Abstract

Is my experience of the color red the same as yours? Do movies look realistic to dogs? While these questions may at first seem similarly unanswerable, they are in fact quite different! While philosophers still debate on the coherence of the former, the latter is resolved mainly through the use of Linear Algebra.

As an exciting interdisciplinary adventure involving linear algebra, real analysis, cell biology, and evolutionary history, we work together in this talk to precisely express the question (is the response of a dog’s retina to the stimuli of a natural vista, and a TV displaying the same image equal?), and lay out a path towards its solution.

Along the way we discover the mathematical underpinnings of why humans believe in three primary colors, how newspapers, phones, and televisions exploit the imprecision of our eyes, and the vast difference between sight and hearing. Perhaps, the star of the show relating all these things is the Rank-Nullity theorem of elementary Linear Algebra!

Occurrences

So far I have only given this talk on one occasion, as the end to the linear algebra unit in my introduction to proofs course (Math 56 at Stanford) in Spring of 2022. I think the idea needs some more polishing, but I hope to give it as an undergraduate colloquium down the road!

Slides

Here is the deck of slides from my first attempt at this talk!