Most of us grew up with some sort of taffy. I'm used to the salt water taffy that is cooked and the pulled and pulled and pulled until it's just right. Sometimes you can buy it a tourist places where its made using a machine. One mathematician got the idea to apply math to making better taffy pulling machines.A taffy pulling machine takes a piece of candy, stretches it, folds it again and again to incorporate air so eventually it develops its characteristic chewy texture. As the taffy is stretched, its length increases exponentially by the same ratio. It is the stretch ratio, that is what captured the mathematicians interest.
When a human stretches the taffy, they stretch it and then fold it in half. They stretch it again and fold it in half again and continue until it reaches the proper consistency. Mathematically, it uses a multiplication factor of two. On the other hand, when mechanical pullers are used, the multiplication factor turns out to be an exotic irrational factor.
It was discovered that pulling taffy by machine could be modeled using topological dynamics which studies the long term changes over time in a mathematical space. This is the same mathematics used in glass blowing and in drug preparation. It also describes how viscous materials need to be mixed together.
As part of his research, Jean-Luc Thiffeault read patent application on taffy pullers. He was looking at how a two dimensional material is stretched exponentially in one direction while shrinking in another. The first taffy pulling machine was patented back in 1893 but never was made due to not being developed enough. The first recognizable patent was filed in 1901 and granted in 1906. This machine is mathematically the same as the 3 rod machines used today but no one is sure if it was ever made.
In 1908, two men patented a simplified 3 rod machine that formed the basis of today's machines. In addition, businessman Herbert L. Hildreth of Maine built a taffy empire in the early 1900's. One of his employees patented a four rod machine in 1901 but it wasn't granted until 1903. Hildreth was not thrilled about this and ended up purchasing the patent for $75,000.
Due to all these machines being patented at about the same time, people began filing lawsuits and the Taffy patent wars went all the way up to the Supreme Court. The court declared that the two rods would move the candy somewhat but they could not properly stretch the material. To properly pull the material, the machines needed three rods.
Currently, there are two taffy pulling machines in use today. One has three rods, the other has four rods but they produce the exact same stretch factor of 1 + sqrt 2 or the silver ratio. Using this information and information from various patents, Thiffeault built a 6 rod machine based on a four rod which stretches the taffy about twice as much as current machines do.
I found this quite interesting. I hope you enjoyed it too. Let me know what you think, I'd love to hear. Have a great day.
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