## TED TALK RESPONSES

**Editor's Note: Maddy S. ('17)**watches and responds to three TED talks as part of her ExploreMath project.The first of three TED Talks that I watched was about the connections between relatively simple middle and high school math, with how animators for Pixar use it in their films. Animator Tony Derose begins the talk with an animation of Woody from Toy Story, being moved and walked along a graph. He explains that the X axis of the graph, can be programed into a computer, to determine how far left and right along the screen Woody’s character is, and the Y-axis does the same but for up and down. A predesigned animation of Woody can move, simply by having been programmed between two coordinates. Derose points out that in addition to geometry trigonometry, differential and integral calculus are also all important parts of this animation process. Trigonometry functions can be used to rotate an animated Character, or determine their depth on an image. Additionally, a process called subdividing is what is used to soften an image, and ultimately create what exactly a character looks like. Subdividing is when the original points of a shape are plotted, and the midpoints of all the points are found, and then connected to one another to create a new shape with softer edges. Subdivision can turn a square into a circle, and transform any original and very simple animation into something much more complex.

What I learned from this TED Talk I found particular fascinating, and was a piece about how Vincent Van Gogh potentially understood something about Turbulent flow, which scientists today still hardly begin to understand. The circular brushstrokes making up the sky, stars, and clouds in starry night follow the same movements as those noticed in turbulent flow. While there is no complete definition of turbulence, Russian scientist Andrey Kolmogorov discovered that all patterns in turbulence are self-similar, and repeat themselves at the same scale during the 1950’s. Many of Van Gogh’s paintings, but only those painted after or during his psychotic break represent patterns that fit Kolmogorov’s equation nearly exactly. This is not true to any other famous impressionist paintings from the time, or at all. In Van Gogh’s paintings he was able to use those variously colored lines to capture not just what he saw, but also the movement of what he was seeing, including luminance. Luminance is the intensity of light in colors. One part of the brain in the visual cortex see’s light contrast and motion, but not color, and blends together colors with the same luminesce. Another one of the brain’s subdivisions can still see colors, and make out differences even between colors of the same luminance. What Van Gogh proved he was able to do when painting the “Starry Night,” is tap into both parts of the brain at once, creating the illusion of movement, and displaying a deeper understanding of turbulence than many scientists today.

The Last TED Talk that I watched was by a mathematician named Dennis Wildfogel, who begins by raising a point his fourth grade teacher made when she said, “there are as many even numbers as there are numbers.” The point she raised was more than a bit intriguing to me, logically there would be something like double the amount of numbers to even numbers, yet mathematically they both sum to infinity. Wildman speaks about other systems of counting, and how you can count when you know the number of one thing proportional to another, and if you know the number of chairs in a room, and every chair has a person, you can assume the amount of people to be the same. This is one way to prove that actually the number of even numbers and numbers can be considered equal infinities because for every even number there will always be another number to match it up with, and vice versa. On the other hand, while it seems apparent that some infinities are equal, others are to be bigger or smaller than others, and yet this is a statement that can both be never proven true and also never proven false. Georg Canter came up with the idea that infinities come in different sizes, otherwise known as the continuum hypothesis, in 1900. Later in 1920, it was proven to never be false, but then later work proved in 1960 it became apparent that it can also never be proven true. Ultimately, the size of infinity is something that can never be known definitively as true or false.