{"id":445474,"date":"2026-02-25T21:36:10","date_gmt":"2026-02-25T21:36:10","guid":{"rendered":"https:\/\/www.newsbeep.com\/uk\/445474\/"},"modified":"2026-02-25T21:36:10","modified_gmt":"2026-02-25T21:36:10","slug":"schrodingers-century-old-color-theory-completed-by-us-scientists","status":"publish","type":"post","link":"https:\/\/www.newsbeep.com\/uk\/445474\/","title":{"rendered":"Schr\u00f6dinger’s century-old color theory completed by US scientists"},"content":{"rendered":"

Researchers in the US have finally completed the missing mathematical pieces of theoretical physicist Erwin Schr\u00f6dinger\u2019s century-old color theory, based on his geometric model describing how humans perceive color. <\/p>\n

In the 1920s, the Austrian-Irish scientist proposed a mathematical model of color perception based on visual response. He suggested that the full range of human-visible colors could be mapped as a three-dimensional geometric shape defined by cone-cell responses.<\/p>\n

Now, a team of researchers led by Roxana Bujack, PhD, a computer scientist at Los Alamos National Laboratory (LANL), used advanced geometry to show that saturation, hue, and lightness aren\u2019t shaped by culture or experience.\u00a0<\/p>\n

The scientists finalized Schr\u00f6dinger\u2019s model and showed that these attributes are built directly into the mathematical structure of human vision, and not just \u201cin the eye of the beholder.\u201d <\/p>\n

\u201cWhat we conclude is that these color qualities don\u2019t emerge from additional external constructs such as cultural or learned experiences but reflect the intrinsic properties of the color metric itself,\u201d Bujack stated. She said the metric describes color differences as measurable geometric distances.<\/p>\n

Schr\u00f6dinger\u2019s color puzzle<\/p>\n

Human vision depends on trichromacy, meaning that it uses three types of cone cells (photoreceptors) in the retina \u2013 red, green, and blue \u2013 to\u00a0detect wavelengths<\/a>\u00a0and produce color vision. In the 19th century, German mathematician Bernhard Riemann first proposed that these perceptual spaces are not straight, but curved.<\/p>\n

In the 1920s, Schr\u00f6dinger defined the perceptual attributes of hue, saturation, and lightness<\/a>. He suggested these qualities arise from a metric of color perception in his Riemannian framework. His definitions provided a century-long framework for understanding color attributes.<\/p>\n

\"\"Results from the color perception experiments the team conducted. Image credit: Los Alamos National Laboratory (LANL)<\/p>\n

However, while working on algorithms for scientific visualization, the researchers detected shortcomings in Schr\u00f6dinger\u2019s mathematical foundations<\/a>. This opened the door to further refining the mathematical understanding of color perception.<\/p>\n

The team found that the neutral axis, the line of gray tones that runs from black to white, was a major problem. They realized that Schr\u00f6dinger had never actually defined the axis mathematically, even though his definitions rely on how colors are positioned relative to it.<\/p>\n

Fixing the gap<\/p>\n

To define the neutral axis, the team worked outside of the Riemannian model. It marked a significant breakthrough in the mathematics of visualization. They also corrected two additional effects. <\/p>\n

They also addressed the Bezold- Br\u00fccke effect, in which increasing brightness can make a color appear to shift in hue. The team did this by using the shortest path, instead of a straight line, in their geometric model of color perception. <\/p>\n<\/p>\n

The scientists also used the shortest path in a non-Riemannian space to address the phenomenon of diminishing returns in color perception. \u201cUnderstanding color perception is an important component of visualization science, a critical capability that informs many useful endeavors,\u201d they concluded in a statement<\/a>. <\/p>\n

Their work, presented at the Eurographics Conference on Visualization, represents a culmination of a project on color perception. The same project also delivered a pioneering study<\/a> in the\u00a0Proceedings of the National Academy of Sciences in 2022.<\/p>\n

Their current paper has been published<\/a> in the Computer Graphics Forum, the official journal of the Eurographics Association.<\/p>\n","protected":false},"excerpt":{"rendered":"Researchers in the US have finally completed the missing mathematical pieces of theoretical physicist Erwin Schr\u00f6dinger\u2019s century-old color…\n","protected":false},"author":2,"featured_media":445475,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[24],"tags":[161776,161777,18713,161778,2302,161779,90,58301,56,54,55,659,69513],"class_list":{"0":"post-445474","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-physics","8":"tag-century","9":"tag-color-recognition","10":"tag-erwin-schrodinger","11":"tag-los-alamos-national-laboratory","12":"tag-physics","13":"tag-saturation","14":"tag-science","15":"tag-theory","16":"tag-uk","17":"tag-united-kingdom","18":"tag-unitedkingdom","19":"tag-usa","20":"tag-vision"},"_links":{"self":[{"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/posts\/445474","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/comments?post=445474"}],"version-history":[{"count":0,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/posts\/445474\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/media\/445475"}],"wp:attachment":[{"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/media?parent=445474"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/categories?post=445474"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.newsbeep.com\/uk\/wp-json\/wp\/v2\/tags?post=445474"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}