What was the Trail of Tears?

The Trail of Tears is the name given to the forced removal of the Cherokee people from their rightful lands in the Southeastern United States to new territory in what is now Oklahoma, west of the Mississippi River.  The march was ordered by President Andrew Jackson and occurred in the years 1838 and 1839 as per both the Indian Removal Act of 1830 and the Treaty of New Echota in 1835.

In 1830, Andrew Jackson signed the Indian Removal Act into law, which allowed him to exchange lands occupied by Native American tribes in existing states for unsettled lands west of the Mississippi River.  This meant relocating entire tribes thousands of miles away from their native lands, and few were willing to undergo the change.  Many, such as the Seminoles in Florida, attempted to resist with military action; these uprising were violently quelled, and noting the ineffectiveness of such a strategy the Cherokees instead approached the problem administratively.  The Cherokee tribe of the Southeastern United States were highly organized and had their own elected government representatives, and they took the issue to federal court.  The Supreme Court ruled the forced extradition of the Cherokee people was unconstitutional, and yet Jackson refused to adhere to this ruling; amid an environment in which other tribes were being removed from their homes and shown no mercy along the way, some Cherokee citizens agreed to the Treaty of New Echota, accepting payment and new lands as compensation for the relocation.  This treaty gave Jackson the leverage he needed to force the entirety of the Cherokee nation – some fifteen thousand individuals – to undertake the long, hard road from Georgia to an area in present-day Oklahoma.  The Native Americans suffered immensely during the journey, almost a quarter of them losing their lives along the way.  The devastation and sorrow this relocation caused led the Cherokees to give the journey the name “The Trail of Tears,” a moniker embraced by history as testament to the injustice faced by these individuals.

How can one compare Beowulf to Sir Gawain and the Green Knight?

When we read Beowulf, we see a ideal heroic character. He slays the evil creatures, he overcomes every obstacle in his life, he respects the community he lives in, also look for 'comitatus'. From the beginning to the end, Beowulf reflects the good side, aiding the people who need help (against Grendel especially) and receiving praise after every deed. 

But in Sir Gawain and Green Knight, everything is not so bright about Sir Gawain, he does not prevail any deed unlike Beowulf. He actually 'fails' in his journey to Green Chapel. He betrays Lord Bertilak by not giving the girdle to him when they're exchanging items. Also, he loses faith by accepting the girdle, trying to elude his fate whereas Beowulf is deeply bounded with his religion. Sir Gawain is afraid of Green Knight all the time while Beowulf never scares of dying. In fact, dying is depicted as a 'resolution' in Beowulf, even Beowulf himself is aware of that every man has to die, so the goal of his life is to make best of it, this theme is also important in Homer's Iliad.

One last point, when Green Knight enters the Camelot court, and offers a challenge, nobody attempts to accept it even Sir Gawain. If he was a real true hero, he'd accept it before King Arthur unwillingly accepts it.

Still these are my comments, they could be wrong or not well explained.

What are differences between the Aztecs and the Roman Empire?

There are obvious differences between the Roman Empire and the Aztecs. Rome controlled a much larger area than the Aztecs. Rome at its height had authority over one and a half million square miles compared to the Aztecs which ruled over less than one hundred thousand miles. This is probably due to the fact that agricultural production was much more difficult in Mexico than it was on the Italian peninsula. The Aztecs chose their land in an area that was swampy. They had to overcome this limitation by constructing islands called chinampas. The preparation of the land would have required a great deal of effort before crops could even be cultivated. Rome was located in a very fertile area and farming was much easier.

The political system of Rome, even during the period of emperors, afforded citizens more participation in government. The Roman emperors were never as powerful as the kings of the Aztec empires. Much of the power of the Aztec king derived from religion being such a central part of the Aztec culture. Religion dominated every facet of Aztec life and was so extreme that it called for human sacrifice. In Ancient Rome, religion was tolerated but did not dictate the politics of the state. There was a greater variety of religions in Rome while the Aztecs were united under one religion.

One final difference was found in the militaries of the two empires. While both relied on their military for expansion, the weapons of the Romans were stronger and more sophisticated than that of the Aztecs. The Romans also had a full-time professional army.  While the Aztecs considered all men soldiers they did not use them on a full-time basis.

How does numerology appear in The Old Man and the Sea? What do the numbers 3, 7, and 84 symbolize?

Great question. The two types of ideas you will be seeing here come respectively from Christianity/Biblical thought and from major-league baseball. The numbers 84, 7, and 3 are each significant in the numerology debate around The Old Man and the Sea. 3 and 7 are both powerful numbers in Biblical numerology. 3 is the number of the Patriarchs (Abraham, Issac, and Jacob), and is also the number of days until Jesus rose from the dead. 7 is the number of days within which the world was created, and symbolizes perfect spirituality. 

Santiago begins fishing on the first day without any catches (not knowing it is going to last that long, obviously) and our story starts on the 84th day without any luck. Some say that Hemingway constructed this time period as if it had occurred starting on Christmas in the year he had written the book, 1951, and with the 84th day being 3 days before Good Friday, with his struggle with the marlin culminating on Good Friday. 84 days at sea with no fish + 3 days struggling with the marlin = 87. However, there is a one-day variation in the numbers, and Good Friday lands on the 88th day.

Regarding the struggle with the marlin, it took 3 days and Santiago struggled to land the fish and fight off sharks 7 times. Hemingway was a devout Catholic, and he often incorporated Christian references into his writing. Another example of numerology here is the number 40. It is used to divide the days that Santiago still fished with Manolin counting from the first day of no fish, until day 40 when Manolin is forced to leave him. 40 was the number of years that Moses and the Jews were exiled to the wilderness, and 40 was also the number of days that Jesus was exiled to the wilderness. It is easy to draw a parallel between God (in the case of Moses and the Jews) and the test of Satan (in the case of Jesus) keeping one in the wilderness, to Santiago being trapped alone at sea at the mercy of a huge marlin.

Another opinion is that the 87 days correspond to several baseball games played during 1951. Santiago often parallels his experience at the time with DiMaggio, and it could be Hemingway decided to create a parallel with the entire timeline. This timeline (84 days at sea with no fish + 3 days struggling with the marlin = 87) only works with the year 1951 to correspond to several baseball games.

Define resting membrane potential and its physiological function in cells.

All cells are contained within a membrane. The resting membrane potential refers to the difference in voltage between the fluids inside of a cell and the fluids outside of a cell when a cell is in its 'resting' state. The resting membrane potential is generally -70 to -80 millivolts (mV). This is because the inside of the cell contains more electrically charged ions with a negative charge. The inside of the cell contains a high concentration of negatively charged particles, as well as a low concentration of positively charged sodium (Na+) and potassium (K+) ions. Outside of the cell there is a higher concentration of Na+. Particles in a fluid flow from high concentration to low concentration so that they are evenly distributed. K+ naturally wants to flow out of the cell and Na+ wants to flow into the cell to even out this concentration gradient. The membrane keeps most of the the channels through which Na+ flows into the cell closed when it is at rest. Additionally there are channels that pump extra Na+ ions out of the cell. In this way the cell actively maintains the resting membrane potential.

The electrical potential is physiologically important because it allows cells to transmit electrical signals. If an excitable cell, such as a nerve, muscle, or endocrine cell, receives a stimulus that raises its charge to -55mv, the Na+ channels open up allowing Na+ ions to rush into the cell. This causes a further increase in charge up to +30mv. This rapid change in membrane potential allows nerve cells to transmit signals, causing muscle cells to contract or endocrine cells to release hormones, among other things.

What is the meaning of "the skies are painted with unnumbered sparks. They are fire, and every one doth shine; but there's but one in all doth hold...

CAESAR: I could be well moved, if I were as you;
If I could pray to move, prayers would move me;
But I am constant as the northern star,
Of whose true-fix'd and resting quality
There is no fellow in the firmament.
The skies are painted with unnumber'd sparks;
They are all fire and every one doth shine;
But there's but one in all doth hold his place.
Act 3. Scene 1

Julius Caesar has behaved modestly and even humbly up to this scene, but Shakespeare evidently wanted to reveal the man as supremely egotistical and arrogant just before he was killed. This would seem intended to justify Cassius, Brutus, and all the other conspirators in the assassination. Caesar is every bit as ambitious as Cassius and Brutus believe, perhaps even more so. Caesar finds no man who can compare with him. He has to look up into the skies as if he is comparing himself with the gods and demigods. 

In Caesar's time it was believed that the earth was stationary and all the stars and planets revolved around it. Even the sun revolved around the earth rather than the other way around. Caesar is saying that all the stars in the heavens, which are all sparks and all fire, are in constant motion except one. That would be Polaris, the Northern Star, which is directly above the North Pole and therefore does not appear to move as the earth rotates. All the other stars appear to move with the earth's diurnal rotation and annual revolution around the sun. Caesar compares himself with the Northern Star in being immovable. He is superior to all other men in begin steadfast, determined, unshakable, strong, self-confident, and always correct in his judgments. He has never spoken this way before. He is becoming intoxicated with the prospect of being crowned king. Ironically, he is just a few steps away from being stabbed to death by the men he so despises.

He obviously has a very high opinion of himself. If he had lived he would not have been satisfied with becoming king. The next step would be to become emperor, and after that he would want to become a god. He would easily become declared a god by the senate because he owns the senate already and would solidify his ownership if he became ruler. His successor Octavius became a god and most of the emperors who followed Octavius also became gods by senate decree and had to be worshiped in Roman temples.

Shakespeare has waited to illustrate Julius Caesar's hubris until just before he is stabbed to death. This is dramatically effective and validates the conspirators' violence. Caesar would have become a tyrant if he had been allowed to live. That is what Brutus is afraid of and what he foresaw. In Act 2, Scene 1, Brutus thinks long and hard about leading the assassination attempt. If he had not agreed to participate, Caesar would probably have lived.

He would be crown'd:
How that might change his nature, there's the question.
It is the bright day that brings forth the adder
And that craves wary walking. Crown him? that;
And then, I grant, we put a sting in him
That at his will he may do danger with.
The abuse of greatness is when it disjoins
Remorse from power, and, to speak truth of Caesar,
I have not known when his affections sway'd
More than his reason. But 'tis a common proof
That lowliness is young ambition's ladder,
Whereto the climber-upward turns his face;
But when he once attains the upmost round,
He then unto the ladder turns his back,
Looks in the clouds, scorning the base degrees
By which he did ascend. So Caesar may;
Then, lest he may, prevent. And, since the quarrel
Will bear no color for the thing he is,
Fashion it thus, that what he is, augmented,
Would run to these and these extremities;
And therefore think him as a serpent's egg
Which hatch'd would as his kind grow mischievous,
And kill him in the shell.

It is significant that Brutus says the climber-upward "Looks in the clouds," because that is more or less what Caesar has been doing. He uses the stars as analogies with men in his speech in Act 3, Scene 1--but this is certainly not the first time that he has stood on his balcony at night and gazed up at the stars, planning to be there among them someday--and not just one of them but the principal one, the North Star.

Nicolaus Copernicus, who lived some 1400 years after Julius Caesar, established that the movements of the sun and stars were illusory. They appeared to move as they did because of the earth's rotation on its axis every twenty-four hours and its revolution around the sun every 365 days.

Why is Madame Losiel disconnected from her life at the beginning of "The Necklace"?

In Guy de Maupassant's short story "The Necklace" Madame Loisel is disconnected from a life which she finds common and mundane. Although she is "pretty and charming" she is restrained by the rigid class system of 19th century France. She longs for a different life. She wants all the comforts and trappings of the very wealthy. She is simply not satisfied with her middle class existence.

She's not poor. After all, she has her own maid, a hard working husband, and seemingly very few cares. Yet it is not enough. She spends her time daydreaming about all the things her middle class husband cannot afford. De Maupassant writes:

She would dream of silent chambers, draped with Oriental tapestries and lighted by tall bronze floor lamps, and of two handsome butlers in knee breeches, who, drowsy from the heavy warmth cast by the central stove, dozed in large overstuffed armchairs. 

One of the ultimate morals of the story is to be careful what you wish. When Madame Loisel's dream comes true and she does live the life of a wealthy woman for one beautiful evening and it ends up costing her that comfortable middle class life as she is plunged into poverty because of the loss of the necklace.