January 30, 2012

Healthy Curiosity

By Melvin J. Howard

Math a scary and boring subject for many but math given the right variables could give you a probable outcome to just about anything. Events can be quantitatively described as probable or improbable when compared to the total number of possible outcomes. But when the total number of outcomes cannot be specified, there are no grounds for calculation. Intuitively, it seems like a very improbable event that I would unexpectedly meet an old college girlfriend in a British airport. But how can I quantify this probability? Do I include all of the other people I have ever known and the total number of people in British airports? Improbable events and coincidences occur all the time even though they occur with low probability. Given a high number of possible improbable events, it is highly probable that some of them will occur. We only notice the "coincidences" that do occur, not the ones which do not occur. The occurrence of improbable events does not necessarily require paranormal or supernatural explanations.

Additionally, some coincidences are more probable than we might expect due to our lack of appreciation of actual probabilities. The probability of two people not having the same birthday is 364/365 (multilpying the 364 days remaining for the second person times the 1/365 probability of the birthday of the first person). 1 - 364/365 = 0.275% chance of having the same birthday. But for 23 people there is a greater than 50% chance that at least two of them will have the same birthday because
P(same birthday) = 1 - (364/365)(363/365)...(343/365)  0.5

Although flipping a coin or rolling dice are treated as random processes they are not. Whether a coin comes up heads or tails is determined by the trajectory of the coin, the speed of rotation, the angle of rotation, air resistance, material characteristics of the surface on which the coin is thrown, the force of gravity in the location, etc. The same can be said for a roll of dice. There are so many variables, the variables are so hard to measure and the interaction of the variables is so complex that the flipping of a coin or rolling of dice are practically speaking "random". Said another way, the processes can be treated epistemologically as being random although metaphysically they are not -- they are deterministic.

In 1961 a research meteorologist at MIT named Edward Lorenz was using a set of equations to model weather on a computer when he discovered that rounding his initial numbers to three decimal places produced dramatically different results from those obtained by using six decimal places. Systems so sensitive to small variations in initial conditions have been called "chaotic", but they are more accurately described as pseudo-random -- just as so-called random numbers generated by computer are called pseudo-random. Again, the phenomena are metaphysically deterministic, but their unpredictability renders them epistemologically random no different from rolling dices or flipping coins.

In arguing against the Copenhagen Interpretation of Quantum Mechanics Albert Einstein made the infamous remark, "God does not play dice with the universe." I call the remark not logical because it is usually quoted to display how irrational Einstein's beliefs were when it came to spookiness at a distance. Which Einstein could not get his head around when it came to quantum physics?  Neils Bohr, Werner Heisenberg and others in the Copenhagen School proposed that randomness is a metaphysical condition of subatomic particles, whereas Einstein argued that randomness as a phenomenon is an artifact of our ignorance of underlying deterministic processes and forces limitations on our knowledge. Probability bridges the gap between descriptive statistics (average, standard deviation, histograms, etc.) and inferential statistics (decision-making statistics).

Decision-making is based on the probability of an event occurring times the payoff of the event - a cost/benefit decision. More formally:

Expected value = probability X payoff It would seem advantageous to wager $1 on the chance of winning $10 by rolling a snake-eye (one) with a single die because the expected value is probability X payoff = (1/6) X $10 = $1.67 which is greater than the $1 cost. But there is a 5/6 chance of losing the $1, which could be critical if you need the money to buy bus-fare. Non-monetary factors are often important in cost/benefit calculations - with benefits more often being more difficult to quantify and calculate than costs. I believe that I have learned a great deal about myself  by observing the world around me I also believe that I have grown as a person in learning to control my impulsiveness and impatience. I have learned humility in the face of my many false forecasts.  Life survival is a process of risk management. I believe the universe is teaching me wisdom and good judgment that has helped me (and, hopefully, others) in managing many many areas of life. I still have lots to learn. The learning is on a very deep level of personality much deeper than factual knowledge because in many cases I already know the mistakes but have not gain enough mastery over myself so as to not make them. Which is what life is all about no matter the profession Doctor, Lawyer, Judge, Fireman, CEO, homemaker. We all make mistakes the question is do you learn from them?