Have you ever confronted a problem, knew a few bits of relevant information, but could not make any progress...until all of a sudden, the solution process occurs to you. That's intuitive problem solving...difficult to explain and impossible to replicate with a computer. But, it occurs and is not magic.
Peter Dodds, a UVM mathematics professor, studies complexity, especially in relation to intuitive problem solving. He sumarizes: "In its most simple form, a complex system is many distributed parts interacting in some distributed way, giving rise to some interesting, often unexpected, macrophenomena."
His example: Consider a neuron. Alone, it's a cell that conducts a chemical signal. But, when billions are woven together with links that adapt and change over time, the result is a brain able to intuitively solve problems.
Complexity theory helps explain how chaotic groups of army ants build bridges or chaotic air currents become a single tornado. By better understanding this rapidly developing field of complex systems science, researchers hope to improve hurricane forecasts, understand the effects of phosphorous pollution in a watershed, slow the spread of invasive species, make intelligent robots, and untangle the genetic and environmental threads that cause heart disease.
Due to the nonlinear mathematics underlying a complex system, one plus one might exceed two, as Aristotle claimed. But complex systems science adds a twist to his claim in that "the whole becomes not only more than, but very different from the sum of its parts."
A Suggestion: Do further research on complex systems science, especially as connected to intuitive problem solving. You will find mathematics woven throughout.
Source: ScienceDaily, November 24, 2008