Global Journal of Science Frontier Research, H: Environment & Earth Science, Volume 22 Issue 5

Deterministic laws, which “apparently make the world algorithmically comprehensible,” according to Bertuglia and Vaio (2005), are reduced from large data sequences (thanks to phenomenological recurrences). But systemic complexity is difficult to be completely described in a deterministic way – certain properties of complex systems are emergent (they are not intrinsically identifiable in any of their parts taken individually) (BERTUGLIA and VAIO, 2005). The complexity demonstrates that causality is not linear since in the long term, it acts so that the links between causes and effects of systemic phenomena can dissolve (not being identified), as highlighted by Bertuglia and Vaio (2005). In the short time, if causality can be successfully “explained” by the “set of encoding, decoding and implication processes” of “deterministic” laws, then a model could be built (BERTUGLIA and VAIO, 2005). The “butterfly effect” became the “popular slogan of chaos” (SMITH, 2007). Chaos, in the scientific sense, is a particular aspect of how something changes over time (in fact, change and time are the two fundamental themes that together form the basis of chaos), according to Williams (1997). Thus, chaos presents problems that challenge accepted ways of working in science, breaking down the lines that separate scientific disciplines – severing the principles of Newtonian physics, and eliminating the Laplacian fantasy of deterministic predictability (GLEICK, 1987). In various configurations, chaotic behavior can be observed, even if the equations that describe the system are not. Even elementary systems, described by simple equations, can have chaotic solutions (to the surprise of many scientists). Furthermore, the same system can behave predictably or chaotically, depending on little changes in a single term of the equations that describe it (SPROTT, 2000). Understanding that the study of chaotic behavior has received substantial attention in many disciplines, Berliner (1992) reviews mathematical models and definitions associated with chaos, emphasizing the relationship between chaos mathematics and probabilistic notions (pointing aspects of particular interest to statisticians and probabilistic), since chaos is related to complex “random” behavior and forms of unpredictability (BERLINER, 1992). Chaotic processes are not random – but there is a relationship – as even simple rules can produce extreme complexity (a mixture of simplicity and unpredictability). It is widely understood by the scientific community that being “deterministic” does not mean being “predictable” (SPROTT, 2000). As there are different ways of quantifying what is meant by complex or unpredictable behavior, a universally accepted mathematical definition of chaos does not seem to exist (some definitions related to chaos involve notions of ergodic theory – positive Liapunov exponents and the existence of continuous ergodic distributions) (BERLINER, 1992). Regarding the concept of chaos and the concept of probability, Bartlet (1990) also recognizes the relationship of their properties with the concept of chance: “it can be said that events are governed in part by the operation of the “laws of chance” (BARTLET, 1990). For Bertuglia and Vaio (2005), chaos and chance manifest themselves in the same way, both characterized by the disorder – in chaos, determinism is present but hidden (apparent disorder). In chance, there is the absence of determinism (real disorder, in random phenomena) (BERTUGLIA and VAIO, 2005). “The methods used to distinguish deterministic processes from stochastic processes are based on the fact that a deterministic system always evolves in the same way, starting from certain conditions” (BERTUGLIA and VAIO, 2005). The law of dynamics generates a single state consequent to a given state, according to the author. On the other hand, in a stochastic or random system, consequent to a given state, there are more possible states among which the dynamic system somehow selects (according to a probability distribution) (BERTUGLIA and VAIO, 2005). In practice, however, it cannot be assumed that a time series consists of data that result only from a deterministic law, having no stochastic components (BERTUGLIA and VAIO, 2005). Any series of experimental data is always “mixed with a stochastic process” that overlaps it, as background noise (called “white noise”), which reduces the quality of the information – this is due to a series of reasons (for example, there are unavoidable practical difficulties in measuring data, or data when measured never constitute a continuous sequence in time, and also any measurement is always affected by approximations of various types and origins) (BERTUGLIA and VAIO, 2005). And, to be sure of obtaining only the deterministic law for a system, it would have to be “closed” (no interaction with the outside environment). Thus, it would undoubtedly be deterministic since all its dynamics would be endogenous (BERTUGLIA and VAIO, 2005). However, in practice, the number of variables needed to consider the system closed would be so high as to make the calculation time unacceptably long to effectively identify the deterministic law at the origin of the observed dynamics, according to Bertuglia and Vaio (2005). That is, “it would certainly be closed and deterministic in theory, but impossible to treat from a practical point of view” (BERTUGLIA and VAIO, 2005). Chance plays a central role in human understanding of the nature of things – a probability that is neither “0” nor “1” corresponds to an uncertain event; however, ignorance about it would not be total – since “chaos limits the intellectual control we have over the world” (RUELLE, 1993). © 2022 Global Journals 1 Global Journal of Science Frontier Research Volume XXII Issue V Year 2022 20 ( H ) Version I Autonomous Technology in Scenario by Rare Geophysical Processes (Underwater Focus)