How does a person see color? Several generations of scientists had a mathematical answer to this question – a three-dimensional color space. Its model was proposed by the scientist Bernhard Riemann, and Erwin Schrödinger and Hermann von Helmholtz developed it. Their discovery was used in science and industry for more than 100 years, until the new research accidentally found an error in the scientists’ calculations.

Our original idea was to develop algorithms to automatically improve color maps for data visualization, to make them easier to understand and interpret,” says the study’s lead author, Roxana Bujack.

However, during the work, scientists were quite surprised when they realized that the old and established application of Riemannian geometry did not work. Research at the intersection of mathematics, biology, and psychology has shown that Riemannian geometry overestimates the large differences between colors. It turned out that a large difference between colors is perceived as less than the sum you would get if you added up small differences in color that lie between two widely separated shades. Riemannian geometry could not explain this effect.

“We didn’t expect this, and we don’t know the exact geometry of this new color space yet,” says Roxana Bujack.

At the same time, an accurate mathematical model of color space perception is necessary to create industry standards. The new finding could improve understanding of how humans see color. This has the potential for better visualization of scientific data, improved color rendering in televisions, paint and textile industries, etc.