Aryn Plax
Metro Editor
Eugenia Cheng discussed applications of math in baking, braiding and other aspects of everyday life during her lecture “How To Bake Pi” Wednesday at Scripps College.
Cheng said that one can appreciate math without necessarily knowing how to do math, just as one can appreciate music or food without knowing how to make it.
She credited her mother with incorporating mathematics into her daily life in fun and stimulating ways, which shaped her current view of math. She said the lack of parents and teachers who introduce mathematics the way her mother did leads students to have little understanding of everyday applications of math.
“That’s why I started writing books,” Cheng said. “So that I can share those things with everybody, even if you don’t have someone in the family who can share it with you.”
Cheng defined mathematics as the study of how logical things work. However, she said that nothing actually behaves logically.
“In order to study anything logically, we have to ignore the pesky details that get in the way of it behaving logically so that it can turn into something more ideal,” Cheng said. “And that move of forgetting those details is a process of abstraction, where we move from the real world of actual objects to the abstract world of ideas.”
In her book “How To Bake Pi,” Cheng teaches mathematical concepts by drawing analogies to cooking.
She introduced mathematical structures from her book and drew analogies using Bach’s music, juggling, hair, factors of 30, cake and custard.
The first mathematical structure was a braid in which two of the leftmost strands cross over each other twice, the second to right strand crosses over the other two between the first and second intersection, and the rightmost strand crosses over the other two after the leftmost strands’ second intersection. She called this mathematical structure the “Bach braid.”
Cheng compared the mathematical structure to Bach’s Prelude in G Minor: Book 2 of the Well-Tempered Clavier.
“There are separate lines of music that wind their way around each other, but each one is like its own melody,” Cheng said.
Cheng led the topic of juggling by asking an audience member to juggle across the stage. Cheng said the paths each ball made as they traveled from one end of the stage to the other formed a three stranded braid similar to a hair braid.
She compared this braid to the Bach braid and said that strands of the Bach braid “float around.” She said that mathematicians studied the relationship the individual strands had to each other.
“It turned out later to have applications in all sorts of things, possible, for example, in early diagnosis of Alzheimer’s disease, which is thought to maybe having to do with some brain cells getting tangled up in wrong ways, and you want to be able to tell whether it’s really a different tangle than the one it’s supposed to be,” Cheng said.
Cheng segued into discussion of the factors of 30 by saying they have a “natural geometry.” She put “30” at the top, and under the number were three branches, all of which are factors of 30. The number six was under the first branch, the number 10 was under the second branch, and the number 15 was under the third. Two, positioned directly under six, had one branch connected to six, and one branch connected to 10, as two is a factor of both six and 10. Five, positioned directly under 15, had one branch connected to 10, and another connected to 15, as five is a factor of both 10 and 15. Three, positioned underneath 10, had a branch connected to six and a branch connected to 15. One, positioned underneath three, had a branch underneath two and five. The branches connecting these factors of 30 formed a cube, which Cheng said was the number set’s “natural geometry.”
Cheng talked about mathematical patterns that could be compared to the inside of a Battenburg cake. The inside Battenburg cake is divided into four squares, in which the top left and bottom right square are the same color, and the top right and bottom left square are the same color.
She compared this to a table in which one multiples positive and negative numbers: multiple one with one, and get one in the top left square, multiple negative one by one to get negative one in the top right and bottom left squares, and multiple negative one and negative one to get one in the bottom right square.
Cheng compared the order of operations in a math problem to the order in which one mixes ingredients to make a custard or cake dough.
Sometimes, changing the order of operations in an equation will result in the same number, just as combining cake ingredients in a different order will still result in cake dough.
However, changing the order of operations in an equation can result in an entirely different number, just as combining ingredients of a custard in a different order will not result in a custard.
She talked about the joy of learning math for its own sake, rather than for the practical applications.
“Math suffers from a burden of having to be useful,” Cheng said. “We talk about the applications of it because it’s useful. That’s like introducing someone to your friend and saying, ‘I’d like you to meet my friend, she’s very useful.’ Whereas math is amazing, and a lot of the mathematical breakthroughs that have happened have done so because mathematicians were simply curious, and the applications came hundreds, possibly thousands of years later. The most famous one is a piece of number theory from three hundred years ago that now is the basis of cryptography on the internet.”
“Sometimes it’s not the application that drives us,” Cheng said. “Sometimes it’s just the sheer curiosity.”
Cheng concluded her lecture by defining category theory, a mathematical interest she expands upon in her book “How to Bake Pi,” as “the mathematics of mathematics.”
“I think that logic is at the core of everything we do,” Cheng said.
Claudia Renero, junior at Chaffey High School, said she loves math and was most interested in Cheng’s relating of mathematics and three-dimensional geometric shapes to baking.
“I will apply it completely to my classes,” Renero said. “It gave me new energy for learning in my math classes, and I’m thinking of taking more mathematics classes when I go to college.”
Scripps student Ella Shahn worked at the event, helping scan tickets and organize the book signing following the lecture. Shahn said she was most interested in Cheng’s discussion of three dimensional shapes and visual representations of mathematical concepts.
“I loved the Bach piece and the way she visually represented that,” said Shahn, junior sociology major.
Gretta Richardson, also a Scripps student, worked as an usher for the event. She said she was impressed by Cheng’s connecting of mathematical concepts to everyday things, such as baking and hair braiding.
“It kind of made me miss math a little bit,” said Richardson, sophomore politics major. “I haven’t taken math since senior year of high school so now I’m thinking maybe I should take a math class just for kicks.”
Aryn Plax can be reached at aryn.plax@laverne.edu.
