Do you know how many times you use “Probably” in a day? The word refers to the possibility of a certain event happening. Irrespective of our ability to calculate probability, we frequently estimate, compare and make decisions based on probability. It is a subjective degree of belief in the occurrence of an event. The concept of probability has philosophical, psychological and scientific interpretations. Putting simply, probability of an event is the ratio between the number of favorable events and the number of all equally possible cases.
Evolution of probability theory
Initially probability theory was inspired by games of chance in the 17th century. However its complete axiomatisation had to wait until Kolmogorov’s ‘Foundations of the Theory of Probability’ in 1933. Over time, probability theory found several models in nature and became a branch of mathematics with a growing number of applications. In physics probability theory became an important tool in Thermodynamics and Quantum Physics.
Probability is the reason why a vast majority of phenomena from nature and society are considered stochastic (random). Their study cannot be deterministic. Probability theory deals with the laws of evolution of random phenomena. Rolling a die, tossing a coin pushed us to focus on prediction taking us away from the initial relative ratio proportion of probability. The distraction towards random elements was owing to the details like the initial impulse of the die, the die’s position at the start, characteristics of the surface on which the die is rolled, and so on. A drunkard reaching home, the time it takes him to travel a fixed distance varies because of random elements (traffic, meteorological conditions, amount of alcohol, etc). These were the details which forced us to assume that the essential conditions of each experiment are unchanged (“ceteris paribus”).
This focus on prediction and cause and effect took us to develop experiments and its results and focus on developing methods to study random phenomena. This was despite the fact that an equal aspect of probability is about relative frequency. How many times you may repeat an experiment in identical conditions, the relative frequency of a certain result (the ratio between number of experiments having one particular result and total number of experiments) is about the same.
Event focus, evolution of phenomenon, quantity focus and conditions focus complicated this further. Probability is not the expression of the subjective level of man’s trust in the occurrence of the event, but the objective characterization of the relationship between conditions and events or between cause and effect. The probability of an event makes sense as long as the set of conditions is left unchanged. Any change in these conditions changes the probability and consequently the statistical laws governing the phenomenon. So, if the initial conditions can never stay constant, can science ever find a solution?
This is why the notion of a butterfly ruling our life seems valid and this is the same reason why the idea of long term predictions is considered impossible. Will our life remain random? And will we ever come out of this quandary that even though systems are deterministic, meaning that their future dynamics are fully determined by their initial conditions, with no random elements involved, they are still chaotic? Isn’t it strange living this deterministic chaos?
We want to believe life is random, though the same random theories talk about relative proportion and patterns. We want to develop theories of randomness, though we have scientific history of predictability and order in physics. The drunkard’s behavior has an order, but we don’t consider it one. Human beings have problems with extremes. If there is an extreme mankind can’t explain, we get into thoughts of disorder, unpredictability, lack of equilibrium and inefficiency. The very fact that market crisis is a case of inefficiency for us, while earthquakes are natural predictable disasters, also shows our double standards in our treatment of extremes. We built economics around normalcy and when Mandelbrot proved that extremes were normal, our whole world of order seems to have collapsed.
Are we addressing extremes?
What are we doing now to address it? We are creating new subjects, econophysics, econoscience, econobiology and behavioral finance address the extremes. Though we have done a good job illustrating extremes in economics (far away from normalcy), we are still struggling with explaining the order in this chaos. We can’t seem to know why there is an order in these extremes, why do they repeat. Just because we can’t seem to explain the timing of the extreme, we say everything is random. Because if we would call it ordered, we would be expected to know the recurrence of the next extreme.
The Time decay
Showcasing an order in time would prove that there are no butterflies causing Armageddon. It would also prove that randomness is not owing to initial conditions, but because there is a limit to which one can understand and model time. Last time we illustrated cases on global assets and how time decayed in a similar form. This time we have picked up some random events like the chronology of Indian history starting Indus valley civilization from 3000 BC to the latest political elections, the chronology of battles starting ‘The Marathon battle’ in 490 BC till ‘The Battle of Dien Bien Phu’ in 1954, the chronology of US Naval history starting the commissioning of building six frigates on 27 March 1794 till the recent 200 year anniversary in 1997 and the chronology of Roman Empires starting Augustus in 27 BC to Romulus Augustus in 475 AD. Guess what? The so called random events in time decayed proportionally.
Now what is the probability that time decay in four random events in history decay in a similar exponential way? And what is the chance that this time decay in historical events is similar to the time decay in global assets like Gold, Oil, Dow, Sensex, BET, etc.? Well, for us, at Orpheus, the probability is 100 per cent, as we are not speaking about a chance decay, we are speaking about a pattern of time. Bloggers like Paul Kedrosky from ‘Infectious Greed’ talk about the end of behavioral finance illustrating how Richard Thaler’s fund underperformed. This is an old post, but the very fact that practical utility of the behavioral models is challenged on the web, suggests that there is more work to be done. Apart from the behavioral models, what really surprises us, is how the world bought into the story of butterflies in Brazil setting off tornados in Texas?
Time is too bland to become a hot selling story. But it is indeed shocking how, helpless human beings, are pitched to be unaware of the black swan. Randomness gives humans a feeling that they are lost in a labyrinth. But, if the man is indeed in a labyrinth, a constant failure to search for a route will force him to see failure patterns and, sooner or later, he will find a way out of the maze. Even if humans are greedy and fearful, they are not dumb with a blank page in their head, ready to drift with the wind where it takes them. The wind has a direction in its drift. Nothing propagates in life if it is random, nature cannot be random, propagation, growth is ordered, because the time we live in has proportion, pattern and decay.