معمارِ حرم باز بہ تعمیرِ جہاں خیز
از خوابِ گِراں خوابِ گِراں خوابِ گِراں خیز
----------------------------------
ادھر آ ستمگر ہنر آزمائیں
تو تیر آزما ہم جِگر آزمائیں

Tuesday, 27 December 2011

Understanding Randomness


The mind has delved into the realm of the “random”. Thus it asks the pivotal question, what is random? What constitutes random? Is random truly random? I remember my lecturer once telling the class for one of my engineering courses, “In digital world the random numbers generated are not ‘truly’ random because the system needs a ‘seed’, which is acted upon by few mathematical operators to generate this ‘random’ number”.

Accepting this premise for the argument’s sake, question arises that which ones are ‘truly’ random numbers? Randomness as a phenomenon goes beyond numbers as well to more abstract domains of words, letters and thoughts. A teacher once in school told us about the motion of molecules while lecturing on Brownian motion. He called it to be ‘random’. I guess this was officially the first time I came across the term which I understood to mean ‘something that cannot be determined prior to it occurring’ or simply ‘unpredictable’. Coming back to Brownian motion, one is compelled to further inquire whether it is unpredictable or not?

In order to understand the alleged ‘randomness’ of motion of molecules, let us perform a thought experiment. Excuse it to be an overly sciency narrative but anyways. Suppose we take an ideal gas at a temperature of zero Kelvin. It should have zero volume and zero energy. Now if this gas is supplied with a small amount of energy, the molecules would absorb this energy and thus start their vibratory motion while registering a proportional change in volume. These molecules owing to very high density of matter will have ‘elastic’ collisions with each other. These collisions will make the molecules to move in different directions. If properly analysed which the energy level of these molecules and other mechanical factors, the direction of travel after the collision can be calculated using elementary algebra. As my understanding of the word ‘unpredictable’ goes it does not include anything that can be calculated. So how come the motion is random? Or maybe the right question to ask would be; is it really ‘random’?

The scientific world is filled with processes that are called ‘random’ processes. The list includes Bernoulli Process, Dirichlet Processes, Gamma Processes and many others. But they all fall in the category of Brownian motion. The most convincing types of so-called ‘random’ processes are the ones of type alpha-particle emission as it seems not possible to calculate the emission prior to its occurrence. But having said this there is a possibility that these processes are random because our current technological level is not sufficient to ascertain the occurrence of event. So they might not be truly random but are random for us observers. This brings us to famous quotation from Einstein who while talking about randomness at sub-atomic level famously said, “God does not play dice.” To this Niel Bohr replied, “Do not tell God what to do”. Although I do not have any scientific proof to substantiate my claims, but building up from the above given arguments the possibility should not be overlooked that the processes are not truly random rather label as such due to either in availability of sufficient technology to ascertain or the calculation is too difficult to make. Whether they are sub-atomic processes, biological processes or any other including neurological or psychological process are not truly random per se. Who knows, maybe Einstein was right.