You ever read a study and think, “yeah, this one was personal”? 

A new paper from a trio of physicists has taken aim at that most frustrating manifestation of office diplomacy: the quest to schedule a meeting. The question at hand: how difficult is it to find a time when all participants are free?

The results, as you may have guessed from experience, weren’t great.

“We wanted to know the odds,” said Harsh Mathur, professor of physics at the College of Arts and Sciences at Case Western Reserve University in Cleveland, Ohio, and one of the authors of the study, in a statement. “The science of probability actually started with people studying gambling, but it applies just as well to something like scheduling meetings.” 

Using mathematical modeling techniques, the team figured out how the probability of being able to schedule a meeting changes – the answer being that it drops sharply as the number of participants increases. 

But the more the team looked at the data, the more interesting it became. “Our research shows that as the number of participants grows, the number of potential meeting times that need to be polled increases exponentially,” Mathur explained. 

“The project had started half in jest,” he said, “but this exponential behavior got our attention. It showed that scheduling meetings is a difficult problem, on par with some of the great problems in computer science.”

See, the data also revealed something else: a tipping point, at which scheduling a meeting becomes all but impossible. That figure isn’t all that large, it turns out – a measly four or five participants, depending on how many potential timeslots are available.

It’s a sudden change reminiscent of a very common physical phenomenon: that of the phase transition. This most commonly refers to substances changing from one state of matter to another – ice melting into water, for example, or water into vapor – and their elucidation through math was nothing less than a “triumph of physics,” Mathur said. 

“It’s fascinating how something as mundane as scheduling can mirror the complexity of phase transitions,” he added.

More than meetings and physics euphoria, though, does this study have any wider implications? In fact, it does, the team says. “The models we produced were mathematically sophisticated and could be useful more widely,” said Mathur in another statement, while co-author Katherine Brown, a theoretical physicist and Associate Professor of Physics at Hamilton College, New York, points out that “any problem that requires stakeholders to reach consensus may benefit from this approach.”

“This might include, for example, a climate conference in which every nation must agree on the final report,” she suggests.

But while its applications might be able to save the world, at its heart, the study tells us what so many of us already knew: that scheduling meetings is a real drag.

“Consensus-building is hard,” Mathur said.

“If you like to think the worst about people, then this study might be for you.”

The study is published in the European Physical Journal B.