Friday, December 26, 2008

the Normal Distribution Theory

For a while I’ve been brooding over a fantastic hypothesis, which I like to call the Normal Distribution Theory. This theory is truly a theory of everything, at least for the living world. And it’s remarkably simple- no complex equations and no counter-intuitive physical formulations. It just says that any reasonably sized population will show a normal distribution when any reasonable attribute is considered. Take for example, the population of moose in, say, Saskatchewan (a province in Canada). Consider some reasonable attribute of moose, like the height of their antlers for instance. (It could even be the diameter of their left forelegs, or simply their height, it really doesn’t matter.) Now, this theory says that if you plot a graph of this attribute against frequency, you are going to get a normal distribution curve. And for those who missed their yearly dose of ProbStat, a normal distribution curve is simply one that looks like this, and which says that most moose will have average sized antlers, with the number of moose with antler size X decreasing as X deviates more and more from the average. This conclusion seems intuitively obvious, and if you don’t require the curve to be symmetric, it is obvious. Another thing about taking animal populations and animal attributes is that you cannot seem to come up with an attribute that is not reasonable; everything from the length of tongue to hunting success percentage seems perfectly OK. This universality of reasonableness of attributes is actually quite reasonable – after all, none of these attributes can be changed by the animals themselves. They are simply a result of a random process called mutation, and random processes give normal distributions, right? You’ve probably understood what I’m really hinting at. Are human traits reasonable attributes? If we take the population of human beings in Saskatchewan, and the relevant attribute as the number of times each person has stolen something in his/her life, will the corresponding graph show a normal distribution? I argue that it will, and that for a sufficiently large population of human beings, any attribute is reasonable, in that it will produce a normal distribution. OK, let us for a moment accept that this statement is indeed true (trust yer intuition!). The implications are awesome. Does this mean that the concept of destiny is true and that no one can escape it? After all this seems to be an obvious corollary of the Normal Distribution Theory, given that the theory suggests that there will always be some people who will steal a hell of a lot, and some who won’t steal at all. That means no legislation, no religious doctrines, or no personal ethics can change fate, right? Actually, no. Suppose stringent legislation is introduced to counter the rising number of thefts in the province. Then the graph changes in such a way that the average number of thefts per person reduces, but the normal distribution remains. Ergo, people who use the Normal Distribution Theory as a seemingly scientific way of proving that destiny is true and immutable are probably wrong. A bigger and scarier implication of this theory is the distortion of personal ethics it can cause. Person X says “Hey, isn’t everything supposed to follow a normal distribution? So the world needs rapists like me. Everybody can’t be good right? I’m only doing the world a favour.” And so Y turns to arson, Z robbery and W vandalizes for kicks. If people like these become significant in number, they can change the nature of the graph. It’s true that the structure remains unaltered, but the graph shifts in the coordinate space. And this can be very, very dangerous. Suppose we know, through some advanced statistical studies, how much the average crime rate in a population can increase and still prevent self-destruction. Then we know that shifting of the corresponding attribute graph can catapult it right into the unsafe zone, where self-destruction is not impossible. Personal choices do matter. If you decide to not use that plastic shopping bag today, you might actually have shifted the plastic use graph into a zone where it’s environmentally sustainable. A heady thought. But one that won’t surprise a true reductionist – “The whole is merely the sum of the constituents and their interactions.