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Here’s what you’ll learn when you read this story:
In a study on mathematicians solving mind-melting problems, video footage showed behavioral changes right before someone had a “eureka” moment.
As behaviors shifted, the most significant changes involved making connections between things that had not previously been connected.
While this study was done on mathematicians, the researchers think their method of predicting when someone is about to realize something could fit any discipline.
What happens right before the proverbial lightbulb goes off, before an insight is revealed, before someone pulls an Archimedes and leaps from the bathtub at a revelation that just struck like a crack of electricity?
It turns out that there is a way to pick up on the slight behavioral changes that give away when a “eureka” moment is about to happen. To see if it was possible to catch an oncoming “eureka” in real time, psychologist Shadab Tabatabaeian from Georgetown University led a study that followed doctorate-level mathematicians as they struggled through seemingly unsolvable problems pulled from the William Lowell Putnam Mathematical Competition.
Watching hours of recorded footage—most of it taking the form of scenes of frustration at a blackboard—Tabatabaeian and her research team had a eureka of their own. There was always a noticeable shift in behavior just minutes before the mathematicians would finally see where an answer was hiding. Movements that had been repeated ad nauseam suddenly changed, and new connections were made between things that were seen as unrelated before. When they were on the edge of solving a problem, their behavior would become less predictable.
“These moments were often accompanied by sudden movements and emotional exclamations, not unlike Archimedes running naked through the streets of ancient Syracuse yelling ‘eureka,’ though admittedly less dramatic,” the researchers said in a study recently published in the journal PNAS.
This stretches beyond math. Since behaviors associated with being on the brink of a discovery should be universal, Tabatabaeian thinks they would likely show up in just about any discipline, as should initial reactions after a discovery. The mathematicians observed would often claim they were genuinely surprised when answers appeared to them, and when asked whether they could explain how they reached their conclusions, most were unable to explain why an insight hit them. It seems that the “sudden flash of lightning” feeling quoted by mathematician Carl Gauss is not an empty metaphor.
Eureka moments land so abruptly that Tabatabaeian likens them to critical transitions, or “sudden shifts from one stable regime to another” that occur in anything that qualifies as a complex system—whether it is your own hand-eye coordination or something as vast as an entire ecosystem. Systems like this end up on the verge of a tipping point when they begin to become unstable. There are some early signals that indicate high risk of a segue into a new regime, and these signals have successfully predicted transitions in many systems.
When applying the idea of eureka signals to mathematicians, the researchers had to consider the system of a mathematician. For some reason, as they found, mathematicians often prefer chalk and a blackboard, so these are included in the system along with the actual mathematician and anything already written on the blackboard. There are some parallels to an ecosystem here—mathematicians create what Tabatabaeian terms “notational niches” for different parts of the problem. They will then go about figuring out the problem through writing, gestures, and glances from one niche in the system to another.
Before that lightbulb flashed in their minds, the mathematicians showed changes in blackboard activity. There were sudden shifts from one written niche to another. As someone approached an insight, these shifts—the product of a new way of thinking versus the previous way—would increase until the moment of confusion turned to clarity. In the case of one mathematician, attention shifted to different niches than before, and links were discovered between elements of the problem that had previously not been thought to be connected.
It turned out that most pre-eureka behaviors were similar, though they may have differed slightly depending on the individual. Mathematicians who are just about to come to a solution tended to shift their focus from a niche on one area of the blackboard to another and make unprecedented connections. This indicated when insight was imminent.
“Old ideas can be rediscovered with a single glance,” Tabatabaeian said. “New connections can be discovered by accident as one’s hands and eyes are drawn across the blackboard. The entire distributed system of situated activity may be the engine of […] insight.”
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