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Reason to applaud: New paper from StFX math professor and students finds people always speed up when clapping together

January 29th, 2018
Dr. Ryan Lukeman

Ever wonder what happens when humans clap together? They always speed up!

That’s the result of a new paper published in January 2018 by StFX mathematics professor Dr. Ryan Lukeman and two of his students Kennedy Murphy and Michael Thomson, both now graduates, who together study collective human rhythmic behaviour, through clapping, in the paper, 'Groups clapping in unison undergo size-dependent, error-induced frequency increase' which appears in Nature Scientific Reports.

It’s a mathematical analysis of what happens when humans clap together.

“The question came to me during a Wilco concert years ago,” Dr. Lukeman says. “At one point in a song, the drummer stopped playing, and the audience was clapping along, keeping the beat. Very quickly, they lost the tempo, and the band members made a comment about how the audience is reliably poor at keeping time. I wondered why this might be—what about many people keeping time is more challenging than one person on their own? Since I had a background studying collective phenomena from a mathematical perspective, this seemed a perfect example of an emergent group pattern that we could study through individual interactions.” 

Dr. Lukeman says the research question remained only a curiosity until a few years later, when student Kennedy Murphy, now a data scientist, began a summer research position.

“He had some background in audio recording, so we started up some experiments recording individuals and pairs under the command to clap in unison. A year later, Michael Thomson (who now works as a senior economic analyst), also in a summer research position, continued the project, and eventually did the recordings of large groups. Here, we used about 40 different StFX classes of various size, up to a few hundred students at once. We’d simply turn off the lights, and ask the students to clap in unison, and record the group behaviour for a minute or two.” 

Kennedy Murphy

Michael Thomson

Dr. Lukeman says they found that groups were able to very quickly attain synchrony clapping together collectively. This wasn’t surprising, he says, as we see this kind of behaviour at sports events and concerts frequently.


“But, we also found that—every single time, in fact—the group would speed up, and furthermore, larger groups sped up more quickly. We later found a TED talk given by a rather famous applied mathematician, and one of the world’s foremost experts on the mathematics of synchrony, Steven Strogatz, who ran a similar experiment on his audience. They too sped up, and he commented that he had expected them to synchronize, but was surprised that they speed up. If it wasn’t obvious to Steven Strogatz, I figured we were on to something!”

“Observing the experiment was quite spectacular, typically, it would take one to three seconds for participants to find synchrony, then once it emerged, participants would reliably and collectively speed up," says Mr. Thomson who during his senior year conducted experiments with classes across faculties with class sizes varying between seven to 220 students. The only directive given to students wat that, after they turned off the lights and indicated they start, they synchronously applaud until otherwise directed.

The effects were particularly profound in larger groups, he says, where, from the initial cacophony of applause, small, disjointed pockets of synchrony would emerge in the group.

Then, all of a sudden, once groups merged into unison, the collective group would rapidly speed up the rate of synchronous applause, up to a point where they could no longer maintain effective synchrony, thus ending the experiment, he says.  

For each experiment, Mr. Thomson collected an audio recording, from which they were then able to extract, programmatically, the times at which the group collectively applauded.

The next phase was to model this process. Using what they had observed of individuals and pairs, they were able to scale up a collective model that tested two competing hypotheses: that humans naturally speed up individually, and the collective response is simply an average of this individual tendency, versus the speed-up arising from the human interactions during the experiment.

They found the latter to be consistent with their observations - that people respond to small timing errors made by other individuals, but more sensitively if they are just about to clap, than having just completed a clap.

“The results have application in understanding musical rhythmic behaviour, and how information spreads in collectively interacting human groups,” Dr. Lukeman says.

“More broadly, determining the inter-individual interactions that explain group level observations is of primary importance to understanding complex systems. And, there is an educational use for this: the study system provides an immediate and simple way to demonstrate concepts of synchrony and coupled oscillators to students.”


Dr. Lukeman says the study was also a good way to expose undergraduate students to research, something he says has become the primary focus of his research program.

“The opportunity for a student to, under guidance, delve deeply into a topic, to discover something novel, and to share it with the world is transformative to the undergraduate experience, and something I think we do quite well here at StFX,” he says. “And, from my perspective, I get to interact with very talented students who often take the lead on projects, and push the boundaries of my research program. It is tremendously rewarding.”

Both students say the experience was extremely beneficial.

After his 2015 graduation, Mr. Thomson went on to Western University to receive an MA in economics in 2016. He is now a senior analyst at Analysis Group, an economic consulting firm, in the San Francisco office.

“Typically, my work on cases involves a vast array of research and data analysis, both of which have been bolstered immensely by my research experience with Ryan at StFX. My academic background and applied analytical skillset which I fostered at StFX have proven indispensable while working closely with PhD and MBA graduates,” he says. “Additionally, my coding experience has taught me to be able to quickly learn new coding languages to be able to analyze different problems using various data sources from clients.”

Mr. Murphy, who graduated in 2014 and got a job as a data scientist at a start-up based out of Moncton, NB called Fiddlehead Technologies, agrees his experience at StFX was a big help.

“Doing research at StFX helped me after graduation because it prepared me to bridge the gap between academics and its application. The majority of my work today is time series based, which is directly comparable to what I did at X. I’ve also worked closely with professors in the region, as well as abroad to develop key features within Fiddlehead’s repertoire. This would have been more challenging if not for the time I spent parsing through academic papers, and applying their methods.”


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