In Acts 7:56 why does Stephen see Jesus "standing"?

Question:
and he said, "Behold, I see the heavens opened up and the Son of Man ~standing~ at the right hand of God."  Acts 7:56 (NASB)

All of the time, except for this time, Jesus sits at the right hand side of God.
Why is He standing rather than sitting?
Comment: According to the NAC commentary there is a 'useful discussion' on this subject in  Haenchen's commentary on Acts (page 292)  http://www.amazon.co.uk/Acts-Apostles-Commentary-Ernst-Haenchen/dp/066420919X
Answer: There are about 16 New Testament references to Jesus or the Son of Man being at God's right hand.  Acts 7:55-56 is unique in describing the Son of Man as standing (twice), four verses describe him simply as "at" God's right hand (Acts 2:33, 5:31; Rom.8:34; and 1Pet.3:22), and the remainder describe him as seated (Mt.26:64; Mk.14:62, 16:19; Lk.22:69; Acts 2:34; Eph.1:20; Col.3:1; Heb.1:3, 8:1, 10:12, and 12:2).  Mark 14:62 is typical of the latter:

Again the high priest asked him, "Are you the Messiah, the Son of the
  Blessed One?"  "I am," said Jesus. "And you will see the Son of Man
  sitting at the right hand of the Mighty One and coming on the clouds
  of heaven."

Though the full statement is missing, the image is likely rooted in Daniel 7:13-14:

In my vision at night I looked, and there before me was one like a son
  of man, coming with the clouds of heaven. He approached the Ancient of
  Days and was led into his presence. He was given authority, glory and
  sovereign power; all nations and peoples of every language worshiped
  him. His dominion is an everlasting dominion that will not pass away,
  and his kingdom is one that will never be destroyed.

On the Day of Pentecost Peter also drew on precedent, Ps.110:1, declaring:

"God has raised this Jesus to life, and we are all witnesses of it.
  Exalted to the right hand of God, he has received from the Father the
  promised Holy Spirit and has poured out what you now see and hear.
  For David did not ascend to heaven, and yet he said, 'The Lord said to
  my Lord: "Sit at my right hand until I make your enemies a footstool
  for your feet."'  Therefore let all Israel be assured of this: God has
  made this Jesus, whom you crucified, both Lord and Messiah." (Acts
  2:32-36)

Though the distinction between being merely "at the right hand" and "seated at the right hand" is not explicit in the texts, many commentators find meaning in the Son of Man being seated in authority and judgement, his work complete and his footstool a typical ANE icon of dominion over his foes.  The 'Session of Christ', as it is called, is one of the doctrines specifically mentioned in the Apostles' Creed.
This makes Stephen's vision of Jesus standing all the more curious:

But Stephen, full of the Holy Spirit, looked up to heaven and saw the
  glory of God, and Jesus standing at the right hand of God. "Look," he
  said, "I see heaven open and the Son of Man standing at the right hand
  of God."  (Acts 7:55-56)

Just as Stephen declares the bankruptcy of the Jewish religious system and accuses the Sanhedrin of betraying and murdering God's prophet, Stephen has a vision of Jesus standing.  The text does not explain the significance, but it may parallel Jesus' trial before the Sanhedrin; where he once stood accused, he now stands vindicated.  Or, more typically, commentators see in the story of Stephen's vision a picture of the Savior standing beside those who testify on his behalf, or perhaps the Good Shepherd greeting the soon-to-be-martyred saint.(1)
.
(1) F.F. Bruce, Commentary on the Book of the Acts (Eerdmans, 1964), pp.167-168.
Comment: "  or perhaps the Good Shepherd greeting the soon-to-be-martyred saint ", This may be the reason, Acts mentioned Jesus standing to welcome Stephen.
Comment: @shakAttack  Saints don't go up to the sky when they die, only when the resurrection occurs.
Comment: Jesus said after his resurrection not touch Him as He has not been to see the father and then again it is written that Jesus said to the thief that he will be in the heaven with him today. So it may mean that there are some levels of heaven.
Comment: @shakAttack  No, he told the thief he would be with him in "paradise" and he was... the garden in which Jesus was laid.
Comment: I have since come to see Stephen's vision as rooted in the apocalyptic picture painted by Daniel: the Son of Man is granted authority by the Ancient of Days who is himself seated on the throne.  See my answer here: http://christianity.stackexchange.com/a/46903/18722
Answer: The verb ἑστῶτα means the right hand of God is the place where Jesus is.  It does not always mean standing.

85.40 ἵστημιa: to cause to be in a place, with or without the accompanying feature of standing position --
Louw, J. P., & Nida, E. A. (1996). Greek-English lexicon of the New Testament: based on semantic domains (electronic ed. of the 2nd edition., Vol. 1, p. 726). New York: United Bible Societies.
Comment: The grammar here is an intransitive perfect, for which BDAG supplies this:  C. intr., perf. and plupf.
① to be in a standing position, I stand, I stood of bodily position, e.g. of a speaker J 7:37; Ac 5:25, of hearers J 12:29 or spectators Mt 27:47; Lk 23:35; Ac 1:11, of accusers Lk 23:10. Cp. J 18:5, 16, 18ab, 25; 19:25; Ac 16:9 al.
② to be at a place, stand (there), be (there), w. the emphasis less on 'standing' than on 'being,   I'm not a grammarian by any means. It could be unanswerable but I think it is generally taken as standing.
Answer: The background of Stephen's vision from an intertextuality perspective (which is, I believe, a distinctive feature of the scriptures and perhaps the most eloquent testimony to the divine provenance of the scriptures) is, I believe found in the interaction between Jehoshaphat and Micaiah, a true prophet of the LORD.

Jehoshaphat, the king of Judah approached the king of Israel and asked him to inquire of the LORD whether he would grant them victory. So the king gathered 400 prophets together and they all, in various gestures and prophecies assured that they should go to war and the king that God would grant the king victory:

1Ki 22:6  Then the king of Israel gathered the prophets together, about four hundred men, and said unto them, Shall I go against Ramothgilead to battle, or shall I forbear? And they said, Go up; for the Lord shall deliver it into the hand of the king.

However, Jehoshaphat seems to have had a nagging sense that the prophets and their prophecies could not be counted on so he asked if there were another prophet available that they could consult:

1Ki 22:7  And Jehoshaphat said, Is there not here a prophet of the LORD besides, that we might enquire of him?

The king of Israel said that there was this other prophet named Micaiah but he never seemed to say the things he wanted to hear!:

1Ki 22:8  And the king of Israel said unto Jehoshaphat, There is yet one man, Micaiah the son of Imlah, by whom we may enquire of the LORD: but I hate him; for he doth not prophesy good concerning me, but evil. And Jehoshaphat said, Let not the king say so.
1Ki 22:9  Then the king of Israel called an officer, and said, Hasten hither Micaiah the son of Imlah.

It was for this reason that he had heaped together the "agreeable" prophets:

[2Ti 4:3 KJV] 3 For the time will come when they will not endure sound doctrine; but after their own lusts shall they heap to themselves teachers, having itching ears;

Micaiah, mocking the king, told him what they wanted him to hear:

1Ki 22:10  And the king of Israel and Jehoshaphat the king of Judah sat each on his throne, having put on their robes, in a void place in the entrance of the gate of Samaria; and all the prophets prophesied before them.
1Ki 22:11  And Zedekiah the son of Chenaanah made him horns of iron: and he said, Thus saith the LORD, With these shalt thou push the Syrians, until thou have consumed them.
1Ki 22:12  And all the prophets prophesied so, saying, Go up to Ramothgilead, and prosper: for the LORD shall deliver it into the king's hand.
1Ki 22:13  And the messenger that was gone to call Micaiah spake unto him, saying, Behold now, the words of the prophets declare good unto the king with one mouth: let thy word, I pray thee, be like the word of one of them, and speak that which is good.
1Ki 22:14  And Micaiah said, As the LORD liveth, what the LORD saith unto me, that will I speak.
1Ki 22:15  So he came to the king. And the king said unto him, Micaiah, shall we go against Ramothgilead to battle, or shall we forbear? And he answered him, Go, and prosper: for the LORD shall deliver it into the hand of the king.

1Ki 22:17  And he said, I saw all Israel scattered upon the hills, as sheep that have not a shepherd: and the LORD said, These have no master: let them return every man to his house in peace.

But the still small voice inside the king persisted:

1Ki 22:18  And the king of Israel said unto Jehoshaphat, Did I not tell thee that he would prophesy no good concerning me, but evil?

So Micaiah tells him the dreaded truth that the army of the LORD would side with their enemies:

1Ki 22:19  And he said, Hear thou therefore the word of the LORD: I saw the LORD sitting on his throne, and all the host of heaven standing by him on his right hand and on his left.

The rest of the chapter is an excellent read about how God would "choose their delusions" but I think that gives enough background to appreciate the allusion.
Stephen was being pressured to give "the right answer", but when he didn't they killed him. But before he died he saw a vision of the "son of man" (the Messiah) at the head of the heavenly armies, preparing to judge Israel! In other words, by alluding to the prophet's vision of the LORD's army prepared to destroy Israel he assured the leadership of Israel that had rejected the Messiah and the spirit within his anointed servants that in their rebellion against Rome they would be fighting against the son of God, heading the Armies of the LORD.
There is further evidence that Stephen's vision (or whatever it was) was suggesting that because they rejected the prophets they would be visited by an invading army:

[Zec 7:11-14 NIV] 11 "But they refused to pay attention; stubbornly they turned their backs and covered their ears. 12 They made their hearts as hard as flint and would not listen to the law or to the words that the LORD Almighty had sent by his Spirit through the earlier prophets. So the LORD Almighty was very angry. 13 " 'When I called, they did not listen; so when they called, I would not listen,' says the LORD Almighty. 14 'I scattered them with a whirlwind among all the nations, where they were strangers. The land they left behind them was so desolate that no one traveled through it. This is how they made the pleasant land desolate.' "

I was recently struck with the fact that Daniel said that Michael would "stand up" in the great tribulation:

[Dan 12:1-4 KJV] (1) And at that time shall Michael stand up, the great prince which standeth for the children of thy people: and there shall be a time of trouble, such as never was since there was a nation even to that same time: and at that time thy people shall be delivered, every one that shall be found written in the book. (2) And many of them that sleep in the dust of the earth shall awake, some to everlasting life, and some to shame and everlasting contempt. (3) And they that be wise shall shine as the brightness of the firmament; and they that turn many to righteousness as the stars for ever and ever. (4) But thou, O Daniel, shut up the words, and seal the book, even to the time of the end: many shall run to and fro, and knowledge shall be increased.

[Rev 22:10 NKJV] (10) And he said to me, "Do not seal the words of the prophecy of this book, for the time is at hand.

[Rev 12:7-9 NLT] (7) Then there was war in heaven. Michael and his angels fought against the dragon and his angels. (8) And the dragon lost the battle, and he and his angels were forced out of heaven. (9) This great dragon--the ancient serpent called the devil, or Satan, the one deceiving the whole world--was thrown down to the earth with all his angels.

[Jhn 12:31 NLT] (31) The time for judging this world has come, when Satan, the ruler of this world, will be cast out.

Please see also:

[Isa 66:4 NKJV] (4) So will I choose their delusions, And bring their fears on them; Because, when I called, no one answered, When I spoke they did not hear; But they did evil before My eyes, And chose [that] in which I do not delight."

[2Th 2:9-12 NLT] (9) This man will come to do the work of Satan with counterfeit power and signs and miracles. (10) He will use every kind of evil deception to fool those on their way to destruction, because they refuse to love and accept the truth that would save them. (11) So God will cause them to be greatly deceived, and they will believe these lies. (12) Then they will be condemned for enjoying evil rather than believing the truth.

KJV unless otherwise noted.
Comment: The seeing is not of the eyes as much as it is of the mind - yet you still don't **know** who I am - when we 'see' Christ - who he is, what he does, we get to *know* the Father.
Comment: What is also of interest, 1Ki 22:19 shows that the son is not part of this vision. Either he was busy elsewhere or he didn't exist yet!
Comment: Hi user48152 and thank you for your comment. The way I look at that is... imagine someone standing behind a curtain so you can't see them. Then imagine someone else nearby holding a mirror such that when you look his way, you see the one behind the mirror. That is how I understand the role of Christ... as a mirror so that when you look at him, you see the Father:  *[Jhn 14:9-11 NLT] (9) Jesus replied, "Have I been with you all this time, Philip, and yet you still don't know who I am? **Anyone who has seen me has seen the Father!** So why are you asking me to show him to you?*
Comment: Exactly: *Wisdom of Solomon 7:26 She [Wisdom] is a reflection of eternal light, a perfect mirror of God's activity and goodness.* https://biblehub.com/gntd/wisdom/7.htm
Answer: I would not read too much into the text, Acts 7:56. Yes, there are other passages of Jesus seated at the right hand of God, (that is, in the place of honor, power, and authority). Acts 2:32-36.
Stephen was the first "martyr" who gave a witness for Jesus at the cost of his life. Maybe Jesus rose to welcome him? And whether or not Jesus is sitting or standing at the right hand of God He is still deserving of being in the place of honor, power, and authority.
Comment: :) which part of,  'Jesus at the right side of GOD' doesn't trigger serious thought? Jesus is God and is also next to God? ummm what !? You're right, we shouldn't read too much into the text - not when it's speaks the truth plainly.
Answer: Does Jesus sit or stand at the right hand of God?
Psalm 110:1 A Psalm of David. The LORD said unto my Lord, Sit thou at my right hand, until I make thine enemies thy footstool.
Acts 7:55 But Stephen, full of the Holy Spirit, looked intently into heaven and saw the glory of Godand Jesus standing at the right hand of God.
The LORD'S invitation to Jesus to sit.
Standing at the right hand of God. Stephen was the first to bear witness that he had seen Jesus in heaven and standing at the right hand of God, as prophesied at Ps 110:1. In this Psalm we read the  the LORD'S  invitation to the Davidic  king to sit down at his right hand reflects the king's position as the LORD'S vice-regent.
Answer: Jesus sitting is figurative of the many truths already expressed.
Stephen is totally reliant in the spirit (being 'full of the spirit' according to God's provision for this occasion) on Jesus and his God for the support and every spiritual gift to enable his proclamation to the Jews and the subsequent stoning.
Until this vision, nothing had happened to him - he had simply told them off for their hard and stubborn hearts.
To see Jesus standing is an encouragement for Stephen to know that his Lord is actively with him and providing what is necessary - rather than sitting which denotes a more inactive/inattentive participation in Stephens moment of trial.

But He answered them, "My Father is working until now, and I Myself am working." John 5:17

While the mission of defeating evil and death is already finished at the cross. Jesus and his Father are still working. Jesus, the new Lord, is the chief one through whom the Father is doing everything - giving life, sending the Spirit, judging etc.
There is much yet to do in the lives of the saints present and to come and Jesus hasn't got a moment to waste, idly sitting around! He is girded for action symbolised by his standing with Stephen - ever ready!

Put on the full armour of God, so that you will be able to stand firm against the schemes of the devil. 12 For our struggle is not against flesh and blood, but against the rulers, against the powers, against the world forces of this darkness, against the spiritual forces of wickedness in the heavenly places. Eph 6:11
Answer: The word in question is ἵστημι, histēmi:

And he said, "Behold, I see the heavens opened, and the Son of Man standing at the right hand of God." (Acts 7:56 ESV)
καὶ εἶπεν ἰδοὺ θεωρῶ τοὺς οὐρανοὺς διηνοιγμένους καὶ τὸν υἱὸν τοῦ ἀνθρώπου ἐκ δεξιῶν ἑστῶτα τοῦ θεοῦ

Stephen debated with other Jews in their synagogue, and from the speech he gives to the Sanhedrin, he argues from Scripture:

9 Then some of those who belonged to the synagogue of the Freedmen (as it was called), and of the Cyrenians, and of the Alexandrians, and of those from Cilicia and Asia, rose up and disputed with Stephen. 10 But they could not withstand the wisdom and the Spirit with which he was speaking. (Acts 10 ESV)

Stephen was a Hellenist, a Greek speaking Jew. Therefore, his use of Scripture would have been from the LXX. The first use of ἵστημι, in Genesis means establish:

And I will establish my
covenant with you, and you shall come into the
ark, you and your sons and your wife and your
sons' wives together with you. (LXX-Genesis 6:18 NETS)

The translation of the participle ἑστῶτα corresponds to adding "-ing" or "-ed" to the basic verb. In the case of Acts 7:56, either standing or established. Perhaps what Stephen is saying is better understood along the lines of the significance of being at the right hand, not as standing: Behold, I see the heavens opened, and the Son of Man established at the right hand of God.
In which case, Stephen saw a fulfillment of one of Daniel's visions:

13 I was watching in the night visions, and lo, as it were a son of man was coming upon the clouds of heaven. And he came as far as the ancient of days, and the attendants were present with him. 14 And royal authority was given to him, and all the nations of the earth according to posterity and all honor was serving him. And his authority is an everlasting authority, which shall never be removed — and his kingship, which will never perish. (LXX-Daniel 7 NETS)

Daniel saw the Son of Man being given royal authority. That is, He was at the right hand of the Ancient of Days. Stephen saw the heavens opened and the Son of Man established at the right hand of God. Stephen would not be speaking of a physical position such as standing; in actuality He may have been seated. But Stephen is making a statement which placed emphasis on His authority, established at the right hand.


How should I securely generate random passwords when importing new users?

Question: I need to generate random passwords when importing new users from an external source.  I'm currently doing it by taking a random assortment of 8 lowercase/uppercase letters, and numbers.  I am also using Ruby's rand as a PRNG.  Is this cryptographically secure?
Comment: The popular web comic XKCD did a very amusing and informative post [ [Link](https://xkcd.com/936/) ] on this once. There has also been a lot of discussion [ [Link](https://security.stackexchange.com/questions/62832/is-the-oft-cited-xkcd-scheme-no-longer-good-advice) ] over how accurate the information was. Regardless of the opinions on the matter, a few decent passphrase generators have arisen from the post and discussion, such as [XKpasswd](https://xkpasswd.net/s/)
Comment: Your edit changed your question, somewhat invalidating existing answers (mine among them). In cases like these, I would generally recommend asking a new question instead of changing an existing one (it seems that you really have two or even three questions; is Ruby's rand cryptographically secure, is generating 8 char alphanum passwords a good idea, and possibly one about the password generation system as a whole (we would need more information about it to answer that though)).
Comment: I think you may be asking the wrong question. Are you sure you "need" to generate random passwords? There are likely better alternatives when importing users from another system.
Comment: @123 Ok, maybe not invalidated, it's probably still somewhat related to the question. Either way, I'm happy that it helped :) And yes, my comment was more of an fyi for the future. As there are now additional answers, rolling the question back and asking a new one would invalidate them, which wouldn't be good.
Comment: @tim Fair enough, probably should have asked an additional question.  Although I don't think the edit invalidated your answer - it was valuable to me, hence the upvote :)
Comment: What is your threat model, and how good are your users at changing passwords?  When I was an admin, I would pick a random 2 digit number, and set their initial password to `UnsafePassword43` or something like that.  Figured it'd remind them that they should change it because I know it.  Also, by making it that weak, it was easier to later to a scan to see who had actually changed their password -- identified trouble users before the trouble arrived!
Comment: If you generate a random password, how is the user going to know it? Are you going to write them down in plain text somewhere and provide it to them? If they're just going to reset their passwords anyway (which I hope you're forcing them to), why do you need *any* password stored? Couldn't you just put an invalid hash in and let the authentication system fail?
Answer: First of all, you need to use a secure random number generator, like Ruby's SecureRandom.
Second, you should choose a target security level for the generated passwords, i.e., how hard should they be to crack?  Security levels are often given in bits, i.e., the base 2 logarithm of the number of distinct equiprobable passwords.  In simpler words:

A 64-bit security level means that there are 2^64 distinct passwords, and your system is just as likely to be choose one as any of the others;
A "random assortment of 8 lowercase/uppercase letters and numbers" is 62 distinct characters, which means that choosing one such character at random provides log2(62) ≈ 6 bits of security.  Choosing 8 such characters independently at random provides log2(62) * 8 ≈ 48 bits of security.

48 bits is crackable in practice for a really dedicated attacker; I would recommend about a 64-bit security level as the bare minimum for passwords, and I prefer about 80 bits for my own.  With lowercase/uppercase letters + digits, you need 11 random characters for a 64-bit security level, and 13 characters gives you a 78-bit security level.
Before an edit your question asked about the effect of adding symbols to your passwords as well bumps the alphabet size to about 95 characters, and log2(95) ≈ 6.6, which brings those password sizes down by one character: 10 characters for a 64-bit password and 12 for a 79-bit password.  If you're generating passwords at random, you can therefore see that it's not a huge effect.
Comment: @atk: That's very straightforward.  If the password guessing speed is `s` guesses/second, and the password strength is `n` bits, then `(2^n / s)` is how long the attacker takes to try all passwords.  On average the attacker succeeds halfway through, so `2^(n-1)/s` is the average time to crack an `n`-bit strong password.
Comment: where is your math showing the speed of various attacks vs the strength of a password?
Comment: that's the formula for time taken, not actual time taken. What really matters is *the amount of time it actually takes to crack the password of the length you recommend, vs the amount of time that the password will be live*.  hashcat provides good baseline attack speeds for various algorithms, from which time can be calculated.
Comment: also, that's only for offline attacks.  it's equally important to calculate the speed at which the attacker can test a single password across all users. If, for example, you have 2^(n-1) users with live randomly generated passwords at any given time, then one of them is likely to have the guessed password.  If the server(s) can support all of those users logging in simultaneously, then the attacker can use the server's computing resources to perform the attack.
Answer: In Ruby, you can simply use SecureRandom.hex for random passwords that the user needs to change.
[1] pry(main)> require 'securerandom'
=> true
[2] pry(main)> SecureRandom.hex
=> "c3c4fe04dcc0d388fa37fc5991423a5d"
[3] pry(main)>

It uses the OS-provided secure random number generator, while the rand() function is a Mersenne Twister (easy to predict once you see the output).
The default length is perfectly fine as well.
Answer:
8 lowercase/uppercase letters, and numbers

This is the bare minimum of a weak password policy. Especially 8 characters are not enough.
As you are generating your passwords, why restrict yourself to passwords which are quite weak and easily bruteforced? I would suggest at least 64bits, but there is really no good reason not to go with 128/160, which would be more secure.
You will also have the problem of distributing the passwords, which will likely be insecure (probably email?).
Because of this, I would strongly suggest to make these one-time only passwords which the user must change after the next successful login (so basically it becomes a password reset token).
Comment: @LuisCasillas ~20-30 characters (example: `HCSmhvWyiRjfOtNLqut3`) may sound like much, but seems fine to me, especially if you consider that the user only uses it once. Of course, it depends a bit on the use-case. If it's eg send via snail mail and needs to be typed in via smartphone, it would indeed be a usability issue. If passwords should be generated that the user continues to use, that would be a different issue - one I would [recommend against](https://security.stackexchange.com/questions/85934/why-does-the-user-pick-the-password/85935#85935).
Comment: There is a good reason not to go with 128- or 160-bit passwords, which is that they'd be hella long.
Comment: Depending on the system and the attacker, for example if we're only looking at online brute-force, 8 characters randomly could easily provide appropriate security.  when discussing brute-force it's important to differentiate between online brute-force (where realistically the appropriate control is anti-automation and account lockout) and offline brute-force where probably password storage algorithm is likely the most important control (along with password length). AFAIK with bcrypt used (and a decent work factor) 10 chars pure random would deter most attackers, even offline
Answer: The way you do it is generally fine.
Make sure you use a secure random number generator. Some PRNGs create predictable output, making it possible to guess another user's password from my own.
The more possible outcomes your algorithm has, the more secure the password will be. This means that the longer the password, the more secure it is. However, a longer password will also be harder for the user to type. You use eight characters, which is a bit low. I recommend at least 10 characters.
In the same way, including punctuation characters increases the security a bit.
To make passwords easier for your users, you may want to remove characters that look alike, such as 0, o and O. There are also algorithms that create somewhat rememberable passwords, such as "NaughtyChopstick21@". However, it is often better if users use a password manager or create a memorable and secure password themselves.
Comment: @123 No, it is "a modified Mersenne Twister" [(source)](https://ruby-doc.org/core-2.2.0/Random.html)
Comment: I am using Ruby's `rand`.  Do you know if this is cryptopgraphically secure?
Answer: Your password requirements could be better but will probably work as a temporary password.  I'd be more concerned about how you are going to distribute those passwords.  Probably by email?  If you are that is very insecure.  If you do go this route you should allow the passwords to be used only one time.
rand is not cryptographically secure.  I would look into using sysrandom instead.
Answer: For randomly generated passwords there are two important measures:

Make the entropy of the password high enough
Make it as user friendly as possible.

You need to decide how many bits of security is necessary. 8 alphanumeric characters does not provide enough entropy, there are two ways you can improve that:

Use a larger set of possible characters
Use a longer password

Making the password longer is the more efficient of the two at increasing the entropy of your passwords. It is also the most user friendly approach because the more different characters you use the harder they will be to type. And even if they are not going to be typed by the user, the more different characters will also make the password harder to copy-paste and more likely to trigger interoperability problems.
I would say you have already gone too far by using all the alphanumeric characters. To make it more user friendly I would recommend sticking with only lower case letters. And to make it secure I would recommend to make the password long enough.
Assume your security goal is 64 bits, you could either go with:

14 random lower case characters
10 random characters from all printable ASCII characters

The inconvenience of having to deal with all the special characters is much worse for the user than the inconvenience of having the generated password be 4 characters longer.
Answer: With any password system and it's security you really have to consider more than just the length/randomness of the password, it's really more important to think about how they'll be attacked.
There's two ways passwords get attacked

Online brute-force.  Here the attacker is attacking the user's password via your system.  Unless your user has chosen a password that can be guessing before the account lockout kicks in, the attacker won't succeed in getting in.  8 generally random characters are very very unlikely to be guessed in this scenario.  Important things for you to do here is ensure your system blocks attackers and try to ensure users don't choose very common passwords like 123456.
Offline brute-force Here the attacker has a copy of your password database (presumbably via a flaw such as SQL Injection, if it's a web based system) and is trying to crack the passwords.  Likely the most important control here is what algorithm you're using to store the passwords.  Here's I'll defer to Thomas Pornin to explain the options but it's worth noting that ruby has decent library support for bcrypt (Rails uses it for SecurePassword).  Password length is also important here as is randomness, but cracking 8 char generally random passwords hashed with bcrypt and a decent work factor, is a non-trivial thing for most attackers.  Without knowing your risk model I can't say it'll be fine, but I don't see it as dreadfully bad either.

On your point about cryptographically secure, as others have said ruby SecureRandom is better than Rand
Answer: Use five-word, randomly generated passphrases instead. You could adapt the wordlist found here:
https://www.npmjs.com/package/niceware
Make them all lower case - easy to type, easy to memorize if needed.


How to store ice cream so that it is easy to scoop

Question: Whenever I eat ice cream (store bought), I have to work really hard to get it into my bowl. It always freezes when I put it in the freezer and makes it very tiresome to scoop. What are some good ways to store ice cream, so it doesn't freeze and is easy to scoop? Note: I'm not asking what to do when the ice cream is frozen, just how to make sure it doesn't get frozen. Also, I have ice cream at about the same time every night (I'm an addict), so it would need to be stored for about 24 hours, and I think that a refrigerator would cause it to melt after that long.
Comment: Is it homemade or do you buy it? I'm asking because if ice cream has too much water and not that much fat it becomes rock solid. So either buy better quality ice cream or if you are making it put more milk. Also you can set fridge thermometer on a higher temperature, but that is the worst solution..
Answer: There seems to be a way to achieve this without having to place the ice cream on the counter to defrost for a few minutes.
You can place the ice cream container into a zip lock bag and then place it in the freezer like below:

And it should be as soft as the first time you bought it !
If that doesn't float your boat, you could cut the ice cream into smaller blocks with a knife.
The reason the ice cream goes hard is because:

robbing your ice cream of its creaminess.
  crystals trapped inside melt. This is fine if you plan to eat your ice cream right away, but when you re-freeze partially-melted ice cream, those ice crystals re-form—but this time they're bigger and crunchier, robbing your ice cream of its creaminess.

Source
Comment: Are you putting the ziplock bag in the freezer or fridge?
Comment: You should be putting it in the freezer @Minnow
Comment: I don't understand the underlying reason. Would you mind elaborating? What changes between putting the ice cream tub straight into the freezer with or without the zip lock bag? If the crystals refreeze, wouldn't they do that either way? (Not rhetorical - I'm asking because I'd like to know.)
Answer: To get softer ice cream, it can't be as cold. It must be just slightly past the point of freezing and no more. You can raise the temperature slightly in the freezer, but that won't do much since freezers are made to freeze. Sometimes there's a cold spot in the refrigerator where stuff freezes. You can lower the temperature in the refrigerator to possibly take advantage of that and store the ice cream there instead.
If you eat that much ice cream, consider getting a small freezer just for the ice cream, cheap. Check used appliances for sale.
Answer: Dip the scoop in warm water and then scoop the ice cream.For next scoop do the same thing.
By doing this the ice cream doesn't stick to scoop.
Comment: Though this is an answer to *a* question, it is not an answer to *my* question. I asked how to store ice cream, you answered what to do when it is frozen.
Answer: I've had this same question myself and recently discovered that putting the ice cream in the part of the freezer that is furthest from where the cold air enters the freezer can make scooping significantly easier. For example, I have a side-by-side refrigerator and putting the ice cream at the bottom of the freezer helps a lot:


Why are the royal guards so powerful?

Question: In the latest episode 85, Pitou easily killed Kite even though Killua said Kite is as strong or stronger than a Nen Master.  I thought chimera ants had nen similar to that of humans.  How come they are so strong?
Answer: Before the royal guard was born, the chimera ants became aware of humans with 'excessive life force' (a.k.a. nen) and the queen ordered them to hunt down any nen users that were in the area for her consumption. We know that there were hunters in the country at the time, like Ponzu and Pokkle's group etc. We can assume that the queen consumed these hunters and the royal guard inherited the nen abilities.
The rest of the chimera ants are receiving (as of episode 85) their nen abilities the regular way - through the "baptism" which awakens nen in a person. This is how most humans acquire nen abilities, as was probably the case with Kite.
The overwhelming strength of the royal guard can be attributed to:

They are born able to use nen, unlike human most nen users who are "baptised". This gives them an advantage because their understanding and ability to use nen is innate, not learned through years of training and study.
Chimera ants are insects by nature and are usually brutal, savage, and cruel. This leads to more menacing battle auras, which can hinder the fighting ability of a human opponent if the aura is intimidating enough. For example, Pitou's aura was menacing enough to scare away Gon and Killua.
Chimera ants also have the properties of any animals or humans that were eaten. This means that any member of the royal guard is going to have incredibly fast animal-like reflexes, the intelligence of the best humans, and the strongest muscles between animals/humans.

The combination of these means that the royal guard is going to be significantly stronger than most average hunters.
Kite was also at a disadvantage because he lost his arm protecting Gon and Killua before he fought Pitou.
Answer: Since Pokkle didn't get eaten before Pitou was born, and since he is mentioned as the first "rare human" they've encountered, the Queen shouldn't have eaten any humans with Nen-abilities before conceiving the Royal Guard. Out of Pokkle's group, none of the four members were eaten by the Queen and there has been no mention of other "rare humans" before the Royal Guard was conceived.
How they still managed to be born with such strong Nen-powers is a mystery, since, as they say themselves, the "rare humans" are worth 1000 normal ones. So just to achieve the level of a normal Nen-user, the Queen would have to eat 1000 normal humans, and for the Royal guard to be dozens of times stronger than that, she would have needed to consume close to a hundred thousand humans for each of the Royal Guards.
The population is certainly big enough to provide that many, but given the time she had to eat that much, and subtract all the food that went to make the foot soldiers, captains and squadron leaders, not to mention the King himself, there is no way she had the soldiers to procure, let alone eat, that vast amount of humans.
Answer: I think that the reason why the royal guards were so powerful was because one, The chimera ants evolve at a rapid rate and considering the amount of time for the chimera ants to evolve to the rate of pitou, it should be an easy feat.So, in conclusion, pitou is as strong as she/he is because pitou had lots of time to evolve and is at near the pinnacle of evolution only underneath the king.

Why are the royal guards so powerful?


Sync code across computers

Question: Right now I manage a small team of developers.  We use subversion for all of our code.  Interested to know if there is a tool that enables developers to all work from the same code base versus each having their own local code?
Comment: You need to post why you want to do that.
Answer: There are many ways to do this but I don't think you should try.  Private working copies of source code is a proven method that was created specifically to prevent developers from having to work on a single copy of the code base.
Source control is a good thing and I wouldn't recommend moving away from it.
Answer: I dont quite understand your question. Maybe you need source control system like git or bazaar - they have local branches (each dev may have his own) and allow sync'ing code with centralized repositories.
Answer: You could put the code on a network share, but I highly agree with Andrew Hare's view that you should stick with private working copies (+1 to his answer from me).
If you could post your reason behind this question, perhaps the community can help you find a good solution to the actual problem.
Answer: This cannot possibly be what you want. The whole point of using source code control is so that you don't work on the same physical copy of your source tree.
Please elaborate on what problem you really want to solve.
Answer: For some reason it seems like you aren't using SVN correctly.  SVN enable you to all use the same code base.  The code base is stored in the svn repository.  You edit your local copy, and then when you are satisfied with those changes, you commit them to SVN.  If you want a copy of the current code base, you can export it from SVN.  Editing your own local copy and then committing to the repository ensures that you aren't overwriting anybody else's changes.
Answer: I have to agree with Andrew Hare, source control is a good thing and should be used. It enables you to roll back one developers changes in a very controlled way

Sync code across computers


SpaceX's Starlink and astronomy

Question: I was reading articles about Starlink and some concerned astronomers that SpaceX Starlink will lead to more space junk and eventually the death of ground based astronomy. I am just wondering how realistic these concerns are?
Comment: Welcome to stackexchange! Great question. It might be ruled as a duplicate of [Has SpaceX made any commentary on StarLink posing a threat to astronomy?](https://space.stackexchange.com/questions/38561) and you might like [this question](https://space.stackexchange.com/questions/39165/is-it-feasible-to-paint-spacex-starlink-satellites-black-so-as-not-to-frequently) and [this question](https://space.stackexchange.com/questions/39263).
Comment: Thanks Christoph for the links. Looks like the same question have been asked before. No proper answers though for the first question.
Comment: It's going to be a big issue for ongoing and future sky surveys (such as LSST). [Here](https://twitter.com/lcjohnso/status/1196370554414125056) is an image taken with a smaller survey camera (DECam on the 4-m Blanco at CTIO) during a pass of the recently launched batch of Starlink satellites
Comment: https://www.reddit.com/r/space/comments/eaxysu/spacex_to_make_starlink_satellites_dimmer_to/?utm_source=reddit-android SpaceX made a statement.
Answer: I posted this a while back on Twitter (@rocketscient1st) when the first Starlink was launched:
Conducted a simple analysis on a complete Starlink Phase 1 constellation.  1584 satellites: 24 planes with 66 satellites each. 53° inclination; 550 km altitude.  I assumed the relative phasing as I have no direct information. I do not know the absolute magnitude of the Starlink satellites.  I'm simply looking at lighting conditions.  Some existing satellites are naked eye visible.  Others are much dimmer and require binoculars. Others like old Iridiums flare.
I ran an analysis to determine number of satellites visible under the following conditions: Satellite in full sunlight.  Observer with sun -6° below horizon (end of civil twilight).  I also limited to satellites visible at least 5° above horizon. I did not try to account for reflection angle (sun-satellite-observer angle).   This can significantly impact the brightness of the satellite, especially any flaring.   Satellite attitude and surfaces will also affect the brightness. Analysis was for end of May at 38° latitude.  This roughly equates to latitude of San Francisco, Washington, DC, Madrid, Istanbul, Seoul.  I ran the analysis for 3 days, which should provide a decent average for a constellation of this size.
For satellites in a quasi-terminator orbit (much like just launched satellites) observer may potentially see a given satellite up to 5 times in one night.  Satellites may stay in sunlight for up to 5 continuous days before orbit precesses enough to restart eclipses. Satellites in other planes (besides the quasi-terminator) may only be visible once during the night or not at all for any given night.
As others have mentioned, there is already a lot of satellites and junk up there.  The impact of Starlink satellites will depend on just how bright they are.  Initial reports by @Marco_Langbroek was that they could be seen naked eye, but latest passes required binoculars.
At the start and end of the night about 50 satellites are simultaneously visible that meet the criteria listed above.  The satellites are distributed primarily in the direction that the sun set (in the evening) or will rise (in the morning). At midnight 18 satellites are still visible.  The visible satellites are distributed north of the observer.
Comment: of possible interest: [What is the LSST's plan to address frequent satellite trails in data?](https://astronomy.stackexchange.com/q/33540/7982)

SpaceX's Starlink and astronomy


Why is writing zeros (or random data) over a hard drive multiple times better than just doing it once?

Question: Lots of different programs, such as Darik's Boot and Nuke, let you write over a hard drive multiple times under the guise of it being more secure than just doing it once. Why?
Comment: I would just throw it into a campfire until the metal melts.
Comment: Related: [How can I reliably erase all information on a hard drive?](http://security.stackexchange.com/q/5749)
Comment: Relevant: [Overwriting Hard Drive Data](https://web.archive.org/web/20090315092550/http://sansforensics.wordpress.com/2009/01/15/overwriting-hard-drive-data).
Answer: Summary: it was marginally better on older drives, but doesn't matter now. Multiple passes erase a tree with overkill but miss the rest of the forest. Use encryption.
The origin lies in work by Peter Gutmann, who showed that there is some memory in a disk bit: a zero that's been overwritten with a zero can be distinguished from a one that's been overwritten with a zero, with a probability higher than 1/2. However, Gutmann's work has been somewhat overhyped, and does not extend to modern disks. "The urban legend of multipass hard disk overwrite and DoD 5220-22-M" by Brian Smithson has a good overview of the topic.
The article that started it is "Secure Deletion of Data from Magnetic and Solid-State Memory" by Peter Gutmann, presented at USENIX in 1996. He measured data remanence after repeated wipes, and saw that after 31 passes, he was unable (with expensive equipment) to distinguish a multiply-overwritten one from a multiply-overwritten zero. Hence he proposed a 35-pass wipe as an overkill measure.
Note that this attack assumes an attacker with physical access to the disk and somewhat expensive equipment. It is rather unrealistic to assume that an attacker with such means will choose this method of attack rather than, say, lead pipe cryptography.
Gutmann's findings do not extend to modern disk technologies, which pack data more and more. "Overwriting Hard Drive Data: The Great Wiping Controversy" by Craig Wright, Dave Kleiman and Shyaam Sundhar is a recent article on the topic; they were unable to replicate Gutmann's recovery with recent drives. They also note that the probability of recovering successive bits does not have a strong correlation, meaning that an attacker is very unlikely to recover, say, a full secret key or even a byte. Overwriting with zeroes is slightly less destructive than overwriting with random data, but even a single pass with zeroes makes the probability of any useful recovery very low. Gutmann somewhat contests the article; however, he agrees with the conclusion that his recovery techniques are not applicable to modern disks:

Any modern drive will most likely be a hopeless task, what with ultra-high densities and use of perpendicular recording I don't see how MFM would even get a usable image, and then the use of EPRML will mean that even if you could magically transfer some sort of image into a file, the ability to decode that to recover the original data would be quite challenging.

Gutmann later studied flash technologies, which show more remanence.
If you're worried about an attacker with physical possession of the disk and expensive equipment, the quality of the overwrite is not what you should worry about. Disks reallocate sectors: if a sector is detected as defective, then the disk will not make it accessible to software ever again, but the data that was stored there may be recovered by the attacker. This phenomenon is worse on SSD due to their wear leveling.
Some storage media have a secure erase command (ATA Secure Erase). UCSD CMRR provides a DOS utility to perform this command; under Linux you can use hdparm --security-erase. Note that this command may not have gone through extensive testing, and you will not be able to perform it if the disk died because of fried electronics, a failed motor, or crashed heads (unless you repair the damage, which would cost more than a new disk).
If you're concerned about an attacker getting hold of the disk, don't put any confidential data on it. Or if you do, encrypt it. Encryption is cheap and reliable (well, as reliable as your password choice and system integrity).
Comment: I should point out that US Government when it wants to wipe any storage media that contains senistive documents, will destory the media itself, in the case of a hdd its placed in a furnance.  In the case of disk media ( CDR, DVDR ) shredder does a wonderful job.
Comment: The purpose of Gutmann's 35 passes was to provide a "universal" wiping pattern that would work on any drive in use at the time, without the user needing to know what encoding system the drive used.  It consisted of five patterns each done twice to cover MFM (the low storage density of MFM drives made them particularly vulnerable to data remnance), 15 patterns to cover (2,7)RLL, 18 patterns to cover (1,7)RLL, and eight passes with random data to try to deal with PRML.  Since there's some overlap between patterns, this totals up to 35 passes.
Comment: Indeed, Gutmann's findings do not extend to modern disk technologies, but that's not where research ended. Also, companies like Heise Security showed it is possible with modern (read: current) discs under the correct conditions. Physically destroying the media (as @Ramhound correctly stated) is probably the safest way to do it... yet, even those media will be multi-written and then low-level formatted before they are passed on for destruction.
Comment: It should be noted that the CMRR utility fails for modern drives too simply because it's a DOS tool; and DOS does not understand SATA or other kinds of recent HDD controller systems.
Comment: If a drive decides that a sector seems dubious and redirects all future writes somewhere else, will most secure-erase programs *ever* overwrite the original, or will they simply keep hitting the remapped sector?
Comment: @supercat I don't know. In principle, they should ensure that all sectors are physically unreadable, but that relies on an optimal implementation. Secure erase firmware is often very opaque. It's hard to test independently because the recovery attacks on logically-but-not-physically-erased sectors aren't cheap.
Comment: Guttman is a real madlad...
Comment: @Ramhound And you can re-place the disk ashes in the furnance many times over to increase security!
Comment: @JuanPerez - Except if it's an SSD, if it's an SSD, then you must place the ashes on a Falcon 9. *The rules for disposing of an SSD is crazy.*
Comment: @Billy ONeal The hdderase.exe utility bypasses DOS and talks to the drive directly. The reason why it doesn't work for newer drives is that it needs to act as a device driver for both the controller (difficult to do) and the drive (generic commands will mostly do). The developer didn't have knowledge of the not-yet-existing hardware, so he couldn't have added support.
Comment: @Ramhound [For an SSD, it depends if you ask the US government or the US government!](https://security.stackexchange.com/questions/37317/secure-wiping-of-eeprom-and-flash-memory/37322#37322)
Comment: @Gilles'SO-stopbeingevil' - That answer isn't accurate. The US Government destroys any media that has anything higher than CUI on it.
Answer: There is a well-known reference article by Peter Gutmann on the subject. However, that article is a bit old (15 years) and newer harddisks might not operate as is described.
Some data may fail to be totally obliterated by a single write due to two phenomena:

We want to write a bit (0 or 1) but the physical signal is analog. Data is stored by manipulating the orientation of groups of atoms within the ferromagnetic medium; when read back, the head yields an analog signal, which is then decoded with a threshold: e.g., if the signal goes above 3.2 (fictitious unit), it is a 1, otherwise, it is a 0. But the medium may have some remanence: possibly, writing a 1 over what was previously a 0 yields 4.5, while writing a 1 over what was already a 1 pumps up the signal to 4.8. By opening the disk and using a more precise sensor, it is conceivable that the difference could be measured with enough reliability to recover the old data.
Data is organized by tracks on the disk. When writing over existing data, the head is roughly positioned over the previous track, but almost never exactly over that track. Each write operation may have a bit of "lateral jitter". Hence, part of the previous data could possibly still be readable "on the side".

Multiple writes with various patterns aim at counterbalancing these two effects.
Modern hard disks achieve a very high data density. It makes sense that the higher data density is, the harder it becomes to recover traces of old overwritten data. It is plausible that recovering overwritten data is no longer possible with today's technology. At least, nobody is currently positively advertising such a service (but this does not mean that it cannot be done...).
Note that when a disk detects a damaged sector (checksum failure upon reading), the next write operation over that sector will be silently remapped to a spare sector. This means that the damaged sector (which has at least on wrong bit, but not necessarily more then one) will remain untouched forever after that event, and no amount of rewriting can change that (the disk electronic board itself will refuse to use that sector ever again). If you want to be sure to erase data, it is much better to never let it reach the disk in the first place: use full-disk encryption.
Comment: +1 for this answer for going over the details of the science.  As a computer scientist and full stack software engineer, this is the kind of answer that actually answered the question for me.
Answer: The answers provided so far are informative but incomplete. Data are stored on a (magnetic) hard disk using Manchester coding, such that it's not whether the magnetic domain points up or down that encodes one or zero, it's the transitions between up and down that encode the bits.
Manchester coding usually starts with a little bit of nonsense data suitable for defining the 'rhythm' of the signal. It's possible to imagine that if your attempt to overwrite the data with all zeroes once wasn't exactly in phase with the timing under which the original data were stored, it'd still be super-easy to detect the original rhythm and edges, and reconstruct all of the data.
Comment: That's a good point, but there's a long way from "it's possible to imagine" to "you can actually recover information". As far as I understand Wright et al's work, they did take this alignment issue into account.
Comment: Graham - it used to be relatively easy. It isn't so much these days - tolerances are tighter, and transitions are much smaller.
Answer: A nice question with takes a two-part answer:

When talking about "ye average hard disc", there's a first reason why to overwrite multiple times.
In short: HDs are like magnetic discs. There's the chance of remaining "shadow bytes" that could be recovered. That's the reason why NSA and co have been using multiple-overwrites for ages. These "shadow bytes" are nothing more than "ghosty" remnants of formerly deleted and overwritten data. HD recovery companies actually use those to recover critical data when it's lost.
Another way would be to use strong magnetics to kill your HD, but that way - chances are big you'll either not use a strong enough magnetic force, or you'll destroy more of your HD than you'ld want to. So that's not really an option.
You'll probably also want to check some of the data-erasure standards for more detailed information http://en.wikipedia.org/wiki/Data_erasure#Standards and notice that the standards only overwriting 1 time, always make data-erasure-verification mandatory.
On "some operating systems" (note that I'm not starting a political discussion about the best or worst operating system here), this erasure-verification is not as solid as it should be... which means their "erasure-verification" is actually unsafe enough to worry about than even starting to think about potential shadow-byte remnants which could be recovered.

UPDATE
Since this is such a much-discussed subject, with many people saying "pro" and "contra" while quoting the "Secure Deletion of Data from Magnetic and Solid-State Memory" paper, published by Peter Gutmann in 1996 ( http://www.usenix.org/publications/library/proceedings/sec96/full_papers/gutmann/index.html ), the following should be noted:

...Security researchers from Heise Security, who have reviewed the paper presented at last year's edition of the International Conference on Information Systems Security (ICISS), explain that a single byte of data can be recovered with a 56 percent probability, but only if the head is positioned precisely eight times, which in itself has a probability of occurring of only 0.97%. "Recovering anything beyond a single byte is even less likely," the researchers conclude...

( source: http://news.softpedia.com/news/Data-Wiping-Myth-Put-to-Rest-102376.shtml )
On the other hand, there are military and governmental data-erasure that define multiple overwrites as a must. (I will refrain from judging that, but you should think about the "why" of this fact.)
In the end, it's a question of "what data" you want to "protect" by erasing it, and how important it is that the erased data will be unrecoverable in any potential case. Let's put it this way: if you want to delete your personal dairy, you probably don't need to overwrite each and every free sector... but if you're working on plans for a nuclear power plant or some "secret project" for your government, you'll not want to let a single byte as is.
When people ask me personally, I always answer: "better safe than sorry. There are solid standards defining multiple-overwrites of freed sectors as a must. There is a reason for that. Scientific papers (even recent ones) show that recovery of erased data is possible using different means. Even when the chance is small, I wouldn't take the risk and I think it would be unprofessional to advise anyone not to think about that risk."
I guess that wraps it up best.
WRAPPING IT UP
So, to correctly answer your question:

Lots of different programs, such as Darik's Boot and Nuke, let you write over a hard drive multiple times under the guise of it being more secure than just doing it once. Why?

They do that, based on Gutmann's paper and the existing standards used by governmental institutions.
Comment: @e-sushi, Can you cite a source on *HD recovery companies actually use those to recover critical data when it's lost*?
Comment: "*NSA [...] have been using multiple-overwrites for ages*" Any source for this? My source say they have used physical destruction and not multiple-overwrites. Would love if you had a solid reference.
Comment: @GeorgeBailey Very slightly better, but not so much that overwriting with zero bytes isn't effective; see http://grot.com/wordpress/?p=154 and the Wright, Kleiman and Sundhar paper or my answer.
Comment: Just guessing, but it seems to me that writing random instead of zero bytes would be better as far as hiding the shadow goes...
Comment: Source of that? A friend of mine runs a data-recovery company. So there's no "link" I can provide. Anyway, I've updated my answer with some more information to give you some of the useful details you seem to be missing.
Comment: @NicolasRaoul solid references about a top sekret government agency in the states?


Why is the null hypothesis often sought to be rejected?

Question: I hope I am making sense with the title. Often, the null hypothesis is formed with the intention of rejecting it. Is there a reason for this, or is it just a convention?
Comment: Very closely related: [meaning of p values and t values in statistical tests](http://stats.stackexchange.com/questions/31), [understanding p-value](http://stats.stackexchange.com/questions/44769), [effect size as the hypothesis](http://stats.stackexchange.com/questions/23617/), [why is the null a point value](http://stats.stackexchange.com/questions/8196), ["you can't reject the null"](http://stats.stackexchange.com/questions/85903). For more like these, [search our site](http://stats.stackexchange.com/search?tab=votes&q=null%20hypothesis%20test%20is%3aquestion).
Comment: https://en.wikipedia.org/wiki/Null_hypothesis
Comment: maybe this can help http://stats.stackexchange.com/questions/163957/what-follows-if-we-fail-to-reject-the-null-hypothesis/164094#164094
Answer: The purpose of statistical hypothesis testing is largely to impose self-skepticism, making us cautious about promulgating our hypothesis unless there is reasonable evidence to support it.  Thus in the usual form of hypothesis testing the null hypothesis provides a "devils advocate", arguing against us, and only promulgate our hypothesis if we can show that the observations mean that it is unlikely that the advocate's argument is sound.  So we take $H_0$ to be the thing we don't want to be true and then see if we are able to reject it.  If we can reject it, it doesn't mean that our hypothesis is likely to be correct, just that it has passed this basic hurdle and so is worthy of consideration.  If we can't, it doesn't mean that our hypothesis is false, it may be that we just don't have enough data to provide suffcient evidence.  As @Bahgat rightly suggests (+1) this is very much the idea of Popper's falsificationism idea.
However, it is possible to have a test where $H_0$ is the thing you want to be true, but in order for that to work, you need to show that the test has sufficiently high statistical power in order to be confident of rejecting the null if it actually is false.  Computing statistical power is rather more difficult that performing the test, which is why this form of testing is rarely used and the alternative where $H_0$ is what you don't want to be true is normally used instead.
So you don't have to take $H_0$ to oppose your hypothesis, but it does make the testing procedure much easier.
Answer: Karl Popper says "We cannot conclusively affirm a hypothesis, but we can conclusively negate it". So when we do hypothesis testing in statistics, we try to negate (reject) the opposite hypothesis (the null hypothesis) of the hypothesis we are interested in (the alternative hypothesis) and which we can not affirm. Since we can specify the null hypothesis easily, but we don't know what exactly the alternative hypothesis is. We may hypothesize for example that there is a mean difference between the two populations, but we cannot point out how wide the gap would be.
See also Don't believe in the null hypothesis?
Comment: I am not quite sure whether Popper's logic of falsification can be 100% applied to statistical hypothesis testing after Fisher/Neyman. After all Popper says that "We cannot conclusively affirm a hypothesis, but we can conclusively negate it". If I recall correctly, Popper said that a hypothesis is to be framed clearly in order to make it accessible for falsification. As you point out we attempt to reject the null hypothesis. Not sure if Popper intended to falsify the null hypothesis.I think he rather would want to falsify the alternative hypothesis,or the one that actually has a meaning to us.
Comment: @DikranMarsupial, yeah I know his works and also read "Conjectures and Refutations" and after spending some months contemplating what he wrote, I don't think that what he wants is being achieved with hypothesis testing as we do it. He also refuses inductive reasoning over deductive reasoning. Aren't we kind of making inferences all the time? His logic mostly applies to Physics, e.g. his prime example is how Einstein deduced by his calculation that gravity will distort space time and hence bent light. This was then tested on multiple occasions and could not be reject since then.
Comment: Hypothesis testing does achieve part of his scheme which is that we make our hypotheses explicity testable and falsifiable (at least in probability).  In fact statisticans go further, and actually require the test to be performed before proceeding further.  I suspect he might approve of Bayesian hypothesis testing rather more than the frequentist equivalent.  I don't think falsificationism is fully satisfactory in isolation anyway, so I don't mind Popper not fully approving! ;o)
Comment: If I understand your question correctly, standard frequentist hypothesis test are non-symmetric (the alternative hypothesis does not even appear in its formulation), so not being able to reject the null hypothesis does not mean that it is true and the alternate hypothesis is false.  It could be that the null hypothesis is false, but there is not enough data to provide the evidence to show that it is false.  The self-skepticism imposed by the test is due to assuming that $H_0$ is true until "proven" otherwise.
Comment: @DikranMarsupial but I am open for falsification of my statements :) Great topic though.
Comment: @BahgatNassour,you are absolutely right (in both the answer and your comment). I was a bit sloppy with my wording when I said "we try to collect evidence for our alternative hypothesis".What I meant by this is that we set up experiments with the goal to reject the null hypothesis in favour of our alternative hypothesis, which is the one we usually care about, i.e. the one we are seeking "support" for. However, Popper says that in order to corroborate our hypothesis (the one we care about) we have to try to falsify it.And in my opinion this is not exactly what we do. That's all I wanted to say.
Comment: Do statisticians reject the law of the excluded middle?
Comment: It is possible to have a test where you can swap $H_1$ and $H_0$ and not be able to reject either of them.  So to answer your question directly, statisticians do not reject the law of the excluded middle, it is just that the test cannot establish either hypothesis to be unambiguously true or false.
Comment: @Stefan, Popper's book "The Logic of Scientific Discovery" has a chapter on probability, but I couldn't tell you off-hand what it says.
Comment: After all with statistical hypothesis testing we try to collect evidence **for** our alternative hypothesis to come out significant.
Comment: @Stefan You wrote in your first comment "**As you point out we attempt to reject the null hypothesis**" in your second comment you wrote "**we try to collect evidence for our alternative hypothesis**" , So First : my question , when we test the null hypothesis are these two events (your comments) equivalence / similar events or not ? . Second : After we formulate $H_0$ we test this hypothesis itself regardless of $H_1$ If I reject this hypothesis that means any another opposite hypothesis ( which is $H_1)$ is more likely to be true
Answer: This is a fair and good question. @Tim already gave you  all you need to answer your question in a formal way, however if you are not familiar with statistical hypothesis testing you could conceptualize the null hypothesis by thinking about it in a more familiar setting.
Suppose you are being accused of having conducted a crime. Until proven guilty, you are innocent (null hypothesis). The attorney provides evidence that you are guilty (alternative hypothesis), your lawyers try to invalidate this evidence during the trial (the experiment) and in the end the judge rules whether you are innocent given the facts provided by the attorney and the lawyers. If the facts against you are overwhelming, i.e. the probability that you are innocent is very low, the judge (or jury) will conclude that your are guilty given the evidence.
Now with this in mind, you could also conceptualize features of statistical hypothesis testing, for instance why independent measurements (or evidence) are important, since after all your deserve a fair trial.
However, this is example has its limitations and eventually you have to formally understand the concept of the null hypothesis.
So to answer your questions:

Yes there is a reason for the null hypothesis (as described above).
No it's not just a convention, the null hypothesis is the core or statistical hypothesis testing or else it wouldn't work they way it is intended to.
Answer: It is not taken for granted that the null is always to be rejected. In model fit testing, the null is usually that the model fits well, and that is something desirable that we would hate to reject. It is, however, usually true that the sampling distribution of the test statistic is easier to derive under the null, which is usually far more restrictive than the alternative. The null that the mean difference between two groups is zero leads to a $t$-test; the null that the two distributions are the same leading to Kolmogorov-Smirnov test; the null that the linear regression model does not need nonlinear terms via Ramsey RESET test; the null that a latent variable model describes the observed covariance matrix adequately leads to a parametric space of lower dimension than an unrestricted alternative, and an asymptotic chi-square test of the distance to the smooth parametric surface in the space of $p(p+1)/2$ covariances defined by the model. So my take on this is that, as @whuber put it in the comment below, the null is usually a crucial albeit convenient technical assumption. The null is either a point (potentially multivariate) in the parametric space, so that the sampling distribution is fully specified; or a restricted parametric space, with the alternative that can be formulated to be complementary in that space, and the test statistic is based on a distance from the richer set of parameters under the alternative to the set with restrictions under the null; or, in nonparametric rank/order statistics world, the distribution under the null can be derived by the complete enumeration of all possible samples and outcomes (often approximated by something normal in large samples though).
Taking the null as something different (e.g., that the means of the two groups differ by at most 0.01, with the alternative differ by more than 0.01) requires a more complicated set of derivations, e.g., looking at the worst possible situations, which in the above case would still boil down to the point null against a one-sided alternative. The worst case on the right is $H_0: \mu_2 = \mu_1 + 0.01$ vs. $H_1: \mu_2 > \mu_1 +1$, and on the left it is $H_0: \mu_2 = \mu_1 - 0.01$ vs. $H_1: \mu_2 < \mu_1 - 1$.
Comment: +1 Although the references to the philosophy of science are appealing, Fisher and Neyman-Pearson preceded Popper and, I believe, were driven primarily by this crucial technical issue to create the asymmetry between the null and alternate hypothesis.
Comment: @whuber and StasK: Would you be able to expand a bit more regarding the "crucial technical issue" which I believe refers to StasK 's comment that the test statistic is easier to derive under the null? Maybe I should ask a new question where this could hopefully be addressed.
Comment: That (using a simple model unless it is rejected) may be frequent practice, but I am not sure it is necessarily good practice...
Comment: @whuber, exactly, but for some reason **null** hypothesis testing is so often put in context with Popper's philosophy. But the concept of the _null hypothesis_ goes back to Fisher and Neyman-Pearson (as you mentioned). The only thing they had in common though is that they both used/proposed hypotheses to acquire knowledge - and with respect to acquiring knowledge and the scientific method, Popper was clearly more influential. So I think that's the reason why the concept of hypothesis testing (including NHT) in general is linked to Popper... I might be wrong though.
Answer: The law of parsimony (also known as Occam's razor) is a general principle of science.  Under that principle, we assume a simple world until it can be shown that the world is more complicated.  So, we assume the simpler world of the null hypothesis until it can be falsified. For example:
We assume treatment A and treatment B work the same until we show differently. We assume the weather is the same in San Diego as in Halifax until we show differently, we assume men and women are paid the same until we show differently, etc.
For more, see https://en.wikipedia.org/wiki/Occam%27s_razor
Answer: If I can draw an analogy to logic, a general way to prove something is to assume the opposite and see if that leads to a contradiction. Here the null hypothesis is like the opposite, and rejecting it (i.e. showing that it is very unlikely) is like deriving the contradiction.
You do it that way because it's a way to make an unambiguous statement.
Like in my field, it's much easier to say "The statement 'this drug has no benefit' has 5% chance of being right" than it is to say "The statement 'this drug has benefit' has 90% chance of being right".
Of course, people want to know how much benefit is being claimed,
but first they want to know it isn't zero.
Answer: The null hypothesis is always formed with the intention to reject it that is the basic idea of hypothesis testing. When you are trying to show that something is likely to be true (e.g. a treatment improves or worsens a disease), then the null hypothesis is the default position (e.g. the treatment does not make a difference to the disease). You generate evidence for your desired claim by accumulating data that is (hopefully) so far away from what should have happened under the null hypothesis (in the example patients that are randomized to receive the treatment or a placebo having the same expected outcome) that one concludes that is very unlikely to have arisen under the null hypothesis so that you can reject the null hypothesis. In contrast failure to reject the null hypothesis does not necessarily make it very likely that the null hypothesis is true (just because a clinical trial failed to show a drug works does not mean that the drug really does nothing).


Can Ethernet frames only be transmitted in a LAN?

Question: In the LAN depicted in the picture below, am I correct in saying that devices do not have IP addresses? There is no router and also only Ethernet frames (with source and destination mac address would be transmitted) and not IP packets. Is that a correct assumption?

Comment: It used to be possible for computers to communicate on a LAN without IP addresses, but they still needed a layer three protocol to use instead of TCP/IP. In the second half of the 1990s, NetBEUI, SPX, and DLC/LLC were all protocols that were used to communicate (locally only) on Ethernet LANs that did not require IP addresses. Those protocols might still be in use today, but I think most systems have been built to assume TCP/IP will be used exclusively as the layer 3 protocol, so support for other protocols may have been removed.
Comment: Ethernet frames will be transmitted. Those frames may or may not contain IP packets.
Comment: We cannot tell from the image alone. In a standard installation with common operating systems they would, as you must know, unless you take special configuration measures. So your question must be *whether it's possible*, right? And since (ordinary) switches are basically optimized hubs, operating with hardware addresses, you could indeed send non-IP ethernet frames across the network.
Comment: While Ethernet and IP are a very common combination, they don't necessarily have to be used together. One extreme example is [IPoAC](https://en.wikipedia.org/wiki/IP_over_Avian_Carriers) (Carrier pigeons instead of Ethernet).
Comment: Did any answer help you? If so, you should accept the answer so that the question doesn't keep popping up forever, looking for an answer. Alternatively, you can post and accept your own answer.
Answer: No, that's not correct. You don't need a router for two hosts to communicate using IP as long as they're in the same network.
Answer: NO. IP packets are encapsulated inside Ethernet frames.  It's not one or the other.
Answer: Ethernet communication is local only (segment) - across all switches (or repeaters) within a single VLAN (when other VLANs exist).
IP packets are transported as payload (layer 3) inside Ethernet frames (layer 2) or any other suitable link layer.
Due to the local-only restriction the IP communication in this network is confined to the local subnet. Multiple subnets can co-exist in a single L2 segment but they can't communicate with each other. Communication across subnets requires routers.

can Ethernet frames only be transmitted in a LAN

Yes. Ethernet frames can only be transmitted in a LAN (as in "LAN = a segment connected by switches") - note that today, technologically a "LAN" as a layer 2 segment has no geographically defined limit any more; fiber links can reach dozens or even hundreds of km. Also note that the segment can also be bridged through a tunnel (L2TP, VXLAN, ...), letting you transmit Ethernet frames globally.
Answer: No, you can't deduce that from just the picture.
You could have hosts without IP addresses, but you could also have IP addresses. You don't need a router to assign IP addresses. You could:

have a host running a DHCP (or even BOOTP) server providing IP addresses to the other hosts
have hosts with manually configured IP addresses
have hosts using auto-configuration IP addresses (IP addresses in the 169.254/16 network)

As for traffic, provided we are indeed talking about Ethernet switches and interfaces, you can have Ethernet frames running through the network, and these Ethernet frames could contain anything, including IP packets. Without a router connected to the outside world, they would not be able to reach other networks (or the Internet at large), but the hosts could speak IP between them provided they somehow got IP addresses as described above.
Answer: Yes and no. At the data-link layer (Ethernet in this case), there is no concept of an "IP address": the only address that exists is the MAC address. Frames that are sent can be marked as containing IP packets (EtherType 0x0800/0x86DD), but it's up to higher-level layers to decide what to do with the data.
So if you're looking at this solely at the point of view of the Ethernet interface, you would be correct. However, looking at this from the point of the device using the interface, you would be incorrect: it would see the network from the TCP/IP or UDP/IP layer and would usually be completely indifferent to what exists beneath that.
A wrinkle that can occur is if you start using VPN tunnels. If you set up a VPN in bridge mode (let's say between switches 2 and 3), you now have a layer 2 frame encapsuled inside a higher-level packet!
Answer: There are solutions (eg Ethernet over MPLS) that actually allow transferring ethernet frames over a WAN - these are in production use in some applications but still somewhat exotic. Used in scenarios where you want multiple physically separate machines - in different buildings or even towns or countries, so that eg a local disaster will not wipe the whole setup out - able to quickly take on a given, identical IP address as needed without having to change routing or wait for DNS propagation.
There are non-IP packets to be found even on a modern LAN: ARP, a helper protocol IP uses to associate IP addresses to MAC addresses. Various discovery protocols for network-connected devices (which you want to be able to discover without knowing beforehand eg what address they were given by a DHCP server). Sometimes, legacy NetBEUI broadcasts if older Windows machines are involved. Spanning tree and LLDP, which is the shop-talk between intelligent network switches (they are actually gossiping about the expensive macbooks acting entitled!).
Answer: What you say is more or less correct: None of your switches have IP adresses. But your hosts do have a IP and the ethernet frames that pass the switches contain the IP's of host1 and host34. Your switches just don't care about those IP's.
A bit more info about the basic devices:
(These are all theoretical devices, many real-life devices take on some properties of device A and some of device B)

Hub

All types of data will always move over hubs even if it's not a ethernet packet. A hub will just read all bits it sees and sent them back out again on every port. It doesn't have a MAC or IP because it doesn't care about the fact that the bits are ethernet packets.

Switch

A switch will:

Discard everything that's not a ethernet packet.
Make decisions on what do with the packet based on everything in the packet except the ethernet frame (the payload). In most cases this decision is only based upon the destination MAC address.

A switch has a MAC so that it can communicate with other switches and more advanced devices. A switch is a smart hub.

Router

A router will:

Discard everything that's not a IP packet.
Make decisions on what do with the packet based on the header of the IP packet but it doesn't care about the data in the IP packet. In most cases this decision is only based upon the destination address

A router has a IP for each port so that it can communicate with other routers and more advanced devices. Since these IP packets are in Ethernet packets it will also have MAC addresses.
A router is smart switch.

Network card of a computer

This is like a switch with 2 ports where 1 (virtual) port is connected with a cable and 1 port is connected with the operating system of the computer.
It has a MAC but contrary to what you may think no IP.

Firewall

A firewall cares about everything.
A firewall is a smart router and has a MAC and IP's

Operating system of a computer

This is like a firewall:

That doesn't look at the data in a TCP/UDP/ICMP packet but does look at the header of those packets
Where a virtual port is connected to each network card. It sends/receives IP packets to/from the network cards and these cards create Ethernet packets with the IP packets as frame or strip them from everything except the frame.
It also has virtual ports that are connected to applications. There are 1 (ICMP) + 2^16 (TCP) + 2^16 (UDP) ports.

It has multiple IP's (1 for each network card) but no MAC

A cable

This is like a hub with exactly 2 ports
It does not have a IP or MAC.
This is a simplified version of the theory, I ignore a lot of things (e.g. There is both IPv4 and IPv6). It's simplified but should be correct enough.
Comment: There are a fair amount of inaccuracies here.  While you're generally correct, a router is not a "smart switch" and a switch is not a "smart hub."  Also, switches forward based on destination MAC, not "everything in the packet except the Ethernet frame.  IMO, your answer is more confusing than helpful.
Answer: Yes
Just for fun: YES.

Can Ethernet frames only be transmitted in a LAN?

Yes, Ethernet frames in a strict sense are only transmitted in a LAN. In a WAN, you will have other formats.

In the LAN depicted in the picture below, am I correct in saying that devices do not have IP addresses?

Yes. The yellow line as many switches, which, as related to the packages between the two hosts, do not have IP addresses.
Modern switches can obviously have IP address of their own for their own configuration (i.e., if they offer a management web GUI). But simple household switches, even if they are rather intelligent (i.e. if they do not broadcast any and all ethernet packages on all ports, like they did in the stone age of networking), need to have no IP address at all.
Remark regarding comments: this is equivalent to saying that all the switches between those hosts are part of one subnet (i.e., one IP netmask). This is, admittedly, to some extent an assumption, as these days there can be very complicated switches, and some people may even call routers switches. But still; per default I would assume that a chart labeled with switches contains switches. They may (in fact, they most certainly will) look at the IP address to make the decision on which port to send a package. But they do not introduce new IP addresses as part of the path the packet takes.
Comment: Wireless uses 802.11, not Ethernet.  Also, IP is not a WAN protocol.  PPP, HDLC, PoS, Frame Relay, etc are all examples of WAN protocols.
Comment: In the diagram, how would you know devices don't have IP addresses?
Comment: The switches aren't generating traffic, the hosts are.  I think you're misinterpreting the OPs question.
Comment: @RonTrunk, thanks for the corrections, I have removed these details as they are not so critical, and I fell into the same trap as the OP regarding mixing up ISO levels.
Comment: @RonTrunk, `In the diagram, how would you know devices don't have IP addresses?` => because they are labeled "switch". I would expect them to be labeled "router" if they are routing (i.e., if there are multiple IP subnets involved here).
Comment: @RonTrunk: I'm not sure that I understand where you're coming from, but sure, me misunderstanding the question is always a possibility. The OP will surely comment here if he thinks my answer has some merrit at all... ;)


Can I use 10\$\mu\$F caps in a MAX232?

Question: this is just a quick and dirty question. I don't understand the purpose of the  1 \$\mu\$F caps in the MAX232 circuit. What do they do, exactly? Can they be skipped? Can they be swapped with 10 \$\mu\$F caps?
Comment: Did you read the manufacturer's datasheet? You do not specify if it is a Maxim MAX232 or a Texas Instruments MAX232(N). For starters they will tell you why the capacitors are needed. I don't know if it will work, because I prefer to follow the recommended usage so that my circuits are reliable, and ceramic 1.0uF capacitors are cheap enough I keep plenty of spares on-hand.
Comment: If you did try this. I would like to know the results you had with using 10uF caps with a MAX232 (which manufacturer if known please).
Answer: They're definitely required! For their function look at the block diagram

You'll see that they're connected to the voltage doubler and voltage inverter. These create +10V from the 5V power supply and -10V resp. This is done by charge pumps.

An oscillator will control the switches so that either S1 and S3 are closed or S2 and S4. When S1 and S3 are closed C1 is connected to ground and V+ and charged to V+. When S2 and S4 are closed the top of C2, which is V+ higher than the bottom is connected to ground, so that the bottom now is V+ below ground. Via the switches the charge flows to C2, which will then have a negative voltage. So that's for the inverter. The same principle is used to double the incoming voltage.
C1 and C2 are the external 1\$\mu\$F capacitors. If they're omitted there won't be any +10V or -10V and no signal at the drivers' outputs.
In its datasheet Maxim recommends 1\$\mu\$F for the MAX232, 100nF for the MAX232A. I wouldn't recommend using 10\$\mu\$F instead of the 1\$\mu\$F. The switches might have some resistance and the capacitor may not get fully charged in the time one pair of switches is closed.
edit
In a comment to another answer which said 10\$\mu\$F will probably be OK someone said:

It should always be OK to use larger sized caps but they are required. The caps are part of charge pumps that produce and store +/- ~7 volts for RS-232 (I measured mine).

He didn't say, but it looks like he used 10\$\mu\$F. If you use the recommended value of 1\$\mu\$F you should get \$\pm\$10V. The 7V seems to confirm my doubts about the charging of the larger capacitors.
Comment: If the output capacitor is nearly charged and the amount of current drawn from the charge pump isn't too high, the chip shouldn't care whether one is using the recommended caps or one gigafarad caps. If the output cap isn't, or doesn't stay, nearly-fully charged, however, that could cause excessive power dissipation in the chip.  I would expect that the chip is designed to avoid damage if the charge-pump output is shorted to ground when using the recommended caps; using larger caps in such case could cause over-stress.
Answer: The purpose of the 4 capacitors is to generate the +/-12 volts needed for RS232 communications. The MAXIM and TI MAX232 datasheets recommend 1uF capacitors.
Answer: The MAX202 is a better choice, it can use 100n ceramic capacitors.
Comment: "It's slightly cheaper."  It is? MAX202 in 16 pin DIP qty 1: $3.86 ( http://search.digikey.com/scripts/DkSearch/dksus.dll?Detail&name=MAX202CPE%2B-ND )  MAX232 in 16 pin DIP qty 1: $1.16 ( http://search.digikey.com/scripts/DkSearch/dksus.dll?Detail&name=296-1402-5-ND )
Comment: What are the downsides of the MAX202? If you can just replace the MAX232 with it and use 100n caps then why is everyone still using the MAX232?
Comment: There are no downsides. I think it's caused by people looking at old designs, they just don't know that the much better MAX202 exists. It's slightly cheaper.
Comment: Also, the MAX232 data sheet states that the MAX202 is a better device! ESD performance is improved. There isn't any point in using the MAX232.
Comment: The MAX202CDR costs $0.48 and the MAX232ECDR costs $0.65 from TI for 1 ku. That's the SOIC package device. It's a big difference!
Answer: They are used for the converter inside to make a negative voltage for the RS232 lines (which is +/-). Honestly, I don't see why you would prefer a bigger cap, as they normally become more expensive and larger..
Comment: I don't prefer them. They are all I have right now. So just wanting to use parts at hand to solve problem at hand.
Answer: From the data sheet for the ESD protected version under Applications Information (page 13):

The MAX202E, MAX206–MAX208E, MAX211E, and MAX213E require 0.1µF capacitors, and the MAX232E and MAX241E require 1µF capacitors, although in all cases capacitors up to 10µF can be used without harm.

and

Use larger capacitors (up to 10µF) to reduce the output impedance at V+ and V-. This can be useful when "stealing" power from V+ or from V-.

The data sheet for the non-ESD-protected version doesn't include this information.
From reading the data sheets, I find the following differences between the MAX202E and MAX232E:
<code>              MAX202E    MAX232E
Icc    mA      8 - 15     5 - 10
Iclk   kHz      230        140
Caps   µF       0.1         1
</code>
Otherwise, they seem to be the same.

Can I use 10\$\mu\$F caps in a MAX232?


Best home workout that targets the pectoralis minor or the lower chest?

Question: I have a good amount of upper chest but lack lower chest, giving my chest a somewhat breast-like appearance. I've gone online to figure out which home exercises I could do that targets mainly the lower chest and all I could get is incline pushup.
But the thing with that is, it's too easy. Isn't there a harder form of exercise that targets my lower chest so that I can efficiently cause progressive overload OR do I just need to do as many incline pushups as I can handle, increasing it gradually?
Comment: If you find it too easy, do it with a backpack that you filled with heavy stuff (books for instance)
Comment: Since you are unware of dips or the backpack idea or simply doing them pre fatigued, i would get a 2nd opinion on your chest - is it really lacking to the point where you need to target it more or is it just your subjective impression or the natural shape of your pecs - or perhaps something else?
Answer: Anatomically speaking you can't  isolate a muscle into parts but the Pectoralis Major  is split into two heads which makes it easier.

Common myth is that the more you press in an incline  the more upper Pectoralis you use, which is quite the opposite since the upper/clavicular Pectoralis is almost horizontal  and not vertical.
J Hum Kinet. 2017 Jun
This study  shows that
Unlike popular belief, vertical movements don't  work the upper chest more, due to it's  position the muscle  is always active. Going from decline/flat to incline only reduces triceps activity while increasing biceps activity.
Boeckh-Behrens & Buskies. 2000 found that decline work (Dips/inverted bench press)
Uses even more upper chest.

From this chart things like dips or inverted bench press are best for upper chest development  but also best for "lower chest" too.
If you do Dips I suggest sticking with bodyweight  only for safety and to progress just add more repetition every time you train.
Comment: I removed the studies that you edited in from another answer, as they do not do anything to answer the question and are noise.