Your brain likes patterns and categories; by grouping related ideas together, it can store and recall information quickly. Real-life continuous domains (like time, temperature, and taste) are inherently composed of infinitely many points of information, which our brains segment into finitely many categories for convenience (such as morning/afternoon/evening/ night, or sweet/sour/salty/bitter). This phenomenon is well-documented and is a topic of interest in the behavioral, cognitive, and social sciences.

The set of colors is another example of a continuous domain, which in English is segmented into categories called “blue,” “red,” “green,” etc. In this talk, I discuss how we apply mathematics —including linear algebra, geometry, and probability—to real-world data to study the occurrence of different categorizations schemes of the color space. I then outline several related open projects, which could be pursued as part of a 199 Reading/Research course in the Spring or Summer sessions.