In a world where setting up a simple meeting can feel like herding cats, recent findings from Case Western Reserve University highlight how much harder it gets to find a good time for everyone as more people join the conversation. This study explores the intricate mathematics involved in this everyday dilemma and sheds light on why scheduling can often be so challenging.
In a world where setting up a simple meeting can feel like herding cats, recent findings from Case Western Reserve University highlight how much harder it gets to find a good time for everyone as more people join the conversation.
This research, published in the European Physical Journal B, examines the mathematical intricacies of this routine activity and provides fresh perspectives on why it often seems so difficult to arrange meetings.
“If you enjoy thinking the worst about people, you might find this study interesting,” joked researcher Harsh Mathur, a physics professor at CWRU’s College of Arts and Sciences. “However, it’s about more than just Doodle polls. We initially aimed to investigate polling, but we discovered there’s a lot more going on.”
The researchers applied mathematical modeling to assess how likely it is to successfully schedule a meeting, taking into account factors such as the number of attendees (m), the available meeting times (Ï„), and how often each participant is unavailable (r).
What they discovered was that as the number of participants increases, the chances of successfully organizing a meeting decrease significantly.
Specifically, the likelihood drops sharply once more than five people are involved, particularly if the availability of participants remains unchanged.
“We aimed to determine the odds,” Mathur explained. “The study of probability originated from analyzing gambling, but it equally applies to scheduling meetings. Our findings indicate that as the number of participants increases, the number of possible meeting times requiring polling grows exponentially.”
“The project began partly as a joke, but we found this exponential pattern hard to ignore. It demonstrated that organizing meetings is a challenging problem, comparable to major issues in computer science.”
‘More to the story’
Interestingly, the researchers identified similarities between scheduling issues and physical processes. They noticed that when the likelihood of a participant declining a suggested meeting time rises, there comes a critical juncture where the chances of successfully arranging the meeting plunge drastically. This is akin to “phase transitions” in physics, such as ice transforming into water, according to Mathur.
“Mathematically understanding phase transitions is a major achievement in physics,” he said. “It’s intriguing how something as ordinary as scheduling can reflect the complexities of phase transitions.”
Mathur also pointed out the broader ramifications of this study, which extends from casual situations, like sharing appetizers in a restaurant, to more complex circumstances, such as forming climate policy reports where consensus is vital.
“Building consensus is challenging,” Mathur mentioned. “Much like phase transitions, it’s a complicated process. Yet, that’s where the elegance of mathematics shines — it equips us with tools to comprehend and quantify these obstacles.”
He added that the study enhances understanding of the complexities involved in group coordination and decision-making, with potential applications across diverse disciplines.
Alongside Mathur, physicists Katherine Brown from Hamilton College and Onuttom Narayan from the University of California, Santa Cruz, contributed to this research.
