Why, while looking through the behavioral lenses, we see the world of simple dependencies and not consequences of complexity? Observing the world directly accessible to our senses, local, homey, familiar, which we understand well, our experience is that events always align around a certain average. They are frequency-stable. Let us consider a coin throw. The probability of throwing an eagle or tails is 50/50. The probability of throwing a series of eagles or tails one by one decreases with the length of the series, arranging itself in the normal probability distribution known by the name of its discoverer a Gaussian distribution, or else – a bell curve. But the world is not equivalent to throwing a dice or a coin. The world is a complex system. A complex system is characterized by the ability of its elements to relate, influence each other, as well as by their adaptability. A Gaussian normal distribution refers to independent events that do not affect each other, do not have internal memory. And we, embedded in anthropogenic complex systems, are governed, as Nassim Nicholas Taleb described it in his book The Black Swan, by our ignorance(35) – an unread library, what we do not know about, hidden from our eyes, dependencies between seemingly unrelated yet at a deeper level connected events.

The world, on the other hand, being a complex system, constantly generates events that surprise us. Speculative bubbles, crises, world wars, local military conflicts, natural disasters – the scale of which seemed unlikely (e.g. the earthquake that resulted in the tsunami that destroyed Fukushima), like demises of companies, currencies, entire societies

In the 1960s, Benoît Mandelbrot presented to the economic community(36) that the time-based chart of changes in commodity and securities prices has the so-called „fractal dimension”(37). Chaotic charts of price changes depicted on different time scales are self-similar. This observation also applies to currency, bonds and derivatives markets. The fractal dimension of such charts does not conform with the normal, Gaussian risk distribution, but fits the power-law distribution of events in complex systems. And complex systems have their connectivity, influence, adaptiveness and memory.

The logic of fractal randomness is different from the Gaussian one. It is the logic of the probability of occurrence of events in some form of interdependence that is often difficult to directly notice. Measured probabilities of occurrence of various phenomena – distribution of wealth, valuation of financial instruments, earthquakes, size of companies, reaction of markets, timely and qualitatively correct performance of a product or service have their exponents. But while trying to determine the probability of unlikely, rare events – ”black swans,” as specified by Taleb – we encounter barriers related to measuring the exponent(38). The less likely an event, the more hidden the dependency, the more accuracy we need to achieve based on data collected in the past. And the slight inaccuracy of the estimated exponent implies a radical change in the forecasted result. Of course, we can trust some theory and deliver our estimates based on its model, but both the theory and the model always involve certain simplifications, weaknesses. There are some dependencies unnoticed or omitted as part of the simplifications, so you cannot blindly refer the result to reality or else we may end up with catastrophic consequences.

The human mind intuitively navigates in the classical land of Gaussian probabilities. The world, on the other hand, being a complex system, constantly generates events that surprise us. Speculative bubbles, crises, world wars, local military conflicts, natural disasters – the scale of which seemed unlikely (e.g. the earthquake that resulted in the tsunami that destroyed Fukushima), like demises of companies, currencies, entire societies. Unfortunately, we are co-responsible for this dangerously growing scale of the events – together with the increase in the complexity of the anthropogenic system.

Nassim Nicholas Taleb in The Black Swan formulates the fundamental truth that he recommends to accept as the basis for all modeling(39):

THE WORLD IS EPISTEMICALLY OPAQUE.

We will never know everything about it. We will not see all relationships, dependencies. The world, in particular the animate one, and even more so our anthropogenic one, is a complex system. It consists of independent yet communicating elements that affect each other, adapt to each other and remember the past to a certain extent (enough to complicate the future). In such world all models have hard constraints – namely the difficult, and sometimes impossible to be accurately determined exponents of probability of events that can occur within these models. They have the expiry date that guarantees their correct operation, yet unknown due to changes caused by the adaptation of the elements that make up those models.

Must we, therefore, refrain from estimating uncertainty, unpredictability and risk? Does modeling reality make sense? In regard to this matter I give the floor to Taleb: As I have already mentioned, for grassroots empiricists the world really looks different in terms of epistemology. In this perspective, there is no 'the’ equation that rules the universe; we need to observe data and make hypotheses about the course of real processes, then „calibrate” and adapt our equation based on additional information. As the events unfold, we compare what we see with what we expected to see. The discovery that history is moving forward rather than backwards usually teaches humility, especially those who are aware of a narrative fallacy. The belief is that businessmen have huge egos, but in reality they often do their homework in humility while observing differences between the decision and its consequences, between precise models and reality(40).

Nonetheless, modest and limited activities of „grassroots empiricists” did not satisfy human mind with its need for bigger ideas. Hence the need for further-reaching descriptions, divisions and classifications of thinking how to deal with variability, with the complexity of the world.