Excerpt from Probability Measure and Public Health
What makes an event random?
To some individuals, random events appear to have no definite purpose, aim or direction, the result of an incomprehensible combination of events. Following no logical order, their occurrence is not the result of a cohesive series of steps, but instead are part of an unintelligible pattern.
A tornado demolished a sequence of three houses on an urban block, leaves the fourth undamaged, and moves on to destroy the rest of the homes in the neighborhood. Cards appear randomly in a game of poker. A patient appears randomly at a physician’s office. Radioactive particles strike a Geiger counter randomly. Fire spares some horses while incinerating others.
We are the observers watching what occurs and recording the result. We see the arrival of a mother and child to an emergency department, or we watch with fear and awe as a super hurricane moves, stalls, and moves again, nature controlling this event. At the end of the exercise or experiment, an outcome is observed whose precise occurrence was unknown and unpredictable, and we say that it was a random event.
But are they really random?
Sometimes use of the term random merely represents our ignorance of the underlying mechanism. For example, it one were given the sequence of digits 592653, some would say that this is a random pattern of digits, while others might recognize this as the sequence of digits in π = 3.141592653….. The sequence of digits for pi is interminable, and does not repeat. Without a discernible pattern, the digit sequence is unpredictable, exhibiting some of the characteristics of a random sequence. However, they are generated by a discernible and reproducible mechanism, failing this test of randomness.[1]
There are other complications embedded in the concept of randomness. Consider the mother and child arriving to the emergency department (ED). To the observer in the ED who had no foreknowledge of what compelled the subjects to visit the ED, their arrival at 10:03AM, following no knowable pattern, appeared random. However, to this mother (who first noticed her child’s illness, then consulted with family and an older, befriended neighbor, then made a conscious decision to go to the doctor) her activity was purposeful and determined.
These actions from the mother’s perspective are not random at all, but the consequence of her conscious thought and deliberate action. The same could be said of the gentlemen arriving to the ED with the worst chest pain of his life, or the daughter bringing her father in because he suddenly lost control of the right side of his body. From the perspective of each of these subjects there was nothing uncertain about their arrivals at all.
So, is randomness, like beauty, in the eye of the beholder? Is randomness an inherent property, or simply a reflection of our inability to know all?
Religion and randomness
Discordians, who believe that both order and disorder are illusions imposed on the universe by humans, have a strong belief in randomness and unpredictability. Alternatively, Hindu and Buddhist philosophies state that any event is the result of previous events (karma), and as such, there is no such thing as a random event or a first event.
The development of probability was delayed approximately one thousand years in part because there was no longer room for the random event in modern culture, all events being determined either by man or God. Martin Luther, considered by many to be the founder of Protestantism, believed that, based on his interpretation of the Bible, not only were there no random events, but that there essentially was no free will either. If indeed purpose governs the universe, then randomness is impossible. [2]
However, not all Christians believe in the absence of free will. For example, C. S. Lewis, a 20th-century Christian philosopher wrote: “God willed the free will of men and angels in spite of His knowledge that it could lead in some cases to sin and thence to suffering: i.e., He thought freedom worth creating even at that price.” He later went on to say that God “gave [humans] free will. He gave them free will because a world of mere automata could never love…”
Random models in a purpose driven universe?
However, even if we grant for a moment that purpose governs the universe, that, as Einstein said “God does not throw dice with the world,” then random laws still have a role. Consider the emergency department example above. Each patient, each arrival, was determined purposeful, yet models based on random processes, e.g., the binomial model, the Poisson model, and the negative binomial model continue to function well in describing the overall system.
We learn about the overall process by studying these random models. We can understand measures of central tendency and dispersion (means and variances), and we can compute the likelihood of events. Even though each arrival is nonrandom, the characteristics of these arrivals in their ensemble resemble a random process; so much so that models based wholly on probability can describe them.
That is not to say the individual arrivals or results are random; in fact, none of them are. However, the entire system can adequately be characterized by a random process, even though the process itself would be seen as wholly deterministic if only our knowledge about it was infinite.
A fine example of this is managing the arrival of airplanes at an airport. Clearly no plane arrives “randomly”; each adheres to a predetermined flight plan that describes to the minute when the plane takes off, the route it will follow, and when and where it will land. Yet when there are many such nonrandom arrivals, the ensemble is as though the system was governed by random arrivals, and, using the Poisson process[[i]] we can learn about the behavior of the entire system.
In some sense randomization is the first structure that we can place on understanding a complicated system. For example, suppose we wanted to learn about the Bangladesh culture. We know no one from Bangladesh, and cannot travel there. However, what we can do is hang a microphone over its largest city. Now this is certainly a woefully inefficient way to learn about the people of this country. We would not learn their dialects, neither would we learn of the cultural intricacies of its peoples.
However, we would learn some things. For example, we would discover that that there is more activity during daylight hours than during the late evening, and that some days have more activities then other days. This is useful information in a vacuum of ignorance. We would know nothing of the details of every conversation, but collecting information about the sum total of the spoken words teaches us something of value.
This is what the application of the random model does. We rely on the random model to prove some overall characteristics. The individual outcomes are not random, but the aggregate of events behave as though they were. The model provides illumination about some of the characteristics of the deterministic process, whose intricacies we do not and may never know.
So also for the roll of die. We compute probability rules that successfully govern and predict the outcome of a single roll of two die. Yet, in today’s age, one can compute the exact outcome of any role. We need only the most modern, intricate, and fast computer, plus the weight, height, and balance of each die, the speed, direction, and torque of the roll, the ambient temperature and humidity, and the elasticity of the surface the die strike on the first and subsequent landings.
Given sufficient computing power and control of the immense equations one must understand to manage the physics of this, one could predict each outcome. It is deterministic. Yet, the resultant of all of these forces while not random, resembles a random process enough so that 17th century gamblers and mathematicians could deduce the patterns and probabilities of outcomes. It is a property of the resultant or ensemble of deterministic forces that permits probability based models to be accurate in predicting the system’s behavior.
Another perspective is to simply say that in our universe, events can have different properties. We say that randomness or deterministic are two contradictory properties, but that may appear to be true simply from our limited perspective. Just as light has properties of particles and also those of a wave, so to can events have properties of randomness and determinism.
[1] Such a sequence is described with the sobriquet “pseudorandom”.
[2] To some degree this sense is alive and well today in the ongoing debate about evolution, with those who advocate for God determined evolution or intelligent design contend with evolution’s proponents who argue that evolution is based on random genetic variations, that are nonrandomly selected by environmental stresses.
[i]. N. Bauerle, O. Engelhardt-Funke and M. Kolonko On the Waiting Time of Arriving Aircrafts and the Capacity of Airports with One or Two Runways March 30, 2006.