In order to introduce what probability is, provide elementary information about probability theory and link it to the world around us, I will use the excellent book of Michał Heller Philosophy of Chance („Filozofia przypadku”). The author, while explaining in his book what randomness is, draws attention to the very interesting property of the human mind – a high probability, a high frequency of occurrence of an event is perceived by human beings as a sufficient justification for its appearance. On the other hand, a small probability, a small frequency of occurrence of an event gives rise in the human head to the need to justify it(5). This property of the human mind results – in the opinion of Michał Heller – from the way the environment influences it:

The feature of the world which forced certain behaviors is its frequentist stability, namely that property of the world thanks to which the longer sequence of random events, the more frequency of occurrence of an event in this sequence approaches a certain number. Let us emphasize – it is the property of the world, not the theorem of the mathematical theory of probability. Should the world not have that feature, the strategy of adapting to often occurring events would not bring any evolutionary benefit. The appearance of a low probability event, i.e. of a random occurrence, is astonishing and demands justification as it is not „justified” evolutionarily. (…) The mind, simply by way of interaction with the environment, coded that certain events occur more often than others and it would pay off to use that knowledge. In this way, the structure of the mind has adapted to the structure of the world (to its frequentist stability)(6).

A small probability, a small frequency of occurrence of an event gives rise in the human head to the need to justify it

While discussing various definitions and case definitions, Heller draws attention to the fact that a small probability corresponds to our sense of surprise which we associate with something accidental, an event the appearance of which we are not sure, namely, the one we assign a probability less than one(7) (one means being certain about the occurrence of a given event). During their struggles with history people learned to use that „sense of surprise” both in practice and theory, which gave rise to the theory of probability with its contemporary, canonical form as a special case of mathematical measure theory developed by Andrei Kolmogorov.

How can you interpret probability? Heller gives two interpretations: subjective (epistemic) and objective (ontological). The subjective interpretation of probability is that probability is the measure of our ignorance of the actual state of affairs(8). We do not know if any events have occurred, we do not know if there are any cause-and-effect relations between them, we do not have full knowledge of the condition and functioning of the system regardless of whether it is a physical system – as a coin toss, or anthropogenic – as a company, a city or, eventually, the whole society. Whereas an objective interpretation of probability implies that probability is a measure of indeterminacy or non-determination of an event or a sequence of events indeed occurring in nature(9). In other words, the sources of uncertainty are reasons independent of the observer and his state of knowledge. Heller quotes here the works of Marian Smoluchowski in which the scientist considered random occurrence as a special kind of causal relationship. We witness it when a small cause causes a great effect, i.e. when a small disturbance of initial conditions causes large differences in future trajectories of the system(10). In nature, a typical example of this may be weather phenomena, especially violent ones – storms, hurricanes or cyclones. In anthropogenic systems, these will be revolutions, violent collapses of social systems, stock exchange panics.

In practice, writes Heller, both of these interpretations occur concurrently, or even mix and overlap. They illustrate – I will add here – actually happening events, intermingling of stability and instability prevailing in the world around us as well as our knowledge of the functioning of the systems in which we are embedded. It is worth recalling the above described behavioral lenses, Kahneman’s Systems 1 and 2, Haidt’s Elephant Rider, Mischel’s hot/cool systems – all of them can be treated as modules of our mind used to estimate the probability: of success or failure, dependence between phenomena, cause and effect consequences, effectiveness of undertaken actions. These behavioral lenses contributed to the creation of the probability theory, which in turn gives grounds to today’s banks, stock exchanges, financial systems, insurance and medicine proceedings. Using our personal, individual behavioral lenses, we make more and better attempts to predict how the environment will change under the influence of our actions as individuals but also as a community.

As I described in the example of behavioral sciences and probability theory, each of us has the natural inclination to model the world around. Modeling – whether unconscious or conscious – is to result in benefits, achieving goals, avoiding risks. We model not only at the individual but also at community level: of enterprises, organizations, institutions, societies, states, international corporations or inter-state organizations. However, while individual modeling takes place with personal control and on the account of each individual, modeling at the level of the community is not simple, accessible or understandable for everyone. And the scale of the potential consequences of adopted models, the scope of responsibility, risk and uncertainty are incomparably greater. To bring the problem of modeling reality closer, I will confront classical (still widely used by enterprises, organizations, institutions and governments) ways of describing the world with a new view and new ideas how to deal with the complexity of what surrounds us.