The hard facts:
(a) The acceleration of gravity on Earth is g ~ 9.8 m/s^2;
(b) π^2 ~ 9.87.

The question: Is that pure chance?

The naive answer: Sure. Just change the units, the similarity is gone. Just change the planet, the similarity is gone.

Yet… a little bit of historical research tells us that it is not pure chance. How come?

Of course, if there is a connection between the two values, it must be historical, not physical. The similarity between the two values is just on Earth, and with our units. But how is the meter defined? The definition has evolved with time (and in the US they still use units related to the lengths of their extremities… ains…). For a long time, it was one ten-millionth of the length of the Earth’s meridian. So the relation to the Earth is ensured in the definition, no doubt.

No magic involved, just history. It was the French National Assembly, during the Revolution, defining the meter. They wanted a universal definition, and they came up with that one. But it was not the first one… Before, there were others.

As far as we know, it was the marvellous mind of John Wilkins the first to conceive the idea of meter. And what was his definition? No wonder, the length of a seconds pendulum. That means: a pendulum whose period is two seconds. Now, for a bit of physics, remember that, within the small angles approximation, the period of a pendulum is

Now, imagine that we were using Wilkins’ meter. Then with a pendulum of length 1 length-units, we would have a period 2 time-units. Just solve for g and… hey! You get… π^2.

Wilkins’ idea went all the way down to Huygens, and to Talleyrand, who proposed it to the French revolutionaries. Technical difficulties, mostly the fluctuations of length with temperature, made them change the choice, but nonetheless picking up a close value.

The Facebook statistics recently provided by Alexa--such as that the site adds an astonishing 600,000 users per day--are worthy of serious contemplation by social scientists still playing catch-up when it comes to this and other forms of online communication. But at the risk of seeming curmudgeonly (I imagine my fellow friends, Facebook devotees all, rolling their eyes), I want to make a prediction. Social scientists are very fond of "capital," which is a type of resource with a plausible connection to some desired outcome. These include economic capital (money), human capital (skills), cultural capital (powers of discernment vis-a-vis cultural objects), conversational capital (interesting things to talk about) and social capital (social connections). To this list I predict that we will eventually want to add something that I am tempted to call anti-social capital, which is a snarky (and imprecise) term for the absence of ties of a certain type, namely those whose main consequence is that you spend a lot of time online communicating with people who, like you, have a lot of time to spend socializing online. It's not hard to foresee why someone without such connections would fare better at school, in the workplace, and in their family relations than someone with them, other things being equal.

Of course, the problem is not merely time diverted from more serious pursuits--exercise, learning, thinking long and hard about life's problems, interacting with those with whom one shares microbes--but also the disclosure of personal and potentially damaging information. That might point to yet another kind of capital, which I'll call non-self-disclosure capital, which is the state of not having made public (especially online) information about yourself that could result in a serious loss of face, life prospects, and possibly safety if the information gets circulated beyond its intended audience.

All too frequently, someone makes a comment about how a large number of Facebook Friends must mean a high degree of social capital. Or how we can determine who is closest to who by measuring their email messages. Or that the Dunbar number can explain the average number of Facebook friends. These are just three examples of how people mistakenly assume that 1) any social network that can be boiled down to a graph can be compared and 2) any theory of social networks is transitive to any graph representing connections between people. Such mistaken views result in broad misinterpretations of social networks and social network sites. Yet, time and time again, I hear problematic assumptions so let me start with some claims:
1. Not all social networks are the same.
2. You cannot assume network transitivity.
3. You cannot assume that properties that hold for one network apply to other networks

To address this, I want to begin by mapping out three distinct ways of modeling a social network. These are not the only ways of modeling a social network, but they are three common ways that are often collapsed in public discourse.
(a) As a Sociological "personal" Netwrok
(b) Behavioural Social Networks
(c)Publicly articulated social networks

At this point, I would hope that most of us would realize that Friends != friends. In other words, who you connect to on Facebook or MySpace or Twitter is not the same list of people that you would say constitute your closest and dearest. The practice of publicly articulating one’s social network can be quite fraught because there are social costs to the process of public articulation. Issues of reciprocity emerge and people find themselves doing a lot of face-work to navigate the sticky nature of having to account for their social relations in a publicly accountable way. Thus, the list of who you might list as a Friend is often a mix of friends, acquaintances, family members, people from your past, fans, professional colleagues, familiar strangers, and people you don’t particularly like but don’t want to offend. Oh and the occasional celebrity you think is interesting.

These networks are NOT the same. Your mother may play a significant role in your personal network but, behaviorally, your strongest tie might be the person who works in the cube next to you. And neither of these folks might be links on your Facebook for any number of reasons.

Our instinct then is to ask: which is the “real” social network? Frankly, it depends on who you ask. Your mother may be cranky that you don’t talk to her as often as your colleague and she may resent your refusal to Friend her on Facebook, but this doesn’t mean you love her any less. Of course, this doesn’t stop her from thinking you don’t love her. If we’re trying to understand emotional affinity, the behavioral and publicly articulated social networks aren’t particularly helpful. But if you’re mother thinks that time is not only a proxy for emotional depth but a proof of it, your behavioral social network might really upset her.

The truth of the matter is that there is no “real” social network. It all depends on what you’re trying to measure, what you’re trying to do with those measurements.