Did you unwittingly save or take a life yesterday? How about last month? Or, for that matter, during all your previous life? The short answer to the last question, justified by the famous butterfly effect metaphor, is "yes". The longer is "quite probably, but in practice, it's impossible to tell". The indirect consequences of one's actions, as well as the indirect causes of any observed event, will typically remain unknown, and practically also unknowable. Events that are behind a long enough chain of causal relations are treated as effectively random, as far as the subject is concerned. The natural question then is: what is randomness from a human perspective, and how does that affect our decisions?
Discussion of randomness with anyone vaguely familiar with physics concepts nearly invariably comes down to pointless arguments about free will and the nature of quantum randomness. Surely (as pointed out by Philip Ball in the book Critical Mass), there is a profound philosophical difference between things being unknowable in principle and in practice. But while quantum mechanics does seem seem to indicate that there is true randomness in nature, these concept are luckily irrelevant to the principal point. Indeed, physicists have dealt with the mathematics of random events even in the era of pure mechanistic determinism.
The most significant principle of the field of statistical mechanics is that when we do not or cannot know the state of a particular process exactly (such as the location and speed of every gas molecule in a box), we can nevertheless model it as a random process with some degree of uncertainty. Furthermore, given a lack of information, we have no other choice than to accept a level of randomness in our model.
Inverting the above logic, one can take it a step further and define subjective randomness as lack of information. That is, the less one knows about something, the more random he can consider it. This definition makes an interesting change to the whole concept of randomness as it is suddenly transformed (one might say "demoted") from a purely mathematical concept to a subjective phenomenon. Since the amount of information about a topic varies between people, so does the subjective randomness. Televised poker games are a good example: the spectators who see all players' cards have more information and thus less randomness in the game than the players. There is still some excitement left for the TV watchers as well, as they don't know the full contents of the deck or the decisions made by the participants.
While this concept works well even at the extremes of the amount of uncertainty, they are not the interesting cases: the full-information case is one of determinism (which is boring), and the no-information case implies total subjective randomness - pure random noise (which is irrelevant). As is often the case, the most interesting things happen in the transition zone. This is where people make, often unconsciously, decisions based on statistical models of events that are, at least in principle, completely predictable (in the poker games, the broadcasters do their best to keep the viewers' interest up by giving them just the right amount of information to keep it interesting).
If the amount of information available on a subject is perceived as determining the degree of randomness, one could as well give a sort of a Bayesian treatment to two randomness-related everyday concepts. Firstly, odds are the a priori probability, the individual's estimate of the probability of something happening before the event. Secondly, luck can very well be said to exist, and without any supernatural notions - but only in the a posteriori sense, or after the fact. Luck is then consistent with the information theory concept of self-information, or the amount of "surprise" presented by the result of a random event. Small surprise value implies neutral luck, while good or bad luck are related to high surprise value combined with an estimate of the favourability of the outcome.
Of course, nobody uses such involved definitions in their everyday lives. Still, this line of thinking can make it clearer to see how people make decisions subconsciously, based on personal estimates of odds. It also highlights the importance of clear thinking and the dangers of prejudice (that is, flawed estimation due to personal bias) in decision-making where probability and risk are weighed.
Further reading: Philip Ball, "Critical Mass: How One Thing Leads to Another" (2004), ISBN 0-434-01135-5.
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