Colors and Incomputability

Donald Spector
Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture (2016)
Pages 337–344 Regular Papers


This paper explores some surprising connections between the frequencies of light we observe and foundational questions in the mathematics of real numbers and the theory of computation. We find that these foundational issues imply limitations on what can be seen, separate from any limitations from the laws of physics. Furthermore, it turns out that, given the kinds of observations one can make of light, the most reasonable expectation for the actual frequency of light underlying any set of observations is that that frequency comes from a particularly unusual class of uncomputable numbers called generic real numbers.