"If you want to know when mathematicians are about to have a breakthrough, you don't need to look inside their heads. Just watch their movements at a chalkboard. I've always been super intrigued by this tension between how abstract and conceptual mathematics is, on the one hand, and then just how physical the actual activity of mathematics is, says Tyler Marghetis, a cognitive scientist at the University of California, Merced. He wondered whether he could use the manual labor of math to deduce"
"Complex systems sometimes abruptly change state. It can happen when metals become magnetic, when algae overtake a pond or when a horse goes from a walk to a trot. Often a period of instability precedes the tipping point. Some neuroimaging suggests that such a change also happens in the process of insightwhen the brain is stuck in a rut, wobbles and then finds the right track. This study illustrates that process at work."
"The researchers recorded six mathematicians at chalkboards as they each spent about 40 minutes working on two math proofs and thinking aloud. Observers made a note each time a solver shifted attention to other parts of the board by writing, erasing or pointing at equations, diagrams, or other inscriptions."
Mathematicians' physical interactions with a chalkboard exhibit measurable behavioral patterns that precede moments of insight. Six mathematicians were recorded solving proofs for roughly 40 minutes while thinking aloud, and observers logged attention shifts tied to writing, erasing, or pointing at board inscriptions. Analysis applied complex-systems tools to reveal increased instability and variability in attention switching prior to abrupt transitions to solution. Periods of wobbling among board regions reliably rose before breakthroughs, indicating a behavioral tipping point that marks an imminent cognitive shift from being stuck to finding the correct path.
Read at www.scientificamerican.com
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