i think my path is correct but still gives the same error 'php.exe' not recognized

Question: my symfony sandbox is inside the htdocs of my xampp folder which is inside the program files in c drive
i.e.
c:\program files\xammp\htdocs\sf_sandbox\
but when i try to run the command symfony -v it gives the error
'php.exe' is not recognized as an internal or external command
can somebody help me? what am i doing wrong?...
Answer: In this case you need to include the php folder or directory path to the all the global paths available in command line interface.
right click on the My Computer icon of the windows and you will be able to see the screen as given below
Click on the Advanced Tab of this window and then click on the Environment Variables button of the window
In the new window select TMP variable and then select Path variable and click on edit button.
At the end of the variable value field add the path of the directory (containing the php.exe sometimes its not what is given here. i.e. i had one situation where it was E:\wamp\bin\php\php5.2.8) for php (here it is ;C:\wamp\php) also put a semcolon (;) to seperate the path with the other existing paths.
Now one by one click ok for each window opened and restart your computer and the task is complete.
To check it just type php -v and press Enter.
Answer: What happens when you try to execute php from command line?
Have you tried adding path to php.exe to PATH environmental variable?
Answer: You may wish to try to adust the path to have c:\progra~1\xammp\htdocs\sf_sandbox in it.  The short name for any long path in DOS has been the downfall of many applications and they must be handled properly.  If you open a dos window and issue:
<code>cd \
dir /x
</code>
you will get a list of short names in 8.3 format.


Find distance from star to star?

Question: How do you find the distance from a star/planet/black hole to another? I know people can calculate the distance from Earth to a star, but what about from one to another?
Answer: If you know distance from Earth to both objects and the angle between them viewed from Earth, it is just a matter of trigonometry.
Comment: @FrancescoMontesano It is still trigonometry, just not Euclid's one.
Comment: That's true if the distance are less than few millions of ligthyears. Otherwise you have to account for cosmological effects and possible cosmic curvature
Comment: its 3 dimensional trigonometry just almost similar to what we use, but far more complex when considering the fact that you are measuring distance of two objects in the vast universe and not on a sheet of paper.
Comment: The key with cosmological distances is using the appropriate distance measure depending on the purpose of the measurement. Transverse comoving distance can be used to measure distances that take the expansion of the Universe into account and don't vary with time.
Answer: You only need two-dimensional trigonometry if you know the distances to the two stars and their angular separation. Any two-dimensional plane can be defined by three points that lie on it so we just use the plane containing the two stars and the Earth.
You can use Earth as the origin and the closest star as a point on the $x$-axis ($x_1$,$y_1$) where $x_1$ is the distance and $y_1$ is zero. You then can use the distance of the second star and its angular separation from the first star (which is on the $x$-axis) to plot a point ($x_2 = \text{distance} \times \cos(\text{angle})$, $y_2 = \text{distance} \times \sin(\text{angle})$). The distance between those two points is $$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$
Comment: When dealing with stars in the milky-way or even galaxies in the local group you are right, and simple flat-space (euclid) works just fine. However, for the very long distances you have to account for light travel time. The universe is expanding and the rate of acceleration has changed in the past. Objects at very different (large) distances can then be thought of as being set at a different age of the universe and therefore at a different sized universe. This is what enters in the equation as 'cosmological' effects.
Comment: I don't think that was in the question.  Also, if that is the case then you have to take into account all motion of the star.  For instance SDSS J091759.5+672238 have moved 400 light-years since the light we are seeing left it.  I also don't hear assumed movement taken into account since there is no universal 'now' in relativity.  For instance I always hear the furthest galaxies are about 13 billion light years away, not 26 billion.
Comment: This does not apply to large distances, as noted by Francesco.
Comment: Please explain more, I don't see why since space has been shows to be flat over most of the universe and the 'cosmological effects' aren't explained.  The fact that it does not explain exactly does not make it invalid just like we can still use Newton's equations for approximations and ordinary tasks instead of invoking general relativity (they got us to the moon).

Find distance from star to star?


Prove that $\forall p \in \Bbb P;p \ne 5,$ $F_{p^n - \left(\frac{5}{p}\right)p^{n-1}} \equiv 0 \mod p^n$

Question: Prove that $\forall p \in \Bbb P,n \in \Bbb Z^+;p \ne 5,$ $F_{p^n - \left(\frac{5}{p}\right)p^{n-1}} \equiv 0 \mod p^n$ and $F_{5^n} \equiv 0 \mod 5^n$, where $\left(\dfrac{5}p\right)$ is the Legendre symbol and $F_m$ is the $m$th Fibonacci number, with $F_1=F_2=1$. This is a generalization of the identity $F_{p-\left(\frac{5}p\right)} \equiv 0 \mod p$. Is the generalization well-known? I was trying to find an upper bound on the index of the first Fibonacci number dividing any integer $m$, which would then be the product of the indices associated with the largest power of each prime dividing $m$.
Comment: I would guess that in the case $p\neq5$ a formula like this can be proven by studying the Galois ring $\mathbb{Z}_{p^n}[\sqrt5]$ (so either the ring or its quadratic extension). The structure of the unit groups of those rings is known. Thinking... (this will take a while, also we have a department-wide junket today, so I won't be posting a solution any time soon). +1 to a fun question.
Answer: It is known that if $p$ is an odd prime factor of $F_n$, then $\frac{F_{p n}}{F_n}$ is divisible by $p$ but not by $p^2$. For $p=2$, the situation has to be handled more carefully, but is also well known (cf. e.g. N.N. Vorobiev, Fibonacci Numbers, p. 76).
Comment: Thank you. I'm having difficulty finding an english version of this online. Is it worth buying?
Comment: The result should online be available as Thm. 1 in J.H. Halton, On Divisibility Properties of Fibonacci Numbers, Fib. Quat. 4.3 (1966), 217-240. The book is nice to have, but not necessary.


Annihilator of two subspaces of vector space

Question: Let $V$ be a vector space. If $W_1,W_2$ subspaces of $V$ then $(W_1\cap W_2)^0=W_1^0+W_2^0$.
One way is very clear, and it's $W_1^0+W_2^0\subseteq (W_1\cap W_2)^0$. But I cant quite understand how to prove the other way?
I tried writing a base for the intersection and expanding it to each of the other spaces, then operate $t\in (W_1\cap W_2)^0$ on a linear combination of a generic vector from $W_1^0+W_2^0$ which I wrote a a linear combination of the base I expanded. Got stuck. Is that even the right way?
Answer: We know that if U and V are two subspaces of a finite-dimensional vector space: $\dim (U+V)=\dim U + \dim V -\dim (U\cap V)$. To prove the equality requested if suffice to show that $\dim (W_1^0+W_2^0)=\dim  (W_1\cap W_2)^0$. This is a direct consequent from the previous equality and the fact that
$W_1^0\cap W_2^0=(W_1+ W_2)^0$ and $\dim U^0=\dim V-\dim U$ for all subspace $U$ of $V$.
Answer: The main thing you need to use here is that a linear form defined on a subspace can be extended to a linear form on the whole space. To do this, just complete any basis of the subspace to a basis of the whole space, and define the linear form to be $0$ on the added basis vectors.
Now given a linear form $\alpha$ that vanishes on $W_1\cap W_2$, we wish to write it as the sum of a linear form $\alpha_1$ that vanishes on $W_1$ and a linear form $\alpha_2$ that vanishes on $W_2$. Consider the restriction $\beta_1$ of $\alpha$ to $W_1$; it needs to be zero (only) on $W_1\cap W_2$. We first wish to extend $\beta_1$ to a linear form $\beta_2$ on $W=W_1+W_2$ that vanishes on $W_2$, which can be done as follows. By the second isomorphism theorem one has $W/W_2\cong W_1/(W_1\cap W_2)$, and $\beta_1$ defines a linear form on $W_1/(W_1\cap W_2)$; through the isomorphism it gives a linear form on $W/W_2$ which lifts to our linear form $\beta_2$ on $W$ that vanishes on $W_2$. Now further extend $\beta_2$ to a linear form $\beta$ on all of $V$. By construction $\beta$ coincides with $\alpha$ on $W_1$ and vanishes on $W_2$. One can therefore take $\alpha_1=\alpha-\beta$ and $\alpha_2=\beta$.
Comment: I find two complementary subspaces, say $U_1$ and $U_2$ such that $W_1 = U_1 \oplus W_1\cap W_2$ and $W_2 = U_2 \oplus W_1\cap W_2$, and then we can find a third subspace $U_3$  such that $V = U_3 \oplus U_1 \oplus W_1\cap W_2 \oplus U_2$. Now by taking a basis for each of these subspaces, I can define a linear functional that annihilates $W_1\cap W_2$ as a sum of two linear functionals. Do I understand this right, is this what your solution means ?


torment...sulphur...in the presence of the Lamb: Rev 14:10

Question: Struggling to grasp this verse a bit and its consequences. Can you help? I have often felt that the descriptions of hell throughout the Bible do not paint a clear picture on the debate: is hell perpetual torment or not? In the past I have learned to hedge my bets a little and talk of separation from God (what Jesus suffered on the cross). This form of judgement seems perfectly in line with what some describe awaits those unrepentant sinners in hell. Yet the lamb is right there, presumably watching (this reminds me also of the mass drownings in Noah).
Comment: This question is far too broad. Is it a question about how to exegete Revelation 14.10 specifically (the title), or is it a question about the theology of hell in general (the full paragraph)?
Answer: The plain and normal reading of the Scriptures indicate that eternal damnation is experiential and actual. There is no dispute that Jesus spoke more about eternal damnation in the gospels than he spoke about righteousness and eternal life. If eternal damnation is real, then how or why would the Lamb of God allow perpetual torment for sinners? The Apostle Paul provides the patience of the Lord as the lens through which we are to understand this most difficult of concepts in the Bible.

Romans 9:22-23 (NASB)
22 What if God, although willing to demonstrate His wrath and to make His power known, endured with much patience vessels of wrath prepared for destruction? 23 And He did so to make known the riches of His glory upon vessels of mercy, which He prepared beforehand for glory

There are sinners who are condemned, but before their eternal banishment, they had experienced the patience of God. The Apostle Peter mentions this same patience.

2 Peter 3:14-15 (NASB)
14 Therefore, beloved, since you look for these things, be diligent to be found by Him in peace, spotless and blameless, 15 and regard the patience of our Lord as salvation; just as also our beloved brother Paul, according to the wisdom given him, wrote to you

Both Peter and Paul recognized that salvation is the result of the patience of the Lord toward sinners. Before the flood hit the earth in the days of Noah, the patience of the Lord continued for 120 years (Gen 6:3) as Peter indicates that the time ran out.

1 Peter 3:18-20 (NASB)
18 For Christ also died for sins once for all, the just for the unjust, so that He might bring us to God, having been put to death in the flesh, but made alive in the spirit; 19 in which also He went and made proclamation to the spirits now in prison, 20 who once were disobedient, when the patience of God kept waiting in the days of Noah, during the construction of the ark, in which a few, that is, eight persons, were brought safely through the water.

So while he is patient with all sinners, the Lord calls sinners to himself. The Apostle Paul indicated that his salvation resulted from this patience, as he had regarded himself the worst of sinners imaginable.

1 Timothy 1:13-16 (NASB)
13 even though I was formerly a blasphemer and a persecutor and a violent aggressor. Yet I was shown mercy because I acted ignorantly in unbelief; 14 and the grace of our Lord was more than abundant, with the faith and love which are found in Christ Jesus. 15 It is a trustworthy statement, deserving full acceptance, that Christ Jesus came into the world to save sinners, among whom I am foremost of all. 16 Yet for this reason I found mercy, so that in me as the foremost, Jesus Christ might demonstrate His perfect patience as an example for those who would believe in Him for eternal life.

The Apostle Paul was not only a blasphemer, but as the zealous Pharisee his self-appointed mission was to force Christians to renounce Jesus Christ, and therefore to cause them to blaspheme (Acts 26:11). He was therefore the worst sinner in the world from the perspective of heaven, since his sins were related to blasphemy.
But the patience of God was why he was saved.
In other words, the Lord is in the business of saving sinners, and in the process his patience continues to endure. The following syllogism will help to understand the concept.
<code>  The saved are sinners (for whom the Lord was patient),
  but not all sinners (for whom the Lord was patient) are saved.
</code>
The statement is not intended to be tautological, but to provide the nuance that the Lord is patient with all sinners wishing for them all to be saved.

2 Peter 3:9 (NASB)
9 The Lord is not slow about His promise, as some count slowness, but is patient toward you, not wishing for any to perish but for all to come to repentance.

In conclusion, the patience of the Lord applies to all sinners. It is the explicit desire of the Lord that all be saved, because Christ died for all sinners (1 Jn 2:2).  Those who are not saved will suffer eternal torment, but not because the Lord was not patient with them at one time.
Comment: (-1) because you did not answer the question and instead provided a theodicy.
Comment: @Joseph I believe you DID answer the question: the Mercy of God is available for all, therefore no one has an 'excuse' on the Day of Judgment. However, those who have been redeemed by the Lamb, have 'passed through' judgment and are in the Lamb's Book of Life.
Answer: Your question seems similar to me to one answered by the Romanian (Orthodox) monk, Elder Cleopa, in his book The Truth of Our Faith.  Namely:

There is a very old view that God is All-Good, that His love is
  unlimited toward man and because of this it is practically impossible
  for Him to chastise men with eternal suffering.  He is the Father of
  all and what kind of Father would chastise His disobedient children
  with eternal torture?  Isn't a father supposed to forgive his
  children? Wouldn't our heavenly Father be so much more disposed to
  mercy and forbearance towards us?

To this, he answers:

Truly, God is forgiving and long-suffering towards those who fall into
  sin in this life, for the time of our correction is now, in this life,
  and the acquisition of His forgiveness depends on our own repentance.
  In the life on the other side of the grave, however, we no longer are
  able to repent, to change our minds, given that there God does not
  judge us according to His omnipotence and goodness, but in accord with
  His impartiality and righteousness [viz. John 9:4], rewarding each
  according to his deeds [Matthew 10:41;25:35].  If God were to forgive
  all the sins of men without justice or fairness, what would be the
  point of continually alarming us with the terror of eternal torments
  if, in fact, they didn't exist?  How is it possible for God to tell us
  lies instead of truth?

He continues,

God offers eternal joy to the righteous, who struggled for a time to
  carry out good works here on earth, but as a just and righteous God,
  He also chastises eternally the ungodly that transgressed in this
  temporal life.  Why is it so?  Because the wounds incurred from sin
  that are not healed in this life through the appropriate repentance
  will remain infected eternally in the presence of God.  If we mock and
  scorn the Person of God by committing sins with our free will, we must
  remember nevertheless that His glory, power and righteousness and all
  His divine characteristics have no end.  In the same way, on account
  of the sins we have not repented for, the torments of hell will also
  be unending.

Your calling attention to the Scripture in Revelation also brought to mind something an American Orthodox monk, Seraphim Rose, wrote that could help explain the role the presence of the Lamb:

For most men today "life" is a small thing, a fleeting thing of small
  affirmation and small denial, veiled in comforting illusions and the
  hopeful prospect of ultimate nothingness; such men will know nothing
  of Hell until they live in it.  But God loves even such men too much
  to allow them to simply "forget" Him and "pass away" into nothingness,
  out of His Presence which alone is life to men;  He offers, even to
  those in Hell, His Love which is torment to those who have not
  prepared themselves in this life to receive it (Nihilism, p. 99)
Comment: No, that's not what he is trying to convey.  Fr. Seraphim's thesis is that God's presence and love is not something that one can escape.  It will be a source of joy for those who have sought communion with Him and lived a life of repentance, but a source of torment for those who turned away for Him or didn't even bother to seek Him.  In this sense, we make our own hell.  Another Orthodox writer, Kallistos Ware pointed out that the same is true in our relations with other people ...
Comment: Hello. I'm sorry for interrupting but I'm confused. Is Seraphim saying that God loves men too much to simply let them cease to exist (where they wouldn't even care if they don't exist because they have no consciousness to care about anything), so he shows his love by tormenting and burning them in fire forever?
Comment: "Egocentricity is the death of true personhood. Each becomes a real person only through entering into relation with other persons, through living for them and in them. There can be no man, so it has been rightly said, until there are at least two men in communication ..."
Comment: "The same is true, secondly, of love. Love cannot exist in isolation, but presupposes the other. Self-love is the negation of love. As Charles Williams shows to such devastating effect in his novel Descent into Hell, self-love is hell; for, carried to its ultimate conclusion, self-love signifies the end of all joy and all meaning. Hell is not other people; hell is myself, cut off from others in self-centeredness."

Ware, Kallistos. The Orthodox Way (Kindle Locations 409-414). St Vladimir's Seminary Press. Kindle Edition.
Comment: Okay I think I understand. Are you saying there is no fire or torture, but men will be mentally tormented because they do not desire God's love- but he will give it to them anyways?
Answer: Examining Revelation
Your question is regarding Rev 14:10, but also by implication involves v.11 as well, and needs v.9 for context also, so Rev 14:9-11 (quoting here NKJV):

9 Then a third angel followed them, saying with a loud voice, "If anyone worships the beast and his image, and receives his mark on his forehead or on his hand, 10 he himself shall also drink of the wine of the wrath of God, which is poured out full strength into the cup of His indignation. He shall be tormented with fire and brimstone in the presence of the holy angels and in the presence of the Lamb. 11 And the smoke of their torment ascends forever and ever; and they have no rest day or night, who worship the beast and his image, and whoever receives the mark of his name."

Your question involves two main points:

Is the torment forever?
If so, does that torment involve a separation from God?

Both of those questions are answered in v.10-11, though the former is more implied than directly stated in this passage.
First, it is "the smoke of their torment" that is noted to have an eternal quality of ascending forever. But for smoke to ascend forever, there must be something that is forever burning (hence the implication). It is explicitly stated that the smoke arises from "their torment" (v.11), which relates to v.10, where the torment is of the person, who "shall be tormented with fire and brimstone." So the torment of burning lasts forever, as it is forever sending up smoke from that burning.
Second, "in the presence of the holy angels and in the presence of the Lamb" explicitly notes the lack of physical separation to the Lamb. The Lamb is mentioned 29 times in the Book of Revelation and is a reference to Jesus Christ. This reference is most explicit in the Apostle John's gospel, rather than in the Book of Revelation (which he also authored), for in his gospel he notes John the Baptist's declaration that Jesus was the "Lamb of God" (Jn 1:29, 36; cf. 1 Pet 1:19). The association of Jesus to this picture is essentially assumed in Revelation.
So if one holds a trinitarian view of God (as I do), then the answer of an eternal separation from God is already found, since Jesus is God—there is no such separation found in eternity, at least with respect to the experience of the smoke from the burning. But recall that this burning is also associated to "the wrath of God" (v.10), and wrath is a very personal expression, not something done in disassociation with the object of wrath. So God himself has a "presence" involved in this torment.
Now should one not want to take the trinitarian view for granted, that the God and the Lamb become inseparable is found in Revelation itself:

Rev 21:22 makes it clear that there is a unity between "the Lord God Almighty and the Lamb," who combined "are its [holy Jerusalem's, v.10] temple." That is, they function in unity as the singular temple.
Rev 22:1 makes it clear that there is a singular "throne of God and of the Lamb" from which a singular "pure river of water of life" proceeds.

So where the Lamb is, God is, and vice versa. If the torment occurs forever in the presence of the Lamb, then it occurs in the presence of God also; if the wrath of God is being expressed eternally, then the Lamb is involved in that expression.
Third, who is here being tormented? Specifically those who worshiped "the beast and his image" and who received the beast's "mark on his forehead or on his hand" (v.9). Is this any different of a place or experience from others noted as being tormented eternally? No. The language used makes it clear that this burning occurs in the same place as those who lead in this rebellious work, that is, Rev 19:20:

Then the beast was captured, and with him the false prophet who worked signs in his presence, by which he deceived those who received the mark of the beast and those who worshiped his image. These two were cast alive into the lake of fire burning with brimstone.

The burning from fire and brimstone occurs in "the lake" that has such effect. This same lake is the destiny of the devil also (Rev 20:10), as well as all those who partake of "the second death" (Rev 20:14), not having escaped its power "in the first resurrection" (Rev 20:6), which are all those "not found written in the Book of Life" (Rev 20:15), which are all those who have died in their sins (cf. Jn 8:21, 24; 1 Cor 15:17), not having been cleansed from them (cf. 1 John 1:7, 9), and so are known and judged by their unrighteous works (Rev 20:12), which is their sins (Rev 21:8).
Conclusion
So Revelation is fairly clear itself in answering the two parts to the question, and becomes more clear when joined to John's other writings (his gospel and epistles). There is an eternal torment and that torment, as well as its by-product of smoke, is in the presence of God and the Lamb.1
Optional Theological Expansion
The answer above is primary to the BH.SE site, as interpretation of the Book of Revelation, especially coupled to John's other writings, gives the answer to the question (which can be further bolstered by incorporating even more non-Johaninne writings). If you are one who does not like theology being discussed, then there is no need to read further than what was said above.
But for those interested, I will digress on a short theological expansion, as theologically, people have issue with this eternal torment, especially in God's presence, for a number of reasons, and the questioner is obviously wrestling with some of those as well. Some of the chief views that impede ones understanding of God's eternal torment of the unbelieving involve one or more of these false (in my mind) theological viewpoints:

The unbelieving are eternally separated from God.
God is love, and loves all, so He would not torment.
There is no real resurrection, it is just symbolic.

I will briefly give my answer to these points.
Those tormented, rather than being separated from God, are in fact experiencing their burning as part of their experiencing the direct presence of God while still in an unrighteous state. Part of the nature of God is not only that He is love (1 Jn 4:8, 16), but that He is a consuming fire (Heb 12:29), and it is "from the presence of the Lord and from the glory of His power," when His presence is no longer held back from the unrighteous, that this eternal burning comes (2 Thes 1:9; i.e., the "from" there is not in separation, but in source).
But why does God let such torment go on?2 Because in a single sacrifice of His Son, He purchased redemption of all people from the penalty of sin, physical death, and hence all people experience resurrection out of that death on the basis of His paying the penalty. This was God's expression of love to all—to do as He promised, to free all people from the penalty of sin. This freedom is from the first death, and the sacrifice was an act that has a corporate and eternal consequence (that is, it is for all humanity, a universal atonement). It is also an act that can be disbelieved, rejected, and opposed—but not without consequence.
God freeing all humanity in this greatest of all acts of love for them was motivated so that He could save "all the ones believing on Him" so that they "should not perish but have everlasting life" (John 3:16). It was done for all, but only to give life to a subset, the believing.
The rest, the unbelieving, experience "the second death" of Revelation 20. But this second death is distinct from the first death, because now the unbelievers also exist in a resurrected body. There are those resurrected to life and those to condemnation (John 5:29), as both the just and unjust are resurrected (Act 24:15). But Christ conquered the first death, and in that victory that becomes fully expressed at the resurrection, mortality is no more—people cannot die physically in their resurrected bodies (1 Cor 15:53-56).
Jesus's conquest over death affects both the just and unjust, but they each go on to experience two different eternities, a continued life or condemnation to a second death. The latter is the casting into the lake of fire, the place where piecing the above Scriptures together, God has gathered the unbelievers to experience the immersion into His presence, which immersion pairs His nature as a consuming fire against their unrighteousness with their new natures of immortal, resurrected bodies, the result being both the eternal burning of a body never consumed (hence the smoke rising from it forever) and the eternal eating of that body by worms that also never die (Mark 9:42-47; cf. Mat 18:6-9).
So eternal torment of unbelievers is a planned by-product of eternal salvation of believers, for to save the latter, God chose to save all humanity in the resurrection, as saving them from their deserved penalty of sin is a loving act. Christ died for the unjust (1 Pet 3:18), which is all people standing in their own righteousness, for He died for them while they were all "still sinners" (Rom 5:8). But rejecting that act of love makes this act God's only saving work toward the unbeliever. He is the "living God, who is the Savior of all men, especially [the Savior] of those who believe" (1 Tim 4:10). All are saved from physical death in the resurrection, but believers are especially saved, being saved from final condemnation through their faith, for with faith, they are no longer seen as unjust, but just, having the righteousness of God accounted to them for their faith (which is the primary argument of Romans chapter 4).

NOTES
1 For those interested, there is another BH.SE answer discussing eternality and torment in the context of Mat 10:28.
2 The argument that follows after this footnote can be found in more detail in my dissertation, primarily with respect to a universal atonement that brings resurrection, but discussion of the eternal implications of that fro the unbeliever is also touched upon in that work.
Comment: I'm sorry, explain again your idea of the indivisible singularity of God and the Lamb
Comment: @SearchofKings Comments are not the place to explain that, but as I stated, I hold a [Trinitarian view of God](https://carm.org/what-is-the-trinity),
Answer:
"The same shall drink of the wine of the wrath of God, which is poured
  out without mixture into the cup of his indignation; and he shall be
  tormented (βασανισθήσεται G928) with fire and brimstone (θείῳ G2303) in the presence of the holy angels,
  and in the presence of the Lamb" Revelation 14:10

There is one word in this verse that is mistranslated, and the other is very misunderstood. The first is basanizo. According to Thayer's concordance, the first definition of this word is:

"to test (metals) by the touchstone, which is a black siliceous stone
  used to test the purity of gold or silver by the colour of the streak
  produced on it by rubbing it with either metal"

Basanizo means to test the purity of metals. God does not torture or torment anybody. The Scriptures say:

"Behold, I have refined thee, but not with silver; I have chosen
  thee in the furnace of affliction." Isaiah 48:10

And again:

"And I will bring the third part through the fire, and will refine
  them as silver is refined, and will try them as gold is tried: they
  shall call on my name, and I will hear them: I will say, It is my
  people: and they shall say, The LORD is my God." Zachariah 13:9

And again:

"But who may abide the day of his coming? and who shall stand when he
  appeareth? for he is like a refiner's fire, and like fullers'
  soap: And he shall sit as a refiner and purifier of silver: and he
  shall purify the sons of Levi, and purge them as gold and
  silver, that they may offer unto the LORD an offering in
  righteousness." Malachi 3:2

It is believed that basanizo means torture or torment. This is impossible, because our loving Father does not torture anyone. The third definition Thayer gives is "distressed, to be harassed". Since there are only a few occurrences of basanizo, I will go ahead and quote them all and replace the word "tormented":

"And saying, Lord, my servant lieth at home sick of the palsy,
  grievously tormented (distressed/harassed)." Matthew 8:6
"And, behold, they cried out, saying, What have we to do with thee,
  Jesus, thou Son of God? art thou come hither to torment
  (harass/distress) us before the time?" Matthew 8:29
"But the ship was now in the midst of the sea, tossed (distressed)
  with waves: for the wind was contrary." Matthew 14:24
"And cried with a loud voice, and said, What have I to do with thee,
  Jesus, thou Son of the most high God? I adjure thee by God, that thou
  torment (harass/distress) me not." Mark 5:7
"And he saw them toiling (distressed/harassed) in rowing; for the wind
  was contrary unto them: and about the fourth watch of the night he
  cometh unto them, walking upon the sea, and would have passed by
  them." Mark 6:48
"When he saw Jesus, he cried out, and fell down before him, and with a
  loud voice said, What have I to do with thee, Jesus, thou Son of God
  most high? I beseech thee, torment (harass/distress) me not." Luke
  8:28
"(For that righteous man dwelling among them, in seeing and hearing,
  vexed (distressed/harassed) his righteous soul from day to day with
  their unlawful deeds;)" 2 Peter 2:8
"And to them it was given that they should not kill them, but that
  they should be tormented (distressed/harassed) five months: and their
  torment (distress/harassment) was as the torment (distress/harassment)
  of a scorpion, when he striketh a man." Revelation 9:5
"And they that dwell upon the earth shall rejoice over them, and make
  merry, and shall send gifts one to another; because these two prophets
  tormented (distressed/harassed) them that dwelt on the earth."
  Revelation 11:10
"And she being with child cried, travailing in birth, and pained
  (distressed/harassed) to be delivered." Revelation 12:2
"The same shall drink of the wine of the wrath of God, which is poured
  out without mixture into the cup of his indignation; and he shall be
  tormented (distressed/harassed/tested) with fire and brimstone in the
  presence of the holy angels, and in the presence of the Lamb"
  Revelation 14:10
"And the devil that deceived them was cast into the lake of fire and
  brimstone, where the beast and the false prophet are, and shall be
  tormented (distressed/harassed/tested) day and night for ever and ever
  (towards the ages of the ages)." Revelation 20:10

The second word is theion, which is very closely related to the word "theos"- divine/God. Thayer's concordance says:

"Brimstone; divine incense, because burning brimstone was regarded as
  having power to purify, and to ward off disease"

So there are three words in this verse that have to do with purification and refinement- basanizo, theion, and fire.
Obviously this testing and purification cannot last forever and ever (because one ever is never enough!), because the Lamb has better things to do than stand in "hell" for "eternity" and watch people get tested and refined for no purpose whatsoever; but that's outside the scope of this question.
Thank you.
Comment: You omit the remainder of Thayer/Wilke's entry on βασανίζω, in particular: "4. univ. to vex with grievous pains (of body or mind), to **torment**." Then within that same section Thayer/Wilke specifically states, "with ἐν and the dat. of the material in which one is **tormented**, Rev. 14:10." Would you care to explain your omission of the rest of Thayer/Wilke's entry on the verb βασανίζω?
Comment: I changed the translation (with a Thayer approved definition) every time the translation presents an irrational, unreasonable, and incomprehensible theological bias. Actually, torment isn't the worst translation since it means "severe physical OR mental suffering". There are a few translations, such as the ISV, that translate it as "torture". That is the idea theologians have attached to basanizo, but the loving Father we serve desires mercy, not sacrifice. And if there is such a word as "forever" in the Scriptures, Isaiah 57:16 explicitly contradicts this "eternal torture" idea.
Comment: Thank you Andrew. I agree this is about Israel, so does that mean no Israelites are going to hell? There is no (not 'never') peace for the wicked because their thoughts are "tormented" by their actions. However, when every knee bows and every tongue confesses to YHVH, there will be peace. God's mercy endures forever (Psalm 136), and mercy triumphs over judgment  (James 2:13).
Comment: Hello @SimplyaChristian. I went ahead and addressed this as well. Thank you.
Comment: "It is believed that basanizo means torture or torment. This is impossible, because our loving Father does not torture anyone." - That?
Comment: No, I added every instance of basanizo and inserted distressed/harassed because that is the third definition Thayer provides.
Comment: Oh, so you changed the translation in accordance with your theological bias? Nice. Why bother citing Thayer when he obviously did not support your translation? He says it means torment in Rev. 14:10.
Comment: @anonymouswho Is. 57 states internally that v. 16 regards the chosen people Israel. If you continue reading, you'll see _But the wicked are like the tossing sea, which cannot rest, whose waves cast up mire and mud. "There is no peace," says my God, "for the wicked"_ in vv. 20-21. So no, 57:16 does not explicitly contradict that idea.
Comment: Hey Andrew and SimplyaChristian, would you like to take this conversation to chat?
Answer:
Matthew 25:31 "When the Son of Man comes in his glory, and all the angels with him, he will sit on his glorious throne. 32All the nations will be gathered before him, and he will separate the people one from another as a shepherd separates the sheep from the goats.
46"Then they will go away to eternal punishment, but the righteous to eternal life."

This will be fulfilled as follows:

Revelation 14:9 A third angel followed them and said in a loud voice: "If anyone worships the beast and its image and receives its mark on their forehead or on their hand, 10they, too, will drink the wine of God's fury, which has been poured full strength into the cup of his wrath. They will be tormented with burning sulfur in the presence of the holy angels and of the Lamb. 11And the smoke of their torment will rise for ever and ever. There will be no rest day or night for those who worship the beast and its image, or for anyone who receives the mark of its name." 12 This calls for patient endurance on the part of the people of God who keep his commands and remain faithful to Jesus.

Jesus is the judge and the holy angels are executioners. It serves no purpose for the judge to continually supervise the torments. There is no such need.
What is the point of mentioning the angels and the lamb in Revelation? Twofold.

The unrighteous will eventually face Jesus so they will see the truth.
The righteous will be encouraged to be patient so that they will remain faithful despite present suffering.

But no, it does not mean that Jesus will continually watch the unrighteous being tormented forever as if some sadist would.
Good question, one that I would ask myself.
Answer: torment…sulphur…in the presence of the Lamb: Rev 14:10
Revelation 14:10-11  (NET Bible)

10 That person will also drink of the wine of God's anger that has
been mixed undiluted in the cup of his wrath, and he will be tortured
with fire and sulfur in front of the holy angels and in front of the
Lamb. 11 And the smoke from their torture will go up[e] forever and
ever, and those who worship the beast and his image will have no rest
day or night, along with anyone who receives the mark of his name."

If a parent were to punish his child, by placing the child's hands over the fire, no doubt one would say that the parent was cruel , sadist, inhuman. Likewise, God is a God of love and does not punish people in hellfire, the book of Revelation is symbolic prophetic book and most of it should not be taken literally.
Is there existence of hellfire, the answer is definitely " NO " Why?
Back in the days of of the prophet Isaiah God prophesied the nation of Edom would be punished because of their hatred and  hostility towards Israel, the prophecy of Isaiah reads:
Isaiah 34:9-10  (NET Bible)

9 Edom's streams will be turned into pitch and her soil into
brimstone; her land will become burning pitch.  10 Night and day it
will burn;  its smoke will ascend continually.   Generation after
generation it will be a wasteland, and no one will ever pass through
it again.

Is the nation of Edom still burning from generation to generation to our days? Certainly not, the nation of Edom was destroyed and completely disappeared from the surface of the earth, as if totally consumed by fire, its punishment was everlasting, a wasteland an emptiness, that wild animal will possess it. Isaiah continues with his prophecy:
Isaiah 34:11-12  (NET Bible)

11 Owls and wild animals will live there,  all kinds of wild birds
will settle in it. The Lord will stretch out over her the measuring
line of ruin and the plumb line of destruction. 12 Her nobles will
have nothing left to call a kingdom,  and all her officials will
disappear.

Christians reading the Bible learn from Edom's destruction, that her burning is still ascending in a symbolic way.
Answer: In Luke 19:10, Jesus says,

"For the Son of man is come to seek and to save that which was lost."

Then Jesus proceeds to tell the Parable of the Ten Talents, in which he distributes 'talents' to His servants and asks them to make a return on their investment. It then goes on to say how each one doubled their return-except for the one who returned nothing.
But in vs 27, it says

"But those mine enemies, which would not that I should reign over them,
  bring hither, and slay them before me."

Those that are not "with" Jesus are against Him (Luke 11:23),

"He that is not with me is against me: and he that gathereth not with
  me scattereth."

Therefore, there is no 'neutral ground', you are either a Friend or a Foe.
Hell was created for the devil and his angels; (Matt. 25:41)

"Then shall he say also unto them on the left hand, Depart from me, ye
  cursed, into everlasting fire, prepared for the devil and his angels:"

God desires that no man perish, but all come to Eternal Life,(2 Pet. 3:9)

The Lord is not slack concerning his promise, as some men count
  slackness; but is longsuffering to us-ward, not willing that any
  should perish, but that all should come to repentance.

but those who choose against the Grace of God, do so at their peril; they have wittingly(or unwittingly) have chosen to be with Satan, and as such suffer the same consequences as he does. The suffering is Real and the torment is Real; yet the choice was theirs. God gave man immortality, because He created man in His image and likeness. He gave man the freedom to choose Life or Death(Deut. 30:19), to choose life is to live with God for eternity; to choose death is to live apart from God(in Hell) for all eternity.
God fully understands the consequences of this descision, therefore He has made every way available in His Mercy through Jesus to avoid it.


Could we give Mars Earth-like gravity using dark energy?

Question: In the far future, humans are struggling with the idea of whether or not to use dark energy's repulsive-gravity capabilities to surround Mars in a sphere of it (regardless of how, let's assume they have energy manipulation) to simulate Earth's gravity. Disregarding cost and more accessibility, would this be feasible?
Comment: If they can magically manipulate energy with handwavium, they can presumably just directly control gravitons as an easier solution.
Comment: Sorry for the confusion, but I think your original question was much closer to what you wanted to ask.  You are interested in dark matter, not dark energy, as dark matter is what would add to the gravitational force.  The mistake in your original question was the bit about "repulsive" gravity.  You want the standard attractive gravity.  You  don't want dark energy.  I've suggested an edit.
Comment: VTC OT:Unclear.  Are you talking about [this dark energy](https://en.wikipedia.org/wiki/Dark_energy)?  You can never rely on everybody knowing what you're talking about.  You need to bring the basics of a current theory (if that's what you're referring to) into your question.  Links should only be used for supporting information.  Is this a [tag:reality-check]?  If so, present a complete scenario for us to evaluate.  Are you simply asking if a theoretical (read: *fictitious*) concept could be used the way you describe?  Be very specific about what you're asking about.
Comment: I just realized that I may have misunderstood your question due to its ambiguity.  You mentioned the repulsive force of dark matter.  I assumed you meant the attractive force of dark matter (which would work well, hence my answer).  But if you meant the repulsive force of dark energy (which I'm now thinking you meant), then that is a much less straight-forward question.
Comment: I removed the [tag:dark-matter] tag since you just made that one up (and it no longer applies anyway).  I added in one for [tag:mars] and for [tag:gravity].  If there's an *existing* tag for the type of energy, I'm not sure what it would be.
Comment: VTC: I agree with @JBH's rationale here, and their suggested improvements that could salvage the question. Though, from the existing high-quality answers, the answer is likely to be "not very feasible at all"! :)
Comment: Related: https://worldbuilding.stackexchange.com/q/77829/627
Answer: Dark energy does not matter on small scales.
This would not work because dark energy is quite insignificant on small scales - after all, there's a reason we don't see its effects on the motions of bodies in the Solar System or even on stars within the Milky Way. Its density is approximately $8.8\times10^{-30}\text{ g cm}^{-3}$ based on Planck data, which is tiny compared to the density of regular matter or energy in, say, a planet. In fact, a region of space the size of Mars would contain the equivalent of about a milligram and a half of dark energy. That's quite small.
There is expansion on human-sized (or planet-sized) scales, but it's small. In the absence of other gravitational effects, the universe expands according to Hubble's law:
$$v=H_0d$$
where $H_0$ is the Hubble constant and $d$ is the distance to the other object. There is an ongoing (and exciting) dispute about the value of $H_0$, but it's thought to be in the vicinity of $68\text{ km s}^{-1}\text{ Mpc}^{-1}$, meaning that if $d=1\text{ Mpc}$, $v=68\text{ km s}^{-1}$. Even that is quite small compared to normal motions of planets, stars and galaxies. You need to go to distances of dozens or hundreds or megaparsecs before the expansion of the universe - or dark energy - becomes at all relevant.
Let's say you want to change all of that and assemble a ball of dark energy. For an order of magnitude estimate of how unfeasible this is, consider the difference in mass between Earth and Mars - about 0.89 Earth masses. Dividing this by the ambient dark matter density yields a volume of $6\times10^{56}\text{ cm}^3$ - encapsulated by a sphere 5.5 light-years in radius. You would have to sweep up all the dark matter in a 5.5 light-year radius to get an energy density comparable to the one you require.
Regardless of whether or not this is possible, it's highly inefficient.
There's also the slight large problem that dark energy will not increase the gravity of Mars, as its effect is repulsive.
Dark matter has its own problems.
There's been some confusion about whether you want dark matter or dark energy. Presumably, more dark matter would indeed increase Martian surface gravity to an Earth-like figure. However, you have more problems with that - some new, some old. First, the local dark matter density is tiny, roughly $10^{-19}\text{ g cm}^{-3}$. This is about ten orders of magnitude higher than the dark energy density, but small all the same. Again, dark matter is simply inefficient.
You have an even larger problem though: dark matter is collisionless, meaning it cannot form planetary- (or star-) sized structures. Clumping can happen on galactic scales via a number of different mechanisms, but not on Mars-sized scales. Any clump of dark matter of the size you want will dissipate.
Answer: No, dark energy does not work that way as far as we know.

The repulsive effects of dark energy are directly proportional to the distance between the two objects.
The attractive effects of gravity are inversely proportional to the distance between the two objects.
This means that the dark energy's repulsive "force" will only exactly counter the gravitational force at a very specific distance where the two forces are equal, and then only if the dark energy is actually between the two objects.

So even if you were to put Mars under a blanket of artificially concentrated dark energy it would act on the people on the surface in exactly the same way that it would act on the planet itself. So there would be no net change for the inhabitants.
P.S. You would actually do better if you did use dark matter and just concentrate it in the core of mars and have it just use the actual gravity of the dark matter to increase the gravity on mars. Or better yet, just add real mass to mars (it's probably easier).
Answer: Careful what you wish for.

You here assert dark energy has repulsive gravity.  Mars is in a sphere of it.  Presumably instead of pulling down on things from below as gravity seems to do, this effect would push down on things from above.  Ok, cool.  We are heavy again.  Mmm.
You have a lot of this repulsive gravity stuff, and it is all around Mars.  It is enough to effectively increase the perception of gravity to that of Earth.  Earth has 10x the mass of Mars.  That means a push down from above of 90% earth's gravity.
Inside the sphere on the surface of Mars, the vectors of Mars gravity and repulsive gravity are additive, combining to make us heavy.  On the far side of the sphere there is repulsive gravity too.  But now the repulsive gravity counteracts the gravity of Mars.
Mars was counting on its gravity to keep going around the Sun.  But Mars now has an effective mass of -90% that of Earth.

We are heavy down here on Mars, and it is getting dark.  And cold.
Comment: Unfortunately, the sphere of anti-gravity producing matter wouldn't even push down on people inside it. Inside a hollow sphere, the forces cancel out exactly at every point: the part of the sphere above you is closer but smaller than the part of the sphere that's below you, they exert equal force on you in opposite directions, you feel nothing. This happens for any force that drops off with the square of distance, like gravity, magnetism or  electric charge.
Comment: @Robyn: I knew that about hollow earth; very cool to realize it would be true for hollow reverse gravity shell too.  Antigravity dome it is!
Answer: Dark matter doesn't have repulsive gravity — you may be thinking of dark energy, which is a property of space-time rather than a substance that you can put somewhere. Dark matter has attractive gravity, just like regular matter.  Putting a lot of dark matter inside rather than around Mars would indeed increase its gravity, if there were any way of getting it there.
Comment: The OP may have used the [tag:dark-matter] tag, but I'm 99% sure they're not asking about dark matter at all.


Linux joystick seems mis-calibrated in an SDL game (Freespace 2 Open)

Question: I have a USB joystick (Saitek Cyborg 3D) which shows up on my recently installed Ubuntu 9.04 box as /dev/input/js0, and jstest is showing values in the range +-32767 as I would expect. I just dug up a copy of FreeSpace Open, a game which uses SDL and worked with no problems on a previous Ubuntu install about a year ago, and the joystick seems very mis-calibrated. All axes (X, Y, twist, throttle) seem at least 20% off-center. The X and Y axes at least definitely aren't reaching their end points.
A relevant message on the SDL mailing list in January 2009 received no concrete answers.
Here is joy-unix.cpp from the project source. I'm not quite running trunk, but as you can see from the revision log there, no actual code changes have happened to that file for over 3 years.
Answer: I noticed the problem in d2x (a Descent port), which also uses SDL, so I went digging in SDL. testjoystick from the SDL source showed the problem as well. Looking at the SDL linux joystick driver, the problem is mentioned. Search for joydev_pattern in that file and you'll see what they're doing; search for calibrate and they do mention this problem. Basically they use /dev/input/event6 (or whichever) in preference to /dev/input/js0, unless compiled with --disable-input-events, even knowing the event device can't be calibrated (i.e. the calibration set on js0 will be ignored).
Having found all that, Google searches involving that configure option reveal that hidden away in the comments to a Linux howto for fs2_open, someone has actually had this problem already.
I have reported this bug to Ubuntu. To work around, pick any one of:

Set SDL_JOYSTICK_DEVICE=/dev/input/js0 (you could put this in /etc/environment and reboot to apply it everywhere). Edit: SDL will still have the evdev device as a second joystick, so in games like d2x that respond to the second joystick as well by default, visit the options screen and remove those extra bindings.
Recompile libSDL with --disable-input-events.
rmmod evdev (quite likely to lose any unusual input devices you have).
Comment: Exact same problem, exact same joystick.  your first option worked beautifully.  saved me hours of frustration.
Answer: Sounds like the game needs to be provided with the min/max/center axis values from the joystick. The default values might be 0/32768/65536 rather than -32676/0/32760 you're seeing? That's more obviously a lot more than 20% off, so maybe it's trying to auto-calibrate at some point. It also looks like the joytest2 console command can show in-game values which might provide some added insight.
From joy_init():
// Fake a calibration
if (joy_num_sticks > 0) {
    for (i=0; i<JOY_NUM_AXES; i++) {
        joystick.axis_center[i] = 32768;
        joystick.axis_min[i] = 0;
        joystick.axis_max[i] = 65536;
    }
}

I see a calibration function (joy_cheap_cal() at joy.cpp:454) but it's not immediately obvious where that's called from, or if there are other methods within the game for re-calibrating the axis values. I love Freespace, so when I get home I'll download the code and poke around a bit. You might also try running jscal just for good measure?


First story to describe cannibalism in a futuristic society?

Question: What is the first sci-fi story (if any) to describe how cannibalism would look in a futuristic society?
Comment: *The Time Machine* has to be up there.
Comment: @GEdgar That's fine with me.
Comment: The Time Machine gets my vote.  The Food of the Gods by Arthur C. Clarke deserves a nod.
Comment: @releseabe - In the original *Time Machine*, there's no suggestion that there is not reproductive isolation between eloi, humans, and morlocks, so they could be viewed as different species. However, the time period is only about 800,000 years into the future and both groups share a common ancestor. There's also evidence that archaic human "species" (more properly, subspecies) that existed more than 800,000 years ago were interfertile with anatomically modern humans. With that in mind, I am willing to consider them close enough—if not actually the same species—to call it cannibalism.
Comment: Can we give answers where the cannibalism would be a spoiler for the story?
Comment: @GEdgar I'm fine with that.
Comment: @Adamant was thinking time machine except morlocks are no longer same species as eloi, right?
Comment: The author also compares the morlocks' behavior to "our cannibal ancestors," so that is another point in favor.
Answer: Cannibalism was perhaps touched upon in a futuristic setting for the first time in The Time Machine published in 1895 written by H.G Wells
In Chapter 7 -

The Time Traveller barely sleeps that night, and in the morning he and Weena traverse the wood. While they walk he reflects on what has led the Morlocks to eat the Eloi, who are their evolutionary relatives. He surmises that at a certain point the Morlocks ran out of their food source and they were forced to turn to the Eloi. Meanwhile they must have lost, over the years, the cultural taboo against cannibalism. The Time Traveller remarks that this taboo is not a deep-rooted instinct in humans of his own era, but a mere cultural prejudice. Still, in order to stave off his horror, the Time Traveller tries to think about the cannibalism as retribution for the Eloi's selfishness, a natural punishment for the thousands of generations of labor exploitation. Despite this effort, the Time Traveller cannot help but sympathize with the Eloi, as they have better preserved the human form, which, of course, is the Time Traveller's own

Analysis by LitCharts

The Time Traveller often tries to parse what is deeply rooted in human nature and what is simply cultural conditioning. He wonders about fear, first thinking it has disappeared and then realizing that it is still innate. He wonders similarly about kindness, which has endured in one species but not the other. The taboo against cannibalism is a powerful one in the Time Traveller's era—one that might even seem to be a defining trait of contemporary humans—but even that proves not to be inherent to the species. Perhaps the lesson here is that the human qualities that endure are simply those that are evolutionarily advantageous, and it is not useful to cling to traits like intelligence and strength as being definitive of human beings, since they could disappear if the circumstances were right. Despite his attempt to view evolutionary changes as neutral facts, the Time Traveller still finds himself sympathetic to the species that is more recognizably human.

As per Wikipedia -

By the year AD 802,701, humanity has evolved into two separate species: the Eloi and the Morlocks. The Eloi live a banal life of ease on the surface of the Earth while the Morlocks live underground, tending machinery and providing food, clothing, and inventory for the Eloi.

Since you asked for a futuristic setting, its perhaps according to evolution that humans in the future wont be the same and will evolve in something else. It is to be noted though H.G Wells initial motive here was to draw commentary on the rich upper class and the poor lower class.
Answer: The short story The Food of the Gods (1964) by Arthur C. Clarke:

It's only fair to warn you, Mr. Chairman, that much of my evidence will be highly nauseating; it involves aspects of human nature that are very seldom discussed in public, and certainly not before a congressional committee. But I am afraid that they have to be faced, there are times when the veil of hypocrisy has to be ripped away, and this is one them.
You and I, gentlemen, have descended from a long line of carnivores. I see from you expressions that most of you don't recognize the term. Well, that's not surprising—it comes from a language that has been obsolete for two thousand years. Perhaps I had better avoid euphemisms and be brutally frank, even if I have to use words that are never heard in polite society. I apologize in advance to anyone I may offend.
Until a few centuries ago, the favorite food of almost all men was meat-the flesh of once living animals. I'm not trying to turn your stomachs; this is a simple statement of fact, which you can check in any history book…
Why, certainly, Mr. Chairman, I'm quite prepared to wait until Senator Irving feels better. We professionals sometimes forget how laymen may react to statements like that. At the same time, I must warn the committee that there is very much worse to come. If any of you gentlemen are at all squeamish, I suggest you follow the senator before it's to late…
Well, if I may continue. Until modern times, all food fell into two categories. Most of it was produced from plants-cereals, fruits, plankton, algae and other forms of vegetation. It's hard for us to realize that the vast majority of our ancestors were farmers, winning food from the land or sea by primitive and often back-breaking techniques; but that is the truth.
The second type of food, if I may return to this unpleasant subject, was meat, produced from a relatively small number of animals. You may be familiar with some of them-cows, pigs, sheep, whales. Most people—I am sorry to stress this, but the fact is beyond dispute—preferred meat to any other food, though only the wealthiest were able to indulge this appetite. To most of mankind, meat was a rare and occasional delicacy in a diet that was more than ninety-percent vegetable.
If we look at the matter calmly and dispassionately—as I hope Senator Irving is now in a position to do—we can see that meat was bound to be rare and expensive, for its production is an extremely inefficient process. To make a kilo of meat, the animal concerned had to eat at least ten kilo's of vegetable food—very often food that could have been consumed directly by human beings. Quite apart from any consideration of aesthetics, this state of affairs could not be tolerated after the population explosion of the twentieth century. Every man who ate meat was condemning ten or more of his fellow humans to starvation…
Luckily for all of us, the biochemists solved the problem; as you may know, the answer was one of the countless byproducts of space research. All food—animal or vegetable—is built up from a very few common elements. Carbon, hydrogen, oxygen, nitrogen, traces of sulphur and phosphorus—the half-dozen elements, and a few others, combine in an almost infinite variety of ways to make up every food that man has ever eaten or will ever eat. Faced with the problem of colonizing the moon and planets, the biochemists of the twenty-first century discovered how to synthesize and desired food from the basic raw materials of water, air and rock. It was the greatest, and perhaps the most important, achievement in the history of science. But we should not feel too proud of it. The vegetable kingdom had beaten us by a billion years.
The chemists could now synthesize and conceivable food, whether it had counterparts in nature or not. Needles to say, there were mistakes—even disasters. Industrial empires rose and crashed; the switch from agriculture and animal husbandry to the giant automatic processing plants and omniverters of today was often a painful one. The danger of starvation has been banished forever, and we have a richness and variety of food that no other age has ever known.
In addition, of course, there was a moral gain. We no longer murdered millions of living creatures, and such revolting institutions as the slaughter house and the butcher shop have vanished from the face of the earth. It seems incredible to us that even our ancestors, coarse and brutal though they were, could ever have tolerated such obscenities.
And yet it is impossible to make a clean break with the past. As I have already remarked, we are carnivores; we inherit tastes and appetites that have been acquired over a million years of time. Whether we like it or not, only a few years ago some of our great-grandparents were enjoying the flesh of cattle and sheep and pigs—when they could get it. And we still enjoy it today…
Oh dear, maybe Senator Irving has better stay outside from now on. Perhaps I should not have been quite so blunt. What I meant, of course, was that many of the synthetic foods we now eat have the same formula as the old natural products; some of them, indeed, are such exact replicas the no chemical or other test could reveal any difference. This situation is logical and inevitable; we manufactures simply took the most popular pre-synthetic foods as our models, and reproduced their taste and texture.
Of course, we also created new names that didn't hint of an anatomical or zoological origin, so that no one would be reminded of the facts of life. When you go into a restaurant, most of the words you'll find on the menu have been invented since the beginning of the twenty-first century, or else adapted from French originals that few people would recognize. If you ever want to find your threshold of tolerance, you can try an interesting but highly unpleasant experiment. The classified section of the Library of Congress has a large number of menus from famous restaurants—yes, and white house banquets—going back for five hundred years. They have a crude, dissecting-room frankness that makes them almost unreadable. I cannot think of anything that reveals more vividly the gulf between us and our ancestors only a few generations ago…
Yes, Mr. Chairman—I am coming to the point; all this is highly relevant, however disagreeable it may be. I am not trying to spoil your appetites; I am merely laying the groundwork for the charge I wish to bring against my competitor, Triplanetary Food Corporation. Unless you understand this background, you may think that this is a frivolous complaint inspired by the admittedly serious losses my firm has sustained since Ambrosia Plus has come onto the market.
New foods, gentlemen, are invented every week. It is hard to keep track of them. They come and go like women's fashions, and only one in a thousand become a permanent addition to the menu. It is extremely rare for one to hit the public fancy overnight, and I freely admit that the Ambrosia Plus line of dishes has been the greatest success in the entire history of food manufacture. You all know the position; everything else has been swept of the market.
Naturally, we were forced to accept the challenge. The biochemists of my organization are as good as any in the solar system, and they promptly got to work on Ambrosia Plus. I am not giving away any trade secrets when I tell you that we have tapes of practically every food, natural or synthetic, that has ever been eaten by mankind—right back to exotic items that you've never heard of, like fried squid, locusts in honey, peacock's tongues, Venusian polypod…. Our enormous library of flavors and textures is our basic stock in trade, as it is with all firms in the business. From it we can select and mix items in any conceivable combination; and usually we can duplicate, without to much trouble, any product that our competitors put out.
But Ambrosia Plus had us baffled for quite some time. Its protein-fat breakdown classified it as straightforward meat. Without too many complications-yet we couldn't match it exactly. It was the first time my chemists had failed; not one them could explain just what gave the stuff its extraordinary appeal—which, as we all know, makes every other food seem insipid by comparison. As well it might…but I am getting ahead of myself.
Very shortly, Mr. Chairman, the president of Triplanetary Foods will be appearing before you-rather reluctantly, I'm sure. He will tell you that Ambrosia Plus is synthesized from air, water, limestone, sulphur, phosphorus, and the rest. That will be perfectly true, but it will be the least important part of the story. For we have now discovered his secret—which, like most secrets, is a very simple once you know it.
I really must congratulate my competitor. He has at last made available unlimited quantities of what is, from the nature of things, the ideal food for mankind. Until now, it has been in extreme short supply and therefore all the more relished by the few connoisseurs who could obtain it. Without exception, they have sworn that nothing else can remotely compare with it.
Yes, Triplanetary's chemists have done a superb technical job. Now you have to resolve the moral and philosophical issues. When I begin my evidence, I used the archaic word "carnivore." Now I must introduce you to another: I'll spell it out for the first time: C-A-N-N-I-B-A-L….

 tip: Dosco Jones
Comment: Wells was first


Are citations the same as references in IEEE?

Question: It appears that the word citation and references are use interchangeably. Are they the same thing?
https://www.ieee.org/documents/ieeecitationref.pdf
Answer: IEEE uses a style that is common for journal articles and academic works.  The citation is the full "description" of the work -- author, title, date, publication, etc.  The document you linked describes the citation styles for various kinds of works and calls them "citiation standards".
The reference is the in-text pointer to a citation.  While a citation might be:

[3] Bovik, H. Q., "Parallel Languages for Parallel Universes," Otherworldly Computing, 3(391-407),1990.

The reference would look something like:

On the other hand, Bovik [3] asserts that parallel languages have the following properties...

Confusingly, citations are usually listed at the end of the paper in a section called "References", though sometimes you see "Works Cited".  If IEEE has guidelines for the title of this section, I couldn't find it.
Answer: The answer by Monica Cellio is not quite correct.

The heading for the list of references is "References". The IEEE Editorial Style Manual clearly labels this section with that heading:

and

As the title of that section indicates, it contains references:

Many of the terms have multiple meanings, both according to IEEE usage and elsewhere:
A source is a document from which you cite.
A citation is
a. the act of quoting text from a source
b. the quotation
c. the act of refering to the source of the quotation
d. the reference
A reference is
a. a mention of a source of information
b. the source
In short, the terms source and reference can be used interchangeably, and the terms citation and reference can be used synonymously, but they can also mean different things.

tl;dr
In IEEE usage, the words "citation" and "reference" sometimes mean the same things, sometimes not.


ASP.NET Identity Custom with Group-based Roles

Question: Perhaps I've misunderstood the concept of Roles in ASP.NET Identity and the database model, but I'm struggling to wrap my head around how to implement the following scenario: With ASP.NET Identity, it seems a User has permissions globally based on a Role, as opposed to permissions on a more granular level. I'm trying to implement a DB Schema in EF6 with Code-First where a User can be a member of several Groups. Instead of having a global Role however, I want the User to have one role in one Group, and a different Role in another.
For example, a User can create a Group, and therefore be the Group Admin, but could also be a Teacher in the Group and therefore be able to contribute Content. The same User could also be a Student in a different Group, and have different permissions in that Group as a result. Users can perform multiple Roles in a given Group, and their permissions should be based on their Role(s) within that Group.
From what I can see this isn't the intended structure for ASP.NET Identity, as I can't see how to limit the scope of a specific Role to a Group. Also, ideally I'd like to be able to assign a User to a Group, and then  assign a Group of Users to another group, so for example I have a Group of Users and I assign that Group to a specific Role within another Group.
What I have in mind is a Membership table that has UserId, GroupId and RoleId to deal with mapping the Roles to specific Groups, but how would I extend that to have Roles inherited from Groups, and would I be able to leverage ASP.NET Identity to help me manage these Roles or do I have to cook my own solution up from scratch?
Answer: Take a look at this if you haven't already found it and you're working with MVC.
http://typecastexception.com/post/2014/08/10/ASPNET-Identity-20-Implementing-Group-Based-Permissions-Management.aspx
I've been working on the same same issue as you recently. This covers a lot of the requirements but there is a gap - ASP.NET Identity doesn't differentiate between authorization and authentication. In all cases, a user that does not have the required permission gets sent to the login screen. That's fine if they're not logged in, but not if they are logged in and trying to access something that they have no permission for. That is probably address here, but I haven't had time to test it yet.
How to make Authorize attribute return custom 403 error page instead of redirecting to the Logon page


Who are the users "jicofo" and "jvb"?

Question: Today, when I rebooted my home computer after update, I saw, in addition to me, two new users: "jicofo" and "jvb". I certainly did not add these users. Who are they and why do I need them?
Comment: Both are part of Jitsi.
Answer: You, or someone using your computer, has installed Jitsi Meet, a videoconferencing application. The user(s) are created with the application's installation. You need them to use the software.
Comment: Try running *sudo apt purge jigasi jitsi-meet jitsi-meet-web-config jitsi-meet-prosody jitsi-meet-turnserver jitsi-meet-web jicofo jitsi-videobridge2* (you may still have some of those installed, so may need to run them each individually). If that says nothing is found, and you still have the users, you can go ahead and delete them.
Comment: I tried to remove jitsi-meet and got the reply "Package 'jitsi-meet' is not installed, so not removed". Does this mean that these two users are remnants from past installation, and I should just remove them manually?

Who are the users "jicofo" and "jvb"?


Phone Call from weird number

Question: I just got a call from a very weird number. On my phone it displays as "+1 (1) (5 )" and "USA" below.
I answered the call and there was 100% silence. Then about 2 seconds later the call ended.
Next I tried to call the number again, but a default voice from my phone company told me that the number was invalid.
What could this be?
I don't think it's relevant, but I'm from Denmark and I use an iPhone 4S.
Comment: Caller ID can be set to anything by the caller. It doesn't have to be valid nor there is anything that would define a "valid" caller ID from an invalid one.
Answer: With CallerID Spoofing, the number shown can be anything the caller wants it to be. Usually these calls are trying to identify something (modems, fax machines, voicemail box, etc.) Hard to know exactly what this particular one was, but often they are harmless just annoying.
There is an app by Whitepages called "Hiya" that you can download that tries to do some checking of the incoming number and x-ref it with known scammers. It will even do some blocking for you if you set it up.
Answer: I am getting these "1 Ring" phone calls, one recently from 342-777-5555. I answer but they hang up after one ring. So I looked up the phone number instead of calling back right away. This is what I found out:

"One-ring" cell phone scam can ding your wallet
Here's how it works: Scammers are using auto-dialers to call cell
  phone numbers across the country. Scammers let the phone ring once —
  just enough for a missed call message to pop up.
The scammers hope you'll call back, either because you believe a
  legitimate call was cut off, or you will be curious about who called.
  If you do, chances are you'll hear something like, "Hello. You've
  reached the operator, please hold." All the while, you're getting
  slammed with some hefty charges — a per-minute charge on top of an
  international rate. The calls are from phone numbers with three-digit
  area codes that look like they're from inside the U.S., but actually
  are associated with international phone numbers — often in the
  Caribbean. The area codes include: 268, 284, 473, 664, 649, 767, 809,
  829, 849 and 876. If you get a call like this, don't pick it up and
  don't call the number back. There's no danger in getting the call: the
  danger is in calling back and racking up a whopping bill.
If you're tempted to call back, do yourself a favor and check the
  number through online directories first. They can tell you where the
  phone number is registered.
https://www.consumer.ftc.gov/blog/2014/02/one-ring-cell-phone-scam-can-ding-your-wallet
Comment: Please be sure to post the source of your repost.  It wasn't really clear that you were posting someone else's words which could have been taken as plagiarism.  I realize your word choice did kind of point to it being an article though and the wording sounded familiar, so I found the original to link for you.
Answer: So what is this caller id?
Well the called id is definitely invalid since anyone with a call center can change the caller id of the call this is probably one of the two following things:

The caller set it that way and your service provider identified the +1 which is the USA area code and that's why it says USA.
Your service provider noticed that it is a number with no id but it did come from a call center in the US and attached the "+1 (1) (5 )" for there own reasons (Carriers do this to try and inform the user with as much info as possible).

So what is this?
A famous marketing technique to detect valid phone numbers is to call them not using any caller id and check if they answer which would indicate they are valid. Since this is a automated system there is no voice on the other side.
Comment: @O'Niel - It depends, he is just in a database that is verifying its leads. You can prevent this when you know what company is doing this. I do not know the legal issues behind it. (In my country there is a big fight over it since the companies claim the user entered and agreed to get advertising content and that is a type of content in the agreement)
Comment: A little update regarding this: I have not been called a single time by any kind of advertising.
Comment: So with other words. OP is going to get a lot of advertising-calls now, just because he answered the phone-call? Is there a way to prevent this? Is it even legal for companies to do this?

Phone Call from weird number


How do I find the limit of this function?

Question: This is a question from my calculus text. It says $$\lim\limits_{x\to1}\left(\frac{p}{1-x^p}-\frac{q}{1-x^q}\right)$$ where $p$ and $q$ are natural numbers. I know this is an infinity-infinity indeterminant form which can be converted to a $0/0$ form. I tried substituting $x=1+h$ where $h\to0$. But it is not working. What should I do?
Comment: It says that the limit is $(p-q)/2$.
Comment: Hey,I apologize to everyone . I didn't want to wrong anyone I myself was getting the answer 0 but the textbook said it was p-q/2.
Answer: Considering $$A=\frac{p}{1-x^p}-\frac{q}{1-x^q}$$ let $x=1+h$ as you did; so $$A=\frac{p}{1-(1+h)^p}-\frac{q}{1-(1+h)^q}$$ Now, using the binomial theorem or Taylor series $$(1+h)^a=1+ah+\frac 12a(a-1)h^2+\cdots$$ $$1-(1+h)^a=-ah-\frac 12a(a-1)h^2+\cdots$$ Replace $$\frac{a}{1-(1+h)^a}=\frac{a}{-ah-\frac 12a(a-1)h^2+\cdots}=-\frac 1{h}\frac 1 {1+\frac 12 (a-1)h+\cdots}$$Now, long division gives $$-\frac 1{h}(1-\frac 12 (a-1)h+\cdots)$$ Now, replacing $a$ by $p$ and then $a$ by $q$ gives $$A\approx-\frac 1{h}(1-\frac 12 (p-1)h+\cdots)+\frac 1{h}(1-\frac 12 (q-1)h+\cdots)=\frac {p-q} 2+\cdots$$
Using one more term in the binomial expansion and doing the same would have given $$A\approx\frac {p-q} 2+\frac{q^2-p^2}{12}h$$ showing the limit and how it is approached.
Comment: +1 for the extra term calculation $(q^{2} - p^{2})h/12$. I have tried to use similar approach but it avoids long division.
Comment: @ParamanandSingh. In fact, the problem is very simple using only Taylor series (just as robjohn answered).
Answer: The simplest approach is to use the standard limit $$\lim_{x \to a}\frac{x^{n} - a^{n}}{x - a} = na^{n - 1}\tag{1}$$ We have
\begin{align}
L &= \lim_{x \to 1}\left(\frac{p}{1 - x^{p}} - \frac{q}{1 - x^{q}}\right)\notag\\
&= \lim_{x \to 1}\frac{p - px^{q} - q + qx^{p}}{(1 - x^{p})(1 - x^{q})}\notag\\
&= \lim_{x \to 1}\dfrac{p - px^{q} - q + qx^{p}}{\dfrac{(1 - x^{p})(1 - x^{q})}{(1 - x)(1 - x)}\cdot(1 - x)^{2}}\notag\\
&= \frac{1}{pq}\lim_{x \to 1}\frac{p - q + qx^{p} - px^{q}}{(1 - x)^{2}}\notag\\
&= \frac{1}{pq}\lim_{h \to 0}\frac{p - q + q(1 + h)^{p} - p(1 + h)^{q}}{h^{2}}\notag\\
&= \frac{1}{pq}\lim_{h \to 0}\dfrac{p - q + q\left(1 + ph + \dfrac{p(p - 1)}{2}h^{2} + \cdots\right) - p\left(1 + qh + \dfrac{q(q - 1)}{2}h^{2} + \cdots\right)}{h^{2}}\notag\\
&= \frac{1}{pq}\lim_{h \to 0}\dfrac{\dfrac{pq(p - q)}{2}\cdot h^{2} + \cdots}{h^{2}}\notag\\
&= \frac{p - q}{2}\notag\\
\end{align}
The ellipsis ($\cdots$) used above indicates a finite number of terms (based on positive integers $p, q$) and each term is of the form $c\cdot h^{r}$ where $r > 2$. This is because of the standard binomial theorem for positive integer index. In case numbers $p, q$ are not positive integers then we use the general binomial theorem and the ellipsis $(\cdots)$ needs to be replaced with $o(h^{2})$.
Answer: This simply adds a bit of rigor to Claude Leibovici's answer.
Using Landau Big-O notation,
$$
\begin{align}
\frac{a}{1-x^a}
&=\frac{a}{1-(1+h)^a}\\
&=\frac{a}{1-1-ah-\frac{a(a-1)}2h^2+O\!\left(h^3\right)}\\
&=-\frac1h\frac1{1+\frac{a-1}2h+O\!\left(h^2\right)}\\
&=-\frac1h\left(1-\frac{a-1}2h+O\!\left(h^2\right)\right)\\
&=-\frac1h+\frac{a-1}2+O(h)\\
&=-\frac1{x-1}+\frac{a-1}2+O(x-1)\tag{1}
\end{align}
$$
Applying $(1)$ for $a=p$ and $a=q$ gives that
$$
\frac{p}{1-x^p}-\frac{q}{1-x^q}=\frac{p-q}2+O(x-1)\tag{2}
$$
Therefore,
$$
\lim_{x\to1}\left(\frac{p}{1-x^p}-\frac{q}{1-x^q}\right)=\frac{p-q}2\tag{3}
$$
Answer: You can rewrite the function in the form
$$
\frac{p(1-x^q)-q(1-x^p)}{(1-x^p)(1-x^q)}
$$
We assume $p>q>1$ just to do the next computation.
Consider $f(x)=qx^p-px^q+p-q$, so $f'(x)=pqx^{p-1}-pqx^{q-1}$ and
$$
f''(x)=pq(p-1)x^{p-2}-pq(q-1)x^{q-2}
$$
Hence $f'(1)=0$ and $f''(1)=pq(p-q)$. Observe that the same happens with no condition on $p$ and $q$ (provided they're nonzero). Therefore
$$
f(x)=\frac{pq(p-q)}{2}(x-1)^2+g(x)(x-1)^3
$$
for some polynomial $g$.
Note also that
$$
x^p-1=p(x-1)+g_p(x)(x-1)^2
$$
for some polynomial $g_p$, so your limit is
$$
\lim_{x\to 1}
\frac{\frac{pq(p-q)}{2}(x-1)^2+g(x)(x-1)^3}
{(p(x-1)+g_p(x)(x-1)^2)(q(x-1)+g_q(x)(x-1)^2)}=\frac{p-q}{2}
$$
Note that actually the hypothesis that $p$ and $q$ are integer is not really used. The above are the Taylor expansions at $1$, where $g$, $g_p$ and $g_q$ are not necessarily polynomials, but the result is the same.


Change default user folders path?

Question: In previous releases of Ubuntu, I used Ubuntu Tweak to change the paths to the user folders (Music, Documents, Videos, etc). I can't find an option in Gnome 3 to do this, and Ubuntu Tweak's ppa still has no version for Oneiric.
Answer: Open a terminal and write this command:
gedit ~/.config/user-dirs.dirs

Each row is a user folder definition (music, video...), edit as you want. For example, I did not want the videos folder in home, but in a separate disk, and changed the XDG_VIDEOS_DIR parameter this way:
XDG_VIDEOS_DIR="/media/share/Video"

OR simply run:
xdg-user-dirs-update --set VIDEOS "/media/share/Video"

Logout and login back to effect properly.
Comment: To make it effective immediately, run `xdg-user-dirs-update`.
Comment: after i restart or unplug my external disk the folders disappear from that list. any idea how to solve that? http://askubuntu.com/questions/251624/set-default-folders-to-external-hdd-permanently
Comment: From the manual for `xdg-user-dirs-update` I'm guessing that it goes back to the default directories if they exist, so just delete them and it should be good
Comment: @ArthurSpoon Unfortunately, no, this (e.g. deleting ~/Documents) doesn't stop the overwriting of the tweaked user-dirs.dirs file.
Answer: As at today (7 years later!), my experiments seem to show:

These variables are set in the file ~/.config/user-dir.dirs relate to
XDG, which stands for "X Desktop Group"... i.e. they appear to
relate to the "windowing" processes.  But for example, none of these
variables are then accessible by the user (or root) as an environment
variable
It appears that the variable XDG_DOCUMENTS_DIR is the one which is
responsible, in Nemo, for giving one particular directory a
"special" icon
That's what we're all bothered about: how to give one particular
directory a special icon all to itself, signifying "this is your
DOCUMENTS directory"
To give this to a particular directory other than ~/Documents,
-- a. make a link from the directory you want under "My Computer" in the LH panel of Nemo
-- b. change the value of the XDG_DOCUMENTS_DIR variable in ~/.config/user-dir.dirs to this directory, using an absolute path.
-- c. log out and back in: whatever its name may be, in both the LH and RH side of Nemo your directory should now have the "special" DOCUMENTS icon!

NB it is not sufficient, as suggested in a comment above, simply to delete the ~/Documents directory for everything to work OK.  Bear in mind in particular that, if at startup it is found that the  XDG_DOCUMENTS_DIR path actually doesn't lead to a valid directory, the setting for XDG_DOCUMENTS_DIR will be overwritten in user-dir.dirs, replacing it, in principle, with $HOME/Documents... (in fact, oddly, my experiments seem to find that it is usually replaced with $HOME, for some inexplicable reason).
NB2 as an alternative to the above (especially if the "special" icon doesn't matter in particular to you), you could use a symlink ... which you can call "Documents".  In fact, you could have both: a symlink and a special icon for your target file.
NB3 I don't believe you can make a symlink as suggested  ... AND give it a special DOCUMENTS icon! But given this, all seems to be about cosmetics anyway maybe it, um, doesn't matter much!
Comment: Please format you post regarding to this link: https://askubuntu.com/editing-help
Answer: You can still install Ubuntu Tweak and do it with that, if you dont want to mess around with the terminal.

Change default user folders path?


How to resolve Runlog error on Chainlink node

Question: I keep getting the below error when I request data from my node.
<code>error": "rejecting job bd25ae01d8604b268abfbfa764399511 with payment 100000000000000000 below minimum threshold (1000000000000000000)"
</code>
I haven't specified a minimum payment in the bridge (its all set to 0) so I don't understand what the minimum threshold referred to is. Does anyone know how to resolve this?
Answer: The solution was to increase the amount of Link paid to the oracle by the contract. 1 Link works


3D printing problem: waved walls

Question: The problem
When I print with my mElephant 3D printer from Makeblock, the prints come out with waved walls like in the picture below. I am using PLA filament from https://makeblock.lt

What I tried
I tried changing temperatures 190-220, tried to change the flow rate. Also checked if the bolts are not lose. Everything seems good.
My printer
Comment: Are the smooth rods held with a screw in the end on both sides?
Comment: Possible duplicate of [Unidentified problem in printing](http://3dprinting.stackexchange.com/questions/3176/unidentified-problem-in-printing)
Comment: This issue is a mechanical related issue called "Z wobble".
Answer: I had the same problem with ABS, but printing different test objects I found out that the distance between the wavy structures depends on the cross sectional area of the object. Printing the testcube in 70.1% (1/sqrt(2) times of the original size) takes half the time per layer and the distance between two grooves doubles. I was printing ABS with 0.1 mm layer height and the simple bang-bang heat bed controller. The temperature is clearly wandering for 4° with a period of aproximately 2.5 minutes, which corresponds to the groove distances. After changing to a PID controller for the heated bed the temperature stayed within 0.1°C and the problem was gone. Several hundredths of a millimeter thermal expansion of the heated bed can have substantial impact at 0.1 mm layer height!
You can enable the PID controller for the heated bed in Marlin or Skynet firmware by enabling (removing the //) here:

//#define PIDTEMPBED

and disabling (putting // at the beginning of the line) here:

#define BED_LIMIT_SWITCHING

in Configuration.h. Calibration of the PID controller can then be done with the GCODE Command:

M303 E-1 S90 C8

for 90°C. I had to preheat the heated bed before, otherwise the calibration would run into a timeout. The command will return parameters for the PID algorithm. The values can then be applied by the

M304 P579.01 I100.87 D586.0

GCODE command (here for example values). Everything can then be saved to the EEPROM with

M500

Bang-Bang controller:

PID controller:
Comment: Welcome to 3dprinting.stackexchange.com, @uiop!  This is an awesome, informative and well written answer, happy to have you onboard! :)
Answer: Repeating patterns like that usually stem from issues in the Z axis.  This is likely caused by bent screws which in turn cause the X axis to move around.    Are the top of the threaded rods constrained?  If they are, an easy fix may just be to let the top of the threaded rods float around by removing the constraint.  Most Prusa i3's use 5mm threaded rod for the screws and 8mm smooth rod, does your printer use the same setup?
If your printer has 8mm (or 5/16") threaded rod you could try to get some that are straight or the better solution would be to get the 5mm threaded rods and just print adapters to hold the 5mm nut inside the trap.  This would require new couplers (aluminum or rubber/plastic hose), 5mm threaded rods, nuts, adapters (printed) and a small change to the firmware.  This works because the 5mm rod is more flexible than the 8mm smooth rod and less likely to force the carriage around.
If you already have the 5mm threaded rod/8mm smooth rod then I would look to make sure your X axis is tight and does not move around on the Z axis smooth rods.
This would be easier to point out if you include a picture of your printer.
Edit:
If your printer is the mElephant from Makeblock then I would try removing the bearings at the top that constrain the threaded rods and try the print again.
Comment: Thank you for your detailed answer! I updated the question with images of my 3D printer.
Comment: It seems I edited my answer the same time you added the picture.  I would try removing the bearings at the top that the threaded rods are held in if you can easily do that then try that print again.
Comment: removed top bearings, problem persists
Comment: Do you see noticeable movement in the threaded rods?
Comment: @gpson The bearings are part of the problem, not the complete solution of problem (but should be left out). Your steppers have integrated lead screws, any mis-positioning of these lead screws leads to x and y movement of the screw when advancing up or down. You need to separate this movement. One solution is using separate lead screws and springy couplers (but these introduce also problems). A better solution is to remove your lead screw nuts and print a sort of a lift platform that contains this nut, then you separated x and y movement from the lead screw completely.
Answer: I have the same problem with a home made mini extruder. This happens only if the bearing stops rotating together with the extruder gear.
I notice that:

The gear collects burrs of PLA while feeding, so reducing the traction to feed the PLA
The bearing stops rotating when the pressure is too high or too low.
The heat of chamber is too high and starts to smooth the PLA before arrives to the nozzle and needs to regulate the speed of the fan. This creates less force on feeding.
The PLA has a mixture of ABS
PLA has part hardened due overcooking, extremely dry, etc.
The PLA have irregular diameters, for example is nominally 1.75mm but some sections vary 1.8mm or 1.9mm
The nozzle starts to get cold due direct fan air flow. (maybe your main problem)

:) I've been a Quality Engineer for 20 years for plastic and metal processes, so I've had to analyze why I've had lots of problems, especially in cold weather.
I was thinking on buying a new extruder like you have, but if you have the same problem I do, the Extruder is not the problem. You need to check the points I described above.
This is the extruder I have, http://aprendiendo.laconeccion.com/mini-extrusor-3dp.
Answer: Looks like something is catching on the z axis. A bent peice would likely cause much smaller deformations unless it was very obviously bent. Something could be loose, allowing the vertical play, perhaps the motor mounts.
More likely I think is a level-difference between the z-axis worm gears, possibly caused by an obstruction, lack of lubrication, or possibly even the wrong lubrication. That's where I would look. Further, since it's a very consistent pattern, my guess would be your issue can be isolated to the tops and bottoms of the z axis worm gears. Even if it's not the issues I think, the issue most likely located at the top or bottom.
Answer: I had a very similar problem once and the culprit was the relative position of the filament spool and the printer. The spool was standing on a coaster next to the printer and it turned out to be enough to create a pulling force on the filament. I have moved the spool to a shelf above the printer and the problem was gone.
However, your printer seems to have a way more rigid Z axis than mine, so it is unlikely the issue here.
Answer: Is your printer new?
It could be that the factory settings for the step number per millimeter or inch on the "Z" axis stepper motors. I personally have not had this problem however you might want to check out https://www.simplify3d.com/support/print-quality-troubleshooting/.
Hope this helps  :)

3D printing problem: waved walls


How to break a long equation with left indentation

Question:
I need to write a similar equation which needs to be split such that left side is left aligned and right comes exactly under it .. will appreciate the help
regards.
Answer: (too long for a comment, hence posted as an answer)
I suggest you (a) use an align* environment and (b) place the alignment character & at the start of each line:
\begin{align*}
& \Lambda(r\mid \psi, H) = \\
& \frac{1}{(...
\end{align*}

Comment: It helped . but the equation number doesn't update in align* environment, so I used it inside the equation environment and then used aligned i.e.
\begin{equation}
\begin{aligned}
& \Lambda(r\mid \psi, H) = \\
& \frac{1}{(...
\end{aligned}
\end{equation}
Comment: @Shia - Your write-up and screenshot didn't feature equation numbers; that's why I assumed you were interested in unnumbered equation systems. To assign a single equation number to the entire system, use either `\begin{equation} \begin{aligned} ... \end{aligned} \end{equation}` [as you mentioned in your comment] or `\begin{equation} \begin{split} ... \end{split} \end{equation}`.


What could go wrong with installing the DLCs for fallout new vegas on xbox 360 in the middle of the game

Question: I have the DLCs and I'm so tempted to install them for cool stuff and more weapons to complete my collection..but I've heard so many bugs and corruptions that have happened to other people's consoles due to other stuff..and this is something big I'm installing to the game and I'm really excited but mainly anxious...and in the middle of the game? Not at the very beginning or after the battle of the dam..but in the middle at a random point.
Comment: Pushasha's answer should be sufficient. I've never run into any issues myself, I'm not sure where you would have got it into your head that something would go wrong. Where did you read/hear about all these "corruptions" when installing DLCs?
Comment: I don't recall anything going wrong for me.  Really all you can do is try.
Comment: Ok.................................................
Comment: I'll be waiting for more answers...I wanna do it on a special day...probably like on my birthday..but till then I need answers that say it's ok nothing should go wrong
Answer: Nothing should be wrong with installing the DLC in the middle of the game. When DLC is being tested at Bethesda, some of the QA team uses pre-existing saves, while the rest start new games to test. In short, the developers expect you to install the DLC in the middle of a game. So the chance that you'll encounter issues installing it partway through a game is (theoretically) just as high as if you started a new game.
To clarify, if the game worked fine before installing the DLC (excluding known bugs), it should work fine after installing the DLC mid-game. If you encounter bugs after installing the DLC, it likely has nothing to do with the fact that it was installed mid-game -- they would be there no matter what.
Source: Former QA tester for Fallout: New Vegas and Old World Blues.
Comment: @Nelson I have to respectfully disagree. From my experience as a tester and a modder for this game and other games using this engine, the DLC usually affects the original game content in some small ways. The addition of new items, weapons, buildings, quests, etc. sometimes requires the developers to change the original game in some way, usually to prevent the use of the new content from breaking the old (or vice-versa). When we tested the DLC, many of us were split off and asked to test the main game with the DLC installed, to make sure nothing broke.
Comment: @lordzack01 FYI, if my answer sounds non-committal, it's because I don't want to say, "Yes, I am 100% sure nothing will go wrong". Bethesda's engine is a fickle mistress, and an absurdly large number of variable combinations makes it impossible to say that nothing will go wrong. If it helps, I am 99% sure that nothing will go wrong.
Comment: Actually, nothing can go wrong, because the DLCs add content.  It's only when you **remove** DLCs that it can cause problems.
Comment: Ok....  ............... .....
Comment: Ok it's just from research this fallout game was the most unstable and glitchest fallout game made by Bethesda...I've encountered so many new bugs just by transferring the data via data transfer cable ...but it's not prior to the transfer I think it's the new console and the new bugs are varified by fallout wiki aka Bethesda
Comment: @lordzack01 Which is why I didn't guarantee that nothing would go wrong. Not sure what you're talking about with the data transfer cable, but I can assure you that if the game was working fine (excluding the known quest bugs) before you installed the DLC, it should work fine afterward. Any bugs that you encounter are unlikely to be from the fact that you installed it mid-game -- they would be there no matter what.
Comment: Important addition: 100% sure nothing will happen to your old saves as long as you don't save over them. Even if something *did* go wrong after you play a bit, you could still remove the DLC and load the original save to continue without the DLC.