Friday, November 27, 2009

On entropy, randomness and coincidences: a lesson in things I don’t know anything about, but still feel like talking about.

Yesterday I ran into the supervisor for the research project I was working on two years ago. I had not seen her since the project was done, and it took a moment for me to recognize her. What is strange is not so much that I haven’t seen her for two years and then happened to stumble upon her on the tram. What is strange is that I did so on the very day I had spoken about her to a friend. Prior to this, I had not given her as much as a thought in at least a year, probably more. To add to the strangeness, I was talking about my current supervisor to another friend, just as I laid my eyes on my previous one.

Often these things have natural explanations. The fact that I was talking about one supervisor while recognizing another one certainly has – my thesis being the key point of most of my conversations lately, it would have been more unlikely if I hadn’t talked about it at that moment. But even what seem to be freak coincidences sometimes have an explanation. You see someone you haven’t seen in a while, and the following night you dream about them. That is not a coincidence; it’s your unconsciousness playing tricks on you.

Theoretically, yesterday’s incident could have been explained that way too – I could have thought of my supervisor, and then unconsciously put myself in a place where I would be likely to run into her; or I could have been looking for her because I had just thought of her. However, this explanation does not seem applicable in this case, because where I met her is not where I would expect to meet her (the tram to another side of the city than her office building – the place I associate with her). And it is not likely that I have seen her several times and just not recognized her – despite the fact that it took a while yesterday, there was no doubt in my mind from the second I saw her that I knew her face – and I am good with faces. Even if I had seen her before and not recognized her, I would have remembered not knowing where I knew her from. Besides, Oslo is, after all, a city of (internationally small, but Norwegianly) considerable size – and it is not as though I often run into one specific of the 500 000 inhabitants just because I am thinking about him/her.

Thus, the inevitable conclusion is that this was a coincidence.

Now, as you may have learned by now (assuming you have read anything I’ve ever written, including this blog post – and let’s face it – if you’re reading this the probability of you reading this blog post is relatively high), I am random by default. Random becomes me. The more digressions, the merrier; and the more random they are, the even merrier (I just killed grammar in that sentence, didn’t I?). Seeing as randomness, lacking any predictable order or plan, is closely (but confusingly so) related to coincidences, I thought it was appropriate to discuss this relationship today (which ironically isn’t random at all, as it was planned. It also is not a coincidence, seeing as it is a direct consequence of what I believe was a coincidence yesterday). A warning is in order: I might confuse you; I will confuse me…

Several ffriends of mine are ffans of the ffiction writer Jasper Fforde. I have not actually read anything by him myself, but I realize that I need to, seeing as every time one of my friends talks about him I get the (f)feeling he and I have a very similar sense of humour. The other day, one of my friends talked about a book of his she had recently read. From what she said (and from what I later googled), this book appears to be Lost in a Good Book, number two in the Thursday Next series. In this book, the main character discovers that the natural state of chaos seems to be malfunctioning.

Luckily, she is in possession of an entroposcope (not to be confused with an endoscope, mind you!), a tool for determining how much chaos there is in the world. It is a jar filled almost full with lentils and rice (or other suitable thinglings, I should think), and to use it, you only need to shake it vigorously. Chaos is natural, and if the world is chaotic as it should be, the rice and the lentils will mix randomly. The technical term for this would be that entropy (a measure of the number of random ways in which a system may be arranged, often taken to be a measure of "disorder", according to Wikipedia) is increasing (as is normal). If the rice and lentils (or thinglings) happen to mix in a pattern, however, this in an indication that there is too much order around, and unlikely coincidences will happen. The entropy is decreasing, which is bad, since it is a violation of the Second Law of Thermodynamics.

Now, I assure you I won’t take this to the level of physics (as I would fall off way before we got there). Leaving out the technical terms, thus, what we are left with is this: an entroposcope measures whether the world is random (as it should be), or orderly (as it shouldn’t). Now, where does this fit in with my coincidence?

First of all, I had to think long and hard about what a coincidence really is. Again, I consulted the Great Internet, and found (again on Wikipedia – my academic credibility is suffering, but I swear I don’t utilize it for my thesis…) that a “coincidence is the noteworthy alignment of two or more events or circumstances without obvious causal connection”. In short, a coincidence is order where order should not happen. Ergo, a coincidence is an example of decreasing entropy (which we know is bad, but this is rapidly leading me back to physics, so let me stop right there).

Further, though, Wikipedia (which is being extremely helpful today. A coincidence? I think not!) informs me that “probability is the basic tool, or method, to rationally evaluate coincidences”. I managed to avoid the physics, but I can’t quite evade the math. I’m no mathematician, to say the least, and there is one part of math that always was worse than the rest – that of probability (perhaps because it is an analysis of random phenomena, which clearly is not supposed to be analyzed, aka put into order!?).

The basic idea of probability, though, I get. There are a number of possible outcomes to an event. To figure out what the probability for either one of these outcomes are, you take the number of “desired” outcomes (“desired” doesn’t have to mean actually desired, it’s just a way of saying “the outcome we are studying”. Capice?) and divide with the number of total possibilities. If you toss a die (classic example), the probability for the outcome to be an even number is 3/6 = 1/2 = 50%.

Now, back to yesterday’s coincidence. If we remove all other factors, the simple probability for me running into one specific person out of the 500 000 possible ones living in the confined space that is Oslo is 1/500 000. Not the hottest odds. If you add into the mix the coincidental part of it – the probability of me speaking about her on the very day I saw her again after two years – we’re already exceeding my math qualifications. I know, though, that the probability is very, very small. And when something like this happens despite the low probability, the rice and lentils are not-so-randomly forming the letters “decreasing entropy” inside the etroposcope.

Basically, I am sitting here scared to thinglings that I may have violated the Second Law of Thermodynamics and that someone will put me away for it.

I have not yet given up, though. Because there is an alternative way of calculating the probability for this coincidence to happen. See, in essence, there are only two possible outcomes: either I run into her, or I don’t. This means that the chance of me doing so is 1/2 = 50%. With odds like that, I’m not affecting the entropy at all, and it will continue to rise as it is supposed to. In fact, now that I think about it, this is a way of calculating that could (and should?) be applied to every side of life. Take the lottery. With the “normal” way of figuring out the probability, you have about 1/823926435495640564265942659 chance of winning the grand prize. With my way of calculating, though, the odds are much better since the outcomes are the same. Either you win, or you don’t. 50% chance.

Have a great weekend (but don’t blame me if you don’t win the lottery)!

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