From Comics to Cosmic Math
As a youth reading Marvel comic books, Thomas Banchoff became fascinated with the idea of objects in the fourth, fifth, sixth, or higher dimension. Later, as a mathematician, he became a leader in the study of the geometry of higher dimensions.
Mathematician Thomas Banchoff as a ten-year-old student on his way to Chicago to appear on a radio quiz show.
Banchoff creates computer graphics that let you visualize objects in the fourth dimension and beyond. His images show how the concept of dimension has significance in mathematics and in the practical world beyond.
When you realize that a dimension can represent time, temperature, weight, energy, or other variables, you see that higher dimensions are useful in physics, geology, medicine, and even modern art.
Imagine trying to picture what happens in an ecosystem, for example, where rainfall, water temperature, oxygen content, silt depth, and other factors may affect a population of fish living in a lake.
You can measure each of the factors separately, then create two-dimensional graphs showing what the population is at different temperatures or different rainfall amounts. If you wanted to show how the population varies with rainfall and temperature at the same time, you would need a three-dimensional graph. To add another variable, you would need a four-dimensional graph!
Finding ways to visualize such complicated systems to try to understand what is going on means learning to think in higher dimensions, just as we can look at an ordinary photograph or study the visual clues in a two-dimensional painting and imagine the three-dimensional shapes those flat pictures represent.
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