The study, published in the European Physical Journal B, dives into the mathematical complexities of this common task, offering new insights into why scheduling often feels so impossible.

“If you like to think the worst about people, then this study might be for you,” quipped researcher Harsh Mathur, professor of physics at the College of Arts and Sciences at CWRU. “But this is about more than Doodle polls. We started off by wanting to answer this question about polls, but it turns out there is more to the story.”

Researchers used mathematical modeling to calculate the likelihood of successfully scheduling a meeting based on several factors: the number of participants (m), the number of possible meeting times (τ) and the number of times each participant is unavailable (r).

What they found: As the number of participants grows, the probability of scheduling a successful meeting decreases sharply.

Specifically, the probability drops significantly when more than five people are involved — especially if participant availability remains consistent.

“We wanted to know the odds,” Mathur said. “The science of probability actually started with people studying gambling, but it applies just as well to something like scheduling meetings. Our research shows that as the number of participants grows, the number of potential meeting times that need to be polled increases exponentially.

“The project had started half in jest 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.”

‘More to the story’

Interestingly, researchers found a parallel between scheduling difficulties and physical phenomena. They observed that as the probability of a participant rejecting a proposed meeting time increases, there’s a critical point where the likelihood of successfully scheduling the meeting drops sharply. It’s a phenomenon similar to what is known as “phase transitions” in physics, Mathur said, such as ice melting into water.

“Understanding phase transitions mathematically is a triumph of physics,” he said. “It’s fascinating how something as mundane as scheduling can mirror the complexity of phase transitions.”

Mathur also noted the study’s broader implications, from casual scenarios like sharing appetizers at a restaurant to more complex settings like drafting climate policy reports, where agreement among many is needed.

“Consensus-building is hard,” Mathur said. “Like phase transitions, it’s complex. But that’s also where the beauty of mathematics lies — it gives us tools to understand and quantify these challenges.”

Mathur said the study contributes insights into the complexities of group coordination and decision-making, with potential applications across various fields.

Joining Mathur in the study were physicists Katherine Brown, of Hamilton College, and Onuttom Narayan, of the University of California, Santa Cruz.

Lead investigator David C. Whiteman, MBBS, PhD, Cancer Control Group, QIMR Berghofer Medical Research Institute, and Faculty of Medicine, The University of Queensland, Brisbane, Australia, explains, “There has been a general observation in numerous populations that melanomas appear to arise at different rates in men and women. We decided to investigate this observation rigorously and assess whether these differences have been constant through time or across generations by using large-scale data from population registries to investigate long-term melanoma trends in men and women.

The research team analyzed more than 40 years of melanoma data from Queensland, Australia, the USA, and Scotland. These three populations were chosen because historically they have had high (Queensland), moderate (USA), and low (Scotland) rates of melanoma. Over time, the rates of melanoma increased in all three populations, especially among women. In women in all populations, melanomas arise most commonly on the limbs, whereas in men, melanomas arise most commonly on the trunk and head and neck. In both sexes, there has been a steady increase in melanomas on the head and neck with increasing age.

Researchers found that in virtually all investigated populations, women experience higher rates of melanoma than men in early life (up to age ~45 years), but men develop melanomas at higher rates than women later in life (from ages ≥65 years). Furthermore, these sex-specific trends reflect complex patterns of incidence across body sites that vary consistently with age. Thus, in early life, women experience higher rates of lower limb melanomas than men, which persists into older ages. Also, on the upper limbs, women experience substantially higher rates than men from young ages until middle age (45-64 years), after which men experience higher rates. In contrast, on the head and neck and the trunk, melanomas occur at higher incidence in men than in women early in life. On all body sites, the rate at which melanoma incidence rises with age is much more rapid for men than for women.

The study confirms that men and women experience melanoma in different ways. While this is most likely driven by different patterns of sun exposure between men and women, there appear to be inherent differences in the ways in which melanomas develop at different body sites in women compared with men. Understanding the underlying biological differences could provide important clues about the etiology of this enigmatic cancer.

Dr. Whiteman concludes, “Invasive melanomas are potentially lethal cancers that are increasing rapidly in incidence. We need to understand how these cancers arise, and what drives their development, if we are to find better ways to prevent them. Studies like this one suggest that we may need to target our prevention efforts differently for men and women if we are to be effective in our attempts to control this cancer.”

There is growing scientific and public interest in the AMOC, a three-dimensional system of ocean currents that act as a “conveyer belt” to distribute heat, salt, nutrients, and carbon dioxide across the world’s oceans. Changes in the AMOC’s strength could impact global and regional climate, weather, sea level, precipitation patterns, and marine ecosystems.

In this research, measurements of the Florida Current were corrected for the secular change in the geomagnetic field to find that the Florida Current, one of the fastest currents in the ocean and an important part of the AMOC, has remained remarkably stable over the past 40 years.

The study published in the journal Nature Communications, the scientists reassessed the 40-year record of the Florida Current volume transport measured on a decommissioned submarine telecommunications cable in the Florida Straits, which spans the seafloor between Florida and the Bahamas. Due to the Earth’s magnetic field, as salt ions in the seawater are transported by the Florida Current over the cable, a measurable voltage is induced in the cable. The cable measurements were analyzed together with measurements from regular hydrographic surveys that directly measure the Florida Current volume transport and water mass properties. In addition, the transport was inferred from cross-stream sea level differences measured by altimetry satellites.

“This study does not refute the potential slowdown of AMOC, it shows that the Florida Current, one of the key components of the AMOC in the subtropical North Atlantic, has remained steady over the more than 40 years of observations,” said Denis Volkov, lead author of the study and a scientist at CIMAS which is based at the Rosenstiel School. “With the corrected and updated Florida Current transport time series, the negative tendency in the AMOC transport is indeed reduced, but it is not gone completely. The existing observational record is just starting to resolve interdecadal variability, and we need many more years of sustained monitoring to confirm if a long-term AMOC decline is happening.”

Understanding the state of the Florida Current is very important for developing coastal sea level forecast systems, assessing local weather and ecosystem and societal impacts.

Since 1982, NOAA’s Western Boundary Time Series (WBTS) project and its predecessors have monitored the transport of the Florida Current between Florida and the Bahamas at 27°N using a 120-km long submarine cable paired with regular hydrographic cruises in the Florida Straits. This nearly continuous monitoring has provided the longest observational record of a boundary current in existence. Beginning in 2004, NOAA’s WBTS project partnered with the United Kingdom’s Rapid Climate Change program (RAPID) and the University of Miami’s Meridional Overturning Circulation and Heatflux Array (MOCHA) programs to establish the first trans basin AMOC observing array at about 26.5N.

The study was supported by NOAA ‘s Global Ocean Monitoring and Observing program (grant #100007298), NOAA’s Climate Variability and Predictability program (grant #NA20OAR4310407), Natural Environment Research Council (grants #NE/Y003551/1 and NE/Y005589/1) and the National Science Foundation (grants #OCE-1332978 and #OCE-1926008).

The report, published in The Lancet Planetary Health, outlines how cities and businesses have the power to play a crucial role and become the “stewards” of critical Earth systems by demonstrating how they can reduce their environmental impact on the planet. The report summarises key findings of phase one of Earth Commission, founded in 2019 with a team of 18 globally esteemed interdisciplinary scholars as commissioners, involving more than 40 researchers in various working groups.

The report builds on the Safe and Just Earth System Boundaries report published in Nature last year, which found that most of the vital limits within which people and the planet can thrive have been surpassed.

One of three lead authors, Distinguished Professor Xuemei Bai, from ANU, who led the working group on Translation, said that companies and cities have the means to act and drastically transform and reduce pressure on the planet.

“Companies and cities have a huge potential to make a difference, especially if they work towards the same goal, which is to ensure the planet can provide for everyone long-term,” she said.

“They are more nimble and flexible than states, and can reduce their pressure on the planet by setting science-based targets in line with our findings.”

Professor Stuart Bunn, from Griffith University, co-led one of the working groups, which focused on the boundaries of freshwater and nutrient pollution.

The report found the planet’s ability to provide and protect is being stretched past its limits, although it remains possible for humans to escape poverty and harm caused by Earth’s system change, if urgent action is taken.

It found the only way to provide for everyone and ensure societies, businesses and economies thrive without destabilising the planet is to reduce inequalities in how critical Earth system resources, such as freshwater and nutrients, are accessed and used, and how responsibilities, such as reducing carbon emission, are shared, alongside economic and technological transformation.

By 2050, unless urgent transformations are made, the researchers argue that Earth’s climate will deteriorate to the point where there will be no “safe and just space” left.

That means that even if everyone on the planet only had access to the resources necessary for a basic standard of living in 2050, the Earth would still be outside the climate boundary.

The researchers say earth systems face the risk of crossing dangerous tipping points, which would cause further significant harm to people around the world unless energy, food and urban systems are urgently transformed.

The paper outlines a series of recommendations to ensure Earth’s climate remains within this so-called “safe and just space.”

• Firstly, a well-coordinated, intentional effort between policymakers, businesses, civil society and communities can push for changes in how we run the economy and find new policies and funding mechanisms that can address inequality whilst reducing pressure on nature and climate.

• Secondly, fundamental to the transformation is more efficient and effective management, sharing and usage of resources at every level of society including addressing the excessconsumption of some communities, which limits access to basic resources for those whoneed them the most.

• Thirdly, investment in sustainable and affordable technologies is essential to help us use fewer resources and to reopen the safe and just space for all, particularly where there is little or no space left.

The report has been published in The Lancet Planetary Health. It is co-authored by more than 60 leading natural and social scientists from across the globe.