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Random thoughts on things random

April 8, 2013

I have been reflecting philosophically on the idea of random variables. For example, let us say we want to find the height of people attending a particular university. When one decides to examine this data statistically, one is by default making an apriori presupposition that the height of people in that said university is random. What does that mean? It means by default one is presupposing that the height of people are equally likely. Let us call this variable H. By that presupposition, one is assuming that H lacks pattern, or the pattern is uncertain. In some other place, maybe in this blog, I observed that human beings call things random as a bucket for chucking in data whose behaviour we do not know. We do not know or may be we just are not bothering to know?

Take the case of H. Assuming H is random is the same as saying, well we won’t look at other factors in detail. It is because it is hard work. We can for sure, do some regression analysis of H versus say age A and find the relationship between the two. Perhaps height depends on the age of the student? Finding those independent variables is just hard work. Looking at things random is just convenient and expedient. Looking at things random also says we are committed to living in the world of probabilities. Should we jump from this cliff easily?

Yet, some aspects of our world is not governed by probabilities. For example, when mathematicians assert that the sum of internal angels of a triangle is 180 degrees, they did not do this statistically. They did not sample every triangle in the world, measure their internal angles and after examining lots of them made a conclusion that their sum is 180 degrees. It did not happen that way. This judgement was arrived at axiomatically and deductively not inductively.

Events that are considered random may not be random after all. Some results of chaos theory say that certain erratic phenomena in reality follow a certain order.

An example of this is the flipping of a coin. In general, we assume that a coin is not biased and we say that it has equal likelihood of coming up heads as tails. Study shows that this generally held view which is really an ideal view, is not attainable. It is not statistics that governs this phenomenon but physics, and rightly so. In this paper, it shows that the act of flipping a coin and its result depends on its initial conditions. The result of this paper is not entirely unusual because clearly our intuition already says that the act of flipping a coin is dependent on mechanics. Our hugh school physics intuition agrees with that. Where I differ in opinion from this result is that I would deny there is such a thing as an ideal or classic view in practice.

So back again to the variable H. With H therefore we are assuming we will work on its statistics rather than on its genetics; working on the latter is just too hard to do. We will disregard perhaps the students ethnic background, age, diet, health condition etc. and other millions of factors that could affect the height of a student. So working with events make us consider them random, not because they really are like that, dependent of chance; but because finding out the factors that affect them is just too darn hard to do

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