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The Speluncean Explorers; A Case for Humanity
The judge’s opinion that I agree
with most strongly in the fictitious Case of the Speluncean Explorers,
is that of Justice Foster. Foster is able to see beyond the “letter
of the law” to encompass the human effects of this decision. The
laws of our Constitution and our Commonwealth were written by fallible
men, for fallible men; which automatically leaves it open for error and
interpretation.
I do not feel that the law should compel that these
explorers be convicted as murderers. Whether or not they are pardoned
is not as significant an issue as whether or not they should be convicted
in the first place. While theoretically, laws are to be “set in
stone”, realistically, the limitations of human insight dictate
that there must be exceptions to every rule. For this reason, I feel that
Judge Keen’s argument that the explorers should be convicted because
he feels it is the sole task of a judge to determine whether or not a
statute was violated, is far too simplistic for such a complex case.
Furthermore, the purpose of any criminal statute
is not merely to punish a particular crime but to implement justice, which
is an objective, not an absolute concept. While the statute in question
must offer potential murder victims the protective power of the state,
this does not intrinsically translate into meaning that Whetmore's death
must be avenged. Technically, the statute N.C.S.A. (N.S.) § 12-A,
which declares "whoever shall willfully take the life of another
shall be punished by death," was violated. However Keen and those
who agree with him are treating this case as though they were calling
a penalty on a football field. In such a game, the rules are strictly
defined and the breaking of those rules automatically dictates a particular
penalty, or punishment. However what these judges are failing to take
into consideration is that life and justice are not games in that outcomes
are far more weighty than a trophy or another notch on one's belt.
If life is to be treated like a game, and human
beings are the pawns, then we are being controlled by the hands of the
few who have the power to do so. Such a system is not based on justice
but on domination. Those who make the laws and those who enforce them
are provided supreme powers in our legal system, but they are not afforded
the power of God. I do not mean this in a religious or moral sense, but
in a realistic one. No law is absolute because no lawmaker is infallible.
Moreover, it is impossible for lawmakers to anticipate every possible
situation that could come under question. Only a perfect being would be
able to achieve such tasks, and as we all know, humans are far from perfect.
The fact is, if laws were absolute; not open to
interpretation and not considered capable of inaccuracy or miscalculation,
then there would be no need for lawyers, jurors or any legal system whatsoever.
Computers could decide if a statute had been violated simply by examining
the facts. In the Case of the Speluncean Explorers, a computer would undeniably
equate the facts with a guilty sentence, and an automatic execution. However
to think that our justice system has been reduced to such cold and clerical
decision making, as Judge Keen suggests, then the legal profession, and
perhaps the entire human race is bound for an inevitable and rapid demise.
Newton vs. Leibniz; The Calculus Controversy
Like most discoveries, calculus was the culmination
of centuries of work rather than an instant epiphany. Mathematicians all
over the world contributed to its development, but the two most recognized
discoverers of calculus are Isaac Newton and Gottfried Wilhelm Leibniz.
Although the credit is currently given to both men, there was a time when
the debate over which of them truly deserved the recognition was both
heated and widespread.
As the renowned author of Principia (1687) as well
as a host of equally esteemed published works, it appears that Newton
not only went much further in exploring the applications of calculus than
Leibniz did, but he also ventured down a different road. Leibniz and Newton
had very different views of calculus in that Newton’s was based
on limits and concrete reality, while Leibniz focused more on the infinite
and the abstract (Struik, 1948). However, regardless of the divergent
paths these two scholars chose to venture down, the question of who took
the first step remained the primary issue of debate.
Unaware that Newton was reported to have discovered
similar methods, Leibniz discovered “his” calculus in Paris
between 1673 and 1676 (Ball, 1908). By 1676, Leibniz realized that he
was onto something “big”; he just didn’t realize that
Newton was on to the same big discovery because Newton was remaining somewhat
tight lipped about his breakthroughs. In fact, it was actually the delayed
publication of Newton’s findings that caused the entire controversy.
Leibniz published the first account of differential calculus in 1684 and
then published the explanation of integral calculus in 1686 (Boyer, 1968).
Newton did not publish his findings until 1687.
Yet evidence shows that Newton discovered his theories of fluxional calculus
in 1665 and 1666, after having studied the work of other mathematicians
such as Barrows and Wallis (Struik, 1948).. Evidence also shows that Newton
was the first to establish the general method called the "theory
of fluxions" was the first to state the fundamental theorem of calculus
and was also the first to explore applications of both integration and
differentiation in a single work (Struik, 1948). However, since Leibniz
was the first to publish a dissertation on calculus, he was given the
total credit for the discovery for a number of years. This later led,
of course, to accusations of plagiarism being hurled relentlessly in the
direction of Leibniz.
There was speculation that Leibniz may have gleaned
some of his insights from two of Newton's manuscripts on fluxions, and
that that is what sparked his understanding of calculus. Many believed
that Leibniz used Newton's unpublished ideas, created a new notation and
then published it as his own, which would obviously constitute plagiarism.
The rumor that Leibniz may have seen some of Newton's manuscripts left
little doubt in most people’s minds as to whether or not Leibniz
arrived at his conclusions independently. The rumor was, after all, believable
because Newton had admittedly bounced his ideas off a handful of colleagues,
some of who were also in close contact with Leibniz (Boyer, 1968).
It is also known that Leibniz and Newton corresponded
by letter quite regularly, and they most often discussed the subject of
mathematics (Boyer, 1968). In fact, Newton first described his methods,
formulas and concepts of calculus, including his binomial theorem, fluxions
and tangents, in letters he wrote to Leibniz (Ball, 1908). However an
examination of Leibniz' unpublished manuscripts provided evidence that
despite his correspondence with Newton, he had come to his own conclusions
about calculus already. The letters may then, have merely helped Leibniz
to expand upon his own initial ideas.
The question of the date at which these extracts
were made is therefore all important. It is known that a copy of Newton's
manuscript had been sent to Tschirnhausen in May, 1675, and as in that
year he and Leibniz were engaged together on a piece of work, it is not
impossible that these extracts were made then. It is also possible that
they may have been made in 1676, for Leibniz discussed the question of
analysis by infinite series with Collins and Oldenburg in that year, and
it is a priori probable that they would have then shown him the manuscript
of Newton on that subject, a copy of which was possessed by one or both
of them. On the other hand it may be supposed that Leibniz made the extracts
from the printed copy in or after 1704. Leibniz shortly before his death
admitted in a letter to Conti that in 1676 Collins had shown him some
Newtonian papers, but implied that they were of little or no value, -
presumably he referred to Newton's letters of June 13 and Oct. 24, 1676,
and to the letter of Dec. 10, 1672, on the method of tangents, extracts
from which accompanied the letter of June 13, - but it is remarkable that,
on the receipt of these letters, Leibniz should have made no further inquiries,
unless he was already aware from other sources of the method followed
by Newton (Ball, 1908).
While Newton had many allies rallying in his favor,
Leibniz had only one: John Bernoulli, who in a letter, tried to cast doubt
upon Newton’s credibility. When Bernoulli was later asked to comment
on the letter, he denied ever writing it, which caused Newton to aver:
I have never grasped at fame among foreign nations, but I am very desirous
to preserve my character for honesty, which the author of that epistle,
as if by the authority of a great judge, had endeavored to wrest from
me. Now that I am old, I have little pleasure in mathematical studies,
and I have never tried to propagate my opinions over the world, but I
have rather taken care not to involve myself in disputes on account of
them (Ball, 1908).
In 1715, just a year before Leibniz death, the Royal
Society handed down their verdict crediting Sir Isaac Newton with the
discovery of calculus. It was also stated that Leibniz was guilty of plagiarism
because of certain letters he was supposed to have seen (Ball, 1908).
It later became known that these accusations were false, and both men
were then given credit, but not until after Leibniz had already died.
In fact, the controversy over who really deserved the credit for discovering
calculus continued to rage on long after Leibniz’ death in 1716
(Struik, 1948). Newton and his associates even tried to get the ambassadors
of the London diplomatic corps to review his old manuscripts and letters,
in the hopes that they would endorse the finding of the Royal Society
that Leibniz had plagiarized his findings regarding calculus. Another
argument on the side promoting the idea of Leibniz as a plagiarist was
the fact that he used an alternate set of symbols. Leibniz specifically
set out to develop a more meticulous notation system than Newton’s,
and he developed the integral sign ( I ) and the 'd' sign, which are still
used today (O’Connor, 1996) However this action was argued by many
to be merely a way for Leibniz to “cover his tracks” so as
not to get accused of stealing Newton’s material (Boyer, 1968).
The fact that the method was more efficient was considered to be an ancillary
benefit. The fact is that Leibniz sent letters to Newton outlining his
own presentation of his own methods, and these letters focused quite stringently
upon the subject of tangents and curves. Because Newton had been approaching
calculus primarily in regards to its applications to physics, he purported
curves to be the creation of the motion of points while perceiving velocity
to be the primary derivative. Conversely, the calculus of Leibniz was
applied more to discoveries in geometry made by scholars such as Descartes
and Pascal. Since "Leibniz' approach was geometrical," the notation
of the differential calculus and many of the general rules for calculating
derivatives are still used today, while Newton's approach, which has in
many aspects, fallen by the wayside, was "primarily cinematical"
(Struik, 1948).
Despite the ruling of the Royal Society, mathematics
throughout the eighteenth century was typified by an elaboration of the
differential and integral calculus in which mathematicians generally discarded
Newton's fluxional calculus in favor of the new methods presented by Leibniz.
Nevertheless, in England, the controversy was viewed as an attempt to
pilfer Newton's glory simply because of international egotism. Consequently,
as a matter of “national pride”, England refused to teach
anything but Newton’s discoveries of geometrical and fluxional methods
for over a century. So while other countries were integrating various
findings that occurred over time and were progressing in their discoveries,
England remained essentially stagnant in the realm of mathematic discovery.
In fact, it wasn’t until 1820 that England finally agreed to recognize
the work of mathematicians from any other countries (Ball, 1908).
With modern controversies covering such volatile
topics as abortion and gun control, a debate over who discovered calculus
may seem somewhat trivial by contemporary standards. However at the time,
this was a serious issue that not only involved matters of mathematical
discovery but also matters of national pride and allegiance. What is important
to keep in perspective is that no matter who actually discovered calculus
first, both Newton and Leibniz made great contributions to the advancement
of mathematical processes, and both deserve credit for that.
Works Cited
Ball, Rouse. A Short Account of the History of Mathematics'.
4th edition, 1908
Boyer, Carl. A History of Mathematics: 2nd Edition.
New York, New York: John Wiley and Sons, 1968
O'Connor, John J. The Rise of Calculus. St Andrews,
Scotland, 1996.
Struik, Dirk. A Concise History of Mathematics.
New York, New York: Dover Publications, Inc., 1948
With the Implementation of a State Lottery, North Carolina Could Write
Its Own Ticket
For many conservatives, the image of a state lottery
conjures up pictures of seedy criminals, gambling addicts and mothers
spending all of their kids' food money on tickets. In reality, there is
no way something as harmless as a state lottery could suddenly turn good
parents into bad ones and nice neighborhoods into slums. The idea is ludicrous.
Proceeds from a state lottery would be channeled into schools and college
scholarships; the money garnished would be used to build a better future,
not perpetuate a worse one. Substantial funds would go toward sending
students with a B average or better to college, and any monies remaining
would go to technology and capital needs in public schools.
A lottery in North Carolina would generate in the
neighborhood of $1 billion a year. Even after all the prize money is paid
and the operating costs are covered, the state would still net approximately
$300 million. (Nilson, Feb.1999). While these figures are impressive,
some experts worry that the state might become too dependent on lottery
income and that if something were to happen to discontinue the lottery,
the state would be in a very deep financial hole. This argument, however,
is very weak, considering that states with lotteries have steadily and
continually flourished and the popularity of the game is not even slightly
beginning to wane. In addition, although the law does not allow other
state accounts to be used to make up any shortfall in lottery funds, it
does provide for a reserve fund to be created from any surplus lottery
revenues.
Critics also claim that implementing a state lottery
in North Carolina would act as a sort of Robin Hood in reverse; taking
from the poor and filling the silk-lined pockets of the rich. In Virginia,
the state which reaps most of the benefits from North Carolina's non-lottery
status, the median family income for lottery players in 1997 was $29,000.
Families that had a child entering the University of North Carolina in
1997 however had a median income of $55,000. For freshmen at UNC-Chapel
Hill, the median family income was $75,000. This leads some anti-lottery
advocates to assume that if a lottery were implemented in North Carolina,
the lower income families would be spending their paychecks trying to
win the lottery, when in reality all they will be doing is helping send
rich kids to college (Nilson, Jan.1999). This argument is not only weak
but it stereotypes entire classes of people while ignoring the fact that
a kid attending college is a good thing, no matter what type of background
he comes from.
Those who oppose the idea of North Carolina establishing
a lottery system base most of their arguments on the “burden of
the poor”, or the assumption that lower-income families and individuals
will not be able to play the lottery responsibly. Once again, there is
blatant prejudicial stereotyping going on here, and it is insulting to
many people that the government thinks that the masses are either too
stupid or too undisciplined to refrain from going overboard with their
lottery spending. According to an article in the Atlanta Journal-Constitution
“ those earning less than $24,000 a year accounted for less than
9 percent of lottery players, and those earning more than $75,000 accounted
for only 24 percent”.(Nilson, Jan. 1999)
Gambling addiction, just like alcohol and drug addiction,
can strike the rich as easily as the poor. Gambler’s Anonymous’
philosophies are congruent with those of Alcoholics Anonymous in that
they both describe addiction as a disease with which the victim is born;
not as a culmination of environmental and societal influences. Therefore,
the lottery is a choice, not a “burden”. Nobody has to play
the lottery, and those who feel they have to can come from any social
class or economic background. What right does the government have to dictate
how anyone should spend their money, and what right does it have to complain
about generating billions of dollars to further the education of our youth?
Senator Bill Martin, a staunch lottery supporter,
strongly objects to some opponents' claims that lotteries prey on the
poor. "It is a very paternalistic argument saying that folks that
have less money don't know how to spend it and therefore we should stop
them from doing it," Martin said. "Each poll that I've seen
suggests that anywhere from 65 percent to 75 percent of North Carolinians
want the opportunity to vote on it. ... I think that warrants some strong
consideration." (Heath, 1999).
Even when we put all of these issues and arguments
aside, the fact remains that if people want to play the lottery, they
will. Being forced to cross state lines and donate all of the proceeds
to another state is not going to stop anyone who really wants to play.
A substantial number North Carolinians are already playing the lottery
in other states, spending an estimated $80 million a year on games in
Virginia. A North Carolina lottery would reap tremendous financial benefits
by keeping its customers at home. This is something with which 37 other
states have already come to terms. So why is North Carolina still holding
out against the majority? Well, with vociferous anti-lottery representatives
like Bladen County Democrat, Edd Nye spreading their message so vehemently,
it is easy to see why some key players are reluctant to proceed. Nye defends
his position by claiming that it is “bad public policy for the state
to be in the gambling business.” However the lottery can hardly
be equated with state-run casinos. Despite overwhelming statistics to
the contrary, Nye is also not convinced that a lottery would generate
enough revenue to justify its existence. “If the state needs money,
lawmakers should raise it in other ways”. That’s all well
and good, but Nye has yet to offer a comparable alternative.
More important that what the lawmakers want is what
the people want. A poll taken last July by The Charlotte Observer showed
that 68 percent of North Carolinians were in favor of implementing a state
lottery. A year ago, legislators were debating whether or not to allow
the voters to decide if a lottery should be established in North Carolina.
However, many legislators are not convinced that voters will see the lottery
on the ballot any time soon. After all, the lottery bill has yet to go
to a vote in the House, despite the fact that measures have passed the
Senate on three separate occasions in the late eighties and early nineties
(Heath, 1999).
Whether it happens now or later, chances are North
Carolina will eventually follow the path the majority of the country has
chosen and implement a state lottery. Once opponents are able to see for
themselves that the lottery does not inspire moral corruption and societal
decay, they might even stand in line to buy a few tickets themselves.
Representative David Redwine, an Ocean Isle Beach Democrat summed the
truth of the matter up beautifully in the following statement: Most people
I talk to think the lottery is a game. It's like bingo. It's not full
of glitter and alcohol and slot machines going ding, ding, ding. You can
go to McDonald's and scratch off a little thing and win french fries;
what's the difference? (Heath, 1999).
When you look it that way, it is almost impossible
to see the lottery as the “demon” some make it out to be.
The fact is, the lottery is just a harmless game which generates funds
for education and allows people the joy of knowing they could be just
a dollar away from realizing their wildest dreams.
WORKS CITED
Heath, Jena. "Lottery Bill Unlikely in 2000",
North Carolina News & Observer, March 28, 1999.
Nilson, Kim. "Dueling lottery bills fuel debate".
The Fayetteville Oberver, Thursday, Feb. 18, 1999.
Nilson, Kim. "Lottery looks like ‘go’".
The Fayetteville Oberver, Wednesday, Jan. 27, 1999
Death of A Salesman; How Willy Loman Sold Himself Short
Willy Loman, the central character in Arthur Miller’s
Death of a Salesman, is a man whose fall from the top of the capitalistic
totem pole results in a resounding crash, both literally and metaphorically.
As a man immersed in the memories of the past and controlled by his fears
of the future, Willy Loman views himself as a victim of bad luck, bearing
little blame for his interminable pitfalls. However, in my assessment,
it was not an ill-fated destiny that drove Willy to devastate his own
life as well as the lives of those he loved; it was his distorted set
of values.
If Willy Loman had valued acceptance over popularity,
individuality over conformity and devotion over materialism, he would
have considered himself rich in his later years, feeling grateful to have
a wife and two sons that loved him; and that would have been enough. Yet
because he was unable to appreciate the important things in life, he ultimately
opted for death instead, subsequently stealing the opportunity for true
happiness away from those who had managed to find their own versions of
peace prior to his selfish act.
What is truly ironic here is that the act of suicide
is Willy’s warped way of showing Biff that he loves him, yet he
never once comprehends the notion that his acceptance and understanding
would have benefited his son a thousand times more than any insurance
policy ever could. Even if the Loman family had succeeded in acquiring
the insurance money, it would not have eased their grief. Thus Willy’s
distorted perceptions of reality and what truly mattered to his family
blinded him to the things that could have made him and those he loved
exceedingly happy. Spouting off rhetoric such as “Riding on a smile
and a shoeshine,” and “. . . personality always wins the day.”
(p. 65) did little to convince Willy or those around him that happiness
is that easily obtained. After all, he had not managed to obtain it and
neither had his sons. Yet if Willy had loved his sons unconditionally
instead of doling out his love in accordance with his their successes,
he might not have felt like such a failure himself, because if nothing
else, he would have been a success as a father.
Willy Loman could honestly take no pride in the
values he had instilled in his two sons. Case in point: As he preaches
that likeability, above all, is the ultimate goal of mankind, he neglects
to qualify his statements by adding that one should be liked for being
himself, not by adapting like a chameleon to whatever the surrounding
circumstances dictate. The following passage superbly demonstrates Willy’s
twisted perceptions of what it means to succeed in life.
"WILLY: That's just what I mean, Bernard can
get the best marks in school, y'understand, but when he gets out in the
business world, y'understand, you are going to be five times ahead of
him. That's why I thank Almighty God you're both built like Adonises.
Because the men who makes an appearance in the business world, the man
who creates personal interest, is the man who gets ahead. Be liked and
you will never want. You take me for instance, I never have to wait in
line to see a buyer. 'Willy Loman is here!' That's all they have to know,
and I go right through" (p. 33).
Perhaps Willy’s philosophy that charm, popularity
and physical appeal are the catalysts that fling open the doors of opportunity
is rooted in his feelings of inadequacy over his own deficiencies in these
arenas. After all, Willy has built his entire life around the tenet that
“The only thing you got in this world is what you can sell.”
(p. 97), and his failure to sustain his beliefs has weighed unbearably
heavy on his sense of personal failure. If Willy had been true to himself
instead of fretting constantly over the image he and his family were portraying
to society, he might have realized that true success is measured in the
ability to contribute positively to one’s environment and pass on
admirable traits to future generations. Success is not, as Willy perceives,
measured by the number of acquaintances an individual has acquired or
the balance of his bankbook. Had he realized this before committing suicide,
Willy Loman may have been able to not only salvage, but also reconstruct
his family and his life to a point where they would all have been able
to truly appreciate life and the non-superficial pleasures it has to offer.
When Willy complains early on in the play, “The
street is lined with cars. There’s not a breath of fresh air…The
grass don’t grow . . . you can’t raise a carrot in the back
yard.” (p. 17), he is basically demonstrating how barren and unfruitful
he feels his own life has become. Yet what he fails to realize is that
there is beauty all around us if we just now where to look and how to
view it. Had Willy been able to grasp what his son Biff was trying to
tell him about the true nature of happiness; if he had believed his son
that his actions were not perpetrated out of spite, but out of the longing
for a sense of self that Willy had never given him, perhaps Willy Loman
would not have sold himself or his family short. Perhaps instead, he would
had the strength of character to commendably walk away from the biggest
sales gimmick of all time; The American Dream.
WORKS CITED
Arthur Miller, Death of A Salesman, edition: October 6, 1998, Penguin
USA
How Plato Defined and Redefined Justice
Plato described justice differently than most standard
definitions. To Plato, justice meant carrying out one’s duty to
one’s station, i.e. workers work, auxiliaries guard, and guardians
rule. Under this premise, if lying is part of one’s job, it is only
just if one lies. The reason the lie is noble is because it is for a noble
cause: the good of the people.
Plato raised several questions that are still at
the heart of many modern conflicts and heated debates. What is justice?
What is goodness? Does a lack of goodness stem from a lack of knowledge
about justice? Plato examined these questions as separate aspects of a
single theme. He then used his answers to come up with his own rendition
of the perfect existence. Plato’s version of the ideal society was
one in which all people would trust that their position in life was just,
and would carry out the responsibilities of that position without protest.
He believed that the power of wisdom is possessed most abundantly in kings
and philosophers, and that others should accept the authority of those
wise and morally superior leaders.
While there appears to be a logical chain of reasoning
to Plato’s suppositions, there is a chasm of doubt when it comes
to the workability of his plan. It seems as if he is promoting an elitist,
dictatorial society in which the only wise leaders are those who happen
to be what he happens to be; a philosopher.
It is also against the grain of human nature to
accept direction without question, which is a problem Plato was well aware
of, but it is a problem he did not resolve.
Of course, while it may seem that Plato was calling
for his own personal version of utopia, a strong argument can be made
that Plato was in fact pointing out the weaknesses involved with just
such a society. Irony is after all, a remarkably powerful teacher.
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