Math error in a 100-year-old equation is changing everything we know about perceiving color

LOS ALAMOS, N.M. — Unlike science, it’s harder to disprove centuries-old theories of mathematics — certain equations are simply absolute. However, a new study has seemingly done the impossible. Researchers at the Los Alamos National Laboratory uncovered an error in a 3D mathematical space model that explains how our eyes perceive different colors. Understanding the correct formula may help the television and paint industries reformat how they create visual imagery and color.

Nobel Prize-winning physicist Erwin Schrödinger created the 3D mathematical space more than 100 years ago to explain how the eye can identify one color from another. How humans perceive color has helped immensely in the image processing of computer graphics and visualization tasks.

“The assumed shape of color space requires a paradigm shift,” explains Roxana Bujack, a computer scientist with a background in mathematics who creates scientific visualizations at Los Alamos National Laboratory, in a media release.

Bujack says that while it wasn’t the team’s intentions to overturn a foundational theory in math, “proving one of them wrong is pretty much the dream of a scientist.”

The original plan was to create mathematical algorithms to enhance color maps for data visualization with the goal of making them easier to understand. However, when researchers applied Riemannian geometry, which allows generalizing straight lines to curved surfaces, it didn’t work.

In order to perceive different colors, you need to use Euclidean spaces — the type of geometric shapes you probably learned in high school. More advanced models use Riemannian geometry. Each model plots red, green, and blue in the 3D space. Scientists use those colors because they are the most detectable hues in the light-detecting parts of the eyes. As a result, these colors are most often used and blended together in different combinations to create all the images you see on your computer screen.

Using psychology, biology, and mathematic principles, the research team found that Riemannian geometry vastly overestimates the perception of large color differences. The reason why is because people view a big difference in color to be less than the sum if you add up all the small differences in color that lie between two widely separated shades.

“We didn’t expect this, and we don’t know the exact geometry of this new color space yet,” says Bujack. “We might be able to think of it normally but with an added dampening or weighing function that pulls long distances in, making them shorter. But we can’t prove it yet.”

The study is published in the journal Proceedings of the National Academy of Sciences.

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About the Author

Jocelyn Solis-Moreira

Jocelyn is a New York-based science journalist whose work has appeared in Discover Magazine, Health, and Live Science, among other publications. She holds a Master’s of Science in Psychology with a concentration in behavioral neuroscience and a Bachelor’s of Science in integrative neuroscience from Binghamton University. Jocelyn has reported on several medical and science topics ranging from coronavirus news to the latest findings in women’s health.

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