Michael Trott
The Science and Art of Mathematica
Charged Icosahedron Potential Surface. Trott created this image on his notebook computer between sessions of a conference when he was asked a question about charged objects. He tried to explain the phenomena verbally, but to properly communicate the concept the data had to be visualized.
Trott doesn’t call himself an artist, but his book, “Graphica, The Imaginary Made Real: The Art of Michael Trott,” makes a strong argument to the contrary. In “Graphica,” Trott uncovers the innate beauty in a variety of mathematical expressions. His methods serve as a visual explanation of complex mathematical phenomena that cannot be expressed in the real world. His visualizations have not only graced covers of numerous publications; they have even been used in cutting-edge fashion design.
“I think it depends a little bit on the viewpoint of what you consider to be art,” says Trott, about the artistic nature of his work. “It can look striking and it does, in many cases, look very beautiful and very interesting. But it is typically not my intention to make something that is beautiful. It just comes out that way. I think this has pretty deep roots in science itself. It turns out that many things that are elegant from a purely mathematical point of view turn out to be pleasing for the human eye.”
“Visualizing scientific things makes it much easier to grasp what is going on than reading pages of typed formulas.”
Trott credits the ability to create such stunning imagery to advancements in technology. “It not only inspires,” he explains. “It makes this possible.” Trott’s background is in theoretical physics, not computer science, but advancements in modern technology, specifically Mathematica and Mac OS X, allow users to turn a concept from an idea to something tangible that can be used to help scientists understand how things work.
“My primary motivation is to understand how things work,” Trott explains. “Modeling is a way to do this. In most cases I start with the actual scientific problem — say a quantum mechanical time evolution. Once it has been successfully calculated and one ‘understands’ the solution, quite frequently an appropriate visualization comes to mind. With hardware and software getting better by the year, more and more problems open up for investigation. Sometimes things that were only doable on real supercomputers a few years ago, can be done by a fast desktop computer with an advanced algorithm.”
In a worldwide community of scientists that is rapidly moving towards highly specialized fields, effective communication of science and math is becoming both more difficult and more important. A visual language often serves as a common lexicon for people with varied backgrounds.
“Frequently techniques that are used by one field of science turn out to be relevant for other fields,” Trott says. “Visualizing scientific things makes it much easier to grasp what is going on than reading pages of typed formulas. It is also extremely important to create visualizations to communicate science to non-scientists; you need to show what you are doing, why it is useful, and what the point is. I think, especially at the moment, it’s critical that the next generation of young people becomes interested in science.”
Making Science “Convenient”
For Trott, Apple hardware, Mac OS X, and Mathematica create a perfect platform for data visualization. Mac OS X has the built-in tools to make Trott’s work pain-free and efficient, and the operating system’s UNIX-base makes for simple integration into Wolfram’s diverse network of computers. Apple is also a win for Trott from a basic performance standpoint. His Power Mac G5’s dual processors allow him to execute complex calculations on the back end while he interacts with his data in the foreground. With Apple’s transition to Intel, Trott expects to see even greater performance benefits.
Trott often uses the word “convenient” to describe using Mathematica in Mac OS X. At first look, it may seem to be a light word, but the importance of accessible technology often outweighs quantifiable performance metrics or features. Mac OS X breaks down technology barriers by providing a powerful environment researchers can step directly into, without the burden of complex overhead. Scientists like Trott relish the ability to work with technology rather than against it. Putting effective, innovative tools in the hands of brilliant people is what makes advancements in science possible.
NUMB3RS
A side effect of being a multi-faceted scientist — well versed in mathematics, physics, and computer visualizations — is the opportunity to do a variety of cool projects. Trott, along with a team of colleagues, is currently a technical consultant for the CBS show “NUMB3RS,” where the main character is a mathematician who uses functions and statistics to solve crime cases. Trott gets an early release of each manuscript and makes comments and suggestions on the mathematical elements of the plotline. He also prepares various pages of mathematics to back each concept, which the show uses in computer animations and on the main character’s chalkboard, where he thinks out his solutions.
Soccer Doughnuts?
A Dieter Kotschick article in Scientific American explores the geometry of a soccer ball by generalizing on its most defining property: black pentagons surrounded by white hexagons. Michael Trott was brought into the project to explore non-spherical mathematical figures that can be made with the same property. Trott explains: “I had some other ideas of what to do with this, so I thought, let’s make some visualizations of how this works. Some of the transitions are pretty complicated so I decided to make an animation where you actually see things change to make what is happening obvious. As it turns out, relatively exotic special functions play an important role in this example, which maps a torus into a sphere in closed form — created entirely on a Mac. The images were rendered in Mathematica in OS X, and the movie was put together using Final Cut Pro.”