Thursday, April 30, 2015

In Into the Wild, how does McCandless navigate the journey from dreams to reality?

I'm going to answer this question in a literal manner.  


McCandless's dream is to live on his own in the Alaskan wilderness.  He reveres stories by Jack London that seem to romanticize Alaska's rugged beauty and danger.  


McCandless doesn't immediately rush off to Alaska though.  He spends a great deal of time hitchhiking around the western United States living on nothing but rice and water for the most part.  I believe that McCandless used this time to "train" himself for his Alaskan adventure.  Once he felt ready to head up to Alaska, he navigated there in the same way that he had been getting around for the previous months.  He hitchhiked to Alaska.  McCandless's dream was to head to the Stampede Trail and survive for months out there.  The final person that helped McCandless get out there was Jim Gallien.  


McCandless navigated toward his dreams with a single-minded focus.  He traveled alone for much of the time.  He hitchhiked when able and got low-paying jobs as needed in order to pay for any meager supplies required. 

Wednesday, April 29, 2015

`int_(sqrt(2)/3)^(2/3) (dx)/(x^5 sqrt(9x^2 - 1))` Evaluate the integral

`int_(sqrt(2)/3)^(2/3)1/(x^5sqrt(9x^2-1))dx`


Let's first evaluate the indefinite integral by integral substitution,


Let `x=1/3sec(u)`


`=>dx=1/3sec(u)tan(u)du`


`int1/(x^5sqrt(9x^2-1))dx=int(1/((1/3sec(u))^5sqrt(9(1/3sec(u))^2-1)))1/3sec(u)tan(u)du`


`=int(1/(1/243sec^5(u)sqrt(sec^2(u)-1)))1/3sec(u)tan(u)du`


Now use the identity:`sec^2(theta)=1+tan^2(theta)`


`=int(243/(3sec^5(u)sqrt(1+tan^2(u)-1)))sec(u)tan(u)du`


`=int(81sec(u)tan(u))/(sec^5(u)sqrt(tan^2(u)))du`


`=81int1/(sec^4(u))du`


`=81intcos^4(u)du`


Now let's use the identity:`cos^2(theta)=(1+cos(2theta))/2`


`=81int((1+cos(2u))/2)^2du`


`=81int(1+cos^2(2u)+2cos(2u))/4du`


`=81int(1/4+(cos^2(2u))/4+1/2cos(2u))du`


`=81(int1/4du+int(cos^2(2u))/4du+int(cos(2u))/2du)`


`=81(u/4+1/4int(1+cos(4u))/2du+1/2intcos(2u)du)`


`=81(u/4+1/4int(1/2+cos(4u)/2)du+1/2(sin(2u))/2)`


`=81(u/4+1/4(int1/2du+intcos(4u)/2du)+1/4sin(2u))`


`=81(u/4+1/4(u/2+1/2sin(4u)/4)+1/4sin(2u))`  `=81(u/4+u/8+sin(4u)/32+sin(2u)/4)`


`=81((3u)/8+sin(4u)/32+sin(2u)/4)` 


Now recall that we have used `x=1/3sec(u)`


`=>sec(u)=3x`


`=>cos(u)=1/(3x)`


`=>u=arccos(1/(3x))`


Substitute back u and add a constant C to the solution,


`=81(3/8arccos(1/(3x))+1/32sin(4arccos(1/(3x)))+1/4sin(2arccos(1/(3x))))+C`


Now let's evaluate the definite integral,


`int_(sqrt(2)/3)^(2/3)dx/(x^5sqrt(9x^2-1))=81[3/8arccos(1/(3x))+1/32sin(4arccos(1/(3x)))+1/4sin(2arccos(1/(3x)))]_(sqrt(2)/3)^(2/3)`


`=81[3/8arccos(1/2)+1/32sin(4arccos(1/2))+1/4sin(2arccos(1/2))]-81[3/8arccos(1/sqrt(2))+1/32sin(4arccos(1/sqrt(2)))+1/4sin(2arccos(1/sqrt(2)))]`


`=81[3/8*pi/3+1/32sin(4*pi/3)+1/4sin(2*pi/3)]-81[3/8*pi/4+1/32sin(4*pi/4)+1/4sin(2*pi/4)]`


`=81[pi/8+1/32sin((4pi)/3)+1/4sin((2pi)/3)]-81[(3pi)/32+1/32sin(pi)+1/4sin(pi/2)]`


`=81[pi/8+1/32(-sqrt(3)/2)+1/4(sqrt(3)/2)]-81[(3pi)/32+1/32(0)+1/4(1)]`


`=81[pi/8+sqrt(3)/2(-1/32+1/4)-(3pi)/32-1/4]`


`=81[pi/8-(3pi)/32+sqrt(3)/2(7/32)-1/4]`


`=81[pi/32+(7sqrt(3))/64-1/4]`

In Chapter 20 of the novel To Kill a Mockingbird, what does the reader learn about Mr. Raymond? Do you agree with his decision to deceive people?

In Chapter 20, Scout and Dill learn that Dolphus Raymond is not an alcoholic and that he actually is drinking Coca-Cola underneath the paper bag. When Scout asks him why he pretends to be drunk, Dolphus tells her that he tries to give the citizens of Maycomb a reason as to why he chooses to live his life like he does. Dolphus explains how people could never understand why he chooses to associate with African Americans and finds it easier to disguise himself as being a drunk. Dolphus Raymond simply enjoys being around black people but realizes that it is considered a cultural taboo to associate with people of a different race. In 1930s Alabama, segregation is a significant part of society, and Jim Crows Laws prohibit African Americans from utilizing the same public facilities as white people. Instead of continually defending his views and arguing with people, Dolphus finds it easier to pretend that he is a drunk to avoid conflict. I agree with Dolphus Raymond's decision to pretend that he is an alcoholic to avoid conflict. Throughout the novel, certain citizens go to extreme lengths to harm individuals who support African Americans. Dolphus' well-being could be compromised if he was outspoken about his views towards black people and pretending to be an alcoholic could possibly prevent numerous altercations.

What type of language is used in Chapter 21 of To Kill a Mockingbird?

As the novel, To Kill a Mockingbird, is told from the perspective of Scout Finch, the language used is reflective of her rural, Southern upbringing. The manner of speech, colloquialisms, and dialect used in both Chapter 21 and the entirety of Harper Lee's novel capture the spirit of small-town Alabama. Consider the following example:



“I know where they are, Atticus.” Mr. Underwood spoke up. “They’re right up yonder in the colored balcony—been there since precisely one-eighteen P.M. (Lee, Chapter 21).



Mr. Underwood's language reflects the overall setting of the novel: a rural, casual environment. He addresses Atticus Finch by his first name and not as Mr. Finch, preferring informality and familiarity over stiff addresses. Furthermore, he relies on words such as "yonder," which add a Southern flair to his speech. Mr. Underwood's comment also reflects the historical context of the novel, for we see in it themes of racial inequality and segregation.

Turning to another example, consider the following exchange between Atticus and Jem:



"I’ve no idea,” said Atticus shortly. “You’ve been here all afternoon? Go home with Calpurnia and get your supper—and stay home.”
“Aw, Atticus, let us come back,” pleaded Jem. “Please let us hear the verdict, please sir (Lee, Chapter 21).



In the above dialogue, we see Atticus using the tone of a concerned father and Jem acting as a pleading son. One of the more interesting aspects of the Finch children and their relationship with their father is the use of both formal and informal addresses. Scout and Jem refer to their father by his name ("Atticus") but frequently counter this casual address by using the polite, highly traditional "sir."

We see also in Chapter 21 how Calpurnia's language shifts depending on context: 



Calpurnia marched us home: “—skin every one of you alive, the very idea, you children listenin‘ to all that! Mister Jem, don’t you know better’n to take your little sister to that trial? Miss Alexandra’ll absolutely have a stroke of paralysis when she finds out! Ain’t fittin’ for children to hear...” (Lee, Chapter 21). 



Addressing the children, Calpurnia's language is unguarded. She adopts no affectations, but rather, uses language casually and colloquially. Comparing the above passage to Calpurnia's brief exchange with Judge Taylor, we find that Calpurnia caters her language to the changing demands of her social, economic, and racial situations. To draw from earlier knowledge of Calpurnia's character within the novel, we can return briefly to Chapter 12:
 



“They’s my comp’ny,” said Calpurnia. Again I thought her voice strange: she was talking like the rest of them.
“Yeah, an‘ I reckon you’s comp’ny at the Finch house durin’ the week.”
A murmur ran through the crowd. “Don’t you fret,” Calpurnia whispered to me, but the roses on her hat trembled indignantly (Lee, Chapter 12).



We see in the above exchange that Calpurnia has adopted a manner of speech that mimics her fellow church-goers and aligns her more closely to the African-American community in Maycomb. Reflecting on the excerpt from Chapter 12 and those from Chapter 21, we find that Calpurnia's language serves as a response to her environment. The language she uses when addressing a white judge is not the same as the language she uses with members of the Finch household, and furthermore, the language she uses in the Finch household is not entirely the same as the language used to address the members of her church.

The language used in Chapter 21 (and indeed, throughout the novel) gives us insights into the characters' social, political, and racial experiences. It informs us of their economic backgrounds, their levels of education, and their geographic past. We can infer, through the use of colloquialism and slang, whether a character might be urban or rural, and further, we can better understand the type of relationships they have to other characters by examining things like tone, formality, and word choice.

(Primary Source: Lee, Harper,To Kill a Mockingbird. New York: Grand Central Publishing, 1960. Print.)

Tuesday, April 28, 2015

In a tragedy, the heroine or hero usually has a character flaw that leads to their downfall. Is this true in Romeo and Juliet? Why?

Yes, it is certainly true in Shakespeare's Romeo and Juliet that the hero and heroine have a character flaw that leads to their respective downfalls!


It is traditionally argued that Romeo's tragic flaw is his impulsivity. He is impulsive in love (falling madly in love with Rosaline and then shifting those feelings to Juliet; later marrying Juliet after knowing her for less than a day), in his social life (choosing to fight and kill Tybalt rather than stand down after Mercutio is murdered), and in his own life (choosing to kill himself after learning of Juliet's "death"). 


Thus, Juliet's tragic flaw might be her naive loyalty to Romeo. Juliet repeatedly places her trust and faith in Romeo, who--as we can see above--frequently makes poor and/or rash choices and is overly-engaged in the conflict between the Montagues and Capulets. Juliet trusted Romeo to be a responsible husband and ally, and was, therefore, quick to agree to marry him; Romeo betrayed that trust when he killed Juliet's cousin, Tybalt, resulting in his banishment from Verona... and ultimately, Juliet's desperate ploy to save her marriage by faking her own death. 

Explain the dramatic significance of the opening scene of Romeo and Juliet, Act 1, scene 1.

The first scene of the play is significant dramatically because it really establishes the the mood of the story.  The first thing the audience sees is a violent fight between members of the houses of Montague and Capulet, a fight that really takes place without provocation and will ultimately accomplish nothing.  This scene demonstrates how high the tensions between the families (and even their servants!) run as well as how ridiculous and baseless their hatred for one another really is. 


This scene also introduces us to both Tybalt and Benvolio.  Benvolio's line, "I do but keep the peace.  Put up thy sword, / Or manage it to part these men with me," shows us how peace-loving and reasonable and honest he is (1.1.69-70).  On the other hand, Tybalt's line, "I hate the word [peace] / As I hate hell, all Montagues, and thee," acquaints us with how hateful and violent he is (1.1.71-72).  The introduction of these two characters adds some suspense to the tension of this scene, causing us to anticipate further violent interactions and to expect more bad behavior from Tybalt.

Monday, April 27, 2015

How is the king of Brobdingnag, in spite of ruling an isolated kingdom, a wise, humane, peace-loving man?

Despite ruling a physically isolated kingdom that has no real need to be concerned with anyone else because it has no neighbors, the king of Brobdingnag is very interested to learn about the laws and culture of Gulliver's home.  He is horrified when Gulliver begins to acquaint him with the customs of England, and he comes to believe that the British are selfish and warlike and dishonest "vermin."  However, even beyond his disgust, the king develops a rather violent antipathy to both Gulliver and his countrymen when Gulliver tries to tell him about the wonderful virtues of an invention called gunpowder.  Gulliver describes the great damage it can do in almost gleeful terms, speaking about men's limbs positively raining from the skies after their owners have been blown apart by gunpowder's awe-inspiring power.  The king is less than impressed.


The king's response to Gulliver shows just how gentle and wise he is.  Fundamentally benevolent, honest, and peace-loving, the king seems to assess the British in the way that Swift would like the reader to do; it's a rather harsh way to characterize the reality he wished to satirize, but satire is often caustic. 

Thomas Jefferson's election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?

Thomas Jefferson’s election in 1800 can be called the “Revolution of 1800” because it was the first time in America’s short history that pow...