Student uses math to practice century-old art

Paul Heinsdorf is a change ringer at bell towers in Philadelphia.

To explain the relationship between math and change ringing, Paul Heinsdorf walked up to a chalkboard and began writing out permutations.

Permutations — which are the basis of the notes in change ringing — are the ways that number sets can be arranged. Each number is assigned to a bell and the order of numbers tells the participant which bell to ring.

Change ringing is the art of pulling ropes to ring bells in different arrangements with a group of people. This practice originated in 17th-century England when it became a popular hobby. The English held competitions to see which group could perform the most enjoyable sounds, according to the Worcestershire & Districts Change Ringing Association’s website.

“This is heavily mathematics, but this is the wrong way to think about it.” said Heinsdorf, a senior mathematics major. “When I’m in the tower, I end up thinking about it like that, and that always keeps you stuck in whatever permutation you need to be on, but what you’re really doing is looking to see who you’re following at every particular spot.”

Heinsdorf was born in Cleveland and moved to Philadelphia in 1989. When he was in grade school, his mother started change ringing after she inquired about the art form at the Church of St. Martin-in-the-Fields in Chestnut Hill. Soon after, around age 11, he joined her in the bell tower. Now, at 34 years old, he has been ringing on and off since then.   

Ringing often appeals to people with technical degrees in mathematics, engineering and physics. But it is not limited to the mathematically or musically inclined, Heinsdorf said.

He added that people don’t have to be religious to get into change ringing, just patient.

“It’s just a matter of time,” Heinsdorf said. “It doesn’t require a whole lot of strength, it requires the dedication … to make sure that you can develop the muscle memory. It’s like the piano. You can practice the piano, but if you don’t like to play then what’s the point?”

Unlike the piano, change ringing doesn’t use musical notes. Ringers write and follow a sequence of numbers, which can be arranged in different ways.

In January, Heinsdorf’s church held its annual Quarter Peal Weekend. Change ringers traveled from as far as England to attempt a quarter peal, a technique that takes about 45 minutes to complete. A peal is defined as anything over 5,000 changes, which are the transitions between each sequence of every bell striking once.

“At Quarter Peal Weekend, there are a lot of things that people can’t ring in their own churches because they don’t have enough people that know certain things,” said Bruce Butler, the president of The North American Guild of Change Ringers, which organized the event.

Heinsdorf said there aren’t many opportunities to get people from all kinds of professions and walks of life to come together to engage in an activity like this.

Because it requires cooperation and working together to pull the ropes, change ringing has a strong community, Heinsdorf said. For many ringers, change ringing ran in the family. They began because their parents rung and their grandparents rung.

Heinsdorf said some change ringers have ancestry that can trace back to the art’s origins in England.

“There’s the social aspect, the mental aspect, the physical aspect,” Butler said. “Once you learn to ring, you can go into almost any tower in the world and announce yourself as a ringer and you’ll be made more than welcome.”

Butler has rung in more than 3,000 churches all over the world, including Westminster Abbey, St. Paul’s Cathedral in London, every bell tower in Australia and South Africa and all 52 of the North American bell towers.

The community of ringers drew Heinsdorf back to the bell tower in Chestnut Hill over time, when he had the availability. For him, it’s a social group like any other, except it’s based around a lesser-known activity.

“It’s something that otherwise, we’d be missing,” Heinsdorf said. “You do it because, if it wasn’t there, it’d be missing and if you don’t do it, nobody else will.”

Moriah Thoman can be reached at

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