When most of us see a taffy-pulling machine cranking away on a touristy boardwalk, we think of sweet, sweet sugar. Jean-Luc Thiffeault thinks of sweet, sweet math. As an applied mathematician at the University of Wisconsin-Madison, Thiffeault is particularly interested in the way materials like taffy get mixed: In the machine, the candy is stretched and folded over and over to incorporate air and develop its light, chewy texture. As it’s pulled, the original rectangle of taffy gets stretched more and more—its length growing exponentially by the same ratio each time. That stretch ratio is what interests Thiffeault.
When a person pulls taffy, they’ll generally take the lump of candy and stretch it over a hook, bringing the two ends together. Then they’ll take that folded piece and stretch it over the hook again, doubling the length, and so on. In other words, “The human way of doing it is a multiplication factor of 2,” says Thiffeault. Mechanical pullers can do better, often yielding larger, exotic irrational numbers as their stretch factors.
It turns out that taffy pulling can be modeled by an abstract field of mathematics known as topological dynamics, essentially the study of long-term, large-scale changes over time in a mathematical space. (If the word topological sounds familiar, it was in the news recently as part of this year’s Nobel Prize in Physics.) The same mathematics that describes taffy-pulling also has more serious applications: many industrial processes, including glassblowing and drug preparation, require viscous fluids to be mixed in ways that are more like pulling taffy than stirring cream into coffee. “If you’re trying to stir really viscous things, like pharmaceutical industry pastes, you can’t just shake them,” says Thiffeault. “It’s not like mixing paint.”
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