -f to do the import:
sudo zpool import naspool1 -f


Special Relativity and the Light Clock and which direction was the laser pointing?

Question: If I were to make a light clock, I would have some sort of laser pen attached to the top of one of two mirrors. That laser pen would be perpendicular to the surface of either/both mirrors. I would click a 'go' button and a beam of light would bounce between the mirrors. So far so good. Now, we introduce the very speedy observer to system. Lets say he/she gets to observe the moment I click the 'go' button. Which direction was the laser pen pointing for the observer? If perpendicular to the mirrors, why does the light beam strike the 2nd mirror at all?
Comment: What is the orientation of the mirrors with each other in the lab reference frame?
Comment: As I understand it, the light clock uses two mirrors that are parallel to each other so the light beam will bounce between the mirrors indefinitely.
Answer: The laser pen will point in the same direction for the moving observer, but the light ray will emerge at an angle. So the direction of the light ray won't be the same as the direction of the laser tube.
To see why this is imaging looking at a single pulse of light as it travels along the laser pen towards the aperture:

From your perspective, with the laser pen moving towards you, as the pulse of light travels horizontally along the pen it also travels vertically so it moves in a diagonal line. When the light emerges from the light pen it carries on moving in the same diagonal direction.
Comment: @SBateman: relative to the pen the light moves straight along it (to the right as I've drawn the diagram). However because the pen is moving up relative to us, the light is also moving up relative to us. That's why for us the light moves both to the right and up therefore moving in a diagonal.
Comment: Does it make a difference if the observer is moving parallel versus perpendicular to the laser tube/normal of mirror surface?
Comment: Looking at a typical laser pen, there doesn't appear to be more than maybe 3 degrees of deviation from perpendicular in the manner you describe. The tube is narrow and long compared to its diameter so I don't think there is that much room for the beam to exit side-ways.
Comment: Awesome, I think I can visualize that now. This helped as well [link]http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/lightclock.swf  Now, I have another question, of course! But I believe I am supposed to ask it in another question.


What if Euler's formula was defined differently?

Question: At the start of my first year of university in a Foundations module, my lecturer stated Euler's formula for complex numbers, $e^{i \theta} = \cos\theta + i \sin\theta$. In passing he mentioned this is just a definition which conveniently works when you plug the numbers into the Taylor expansions and that you could actually define it differently (a number other than $e$). What would be the consequences of this? Is there any other number which gives interesting results?
Comment: Einstein first tried $E=m\,a^2$, then $E=m\,b^2$, and when he arrived at $E=m\,c^2$ he cried: Heureka!
Answer: Suppose you want the following desirable properties:

$\operatorname{exp}:\theta \mapsto e^{i\theta}$ is smooth
$\exp(x+y)=\exp(x)\cdot\exp(y)$

the first requirement is reasonable since we want the function to be nice, and the second is desirable, because it says most essentially that if we add angles,
we get
$(\cos(x)+i\sin(x))(\cos(y)+i\sin(y))$
which after working out with some trigonometric identities reduces to
$\cos(x+y)+\sin(x+iy)$
so that adding angles does what we would expect on the unit circle.
For any function with these two properties:  $f(0)=1$ and differentiating with respect to $x$ and letting $x=0$ gives
$$f^{\prime}(y) =f(y)\cdot f^{\prime}(0)$$
which solving returns an exponential function $Ce^{a \theta}$ where  $a=f^{\prime}(0)$, although the requirement that $f(0)=1$ forces that $C=1$.
In this case, one could in principle define exponential functions with different bases, but this seems to me inconvenient.
The special thing about base $e$ is that the derivative at $0$ is precisely $1$, which is why we get the clean formulas.
Answer: The simplest possible answer is that your question doesn't make any sense. If we take the point of view that Euler's formula is a definition, then the $e$ in $e^{i\theta}$ isn't really Euler's number anymore, it's just a symbol. The notation $e^{i\theta}$, at that point, is no more meaningful than $f(\theta)$ - it's just a shorthand for $\cos\theta+i\sin\theta$. Thus it doesn't make sense to talk about "replacing $e$ with a different number".
For a slightly more nuanced answer, we can look in more detail at where Euler's formula comes from. In particular, most people would not take it as a definition. The spirit of what your professor said is true, since there are arbitrary (for the purposes of this conversation) definitions involved here, but they happen a few steps before you get to Euler's formula.
First, we define the exponential of real numbers. We say that $a^n$ is $a$ multiplied by itself $n$ times, and then extend that to rational exponents via roots and to irrational numbers by continuity. Once we've done all that, we find that there's an infinite series formula for exponentiation:
$$a^x=\sum_{n=0}^\infty\lambda_a^n\frac{x^n}{n!}$$
where $\lambda_a$ is some peculiar number that depends on $a$ in a complicated way. Now we ask which value of $a$ we would need to pick to make the $\lambda$ go away, and we find the answer is
$$a=e\approx2.718$$
Now, if we want to raise a number to a complex exponent, we can just try setting $x$ to a complex number in the power series. This is just a definition. Another thing that's just a definition is that, since we also have power series for $\sin(x)$ and $\cos(x)$, we can use the same idea to define $\sin(x)$ and $\cos(x)$ for complex $x$. However, given all of those definition, Euler's formula is true. It is a theorem, not a definition. The formula states:
$$e^{i\theta}=\cos(\theta) + i\sin(\theta)$$
Expanding each of those functions in terms of our power series definitions, we get:
$$\sum_{i=0}^\infty\frac{(i\theta)^n}{n!}=\sum_{\text{even }n}\left(\pm\frac{\theta^n}{n!}\right)+i\sum_{\text{odd }n}\left(\pm\frac{\theta^n}{n!}\right)$$
where the $\pm$ symbols mean the signs of the terms alternate (starting with $+$). Even just glancing at this equation, you should be able to see how the two right hand sums will "slot together" (or maybe "zip together" would be more descriptive) to form the sum on the left. If you work out the details, you'll see that the various $i$-s and $\pm$-s will cancel out in the right way to make the equation true.
If we replaced $e$ with a different number $a$, then on the left we would have the $\lambda_a$ factors, and the equation would not be correct at all.


Is there a less pejorative term than "woolgathering" to label purposeful thought that ranges a narrow gamut

Question: When I am writing (usually to give a lecture) I tend to gather data or quotes or other bits into a notebook without knowing in advance whether I am going to use that material.  It can range quite significantly but eventually I have a clearer picture of what material I will or will not use. I don't really think of it as brainstorming since I already have a narrowing solution space and this phase of my process could go on for several months. I use tools, like Evernote, so that whenever I see, or think of, something to be added to my notes I can add them right then and come back for further development in the same notebook. So what term (please don't suggest "research" -- it's less disciplined than that) or idiom should I use to express that phase?
Comment: I would not have considered 'woolgathering' at all for this activity. That term means "Indulgence in aimless thought or dreamy imagining" (https://en.oxforddictionaries.com/definition/wool-gathering), not purposeful thought.
Comment: Are you seeking a term to describe the "purposeful thought" *per* your question's title, or the "gather data" of your question's body?
Comment: Sorry, but, you range a gamut? Also, brainstorming is usually a group activity or one that involves at least two people....
Comment: Why would you not just use **gathering** (or a synonym) as you did in your question? As you say, you've already decided on an idea. Now, you're just putting together supporting documentation. (I suppose you could say you are **documenting** it.)
Comment: @Lambie, sorry for the faux pas. What I meant to say was there is a process that is not word association, or any of a number of other less disciplined forays into thought. Woolgathering, a term I picked up from somewhere, isn't appropriate. I would like a memorable, but more correct idiom to use. Forget trying to use a Thesaurus. They don't really order idioms in a gamut of connotations.
Comment: They say that one of the hardest things for the spouses of writers everywhere to understand is that, when writers are staring out the window, they are _working_...
Answer: Your question's title and elaboration describe different activities.
The "purposeful thought" of your question's title can be called ruminating.

ruminate verb
  1 Think deeply about something.
  'we sat ruminating on the nature of existence'
  - ODO

The gathering of "data or quotes or other bits" is simply called the gathering phase. Here's an example of the term in use (emphasis, mine):

Part of my process of getting ready for a sermon series is to gather all the available resources I can on a particular subject or book of the Bible and see how these resources will serve my preparation time. Most of the time during this gathering phase, I realize that it would be helpful if I order some additional resources to help me with sermon preparation.
  - Pastor's Corner
Comment: Interesting. I would not have considered ruminate as I too prepare for my sermon series or lectures or what have you. I like it but I was hoping for a term to cover the gathering, deepening "ruminating", sifting, sublimating, and final formation phases. That's because I iterate over all these phases quite rapidly bouncing between phases as required. Often times they are being done in parallel so if there were such an idiom to cover all of that then I have the one I am seeking. Otherwise I imply something with distinct, successive phases and that is not what I do.
Answer: I would refer to this process as your discovery phase, whereby you:

may seek disclosure of information that is reasonably calculated to lead to the discovery of admissible evidence [or in your case, "material you will use"]. This is a much broader standard than relevance, because it contemplates the exploration of evidence which might be relevant, rather than evidence which is truly relevant.

Although this term is born of legal lexicon, I think it parallels quite nicely (and non-litigiously) with the process you described.
Comment: The term has similar nonlegal usages as well, for example [in software](https://www.stoutsystems.com/articles/the-software-discovery-phase/).
Comment: nice! in documentation, too, i guess :) "Research" really is a strong contender though, what can i say :)
Answer: If you want a word for purposeful thought about a specific subject, cogitate could apply. It comes from the Latin for "consider" and means to think seriously about a particular subject or problem.

"The calculus homework was harder than I expected, but after I spent
  some time cogitating on derivatives I was able to finish it."

An alternative is to deliberate, meaning to take time to think carefully about a thing, especially about a decision or choice. It's often used to refer to the process juries go through when considering evidence to reach a verdict, but can also be used for any sort of careful decision processing.

"I deliberated for over an hour about which movie to see before I
  asked Clarissa out on a date."
Comment: Right, to mull something over. In fact, the unconscious does its work, say, over a few days, and the ideas pop up. I was going to suggest cogitate, especially since its etymology is so apropos. Ponder and reflect also work to some extent.
Answer: If you want a term for the activity/phase1 of

gather[ing] data or quotes or other bits into a notebook without knowing in advance whether I am going to use that material

you could say you are commonplacing or just keeping a commonplace(-book). From Wikipedia:

Commonplace books (or commonplaces) are a way to compile knowledge, usually by writing information into books. . . . Commonplaces are used by readers, writers, students, and scholars as an aid for remembering useful concepts or facts they have learned. Each commonplace book is unique to its creator's particular interests. . . . Scholars have expanded this usage to include any manuscript that collects material along a common theme by an individual.

While you (and society) have moved on to electronic forms of storage, it sounds like your collections of information and your use of that collection otherwise meet the definition and purposes of a commonplace. Wikipedia specifically notes that commonplaces were often used as

an information management device in which a note-taker stored quotations, observations and definitions. They were even used by influential scientists. Carl Linnaeus, for instance, used commonplacing techniques to invent and arrange the nomenclature of his Systema Naturae (which is the basis for the system used by scientists today). [citation omitted]

As for the verb, Wiktionary1 defines it as

To make a commonplace book.
To enter in a commonplace book, or to reduce to general heads.
(obsolete) To utter commonplaces; to indulge in platitudes.

Although this term has more than a whiff of the Enlightenment era about it, it is also being used today. Examples of usage include the above cited Wikipedia article:

By the 17th century, commonplacing had become a recognized practice that was formally taught to college students in such institutions as Oxford.

As well as

[C]ommon placing is one method used in education, but first and foremost, it is a personal habit that intelligent, thoughtful people have been doing for hundreds of years.
  —Mystie Winckler, "Commonplacing for Moms: 10 Tips to Get Started", Simply Convivial, 2017.

Many other examples in blog articles and Pinterest boards can be found.
A 2015 (scholarly) article directly equates the kind of activities you describe with the older, paper-and-pen(cil) practice:

This paper presents illustrative examples of digital technology that facilitates information sorting and recontextualizing. . . . This way of reusing digital information may be compared to similar analogue information management practices, known as commonplacing, found in early modern Europe.
  —Jon Hoem and Ture Schwebs, "Digital commonplacing," First Monday 20, no. 7 (2015). From the Abstract.

And another blog post specifically recommends the tool you mention, Evernote, for creating a commonplace (though this author's use of the word as a mass noun is a bit odd to my ear):

Here is how you can take the basic concepts of commonplace and build them into Evernote.
  —Taylor Pipes, "Taking Note: How to Create Commonplace with Evernote", Evernote.com, March 4, 2016

1This answer applies to what is asked in the body of the question, rather than the title of the question.
2The OED has a similar definition, but it is paywalled.
Comment: Thanks @1006a! I was unaware of this name for a practice, at least in an electronic form, that I just naturally perform.  This seems to center on having a consecutively built corpus, whereas I might have it in a notebook but more often it is in a versioned electronic form because I iterate and make changes to "facts" I have recorded as I do more . Not only the current state but the process and history of getting to that state is something I capture. I will think about this for a bit -- ruminate (hat tip, Lawrence).
Comment: I've been ruminating over your extremely well put answer.  If there were a memorable idiom for a versioned commonplace (one that tracked where I am currently and also how I got here) that would really be my process.  It would have to be something like..... reaching convergence.  This is a term that comes from routing networks when all of the routers on the network have a single shared picture of that network after all the nodes have reported in, and all the routers have shared their routing tables with each other. That's not very picturesque but that is closer. Historical Convergence?
Comment: So, I'm going to mark this as my "answer" because it was well written and helped me converge on my own partial answer. Unfortunately, "reaching convergence" doesn't encompass capture of versioning metadata as data, nor the serialization of that process into a terminal artifact (lecture, sermon, etc). It's also an obscure reference to highly technical jargon rather than a memorable idiom useful to the mainstream. I might try creating an idiom from scratch. I guess that's what I get for overclocking my brain -- new processes requiring  new conceptual frameworks.
Comment: Glad it helped!
Answer: In the architecture and design fields this is called precedent research or precedent gathering, and is often the stage prior to building a mood board - the gathering of images and concepts relating to one or more elements of the client's brief, and which may, or may not, end up informing mood, tone colour, form, concept or even specific building systems... it's very open-ended, but not unbounded.
Answer:
Meditate
intransitive verb
  1 : to engage in contemplation or reflection
    -  He meditated long and hard before announcing his decision.
transitive
  verb
  1 : to focus one's thoughts on : reflect on or ponder over
   - He was meditating his past achievements.
  2 : to plan or project in the mind :
  intend, purpose
  - He was meditating revenge.

In English the most famous classical usage in that sense would be the translation title The Mediations of Marcus Aurelius.
Answer: construct TFD

To create by systematically arranging ideas or terms.

As in:
When I am preparing a lecture, I tend to construct quotes, data and other pertinent bits into a digital notebook, without knowing in advance whether I am going to use that material.
Answer: Exploring would fit. You're exploring the subject.
From the link, definition 1: "to investigate, study, or analyze : look into ·explore the relationship between social class and learning ability
 —sometimes used with indirect questions "
(This unnecessary copy and paste brought to you by the script that told me my answer would be deleted for brevity.)
Comment: Surely that is the right word. All the others suggested: meditate, cogitate, ruminate convey more intensity than the OP seems to me to describe. Also "ruminate" has a (bad) technical meaning in psychoanalysis that is definitely not what is meant here.


Are auctions permitted according to Islamic laws?

Question: For example, I go and buy something for $100, and auction that something starting the bidding at $1, and then hope for the best.  Almost sounds like a gamble.  Which is why I am asking if auctions are permitted according to Islamic law?
Answer: While buying something for $100 and auctioning it at a starting bid of $1 is a highly questionable business practice (why not just start the bidding at $100?), there's no reason to believe it's forbidden Islamically.  Even the prophet himself is reported to have auctioned off items.
Auctioning is merely a method of determining the final price for a sale; so long as this final price is decided fairly and agreed upon by both parties when the transaction itself takes place, it's just a sale like any other.
Comment: You say "agreed upon by both parties" however, unless otherwise stated, the convention for auctions is they will need to be honored at the price reached even if the seller doesn't necessarily agree to the price. Does that scenario change your answer?
Comment: @banging That doesn't even make sense; why is the seller even auctioning his items if he's not going to agree to sell it?
Comment: He agrees to sell it but he might have been hoping for a higher bid. If the bid he was hoping for wasn't reached, he is still obliged to honor the auction (even though he might not agree to the final bid). Does that make sense? Otherwise, please delete my comments! Peace.
Comment: @banging When he auctions, even if he is hoping for a higher price, he understands the risk that he might be the final bid. The action of auctioning in itself means that one agrees to a specific price and is willing to pay for it, ones intention is secondary.


Multibit desktop wallet not updating Bitstamp exchange rate

Question: For some reason Multibit is telling me bitcoin is at $460 on Bitstamp when it's closer to $490. Why is that?
Answer: The exchange rate updates relatively slowly (every hour or I think for BitStamp) so as to avoid all the copies of MultiBit hitting the BitStamp servers too much.
It is obviously bitcoin that is being sent in a transaction so in any sale or purchase it is the bitcoin figure that you want to agree to rather than the "USD (Bitstamp)" or "GBP (OpenExchangeRates)" figure.


How to compare error metrics for model with and without Seasonality?

Question: I am aiming to guage the difference in my model performance from using data with and without Sesonality removal. My approach to Seasonality removal is taking the log of the column data and then performing 1-lag Differencing. This results in the first value of the column being NaN, which is then removed after all columns are processed. Also, it may be important to note both datasets are standardized after using sklearn.preprocessing.StandardScaler()
Edit 1: I have found a SO post with a very similar issue, however there are no responses. This is the post here
def remove_seasonality(col, drop=False):
    # check if col is stationary, if stationary skip col.
    if stationary_test(col, test=True) is True:
        return col

    # if column not number, skip col
    if not np.issubdtype(col.dtype, np.number):
        return col

    if (col < 0).any(): # check if contains neg values
        # add constant, make values positive
        col = col + col.min()

    log_values = np.log(col + 1) # add 1 to avoid log(0)

    diff = np.diff(log_values, prepend=np.nan)

    if drop:
        diff = diff.dropna()

    return diff

I am using a Tensorflow model composed with Convolutional Layers and GRU's, I am using MAE to evaluate my model performance. The problem is that the log-transform and differencing results in a much smaller magnitude of numbers, so I cannot compare the difference in datasets effect on the MAE.
I'm not sure how to rescale my predictions to be able to compare them, I don't think I can perform inverse differencing on my predictions because that operation requires the first value before Differencing - which doesn't exist.
Alternatively, Is there an appropriate metric I could use to evaluate the difference in data preprocessing without performing any rescaling?
Answer: To find the first value to invert the differencing process, I have used the last data point from the preceding dataset, e.g for my Validation predictions, I used the last value from the Training set. This last value is plugged into this function:
def invert_seasonality(seasonality_vals, last_cum_val):
    invert_vals = np.insert(seasonality_vals, 0, np.log(last_cum_val + 1)).cumsum()
    invert_vals = np.exp(invert_vals) - 1

    return invert_vals


Help with simple Circuit

Question: I am hoping that someone can help me to calculate voltage and current to the LED socket. I see that there are 3 batteries in series, plus a resistor (?). Thank you very much.
Answer: You will have a max open-circuit voltage of about 5V at the LED socket.
As for current, that becomes far more complex & depends as much on your LED as anything else:
The 'forward voltage' of the LED is a fairly fixed value. So, once current is flowing through a given LED, the total current flow is determined by the resistance of any series resistor and the 'overvoltage' of the supply.
Comment: Thank you very much. The LED is a 700mA and 2.9-3.25 recommended forward Voltage. So, in this circuit is the resistor working to limit the voltage?  We ultimately want to replace this with a rechargeable Li-Ion pack. Will this be possible? Thank you again for your help.
Comment: The LED technically limits its own voltage, as it presents effectively a short-circuit to any voltage above its "knee" voltage. However, using this property means allowing the LED to self-destruct by drawing a huge overcurrent. The resistor serves to limit the current, based on the _overvoltage_ available in the circuit. For example, with an LED voltage of 2.9V & a battery pack voltage of 4.5V you'll have around 1.6V of overvoltage. Placing an 8ohm (I think that's what I see labeled on that resistor) resistor in series with the LED means that 1.6V can drive 200mA through the resistor and LED.
Comment: @lagold If you exchanged the 1.5V(nominal) alkaline batteries with a 3.6V-4.2V(nominal) lithium-chemistry cell, the overvoltage at full charge would be reduced, so the current across the resistor & led would reduce along with it. This may pose no problem at all, or it may reduce the light output of the LED too much for your purposes, in which case you would want to reduce the value lf the xeries resistor to bring the current back up.
Comment: Thank you for the great explanation! So the series resistor helps to stabilize the LED current. Makes sense. So we are driving this LED at roughly 200mA and its recommended rating is 700mA. So we could make it 'brighter' if we wanted. This is a spotlight for a 'telescope' that attaches to your glasses (like a dentist uses) to help with fine work .... for those of us who don't have young eyes anymore.  And finally, what current would the LED see without the 8ohm resistor?
Comment: @lagold with no series resistor, the current would increase exponentially with voltage above the LED's 'knee' voltage, until you reached a point where the batteries' internal resistance cancelled the overvoltage, or the LED explodes. LEDs are diodes, not resistors; once you overcome the voltage necessary to forward-bias the diode, they don't do much anything to control their own current past that, which is why all led drive circuits need either a series resistor, or a current-controlled power source.
Comment: If you wanted to push closer to the LED's rated 700ma, a 3ohm resistor, with the same 1.6V overvoltage should give about 533mA current, to allow some testing to see if the increased light output is worth the reduced battery life for you. At 4.2Vmax from a LiPO/LiIon, you could get away with a 2 ohm resistor for 650mA @ 1.3V overvoltage (but you would *not* want to use while charging with that small a "safety margin")
Answer: "Double A" batteries each have a voltage of 1.5v. There are 3, making the total voltage going through the circuit 4.5v. The current is defined by the load, or what current the LED is able to draw. There's a limit to what the batteries can supply, but any LED you'd put in that socket would be well within said limit. Good luck!

Help with simple Circuit


Removing a pedal that has skipped a thread

Question: When getting on my bike I stood on the left pedal and my full weight caused the pedal to skip a thread. The pedal is now squinted and stuck in the crank. The pedals were cheap, but I am hoping to continue using the cranks. Does anyone know a good way to remove the pedal without destroying the crank? I was thinking of trying to drill it out and re-tap the crank but I would rather not if I can avoid it. Many thanks in advance.
Answer: The most likely cause of what happened is the pedal was installed with insufficient torque. This can allow movement in the threads that degrades the crank threads, which are aluminum in most cases and will wear away readily even as the hardened steel pedal threads remain intact. This all being the case, it's likely there's already damage to the crank threads no matter what you do from here. (Even if it were a steel crank, it still wouldn't be as hard and wear-resistant as the hardened material of the pedal spindle).
You could try to minimize damage to the crank by leveraging the pedal back into alignment before unscrewing it. It's possible that works out in your favor compared to driving the pedal out in a cross-threaded orientation. It could also do all sorts of damage itself if attempted. I have seen some pedals that are very low end and/or borderline defective where the threads are badly formed with blunt as opposed to sharp, crisp tips, causing the major diameter of the thread form to not really be what it's supposed to be; this isn't common but if it were the root cause of problem, then forcing the pedal back into position might work.
Ultimately the thread will likely need to be repaired afterward no matter what, which can be done by chasing with a tap if the damage is moderate or only affects a few threads, or installing a helical insert (helicoil) if the threads are toast.
Comment: The other possibility is that someone has swapped the left and right pedals, destroying the threads. I've just got caught out by that on a 2nd hand bike.
Answer: How did you know it skipped a thread?
Pedals become very, very tight even in normal usage. The fact that it's almost impossible to remove a pedal doesn't mean it skipped a thread.
Here are some instructions for pedal removal: https://yarchive.net/bike/pedal_remove.html

Once pedals have gotten beyond the removal with a regular pedal wrench
by hand, they are often too tight to be safely removed without heat.
If you were to force them off, assuming you had a wrench and
sufficient force, you would probably damage the threads in the crank
and possibly the pedal because aluminum would weld to the steel pedal
thread during removal.
Remove the crank and heat the pedal end of the aluminum over the
kitchen stove or equivalent.  When the crank is hot enough to sizzle
when touched with a wet finger, use the wrench and it should come off
about the way a lubricated tight pedal usually does.  If you have a
torch and try this on the bicycle, it is not easier, because you can't
hold the crank as well.

Note you need a true pedal wrench. Nothing else will remove your pedal, not cone wrench (too weak), not normal open ended wrench (not long enough, too wide). If your pedal is one of those with an Allen wrench without flats, it may be impossible to remove it (you may destroy the Allen wrench or the hex head on the pedal), because Allen wrench limits the maximum torque to a very low value. But you could still try with a long high quality Allen wrench and a cheater bar.
More instructions: https://www.sheldonbrown.com/brandt/stuck-pedals.html
Also note that pedals have opposing orientations. So if you removed right pedal and can't remove the left, it may be possible you are actually tightening the left pedal, not loosening, because the left pedal has strange thread orientation.
Don't drill it out, you'll destroy your cranks.
Comment: The hex key sizes used for pedals are big enough to take the torque without any problem. They can withstand much bigger torque than some cheap pedal wrench from bad steel. After all, similar shapes are used to drive even much bigger things. One can always insert a hex key bit into a large automobile ratchet wrench, e.g. a large automobile momentum wrench.
Comment: As pedal axles are steel, @VladimirF is probably right most of the time, but 6mm is a common hex size for pedals and I've seen 5mm. 6mm is marginal (I'd use penetrating oil first) and 5mm unlikely to succeed especially if poor assembly or a failure caused jammed threads
Comment: And even my extremely cheap toolset from Lidl contains an 8mm hex key with 21 cm handle. This can already produce torque too big for tightening the pedals and is normally completely sufficient to take them down after a year of riding. For really stuck pedals one wants something longer or preheat the pedals, though. The 8 mm hex head itself has no problem with very large torques - I mean torques generated by vigorously stepping with full body weight on a 30 cm long lever.
Answer: Remember that heat heals. Heating the crank with a gas stove or a similar flame can do wonders and what couldn't  be moved before can often move with that. I assumed that your cranks are not made of carbon fiber. Do that if the biggest leverage you can do fails. A metal pipe bar put on your wrench to extend it can help you to provide very large leverage.
When trying to use all my power (which is not that big, I do not wight much) I was most successful by placing the wrench in such a way that I could step on it forcefully. That means, below the crank. Be extra careful not to injure yourself. It is better of the chain is on the large chainring and covers the teeth.
Always think about the correct direction of rotation. I suggest the right hand rule (for the right pedal), and the left hand rule (for the left pedal) respectively. When you rotate in the direction where your fingers are pointing, you are forcing the screw to move in the direction of your thumb. It is much more useful than some righty tighty especially when your native language is not English. Also, do not get confused by hex keys that are inserted from the other side, the rule is still valid, you need the pedal to go away from the crank and away from the frame.
Comment: I prefer an electric hot air gun over fire - a workshop version of a hairdryer.  No open flame means its more controllable.
Comment: @Criggie I think I would have also preferred it if I had it.
Answer: Drilling and Retapping a thread into a crankarm is the very-last step before buying replacement cranks.
It can be done by a well outfitted workshop, using a mill and the correct taps, but against you are 3 problems:

Pedal axles are hardened - even the cheap ones are surface hardened and getting then to drill with home tools is a challenge.

The thread specs of a pedal are uncommon.   9/16 inch and 20 TPI, plus you need a left-hand tap on one side.  These are only used on pedal threads, so are exclusive to the bike industry.

Thread Replacements ("Helicoils tm") are also expensive for this spec - again the more-common 18 TPI thread is cheap, but the pedal-specific 20 TPI is expensive.

I suspect your pedal's axle has bent rather than slipping out.  They are generally hard to get straight and if they were only cheap to begin with then replacement might be easiest.
Removal Use a pedal spanner if you can - an adjustable spanner tends to be too wide in many places.  Some pedals only offer a hex socket on the inboard end, but that's generally fancy ones only.
Set the bike like you're about to push off and ride.  The pedal to be removed should be forward, and slightly above the axle.  Set your tool on the flats so that the handle pokes up and you can press it with your heel while the ball/toes are on the pedal.
Use hot air on the end of the crank, and after 20~30 seconds of heating douse the pedal axle only with WD40 or CRC556 or similar.  This is to gently heat the crank while cooling the shaft.
Then get on the bike and push the tool down with your heel while your toes are on the pedal.
Main reason for this is leverage, but it also gets the thread direction correct.
Comment: Surely you wouldn't tap an axle, you'd tap the crank. In the highly unlikely event of the pedal threads being damage, you'd need a die.  For cranks the helicoil kit is £150  (so around 170 USD or EUR) including the taps, but the helicoils themselves are only £5 per arm.  I could send my cranks away and pay £20 (€/$25) per crank to have it done, but one LBS has the tools.
Comment: @ChrisH that's right - you'd re-tap the crank holes with thread inserts to take a new pedal, once the old one is out.   That's assuming the thread is proper-boogered up.   Sometimes a simple chasing of the existing threads with the right tap is enough to get them working again.   OP said pedals were cheap, I'm assuming the plan is to discard once removed.
Comment: I might trusting chasing the threads if it was only the top turn or two that was damaged, but the stress is pretty high and damaged then chased threads will have ben subject to quite a bit of fatigue.  I've come across completely dead threads twice - the 2nd time yesterday and that was caused by someone putting a right pedal in a left thread


How do I get published as a student in Biblical Studies?

Question: I am a newcomer in research studies within Bible and Theology fields. I want to publish my own articles but do not know where to begin. How can I get my papers published formally? I am only a MA student so I am not even sure if I should start publishing yet.
Comment: Did you consider talking to your faculty advisor?
Comment: If you are doing a Masters by coursework and don't have a faculty advisor, did you try asking some of your course professors?
Comment: Doing serious research in **any** field requires finding an advisor. In addition to Darren's suggestion, consider talking to the chair of the graduate program at your department and see if they have a more specific suggestion: without knowing your department this is simply impossible.
Comment: I do not have a faculty advisor only professors per each class, no advisor is given. All I am doing is research in every course and I want to go beyond that. How can it be done?
Answer: Speak with the program director or your individual professors. They should be able to advise you about what journals are ideal for your research and whether your writing is professionally sufficient for academic publication. Many people in fields like theology, philosophy, etc. learn the publishing process just by trying and by polling our professors. Good luck!
Comment: Also, what do you mean by "outsource?"
Comment: Thanks David, I should have said I did this already and the program director said my writing was ideal for publication but he said I would need to outsource and he was not willing to do that at the time. Then I went to my current professor in a class on Johannine Theology. He said I needed to find an advisor but I do not know how to go about doing that.
Comment: If I were you, I would go and review recent publications from respectable authors and journals. Then I would revise your essay as professionally as possible, following the style and structure you found in those essays. Then I would try to submitting to journals. Maybe do not start with the most important theological/Biblical journals, but begin with respected ones. The Journal of Theological Interpretation would be one example. Or you can search for journals at major publishers, like Wiley or Sage. Wipf and Stock may have decent, if smaller, journals for you to practice with also.
Comment: They said "Christian you need to be careful writing. Your writing is great and well done for publication. You need to outsource your research output and input. You are a scholar in rising and taking to the stars. You have exhibited accelerated learning competencies and research ideas but you need to research your positions. You are expected to show your mastery of those pursuits as well."
Comment: Ok, that helps. I am remain less than 100% sure what the director means, but I think it means you need to network more and get more input on your ideas from the general community. Whether by doing a doctorate, going to conferences, reading more widely, networking with established scholars, etc. The last part also sounds like you need to practice the mechanics of research and widen your reading, as well. All that can be very boring, but is vastly important. Most of us only learn this by necessity in a doctorate or by experience in conference presentations.
Comment: Note, I am a PhD theology student who didn't get published until I was already about halfway through my classwork. The writing mechanics have been the hardest part for me not the theology or argument itself, so I think I get where you come from. Good luck!
Comment: Thanks David this is helpful. Can you email me? I would like to network. firstname.lastname@example.com
Comment: Let us [continue this discussion in chat](https://chat.stackexchange.com/rooms/149542/discussion-between-christian-saucier-and-david-ave).
Comment: Alternatively, talk to your pastor or priest. It's possible your denomination has some sort of scholarly publishing arm you could submit your paper to.
Comment: I responded on the chat, Christian. Just fyi.
Comment: "Outsource" usually means "get a contractor to do something for you in exchange for money".  I really hope that's not what the programme director meant.