Acording to R. JENSEN: "Another manifestation of the unpredictability of chaotic dynamical systems is that the time-evolution is computationally irreducible. There is no faster way of finding how a chaotic system will evolve than to watch its evolution. The dynamical system itself is its own computer" (1987, p.179).
However, we can nevertheless compute reliable odds or probabilities for the outcome of these processes (i.e. for example football, or soccer games or turbulent flows). As a consequence probabilistic and statistical theories provide a natural description of average properties of chaotic systems".
"… Since simple models can yield complex, irregular behavior, we can actually hope to develop theoretical descriptions of a wide variety of apparently random, unpredictable natural phenomena using mathematical models which exhibit deterministic chaos" (Ibid).
Hence, the paradoxic situation appears wherein determinism can be partly described from a random base, but never in a such precise way as to allow for rigorous prediction.
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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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