Memory and Criticality

Dear Colleagues,

The subject of paradoxes as generators of new kinds of knowledge, illustrated in the recent book [1] may afford suggestions to trigger a debate on conflicting views into a significant progress of knowledge. The use of the either-or way of thinking yields a stalemate and it is not the proper way to deal with complexity science.

We propose a Special Issue of the journal Entropy that should contribute to shedding light into the following debates:

(1) 1/f noise

How can we combine the assumption that the world is driven by quantum mechanics with the belief that it should fit the second principle of thermodynamics? Is the second principle a consequence of the limitation of human minds, which are forced to describe as random the processes that would require an unlimited computational power to take into account their deep connection with coherence and reversibility? Or, is the opposite condition true: that quantum mechanics is not the ultimate theory of the world, and a suitable generalization of it would disclose the action of genuine randomness? We do not mean to propose a philosophical debate on this specific question, but are only using it as metaphor to outline the complexity problems for this Special Issue of Entropy.

In the case of the dynamics of the brain, there exists a widely shared conviction that the brain works at criticality and that this condition is signaled by the healthy brain generating 1/f noise. However, the 1/f noise spectrum apparently representing a remarkable deviation from randomness has two distinct origins. The former, which is more popular, is compatible with coherence and ultimately with reversibility. It is based on the assumption that the fluctuations generated by complex systems can be properly described by stationary correlation function. These fluctuations are sources of deviation from normal diffusion due to the fact that their stationary correlation functions yield very slow (non-integrable in time) decays. There exists another form of 1/f noise triggered by renewal events with correlation functions that are not stationary. This form of 1/f noise is incompatible with the traditional ergodic assumptions, thereby raising the question of what is the most convenient form of entropic treatment to adopt and to what extent it differs from the entropic treatment to adopt for the former.

(2) Evolutionary Game Theory, Emergence of Cognition

The emergence of cooperation from the interaction of units that are expected to be driven by self-interest is another form of paradox requiring a new way of thinking. In fact, the advocates of the field of evolutionary game theory have been successfully addressing this issue as a result of simplification, such as neglecting social activity not directly involving the paradoxical conflict between cooperation and self-interest, leaving open the question of whether the birth of cooperation may be an emergent process of the same kind as cognition. The emergence of cognition is widely interpreted as a result of criticality, but also criticality is the subject of different interpretations. Some of these interpretations involve renewal crucial events, thereby bringing us back to the open issue of the origin of 1/f noise. Is it possible that the brain, and in general more complex systems, from the biological to the sociological level, may host both forms of 1/f noise?

(3) Bounded Rationality and Criticality

Recent psychological experiments have led to discovering that the human brain may lead to judgment departing from classical logic, thereby leading many researchers to propose the use of quantum probability to explain bounded rationality, in conflict with the view that moving from the microscopic to the macroscopic level where the brain is supposed to operate, quantum mechanics is expected to turn into classical mechanics. There are signs that criticality may explain bounded rationality without involving quantum mechanics. However, criticality of complex systems of small size may generate crucial events and with them a form of 1/f noise that is incompatible with coherence, mainly resting on the unpredictability of crucial events. Do ways exists to analyze real data, physiological and social data, so as to assess if both forms of complexity are in action, and if it is not case, which of them is the genuine source of complexity? What entropic formalism has to be adopted?

[1] B. J. West, K. Mahmoodi, P. Grigolini, Empirical Paradox, Complexity Thinking and Generating New Kinds of Knowledge, Cambridge Scholar Publishing (2019).

Prof. Dr. Paolo Grigolini
Guest Editor

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