Michael Starbird and Edward Burger have written a mathematics book for those of us for whom math just doesn’t add up.
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.
“The idea is that there’s this world that is beautiful, fun and accessible to lots of people, that can make people enjoy the thinking process and enjoy thinking about the really incredible concepts that are in mathematics,” says Starbird, a professor in the Department of Mathematics at The University of Texas at Austin.
The authors not only want to make math more accessible, “but tantalizing and actually enjoyable so people will want to turn the page because it’s intriguing,” he says.
Starbird and Burger, a math professor at Williams College in Williamstown, Mass., (who earned his Ph.D. at Texas), previously teamed up to write a textbook, “The Heart of Mathematics: An invitation to effective thinking,” which is used in colleges and universities around the country.
The new book, to be published in late August, is aimed at “people who are interested in ideas,” Starbird says.
Starbird and Burger find dozens of ways to explain math that are rooted in everyday life and common experience. They present math in a conversational style with humor, surprises and references to the broader culture.
Starbird and Burger visit the produce aisle of the grocery store and ponder a pineapple to explore numbers in nature and the nature of numbers.
Michael Starbird (left) and Edward Burger go after the big math concepts in their new book “Coincidences, Chaos and All That Math Jazz.”
They consider whether similarities between Presidents Lincoln and Kennedy are coincidence or something more.
Deep thought from a pineapple
What does a pineapple have to do with math? Not only a pineapple, but also a pinecone and a daisy and a sunflower and other products of nature?
They help explain a way of thinking.
Start by looking at the pineapple and you might notice there are spiral patterns running in both directions around it. The next step is to count the spirals. Most healthy, well-rounded pineapples will have eight spirals in one direction and 13 in the other.
Examine pinecones, daisies and sunflowers and you see that spirals abound in nature.
Lay out the numbers of spirals found on each item in ascending order and this is what they look like: 5, 8, 13, 21, 34, 55, 89 and so on. The key is that two consecutive numbers in the sequence add up to the next number and so on forever.
They are called Fibonacci Numbers after Leonardo of Pisa, a 13th century mathematician. He was known as Fibonacci because he was a member of the Bonacci family.
Starbird and Burger show that the Fibonacci numbers unfailingly lead to the Golden Ratio, the attractively proportioned shape of the Golden Rectangle that seems to appear in art and architecture throughout the ages.
The math secret here is that you can find mathematical patterns in nature that, with a more detailed look, tell you something about the world.
“The step of looking more deeply with more detail at familiar things in the world is part of the key to opening up new worlds and that’s a terrific strategy,” Starbird says.
The non-math math strategy
Starbird began opening up the world of math to non-math students when the university’s Plan II honors program asked Jim Vick, also a professor of mathematics, and him to develop a course for Plan II students. After one semester of joint effort, Vick and Starbird went on to develop their own Plan II math classes.
His first independent attempts didn’t go all that well in the early years, he says.
He realized that the students were being introduced to the greatest ideas in their other subjects—the greatest music, literature and philosophy.
“Yet what I was giving them (in math) was the first few steps of a ladder they would never climb,” he says.
His breakthrough was to realize that students could be turned on by the great concepts of math—without having to know how to do what some might consider the grunt work of math such as factoring polynomials.
Professor Michael Starbird is a fan of “NUMB3RS,” the CBS television show that began in early 2005.
“I watch it,” Starbird says. “What could be better? Math and murder! I’m all for anything that makes mathematics intriguing.”
In the show, a math-genius professor at the California School of Science and Technology helps his brother, an FBI agent, solve crimes ranging from murder and embezzlement to bio-terrorism.
The math brother, Charlie, schools Don, the FBI brother, and his colleagues about statistics, probability, and chaos every Friday night.
Some in the mathematics community give the show low grades because the mathematical conclusions are not always credible.
In response, the cops, lawyers, doctors, teachers and nuclear plant operators portrayed on TV might tell the math poo-bahs, “Join the club.”
Starbird agrees the show tends to exaggerate.
“The speed with which mathematics gets done on that show is really quite impressive,” he says.
But he is solidly behind the idea of having math play a central role for an hour of prime time every week.
“It has a positive effect on people,” he says. “It can make people curious about math.”
“So part of the philosophy was to come to the realization that we owe it to these students to present what we view as some of the high points of mathematical thought,” he says.
The next step was to figure out how to present the material.
What you don’t do, he says, is use mathematical terms nor the brevity which mathematicians consider so elegant. Neither “is a human activity.”
Instead, Starbird uses stories, surprise and everyday life as the basis for the math course—and the book.
Our daily math
Math and teaching have been a part of Starbird’s life since he was a boy in Southern California. His father taught math, physics and astronomy at a community college and his mother taught remedial English at a junior high school in an East Los Angeles barrio. One pair of grandparents were also teachers.
His father “would bring mathematical and physics problems to the dinner table,” Starbird says. “My brother and I talked about them. Mathematics was just a part of daily life.
“In fact I often look back on that experience and realize how unusual and significant it was,” Starbird says. “That it made mathematics something that wasn’t confined to a classroom and it wasn’t something you thought about just in the confines of school. But instead it was something that was part of your regular existence.”
Starbird earned his Ph.D. in mathematics at Wisconsin and came to The University of Texas at Austin to teach in 1974. His brother Tom got a Ph.D. in mathematics at the University of California, Berkeley and works at NASA’s Jet Propulsion Laboratory in Pasadena.
At Texas, Starbird has won numerous teaching awards and is a member of the university’s Academy of Distinguished Teachers.
He calls the focus on teaching math to non-math majors the third part of his career. The first was his research in the field of topology and his second was in administration as an associate dean in the College of Natural Sciences.
Coincidence? Or not?
It is no coincidence that Starbird teaches and writes to make math more accessible.
And Starbird would argue that things that seem to be coincidences or rare occurrences really aren’t. They can be explained by math, of course.
Since the 1960s there has been a mini-industry of people pointing out the eerie similarities between Abraham Lincoln, assassinated in April 1865, and John F. Kennedy, assassinated in November 1963.
Lincoln was elected to Congress in 1846, Kennedy 100 years later. Andrew Johnson, who succeeded Lincoln, was born in 1808. Lyndon B. Johnson, who succeeded Kennedy, was born in 1908. John Wilkes Booth, who shot Lincoln, was born in 1839. Lee Harvey Oswald, who shot Kennedy, was born in 1939. Kennedy’s secretary was named Lincoln; Lincoln’s secretary was named Kennedy.
Before the Twilight Zone theme goes rocking through your brain, listen to what Starbird and Burger have to say about coincidences.
To start with, there are thousands of facts in the record about Lincoln and Kennedy and it is expected there would be some similarities. As far as those 100-year-apart dates, there should be more in common if there is a supernatural connection. And with the similarity of names involved some coincidences are bound to occur just because of the thousands of names associated with each president.
“The Lincoln-Kennedy similarities don’t come from the grassy knolls of covert cosmic conspiracies, but rather from the mathematical certainties of coincidences,” Starbird and Burger write.
Do the math—everyday
Putting the world into a mathematical context might be interesting and even fun, but what can you do with it?
Observing and analyzing are important in dealing with the world every day, Starbird says.
“You figure out a way to take the world that is coming at you, that is new and different every day and figure out a way to puzzle it through,” he says. “And you try to get insight into it and try to organize it in a meaningful way. And that ability is what mathematics is really all about.
“It’s a question of finding the patterns, finding the symmetries, finding the insights, finding the essence, finding the meaning. Those strategies are what are extremely well illustrated by these abstract mathematical ideas.”
Then again, interesting and fun are important, too.
Starbird says, “I just think life is much more interesting and fun if you’re thinking and thinking about all sorts of things and exploring and questioning and asking, finding things out.”