In Mathematics, Do Coincidences Just Happen?
Just one month ago, many of us were thinking about picnics and fireworks. Some of us might have even been thinking about math in history, at least for a moment. One of my thoughts was that on July 4, 1826, former Presidents Thomas Jefferson and John Adams, who were once fellow patriots and then adversaries, died on the same day within five hours of each other. What are the odds?
If you think that’s not that unusual, consider these facts on Abraham Lincoln and John F. Kennedy:
- Abraham Lincoln was elected to Congress in 1846, and John F. Kennedy was elected to Congress in 1946.
- Lincoln and Kennedy’s name each contain seven letters in their name.
- Lincoln won the election in 1860 and his inauguration was held on March 4, 1861, and Kennedy won the election in 1960 and his inauguration was held on January 20, 1961.
- Both defeated an incumbent vice president for the presidency
- Both their vice presidents and successors were Southern Democrats named Johnson
- Both Johnsons’ were born in ‘08
- Both men were shot in the back of the head and in the presence of their wives…on a Friday.
- Lincoln was shot in Ford’s Theatre and Kennedy was shot in a Lincoln, made by Ford.
Supposedly when American novelist Anne Parrish was browsing bookstores in Paris in the 1920s, she came upon a book that was one of her childhood favorites – Jack Frost and Other Stories. She picked up the old book and showed it to her husband, telling him she loved this book as a child. Her husband took the book, opened it, and on the flyleaf found the inscription: “Anne Parrish, 209 N. Weber Street, Colorado Springs.” It was Anne’s very own book.
A German mother who photographed her infant son in 1914 left the film to be developed at a store in Strasbourg. World War I broke out and the woman assumed her picture was lost forever. Two years later she bought a film plate in Frankfurt (over 100 miles away) to take a picture of her newborn daughter. The film turned out to be a double exposure, with the picture of her daughter superimposed on the earlier picture of her son. Her original film had been mislabeled as unused, and had eventually been resold to her!
A set of twins, Jim Lewis and Jim Springer, were separated at birth and adopted by different families. Unknown to each other, both families named the boys James. Both James participated in law-enforcement training, both showed aptitude for mechanical drawing and carpentry, and each had married women named Linda. Both had sons; one was named James Alan and the other named James Allan. The twin brothers also divorced their wives and married other women – both named Betty. In addition, they both owned dogs which they named Toy!
The internet is full of stories like these. And you most likely have stories of your own which you chalk up to coincidence. Just how likely is it that the same person is hit by lightning twice? Or more practically speaking, if I played the lottery, what really are my chances of hitting the jackpot? David Hand, an emeritus professor of mathematics at Imperial College in London, believes that unusual events and miracles aren’t that uncommon, as he outlines in his book The Improbability Principle: Why Coincidences, Miracles and Rare Events Happen Every Day.
It’s intriguing that neurobiologists, psychologists, educational theorists, and other specialists all agree that the human brain wants to find patterns, look for connections in random events, make sense of chaos, and so forth. Is mathematics a universal “language” we use to order the world around us? Michael Starbird and Edward Burger have written a mathematics book for those for whom math just doesn’t add up. They collaborated on a text Heart of Mathematics (a fun one to read and teach from!) and in Coincidences, Chaos and All That Math Jazz: Making Light of Weighty Ideas, they go after the big concepts—infinity, the fourth dimension, chaos and fractals, Fibonacci numbers, coincidences and more.
Even planet watchers can enjoy some coincidences, one example I read about two years ago. Both Venus and the Moon were 78% full at the same time. If you recall on May 5, 2000 the planets Mercury, Venus, Earth, Mars, Jupiter, and Saturn were positioned in a line with the Sun. Additionally, the Moon was almost lined up between the Earth and Sun. Some people theorized changes in suicide and birth rates was related to this event. Maybe we’ll know more the next time the five planets Jupiter, Saturn, Mars, Venus and Mercury are in the same general part of the sky in September 2040.
Why do so many people think that it’s required to explore philosophical ideas in the arts, language, history, astronomy, etc, but then tolerate only the procedures in mathematics? We should celebrate the beauty of mathematical thinking, the chaos, the modeling, the big ideas, infinity… and coincidences. I’m having pizza for lunch in just a few minutes. What are the odds a reader is eating the same thing?
About the Author
Diane Hollister has been teaching college courses since 1992. In June 2015, she resigned from her full-time position at Reading Area Community College in Reading, Pennsylvania, where all the math courses have undergone some level of redesign. She still teaches online there and now is part of Pearson’s Efficacy team, helping instructors to implement programs and strategies that bolster student success.
She is intrigued by neurobiological research and learning theory, and she was quick to adopt adaptive learning as a new tool in her courses. Not only does she strive to help her students succeed, but Diane enjoys the collaboration with her peers. She has taught a variety of courses and loves learning how new technology and resources can help students be more successful.
Read more of her articles about math, ICTCM, and quantitative reasoning.