Optics, Vision, and Evolution, after Mitchell Feigenbaum 1944-2019

Many people are aware of Feigenbaum's astonishing discovery of the universality of period-doubling, and the constant delta=4.66920 which carries his name.

In the last 13 years of his life Feigenbaum worked on other subjects, and he wrote the manuscript (in TeX) of a book whose title is

"Reflections on a Tube".

This is closely related to his life-long interest in optics and aspects of vision. It deals with the optics of images reflected in a cylindrical mirror (usually called anamorphic pictures). He shows that the eye does not interpret ray-tracing, but caustics. But there are two caustics, and therefore, the viewer can actually see two different images. The visual system will often prefer one over the other. The question is the "which" and "why"? Starting from this discovery, Feigenbaum derived other aspects of this observation, dealing with the vision of fish, the "broken" pencil in water, or aspects of the floor of swimming pools. All these examples show two possible images. His study tells me how a simple study in classical optics can lead to interesting questions about perception and the visual system.

I will give an overview of this project. As I discussed with him, over those 13 years, many aspects of his work, I have edited his manuscript so it can be published as a book which should appear in the foreseeable future.