### Of Randomness and free will

#### by Ravi Tandon

An interesting dinner conversation with a physics and a computer networking graduate student led me to write this rather abstract article today. The topic of discussion was whether there exists free will or not. We discussed basically two aspects of the question. One of the viewpoints (that I supported) was that if the universe is made up of fundamental particles that follow certain well defined sets of laws, then perhaps the universe is governed by a set of stringent deterministic and completely predictable rules. This would imply that our actions are all predestined and thereby the notion of destiny may not be a hokum. Perhaps, we are supposed to fall in love with a certain person and we cannot control it :P. However, our current knowledge of fundamental particles (let’s say) says that laws of nature are not completely predictable. There is a lot of randomness (uncertainty) in the way particles behave. For example, we believe that a particle behaves more like a wave at a fundamental level and is probabilistically present in space. The question then arises is that whether the uncertainty is fundamental to particles i.e. is a particle really present at multiple places or is it the shortcoming of our model of understanding, tools etc. For example, can we really come up with a certain technique that would tell us with very high accuracy that a particle is present in a certain location for all practical purposes. If so, then the only remaining aspect we would need to know is that what were the initial conditions of the universe to be able to predict what is going to happen next.

Now, the trouble here is that we cannot for sure say that a certain initial condition is “the” initial condition for the universe could have been in very many different states at the outset. To overcome this problem one could imagine a finite set of initial conditions and then use the theory (let’s say the prediction function f()) to predict the outcome for each of the possible initial conditions. By observation we could eliminate the starting conditions that do not satisfy our observations to be left with a small set of practical initial states. However, we still cannot rule out randomness because (a) it may not be possible to have a finite set of conditions, (b) we may not be able to rule out all but one initial condition through our observations. Besides, it is evidently not clear that there are only finitely many variables in the theory. If there are infinite variables in the theory, then can that be called as randomness. In other words, is random fundamental to nature or just a shortcoming of our constructs.

The other view-point is that randomness may just be fundamental to the nature, and that there does not exist a fundamental theory that explains each and every phenomenon. Besides, even if get a theory working we cannot be sure that it is “the theory” since, the set of observations to be made are infinite (considering time to be infinite) and that to fit that to a curve is not experimentally possible.

The deeper question to ask is that given a black box that can compute a curve on an infinite number of data points, with infinite variables can randomness be 100% removed. Is randomness really a fundamental to our nature or is it just the lack of understanding of the laws of nature / limitations to our computation abilities / mathematical models that gives rise to randomness. To take an analogy, in a pragmatic world, we believe a coin toss to be a random event. Though, given the values of all the variables involved such as the air resistance, initial momentum of coin, the gravitational force, the nature of the coin. etc. one can surely calculate the number of rotations of the coin and thereby the result of the toss. For a coin toss, therefore, the statement that the result is probabilistic is because of a lack of observational factors that we do not account for. In a sense, the result of a coin toss is random, when at least one of the factors is unknown or the function of coin rotation (the theory of coin tosses) is unknown. Therefore, randomness (here) is a conditional notion and can be eliminated.

This leads to us to the question, if randomness can be accepted to be a conditional concept, then is free will too? Was I destined to write this article because of the initial state of the universe was state A and not state B? Is randomness, then, an effect of our understanding of nature (or rather the lack of it) rather than the causation of our conceptual understanding?

If randomness is a notion borne out of of the fact that the theory of nature just has too many variables, it might well be possible to progressively reduce the randomness through better understanding of the nature (thereby introducing more variables in the equation). It would then mean that as human race progresses and becomes more smarter the amount of determinism in our lives would increase. Can we thereby say that determinism is a much advanced state of existence than randomness ?

I believe, given an ideal world with infinite resources for computation a theory must be possible to predict our action and that randomness (thereby free will) is a conceptual way of accounting for the lack of understanding the complex nature.