V-O-L-A-T-I-L-I-T-Y

Volatility has been associated with deviation of a stochastic process from the mean value. In simpler words it is the measure of tendency of a phenomenon to not result in the expected or result in the expected.
It all seems to have been started by George Brown who noticed the motion of microscopic particles suspended in water. It was a factual behavior of particles in water until Albert Einstein described it mathematically and snowballed a whole new area in mathematics which has been contributed to by the 'n' (still counting) generations after him.
Again in describing the historical development of the concept of volatility i have cheated or rather failed to think deeper because of my specialist approach. I have narrowed my mind to thinking of volatility only in the context of oscillations at microscopic level and been impatient in describing it completely. I am trying to get to Brownian motion and its applications to physics and finance, where volatility has played an important role.
Consider the sport of archery, when a well practiced archer shoots the arrow his volatility (given the objective is to hit bulls eye) would be lower as compared to the not so trained one. Not every thing can be trained for instance, the stock prices may not be trained to go up or go down; or it could not be even trained to reveal where will it move next: up or down, unlike an archer who can get better with practice.
The greatest fallacy of man in the current age is his belief that he can control/predict all processes, man made or natural. What we know of volatility is only the volatility of the process in time and not in possibilities at a given point in time. We do not know what has not happened but only what has happened and looking back one can know what has been deviation over time. Now if one assumes that the different scenarios that have unfolded in past are the only possibilities then the quantified deviation from the average is an estimate of volatility and a pretty bad one.
What is a good estimate of volatility then ? Depends !