The Self-Organization of Insight: Entropy and Power Laws in Problem Solving

Abstract

Explaining emergent structure remains a challenge for all areas of cognitive science, and problem solving is no exception. The modern study of insight has drawn attention to the issue of emergent cognitive structure in problem solving research. We propose that the explanation of insight is beyond the scope of conventional approaches to cognitive science in terms of symbolic representation. Cognition may be better described in terms of an open, nonlinear dynamical system. By this reasoning, insight would be the self-organization of novel structure. Self-organization is a well-studied phenomenon of dynamical systems theory, associated with specific trends in entropy and power-law behavior. We present work using nonlinear dynamics to capture these trends in entropy and power-law behavior and thus to predict the self-organization of novel cognitive structure in a problem-solving task. Future explorations of problem solving will benefit from considerations of the continuous nonlinear interactions among action, cognition, and the environment.

Natural world physical, brain operational, and mind phenomenal space–time

“…Equilibrium is a thoroughly disordered regime, in which (a) there is no free energy and, therefore, no structure [42], (b) all distributions of matter and energy are homogeneous throughout, and (c) no portion of the system is distinguishable from another. The degree of disorder or lost energy is quantified as entropy [43]. All closed systems tend toward greater entropy over time [42,44].…”

“…The remaining energy produces fluctuations in the system, leading to a more disordered state at the microscopic scale. Thus, the influx of energy produces an increase in entropy [43]. In contrast to closed systems, however, open systems usually do not "bottle up" this entropy.…”

“…Five classical physiological bands are shown for the same raw EEG signal: delta (1-3 Hz); theta (4-6 Hz); alpha (7-13 Hz); beta (15-25 Hz); and gamma (35)(36)(37)(38)(39)(40)(41)(42)(43)(44)(45). These basic EEG bands are assumed to reflect different functional processes in the brain.…”

“…That is, what one immediately perceives is the physical object itself (or a part of it); thus there is no problem about inferring the existence of such objects from the contents of one's perception. However, since the "phenomenal objects" subjectively present in one's mind are the end result of a long causal chain of probability (statistical) events 43 happening at different levels of the neuronal system, this view no longer holds true [324]. Indeed, for us as subjects, the reality with which we are directly in touch is necessarily 41 Any definition of the concept of consciousness is bound to be controversial.…”

“…This approach has several assumptions: (a) consciousness exists in its own right; it is separate from other cognitive functions and can be independent from external reality (dream experience, [313][314][315]) and thus should be studied as an independent variable (for the argumentation, see [316]) in its own terms, (b) it is a natural phenomenon, (c) it has some causal powers distinct from purely neurophysiological (non-phenomenal) realm; recent neuroimaging [317] and cognitive studies have demonstrated that mental processes or events do exert "downward" causal influence on brain plasticity and the various levels of brain functioning (see also [318][319][320]) and that the conceptual representation of an ambiguous perceptual stimulus biases sensory processing [321][322][323], and (d) it ontologically depends on brain -the spatial location of the mental phenomenon in the natural world. 43 It should be made clear, that these events are totally outside the consciousness domain: They are either nonconscious entities in the external world (not in the organism), or they are nonconscious biological (neurophysiological) events inside the organism (and/or brain) [72,328]. Consciousness may causally dependent on them, but it does not depend on them ontologically -it can in principle exist in the absence of them (i.e.…”