A Shot at Probability!

Ever since, I have not been a huge fan of probability. Although my engineering majors required me to study it in quite a depth, luckily it is not my bread and butter. The conception that is bothersome is the uncertainty of an event. It has been quite a while that I have been thinking about writing on this topic and now finally I got a chance to have a quality discussion with some brilliant friends of mine which is worth penning down. So this is my attempt to argue some of the fundamentals of probabilistic analysis which surprisingly leads to interesting speculations. The argument under scrutiny is: can things be completely and accurately deterministic and make our lives easier (or instead difficult for some)?

Let’s start with a conventional example. A coin toss (my personal favourite). I am arguing that the event of getting a heads is a deterministic event. What I am saying is that the term “probability” of an event is euphemism for our incompetence to gather the appropriate information about an event. Let me elaborate. In the coin-toss example, if I give you the exact amount of force applied to toss the coin and other environmental factors like air resistance, gravity, etc, etc, we can determine with total certainty the outcome of the toss. Hence probability seems like an un-educated guess, well at least from this example, one can state in crude terms that studying probability is the study of the degree of the lack of information about an event and its consequences.

coin_toss

So to some extent it seems convincing to me that the world behaves in deterministic ways. But that’s too narrow an example to support my case. Let’s consider another example where living beings are involved and the cause-effect relation is not so straight forward. Say there are two guys ‘A’ and ‘B’, in a fairly large setting like a college, who start walking towards a classroom. They start at exactly the same distance from the class. Now what is the “probability” of both reaching the class at the same time? If I don’t tell you anything about their speed or their age or any imaginable thing that might even remotely help you to favour one, then you would say that the probability of a person “A” reaching the class before “B” is just as good as  the probability of “B” reaching before “A”. Further on if I start to add more information about A and B to this problem, the odds start to vary. For instance, I can add the information about their starting time and the speed with which they are walking. Given an ideal world where they walk at constant speed right from their starting point to the destination, it is a 7th grader’s problem to find out the exact time they will take to reach and hence it becomes a deterministic event. In real world scenarios, obviously things are not that straight forward. One of the guys might get a cramp on the way or an asthma attack or a heat stroke. So you can argue that it is impossible to state something as convoluted as this so deterministically. But remember, my argument is that given the “entire information” about the event, one should be able to determine with exact accuracy the outcome of the event. In this case, the entire information might even include the metabolism of those two people or the stress that their muscles can endure to estimate the cramp or neurons firing in their brain during that interval of time and several other unfathomable reasons that could contribute. If we cannot think of all the reasons that might have an impact, then it is our incompetence. One can argue that this will create enormous data and it is impossible to compute the outcome, but that is not the question here. The hypothesis here assumes that we can store and process the enormous data pertinent to that event, and given all that is necessary, we should be able to completely determine an outcome of an event with absolute certainty.

Now comes the interesting part which is mind-boggling. If the above is indeed true, then the consequences are unimaginable. If we extrapolate this hypothesis, it should be possible to model everything in the universe, even our fate and future. Viewing life as an adaptive system which trains and adapts itself to all (currently infinite) inputs that form the cause of the events in the future, one should be able to determine the consequences with certainty. Again, it will definitely require infinite amount of data to solve each of our life equation because of the enormous dependencies, but the possibility of that is not what I am arguing. In fact, I believe the factors that govern the outcome of an event will always be finite since the chaos (or entropy) in the universe is a definite number at any instance, although in true sense it is ever increasing. Hence, for an event, they will converge eventually.

Our universe started with one consolidated entity. After the big bang, the space started to expand and dependencies on one another started to sprout. Now for us, sure, the dependencies are enormous, but one can trace back the dependency tree right from the starting node to the present. On this basis, it is convincing that there could be just one “master equation” with which the Gods wrote our universe and solutions to which are slowly unrolling as our lives span out. Our life events and choices are feeding the master equation with inputs which governs our fate. And because our current choices (or the inputs to the master equation) are based on our past solutions to the same equation, our acts are never ever random or non-deterministic.

Now let me stretch this a little further and throw in the ace which might break this argument, the Heisenberg’s uncertainty principle. Succinctly, it states that the more precisely the position is determined, the less precisely the momentum is known at that instant, and vice versa. Although it is a quantum phenomenon, the ripples of the uncertainty will eventually spread to macroscopic world too. We can take the same example of coin-toss. Suppose I want the coin to land vertically. Even if I calculate the exact parameters that are required to make the coin land and stand vertically, there will always be a “delta” displacement of the coin’s axis from the vertical because it is impossible to determine the position of the coin with certainty while ensuring that it tosses with a certain momentum. This means there is randomness in the outcome since the coin could be inclined on either sides of the vertical axis, although that deviation would not be even visible on the macroscopic scale, but it will definitely make the coin fall on just one side which cannot be determined according to Heisenberg. But Heisenberg’s uncertainty principle and several other laws are a few segments of the whole puzzle. We don’t know the whole thing yet, or referred here as the master equation. Heisenberg’s uncertainty principle when viewed with the missing fragments of this equation could make things deterministic. Scientific endeavours are an attempt to find and put the missing pieces together.

Our lives, future and more, everything could have been chalked out already. All our current laws of nature, science, and humanity are our microscopic view of that universal master equation that we are all knitted to. And probably the lack of knowledge about the complete equation leads us to believe in the randomness of the events and hence their probabilities. Another question with which this discussion ends is whether finding that master equation would mean the end of human pursuits in science and nature? Would we then know everything? And whether as humans we have enough competence in figuring it out or not. And whether to figure out the “master equation” is one of the solutions of that equation or not.

Advertisements