Introductory Seminars for First-Year Students

Harmony and the Universe

Trigonometry, algebra, and arithmetic.

Harmony is a multifaceted concept that profoundly connects music, mathematics, physics, philosophy, physiology, and psychology. In classical Western thought, this is no accident: harmony, at its essence the understanding of how different combinations of tones may sound pleasant or discordant to our ears, was believed to be a reflection of a divine pattern governing the heavens, connecting music to geometry, astronomy, and religion. No less than the whole universe was at stake in the study of harmony.

Through these connections, concepts associated with harmony have guided millennia of scientific and philosophical thought. In this seminar, we will explore the evolution of our understanding of harmony and its immediate application in the function of musical instruments, and employ it as a nexus to understand its role in revolutionary scientific advances in gravity, relativity, quantum mechanics, and cosmology. In these explorations, we will examine some of the fundamental mathematical tools that provide us our current understanding of harmony. We will also see how some concepts surrounding harmony are in tension, if not conflict, and how some great thinkers have followed them down blind alleys and dead ends. 

The aim of the course is to show the enormous consequences of harmony in the evolution of our understanding of the universe, and how science itself progresses in fits, starts, and setbacks as old ideas intermingle with new developments. We will also see how objective/quantitative aspects of harmony interact with subjective/qualitative considerations, and how cultural perspectives and prejudices can affect the progression of science. Finally, we will glimpse how these concepts are applied to contemporary issues in physics such as the study of elementary particles and the structure of the universe. 

Physics is ultimately grounded in the language of mathematics, so equations and numbers will make appearances in the class. However, mathematical derivations and problem solving will not be the focus of the class. Students with diverse backgrounds and interests, particularly non-STEM, are especially welcome in this seminar, with the goal of exploring harmony from as many perspectives as possible.

Meet the Instructor(s)

Hirohisa A. Tanaka

"I recently rejoined Stanford as a professor of particle physics and astrophysics at SLAC. Many years ago, I received my Ph.D. from Stanford, and spent some time in the United States and Canada on both sides of the continent before returning to Palo Alto in 2018. My research is in elementary particle physics, the study of the basic and fundamental building blocks of matter and energy in the universe. I have recently focused on a fundamental particle called the neutrino which, while being virtually imperceptible in every day life, nonetheless is essential in shaping the universe as we see it today, including possibly our very existence. Our research today involves using vast accelerator systems to produce intense beams of these particles, which we send hundreds of kilometers to gargantuan detectors to see how their properties change.

"In exploring harmony and its relation to physics, we can explore a slice of how humans have endeavored to make sense of the world around them, and how one concept and the simple mathematical structure surrounding it continues to guide this quest, while also seeing how preconceived notion of order and structure have both guided and misguided our progress."