The intrinsic complexity of any phenomena and exceeding the reductionist outlook in traditional science show that complexity entails an understanding that transcends a class of complex problems manifesting a myriad of subtle attributes from the lenses of novel ways of thinking and applicable laws. In that regard, evolution, order and complexity reveal the relationship between natural and social worlds, reflecting the required modern way of thinking while challenging the dichotomy of natural and social [Karaca, Y. (2022)].
Proving its existence since antiquity, complexity, as a scientific notion and idea, gained its explicit definition in the 1980s albeit its presence in mathematical systems was noted by Henri Poincaré with regard to three-body problem. During the 1920s, the quantification of complexity of simple mathematical formulae for statistical model was studied. During the 1940s, biological, social systems and other systems were characterized by high complexity considering the different types and behaviors with interconnections and interdependencies employed as the common definition terms. Following a decade, complexity was handled by pure mathematics, which followed the developments in information theory and the DNA structure discovery underscoring the information content of complexity. The content of algorithmic information emerged in the 1960s, which pointed to the shaping of the definition of complexity. Complexity was used in the definitions of other areas in the 1960s and 1970s with computational complexity theory heading a varied direction, while complexity was defined based on the resources required to perform the burdensome computational tasks. The 1980s saw the growth of research in complex systems, the focus having been placed on numerical measure of complexity [Wolfram, S., & Gad-el-Hak, M. (2003).], [Holland, J.H. (2014)], [Bar-Yam, Y., et al. (1998)], [Karaca, Y. (2022) ].
Far-reaching conditions like spontaneous order, non-linearity, feedback, robustness, lack of central control, numerosity, hierarchical organization and emergence as well as variations across thereof fall into complexity which unveils the different deep layers involved in complexity [Karaca, Y. (2022)]. Complexity along with all these variations in networks may also come to demonstrate that our decisions are not dependent on merely one single parameter, but on multiple numbers of parameters which hold hidden information.
Therefore, multifarious adaptive methods within mathematics-informed frameworks have come to the foreground to achieve solutions of complex problems, enabling that the solution will not be shallow or superficial but rather profound, reliable, smooth and robust. Such viewpoints would ensure the maintenance of quality, sustainability and above all meritocracy [Karaca, Y. (2022)].
Complexity thinking, on the other hand, entails a horizon that considers the subtle properties of different domains which indicate the necessity of their peculiar means of solutions and applicability. In neurological system, for example, complexity is concerned with the species owing their existence to the capability of their ancestors related to evolution and adaptation. The correlation between the complexity of brain design and optimality shows that progress can be made in the neurosciences showing the complexity of even very simple nervous systems with complexity being manifested in their structure, function, coding schemes as used to represent information as well as in their stances during the evolutionary history [Koch, C., & Laurent, G. (1999)], [Karaca, Y. (2022)].
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