Earthquakes, blackouts, and Gini

Ramblings of a tired mind follow. Don’t expect much.

It never ceases to surprise how, thanks to Tim Berners-Lee, a short series of clicks (and in this example, three typed words) can lead to dizzying leaps between places, events and concepts. On this occasion I didn’t even have to leave the comfort of wikipedia.

Click one from news section of wikipedia homepage: March 10 Chile blackout. Chile’s electricity network has been left in a fragile state since the earthquake last month. Did the quake contribute to the failure of a single transformer 700km from Santiago, plunging 90% of the country’s population into darkness? The short entry doesn’t make this clear, but maybe earthquake damage elsewhere in the electricity network diminished its redundancy. What kind of a network would allow this, anyway? This reminds me of something I read about a few weeks back.

Typed ‘scale-free network’ then click two: in one of these, the probability distribution for the potential number of a node’s connections follows a power law. I’m not sure whether Chile’s electricity network is scale-free or not, but clearly the loss of that vital transformer would be akin to losing one of the hubs in such a network. Scale-free networks are observed empirically in natural, social and computer settings— the world wide web itself being the foremost example. I wonder if they represent a trade-off between efficiency and fault tolerance. Perhaps I’ll look into this later.

Click three: power law, because I need reminding what that means. Oh yes, when one quantity’s relationship is exponential to that of another quantity in a mathematical formula. I knew that.

Click four: browser back button, to the scale-free page. What was I doing here again?

Click five: on something else I recognise. Pareto distribution. A type of power law distribution (the type of power law you see with scale-free networks? I think so, but I’m not sure. Wikipedia-gained knowledge is shallow, fooling you into believing that you understand something when you don’t). Describes many types of observed phenomena, including sizes of human settlements (few cities, many villages) and meteorites (few big ones, many small ones). And there’s why I recognise it: Pareto first described this relationship in his eponymous “80:20” principle, that 20% of the population control 80% of the wealth. And further down: the Gini coefficient, which I knew before as a measure for social inequality, but never really understood how it equates to an area on a graph between two lines: one straight one which represents equally distributed wealth, and the other curved one (the Lorenz curve) representing a Pareto distribution. I’m still not entirely sure I understand it (I mean, properly understand it) now.

Anyway, no time for that. Back to scale-free networks, and those Chilean blackouts.


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