February 28, 2019

Pinning Down Uncertainty

Cynthia Flores describes how Heisenberg’s famous principle has shaped her mathematical career and worldview

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On this episode of our podcast My Favorite Theorem, my cohost Kevin Knudson and I had the pleasure of talking with Cynthia Flores, a mathematician at California State University Channel Islands. You can listen to the episode here or at kpknudson.com, where there is also a transcript.

Mathematician Cynthia Flores. Credit:
California State UniversityChannel Islands

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I met Dr. Flores when she was a guest on the Lathisms podcast, where I interview Hispanic and Latinx mathematicians. You can listen to her talk about her upbringing in Los Angeles and the professor who made her realize she could become a mathematician here and find the rest of the Lathisms podcasts here.

Dr. Flores studies mathematical physics, partial differential equations, and harmonic analysis, so it is fitting that the theorem she chose to share on the podcast has a physics flavor. Heisenberg’s Uncertainty Principle, known by mathematicians as Heisenberg’s Uncertainty Inequality or Inequalities, is best known as the statement that it is impossible to measure both the position and velocity of a particle at a given point in time with perfect accuracy. But the same theorem takes different forms in different mathematical contexts.

Learning about Heisenberg’s Uncertainty Inequality was a turning point in Dr. Flores’s mathematical career. She had entered graduate school interested in geometry and topology, but when she encountered this theorem in a class by her soon-to-be-advisor, she switched gears and decided to go into mathematical physics. Learning this theorem was a turning point for her personal philosophy as well. I love it when our guests wax philosophical about how they experience their theorems in everyday life. Dr. Flores says that since learning Heisenberg’s Uncertainty Inequality, she has, lived with a mantra that the more precisely you try to plan out your life, the more chaos can sneak in to disrupt those plans.

In each episode of the podcast, we invite our guest to pair their theorem with food, beverage, art, music, or other delight in life. Dr. Flores chose an episode of science fiction cartoon Rick and Morty. You’ll have to listen to the podcast to learn which episode of Rick and Morty will most enhance your experience of Heisenberg’s Uncertainty Inequality and why.

To learn more about the Heisenberg Uncertainty Inequality, Dr. Flores suggests Nonlinear Dispersive Equations by Felipe Linares and Gustavo Ponce, especially exercise 3.14, and this video from the Veritasium YouTube channel that demonstrates the uncertainty principle.

To learn more about Dr. Flores, find her at her website and on Twitter. She was recently chosen as one of 2019's 15 emerging scholars by Diverse: Issues in Higher Education. Read her profile here.

You can find more information about the mathematicians and theorems featured in this podcast, along with other delightful mathematical treats, at kpknudson.com and here at Roots of Unity. A transcript is available here. You can subscribe to and review the podcast on iTunes and other podcast delivery systems. We love to hear from our listeners, so please drop us a line at myfavoritetheorem@gmail.com. Kevin Knudson’s handle on Twitter is @niveknosdunk, and mine is @evelynjlamb. The show itself also has a Twitter feed: @myfavethm and a Facebook page. Join us next time to learn another fascinating piece of mathematics.

Previously on My Favorite Theorem:

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