Part 1: Introduction to Social Network Analysis

Institutions or organizations sometimes have a hard time determining the quantity and quality of their impact. For example, institutions for educational outreach might need a way to quantify how far their program have reached the community and how significant these impacts are. Companies concerned with the cooperation of its employee might need a way to quantify how each employee interact with each other, the quality of these interaction, and how it can affect the company. This is all the question of network, or social network, if you may say. 

Talking about social network might remind us of Facebook. Sometimes an ad might pop up, or maybe a friend suggestion of people you don’t know. But if we think about it carefully, those ads or the friends suggestion are not randomly assigned for us. It closely reflects our circle, who we know and in what context we know these people, which in turn give insight on our interests, daily routine, or even deepest, darkest secrets. 

There is a science for analyzing interaction and relationship between people, called social network analysis. Social network analysis is a study on the interaction and relationship between entities within a defined network. This study encompasses mapping, measuring, and analyzing different parameters in the relationship, as well as how information flow within the network. The entities in questions does not have to be individual; they can be groups, organizations, or even inanimate objects, so long as there are perceived interaction or relationship between them. Since being proposed in the beginning of 20th century, Social Network Analysis has grown to be an independent field with its own methodology and parameter. 

The aim of SNA goes beyond descriptive measure; as explained by Wasserman and Faust (1994), its main purpose leans toward understanding and answering question. I can safely say us corporate slaves at one point in our career probably have personal experience with seemingly harmless interpersonal interaction affecting the progress of the organization as a whole. According to Wasserman and Faust, that is what SNA does; understanding the structure and patterns of these relationship and discover how it affect other people and the organization. R

elationship and interaction are inherently built within organization; regardless of what fields the organization is working on. Butts (2008) specifically describe the field of social network as interdisciplinary, which pointed out the characteristic of SNA as being applicable in diverse fields. 

THE MATHEMATICAL BACKGROUND 

Social network can be represented in many ways, but the more popular and visually appealing way to do it is using ‘web’ that we commonly see in graph theory. These networks are built by ‘nodes’ connected by ‘links’, in which the nodes represent entities, while the links represent relation between them. 

Interestingly enough, graph theory actually acts as mathematical representation for social network analysis. But before we get into that, let’s talk about the definition boundary of some of the terminologies we mentioned above. According to Butts (2008), ‘entities’ in this case must be distinct from one another, can be uniquely identified, and are finite in number, while ‘relation’ must be defined on a pair of entities and there are ‘dichotomous qualitative distinction’ between relations that are present and those that are absent. 

Under this constraint, social network can be represented as graph. In graph theory, graphs are built by ‘edge’ and vertex’, in which an ‘edge’ indeed can connect only a pair of ‘vertex’. This definition fits our need considering the definition of relation and entities we discussed above. 

Many constants and units in graph theory can also be used to represent parameters in social network, for example the order of a graph (the number of vertex), if we put it in the context of social network, represent the size of the network and the number of people in it. A ‘loop’ (edge going out from a vertex back to itself) represent reflective relationship, while ‘multiplex’ graph are those with more than one edge connecting two vertices. 

This article will only talk about graphs without ‘loop’ and are not ‘multiplex’, also known as ‘simple graph’. This explanation might not be adequate to give full insight on the role of graph theory in SNA, however it is enough to cover the basic on why graph theory is suitable to represent network data. Another option to represent network data is to use matrix (Wasserman and Faust, 1994), which will not be discussed here. 

WHAT INFORMATION CAN WE GET FROM IT 

Social Network analysis represented as graph gives information beyond the fact that two people represented by connected nodes regularly talks to each other. Does this mean the more nodes and links in the graph, the better? Does more contact for each person means more benefit for the for the organizations? Turns out, it is not always the case. Let’s see some key parameters which are the focal interests of SNA, i.e. degree centrality, betweenness centrality and closeness centrality. For this purpose, I am going to use the ‘Kite Network’ (figure 1) developed by David Krackhart (Rozental & Helman, 2008) and a graph (figure 2) from an article by Cross (2011). 

Figure 1: Kite Network developed by Krackhardt

Figure 2: Illustration by Cross (2011)

Degree centrality means the number of direct connections a node has. At a glance, it might look like the more connection you have the better. However, what really matters is where those connections lead to and how they connect the isolated network members. For example, look at Diane in Figure 1. She has the most number of connections in her network, however all of the contacts she has are those who already know each other. It means Diane only stays in one clique, therefore only in the same circle of information. 

Betweenness centrality stated the importance of a node in determining whether an information will flow or do not flow in the network. In the previous case, Susan and Diane both have high degree centrality, yet their impact to the organization as a whole will be different, due to this parameter. Diane has high degree centrality yet if she disappears, the people she connected to will still be able to access the information because they are connected to each other. 

On the other hand, Susan in graph 2 also has high degree centrality, yet she connects to people who are not connected to each other. This means, aside from getting a lot of new information, Susan’s position is also very important, because if she disappears, all the network falls apart. 

High betweenness centrality does not have to come with high degree centrality. Take a look at Heather (figure 1). She has small number of contacts, but her position is really important because without her, Ike and Jane will be cut from the circle. Ted (figure 2) also has similar characteristics, low degree centrality with high betweenness centrality. 

This notion is in line with the result by Gray, Parise, and Iyer (2011) on the role of SNA in helping employees become more innovative. They found that more innovative employee do not have bigger network, but instead they have more ‘bridging ties’ aka ties that connect them to employees who are otherwise unconnected. Closeness centrality means how well a node can pose at the center point of a network. Being a center point means being equidistant to both ends of network and therefore being in the best position to monitor the flow of information in the network. This is best represented by Fernando and Garth in figure 2. 

Source:

Butts, C. T. (2008). Social network analysis: A methodological introduction. Asian Journal of Social Psychology, 11(1), 13–41. https://doi.org/10.1111/j.1467-839X.2007.00241.x

Cross, R. (2011). The Most Valuable People in Your Network. Retrieved from https://hbr.org/2011/03/the-most-valuable-people-in-yo

Gray, Parise, & Iyer. (2011). Innovation Impacts of Using Social Bookmarking Systems. MIS Quarterly, 35(3), 629. https://doi.org/10.2307/23042800

Rozental, D. & Helman, T. (2008) SNA: Social Network Analysis. Retrieved from http://www.kmrom.com/Site-En/Articles/ViewArticle.aspx?ArticleID=144

Wasserman, S., & Faust, K. (1994). Social Network Analysis: Methods and Application. Social Networks. Cambridge University Press

Part 2 SNA in Education 

Part 3 SNA: Step by Step

The Egg

by Andy Weir.

Disclaimer: In case the "by" statement does not indicate enough that this mindblowing piece of a short story is written by someone else who is not me, I will say it again; I did not write this. I am posting this in my blog so I can access it easily in the future and you know, because it deserves to be everywhere on the internet.

You were on your way home when you died.

It was a car accident. Nothing particularly remarkable, but fatal nonetheless. You left behind a wife and two children. It was a painless death. The EMTs tried their best to save you, but to no avail. Your body was so utterly shattered you were better off, trust me.

And that’s when you met me.

“What… what happened?” You asked. “Where am I?”

“You died,” I said, matter-of-factly. No point in mincing words.

“There was a… a truck and it was skidding…”

“Yup,” I said.

“I… I died?”

“Yup. But don’t feel bad about it. Everyone dies,” I said.

You looked around. There was nothingness. Just you and me. “What is this place?” You asked. “Is this the afterlife?”

“More or less,” I said.

“Are you god?” You asked.

“Yup,” I replied. “I’m God.”

“My kids… my wife,” you said.

“What about them?”

“Will they be all right?”

“That’s what I like to see,” I said. “You just died and your main concern is for your family. That’s good stuff right there.”

You looked at me with fascination. To you, I didn’t look like God. I just looked like some man. Or possibly a woman. Some vague authority figure, maybe. More of a grammar school teacher than the almighty.

“Don’t worry,” I said. “They’ll be fine. Your kids will remember you as perfect in every way. They didn’t have time to grow contempt for you. Your wife will cry on the outside, but will be secretly relieved. To be fair, your marriage was falling apart. If it’s any consolation, she’ll feel very guilty for feeling relieved.”

“Oh,” you said. “So what happens now? Do I go to heaven or hell or something?”

“Neither,” I said. “You’ll be reincarnated.”

“Ah,” you said. “So the Hindus were right,”

“All religions are right in their own way,” I said. “Walk with me.”

You followed along as we strode through the void. “Where are we going?”

“Nowhere in particular,” I said. “It’s just nice to walk while we talk.”

“So what’s the point, then?” You asked. “When I get reborn, I’ll just be a blank slate, right? A baby. So all my experiences and everything I did in this life won’t matter.”

“Not so!” I said. “You have within you all the knowledge and experiences of all your past lives. You just don’t remember them right now.”

I stopped walking and took you by the shoulders. “Your soul is more magnificent, beautiful, and gigantic than you can possibly imagine. A human mind can only contain a tiny fraction of what you are. It’s like sticking your finger in a glass of water to see if it’s hot or cold. You put a tiny part of yourself into the vessel, and when you bring it back out, you’ve gained all the experiences it had.

“You’ve been in a human for the last 48 years, so you haven’t stretched out yet and felt the rest of your immense consciousness. If we hung out here for long enough, you’d start remembering everything. But there’s no point to doing that between each life.”

“How many times have I been reincarnated, then?”

“Oh lots. Lots and lots. An in to lots of different lives.” I said. “This time around, you’ll be a Chinese peasant girl in 540 AD.”

“Wait, what?” You stammered. “You’re sending me back in time?”

“Well, I guess technically. Time, as you know it, only exists in your universe. Things are different where I come from.”

“Where you come from?” You said.

“Oh sure,” I explained “I come from somewhere. Somewhere else. And there are others like me. I know you’ll want to know what it’s like there, but honestly you wouldn’t understand.”

“Oh,” you said, a little let down. “But wait. If I get reincarnated to other places in time, I could have interacted with myself at some point.”

“Sure. Happens all the time. And with both lives only aware of their own lifespan you don’t even know it’s happening.”

“So what’s the point of it all?”

“Seriously?” I asked. “Seriously? You’re asking me for the meaning of life? Isn’t that a little stereotypical?”

“Well it’s a reasonable question,” you persisted.

I looked you in the eye. “The meaning of life, the reason I made this whole universe, is for you to mature.”

“You mean mankind? You want us to mature?”

“No, just you. I made this whole universe for you. With each new life you grow and mature and become a larger and greater intellect.”

“Just me? What about everyone else?”

“There is no one else,” I said. “In this universe, there’s just you and me.”

You stared blankly at me. “But all the people on earth…”

“All you. Different incarnations of you.”

“Wait. I’m everyone!?”

“Now you’re getting it,” I said, with a congratulatory slap on the back.

“I’m every human being who ever lived?”

“Or who will ever live, yes.”

“I’m Abraham Lincoln?”

“And you’re John Wilkes Booth, too,” I added.

“I’m Hitler?” You said, appalled.

“And you’re the millions he killed.”

“I’m Jesus?”

“And you’re everyone who followed him.”

You fell silent.

“Every time you victimized someone,” I said, “you were victimizing yourself. Every act of kindness you’ve done, you’ve done to yourself. Every happy and sad moment ever experienced by any human was, or will be, experienced by you.”

You thought for a long time.

“Why?” You asked me. “Why do all this?”

“Because someday, you will become like me. Because that’s what you are. You’re one of my kind. You’re my child.”

“Whoa,” you said, incredulous. “You mean I’m a god?”

“No. Not yet. You’re a fetus. You’re still growing. Once you’ve lived every human life throughout all time, you will have grown enough to be born.”

“So the whole universe,” you said, “it’s just…”

“An egg.” I answered. “Now it’s time for you to move on to your next life.”

And I sent you on your way.

The Caste System: A Point of View

I made a presentation about this a few months ago where I basically explained what I think about caste system. It has been bothered me for a long time. However, as much as I am interested in history, I am in no way an expert or eligible enough to claim truth of what I am saying. Nevertheless though, I am a Hindu, have been affected by caste system, and do think a lot about it, so I guess I know what I am saying.

Let’s just ignore what happened in the society and history and just focus on what is dictated by the Vedas. The caste system the way people think it is was never mentioned; we do have Catur Varna though, which is division of people based on their duty in society. There were four groups people can fall into (think about it like Hogwarts houses): Brahman (scholars, teachers; intelligent people the bearer of knowledge), Kshatriya (warriors, soldiers, people in the government, ministers; basically brave people who fight for the country), Vaishya (businessman, vendors, traders; people with business skills and responsible for the economy), and Shudra (the rest; farmer, artists, sculptor, and other miscellaneous).  

It was long ago, so we can imagine that the society were pretty simple that every person can be roughly put into one of these categories. Since it was based solely on skills, it was not rigid at all. Vedas suggested this, and even without referencing to that, the existence of some important people definitely shows it.  The composer of Ramayana, Valmiki, was from a lower caste. Siddharta Gautama was also a Kshatriya (he was a prince) before became a wandering monk later in his life (Brahmin). Some mythological characters also exhibit the permissive nature of Varna system. Ravana was born to a Brahmin father before becoming a King of Srilanka, as well as Parashurama. On the contrary, Visvamitra was born a prince but became a Brahmin. If the so-called caste system was supposed to be that rigid, these stories would be prohibited to be told. 

As we all know, religion can say whatever, but how people apply it and what happens in society can be a whole other case. Yes, I am looking at you, all religions in the world. Just like the caste system; how come these divisions become a hierarchy then?  It was The British. The widely proven and accepted argument by modern scholars and historian is that the division started to grow in rigidity during the time of British colonial. The British were there to rule almost 1 billion of indigenous people, what’s better way to keep them in control other than not letting them have a sense of unity? What’s better way to destroy a nation for their benefit other than favoring one group while oppressing the other? They would not mess up with the Brahmin who was looked up to by a lot of people, and they also give a special treatment to the Kshatriya and Vaishya with whom they cooperate to exploit India. The rest is the Shudras; easy slaves and rough labor, right there. The British knew they can use the system for their benefit, and they made sure to keep it that way. 

Same thing happened in Indonesia, with the Dutch colony and their devide et impera policy. Well, it was more of putting one influential persona against the other, but a lot of tension also happened (a.k.a. created and exploited by the Dutch) between the patrician and plebeian. 

Well, that was the widely accepted theory, but I also have my argument. First of all, I present you the Maslow’s hierarchy of needs.

It is “a theory in psychology proposed by Abraham Maslow in 1943 paper ‘A Theory of Human Motivation’ in Psychological Review” (shameless Wikipedia copy-pasteing). This hierarchy is represented as a pyramid. The four bottom and biggest layers are the basic and fundamental needs, while the top layer is the need for self-actualization. Accordingly, the shape of the pyramid depicts how our basic needs are the ones that we have to fulfill first, most frequently and with the biggest amount, before we can even think about fulfilling the top ones.

In my opinion, this explain a lot of people’s behavior; from a student who can’t do her homework while hungry to a person in a third-world country who can’t give a damn about climate change with their children tailing them crying for food; from a feminist and animal right activist in Germany to a street vendor putting borax in his meatball in Indonesia. That also explains why arguments about climate change and gay rights are practically useless in Indonesia. I actually read a facebook comment using word ‘heteronormative’ one day and seriously I want to strangle that person; get your elitist argument out of Indonesia, our broken economy and starving street children ain’t got no time for that. 

Oh, and me, of course. I cannot think and write about statistical literacy if I don’t have caffeine in my system (IT IS BASIC NEED I SWEAR). 

But I pretty massively digress. Back to the point at hand, I strongly believe this is the root of the hierarchy. Religion, culture, tribes and nation may emerge and vanished only to re-emerge again throughout the history, but one thing that stays is our basic instinct as a human. I think what happened is that people simply had needs and they went a little overboard trying fulfill it, that is all. People liked being respected, being treated as special, being above others. When one a group of people being on the top part of the society and benefit from it, they will try to keep it that way. Similarly, people on the bottom may not like it, but if they are hungry or cold or unsafe, they do not care about that. I think that was what happen between the upper and lower caste back then; well, frankly speaking, that was happen between the upper and lower class of society everywhere and every period of time.

It was even worse because the Vedas and most of other scred text are not accessible to every people, only to the Brahmin, so it was really easy for them to twist the knowledge to satisfy their needs. It became really problematic because it happened on such a gigantic scale through decades that the faulty system became really solid and gradually was accepted as the correct one. And there, we have the caste system.

Seems familiar? Yes, because like I said before, it is human basic needs. Hierarchy happens everywhere, in every society, in every period of history - it is not only in India. India just have really fancy name of it called 'the caste system', so it is really easy for people to single that out. Our basic needs as a human, unfortunately, does not care about religion, regions, race, language – whatever (see Babel). Religion is the result of culture; it is the result of the higher levels of the hierarchy of needs (so many people are going to slap me for this). Unfortunately not all people are on this level of self-actualization, hence they ignore or modify it because they are still struggling with more basic needs, or even if they do follow it, they do it out of fear, which is the need for safety or reward, which is again, a basic need. 

What the hell, this is so philosophical I want to vomit.

Regardless though, this whole case of ‘religion can say whatever, but what happens in society is another case’ thing do happen across time and space as far as religion exist.  The oppression of women in Muslim countries, for example, which think is just the Arab culture, not the religion. Also the terrorism, gendercide, sexism, war, slavery – I can keep going on, but I think my point is clear. It is not about religion, guys, but more like social and historical phenomenon.  So if you want to attack Hinduism, leave out the caste system because it has nothing to do with it. Also, times change. Sudras are even richer than the Brahmin right now, and a lot of people can’t even be classified into only four groups so no one really care. And guess what, another hierarchy emerge, but it is based on clans instead of caste. Like I said, it is the basic needs; it is unavoidable, and it will keep happening. Just be sure to self-actualize yourself enough to not get caught in it.

I swear I'm gonna use the phrase 'precipice of annihilation' at least on once in my blog post.

Statistical Literacy: Reforming the Aim of Statistical Education

This video is a vignette of how statistics can be employed in a meaningful way. As a student who formerly struggle to like statistics, you have no idea how much this intrigue me. I believe the other end of the statistics teaching and learning spectrum, which in this case will be statistics teachers struggling to present statistics as interesting, will find this as intriguing as I do. 

I will be a total bore and start from defining statistics, which widely accepted as a science or practice that related with collecting, analyzing and infer from a large sets of data. The more organized a society is, the more important statistics will be, because certainly you cannot handle each individual data from each member of society separately. We need statistics for that; to collect, organize, and analyze the data as a whole, and from there making inference that gives us information about certain aspect of society. It can be economy, population or environment, just to name of view. 

Given the importance, one can say that statistics can be thought as a separate branch of knowledge. Which it is, but for some reason it gets overlapped a lot with mathematics because statistics, embroiling a lot of counting as it is, is certainly very mathematical. But where does statistics stand compared to mathematics? It is actually one of the five strands of mathematics, along with number sense, geometry, algebra, and measurement. Hence its taught in primary and secondary school as part of the mathematics curriculum. But statistics also stands out quite special because well, we have mathematicians and statisticians, but we don’t have calculust or geometrist … okay, this is just a joke of mine, but you gotta admit it makes quite a sense. Most of the non-teaching professions that employ math usually need math in the form of combined application of all the strands, with one or some fields being emphasized more than the other, but statistics have field of application that stand out by itself. In tertiary education, not all college majors have to take math, but statistics are usually taught because its importance for research. 

But I pretty massively digress. The point that I’m trying to make is that although statistics is part of mathematics, it is also stand out quite differently by itself. This by all means does not translate to it being the special snowflake; more of the opposite, to be honest. Mathematics is glamourized by the nerds as the science of logic and statistics is often pushed to the edge because it is thought to only consist of numbers (a lot of it) and counting. Counting a lot of numbers is boring, it gives you no mental satisfaction, and prone to frustrating mistakes. If students who like math think of it that way, how do you think the math haters gonna be. Me, for instance, although not a very accomplished Olympiad participant, am quite fond of math. I avoided statistics like plague, along with real analysis. Yet, although I looked at real Analysis with intimidation and fear, I admit I underestimate statistics a bit. I thought of it only as a matter of numbers and formulas and god it’s boring because I cannot see what I am doing.

Nonetheless, the blame is not on us the clueless child. The way statistics being taught traditionally focuses on the procedures and formulas, and fails to teach children to look at statistical problem holistically and derive meanings from it. This parochial way of learning apparently leads to misunderstanding and misconception in the adulthood. Some research actually reported a series of result from some psychological research that record how adult understand or misunderstand statistical ideas. This article also gives shorter illustration on how misinterpretation of statistical notion can be a disadvantage. Hence, the education stakeholders in some of the major countries in the world suggested reforming the aim of statistics education, which leads to the idea of statistical literacy. 

What is statistical literacy, you ask? I know, nice phrase isn’t it, I thought so too. Although there is no universal consensus about the definition of statistical literacy, Wallman (1993) gave a quite good definition of it which she wrote for the journal of American Statistical Association. Statistical literacy is “the ability to understand and critically evaluate statistical results that permeate our daily lives – coupled with the ability to appreciate the contribution that statistical thinking can make in public and private, as well as professional and personal decision.” 

Why is it important then? Well, one cannot deny that we live in a data and information laden world. Every day we are bombarded with percentage, census, polling result, graph and diagram, as well as sentences like “2 from 5 people choose Colgate” or “people with dilated pupils 77% more likely to be under influence of drugs”. Experts and advocates use statistics to strengthen their argument and to intimidate unknowing peasants. The misunderstanding and misconception I mentioned above shows quite clearly about how the failure in handling and being critical over information can affect us. Even if it does not do any harm, clearly grasping information better and knowing how to deal with it is needed for people to function efficiently as a citizen in society. Being statistically literate gives edge in personal and professional situation (mostly professional), for example impressing your employer or colleague. 

Now it is our responsibility as a teacher to create environment for students to learn statistics such a way that it is no longer a mere procedures, computation, and image, but also a way to make sense of the world.

BookFest Madness

So there is a book bazaar in Utrecht right now - the place is literally a huge warehouse with a sea of books inside being sold at alarmingly cheap price. I went a little crazy there - and this is not even my final form.

I got scared at my purchase halfway and had to put back half of the book I took. In the end I left with 7 books or so, while it could be around 20.

But I bought these!

Those are The Sand Box and The King Speech. The Sand Box is the book I thought Jarhead is based from - I saw the book and recognize David Zimmerman, the writer, but couldn't remember where. Then I read the summary and was like, oh yeah, this is Jarhead.  But apparently it is not. Oh well. Most of the book there were old books. I tried to find The Fault in Our Stars but failed. The King's Speech is, of course, the book The King's Speech is based from. The big one at the bottom is Time's most important photographs of all time - so proud of myself for recognizing almost half of the photographs in there. 100 points for general knowledge :D

Can't wait for my assignments to end so I ca devour all of these. Preferably ouside in the sun, when the weather is no longer crappy.

PISA 2009 Mathematics Framework