Describe the political innovations the 1787 Constitutional Convention developed for the new nation.

The political innovations developed at the Constitutional Convention centered on the concept of compromise. There were many issues that needed to be resolved in order to develop the new plan of government. One of those issues dealt with the structure of Congress. Large states wanted to have unequal representation in Congress. They wanted representation to be based on the population of a state. Small states wanted to have equal representation in Congress. They feared their...

The political innovations developed at the Constitutional Convention centered on the concept of compromise. There were many issues that needed to be resolved in order to develop the new plan of government. One of those issues dealt with the structure of Congress. Large states wanted to have unequal representation in Congress. They wanted representation to be based on the population of a state. Small states wanted to have equal representation in Congress. They feared their concerns would not be heard if representation in Congress was unequal. An agreement was made to have two houses of Congress. Representation would be unequal in the House of Representatives. It would be equal in the Senate.

Another compromise dealt with the issue regarding if slaves should be used in counting the state’s population. If slaves were counted, this would increase the population of a state, giving it more representatives in Congress. This would favor the South. A compromise was reached, called the Three-Fifths Compromise, in which every five slaves would count as three people.

Finally, there were differences of opinion regarding trade. An agreement was reached that allowed Congress to control trade. However, only imports could be taxed.

What is 'Waiting for Godot' by Samuel Beckett about?

This outstanding play by Samuel Beckett is "about" the desire (some would say "need") of all humans for a purpose and direction in their lives.  For those majority of us, the "purpose" of our lives is to love, honor, and obey a "deity," a "maker" who created us for a purpose, whether that purpose is known to us or not.  Like a physical invention (philosophers have used a paper cutter as an invention whose "need"...

This outstanding play by Samuel Beckett is "about" the desire (some would say "need") of all humans for a purpose and direction in their lives.  For those majority of us, the "purpose" of our lives is to love, honor, and obey a "deity," a "maker" who created us for a purpose, whether that purpose is known to us or not.  Like a physical invention (philosophers have used a paper cutter as an invention whose "need" or purpose came before its creation), the prevailing view is that -- we were invented.  Existentialists, however, suggest that our existence preceded our "essence," and that we "invent" a purpose by making choices.  Returning to the play, we realize that Gogo and Didi are hoping for, wishing for, waiting for Godot, a non-character who, if he would appear, would give them purpose, orders, directions (in both senses of the word.)  The play, then, follows the two universal characters through their daily lives while they wait, performing basically meaningless acts to "pass the time".  The impact of the play's message is made frighteningly clear when at the end of the play, this exchange -- "Let's go."  "Yes, let's go." -- is followed by the stage direction:  "They do not move."  In every good production, the audience is frozen in place for several minutes, because we, too, are "waiting for Godot," for purpose and meaning.  

Do you admire, despise, or pity Captain Ahab? Explain.

This is a great question, because it's easy to do all three, even during the course of a single chapter. However, I actually primarily pity Ahab, because I see him as a tragic, nearly Shakespearean, hero.

Herman Melville's Moby Dick was ahead of its time, as its exploration of existence was more closely aligned with the later tenets of Modernism than with the sensibilities of the 19th century. Overall, you can think of Moby Dick,...

This is a great question, because it's easy to do all three, even during the course of a single chapter. However, I actually primarily pity Ahab, because I see him as a tragic, nearly Shakespearean, hero.

Herman Melville's Moby Dick was ahead of its time, as its exploration of existence was more closely aligned with the later tenets of Modernism than with the sensibilities of the 19th century. Overall, you can think of Moby Dick, the White Whale, as a symbol of existential meaning. Actually, it would be more accurate to think of the whale as a symbol of existential meaninglessness, as the chapter "The Whiteness of the Whale" essentially examines Moby Dick's whiteness and proclaims it to be a symbol of the meaninglessness of life. As such, Ahab's quest is not just the absurd venture of a crazed and crippled sailor; rather, it's a depiction of humanity struggling against the meaninglessness of life. Ahab's pursuit of the whale is a symbol for the universal search for meaning in life, and the captain's ultimate demise is a reference to the impossibility of such a quest. Whether you agree with Melville's gloomy outlook or not, the fact remains that Ahab is a tragic figure, one who dies trying to find the purpose of existence. As such, I cannot help but pity Ahab, despite his craziness and his cruelty. 

What advice does Thoreau offer to his "fellows" about ownership of land and property?

Thoreau says that " . . . when the farmer has got his house he may not be the richer but the poorer for it, and it be the house that got him." In other words, he believes that owning property is actually detrimental to our happiness.

If a man buys a house, he must first work in order to be able to afford that house. Then, once he owns it, he must continue to...

Thoreau says that " . . . when the farmer has got his house he may not be the richer but the poorer for it, and it be the house that got him." In other words, he believes that owning property is actually detrimental to our happiness.

If a man buys a house, he must first work in order to be able to afford that house. Then, once he owns it, he must continue to work harder than he would otherwise need to in order to heat the house and furnish it. He must also care for the land around the house as well, something else that requires funds and additional work. The man will spend so much time working that he'll have hardly any time to pursue hobbies or other interests; he will have little time for himself because he will always be working in order to pay for and/or care for the things he owns. He becomes a slave to those things.

It would be better, then, for him not to own the house or the property because then he would be able to use his time for things that bring him pleasure rather than working.

`h(t) = log_5(4-t)^2` Find the derivative of the function

Derivative of a function h with respect to t is denoted as h'(t).

 The given function: `h(t) = log_5(4-t)^2` is in a form of a logarithmic function.

From the derivative for logarithmic functions, we follow:

`d/(dx)log_a(u) =((du)/(dx))/(u*ln(a)) `

By comparison: `log_5(4-t)^2` vs.`log_a(u)` we should let:

`a=5 ` and `u = (4-t)^2`

 For the derivative of u, recall the Chain Rule formula:

`d/(dx)(f(g(x)))= f'(g(x))*g'(x)`

Using `u=(4-t)^2` , we let:

`f(t) = t^2`

`g(t) = 4-t`...

Derivative of a function h with respect to t is denoted as h'(t).

 The given function: `h(t) = log_5(4-t)^2` is in a form of a logarithmic function.

From the derivative for logarithmic functions, we follow:

`d/(dx)log_a(u) =((du)/(dx))/(u*ln(a)) `

By comparison: `log_5(4-t)^2` vs.`log_a(u)` we should let:

`a=5 ` and `u = (4-t)^2`

 For the derivative of u, recall the Chain Rule formula:

`d/(dx)(f(g(x)))= f'(g(x))*g'(x)`

Using `u=(4-t)^2` , we let:

`f(t) = t^2`

`g(t) = 4-t` as the inner function

`f'(t)= 2t`

`f'(g(t))= 2*(4-t)`

`g'(t)= (-1)`

Following the Chain Rule formula, we get:

`d/(dx) (4-t)^2= 2 *(4-t)*(-1)`

`d/(dx) (4-t)^2= -2*(4-t)`

or

`(du)/(dx)=-2*(4-t)`

 Plug-in the values:

`u =(4-t)^2` ,     `a=5 `  ,  and `(du)/(dx)=-2*(4-t)`

 in the `d/(dx)log_a(u) =((du)/(dx))/(u*ln(a))` , we get:

`d/(dx) (log_5(4-t)^2) = ((-2)*(4-t))/((4-t)^2ln(5))`

Cancel out common factor (4-t):

`d/(dx) (log_5(4-t)^2) = -2/((4-t)ln(5))`

 or` h'(t)= -2/((4-t)ln(5))`

In the original "trolley problem," a train is hurtling down a track and you see that it is going to hit a group of five people; it will certainly...

Here, you will need to answer this question based on your own moral beliefs. The question is one that prompts you to explore your own moral sense, not to find the "right" answer.

On the most basic level, you should point out that there appears to be a simple calculus here of one versus five lives. Thus on the surface, choosing to save the five lives is the logical choice. 

Next, you might talk about...

Here, you will need to answer this question based on your own moral beliefs. The question is one that prompts you to explore your own moral sense, not to find the "right" answer.

On the most basic level, you should point out that there appears to be a simple calculus here of one versus five lives. Thus on the surface, choosing to save the five lives is the logical choice. 

Next, you might talk about your beliefs of personal culpability, asking yourself if your own faith or moral tradition treats allowing death by inaction as less culpable than actively killing someone. In this case, acting makes you a killer but refraining from action leaves you as a bystander. Under your own moral code, there may be some distinction in how you evaluate those two positions.

The next issue you should raise as you develop your own moral stance is the problem of decontextualization. In the first variant of the problem, there is a clear binary choice -- a switch is set to one of two possible positions. In the second problem, our real world experience would suggest that there is no way we could know if the fat man would actually stop the trolley and no way we could assume that he would unresistingly let himself be pushed and land in precisely the right place at the right time. This means that as you discuss the fat man variant, you might critique the possibility of moral judgment without context. 

How would the USA be different without the purchase of the Louisiana territory?

It is always difficult to answer counterfactual questions, because we can't know what would have happened. Maybe the best way to begin to answer this question is to point out a few things that the Louisiana Purchase did. First, it doubled the size of the United States, creating vast new swaths of land to be eventually settled and exploited for resources. Second, it opened the Mississippi River to navigation by American ships, which enabled the...

It is always difficult to answer counterfactual questions, because we can't know what would have happened. Maybe the best way to begin to answer this question is to point out a few things that the Louisiana Purchase did. First, it doubled the size of the United States, creating vast new swaths of land to be eventually settled and exploited for resources. Second, it opened the Mississippi River to navigation by American ships, which enabled the rapid settlement of the Northwest. This was probably the most significant effect of the Purchase. It eventually brought the United States into conflict with the various native peoples who inhabited the region. So what would have happened if the United States had not received the Louisiana Purchase? It is quite likely, especially given the importance of control of the Mississippi to the American economy, that the country would have eventually gained New Orleans, at least, by other diplomatic means, possibly including war. After the United States gained control of the Mississippi, there was really not much of an advantage to any European power in possessing the region between that region and the Rocky Mountains. So the Louisiana Purchase sped up a process that probably would have taken longer (but still would likely have happened) in any case.