For the Natural Science and Mathematics (NS&M) Colloquium on Oct. 19, Katherine Socha visited St. Mary’s to present her lecture, “maggie and milly and molly and may: mathematical stories inspired by the beach and e.e. cummings.” Socha, previously a Mathematics Professor at St. Mary’s, is now the Director of Educational Policy for Math for America.
Socha formatted her lecture around Cummings’s poem, “maggie and milly and molly and may.” The poem is six stanzas long, with the four middle stanzas each telling the story of the one of the four girls who all went to the beach one day. Socha picked a word or topic from each of these middle stanzas and somehow related it to interesting, and sometimes bizarre, concepts in math.
To make the lecture comprehensible to all those present, not only the math majors, Socha limited her use of math equations and advanced math theories. She instead opted to use examples and visuals to explain any mathematical concepts that she mentioned. “This is mathematics as much as a concert is music without having sheet music in front of you,” she said. This approach can also be thought of as “the difference between the ideas of mathematics and the symbols you use to describe out those ideas specifically,” she continued.
In the second stanza of the poem, we are told, “maggie discovered a shell that sang.” In order to relate seashells to mathematics, Socha talked about the Fibonacci spiral, which is created by drawing circular arcs connecting squares in the Fibonacci tiling. The Fibonacci sequence is a pattern of numbers that follows a specific equation. The spiral approximates the curves made by the shells that one would find on the beach.
Children commonly believe they can hear the sounds of the ocean when they put a shell up to their ear, just like Maggie. Socha explained it is not the sound of the ocean, nor is it the sound of the blood rushing through one’s ears, that the shell seems to make. Instead, “you’re focusing certain frequencies and then they’re picking up background noise,” explained Socha. Socha demonstrated this phenomenon by holding up a cup to her ear and explaining that the sound will change as the cup is moved closer or further away from the ear.
In the next stanza, we learn that “milly befriended a stranded star whose rays five languid fingers were.” In mathematics, starfish can be used as an excellent example of symmetry. “Symmetry is our friend; we like symmetry,” said Socha. She then demonstrated how to fold and cut a piece of paper into a perfectly symmetrical five point star. Socha also told the story of how she one day realized this fold and cut pattern only worked on letter sized paper. She thus explained, using trigonometry, what the angle of a certain fold in this process must be to make the star always turn out perfectly symmetrical.
Next in the poem, “molly was chased by a horrible thing which raced sideways while blowing bubbles.” Socha first talked about bubbles, which she described as “classical mathematics.” Bubbles are always enclosing a fixed volume, so the sphere created is nature’s way of minimizing the amount of energy used. Socha interpreted the “horrible thing” as a crab, and discussed animal gaits and their locomotion on land. She discussed both symmetric movement, like the bilateral symmetric motion of a squirrel bounding across the ground, and the asymmetric walk of a human. To help the audience understand, Socha demonstrated a lot of the different animal gaits, including “pronking,” which is the motion gazelles use when they are leaping straight up into the air during pursuit by a predator.
Finally, Socha read how “may came home with a smooth round stone as small as a world and as large as alone.” In relating this to mathematics, Socha talked about rotational symmetry. She discussed the discovery that when a drop of milk hits the still surface of a container of milk, a perfectly symmetrical sphere is created. Small splash rings grow up out of the spherical shape with the same number of “spikes” every time, as long as the distance dropped and size of the droplet remain the same.
Socha also went off onto a small tangent about crop circles. “There are a ton of theories on how crop circles form and they all focus on this magical amazing thing that they’re all perfectly circular,” said Socha. “How could natural causes create something so incredible as a perfect circle?” Because modern agricultural techniques cause corn crops to all grow to the same height, a corn field mimics the mathematical phenomenon of an infinitely flat plane. Just like the ripples created when a rock is dropped into water, when one corn stalk breaks because of something like static electricity, it will have rotational symmetry that will break all the corn stalks around it until the force is attenuated.
“I’ve heard many good things about Katherine Socha and I was not disappointed. I love the way she prefaced the talk, reassuring us that only one slide had actual equations on it,” said junior Christiana Sabett. “As a math major, I will admit that I was expecting it to be more math-heavy, but overall it was quite enjoyable. Katherine engaged the audience well and spoke fluidly. Now that I’ve met her, I do wish she would come back to teach at St. Mary’s.”
“The presentation was a quintessential liberal arts presentation. Analogy and literary reference is something the rest of the ‘general audience talks’ could learn from,” said junior Josh Kaminsky.
The next lecture in the NS&M Colloquium series will take place on Wednesday, Nov. 4 at 4:40 p.m. in Schaefer Hall 106. Dr. Steven Farber from the Carnegie Institution will present his talk entitled, “Chewing the fat with larval zebrafish: How a model organism can help us understand digestive organ function.”