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Entropy and forecasting of risks

April 25, 2013

"If a rope has one end, than it should have another one ...”

From the very beginning it would not be superfluous to express a simple thought that does not immediately fit in the head. At least it should be done, because those, to whom it may seem too obvious or absurd, will not read further and will save their time.

So: All we see around us is a fragments of the absolute event, which is holistic, infinite in time and space and has probability which equals to one.

The absolute event is independent from our perception - it is the never-ending stream in which we can see the individual trickles within the allowed time (fragments).
Generally speaking, probability of each fragment equals to one (entirely determined). For example, the probability that you are reading this article equals to one. At the everyday level, it looks like this - when something happened, it becomes clear that everything was going to this.

However, this is not about fatalism. At least, because we will never get a 100% proof of the determinism.

Because of their complexity and transience, fragments of the absolute event sometimes seem to be improbable or may occur not quite as imagined.

Determinism of the absolute event would not have any practical value, but it does due to one important circumstance - this abstraction does not depend on the direction of time!
Determinacy means that the future* has already happened, but we just are not aware of.*

In particular, causes and consequences are easily reversed, deductive and inductive methods become equivalent. The reason for this "strange property" is that the past and the future have the same determinacy and between them there is no significant difference.

Determinacy of the absolute event generates global ambiguity (bifurcation) - the probability of past events equals to one (as of accomplished), and probability of future events equals to zero (as not existing, but the only possible).Intelligent life always stays at the crest of "bifurcation wave" that grabs future and leaves a past behind.
Paraphrasing K. Marx, we can say that the bifurcation - is the driving force of history.

How quickly this happens, how much time passes between the past and the future? A funny question, but not idle. It would be very convenient if that moment had a finite duration and instead of a sudden leap of the probability to get its gradual increase from zero to one within a certain time. This is somewhat similar to the quantization of time where inside the quanta there are living all those things that do not match to common sense.

Thus, between the recent past and the immediate future there will be a continuous rope, which on the finite number of time quanta will split into an infinite number of individual strands with distributed probability of realization.

By introducing this assumption, we make a deal -* sacrificing abstraction we get the opportunity of the probabilistic choice*, ie the forecasting of events consequences (risks). Extremely good exchange!

Renunciation of the absolute event means that between the past and the future there arises "the arrow of time" (Arthur Eddington, 1928) - time moves in only one direction. From the most general point of view, the concept of directional time arises in any system because of the existence of the borders and the rate of the time is completely determined by the properties of these borders. However, it is too broad topic, so let us back to the prediction of events.

Directional flow of time leads to the fact that causes and consequences became not interchangeable in the interval between past and future - deduction will begin dominate over induction and to understand the causes of the events will always be easier than to predict events. It is possible to give an example - after the incident in the airline the investigation team determines the cases and contributing factors. All of them have long been existed in the airline, but who is ready to make a decision on the night before the accident to cancel the flight?

This is the basic question of risk forecasting, which cannot be circumvented through any trick - the uncertainty of the future is a payment for the possibility of forecasting, the payment for the fact that between past and the future there is a directional time.

The only known function that is sensitive to the direction of time is the entropy. In 1877, Ludwig Boltzmann wrote a famous article about the relationship between entropy and probability of the thermodynamic state. The formula obtained for an ideal gas, was so fundamental that subsequently was carved on the pedestal of the Boltzmann monument in Vienna. For this article is convenient to assume that the entropy is a measure of the disorder of event for which the event would be detected with reasonable certainty. This definition is compatible with the physical interpretation of entropy.

In the words of Max von Laue, Boltzmann saw his ideal in "combining all physical theories in a unified picture of the world." Not surprisingly, the Boltzmann relation corresponds well to the essence of the evolution - the impact of events on the systems of different complexity is determined by the frequency of these events.

Of course, we are only talking about those events that are in our “area of attention” and which we can identify with reasonable certainty. The consequences of such events and their acceptable frequencies are related by the well-defined law of nature and there is not much sense to evaluate them separately. For example, an event that is repeated every day for a number of years, can not be of great significance. An event that occurs once a month, has consequences on the level of being late for work. Events with a probability of 10-5 have consequences at the level of engine failure.

This can be questioned - a low probability events are constantly occuring around us and do not have any effect on us! Is this contrary to the theory of natural selection? No, this is not a contradiction - such events have no effect, because they are all around us, rather than with us. They are not in the area of our attention and are detected due to blind chance - they are not correlated with us.

Let us explain what we mean. In the area of attention there are events that have already happened to us, or may happen due to the cause-consequence relationships (event models) which are known to us. In the center there are the most frequent events, the periphery is populated by more rare events, and the boundary consists of events that did not happen to us, but are considered as possible from the analysis of the known event models.

Evolution, personal experience and education have already took care for the fact that the area of attention will not be too narrow. For an airline, for example, the area of attention is formed by the most qualified professionals and, given the opportunity of event forecasting, is quite adequate. This is expert knowledge.

Events that are in the field of attention, may be conveniently classified according to some reference points - consequences that are well known and understood.
For example, if the consequences of event "A" is somewhat better than complication of the flight conditions, then its likelihood will be a little more than 10-3.
If the consequences are at the level of an emergency, their frequency will be about 10-7 per flight.
Having conducted such analysis of events from area of attention, you will get a full set of allowable probabilities, which determines the targeted level of safety. In carrying out such analysis it is not necessary to always use a formal matrix of risks - everything will succeed by itself and will comply with common sense. In addition, it's nice to know that millions of years of evolution are on your side! Such approach can not be wrong.

In conclusion, let us make one remark concerning the risk assessment approach, which is used by a safety management system (SMS), developed by AVEX Bureau.

The consequences of events may be conveniently measured in the form of monetary losses. In this case, the dependence of consequences from the allowable probabilities will be in the form of a smooth curve, and the events will lined up in a reasonable manner. Furthermore, instead of the two control parameters (probability and severity of consequences) the only one will remain.

This approach has another important advantage over the conventional matrix of risks - the amount of probable monetary losses can always be compared with the cost of risk management activities. The best solution will benefit from a financial point of view.

Financial resources, however, are limited and* it is impossible to control all risks the same time. We'll have to choose from a variety of optimal solutions. Whatever decision made, it will be an event by nature and we can apply all the above said - *global ambiguity, probabilistic nature, the ability to predict and entropy.






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