Monday, October 17, 2011


Identity, it's who we are. But it isn't just who we are to ourselves, it is also who we are to other people. I shall try to keep my thoughts reasonably linear, but this is a topic that has come up in a variety of facets recently, so it may be difficult to isolate it from the surrounding context to discuss in a stand alone fashion.

One important facet of our identity is our cultural heritage. This, in some sense, grounds us to a specific place or places in history, "our ancestors were these people and came from here." It might be argued that many people in the United States lack this sense of heritage, but I think that it would be more accurate to say that they have incorporated the American ideal of settlers and intermixing as their heritage.

The question arises, what must be done to lay claim to a cultural heritage? I would assert that the act of laying honest claim to such a heritage validates itself. Of course, if I were to jokingly claim to be heir to the royal traditions of the Incas, this would not carry a lot of weight. However, if someone genuinely believes themselves to be an inheritor of a specific culture, then it is self evident that their identity is shaped by a sense of inclusion in that culture.

On the other hand, one might hold that, in order to possess a cultural heritage, one must take an active role in exploring that culture. While this is a perfectly valid way to organize people into culture groups, I think it is unnecessarily restrictive. At the risk of seeming ego maniacal, I will provide an illustrative example from my own life, simply because it is the only life with which I am familiar enough to say things with confidence.

Among my mix of European ancestors, I have some Germans and some Italians. And, while this has led me to study a little bit of German and put some effort into learning about German culture, I identify more strongly as Italian, despite having invested less effort in my Italian identity. I believe this is simply because my last name, if you unravel some Ellis Island mishaps, is Italian. So, just by identifying myself by name I am asserting my Italian identity, and it has caused people to react to me differently, thus further reinforcing my "Italian-ness."

And here we see how one's self identity and the manner in which others construct identity groups have such tricky interrelation. As I mentioned earlier, I think organizing people into identity groups based on putting effort into claiming a cultural identity is a valid way of organizing people, by which I mean that the groups that one obtains from such organization will likely share some distinguishing characteristics of interest and this organization doesn't seem to inherently promote ethnic cleansings. However, it may be quite at odds with how other people think about themselves, and indeed, how other people organize the world into cultural groups. So, it seems important to acknowledge that people can come to their identity through a variety of methods.

Further confusing the matter is the practice of assuming identities. For example, a European manga/anime enthusiast who feels their hobby confers a cultural legacy from Japan. First, let me note that this does not apply to every manga/anime enthusiast, just those who feel their hobby includes them in the penumbra of Japanese culture. Secondly, while this notion of cultural heritage may be at odds with the traditional notion of culture as inheritable from one's parents, it is entirely in keeping with both my criterion and, it seems to me, with the contrasting criterion from above, as the person in question both self identifies with Japanese culture and is investing effort into the cultivation of this cultural identity.

This highlights a further complication, in that essentializing Japanese culture down to anime and manga; or even anime, manga, and quirky gadgets; does Japanese culture a disservice, and, depending on one's views, may even be insulting. However, otaku are a part of Japanese culture, so one perhaps should not say that this view of Japanese culture is incorrect, insomuch as it is incomplete. So, toward what concept of a culture ought we direct our efforts in order to "earn" cultural inclusion?

So far we have mentioned three reasonable but incompatible methods for assigning cultural heritage; self identification, cultural participation, and parental inheritance. These are by no means exhaustive, geographical inheritance (Italians are people who have lived in Italy for some duration, which varies from person to person) and nationalism (Italians are citizens of Italy), for example, also have adherents. In light of this complexity, I am inclined to broaden my original position. While I still believe in accepting how others identify themselves, I also believe that we should accept that other people will have other ways of organizing people into cultural groups. That said, not all such organizations are "reasonable," which I would like to address at a later date.

Friday, October 7, 2011

Occupy the Middle!

Before I grow fully involved in talking about identity groups, I would like to finally hash out this post about Occupy Wall Street that I have been trying to write for over a week. Despite, or maybe because of, nebulous and conflicting concerns and desires, the Occupy Wall Street movement has inspired a plethora of related movements, occupying things across the United States and even internationally.

Ideally I might open with what the goals of the movement are. However, as I have noted, such a thing is not easy to formulate. I think it is safe to say that the movements are characterized by an anti-capitalist sentiment, and an accompanying dissatisfaction with the growing economic disparity within the US. The proposed solutions are, unfortunately, less homogeneous.

I think that this is a necessary characteristic of the movements. In order to enjoy such broad popular support, I don't think one can afford to commit to a more specific plan. Ironically, one can witness the same phenomenon within the very political structure that, many of, the protesters vilify. There, just as with the Occupy Wall Street movement, it is arduous to nail down exactly what a politician plans to do, simply because it is easier to garner support by pointing out what problems exist than by proposing specific measures by which one intends to correct them.

By no means to I consider this to be a scathing criticism of the Occupy Wall Street movement. I think it is inherently valuable to gain a platform from which we may air our grievances and question whether practices historically considered social necessities are, actually, contingencies put into place to tailor the system to the benefit of one group or another. However, I believe that true change will not be effective until people develop a plan of action more sophisticated than sitting in a public place until someone else gets sufficiently fed up and fixes the problem to make you go away.

While some have likened Occupy Wall Street to 60's era activism, the movement that most reminds me of Occupy Wall Street is the Tea Party. While they evolved out of radically different ideologies, I think at the heart of both movements is a deep sense of broad dissatisfaction with current domestic affairs. Contrast this with peace protests, civil rights movements, and even religious demonstrations, which all have much more definite goals to which they aspire.

Of course, there are significant differences between the Tea Party and the Occupy Wall Street movements. I think that the plans of the Tea Party were much more concrete, even if the underlying goals which they hoped to thereby accomplish remained quite nebulous. Perhaps correspondingly, I think the aims of the Tea Party translate better into the language of policy and legislation. Unfortunately, I do not particularly believe the change for which the Tea Party advocates can jar our society out of the malaise in which it currently lingers.

While I may not identify with"the 99%," I think their call for a re-conceptualization of "the good life" and our fundamental societal systems is a needed one. That said, I do not see how it is a matter of policy. One cannot legislate what people value, nor an ethic of individual accountability and responsibility. Of course, one might be able to, through legislation, encourage such a culture to develop. Personally I would like to see our nation take moral education and civic involvement more seriously, but that is just my opinion.

Saturday, October 1, 2011

The Abstract Power of Mathematics

Yesterday, as I was walking home, I stepped upon an acorn just to hear the popping sound it makes. Stirred by a moment of pique, I picked it up to investigate what was inside. To my disgust, I saw a couple of maggot/grubby things, which made me feel bad about stepping on it, and all the other acorns upon which I have trod. This got me to wondering, how likely is it that a given acorn has a grub in it?

Since the first one I investigated had a grub in it, I got the impression that it would probably be a fairly likely thing. If only one in every hundred contained a grub, it would be terribly improbable that the first one I examined would just happen to have one. However, I wasn't interested enough to try to remember how conditional probability worked, so I just went home.

After I got home, I went to pay my rent. Walking out of the rental office I saw a maintenance van, which was apparently number 1 in their fleet. Since the van I saw was labelled one, I started wondering about the size of their fleet. If you see a van with a certain number, you can assume the fleet is at least that large, but it doesn't tell you how big it actually is. So, seeing a van with number one seems to indicate a small fleet, otherwise I would be much more likely to see a van with a large number. When I realized that this was, basically, the same problem that had occurred to me earlier, with the grubs in acorns, I decided that who was I to ignore coincidence, and decided to work out the conditional probabilities.

Most of the time people think about probability knowing, approximately, how likely outcomes are and they want to figure out what will happen. For example, if you roll a six sided die, you would be interested in knowing what number you roll. Conditional probability works in reverse, if you know you are in one of a few scenarios and you know what happens, you try to figure out what the likelihood is that you are in a specific scenario. For example, if someone rolls a six sided, eight sided, or twenty sided die and they tell you that they roll a 7, you know they didn't roll the six sided die. For more information on determining conditional probabilities see below*

For simplicity, I decided to assume one out of every so many acorns has grubs. This ignores a large number of cases, for example 2 out of every 3 have them, but we can round those to the nearest considered case. I made this assumption both because it simplifies the calculations, and because it makes the acorn problem: the first acorn I see has grubs when 1 out of n do, the same as the van problem: the van I see is number 1 out of a fleet of n total vans.

One would sort of expect lower numbers in the fleet or higher grub frequency to be the most likely scenario. But, it turns out, if you consider fleets of any number of vans to be possible, then even a fleet of one van, the most likely, turns out to be statistically impossible, or a 0 probability event, if you remember my first post on probability. This is because, although the van's number is 1 100% of the time, or 1/1, if the fleet size is one, the probability of the van's number being one over all possible scenarios turns into the infinite sum of 1/1+1/2+1/3+1/4... which diverges**

Anyway, I suppose the main point of this post is not conditional probability, or the odd things that happen when you let infinity enter things, but rather how wonderful it is that math can take two, ostensibly different problems, like vans in a fleet and grubs in an acorn, and unify them into one, underlying concept.

*Calca I: Conditional Probability

Suppose that you know something happened, say someone rolled a 7 on a die, but you don't know exactly what circumstances led to this occurring, they either rolled a die with 8 sides or a die with 10 sides. To figure out how likely a scenario is given a known outcome, one simply divides the likelihood of the known outcome in that given scenario by the sum of the likelihoods of that outcome in all possible scenario.

For example, the 7 will roll 1/8 of the time on an 8 sided die and 1/10 of the time on a 10 sided die, so the likelihood that an 8 sided die was rolled to obtain the 7 is: (1/8)/(1/8+1/10), or 5/9. This makes a certain amount of sense, the 8 sided die is more likely to produce a 7 than the 10 sided die, so if a 7 rolled, we should think the 8 sided scenario more likely than the 10 sided one.

**Calca 2: The Series 1/n

If we try to find the probability that a fleet only has one van, given that we saw the van numbered 1, out of scenarios allowing the fleet to have any number of vans, we run into a problem. The numerator should be the probability of the observed event in the specified scenario, namely seeing van number 1 in a fleet of one van, or 1/1. However, the denominator should be the sum of the probability of seeing van number one over all scenarios, which is (1/1+1/2+1/3+1/4+...).

To get a feel for how to handle this sum, let us ignore the first term, 1/1. The next term, 1/2, contributes 1/2 towards the total. The next two terms, 1/3 and 1/4, are each greater than or equal to 1/4, and so together will contribute something at least 1/2 in size. The next four terms, 1/5, 1/6, 1/7, and 1/8, are each at least 1/8, so together they will contribute something at least 1/2 in size. Continuing on this way, we notice that the next 2^n terms are always at least 1/(2^(n+1)), and so together contribute something of at least size 1/2. Thus we can think of the sum as being larger than an infinite number of 1/2's being added together. This implies that the sum cannot be a finite number, so the conditional probability of the 1 van fleet scenario is 1 divided by a limit which approaches infinity, so the probability goes to zero.