Why does rice flour or cornstarch produce crispier crusts than wheat flour?

Question: If you add a percentage of rice flour or cornstarch to any sort of breading or pancake, you get a much crispier crust than one made with 100% wheat flour. The Vietnamese banh xeo, which is like a crepe made with just rice flour and coconut milk, no egg, comes out extremely crispy, for example. What is the physical reason that these pure starches cook up crispy?
Answer: My guess would be a lack of gluten in those flours. Gluten makes dough sticky and dense, so adding flours with little to no gluten might make it less sticky and thus crispier.
Comment: I think that is right, but I'm hoping for a deeper structural answer about why pure starch is crispy and gluten is not as crispy, when fully cooked.
Answer: After a quick Google search it is a result of a lack of gluten. From what I gather it is not directly due to the lack of gluten - but rather the lack of direct interaction between starches and gluten.

When starch granules are attacked by enzymes present in flour, they release the sugars that yeast feeds on. Starch also reinforces gluten and absorbs water during baking, helping the gluten to contain the pockets of gas produced by the yeast. Source

For me this is a case of correlation is not necessarily causation, as a couple of other sites mentioned that this can observation also varies from cooking method to cooking method (baking v. steaming etc).
Answer: the same reason cake flour makes a better roux than AP flour, higher starch to protein ratio
the pure starch, zero protein end of the spectrum appears in velveting  How does velveting work?
but you asked why
proteins, when they cook, curdle at lower temperatures, holding onto more water, not crispy, and at higher temperatures, they begin to decompose a Maillard reaction way, getting messy, oily, and burnty, which is not the crispy we're looking for
heat going into starch, beyond the boiling point of water , drives off the water, leaving the starch matrix to cook crispy.  that matrix shrinks a bit, but is still full of holes for water to escape through
heat going into protein, beyond the boiling point of water, drives off the water and begins to create a complex, dense mess of aromatic molecules and eventually soot.  the outside is much less permeable to escaping water, so we tend to dump in more heat, worsening the dense uncrispy crust problem


Skyrim characters before installing Dawnguard

Question: If I started a character before downloading Dawnguard, will my character still be able to become a vampire lord?
Answer: Yes, it is possible to still become a vampire lord before downloading Dawnguard.
Just simply go through the quest line when you download it and you will get to the opportunity to become a vampire lord.
Answer: You will absolutely be able to do either quest line (Dawnguard or Vampire Lord) with old characters, but as always your character must be level 10 to trigger the first quest (Note: I am only sure of this for PC, but other people could confirm for consoles).
However, be aware that a high level character will have no problem doing these quests whereas a level 10 character might struggle.  If you find that it is too hard or too easy for your character I recommend changing the difficulty to make it more suitable.  For example, I played through the Dawnguard side starting as a level 40 wood elf archer/assassin, and I had to play on Master difficulty for it to be challenging enough.
Happy Hunting!


What is the doctrine of the Trinity?

Question: What is the doctrine of the Trinity as defined by Christianity?
Obviously there are three entities involved: God the Father, Christ, and the Holy Spirit, but is there more to the definition?
Comment: It's also important to distinguish between "trinity" and "the Trinity Doctrine. The basic trinity concept is that the godhead consists of three persons (just as binitarians believe in two persons, and unitarians believe in only one person).  The "Trinity Doctrine" goes beyond this and defines a specific relationship between these individuals that is impossible for humans to truly understand (what the Catholic Church calls a "mystery").
Answer: As you already understand, the doctrine of the Trinity states that there is one God, who exists in three persons. The Father, the Son, and the Holy Spirit.
From http://carm.org/trinity

The Father is not the same person as the Son; the Son is not the same
  person as the Holy Spirit; and the Holy Spirit is not the same person
  as Father.  They are not three gods and not three beings.  They are
  three distinct persons; yet, they are all the one God.  Each has a
  will, can speak, can love, etc., and these are demonstrations of
  personhood.  They are in absolute perfect harmony consisting of one
  substance. They are coeternal, coequal, and copowerful.  If any one of
  the three were removed, there would be no God.

...

There is, though, an apparent separation of some functions among the
  members of the Godhead.  For example, the Father chooses who will be
  saved (Eph. 1:4); the Son redeems them (Eph. 1:7); and the Holy Spirit
  seals them, (Eph. 1:13).

I'd like to expand on that, but there's not much I could expand on that hasn't already been covered in depth on this site.  And while it's really not a complex doctrine, all sorts of heretical teachings come about based on a misunderstanding of it, or a rejection of it.   Rather than going into any more detail here, I'd just recommend browsing the various questions tagged "Trinity" here.
Comment: _"If any one of the three were removed, there would be no God."_ Then, according to these Trinitarians, there was no God while Jesus was in the grave.  And how do they explain Jesus' mortality in contrast to God's immortality?
Comment: I don't know.  I searched, and the basic question of what the Trinity is hasn't been asked.  It's not a dupe.  It's just that all the others add valuable insight into the finer details.
Comment: Funny that this question was not asked before. I think it should stand as the kind of question one may ask who is really not aware of the very basics of the subject.
Comment: The correct doctrine of the Trinity rejects that each person has a separate will. There is only on Divine will. In fact, the idea that the Trinity has three wills sounds like Mormon theology.
Answer: The following is an attempt to alleviate much of the confusion in the Christian, 21st century mind, regarding the Doctrine of the Trinity and the confused idea that "God is one Person and the Father, Son and Holy Spirit are each Persons, yet we do not have four persons but three and not three Gods, but one. The old 3 in 1 and 1 in 3 problem." Much of what follows comes from the Westminster Confession of Faith and the Westminster Shorter Catechism.
The Trinity
The Father, Son and Holy Spirit are 3 separate Persons (i.e. each have their own consciousness). They each partake of one essence or nature (that is what makes each Person to be God). The nature of God must never be confused with the 3 Persons, Who are each God. The nature of God is not a person, otherwise we have 4 separate persons. The Bible teaches one essence, or nature, and 3 Persons. (As an  aside, when speaking with Muslims, one needs to be clear on this point). It is confusion to think that three are one and one is three in the same sense. To say that there is One Person Who is God and Three Persons Who are God, is nonsense. And the Bible never makes this mistake. Neither do the creeds (like the Nicene), Calvin, or the later Confessions such as the Westminster Confession (WCF). (As an example from the WCF, consider the following, (speaking about the two natures of Christ), where the phrase "and distinct natures, the Godhead and the manhood" obviously teaches that the Godhead refers to the nature of the Person, not to an actual Person, just as manhood does not refer to a person, but the nature of an individual)....
"The Son of God, the second person of the Trinity, being very and eternal God, of one substance and equal with the Father, did, when the fullness of time was come, take upon Him man's nature, with all the essential properties, and common infirmities thereof, yet without sin; being conceived by the power of the Holy Ghost, in the womb of the virgin Mary, of her substance. So that two whole, perfect, and distinct natures, the Godhead and the manhood, were inseparably joined together in one person, without conversion, composition, or confusion. Which person is very God, and very man, yet one Christ, the only Mediator between God and man"
Essence or nature can be applied to anything. It is akin to a definition. Unfortunately, it is almost impossible to define anything since we are so slow of understanding. For a simple example, Let's define a chair? Does it have 3 legs and a round top? What about 4 legs and a square top? What about steel tubes that curve around like a "S"...and so on. I'm sure you get the picture. It is very hard to fully define even something simple, like a chair!
So moving on from chairs: What is a rock? What is a tree? What is a human? Does a human need two arms? Does a human have to be >3 feet tall? Does a human have to have a certain IQ? In all these examples we are trying to understand what set of characteristics make up the nature of whatever we are trying to define. i.e. What is the nature or essence of a chair (or a rock or a tree or a human)? You will see that the essence of anything is extremely hard to define, even for a chair! Yet, the essence has to be complete in order for that entity to be really all that that entity is. If you take away part of the definition (remove part of the nature) then you have something else. e.g. take away the FULL definition of a chair and you no longer have a chair, you have something else whatever that may be, but you no longer have a chair. The same is true of addition to the nature.
God & nature (or essence)
We are shown clearly what one in essence and more than one person means from the very first chapter of the Scriptures. In Genesis 1 we read, "So God created MAN in His own image; in the image of God He created him; male and female He created them." (Emphasis added) We have MAN and we have two persons who are MAN, Adam and Eve. One MAN, two persons. It is the same with everything else, e.g. One TREE, individual gums, pines and willows. Yet we call them each a tree. One GOD, three Persons Who are GOD, the Father, the Son and the Holy Spirit.
Now apply this to God. What does it mean to be an entity called God (from the Bible)? Summarised, it means to be a Spirit, Who is infinite, eternal and unchangeable, in His being, wisdom, power, holiness, justice, goodness and truth, (obviously not a full definition). It is extremely hard to get a full definition of what it means to be God. But scouring the Bible leads us to at least this summary, as just given.
Now the three Persons, Father, Son and Spirit each have ALL the characteristics just mentioned (Spirit, infinite, eternal, unchangeable etc). And ONLY these 3 Persons have those characteristics. Nothing else at all (even in our wildest imaginations of sci-fi characters) has these characteristics, otherwise those things would also be God. This full set of characteristics comprise the essence of what it means to be God i.e. it describes the nature of a being we call God
The Athanasian creed though is even more circumspect here. And we need to be careful that we do not think that if Father, Son and Holy Spirit are each omnipotent, then we have three omnipotents. No. The nature or essence cannot be divided like that. The three Persons are one in their omnipotence. They are one in their wisdom. One in their eternity, One in their holiness etc.
(Think about another example. There is only one full definition of what it means to be a human. Yet we can see two people, say a brother and a sister. But we do not say that we have two humanities. We have two persons, but they are each fully one humanity or human).
If you were to ask me, "Who do you worship"?
I would answer, "I worship three Persons, The Father, The Son and the Holy Spirit.' I do not worship a nature or essence or set of characteristics.
"But do you worship God as omnipotent, eternal etc?"
"Yes, I worship each of the three Persons as omnipotent, eternal etc."
"Doesn't that mean you worship 3 omnipotents, 3 eternals?"
"No. The three each partake fully of each characteristic e.g. Omnipotence, eternal. They do not each have a part of omnipotence. They are each fully and equally omnipotent. One omnipotence, each fully invested in each of the three persons."
I am one person. You are one person. But we each partake fully of what it means to be human.(Remember.....one set of human characteristics, but e.g. a brother and a sister).
For another example, there is an essence of a chair. But it does not mean that because we have two chairs or a dozen chairs then we have 2 or a dozen essences of chair. No, there is only one essence of what a chair is. And every chair fully partakes of that essence. The essence is not divided between the chairs. They each are a chair because they fully fit what it means to be a chair i.e. they each fully partake of the nature or essence of a chair.
Summary
So if an entity has a particular set of characteristics for God, then that entity must be God.... Just as if any object has ALL the characteristics of a chair, then we say that thing MUST be a chair. It cannot be a tree, since it does not have all the characteristics of what it means to be a tree.
That is also why I can say without reservation that you and I are not God. We simply do not have any of those characteristics (and we certainly don't have all of them). But the Father, Son and Spirit each have ALL of those characteristics summarised above. Thus the Father is God, the Son is God, the Spirit is God. They are equal in power and glory. They each have the same nature.
Part of the confusion about the Trinity today lies in two areas.

For many the doctrine is hard to understand and they say that indeed the doctrine of the Trinity cannot be understood at all. It is said to be "a mystery". But that is not what Athanasius, or the creeds, ever said. When the church fathers, or men such as Calvin, refer to the "mystery" of the Trinity they are referring to the deepness of the doctrine in terms of what comprises the essence of God. And to use modern language, the definition (or the nature) of what it means to be God is indeed mind-blowing [e.g. Just consider eternity (dwelling outside of time). A finite mind has trouble starting with that. But if the Father is the Creator (part of His nature), then He created time. But before time, He was, otherwise He could never have created it. But to be before time means He had no beginning (since you need the concept of time to posit a beginning), therefore God always was. i.e. He is eternal]. And ditto for the Son and Holy Spirit. This essence of what it means to be God is deep, very deep.

But this leads us to the second area of confusion today on this subject.
It is hard when talking about God, not to use pronouns like He, Him, His etc. The problem arises when we translate (in our heads) from the pronouns to become a Person. The Bible never does that. In 99% of the time when the Bible refers to God, one can easily substitute the Father (Who is a Person) instead of the word "God". So far so good. But when the Bible is describing the nature (characteristics) of God, it is wrong to substitute "Person" for "God". That leads to the "One Person is three persons" confusion and then it is said to be a mystery that no one can understand!

The Bible is quite clear. There is one nature (set of characteristics) that makes up any entity Who is God. Just like there is one nature or essence (set of characteristics) that makes up a thing called a chair. There are many separate and quite distinct chairs, but they ALL have the same nature or essence (characteristics) of what it means to be A CHAIR (one chair). Thus the Father is a Person and He has ALL the nature (characteristics) of God. The Son is a Person and He too has ALL the characteristics of God and the Holy Spirit is a Person Who has all the characteristics of what it means to be God. Three Persons, one nature. Not three Persons, one Person.
If we do not separate out nature or essence from Persons, we will forever be in confusion. The church fathers had no such confusion. Jesus had no such confusion. We see that Jesus does not pray to God as an essence, but He specifically addresses the Father, or He sends the Spirit. To think of the essence as a person leads to confusion.
Thus the Bible teaches that the Lord is One (essence (NOT Person)) and that there are three Persons Who each have the full essence (full set of characteristics) that make up God. (I could have said ...full set of characteristics that make up an entity called God, but could not have said...full set of characteristics that make up a Person Who is God). The full set of characteristics (essence) are NOT a Person. Rather there are 3 Persons (Father, Son and Spirit) Who have all those characteristics of what it means to be God.
To show how the modern understanding of Deut 6:4 (the Lord our God, the Lord is one) is confusion, try reading this, substituting Tree for God: "Behold the Tree.  The Tree is one.  And the one tree is three, or there are three that are the one tree"....... Makes absolutely no sense, because I am keeping the same meaning (one tree) for the word "three".
If you read something like the Westminster Confession on this you will see what I am talking about, even from the chapter heading on this subject: "Of God, and of the Holy Trinity" >>>>>modern translation: "Of what it means to be God, and the Three Persons Who are each God". No confusion here.
When we think about God, we need to meditate on what the Bible teaches about the essence of (what it means) to be God (eternity, omnipotence etc) and then adore the Three Persons Who are each fully God (equal in one essence i.e. equal in power, glory, eternity, wisdom, power etc). We cannot separate out the essence, for then we do not have God (remember the chair). But we must separate out the Persons (Father, Son and Spirit) Who are each blessed forever and each fully God.
Addendum
John 10:30 "I and the Father are one"
Jesus cannot mean in this sentence that he and the Father are one person. That they are not one person is patently obvious, unless we think that when Christ prayed to the Father he was praying to Himself! ??
Rather, Jesus speaks to the Father and the Father speaks to Jesus.
If they are not one person, then what does Jesus mean when he says that he and the Father are one?
The context is that he "is speaking of the impossibility of plucking any of the sheep, out of his own and his Father's hands; giving this as a reason for it, their unity of nature, and equality of power; so that it must be as impracticable to pluck them out of his hands, as out of his Father's, because he is equal with God the Father....". Thus the Father and the Son are God, in the same way that two brothers are Human.
Please consider the following commentators on this verse and how they explain the "Oneness of the Father and Jesus". You will note they refer to essence for oneness.
"Now, it is nowhere there said that believers and the Father are one, but such a statement is scrupulously avoided. Numerous attempts have been made to escape from the stupendous assumption of this unity of power and essence with the Father. The whole gist of the assertion reveals the most overwhelming self-consciousness. The Lord declares that he can bestow eternal life and blessedness upon those who stand in close living relation with himself, and between whom and himself there is mutual recognition and the interchanges of love and trust. He bases the claim on the fact that the Father's hands are behind his, and that the Father's eternal power and Godhead sustain his mediatorial functions and, more than all, that the Father's Personality and his own Personality are merged in one essence and entity. If he merely meant to imply moral and spiritual union with the Father, or completeness of revelation of the Divine mind, why should the utterance have provoked such fierce resentment"? See Here
"I and my Father are one. Not in person, for the Father must be a distinct person from the Son, and the Son a distinct person from the Father; and which is further manifest, from the use of the verb plural, "I and my Father", "we are one"; that is, in nature and essence, and perfections, particularly in power; since Christ is speaking of the impossibility of plucking any of the sheep, out of his own and his Father's hands; giving this as a reason for it, their unity of nature, and equality of power; so that it must be as impracticable to pluck them out of his hands, as out of his Father's, because he is equal with God the Father, and the one God with him". See here
"I and my Father are one—Our language admits not of the precision of the original in this great saying. "Are" is in the masculine gender—"we (two persons) are"; while "one" is neuter—"one thing." Perhaps "one interest" expresses, as nearly as may be, the purport of the saying. There seemed to be some contradiction between His saying they had been given by His Father into His own hands, out of which they could not be plucked, and then saying that none could pluck them out of His Father's hands, as if they had not been given out of them. "Neither have they," says He; "though He has given them to Me, they are as much in His own almighty hands as ever—they cannot be, and when given to Me they are not, given away from Himself; for He and I HAVE ALL IN COMMON." Thus it will be seen, that, though oneness of essence is not the precise thing here affirmed, that truth is the basis of what is affirmed, without which it would not be true. And Augustine was right in saying the "We are" condemns the Sabellians (who denied the distinction of Persons in the Godhead), while the "one" (as explained) condemns the Arians (who denied the unity of their essence)". See here
An excellent summary of the above with Scripture references is here.
For Further Reading:
The best book I have read, by far, explaining clearly the Biblical Doctrine of the Trinity is by Dr Gordon H. Clark, The Trinity
Calvin in the 1500's taught what the Bible has to say on the subject (see Institutes, Book 1 Ch13).
See also a Greek Orthodox explanation which is simple but Biblical.
The Trinity is often viewed as a difficult if not self-contradictory concept. Is the Trinity really incoherent? The following article responds with a simple but detailed answer to say "NO". https://trinityfoundation.org/journal.php?id=70
Comment: Should I abandon the concept that God of the bible is person, but say that He is spirit? I mean by person that He is literally made of one "body". I mean by spirit that he is not literally made of matter, but is a spirit being like Holy Spirit is. So in this matter it seems that God of bible is of one essence; spirit being, and manifests in three persons.
Comment: @laovul When the Bible uses the term "God", it is nearly always the Father that is being referred to. And of-course He is a real person. As He partakes fully of what it means to be God, i.e. the set of characteristics (essence), so the Son (Christ) and the Holy Spirit also have the same essence (set of characteristics). Thus they are God also, but they are separate persons. But we do not have 3 essences or 3 separate sets of characteristics that make a person God. No, one essence. Each of the 3 persons has that set of characteristics and are thus each God. We do not have 3 eternals, only one.
Comment: We do not have 3 omnipotents, only one. Not 3 essences, only one. There is only one set of characteristics that make an entity God. Each of the 3 persons have that set of characteristics. Being a spirit is only one part of the essence of what it means to be God. You cannot say that if an entity is a spirit then it must be God. No, because that entity must also be infinite, eternal and unchangeable in His being wisdom, power, holiness, justice, goodness and truth. If you have all those (and many more) in one person, then that person must be God (at least that is the God of the Bible).
Comment: A bit repetitive but possibly the finest treatment of the subject I have yet seen.
Answer: The doctrine of the Trinity is the logical construct whereby three of the most obvious but otherwise seemingly contradictory bits of Scripture are reconciled.  Namely:

That the Creator of the Universe (God the Father), YHWH to the Jews was God
Point one is not in dispute - the work of the Creator who proclaims himself to be God is God.

That Jesus, the Incarnate "son of God" was God
Point two - that Jesus the Christ is God is the defining belief of a Christ-ian (regardless of what this site's definition may be!).  That Jesus claimed to be God is pretty well established, both throughout the book of John, and in other questions on this site.

That there is only one God
Point three - that there is only one God, is made throughout the Old Testament.  You cannot be mono-theistic and believe in more than one God.

The basic definition of the Trinity was popularized and credalized in the Nicene Creed, in which monotheistic Christians declare belief in God the Father, God the Son, and God the Holy Spirit. Furthermore, the Nicene Creed says that God the Son is "of one Being with the Father," and that the Holy Spirit proceeds "from the Father through (or and) the Son." This is the most widely held formulation of the Trinity - and is accepted by all but the most fringe of Christians.
Reconciling that God is one, and yet exists as three distinct persons is the central "problem" of the Trinity, and most heresies about the nature of God come from over stressing either their oneness or their distinctness.
It is not tritheism (meaning that there are three Gods) nor is it one God who just appears in three different forms. It is not a matter of "1 + 1 + 1 = 1", but rather "1 x 1 x 1 = 1".
Some have said, that the Trinity can best be expressed as three individuals, so closely intertwined, as to be indistinguishable, and yet of such distinct personality as to form a community even within in itself.  As in a marriage, where two become one, the Trinity reflects that closeness, and, since marriage is often likened to a sign of the Trinity, supercedes it.  (Signs are less than the thing they point to.)  Whatever the nature of the Trinity, it is a core doctrine of all Nicene Christians that rejects any idea that God is more than One and simultaneously less than Three.  It is the "Three-In-One" Godhead.
It is always contentious. and other questions show why many analogies just don't work.
That this "mystery" has no earthly equivalent is not, however, an impossible defect - for it is simply understood that "God's ways are higher than our ways, and his thoughts higher than our thoughts."  In other words, there is no law that says mortals need to be able to understand God's nature, just because there is no terrestrial equivalent.
Comment: Only thing I'd contend is that YHWH might refer to the whole of God rather than just the Father.
Comment: Could a reasonable earthly equivalent be a company that has one president, but there are three persons who have that title?  And let's say that they were always in agreement on every decision.
Answer: On birth of Jesus Christ and His life, Death and Resurrection, it became essential to conceive the Doctrine of Trinity. Most obvious and direct evidence for Trinity originate from Bible depicting Jesus Christ and Holy Spirit with Nature of God. Therefore, if Father is God, Son is God and Holy Spirit is God than that's it.
Father being God is acceptable to many which is as easy as accepting existence of God.
Jesus as God:
Instead of quoting all those verses from NT, where Jesus is depicted as same as God, here are few more events that leads us to know about this claim.

To quote Church historian Jaroslav Pelikan, he has pointed out that the oldest Christian sermon, the oldest account of Christian martyr, the oldest pagan report of the church, the oldest liturgical prayer, 1 Corinthians 16:22, all refer to Jesus as Lord and God.

Pelikan said, "Clearly, it was the message of what the church believed and taught that 'God' was an appropriate name for Jesus Christ." Do you see any possible way this could have developed, especially so soon, if Jesus had never made transcendent and messianic claims about himself? Not unless you're prepared to argue that the disciples completely forgot what the historical Jesus was like and that they had nothing to do with the traditions that start showing up twenty years after his death."

.2.     He was crucified precisely for this charge when He declared that He is the Son of God thus making Himself equal with God.
.3. Think of the story of Jesus walking in the water, found in Matthew 14:22-33 and Mark 6:45-52. Most English translations hide the Greek by quoting Jesus as saying, "Fear not, it is I." Actually, the Greek literally says, "Fear not, I am." Those last two words are identical to what Jesus said in John 8:58, when he took upon himself the divine name "I am," which is the way God revealed himself to Moses in the burning bush in Exodus 3:14. So Jesus is revealing himself as one who has the same divine power over nature as Yahweh, the God of the Old Testament.
.4. One of the most striking is his forgiving of sin. If you do something against me, I have the right to forgive you. However, if you do something against me and somebody else comes along and says, "I forgive you," what kind of cheek is that? The only person who can say that sort of thing is God himself, because sin, even if it is against other people, is first and foremost a defiance of God and his laws. So along comes Jesus and he says to sinners, "I forgive you." The Jews immediately recognize the blasphemy of this. They react by saying, "Who can forgive sins but God alone?" Not only did Jesus forgive sin, but he asserted that he himself was without sin. And certainly sinless-ness is an attribute of deity.
.5. The way God was going to save the world was by his Son dying. God, in his divine nature does not die. So He had to come as a human being to accomplish that task. And Jesus believed he was the one to do it. Jesus said in Mark 10:45, "I did not come to be served but to serve and give my life as a ransom in place of many." This is either the highest megalomania or it's the example of somebody who really believes, as he said, "I and the Father are one." In other words, "I have authority to speak for the Father; I have power to act for the Father; If you reject me, you've rejected the Father."
Holy spirit as God:
There are these verses and many more that depict Holy Spirit as the Person of Trinity.
1 Corinthians 2:11; 1 Corinthians 6:11; 1 Corinthians 6:19; 1 Corinthians 12:13; 2 Corinthians 3:5; 2 Corinthians  3:17-18; 2 Corinthians  13:13/14;Galatians 6:8; Ephesians 2:17-18; 1 Thessalonians 1:2-5; Hebrew 3:7-11; 2 Peter 1:21 etc.

2 Cor 13:14 and Mt 28:19 both prove the personality of the Holy Spirit. In both passages, there is a "person, person, person" sequence. (Father, Son, Spirit).
2 Cor 13:14 concludes with these important words: "be with you all". Three things are to be with you: "May Christ's grace be with you. May God's love be with you. May the Spirit's fellowship/sharing/companionship be with you."  This exactly echoes the promise of the "comforter" in John 14:16-17, "And I [Jesus] will ask the Father, and He will give you another [Gr. allos: of the same kind as Jesus] Helper, that He [the Holy Spirit] may be with you forever; that is the Spirit of truth, whom the world cannot receive, because it does not behold Him or know Him, but you know Him because He abides with you, and will be in you."  So Paul's desire in 2 Cor 13:14 for Christians to have the "fellowship of the Holy Spirit" is EXACTLY what Jesus promised in John 14:17 of the Spirit: "He abides with you, and will be in you".
The verse 2 Cor 13:14 says that the "person of Jesus Christ" is the source and supplier of grace, the "person of God" is the source and supplier of Love and the "person of the Holy Spirit" is the source and supplier of fellowship.

Conclusion:
Trinity is depicted in amorphous manner in OT and explicitly in NT. The reason for it being explicit in NT is when Jesus came into this world, the true nature of One Almighty God was also revealed through His message. God the father was revealed in OT. Second person was revealed by arrival of Jesus and the third person was revealed after Jesus was glorified. That is why we find most of the references to God the father in OT, God the Son in Gospels and majority of the references in explaining God the Holy spirit, after Jesus was glorified.
Answer: The doctrine of the Trinity as defined by Christianity is three persons in one Godhead.
God is a Trinity. The Bible says so.
The Trinity is revealed in the New Testament not in the Old Testament.

Deuteronomy 29:29 (NIV)
The secret things belong to the LORD our God, but the things revealed
belong to us and to our children forever..
Proverbs 25:2 (NIV)
It is the glory of God to conceal a matter...

The Lord Jesus did clearly reveal that there exists three persons who've the same nature. He revealed this by making known the one name of the three persons.Their one name is expressive of their one nature ( cf: Exodus 3:14).

Matthew 28:19 (ASV)
Go ye therefore, and make disciples of all the nations, baptizing them
into the name of the Father and of the Son and of the Holy Spirit:

God did create both male and female. This two people were given one name and this one name expresses their one nature.

Genesis 5:2 (ASV)
male and female created he them, and blessed them,  and called their
name Adam, in the day when they were created.

We should call the male and female who have the same name collectively as 'two humans' because of their human nature (human genome) which consists of parts but we should not call the three persons who have the same name as 'three gods' because their one divine nature is spiritual and hence, indivisible.

John 4:24 (NIV)
24 God is spirit, and his worshipers must worship in
the Spirit and in truth."
Comment: "*God is a Trinity. The Bible says so.*" — Really? Which chapter and verse. (Not counting the inserted [Johannine Comma - Wikipedia](https://en.wikipedia.org/wiki/Johannine_Comma) of 1 John 5:7.)
Answer: I don't know if I can add anything useful, but there are some different things I can say.
One might wonder why it makes sense for God to be Trinity.  The only discussion of this question that I have ever read is found in Kallistos Ware's The Orthodox Way.  He writes, in part:

"I believe in one God": so we affirm at the beginning of the Creed.
  But then at once we go on to say much more than this. I believe, we
  continue, in one God who is at the same time three, Father, Son, and
  Holy Spirit. There is in God genuine diversity as well as true unity.
  The Christian God is not just a unit but a union, not just unity but
  community. There is in God something analogous to "society". He is not
  a single person, loving himself alone, not a self-contained monad or
  "The One". He is triunity: three equal persons, each one dwelling in
  the other two by virtue of an unceasing movement of mutual love. Amo
  ergo sum, "I love, therefore I am"
Why, then, believe in God as Trinity? [The] two most helpful ways of entry into the divine mystery are to
  affirm that God is personal and that God is love. Now both these
  notions imply sharing and reciprocity. First, a "person" is not at all
  the same as an "individual". Isolated, self-dependent, none of us is
  an authentic person but merely an individual, a bare unit as recorded
  in the census. 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. 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.

The doctrine of the Trinity was first articulated for the entire Church at the First Ecumenical Council in Nicaea in 325.  The Nicene Creed affirmed what all Christians believe about the Trinity and its individual Persons:

We believe in one God, the Father Almighty, maker of all things
  visible and invisible; and in one Lord Jesus Christ, the Son of God,
  the only-begotten of his Father, of the substance of the Father, God
  of God, Light of Light, very God of very God, begotten (γεννηθέντα),
  not made, being of one substance (ὁμοούσιον, consubstantialem) with
  the Father. By whom all things were made, both which be in heaven and
  in earth. Who for us men and for our salvation came down [from heaven]
  and was incarnate and was made man. He suffered and the third day he
  rose again, and ascended into heaven. And he shall come again to judge
  both the quick and the dead. And [we believe] in the Holy Ghost. And
  whosoever shall say that there was a time when the Son of God was not
  (ἤν ποτε ὅτε οὐκ ἠν), or that before he was begotten he was not, or
  that he was made of things that were not, or that he is of a different
  substance or essence [from the Father] or that he is a creature, or
  subject to change or conversion—all that so say, the Catholic and
  Apostolic Church anathematizes them.

The Creed was amended at the Second Ecumenical Council in Constantinople in 381, to affirm that the Lord's "Kingdom shall have no end" (a refutation of the heretical teaching of Marcellus of Ancyra) and affirmed the Holy Spirit:

And [we believe] in the Holy Ghost, the Lord and Giver-of-Life, who
  proceedeth from the Father, who with the Father and the Son together
  is worshipped and glorified, who spake by the prophets.

The earliest dogmatic theology that was undertaken within the united Church (i.e. prior to the East-West schism of 1054) that I am aware of is John of Damascus' An Exact Exposition of the Orthodox Faith, a work written in Greek in the 8th century.  In it he includes a large section entitled, "Concerning the Holy Trinity", wherein he explains aspects of the relationship between the three Divine Persons:

[All] that the Son and the Spirit have is from the Father, even their
  very being: and unless the Father is, neither the Son nor the Spirit
  is. And unless the Father possesses a certain attribute, neither the
  Son nor the Spirit possesses it: and through the Father, that is,
  because of the Father's existence, the Son and the Spirit exist, and
  through the Father, that is, because of the Father having the
  qualities, the Son and the Spirit have all their qualities, those of
  being unbegotten, and of birth and of procession being excepted. For
  in these hypostatic or personal properties alone do the three holy
  subsistences differ from each other, being indivisibly divided not by
  essence but by the distinguishing mark of their proper and peculiar
  subsistence.  Further we say that each of the three has a
  perfect subsistence, that we may understand not one compound perfect
  nature made up of three imperfect elements, but one simple essence,
  surpassing and preceding perfection, existing in three perfect
  subsistences. For all that is composed of imperfect elements must
  necessarily be compound. But from perfect subsistences no compound can
  arise. Wherefore we do not speak of the form as from subsistences, but
  as in subsistences4. But we speak of those things as imperfect which
  do not preserve the form of that which is completed out of them. For
  stone and wood and iron are each perfect in its own nature, but with
  reference to the building that is completed out of them each is
  imperfect: for none of them is in itself a house.  The
  subsistences then we say are perfect, that we may not conceive of the
  divine nature as compound. For compoundness is the beginning of
  separation. And again we speak of the three subsistences as being in
  each other, that we may not introduce a crowd and multitude of Gods.
  Owing to the three subsistences, there is no compoundness or
  confusion: while, owing to their having the same essence and dwelling
  in one another, and being the same in will, and energy, and power, and
  authority, and movement, so to speak, we recognise the indivisibility
  and the unity of God. For verily there is one God, and His word and
  Spirit.

What is the doctrine of the Trinity?


Secure disposal of 3D prints

Question: The company I work for is protective of IP and has security procedures for disposing of anything that could be stolen for industrial espionage.  Paper gets shredded and sent to trusted recycling center, all old data storage media gets obliterated, but what do we do with 3D prints?  For any functional prototype, I have 10 or more early versions and failed prints.  Is there a good way to dispose of these so that they are unrecognizable?  Given the volume of prints I need to dispose of, it should be safe, cheap, and able to handle large batches.
Comment: I doubt that this is a new problem. Maybe the concern around IP is, but design companies should have solved this decades ago.
Comment: Well, what did you do with prototype models before using 3D printers to produce them?
Comment: @SeanHoulihane many design companies destroy prototypes in many ways: some keep a stove to *burn* their wood/paper prototypes and sketches, others use a waste compactor, others again use old, massive prototypes as stock to machine new, smaller prototypes from. Yet these don't work for 3D printing well
Answer: Big batches need you to be time efficient - or use a method that uses little work. So my suggestions are mainly needing oversight. Keep a fire extinguisher and safety gear handy though!
Melting together
Most filaments are melting at or around 200 °C.
I recently got rid of my box of (PLA) waste material by putting them on a tray and melting them together in a standard kitchen oven at 200 °C for about 1-2 hours. The resulting plate of plastic destroyed all structure that could be identified. This plate can be then broken up or recycled without the risk to disclose any company secrets.
I suggest to use a baking paper under the filament to be molten or a teflon coated tray, as the filament will be REALLY sticky to a blank metal surface.
About 4 liters of broken prints resulted in approximately a 5x450x300 mm sheet. If you make sure that no filament can touch the heating elements, you can get rid of quite a lot of material in each batch.
Don't do this with ABS and don't contaminate your food trays with plastic rests - use specially marked ones that are for disposal of prints only.
Green destruction
If you want to be green when destroying prints: a box solar cooker with a glass lid easily runs at 200 °C, is decently cheap and runs all day on just a couple seconds of adjusting every hour or so. You have to set it up in an access restricted area, but as long as the sun shines, it runs pretty much for free. Just make sure to put the prints to be destroyed onto some kind of non-combustible carriers, like tinfoil or aluminium trays.
ABS in Acetone
If you use ABS, exposing it to acetone fumes for a short time (seconds to half a minute will smooth the surface. Give it some minutes can destroy the structure into a batch of plastic waste without heat that hardens as the acetone evaporates again, though complex structures might need as much as an hour. Dunking ABS into acetone results in pure chemical waste, that is just a waste of acetone.
To save acetone and a way to the chemical waste disposal, try this:
Put a batch of several prints into a large, airtight box that isn't made from ABS. Pour some acetone on a tray and add a paper towel to generate a consistent acetone atmosphere in the box. Make sure to keep the tray on the floor of the box but in a way so no print will fall into it. This should dispose of the prints by merging them into a huge lump within about an hour.
Do this outside & keep fire away.
Comment: The acetone merge system leaves a lot of acetone dissolved in the ABS which will be outgassing for months.   If the concern is fumes from the hot ABS, heating in a ventilated oven should be enough.  You might consider disposable aluminum trays to hold the plastics and the resulting slabs.   I have concerns the three shredder solutions would leave too much information.   They are built for separating items into small pieces,  not for information hiding.
Answer: A plastic shredder machine it's better then a melting/burning solution. It is faster and it doesn't produce fumes. Imagine burning PET bottles.
For the shredder you need nothing but electricity for the motor. For plastic melting it would be much higher consumption. Additionally you could reuse shredded plastic for filament machine like Filastruder or Strooder.

There is a nice article about shredders on 3dhubs from 2015.
Then it depends on your budget. Around 400$ you can build one. A nice tutorial on preciousplastic.com. For 1000$ you can find shredder machines on Alibaba.
Answer: If your company has a shredder which would handle large amounts of paper at one time, it should be able to handle the plastics from 3D printing. Most larger shredders can handle paper clips and staples. 3D plastics would be even less of a burden than them. You may need to break the pieces down into smaller chunks, but I doubt it would be an issue. Even destroying most prints by hand shouldn't be too arduous.
Secondarily, you could also melt them using something hot ... a heat gun would probably do the job without issue. They get in excess of 1100°F. Since we usually melt filament at around 200°C (~392°F), a heat gun should be more than hot enough to make it an unrecognizable blob of plastic.
Comment: You can even recycle the failed print to make filament again. One more great use ABS is to make ABS juice.
Comment: @Himanshu Recycling prints to filament isn't cost-effective, especially so for an engineer working at a company. I also doubt that anyone needs *that* much ABS juice (to the tune of using up many failed prints).
Comment: Heat is the most easy way
Answer: There are industrial shredders that will destroy just about anything. They are not cheap, at least from a hobbyist point of view. You might look into them because they might be right for the size of your company.
Otherwise, you can simply melt them in a hot oven or with a heat gun. I would be careful about getting them too hot because some filaments release toxic fumes when heated and that might pose a hazard risk with potential liability risk.
Answer: My 2 cents. If you have a CNC machine, you could "mill" them down. other than that, garden shredder/mulcher might suffice.
Comment: PLA is biodegradable, but not in a private compost - you need to put it into an industrial composting setup to destroy it. On the other hand ABS and PC are absolutely **not** biodegradable, making composting them impossible. Plus, hiding the to be destroyed IP objects in the front garden for months is a lawsuit waiting to happen. Milling down the prints will create a lot of filament shredds and pieces that could give information about some parts of the print if recovered.
Comment: @Trish, I never said put it in the garden. After it's shredded, you throw it away.
Comment: @Trish Did you ever saw the shreds of a CNC? I bet you you are not able to reconstruct the original part from it not even parts of that part. And at this point I only talk about only the shreds of one part not multiple milled down parts in on batch of shreds.
Comment: But using a CNC to shred something down is a missuse of the machine. I blocks the machine for other tasks and just a fine shredder would be better.

Secure disposal of 3D prints


Centre of instantaneous rotation problem

Question: Is there a point of Centre of Instantaneous Rotation (CIR) for every type of motion or only for cases of rolling?
Comment: What do you think, and why?
Comment: Related post: http://physics.stackexchange.com/a/88597/392
Comment: In the plane there is a point and in 3D there is a screw axis (see answer below). The point in 2D is where the 3D screw axis intersects the plane of motion. You can get to all the planar relationships from projecting the 3D problem down to a plane.
Answer: For a 3D rigid body there is always an instantenous screw axis. This consists of a 3D line (with direction) and a pitch. The pitch describes how much parallel translation occurs for each rotation of the rigid body. A pure rotation has zero pitch, whereas a pure translation has an infinite pitch. ( 3D Kinematics Ref. html,  University of Pennsylvania Presentation ppt, Screw Theory wiki)
Screw Properties

Given a moving rigid body, a point A located at $\vec{r}_A$ at some instant has linear velocity vector at the same point $\vec{v}_A$ and angular velocity $\vec{\omega}$.
The screw motion axis has direction $$\vec{e} = \frac{\vec{\omega}}{|\vec{\omega}|}$$
The screw motion axis location closest to A is $$\vec{r}_S = \vec{r}_A + \frac{\vec{\omega}\times\vec{v}_A}{|\vec{\omega}|^2}$$
The screw motion pitch is $$h = \frac{\vec{\omega} \cdot \vec{v}_A}{|\vec{\omega}|^2}$$

where $\times$ is the cross product, and $\cdot$ is the dot (scalar) product.
Proof
Image point S having a linear velocity $\vec{v}_S$ not necessarily parallel to the rotation axis $\vec{\omega}$. Working backwards (from S to A), the linear velocity of any point A on the rigid body is
$$ \vec{v}_A = \vec{v}_S + \vec\omega \times ( \vec{r}_A-\vec{r}_S) $$
This is used in the screw axis position equation $|\vec{\omega}|^2 (\vec{r}_S-\vec{r}_A) = \vec{\omega} \times \vec{v}_A$ (from above) as
$$ |\vec{\omega}|^2 (\vec{r}_S-\vec{r}_A) = \vec{\omega} \times \vec{v}_S  - \vec{\omega} \times \vec\omega \times ( \vec{r}_S-\vec{r}_A)$$ which is expanded using the vector triple product as
$$ |\vec{\omega}|^2 (\vec{r}_S-\vec{r}_A) = \vec{\omega} \times \vec{v}_S - \vec{\omega} (\vec{\omega}\cdot (\vec{r}_S-\vec{r}_A))+ |\vec{\omega}|^2 (\vec{r}_S-\vec{r}_A)$$
$$ \vec{\omega} \times \vec{v}_S = \vec{\omega} (\vec{\omega}\cdot (\vec{r}_S-\vec{r}_A)) =0 $$
since right hand side is always parallel to $\vec{\omega}$ and the left hand side is always perpendicular to $\vec{\omega}$. The only solution to the above is the velocity at the screw axis S to be parallel to the rotation
$$ \vec{v}_S = h \vec{\omega} $$
and the velocity at A becomes
$$ \vec{v}_A = h \vec{\omega} + \vec{\omega} \times (\vec{r}_A-\vec{r}_S) $$
Comment: Related answer: http://physics.stackexchange.com/a/86020/392
Answer: I assume you are talking about a rigid body in motion in a plane.
Consider any two different points on the body, A and B.
At any point in time, each one has a velocity vector $\vec{v_A}$ and $\vec{v_B}$ (assuming neither one is, itself, the center).
Consider the line normal to $\vec{v_A}$, call it $n_A$, and likewise $n_B$.
Where these two lines intersect is the instantaneous center.
If the two lines are parallel, the motion is pure translation.
If you want to extend it to 3 dimensions, $n_A$ and $n_B$ are planes normal to $\vec{v_A}$ and $\vec{v_B}$.
Where they intersect is a line, an "axle" if you like.
Comment: I was confused with why in case of rolling motion the "instantaneous axis of rotation"(IAR)  was introduced. Why couldn't we just use axis through the center of mass. Looked for (1) what IAR actually is,  (2)should it always be zero (in the case of rolling motion on a surface), and (3)can there exist another such axis rather than the point of contact between the surface and the object for which the answers I were mathematical, so I couldn't get that. Could you help me with that? I didn't post the question separately cause it'd probably be closed as duplicate.
Comment: Well, I know what IAR is and based on your answer the third question can be answered; for an object rolling on a surface it is the only instantaneous axis of rotation, and I think for every instant it is at rest. Am I right?
Comment: @suiz: I'm not sure I understood your question(s), but the simplest example is a wheel rotating on a roadway. Suppose you take a photograph with very short exposure but not instantaneous. In that short exposure time, every point on the wheel will be seen to be tracing a circular path around the point of rolling contact. Sometimes these things are hard to understand if you haven't yet learned calculus, because in calculus you deal with infinitesimal quantities - quantities that are as small as possible without being zero.
Answer: The fact you are stating is quite general in fact and even extends in a related form to 3 dimensions also.
It is known as Chasles's rotation theorem:
        Any general displacement of a rigid body can be represented by a translation plus a rotation.
In the case of motion of a body in a plane,the axis intersects the given plane in a point which we can call the instantaneous centre of rotation.Even in the case if doesn't intersect,we say the centre of rotation is at infinity.
So,yes any motion of a body in a plane has an instantaneous axis of rotation.
Comment: Actually, the name is Chasles' theorem: https://en.wikipedia.org/wiki/Chasles%27_theorem
Answer: Instantaneous rotation axes appear just studying the motion of rigid solid bodies.
Consider a rigid solid body ${\cal B}$ moving in the three space. To study its motion, fix a point $O \in {\cal B}$ and a triple of orthonormal axes ${\bf k}_1$, ${\bf k}_2$, ${\bf k}_3$ at rest with ${\cal B}$
centred at $O$.
We can now describe the motion of ${\cal B}$ with respect to a fixed orthonormal triple of axes ${\bf e}_1$, ${\bf e}_2$, ${\bf e}_3$.
If $P\in {\cal B}$ is a particle of matter of ${\cal B}$ determined by ${\bf x}_P = \sum_{i=1}^3 x_{Pi} {\bf k}_i$, and these components do not change in time just because ${\cal B}$ is a rigid body, its position ${\bf y}_P(t)$ in the space is given by:
${\bf y}_P(t)= {\bf y}_O(t) + {\bf x}_P$ that is, in components:
$$y_{Pi}(t) = y_{Oi}(t) + \sum_{j=1}^n R_{ij}(t) x_{Pj}\quad (1)$$
where ${\bf k}_j(t) = \sum_{i=1}^3 R_{ij}(t){\bf e}_i$ and $R(t) \in O(3)$ is a given rotation.
Now consider the $t$-derivative for $t=0$, when ${\bf k}\equiv {\bf e}_i$,  of (1). We can fix arbitrarily the instant $t=0$ changing the origin of time so this value does not play any fundamental role and we can re-define the triple of ${\bf e}_i$ in order that ${\bf k}(0)\equiv {\bf e}_i$ is valid for $i=1,2,3$.
$$\frac{dy_{Pi}}{dt}|_{t=0} = \frac{dy_{Oi}}{dt}|_{t=0} + \sum_{j=1}^n \frac{dR_{ij}}{dt}|_{t=0} x_{Pj}\quad (2)\:.$$
This identity can be used to study the first approximation of the motion of the body ${\cal B}$ in a neighbourhood of $t=0$:
$$y_{Pi}(t) = y_{Pi}(0) +  \frac{dy_{Pi}}{dt}|_{t=0} t + O(t^2)$$
so that, exploiting (2):
$$y_{Pi}(t) = y_{Pi}(0) +   \frac{dy_{Oi}}{dt}|_{t=0}t + \sum_{j=1}^n \frac{dR_{ij}}{dt}|_{t=0} x_{Pj}t + O(t^2)\qquad (3)\:.$$
Using the Lie group structure of $O(3)$ (or also by direct inspection), it is possible to prove that, as $R(0)=I$, there exists a vector $\omega(0)$ such that ($^*$):
$$\frac{dR}{dt}|_{t=0} = \omega(0) \times \qquad (4)\:.$$
Finally evaluating  (1) for $t=0$ we find
$${\bf y}_P(0) = {\bf y}_O(0) + {\bf x}_P(0)\qquad (5)$$
where all vectors are indifferently decomposed w.r.to the basis of the ${\bf e}_i$s
or that of ${\bf k}_i$s, just because they coincide for $t=0$. Inserting (4) and (5) in (3), we eventually achieve:
$${\bf y}_{P}(t) = {\bf y}_{P}(0) +  {\bf v}_O(0) t + \omega(0)\times {\bf y}_p(0)t  + O(t^2)\qquad (6)$$
where, obviously ${\bf v}_O(t):= \sum_i \frac{dy_{Oi}}{dt}|_{t=0} {\bf e}_i$.
For a generic instant $t_0$, defining $\Delta t = t-t_0$ we would similarly obtain:
$${\bf y}_{P}(t) = {\bf y}_{P}(t_0) +  {\bf v}_O(t_0) \Delta t + \omega(t_0)\times ({\bf y}_P(t_0)- {\bf y}_O(0))\Delta t  + O(\Delta t^2)\qquad (7)$$
Eq.(7) says that, in the neighbourhood of every instant ($t=t_0$ in our case), the motion of ${\cal B}$ is the superposition of a spatial translation along ${\bf v}_O(t_0)$ and a rotation around the unit vector parallel to $\omega(t)$ passing through the instantaneous centre $O(t)$. The axis is the instantaneous rotation axis by definition.
Using (7) that is valid for every choice of $O$, if the motion of not of pure translation, we can always change $O$ in order that at the interesting time ${\bf v}_O(t_0) \times \omega(t_0)=0$ so that ${\bf v}_O(t_0)$ and $\omega(t_0)$ are parallel. Notice that the new  $O(t_0)$, in general, is not a point of matter of ${\cal B}$ but a geometric point in the space. In this case (7) reduces to a pure rotational motion around $O(t_0)$ plus a translation along the rotational axis  (in a neighbourhood of the considered instant of time). This point $O(t_0)$ is an the instantaneous rotation center. Actually there is a whole axis with the same property: that passing for the found $O(t_0)$ directed along $\omega(t_0)$.

Footnotes.
$(^*)$ As $t \mapsto R(t)\in O(3)$ and $R(0)=I$, then $dR/dt|_{t=0}$ is an element of the Lie algebra of $O(3)$. The Lie algebra of $O(3)$ is made of all real antisymmetric $3\times 3$ matrices. If $A$ is such a matrix, it immediately arises that there is a vector $\omega_A$ such that $A{\bf u} = \omega_A \times {\bf u}$ for all vectors ${\bf u}$.
Comment: You mentioned using the Lie group structure of $O(3)$.Could you please elaborate further on that subtle point?.Because that statement was really the crux of your proof.
Comment: The Lie algebra of $O(n)$ is made of all antisymmetric $n\times n$ matrices (this can be easily proved). For **$n=3$** an antisymmetric matrix $A$ is always of the form $\omega_A \times$ for some vector $\omega_A$.
Comment: As $t \mapsto R(t)\in O(3)$ and $R(0)=I$, $dR/dt|_{t=0}$ is an element of the Lie algebra of $O(3)$.


How close would the sun have to get to Earth for there to be severe consequences?

Question: According to earthsky.org the Earth gets 3 million miles closer to the Sun than its usual distance of about 93 million miles on average.

My question is, how close would the earth have to be to the sun for there to be problems with our survival?
Comment: Sure, but thats not my question
Comment: The Earth is currently inside the Goldicks Zone. If the Earth goesanywhere outside the Goldilocks Zone then there will be severe circunstances be it near the Sun or away from it.
Comment: That happens every year.  There's nothing unusual about it.
Answer: I'm going to use Gm (1 gigameter = $1\times10^9$m) and degrees Celsius for this answer.
By getting closer to the Sun, probably the most major problem would be the increase in temperature.
A while ago I wrote a program that calculates the effective surface temperature of a planet. Having dug it back out, I've played around with the values a bit. It's important to note that the effective temperature is not the same as the actual surface temperature, since it doesn't account for Earth's atmosphere. If Earth had no atmosphere, it would be the correct actual temperature.
At our current distance of (avg.) 149.6Gm, the effective temperature is 257K, or -16°C (some websites cite other values ±2°C). NASA cites an actual average temperature of 15°C. Assuming a linear relationship between effective temperature and actual temperature, we can assume that $T_{actual} = T_{eff}+31 \pm 2$.
So, what would happen if we moved, say, 10Gm closer?
Well, the effective surface temp is now -7°C, and I'm guessing the actual temperature would be about 24°C. This is an increase of 9°C. We would probably still be able to survive, but with difficulties. For starters, the sea level would rise by over 40m, leading the world to look (at the best) like this. Not an easy situation, but nevertheless survivable.
Of course, there would be other effects like an increase in extreme weather, the mass extinction of species, and probably a whole load of things that are hard to foresee, but I'm not going to try to predict them.
So, what about a move towards the Sun of 20Gm?
The effective temperature is now ~3°C, and the surface temperature is about 34°C. Things start to get bad now. All of the ice caps have melted. Once fertile areas are now barren deserts. Surviving is hard, but possible, although famine is now a major problem across much of the world (especially around the equator). The Gulf Stream may have stopped, oddly enough cooling down some of western Europe and all of Britain. It's not looking good.
What about 50Gm?
The effective temperature is 42°C; the actual one is around 73°C. Where the Sun's habitable zone begins and ends is disputed, but now, at 0.65AU away from the sun, it's quite likely that we're not in it. It's very hard to predict what happens now. Humans would likely have to stay underground to remain alive, and food would be a major issue. The ecosystem would be pretty much destroyed, having not had a chance to adapt to the new temperature.
For fun, if we moved 100Gm closer, we'd be at about 205°C. Ouch. We're closer than Mercury now, and look how that planet's coping. Mercury ranges from -173°C to 427°C depending on various factors. Survival without massive life support is not possible.
Any closer, and things just get worse.
Hope this is a suitable answer for your question!
Comment: When you consider feedback mechanisms, change in albedo and greenhouse gas both CO2 and Watervapor, you should increase your T'actual and T'effective upwards.   Look at Venus' T'actual and effective or Earth's during the last ice age.    You need to adjust your 31 degree estimate upwards significantly as Earth moves that much closer to the sun.  (accurate estimates are obviously impossible, but your estimates are clearly too low).
Comment: Excellent what-if style answer.
Comment: @userLTK Yeah, I'm guessing most things in this answer: "Assuming a linear relationship between effective temperature and actual temperature" was what I was doing with calculating the $T_{actual}$ because it's extremely hard to accurately work out how they are related. My temperature estimates, if anything, are minimum bounds.
Answer: The Earth passes within 91.4 million miles for just a brief time, then it moves back further out and 6 months later it's 94.5.  That 3.4% and change closer works out to 7% more solar energy, but that's just for closest and furthest points.   Over the closest and furthest month, the variation is smaller and (perhaps obviously), it averages out over the entire year.
There's two ways to address to this question - how eccentric the Earth's orbit can get which would make the perihelion closer and aphelion further, or, the 2nd way, how much closer can you make the semi-major axis, which defines orbital period.
Earth's present eccentricity is 0.017 and decreasing (Wikipedia article above).  For simple approximation and low eccentricity orbits, the eccentricity 0.017 translates into (doubling it) a 0.034 (or 3.4%) variation perihelion to aphelion, which works out to a (1.034^2), about a 7% variation in solar energy.
Earth's peak eccentricity of 0.0679, (this time I'll do the math), closest point (1-0.0679) = 0.9321 and farthest (1+0.0679)= 1.0679.   The ratio 1.0679/0.9321 = about 14.5% which works into a 31.3% variation in solar energy closest to farthest.     14.5% and 31% energy variation may sound like a lot, but consider that the winter/summer solar energy variation in latitudes away from the equator can be considerably over 100%.  So, 31% isn't world ending, in fact, the Earth handles those 31% days without too much trouble, though they can trigger or end ice ages depending on how it lines up with other Milankovich cycles.  We should also remember that it's 31% hottest to coldest, it's about 14.5% hottest to average, and again, just for one day then that number begins to drop.
14.5% size change isn't as much as it sounds either, that's about the variation between the largest full moon or supermoon and the smallest (micromoon), though the average full moon variation is between perigee and apogee 11% and 12% in diameter.  How often do you look at a full moon and say "that's bigger than the full moon 4 months ago".  That's not to say nobody notices, but many of us wouldn't recognize a supermoon without being told when to look for it, though it's fairly obvious if we could see them side to side.

So what effect does Earth's periodic 0.0679 eccentricity have?  Apart from triggering or perhaps ending an ice age, not that much..   You could push Earth's eccentricity pretty far without much danger to Earth, though past a certain point, crashing into Venus might become a concern.
Lets have some fun and push Earth's eccentricity up to 0.15 (that's about half way between Mars' and Mercury's eccentricity.

Perihelion 0.85% of the semi-major axis, Aphelion 1.15%.   At perihelion the solar intensity would be (1/.85)^2 = 38% stronger than normal.  That might cause scorching heat in some places where the Perihelion lined up with summer, and you might get some bitter cold weather when the Aphelion lines up with winter (note, this doesn't always happen, perihelion slowly cycles around the calendar every 26,000 years or so).  But when it lines up you might see some seasonal-weather extreemes, but Earth could (I think) survive even a 0.15 eccentricity.   The views of Venus at Perihelion would be impressive too, Venus would stay in the sky longer and be larger and brighter.
Push Earth's eccentricity to about .26 and Earth and Venus would get uncomfortabaly/scary close and might crash into each other.   Fun to think about, but a potential planet killer.
But apart from creating potentially greater variation in seasons, some very wild weather and perhaps triggering an ice age (perhaps the biggest ice age since snow-ball Earth) or accelerating climate change (it all depends on how the 3 Milankovich cycles line up with each other), You could push Earth's orbit surprisingly close to the Sun, half way to Venus or even closer at perihelion, without ending life on the planet.
Now, if you adjust Earth's semi-major axis, which makes the orbit faster or slower, and changes the length of the year - with that, there's much less variation.    @JThistle covered this.   If you push Earth's semi-major axis just a few percentage points closer to the sun, Earth would heat up and it would get bad quickly.  In fact, I think his estimates are conservative.  There are already some pretty good estimates out there on this, just google "what will the Earth be like in 500 million years or a billion years" for a few articles.  Here's one.   The sun is growing slowly larger and more luminous, about 1% every 100 million years.  That will be a significant problem as soon as 500-600 million years from now, perhaps less.  Likewise, just a 2.5%-3% push closer to the sun would have a similar effect.  You can't reduce Earth's semi-major axis by much without causing serious problems.   Just 1% might be enough to melt Greenland over time, raise sea levels and prevent future ice ages.
Similarly if you push Earth just 1-2% further away, Earth could enter permanent ice ages (fortunately we can fix that by burning oil and coal), but sans man made greenhouse gas, just 1%-2% further away would trigger perhaps a permanent ice age for the next several million years and perhaps, dangerously low CO2 levels, at least until Antarctica drifts north enough for it's ice to melt.    It would be nice to be told to burn oil for the "good of the planet" though.  :-)
This is all very ballpark, but the Earth is, surprisingly, at a very good distance from the sun and just a few % one way or the other could be very bad, though in 15-25 million years when Antarctica is brushing up against South America and is no longer covered in ice, when that happens, Earth will have greater wiggle room away from the sun, but not closer to the sun.
Precise mathematical answers to this question are obviously impossible.  I'm just giving approximations.
Answer: Without any significant change in orbital distance, there have been a variety of long-term (millions of years) tropic or ice ages, and transitions from one  to another led to rather a lot of extinctions.
In the same vein,  a nice big solar eruption could wreak havoc independent of orbital distance changes.
I"m not arguing with the other answers; just pointing out that time scale matters.
Comment: I feel like this is more of a comment. It doesn't actually answer the question at all.


Slow booting / starting after apt-get update 12.04

Question: I have just bought a new Lenovo Ideapad Z580, which came with Windows 8.
I have since, removed that and installed 12.04 on top. Everything works fine. However, after I have to updated all 272 updates using update manager, my machine now takes about 15mins to get to the password/login page. Once I have logged in everything works fine.
I have a before and after bootchart image if that helps (should I save it online e.g. pastebin, or can I attach it here?). It's very odd, in that the slow image has the opening init command taking over 1000 seconds, before the boot process kicks in.
Since having this issue I have tried multiple things to fix it with no success.
Yesterday however, I did spend the entire day updating 5-10 updates at a time, to see if I could find the culprit for the slow boot. After going through all of them, I managed to get everything installed fine! It worked!! Then I went to install Mate on top, and bang, back to 15 minute boot times. Uninstalling Mate, didn't fix this!
I currently have it working because I removed the latest kernel 3.2.0-35, so now have 3.2.0-29.
I did this by doing
sudo apt-get purge linux-image-3.2.0-35-generic
sudo update-grub2
However, even though it is working now, I know that if I upgrade anything I will be left with the 15 minute boot times again.
Hopefully someone out there can help.
Thanks
Russ
Answer: Ideapad Z580 users seem to be experiencing an ACPI issue.  Booting with ACPI=Off works but I have read this cripples hyperthreading (so what is the point?)    Here is a related thread:
Ideapad Z580 won't boot kernels above 3.2.0-32


Let $T:V→V$ be a linear transformation satisfying $T^2(v)=-v$ for all $v\in V$. How can we show that $n$ is even?

Question: Let $V$ be a real n dimensional vector space & let $T:V→V$ be a linear transformation satisfying $T^2(v)=-v$ for all $v\in V$. Then how can we show that $n$ is even?
I am completely stuck on it. Can anybody help me please?
Comment: @John: It's part of the whole "if everyone would act like this, then everyone would hate this website" unwritten rules.
Comment: Yeah, it's called "the epsilon relation", but it has a better symbol than $\epsilon$. You can use `\in`.
Comment: @JohnSmithKyon: Please don't go around and ping *everyone*.
Comment: @AsafKaragila What's the rule against this please?
Comment: @AsafKaragila fine fine. i guess just a few people ;)
Answer: Since $T^2(v)=-v \ \ \forall v \in V \Rightarrow T$ does not have any real eigenvalues (if $T(v)=\lambda v, \ v\neq0\Rightarrow T^2(v)=\lambda^2 v = -v \Rightarrow \lambda^2=-1$ ). If $n$ is odd the characteristic polynomial of $T$ has odd degree therefore at least one real eigenvalue ↯.
Comment: Wow! Brilliant!
Answer: Since $T^2(v) = -v$ for every $v \in V$, we have $T^2 =  -I_n$, where $I_n$ is the $n\times n$ identity matrix. Therefore,
$$\det(T)^2 = \det(T^2) = \det(-I^n) = (-1)^n.$$
If $n$ is odd then $(-1)^n = -1$ and thus $\det(T)^2 = -1$. But this is impossible since $\det (T) \in \mathbb{R}$.
Answer: A very simple argument, which basically uses just the existence of the complex numbers as a degree $2$ extension field of the real numbers but nothing else, is as follows.
Make $V$ into an $\mathbf R[X]$-module by having $X$ act as $T$ (and so $(\sum_ka_kX^k)\cdot v=\sum_k a_k T^k(v)$ for arbitrary polynomials). Since $X^2+1$ acts as $T^2+I=0$, the module structure passes to the quotient ring $\mathbf R[X]/(X^2+1)\cong \mathbf C$ and $V$ becomes a complex vector space. But then as a real vector space it is even-dimensional (any basis as complex vector space gives rise to a real basis twice as large, by taking the multiples by $1$ and by $\mathbf i$ of all the basis vectors).
The same reasoning shows that if a $K$-linear operator $T$ satisfies an irreducible polynomial equation over $K$ of degree $d$, the $K$-dimension of the space on which $T$ acts must be divisible by $d$.
Comment: This is really the most natural proof, 1+.
Answer: The following argument does not make use of the order completeness of ${\mathbb R}$ or of the fundamental theorem of algebra. Therefore it works also with ${\mathbb R}$ replaced by ${\mathbb Q}$.
Assume $U$ is an arbitrary invariant subspace of $T$. Given any $y\in V\setminus U$ (in particular $y\ne0$) we can form the span $W:=\langle y, Ty\rangle$, which is obviously an invariant subspace, too. Suppose that for some real $\alpha$, $\beta$ we have
$$z:=\alpha y+\beta Ty \in U\ .$$
Then $\alpha z -\beta Tz=(\alpha^2+\beta^2) y$ lies in $U$ as well, which implies $\alpha=\beta=0$. Applying this to the case $U=0$ we infer that ${\rm dim}(W)=2$. For arbitrary invariant $U$ we conclude that $U\cap W=0$, so that $U':=U\oplus W$ is an invariant subspace of $T$ of dimension ${\rm dim}(U')={\rm dim}(U)+2$.
This allows the construction of an ascending chain of even dimensional invariant subspaces $U_{2k}$ $\ (k\geq 0)$ of dimension $2k$, which eventually has to end. At this point $U_{2n}=V$.


Can anyone tell why this Hibernate query is invalid?

Question: I have criteria query that, when executed, results the following exception thrown:
java.lang.IllegalArgumentException: org.hibernate.QueryException: illegal syntax near collection: id [select generatedAlias0.permissions from temp.package.commons.user.Role as generatedAlias0 where generatedAlias0.id=2L]
at org.hibernate.ejb.AbstractEntityManagerImpl.convert(AbstractEntityManagerImpl.java:1222)
at org.hibernate.ejb.AbstractEntityManagerImpl.convert(AbstractEntityManagerImpl.java:1168)
at org.hibernate.ejb.AbstractEntityManagerImpl.createQuery(AbstractEntityManagerImpl.java:320)
at org.hibernate.ejb.criteria.CriteriaQueryCompiler.compile(CriteriaQueryCompiler.java:227)
at org.hibernate.ejb.AbstractEntityManagerImpl.createQuery(AbstractEntityManagerImpl.java:437)
at temp.package.dao.impl.DefaultDAOService.getProperties(DefaultDAOService.java:585)

As can be seen in the code box, the query that raises the error is:
select generatedAlias0.permissions from temp.package.commons.user.Role as generatedAlias0 where generatedAlias0.id=2L

The id attribute is the entity's attribute which was annotated with @Id @GeneratedValue. Basically I'm trying to load the attribute "permissions", which is a collection uninitialized at the time, for the role object whose id is 2. The id attribute is of long type.
Any ideas on why this query would fail?
I can post the code that creates the criteria query here, but it is fairly complicated (as it generates based on a LDAP filter, etc), so I'm hoping the error will be visible from the generated query string and the exception. Please let me know if that's not the case.
Follow-up: The criteria query that generated this error was built this way:
EntityManager entityManager = getEntityManager();
CriteriaBuilder criteriaBuilder = entityManager.getCriteriaBuilder();

CriteriaQuery<Object> criteriaQuery = criteriaBuilder.createQuery();

// queryScopeClass is assigned to type temp.pack.commons.user.Role
Class<? extends T> queryScopeClass = role.getClass();

Root<? extends T> from = criteriaQuery.from(queryScopeClass);

Predicate predicate = criteriaBuilder.equal(from.get("id"), new Long(2));
criteriaQuery.where(predicate);

// attempting to get just the role's permissions
CriteriaQuery<Object> select = criteriaQuery.select(from.get("permissions"));
TypedQuery<Object> typedQuery = entityManager.createQuery(select);

return typedQuery.getResultList();

The Role and Permission classes have been mapped with JPA and some Hibernate annotations like this:
public abstract class Role implements Serializable {

 /**
  * The id of this role. Internal use only.
  *
  * @since 1.0
  */
 @Id @GeneratedValue
 protected long id;

 /**
  * Set of permissions granted to this role.
  *
  * @since 1.0
  */
 @OneToMany(cascade = { CascadeType.PERSIST, CascadeType.MERGE }, mappedBy="sourceRole")
 protected Set<Permission> permissions = new HashSet<Permission>();

...

}

public class Permission implements Serializable {
 private static final long serialVersionUID = 1L;

 /**
  * The id of this permission. Used internally for persistence.
  *
  * @since 1.0
  */
 @Id @GeneratedValue
 @Column(name = "PERMISSION_ID")
 protected long id;

 /**
  * The group to which the owner of this permission is being granted permission to.
  *
  * @since 1.0
  */
 @ManyToOne(cascade = { CascadeType.PERSIST, CascadeType.MERGE })
 @JoinColumn(name = "TARGET_ROLE_ID")
 @ForeignKey(name = "FK_TARGET_GROUP_PERMISSION_ID",
   inverseName = "FK_PERMISSION_ID_TARGET_GROUP")
 protected Group targetGroup;

 /**
  * The role that has been granted this permission.
  *
  * @since 1.0
  */
 @ManyToOne(cascade = { CascadeType.PERSIST, CascadeType.MERGE })
 @JoinColumn(name = "SOURCE_ROLE_ID")
 @ForeignKey(name = "FK_SOURCE_GROUP", inverseName = "FK_GROUP_PERMISSIONS")
 private Role sourceRole;

...

}

I was expecting the call to typedQuery.getResultList() to return a list of collections with just one element: the collection of permission objects for the role with id = 2. This is an attempt to select just the "permissions" collection from the object role with id = 2.
I'm new to criteria queries and I'm having a hard time finding what's wrong with it.
Comment: What data type is permissions?
Answer: Without more information, it sounds like you are trying to do something like:
select rp
from Role r
inner join r.permissions rp
where r.id = 2

Can you post your annotated entities and a sample of your Criteria?


Difference between a munkar hadith and a mudtarib hadith?

Question: i search it form site and read different scenario but am confused whats the actually difference.
explain me the actual difference of munkar and mudtarib hadith.
Answer: The Scholars of Hadith differed over the meanings of the classifications of Hadith. However, what is generally meant by Munkar is that 1. the Isnad is weak, for example there may be a break in the Isnad or one of its narrators lost his memory and 2. the meaning of the Matn opposes something more authentic than it which is established.
Mudtarib refers to the narration which is 'mixed up' either in its Isnad or in its Matn or both. An example of this is when a narrator reports the individuals or the names of individuals in the wrong order or when he mixes the wordings of two different Hadith together.
Both Munkar and Mudtarib are types of weak Hadith but Mudtarib is more specific. Note that a Munkar Hadith can be graded as such because it is Mudtarib in both its Isnad and its Matn.


WPF ListView items duplicated

Question: I am having a unique trouble with my program. Let me explain the scenario.
I have a ListView that is bound to a ObservableCollection which is initially empty. The observable collection gets it data from an IAsync service.
After loading, the listview shows duplicate of the items. I used snoop to check the bindings and its confirmed that the items source that it is bound to has 2 items, but the listview has created 4 items. Also interestingly the duplicate entries are bound to the right item.
Can anyone shed some light on this matter ?
Comment: Can you supply the code?
Comment: Please show XAML and ViewModel/code behind
Answer: Try turning off virtualization
VirtualizingStackPanel.IsVirtualizing
Or you may be able to virtualize but turn off recycling
VirtualizationMode Enumeration

WPF ListView items duplicated


What is the connection between Asherah and the custom of Christmas Trees?

Question: Has there been any serious studies into the relationship between the Asherah tree and the Christmas trees, with the possibility of the former being the source of the latter?
Comment: There is no correlation. Decoration of the yule tree with lights is a middle European thing that is not even that ancient. Any Asherah worship was long dead before it became popular.
Comment: Can you provide some context or explanation about the Asherah tree, for those of us unfamiliar with it?
Comment: @C.M.Weimer Turn that into an answer?
Answer: There is no historical connection.
The cultures that worshiped Asherah were mostly destroyed when the Babylonians invaded the kingdom of Judah and took a large portion of the populace as captives. The last reference to Asherah worship in the Bible is 2 Kings 23, during the reign of Josiah (r. 640 to 609 BCE).
Christmas trees became popular in Europe starting in Germany in the 1500s. There is no historical or cultural connection to the practices within Judah.
Comment: Thanks for doing what I had forgotten to do. Any chance to introduce citations for the claim? With that, I think it would be the perfect answer.
Answer: Well as far as I can see through many scripture in the old testament, the mention of the ASHERA tree is documented and is the consort of YHWH one the seventy sons of El. Basically the symbol of ASHERA was a tree or a cutting or formation of a pole or Tatum totum totim pole or tree of life and or knowledge or any wooden form of worship and sacrifices were made unto it. So when you put up your X mas tree you would have no understaning of its origen or myth by many different cultures which have been altered hence the word Alter. To change message and meaningful ness through time.
Comment: I recommend you bring sources for your answer, verses from the Bible, etc.
Comment: "As far as you can see"?  Can you provide any justification for this?
Answer: The garden of eden part of Genesis myth is possibly derived from the Asherah and other Mesopotamian myths. Not the Christmas tree, which has its origin in other pagan rituals.
In the Kuntillet 'Arjud and Khirbet el-Kom inscriptions, Asherah is named with Yahweh -- probably as his consort. In Canaanite myth, Asherah (Ug. Athirat) was the consort of El, the creator god, and she begat the seventy lesser gods, the sons of El. Asherah became Yahweh's consort through an identification of El with Yahweh (seen throughout the OT). In Canaanite texts, Asherah is called the "Mother of All" and one of her titles was qnyt 'ilm "Creator of the Gods". It is interesting that qnh is an unusual word in Hebrew for "create" as it usually means "acquire" (El, in contrast, was called bny bnwt "Creator of Created Things" in the Ugaritic texts). The notion of Eve as a creator goddess also appears in muted form in Genesis 3:20, 4:1 where Eve is called "the mother of all living" and Eve says after the birth of Cain, "I have created (qnh) a man with the help of Yahweh," employing the same verb as applied to Asherah in the Ugaritic texts. The latter quote is also very similar to a statement regarding the Akkadian creator goddess Aruru (= Sumerian Ninhursag):

Aruru zi-ir a-mi-lu-ti it-ti-shu ib-ta-nu

"Aruru, with the help of [Marduk], created the seed of mankind" (KIB, vi. I, 40).

Another clue that Eve's identity originally was not as it is given in the story can be found in the name: Hebrew chwwh, being related to Aramaic chwyh and Phoenician chwt "snake". Chawat appears in a Phoenician inscription as one of the names of Elat "Goddess", that is, Asherah.
It is in Proverbs where we meet Asherah as Wisdom personified. She appears as a creator goddess in Proverbs 8:22-31 and the following chapter describes a banquet that Wisdom hosts in her palace (Proverbs 9:1-6). In the Ugaritic texts, we read similarly of Asherah and her consort El hosting banquets in their mountain palace (cf. KTU 1.1 IV 26-35).
Proverbs 3:13-18 contains some paronomasia between the name Asherah ('ashrh) and the word "happy" ('ashre), which is paired with the "tree of life" in a chiasm:

"Happy ('ashre) is the one who finds wisdom .... She is a tree of
life ('ts chyym) to those who lay hold of her; those who hold her
fast are made happy (m'sshr)." (Proverbs 3:13, 18; cf. 11:30; 15:4)

The expression is nearly identical to "the tree of life" ('ts h-chyym) of Genesis 2:9, which refers to a specific mythological tree while the "tree of life" in Proverbs refers to a more abstract Wisdom, but the verse also plays on the name Asherah. It is interesting that Wisdom is identified with the "tree of life" when a "tree of knowledge of good and evil" (e.g. "wisdom") is distinguished from the Tree of Life in the Eden narrative. Many scholars since the time of Wellhausen have suggested that this second tree originated as a doublet of the first.


Best Portable Recorder For Art Installations

Question: Guys, I'm a poet who is going to do an experimental poetry project. I want to record sounds of the landscape for my show. I guess it's something like doing filed recording. What portable recorder do you recommend for someone new in the field but who wants the best audio? I don't want to spend more than $150.
Answer: Zoom H2 is a safe bet.
Answer: I can personally recommend the Zoom products. I personally have the H4n Series which is a bit more pricey - http://www.zoom.co.jp/english/products/h4n/ However they have a great reputation for portable recorders and the mics are very high quality.  If the other guys are saying the H2 is a good shout, id go for it!
Hope this helps!
Gillian
Comment: I went to the Chicago Museum of Modern Art and recorded a lot of different crowd & room sounds with the H2. I highly recommend that if you're not getting the H4.
Answer: You might consider renting some gear if this is a 1 time deal.  Many cities have audio rental houses.  You can probably get a Zoom H2 for $20-30/day or less.
DO you have more specific info on what you want to capture?  The more we know about what you are recording, the more the SSD community can help.  Is it possible that a sound library of ambiances might work?


Nikkor f/1.8G 35mm or 50mm?

Question: I'm new to photography. I got a Nikon D3100 with the 18-55 kit lens.
I was looking to buy a f/1.8 prime lens, and I found two options:

AF-S DX NIKKOR 35mm f/1.8G
AF-S DX NIKKOR 50mm f/1.8G

How should I go for choosing one or the other?
Answer: The question here doesn't — or shouldn't — come down to what we prefer, but rather what you want to use it for. These lenses (because of their different focal length) have a significantly different angle of view, which means that they serve different purposes. Eventually, you may find that you want both.
On your APS-C Nikon, the 50mm lens acts as a short portrait lens. It's kind of awkward for most anything else, but is just about perfect for taking head-and-shoulders portraits. I say awkward because it's not enough "reach" to pick out details like a longer telephoto lens, but is narrow enough that it's difficult to frame indoor scenes. That doesn't mean you can't use it more generally, of course.
The wider 35mm acts as a normal lens — it gives a comfortable and versatile field of view that doesn't feel either wide-angle or telephoto. For that reason, if you're just going to pick one of the two, this is probably going to be your best bet. But it depends on what you're looking for — a portrait lens may be just what you need.
Comment: I know this is an old answer, but it's still hard to square "kind of awkward for most anything else" with "that doesn't mean you can't use it more generally."
Comment: You _can_ use it, but it's... awkward. I'll try to think of an alternate phrasing. :)
Comment: @mattdm "Doesn't mean you can't use it as a walkaround lens" perhaps or something of that ilk?
Answer: I prefer the 35mm. I actually have the d3100 and upgraded to the nikkor 35mm f/1.8 a few months ago.
I will get the 50mm however, but use it only for portraiture (not the best, but still cheap, fast and compact).
As an exercise try to shoot all day at 35mm with your kit lens. And then 50mm. You will know for sure what you need.
Comment: Using the kit lens to try both is a great idea! use some tape to fix it in position and you can try it out.
Answer: As indicated above, it is what you want the lens for that will be the deciding factor. I would also emphasize using the kit lens at 35mm and 50mm to see what you will like best. Tape the lens so it won't zoom when being used after setting the focus. However I have the 50mm f/1.8 lens for portraits, and am not happy with it. It works just fine, but I should have purchased the Nikon 85mm f/1.4D AF Nikkor that is for a full frame F3, but will work with my 3 DSLR camera's just fine. When using my film Nikon camera's I usually had a 100mm lens on for portraits, and just didn't think it through completely when purchasing the 50mm lens. The 50mm lens is only equal to a 75mm lens, not even close to the 80mm I consider the minimum for a portrait lens. Hope this helps you in your decision.
Answer: These two lense are mostly equivalent in a lot of things--build quality, price range, focus motor features, image quality, age of design...
So the one big difference between them is 35mm vs. 50mm.
50mm is special in one way.  The magnification of the lens most closely matches that of the human eye and there's little distortion. In other words, if you compose a scene with both eyes open, what you see through the viewfinder will match what you're seeing through the unaided eye. Composition, then, simplifies down to the simple act of framing. But because of the APS-C sensor size, the field of view of a 50mm lens on a crop body may be narrower than you'd like for walkaround use, or for composition in small spaces.
35mm is special in a different way.  If a lens has a focal length equal to the diagonal dimension of your image format (i.e., the sensor), the field of view that's yielded is considered "normal".  It's what 50mm yields on full frame, so if you were shooting FX, the 50mm would be normal both in magnification and in field of view. But on APS-C, you can't have both in one lens.  So the field of view a 35mm lens gives you on a DX camera is more natural for general purpose walkaround and portrait use, but if you shoot with both eyes open, what you see through the viewfinder will look farther away than what you see with the unaided eye. And there is a slight distortion to achieve this, so for portraits, you can inadvertently get a bit of a funhouse mirror effect if you aren't careful with your composition.
Which one you would prefer is up to you, and will depend greatly on what you shoot the most and what working distances from your subject you prefer.
The only other (slight) difference I can think of is the 35/1.8 has a close focus distance of 30 cm, while the close focusing distance of the 50/1.8 is 45 cm.
Answer: Basically, this will depend on your needs as a photographer. I guess you should first figure that out. Anyway, both lenses are perfect for portrait and landscape photography. Both have motors (so they are perfect for your D3100). Because of the f1.8 aperture, both are good in low-light conditions. If I have a D3100 camera or any DX format camera, I would just flip a coin to decide--both lenses are okay on a DX format camera. But, if I have a Nikon FX format or full frame camera, I will definitely get the NIKKOR 50mm f/1.8G lens. Well, actually, if I have a FX format camera I'll just get the NIKKOR 50mm f/1.8D lens. It is cheaper and is as powerful as the other 50mm lenses. The 35mm lens is not very compatible with a FX format camera.
Answer: I have both lenses. Both are awesome lenses. For 35mm you will get some more wider that's all the difference.
Answer: My preference in this case would be the 50 mm lens, because my interest is in landscape photography. While the 35 mm lens would give you a better field of view, it's better to use a 50 mm lens and then get to the desired field of view by compiling a panorama, as that yields a higher resolution image. Even if the resolution of the picture taken by a 35 mm lens would be good enough, the higher the resolution of the image, the more room you have to improve the image in post processing. E.g. simply reducing the resolution of the panorama compiled with the 50 mm lens to obtain a picture you could have shot directly with the 35 mm lens, will significantly reduce the noise.
Answer: I had the same question a while back and the advice I was given was to use the kit lens at aprox 35 and at aprox 50 for what I would normally photograph, and then analyze the pictures afterwards and decide which look I preferred.  One thing of note, is that its not just focal length that is different, but also background compression.  In otherwords, the 50mm will bring background elements a little closer than the 35mm lens.  When you take a few pictures at 35mm, take the SAME frame at 55mm and you should see the difference.
Ultimately, I found I enjoyed the 50mm the best, so went with it.  When I need something a little more wide, I just use panorama techniques and stitch multiple images together after the fact. The Brenizer Method works quite well at 50mm.
Also, the 50mm is a full frame lens, so if you upgrade to full frame in the future, you have one less lens to replace.  The 35mm would still work on the full frame camera, but it will downgrade the sensor into "crop mode".
If you need to take lots of shots where you need a wider lens, and will not have the time to stitch or there will always be lots of moving objects, then the 35mm would make a better option.
Answer: Maybe this will help.
Nikon D3300, Nikkor 50mm f/1.8 D NOT G.

You tell me. JPG format, small, 6MP resolution, no lightroom, photoshop-straight out of the camera.

Nikkor f/1.8G 35mm or 50mm?