Sunday, 25 November 2012
Do the laws of probability work?
In writing my last blog, I started to think about the laws of probability. Having done A level Maths with Statistics at Sixth Form College, I am familiar with the laws of probability but I have always been conscious that life does not seem to conform to these laws in practice. However, when I began to really think about the laws of probability I began to see that they do not even stack up logically as a framework. They purport to describe the way that life operates in terms of describing the likelihood of any given event. They describe the likelihood of something happening and the average times that event will happen given any number of operations. Take the situation of a die and the probability of rolling a six. I have watched in many games that I have played that when I am most concerned or attached to rolling a six it does not happen. I have watched the same happen to others, indeed when I began to record this phenomenon for me and for others I began to notice that some people would throw considerably more sixes when they needed them and others could go for sequences of up to 12 or more turns (in some cases it might have been more but for the fat the game ended) without rolling a six. Now the laws of probability would say that chances like this can occur but over time these will average out. Yet if this is the case, then what the laws of probability are really saying is that taken at a sufficiently large sample level this is how life is working, which means that at any smaller sample level it is not how life is working. In this sense the laws of probability have to discount the reality that unusual and unexpected things happen which are counter to these averaging laws. In effect it means that the laws of probability do not describe how life is working at all since there is no guarantee that even in large sample sizes they will fully conform to the average. Indeed most statistics are expressed in the form of 95% or 99% confidence levels, ie. that we can be 95% confident that a particular outcome will fall with certain parameters. Yet even here, I was conscious that completely anomalous data did occur which were completely outside these parameters but since they were the exception rather than the rule they were discounted. From this perspective, the laws of probability are based on the assumption that life is dictated by random events and “chance”, further than this, it is an entirely hypothetical construct. In life, a coin does not have a 50% chance of landing heads or tails, it is definitely going to land whichever way it is going to land. Since the future is a construct of the human imagination (the only moment that actually exists is now), so is the idea of probability.
Taking two practical examples of this; the recent article in the New Scientist about the Financial Crisis described a network of relationships between key companies involved in the crisis which closely mirrored that found in natural biological systems. It was this dependency on key companies which sat at the heart of the network which made the financial crisis possible, because this small group of companies was so disproportionately significant in the economic structure of the world. Looking at probability, it would be clear that each individual involved in these companies. The individuals operating within these organisations would no doubt suggest that their lives were governed by chance and a series of probabilities about which they made choices, yet the reality is that their actions collectively aligned to natural systems, ie. it was only going to play out that way and there wasn’t really choice. Now, I accept that it might be possible to construct the probabilities for their individual actions to create or mirror this eventuality but this feels like retro-fitting the maths to the facts. Of course, this brings us into the realm of free will and fate. Our probability construct assumes that our existence is predicated on free-will with a range of possible avenues available at any point in time. I also recognise that at a broad general level, probability has it’s value as a model but only in so far as we recognise it is a construct based on certain assumptions and that these assumptions have limitations and may not be an accurate reflection of reality.
I remember a project that I undertook whilst studying a module for my Chartered Institute of Personnel and Development exams, itwas on regression analysis which takes trends and then applies them to data and smooths out anomalies. I had decided to do my project on the link between unemployment and inflation. It was a generally understood rule at the time that in order to control inflation one had to have high unemployment and similarly that lower unemployment came at the cost of high inflation. Whilst there did seem to be some inverse correlation between the two there were certain spikes in the data where there was no correlation at all. This troubled me at the time because I felt that this was indicative of the fact that there only appeared to be a correlation between them. As it turned out, this later proved to be the case.
The laws of probability, it strikes me, are simply generalisations. Most of us are aware that generalisations can be helpful but only to a limited extent and with many dangers if you think they apply to the individual or particular. The famous notion that if you gave a group of monkeys a keyboard and infinite time the chances are that they would come up with the works of Shakespeare I do not believe to be true. If we are not careful then Maths (in itself a construct for reality rather than reality itself) becomes like counting the number of angels on the head of pin. The chance of any event in our lives happening is both infinitely improbable given the other possible alternatives and highly probable (given that we have to be or do something and it did happen). Yet really there is no chance involved, it simply did happen. In this sense, I suspect that we may well find that the laws governing quantum mechanics are not made up of uncertain, chance probabilities in the way modern physicists currently suppose, but rather that we do not have sufficient ability to see the detail which we currently generalise through probability. I do not think that we will find that there are multiple other realities happening concurrently with our current one (this. for me, is a fallacy based on not separating imaginative constructs (chance and probability) from reality). In this sense I think Einstein’s famous quote that “God does not play dice” might yet prove to be true. In fact, at a broader level, I’m not sure that God plays dice at all. Most of our current models such as evolution are based on this notion that the universe is both random and dictated by chance. These are interesting assumptions but we forget at our peril that they are not external objective (external) facts, but rather internal subjective constructs.