User:Brianahs86/sandbox

Brian Ahn Fatemeh Yarahmadi Math 22

Answer to the following questions: a)	What is a graph?
 * Formal definition of graph is a finite vertex set V and edge set E containing size 2 subsets of V. G = (V, E)

b)	Write one example of a graph with vertices and edges
 * G = (V, E) where V = {1, 2, 3, 4} E = { (1, 2), (1, 3), (1, 4), (2, 3) }

c)	What is the degree of a vertex?
 * The number of vertices adjacent to vertex v, denoted d(v)

d)	Define “walk” and one example of a walk
 * A walk is a sequence of adjacent vertices (repetition allowed).

For instance, G = (V, E) where V = {1, 2, 3, 4} and E = { (1, 2), (1, 3), (1, 4), (2, 3) } walk can be written as W = 1, 4, 1, 2, 3 e)	Define a connected graph and write one example of a connected graph
 * A graph is connected, if for all vertices x and y, there is a path from x to y.

For instance, G = (V, E) where V = {1, 2, 3, 4} and E = { (1, 2), (1, 3), (1, 4), (2, 3) } f)	Define a trail and one example of a trail
 * A trail is a walk with no repeated edges.

For instance, G = (V, E) where V = {1, 2, 3, 4} and E = { (1, 2), (1, 3), (1, 4), (2, 3), (3, 4)} T = 3, 2, 1, 3, 4 g)	Define an “Eulerian” graph and one example of “Eulerian” graph
 * A graph (or multigraph) G is Eulerian if it is connected and G contains a closed trail that uses every edge. In other word, if a graph G is connected and every vertex has even degree, then G is Eulerian. Every Eulerian graph is drawable if and only if it begins and ends at the same point.

For instance, G = (V, E) where V = {1, 2, 3, 4, 5} and E = { (1, 2), (1, 3), (1, 4), (2, 5), (3, 5), (4, 5), (3, 4), (2, 4) } it is drawable, but cannot ends at the starting point. So, it is not a Eulerian. For instance, G = (V, E) where V = {1, 2, 3, 4} and E = { (1, 2), (2, 3), (3, 4), (1, 4) } it is drawable, and starting point is the same as the end point. So, it is a Eulerian. h)	Define an “Hamiltonian” graph and one example of “Hamiltonian” graph
 * A graph is Hamiltonian if it contains a cycle that goes through every vertex.

For instance, G = (V, E) where V = {1, 2, 3, 4, 5} and E = { (1, 2), (1, 3), (1, 4), (2, 5), (3, 5), (4, 5), (2, 3), (3, 4) } it is a Hamiltonian graph since it contains the cycle that visits every vertex exactly once, and then get back to the started vertex.

Pros and Cons – Stanley Milgram

I was researching about one of Milgram’s works, six degrees of separation. However, I was being more interested about his life since he is the one who accomplished one of the most important graph theories in the world, and he was both a mathematician and philosopher, in my perspective view. I believe many of famous mathematicians were not only good at mathematics, but also good at understanding of philosophy. I have researched about his life and read a book to understand about his life. Below is the result from my studies.

•	Life (Lifetime/Career) -	Stanley Milgram was born in New York in 1933, and he graduated from Queens university in 1954. He majored in politics, but he was interested in psychology and took a summer semester psychology course to enter Harvard’s Ph.D. in Psychology. Then, under the guidance of a renowned psychologist Gordon Allport, he received his doctorate by writing a thesis on human obedience to discipline. Later, at Princeton University in New Jersey, he conducted several experiments related to “Asch conformity experiments” with Solomon Asch. Milgram has also studied other areas, such as the reason why people using public transportation yield their seats, “the six-degrees of separation theory,” that everyone in the world is connected when only six people pass, human aggression, and non-verbal communication. He also produced documentary films. There are ‘Obedience’, which deals with experiments conducted at Yale University, and ‘The City and the Self’, which deals with the effects of urban life on human behavior. Thomas Blass, an American social psychologist, Holocaust survivor, and professor emeritus of psychology at the University of Maryland, wrote ‘The Man Who Shocked the World: The Life and Legacy of Stanley Milgram’ in 2004. Stanley Milgram died in New York City in 1984.

•	Analects -	“Death camps and gas chambers were built, where bodies were poured out every day as if producing products. This inhuman policy may have come from one person’s head at first, but it could be implemented on a large scale because many people obeyed the order.”

-	“People are angry. They act in hate and explode anger. But it is different here. Something much more dangerous is revealed. It is the ability to give up each person’s personality. Each unique personality seems to have melted into a large institutional structure.”

•	Overview -	In 1961 and 1962, one of the leading psychological experiments in human history was conducted at Yale University. Researchers introduced the experiment to volunteers as a study of memory and learning. One of the two test participants with white gown, who participated in the experiment, played the role of a ‘teacher’ and the other played the role of a ‘leaner’. The learner who tied to a chair with a string had to memorize the words written on the paper. If the learner cannot memorize the words, the teacher applies a weak electric shock to the learner. Whenever the learner spoke the word incorrectly, the teacher increased the voltage slightly, following the direction of the experiment supervisor. The learner squeaked at first and then screamed more and more painfully as the voltage increased. The participant in the role of the teacher did not know that electricity did not actually flow through the electric shock device connected to the learner. Participants in the role of learners played acting as a painful without actually being painful. The focus of this experiment was not on the leaners, victims, but on the reaction of teachers pressing the voltage button. It was about ‘how will the participant in the role of the teacher cope with experiments that are putting more and more pain on humans in defenseless situations?’. This experiment is one of the most famous experiments in the history of psychology. What does this experiment mean?

•	The most famous experiment in the history of psychology -	Milgram asked many people to predict the results of the experiment before conducting the experiment. Most people expected that the teacher would immediately give up the experiment when the electric shocked learner made the first painful sound. It is only an experiment, so there is no reason to rase the voltage ignoring the painful learner’s needs. Milgram’s thoughts were the same. But how was reality? Most of the participants in the role of the teacher were under tremendous strees and thought that they should not suffer anymore. Then, logically thinking, the next step is that the teacher must force the experiment supervisor to stop the experiment. However, in reality, it did not go in that way. Most of the teachers continued to increase their electric shock little by little at the command of the supervisor. According to Milgram, “After all, the highest voltage was passed.” As they struggled to ignore the learner’s plea to scream out loud.

•	The normality of evil -	Milgram’s experiments have been controversial for a while. Many people refused to accept the fact that normal human acted like this. Many scientists have tried to find the formal loopholes in this experiment. However, the results were the same in other experiments repeated all over the world. The results of this experiment shocked people. People wanted to believe that those who participated in Milgram’s experiments were sadistic and unusual. However, he emphasized that the people of various classes and professions who participated in his experiments were extremely normal, but were placed in very unique situations. Then, why did not the participants who had to give pain to others give up the experiment? Milgram says that most of them knew that their actions were not right. They did not want to apply an electric shock to the learners. This was especially true when learners began to refuse shock. Nonetheless, despite the thought that the experiment was cruel and nonsense, most of them did not escape the experiment. In doing so, they justified their actions by creating the following defense mechanisms.

a)	Focus on the scientific side of the experiment. Everyone has a desire to demonstrate abilities in their work. Therefore, succession of the experiment is much more important than the well-being of the participants.

b)	The ethical responsibility for the experiment is passed on to the supervisor responsible for the experiment. This is in line with the defensive attitude of “I just followed orders”, which is common in war crimes trials. Ethical responsibility or conscience for victims translates into determination to satisfy the commander or leader.

c)	It cannot be helped if it is for a big purpose or plan. If soldiers from past wars fought for religious or political ideology, Milgram’s experimental participants had a scientific justification.

d)	Ignore learner values. Learners were treated as “It is cheap to be punished because they are too stupid to memorize these simple words”. Ignoring intelligence or personality is a common method used by dictators to order to get rid of certain groups of people. “They have no value, and they don’t care if they disappear from the world. If they disappear, the world will be a better place to live”. Milgram analyzed that more shocking than the fact that the participants’ moral consciousness disappeared is they analyzed that they were adapted to a new environment. Participants felt more obliged and obedient to those who ordered them than those who were harmed by them. Participants did not give up on the experiment themselves. Surprisingly, it was considered as rude to disobey the order of the experiment’s supervisor. It was a violation of the original promise to voluntarily participate in the experiment and refuse to experiment in the middle. The desire to satisfy the authority was stronger than the ethical conscience of the screaming victims, according to the experiment. Even in the middle of the experiment, the teachers were quite polite. Milgram described a participant as follows. “He said he was talking about the same way as he was chatting with drinking a cup of tea, even though he thought he was killing someone”.

•	More terrifying than remorse, ‘Being Separation’ -	Milgram analyzed that human nature, subject to authority, evolved to survive. All human work proceeds according to the hierarchical hierarchy between leaders and followers. Human beings as a community are reluctant to bounce alone. Even more painful than a remorse for harming another unprotected person is the fear of being alone. The natural will, which is not allowed to harm others, is completely different within the social hierarchy. Individual human beings are responsible for everything they do and think spontaneously. However, human beings belonging to a system or class transfer their responsibilities to someone else. From then on, humans give up being themselves and act as “agents” for someone else or something else.

•	Individual to agent -	Milgram was influenced by Nazis' notorious Lieutenant Colonel Adolf Eichmann. Eichmann obeyed Hitler's orders and killed six million Jews. Milgram's experiment confirms Arendt's 'normality of evil' as a fact. Humans are not cruel by nature, but they can be cruel enough at the command of authority.

•	Objection -	Then, who is disobedient to authority? Most of those who participated in Milgram's experiments felt that they had to be faithful to the experiments and supervisors. However, very few of the participants did not think so, rather than the authoritative system, they thought of the person suffering from the chair. Milgram said there was a big difference between pointing out the injustice of the experiment and actually rejecting it. The inadequacy of the experiment was felt by most participants. Rejecting the experiment, however, is a clear difference made by a small group of people with ethical and moral backgrounds who disobey authority. Milgram accuses us that our culture and society only teach us how to obey authority, but not how to disobey morally deserving authority.

Work Cited:

“Thomas Blass.” Wikipedia, Wikimedia Foundation, 1 Apr. 2019, en.wikipedia.org/wiki/Thomas_Blass.

Milgram, Stanley. Obedience to Authority: an Experimental View. Harper Perennial Modern Thought, 2019.

Fessler, Leah. “Researchers Replicated a Notorious Social Experiment That Claimed to Explain the Rise of Fascism.” Quartz, Quartz, 15 Mar. 2017, qz.com/932110/researchers-have-replicated-a-notorious-social-experiment-that-claimed-to-explain-the-rise-of-fascism/.

Cherry, Kendra. “A Brief Biography of Social Psychologist Stanley Milgram.” Verywell Mind, 9 Apr. 2020, www.verywellmind.com/stanley-milgram-biography-2795532.

Stanley Milgram: His Life and Work, www.mtholyoke.edu/~apkokot/MilgramBio.htm.