According to M. BELIS: "Aleatory phenomena present a subjective aspect related to the observer and an objective one, which corresponds with their own nature. The subjective aspect consists of the difficulty to know (by observation or by measure) the perturbing phenomena which exert some influence on the results of the process. The objective aspect is precisely the fact that the process can be influenced by infinitesimal variations of the environmental phenomena, i.e. that it is unstable. While perturbing phenomena generally also take place in deterministic processes, the stability of these latter makes them invulnerable to perturbations. A phenomenon is either random or not, independently of the presence of an external observer, but according to the instability or stability of the causal connection which determines it. As POINCARÉ did notice, the movement of the heavenly bodies is a stable, deterministic phenomenon, independently of the degree of any terrestrial observers ignorance, while dice throwing is aleatory because of the instability of the causal connexion which determines the results" (1938, p.66).
However, POINCARÉ himself has been the first to show that, even objectively, the movements of the heavenly bodies are not rigorously deterministic. He demonstrated the impossibility to find a perfectly exact solution to the three bodies problem and set the first bases of the theory of chaos which is presently being developed (Understanding chaos as randomness within deterministic limits).
M. BELIS pursues nonetheless as follows: "However, after a long succession of experiences a stability of the results appears in cases in which the unstable causal connections are a structural make-up of a number of permanent causes".
This is precisely how most aleatory phenomena, random at short term, show nevertheless at long term an embedding global determinism, which figures basically a kind of statistical limit to randomness.
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Bertalanffy Center for the Study of Systems Science (2020). Title of the entry. In Charles François (Ed.), International Encyclopedia of Systems and Cybernetics (2). Retrieved from www.systemspedia.org/[full/url]
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