Marriage, the official act of forming a family, is a civil right for homo and heterosexual couples alike

Same-sex marriage is a controversial subject. Religious dogmas, the tendency to follow social norms, phobias born out of ignorance, and general difficulty for heterosexual majority to imagine a homosexual life are but a few of the pitfalls that cause confusion when thinking about this subject. Let us propose a teleological argument that puts homosexual marriage on equal footing with traditional marriage between a man and a woman. Once we arrive at this state of equality between the two ideas, it is easy to join Congressman John Lewis in declaring that segregation of same-sex couples is discriminatory and thus not permissible in our post-civil-rights era .

Even though wanting to belong to a group that provides mutual benefits is a natural tendency for humankind, the social animal, all cultures have reserved a specific distinction for marriage. The widest definition of marriage is an officially recognized union that forms a family. This obligates us to define family. Let us examine the definition of family by looking at its form and its function. 

The popular image of a father, mother and children as a family is recognizable across the world. Even the U.S. Census Bureau makes a distinction between a family and a household. This classic definition based on the work of anthropologist like George P. Murdock from first half of the nineteenth century is not the conclusive definition of family form today . Sales teams, military units, religious congregations, athletic clubs as well as other groups that want to exhibit a collective commitment towards a singular goal refer to themselves as a family. This observation affords us a wider perspective on family’s form. 

In expanding the definition of family’s form, we have not strayed too far from the median. The unit consisting of: Mom, dad and kids, though easy for us to conjure, is not a universal composition of family. Multigenerational families are still more prevalent across the world, though declining in numbers. The nuclear family is still a new concept and may turn out to be a fad; a phase born out of economical necessities of our urban lives. This is to say that the composition of family members has never been set in stone. Thus, we can declare that family defined by function is a superset to family defined by form. 

Global variety in definition of family is not limited to form, but it also includes function. Some families, expanded and intrusive, dictate the future of their children through arranged marriages. Some are so paternally dominated that see no reason for the wife to continue living after the husband dies (e.g. Sati or widow burning). In contrast, the fundamentalist function of family, which focuses on procreation, is too limiting. Modern family, free from dogmas, has a more inclusive form and a more pragmatic function. A function based on cohabitation and mutual benefit; a diversification that minimizes uncertainties of life in a dynamic society. 

Consequently, such an inclusive definition of family’s form allows us smooth transition when studying a family’s function. We are free to speculate ideals of support, cooperation, mentoring, and parenting as the bases or telos of forming a family. The realization that the ability to perform a sexual act that produces an offspring is not a mandatory condition for forming a family is very liberating. We are safe to assume that if the traditional childless marriages were valid so is the proposition of a union that lacks that functionality, namely a same-sex one . 

The assertion that procreation is not an integral part of forming a family is an easy concept to accept. Adult members of human species are capable of providing for and parenting children that are not of their own blood relation. Foster parents, single parents, and adopted parents are prevalent examples of this concept in our society. 

So far, we have initially pointed out that expanding the form of family and making it more inclusive is possible without harming the institution. Subsequently, we demonstrated that the function of family is also elastic and allows refining. Now we need to consider the officially recognized aspect of forming a family, namely marriage.

Looking at this vista of human activity, we cannot help but to notice the lofty presence of longevity. It seems that the concept of family, inclusive of children or not, automatically demands an idealistic hope of permanence. It is reasonable to want the union to last into the latter parts of our lives, when we are feral and venerable. Such a contract that, at the very least, is entered into with the hope of perpetuity is an important one. Members of a community moved to form such a union rightfully seek to proclaim it in public and rely on the community’s official recognition to add gravity to their solemn decision. The added complexities of our American way of life: dominance of contract law, vibrant court system, complicated tax rules, edge cases regarding medical procedures, and sovereignty of states and patchwork of legal systems that it generates only amplify the necessity of official recognition of such unions. 

The combination of individuals that form a family is not a sum that represents the individual parts. Insisting that a family have a certain makeup does not ensure the success of the union. Bright, accomplished children from single parent homes, productive families that took in their nieces or nephews, and effective foster parents are all around us. I am thinking of the fictional story of Ann of Green Gables, a bright orphan raised in a farming family that consisted of an old woman and her old brother . I doubt that anyone would point out the old brother and sister as the fictional part of that novel, even when it was first published in 1908.
History has also proved that a family does not have to be strictly homogeneous. We have long learned to trust the viability of families formed by people of different color or creed. Though not long ago the traditionalist would have dismissed such arrangements as unviable, our own president Obama is the product of such a family

In dissecting a modern family and evaluating its parts, it is quite safe to take a position that assumes viability of a family based on the moral, educational, financial, emotional and ethical qualities of its members. In contrast, the position that values a family’s resemblance of traditional makeup can be tenuous at best. A natural evolution of our society as a whole dictates that we are free to form a tight bond with whomever we see fit to be our family. This person could be from a different social class, a different religion, a different color, a different country, or the same sex.

The modern family, at its best, is a deliberate union that answers fundamental needs of sexual satisfaction and emotional belonging as well as abstract ideas of cooperation and future building. It then graduates to consider the feasibility of having children. Naturally, a period of independence after leaving the protection of our parents’ home is there but conceivably more young people postpone marriage to allow time to find such a valuable partner. This has pushed the median age at first marriage for men to thirty years old and for women to twenty-seven .  

This is perfectly in line with our evolutionary growth. This natural behavior, among members of our society, points to the fact that forming a family depends on far more then mating compatibilities. The freedom to look for a life partner without the burden of having to compromise on one’s sexual orientation¬¬¬ is invaluable. Perhaps, the golden ideal of forming a family is to make a commitment to a person that has similar enough aim for the future allowing the pair to support each other as they labor toward that mutual goal.
Based on the premise that marriage is an officially recognized union and having established that parenting children is not exclusive by bloodline, we have been able to demonstrate that neither form nor functions of family are harmed by inclusion of same-sex couples. We have changed the ultimate aim of marriage to be a construct for cooperation rather than one for reproduction. This logic allows us to declare marriage as a civil right rather than a privilege bestrode on a procreating subset of the community. 

Works Cited

Lewis, John. “Rep. John Lewis is a Southerner for the Freedom to Marry.” Online video clip. YouTube. FreedomToMarry, 23 Feb. 2014. Web. 10 Apr. 2014.  
Holland, Aubry. “The Modern Family Unit: Toward a More Inclusive Vision of the Family in Immigration Law” California Law Review. 96 (2008): 1051-52. Web. 1 Apr. 2014.  
Groth, Aimee. “People Are Getting Married Later, And That's Great For Women” Business Insider. Business Insider Inc., 22 March 2013. Web. 14 Apr. 2014.
Tischler, Henry L. Introduction to Sociology. 9th ed. Belmount: Wadsworth Publishing Company. 2007. Print.
Maud Montgomery, Lucy. Anne of Green Gables. Boston: L.C. Page. 1908. Print.

Torture, an evil means to a utilitarian end, will be wrong because we choose it so not because of a moral law.

Cultural morality is too plastic a foundation as it only pertains to the people of that culture and not humankind as a whole. Only humanity based on evolution has the facility to banish torture unequivocally because it results in a more evolved being. This perspective opens to consider the entire specie and forgoes the cultural, geographical, or religious boundaries that ferment an us-against-them rational. The ticking bomb scenario is simply out of context. Humanity that has evolved to shed torture would function on a different setting all together. Such a community would be shameful to know a terrorist has plotted against them rather than vexed by it. If the terrorist is not mentally ill, the community leadership would huddle around that terrorist trying to learn how to compensate for a camouflaged wrongdoing, or fix the misunderstanding to remedy the fundamental cause of the terrorism. How utopian or silly this vision appears to be is a reflection of how far we are from that stage in our evolution. Until then, whenever a society is desperate enough we can predict that their sentimental self would seduce their logical self long enough to let their barbarian self access to torture. As for the reliability of the information gained by torture, Samuel Jackson’s character in Unthinkable takes 97 minutes to demonstrate that reliability of the information is in direct relation with torturer’s commitment to go the distance.

We should not be ashamed of slavery we should understand this repulsive phenomenon

We should not be ashamed of slavery we should understand this repulsive phenomenon
I am reminded of Dr. Myers’[1] writings about psychology, theorizing that our emotional reactions form the most deeply rooted parts of our interaction with the world. Long before any knowledge of diseases, disgust of foul smells protected us from pathogens. When we want to study secretions, cadavers, or other revolting subjects we first have to learn to curb our autonomic reaction to them. We first have to overcome disgust, this evolutionary advantageous reaction that has protected us for ages, and then peruse scientific discoveries.
Similarly, the evil of slavery still festers in the cocoon of our collective shame. Our shame protects this wickedness against the therapeutic rays of the light of cold and subjective study. A continuous arc of progress connects us to the early human that harnessed a beast and lightened his/her load. We, the humanity as a whole, are the heirs of the totality of whatever this progress accumulated and should own the events that brought us here. Yoking an ox was a smart idea. Yoking one of our own was a stupid idea. I feel that this understanding is innate in anyone with a basic knowledge of history and a sense of fairness.
We feel shameful of humanity’s bad decisions just as naturally as we feel proud of its brilliance. Therefore, the shame and guilt associated with the bad decisions are very powerful motivations to want to recoil and abandon the examination necessary for learning and changing. Psychoanalyst, Gilda Graph[2], who writes about the effects of slavery, points out the important distinction between our perception of shame and that of guilt. According to her, we relate guilt with something that we have done wrong. But we feel shameful when we think that there is something wrong with our own self. This points to a deeper and a more fundamental reaction; akin to murder perhaps.
Once we step beyond shame, we can analytically look at slavery, which in various temporary or permanent forms has existed throughout the times in all the cultures. Humanity used and still uses slavery to build monuments, deal with profit of wars, settle bankruptcies, demonstrate religious superiority, and establish large industries. Although race based slavery is one of the more appalling occurrences it is not the only one. This is to say if all humans looked alike slavery would not magically disappear. Not only slavery still exists around the world but also in the United States, according to Washington Post’s Max Fisher[3]. His maps illustrate that of the 30 million slaves around the world today, sixty-thousand live in a nation that fought a bloody civil war, at least in part, over abolishing slavery.
When one group of humans enslaves another group for economic or religious gains, the entire humanity pays a price. When the moral, cultural, and financial costs of slavery are fully appreciated then a simple cost/benefit analyses renders the idea of slavery obsolete. Given such clear data points and with the power of personal responsibility it is conceivable that we can apply social science to the cancer that is slavery instead of having to live with its shameful abstraction.
Works Cited
Fisher, Max. “This map shows where the world’s 30 million slaves live. There are
60,000 in the U.S.” Washingtonpost.com. The Washington Post, 17 Oct. 2013.
Web. 19 Jan. 2013.
Graff, Gilda. “The Name of the Game is Shame: the Effects of Slavery and Its
Aftermath” Journal of Psychohistory, 39(2).(2011)133-144.Web.19 Jan. 2013.
Myers, David G. Psychology. 10^th ed. New York: Worth Publishers, 2011. Print.

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[1] Myers, David G. Psychology. 10th ed. New York: Worth Publishers, 2011. Print.
[2] Graff, Gilda. “The Name of the Game is Shame: the Effects of Slavery and Its Aftermath” Journal of Psychohistory, 39(2).(2011)133-144.Web.19 Jan. 2013.
[3] Fisher, Max. “This map shows where the world’s 30 million slaves live. There are 60,000 in the U.S.” Washingtonpost.com. The Washington Post, 17 Oct. 2013. Web. 19 Jan. 2013.

Fermat’s Last Theorem

In learning about this subject and thinking about complex concepts, it was pleasant to see the process of discovery. Going beyond academic values it was hart warming to see how some of the most brilliant minds in mathematics struggle with questions.

Fermat was a French judge that enjoyed studying mathematics as a hobby. He was studying Arithmetica which is book of Greek text on mathematics. Habitually, Fermat made notes in the margins of the book about the relevant subject that he was considering. When he arrived at the Pythagorean thermo (a²+b²=c²) and in thinking about the whole numbers that could satisfy the equation (3²+4²=5², 5²+12²=13²…) he advanced to realize that the set of whole numbers that satisfied the solution were infinite. However, almost simultaneously, he seemed to know that we will never find an answer to this equation if we changed the exponents (a³+b³=c³, a⁴+b⁴=c⁴… aⁿ+bⁿ=cⁿ). This is to say so long as the exponent was 2 the answer set is infinite and if the exponent was other than 2 the answer set is empty no matter how far one looks for the answer. But evaluating this idea by trial and error is impossible because when we start with the first number we have infinite number of other numbers to yet check. And after checking the first number we are not one step closer to the end of the set of numbers that we should be examining. This limitless nature of possibilities required a mathematical proof based on other previously established theorems. Surprisingly Fermat notes that he knows such a proof but the margin of the book is too small for the elegant proof that he has imagined.
After Fermat’s passing others look at the notes that he had written in the margins and one by one establish an explanation for each scribble and at last we are left with the problem of variations on the Pythagorean thermo for which no one was able to find a proof. The story remains unresolved until the twentieth century. A young man named Andrew Wiles reads about this in a book from his local library in Cambridge England and tries to solve the problem. He studies math and all through his studies he never forgets about this unsolved problem. Latter in his thirties as a professor he is exposed to a paper by a pair of Japanese mathematicians: Taniyama and Shimura, concerning a conjecture (unproven fact) about a different subject. Professor Wiles invested seven years of complete concentration in proving the Japanese conjecture so that he could use it as a tool to prove Fermat’s theorem.
After Wiles announced that he had found the proof and during the peer review process the complicated procedure was not able to be reproduce and it took another year before the issue could be put to rest.
All Elliptic Curves are Modular => Taniyama and Shimura conjecture => Fermat’s last theorem
So finally, even though professor Wiles proved the Fermat’s theorem, we still do not know what solution Fermat actually had in mind. The techniques that Wiles used were not known during Fermat time.
Works Cited
BBC, Horizons. “Fermat’s Last Theorem”. 11/29/2013 <http://www.youtube.com/watch?v=7FnXgprKgSE>.
Wikipedia Fermat’s Last Theorem Version. 11/29/2013 <http://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem>.

Mathematics in Music

Pythagoras, perhaps listening to the sounds of tradesmen at work, started thinking about sounds that were pleasing to hear. We can imagine him watching a blacksmith strike an iron rod to make a sword and noticing that different length blades produced a different sound. Logically he would conclude that the length of a string on an instrument could determine the kind of sound that the instrument produces. These different kinds of sound eventually became known as different notes.
As he went about observing the sound an instrument produced with different length strings, he observed that if the change in length could be represented by a whole number ratio the relating note of music was also pleasing to the ear and harmonious when combined with other notes. Ratios like 9:8, 5:4, 4:3, 3:2, 5:3, 15:8, and 2:1 that today we call Pythagorean Intervals, were at that time recognized for their quality and without the knowledge of sound waves and frequency attributed to gods.
Today we understand wavelengths and can measure their frequencies. If we use a spectrophotometer to measure the frequency of an A note on a violin we should get a reading of 440 hz. Given the 32.5 cm length of the violin string to get to the E note, using Pythagorean Intervals, we shorten the string to 21 and 2/3 cm (32.5*2/3). If we then measure the frequency of the E note, we should get a reading of 660 hz. That “given two notes their frequencies and string length is inversely proportional” is a mathematical representation of the fact that the string producing the E note would be vibrating twice as fast then when it was outputting an A note . Proper fractions and inverse relationships maybe some of the more sophisticated examples of math in music yet at the most basic level each performance starts with “a 1”, “a 2”, “a 1 2 3 4”.

Sports & Mathematics

2 December 2013
From baseball averages to calculating the velocity of a basketball to statistics needed for gambling in sports, math seems to be everywhere. However, math’s graph theory provides a visual scheduling system for teams and players long before any action has taken place on the field. Graph theory classifies a complete graph as one where different points on the graph (vertices) share only one connection. This is to say that if number of points on the graph are represented by n than the number of connections between the points can be predicted to be n-1. If each point is a player or a team, given four players there will be three matches for each player before every player had a chance to face every other player.
todo: put img here
Figure above shows the relationship of player 1 with the other players. Using graph theory, we can show this relationship for all the players with this graph:
todo: put img here
Such a graph maybe an overkill for small number of players but is valuable in more confusing circumstances. The number of connections at each point on the graph is also called the degree of the graph. The degree of the graph above is 3. To calculate the degree of the graph, subtracting one from the number of vertices is easy enough to remember, so I do not know why the formula n[(n-1)/2] is used to complicate the issue! But, this is a good reason to study graph theory in more detail.

George Boole

Boole stood out from the list of mathematicians because of his relations to the Boolean concepts in computer science.  His father, a shoemaker, was interested in science and taught him his first lesson in mathematics. This interest in science led to involvements with a social group in their English town of Lincoln called Lincoln Mechanics' Institution. The group promoted education and held discussions about science.  After a while, Boole’s father became the librarian for the group and provided the conditions to allow Boole to discover and learn foreign languages and mathematics.  Given access to books, combined with encouragements of his father Boole’s self-starting personality lead the way.    
Boole had to support his parents and siblings early on. For a few years, he did this by teaching at village schools and when he turned twenty, he opened his own school in Lincoln. Sources I looked at about him wan to point out that his work and responsibilities left him with little time to further his study but my personal feeling is that the daily grind with students and re hashing the basics probably contributed to insights that worked in his advantage.

Foundations of Boole’s interest in math were as a tool to solve mechanical problems in instrument making. This practical focus evolved into his many papers; one in particular one on differential equations which gained him the Gold Medal of The Royal Society of London. His talent in breaking down a problem into smaller parts and using algebraic formulas to move toward a solution is the basis for Boolean logic we use in computers today. This allowed for logical problems of sentences and words to be presented as algebraic problems, which are eventually solved mechanically. The general idea of classifying objects into sets and replacing the given set with a symbol somehow (my understanding of it is very limited) made 0 and 1 a special set of numbers called idempotent numbers, or numbers that do not changed when multiplied by themselves. In what he referred to as “The Rule of 0” in his book The Laws of Thought Boole states that an argument is valid if and only if after writing it as an equation and restricting the values for the symbols to only 0 or 1 we arrive at a valid equation in algebra. Boolean algebra correlates the operation of multiplication to the word “AND” and addition to the word “OR”.
With the industrial revolution came the use of electricity, a perfect fit for the Boolean logic system. Dividing an abstract problem into its elemental parts that can only be allocated values of 0 or 1 and evaluating the parts in order to validate the larger problem is time-consuming and cumbersome. But, the mechanical system of evaluation combined with speed of electrical circuits make Boolean logic viable. George Boole’s self-educated research method affords us this luxury.

Works Cited
Encyclopedia Britannica, George Boole. 11/29/2013 <http://www.britannica.com/EBchecked/topic/73612/George-Boole>.
Stanford Encyclopedia of Philosophy, George Boole. (2010). 11/29/2013 <http://plato.stanford.edu/entries/boole/>
Reville, William, University College, Cork. “The Greatness of George Boole” (1996). 11/29/2013 <http://understandingscience.ucc.ie/pages/sci_georgeboole.htm>.

Counting and Recording Without Writing

17 November 2013
I can count to 10 on my figures without taking my eye off the job. Perhaps I use the beads and the string to make a strand of 10 beads. This way every time I count from 1 to 10, utilizing the fingers of my hands, I move one of the beads along. This allows me to count up to hundred without losing count. After the counting process is completed, I would use two sticks to record the account. On one stick, I would carve a grove all the way around. One for every bead I had counted, therefore each grove would mark 10 sheep. On another stick, I would mark straight notches to record the counts on my fingers, the ones that were not transferred to the beads. The owner would take the two sticks as the record of his stock.

Vectors

I have always wanted to know about vectors. So far, I only knew that in the computer world if I was dealing with a vector-based image then I could manipulate he size if that image without it becoming pixelated. There is a lot to learn in this area. My basic understanding is that in a simplest form a vector-based line is different from an image of a line. An image of a line is hard coded information about a selection of pixels that form that line. However, a vector-based line is information about the direction and the length of that line. This is the reason that they –vector-based graphics- are always clear and not pixelated. Once we know the direction and the length of the line, we are free to draw it in way that suite our local environment. How this leads to functions, arrays, and what happens with shapes (collections of vectors) should be a fascinating study.

Early History of Numeration

Why did people first need numbers?

Probably the need for numbers is closely tied with people’s sense of tracking items and events in their lives. The number of nights since they last saw the moon in full. The number of livestock that were in pasture yesterday. Number of sunny days required to have a successful harvest. The answers to these questions as well as many others had direct effect on people’s lives. The symbols that are place holders for these answers eventually evolved to become what we currently call numbers and the method of evaluating them is numeration.

What were some of the ways people first kept numerical records?

The easiest method would have been replacement of real object or event with mare accessible substitute. Early human’s fingers were perhaps the most accessible and portable way of substitution. To compensate for the limitations of 10 fingers or 20 fingers and toes tally sticks and knotted strings were used. This led to further refinement and efficiency by grouping. A group could then be represented by a symbol pressed in clay or painted on a surface.

What were the number systems of ancient cultures like?

Once groping and symbolism combined to add efficiency to the system two general systems began to emerge. The literal systems such as the Egyptian and Chines systems used symbols that were noticeable in their daily lives. For instance Egyptians denoted one million with a figure of an astonished man. More abstract systems such as the Roman or Babylonians used more abstract symbols that resembles the alphabet.