Insight and analysis problem solving in microbes to machines

• Gestalt insight-analysis problem solving taxonomy impairs study of intelligence.
• Gestalt taxonomy is redefined here with computational complexity classes.
• Problem discontinuity becomes state transitions in algorithmic outcomes and use.
• Problem restructuring becomes resource reorganization and processing substitution.
• New taxonomy classifies intelligence despite phylogenetic/technological boundaries.

A key feature for obtaining solutions to difficult problems, insight is oftentimes vaguely regarded as a special discontinuous intellectual process and/or a cognitive restructuring of problem representation or goal approach. However, this nearly century-old state of art devised by the Gestalt tradition to explain the non-analytical or non-trial-and-error, goal-seeking aptitude of primate mentality tends to neglect problem-solving capabilities of lower animal phyla, Kingdoms other than Animalia, and advancing smart computational technologies built from biological, artificial, and composite media. Attempting to provide an inclusive, precise definition of insight, two major criteria of insight, discontinuous processing and problem restructuring, are here reframed using terminology and statistical mechanical properties of computational complexity classes. Discontinuous processing becomes abrupt state transitions in algorithmic/heuristic outcomes or in types of algorithms/heuristics executed by agents using classical and/or quantum computational models. And problem restructuring becomes combinatorial reorganization of resources, problem-type substitution, and/or exchange of computational models. With insight bounded by computational complexity, humans, ciliated protozoa, and complex technological networks, for example, show insight when restructuring time requirements, combinatorial complexity, and problem type to solve polynomial and nondeterministic polynomial decision problems. Similar effects are expected from other problem types, supporting the idea that insight might be an epiphenomenon of analytical problem solving and consequently a larger information processing framework. Thus, this computational complexity definition of insight improves the power, external and internal validity, and reliability of operational parameters with which to classify, investigate, and produce the phenomenon for computational agents ranging from microbes to man-made devices.