Recently, someone taught me some interesting concepts about pdfs and CDFs, namely regarding how to match the data to different theoretical distributions and test whether they are a match. This was interesting because while I’ve been quite familiar with those aspects of statistics, I’ve never really spent much time studying or researching them or through them. It’s always been in the background, informing the Confidence Tests and I remember looking at it in more detail when I did the pre-sessional statistics course prior to starting my masters, but really, it’s never something I spent much time thinking about.
That was until recently, when probabilities kind of .crawled their way to the forefront of my interest. As it turns out 5 things conspired to bring this about:
The first contact, I had with the concepts was during one of the episodes of Brian Cox’ Wonders of the Universe, where he was talking about entropy and the second law of thermo-dynamics, which is where the concept originated. At the time, the concept completely blew my mind, which is kind of sad when you think I did natural sciences until the end of secondary school. Somewhere, out there, there is a chemistry teacher and a physics teacher who did not do their jobs very completely. I do remember Lavoisier’s Law which kind of hints at energy conservation, but I’m confident we did not cover entropy in secondary school. Is this normal?
Years after, I started reading the very interesting and well-written, “Decoding Reality” by Vladko Vedral of the University of Oxford, which I cannot recommend enough. Not having a background in IT or telecommunications, I struggled with the information theory and its concepts at first. It seemed too abstract and pretty irrelevant to anything I was reading, so while the books summary awoke my curiosity, I was too unprepared to grasp some of its insights and it just ended up sitting on my bookshelf for about two years.
Then, around 6 months ago, I came across these two very interesting videos on the youtube channels of Vsauce and Veritassium, which once again I cannot recommend enough!
Which kind of provided me with enough of a discussion to really make me interested. But I was still struggling with understanding the concept of entropy and how I could simplify it in my mind. Nicely enough, I came across the bed-room analogy, which basically says that it is easier to make things messy in your bedroom, and that there are a lot of ways of doing so, but there tends to be only one way (or at least fewer) in which your bedroom looks clean. Stupidly simple right, but that’s my go-to-place for entropy. 🙂 (There’s also an equally simple the tower of cards analogy). Anyway, it finally answered the question Eddy Murphy’s character asks in “The Holy Man” asks(1’20): “Why is it easier to destroy stuff than to build it?”. Because “destroyed stuff” is disordered, whereas “built stuff” is ordered and the second law of thermodynamics says that isolated systems move from order to disorder.
Last (and fifth if you are keeping count), but not least, economics as a profession has recently taken an interest in inequality. The aftermath of the financial crisis did something to trigger our interest, as did Piketty’s data collection efforts and some of his more or less contentious conclusions. Nicely enough, it so happened that UNU WIDER (e.g.: this article ) started sending me some work about inequality, so I got to dig down a bit. Finally, I also had to read some articles about economic income inequality for the International Economics course I tutor at SOAS (e.g.: this IMF article) .
How does it all connect? Well, because income inequality is a measure of the features of the income distribution, so we are working with pdfs, and Boltzmann’s formula for entropy in thermodynamics can be applied to information theory. Given an event that can occur with some probability “p“, it’s information entropy, “I(p)“, or the amount of information it has is given by
So we can calculate the entropy of the income distribution ( and indeed this seems to be the basis of Theil index which is so popular with the University of Texas), or really of any other distribution we are interested in.
This, finally tied the whole issue in a nice little bow-tie. Now I’m interested. 🙂 Clearly I’m not an expert, but you know, it’s interesting! Now it’s just an issue of finding something to do with this, and honestly I already have a couple of ideas that are applicable to political science.
So why do I mention this? Because it was interesting for me to realise what had made me care about it and seek to learn. Also because it might be interesting for other people. Who knows, may be you are struggling to find the motivation or interest in the topic necessary to really dig down into it, like I did. In that case may be going through those steps will help you find the focus you need. Let me know!