What is a functionalist society?

There are three sociological perspectives or ways of looking at the world. One of these perspectives is called the functionalist perspective. It views society as having various interconnected parts. For instance, the family may produce and raise children. Another part, the schools, transmit knowledge to the children. So a functionalist society is one having various interconnected parts which all come together ultimately to produce a harmonious, balanced and stable society. The idea of functionalist societies is based largely on the work of Herbert Spencer, a social Darwinist who believed in survival of the fittest and also on the work of Emile Durkheim.

Some functions in society are considered manifest while some are considered latent. For example a manifest function of schools is to educate our children - it is an obvious function. Yet a latent, hidden or unrealized function of schools, is to provide a place where young people can learn to socialize. For example students often find a mate in college.

In The Great Gatsby, how are Wilson and Gatsby similar? Dissimilar? To whom is Nick more sympathetic?

Jay Gatsby and George Wilson are similar in that both of them attempt to achieve the American Dream: the idea that a person can begin with little to nothing, and, through hard work and perseverance, that person can prosper and achieve financial and personal success. Both men try to achieve this dream honestly, and both fail. Wilson continues to try to pursue the dream by honest work, and he just cannot get ahead. Gatsby seems to have decided honest work didn't benefit him much, so he turned to bootlegging (the production, distribution, and sale of illegal liquor during the era of Prohibition). In this way, then, the men differ: they take different paths in their attempts to reach the American Dream; however, they are similar in the fact that neither of them successfully attains it.

Nick seems, in the end, more sympathetic to Gatsby, if for no reason other than that Wilson kills Gatsby for committing a crime he did not commit. Ironically, Gatsby committed a number of other crimes for which he went unpunished, but murdering Myrtle Wilson isn't one of them. Gatsby's fundamental ability to maintain hope that he would, one day, have everything he'd ever dreamed granted him a kind of innocence that Nick seems to admire.

How would you characterize the role of religion in Nazi Germany during the Holocaust?

The Boy in the Striped Pajamas, a young adult novel by John Boyne, takes place during the Holocaust and is told from the point of view of Bruno, a young German boy. Religious themes arise when Bruno meets Shmuel, a Jewish boy who lives on the other side of the fence. The reader understands that Bruno’s new friend is behind the fence of the concentration camp where Bruno’s father works as a Nazi officer. As Bruno gets to know Shmuel, this friendship conflicts with the anti-Semitic propaganda Bruno has been taught.

Regarding religious practices of Nazis, the German population in 1933 was about 67% Protestant and 33% Catholic. While Nazi leadership was somewhat divided in its view of the role of religion, the Nazi party generally viewed religion as somewhat of a threat. Nazism desired to transform German society into a unified national community. Religious differences would threaten that common national identity.

Hitler’s Minister for Church Affairs, Hans Kerrl, supported the idea of Christianity being adopted by the Nazi party into “Positive Christianity” that renounced the Jewish origins of the faith. Hitler’s Protestant Reich Church was a failed attempt to unify Germany’s existing Protestant churches. The Catholic Church and others were persecuted; more than 6,000 clergymen were executed or imprisoned on charges of treason. 

With the onset of war, however, Hitler softened his position on religion. Wanting to eliminate sources of contention within Germany, he announced that his regime would no longer take action against Evangelical and Catholic churches for the duration of the war. While the Nazi party saw traditional religion as a threat, elements of Nazism could be considered semi-religious with Hitler at its center as a sort of demigod.

Compare To Kill a Mockingbird and The Scarlet Ibis. How do they explore the ways in which individuals can be limited by society?

If someone in a community does not measure up to everyone else's standards of how to look and behave in "normal" ways, then people's prejudices seem to surface. As a result, the ones who are deemed unusual or different suffer the effects of discrimination and isolation. In both Lee's To Kill a Mockingbird and Hurst's "The Scarlet Ibis," characters who have different challenges or disabilities in life face injustice and harsh treatment at the hands of family and friends who should support them. The "different" characters that come to mind in these stories are Doodle, Boo Radley, and Tom Robinson.  

First, Doodle suffers the effects of discrimination and isolation within his own family because he is born with physical disabilities that not only embarrass his older brother but also discourage his parents. The parents love Doodle and do not mistreat him, but Brother does. Brother's pride leads him to taunt and push Doodle beyond his limitations only so Brother can have the type of sibling he wants and whom society will accept. Brother explains as follows:

The knowledge that Doodle's and my plans had come to naught was bitter, and that streak of cruelty within me awakened. I ran as fast as I could, leaving him far behind with a wall of rain dividing us . . . Soon I could hear his voice no more.

Brother, like society, sometimes does not know how to deal with people's disabilities. Brother does not understand Doodle's limitations; consequently, Brother only knows that he does not want kids at school knowing he has a disabled little brother. The above passage shows Brother leaving Doodle isolated and suffering alone when he needs help. Brother can be compared to society when it turns its back on those who have special needs. 

In To Kill a Mockingbird, Boo Radley and Tom Robinson are treated similarly to Doodle. Boo Radley possibly suffers from social anxiety, and Tom Robinson is black and has a crippled left arm. The community treats Boo Radley as though he is a monster or boogie man, while people treat Tom Robinson with prejudice more for the fact that he is black than for his deformed arm. As a result, Boo hides in his house every day, and Tom is falsely charged with raping a white girl. Because these characters are treated disrespectfully in society, they tend to withdraw or make decisions they otherwise wouldn't in order to please others or to escape society. It is through the characterization and exploration of these characters' lives that profound lessons are learned. For example, Scout paraphrases Mr. Underwood's comments from Maycomb's newspaper after Tom Robinson is killed while trying to escape wrongful imprisonment:

Mr. Underwood didn't talk about miscarriages of justice, he was writing so children could understand. Mr. Underwood simply figured it was a sin to kill cripples, be they standing, sitting, or escaping. He likened Tom's death to the senseless slaughter of songbirds by hunters and children (241).

Mr. Underwood does his best to inform society of its wrongs, but it takes generations' worth of time to change people's minds from such prejudices. Underwood's remarks also point out a common theme between the two stories, which is that it is wrong to hurt someone in any way simply because he or she is different. Not only that, it is wrong to hurt someone who cannot defend himself for herself because of unequal opportunities in life. 

It is interesting to note that Doodle dies running like Tom does, although, it should be noted, Doodle runs to make his brother happy with him and to accept him, and Tom runs to escape injustice. Boo Radley, on the other hand, runs from society by hiding inside of his house and never interacting with anyone in the community. All three characters never seem to find the justice or kindness they deserve. Because Doodle, Boo Radley, and Tom Robinson are never fully accepted within their families or communities, they are limited to living isolated lives both physically and psychologically. Society never accepts them for who they are. As a result, these three characters are not allowed to do anything more than keep running or keep hiding.

In Animal Farm, what does the Battle of the Cowshed show us about Snowball, Boxer, and Mollie?

The Battle of the Cowshed takes place in Chapter Four when Jones and his men try to recapture the farm. During the ensuing battle, the behavior of certain animals reveals much about their characters.

Snowball, for example, plans the battle tactics by reading a book on Julius Caesar's military campaigns and takes an active role in the fighting. This shows he is a natural leader and is committed to the principle of equality, as he fights alongside the other animals. His reaction to the death of the humans, however, illustrates he is a committed Animalist who still believes humans are the enemy:

War is war! The only good human is a dead one.

In contrast, Boxer's reaction to killing a human during the battle illustrates his soft and sensitive nature. He is overcome with regret and struggles to accept that his actions were justified, regardless of provocation:

I had no intention of doing that… I have no wish to take life, not even human life.

Mollie disappears as soon as the first gunshot is fired. Terrified of fighting and lacking courage, Mollie runs away from the battle and hides among the hay in the manger. She has no interest in fighting the humans, or anybody else — she simply wants peace. 

In The Giver, Jonas’s anxiety about Fritz getting his bicycle shows us what about this community?

Jonas’s reaction to Fritz getting his bicycle shows that his society is very intolerant of mistakes. 

The community is very intolerant of difference.  They are also very strict about rules and social conventions.  Things are done a certain way, and anyone who is a little bit different is brought into line as stringently as possible.  We get small examples of this throughout the book, with public scoldings about taking food home or having hair ribbons untied being routine.  With the discussion of Fritz, we see how deep this behavior goes. 

He knew that his parents cringed a little, as he did, when Fritz, who lived in the dwelling next door to theirs, received his bike and almost immediately bumped into the podium with it.  Fritz was a very awkward child who had been summoned for chastisement again and again. (Ch. 6) 

Jonas considers it completely normal to treat Fritz this way, punishing him because he is awkward.  It is similar to the story we hear later about how Asher was beaten as a toddler for using the wrong word.  Conformity is the ultimate goal, and children are socialized from a young age to not only accept it but enforce it.  Thus Jonas looks down on Fritz. 

Fritz is only nine years old, but he already has a reputation.  Not only that, but the community looks down on his parents too.  For Fritz to be this much of a screw-up, clearly they are doing something wrong.  A parent’s job is to indoctrinate the children to the community’s values. 

His transgressions were small ones, always: shoes on the wrong feet, schoolwork misplaced, failure to study adequately for a quiz. But each such error reflected negatively on his parents' guidance and infringed on the community's sense of order and success. (Ch. 6) 

It is chilling how Jonas dismisses Fritz as infringing on the order of the community when he is acting as most nine year olds would.  In Jonas’s world, perfection is not just aimed for, it is expected.  Anything less than perfection is punished out of people from an early age.  If this does not succeed, there is always release.

Let `f(x) = 3 + x^2 + tan(pi/(2x)) , -1

Hello!

You wrote `f(x) = 3+x^2+tan(pi/(2x)).`

By the definition of an inverse function of `f(x),`  `f^(-1)(3)` is that number `x` for which `f(x) = 3.` Usually we require that such a number must be unique, otherwise `f^(-1)` would be a many-valued function.

a. In other words, we need to solve the equation `f(x) = 3.`

In our problem, `f(x)` takes any value infinitely many times, even at the given interval `(-1, 1),` even at any neighborhood of `x = 0.`

The cause of this is that `tan(pi/(2x))` tends to `+-oo` at points where `pi/(2x) = pi/2 + k pi` for some integer `k.` The `3+x^2` part remains finite and bounded at any finite interval and cannot prevent this behavior of `f(x).` These points are `x_k = 1/(1+2k)` and they tend to zero as `k` tends to `+-oo.`

Regardless of the number of solutions, the equation `f(x)=3,` which is equivalent to `x^2+tan(pi/(2x)) = 0,` cannot be solved exactly.

I might suppose that you misprint the formula, probably `f(x) = 3+x^2+tan(pi/2 x).` In that case, the only solution for `f(x)=3` at the interval `(-1,1)` is `x=0.` This is because `f` is strictly monotone on `(-1,1).` It is not obvious but true. Ask me if you need a proof.

b. If `f^(-1)(5)` exists, then by definition `f(f^(-1)(5)) = 5.`