The Science Institute at Summer Classics

About the Science Institute

The Science Institute draws on St. John’s College’s long tradition of studying science through the discussion of original texts, emphasizing hands-on involvement and experiments. Each weeklong session is an intensive immersion in landmark topics and texts, with twice-daily seminars centered on discussion among participants.

Rather than viewing science as an edifice of facts, we encounter it through the living questions it poses and, in so doing, reenact the experience of scientific discovery. By encouraging each other to express and engage with those questions, we open ourselves to the wonder of inquiry into the mysteries of nature.

Join us this summer to look up into the skyunderstand the imaginary in mathematics, or take a trip to the fourth dimension and experience the St. John’s College approach to a truly comprehensive education.

The Science Institute is open to those who want to delve more deeply into the questions
raised by science and mathematics.

Mr. Pesic, tutor emeritus and musician-in-residence at St. John’s College, Santa Fe, is the director of the Science Institute.

Three seminar programs run concurrently with Summer Classics.

  • Online program meets once daily and runs for two consecutive weeks.
  • In-person program meets twice daily: 10 a.m.–Noon & 2—4 p.m. MT

2021 Science Institute Seminars

ARE IMAGINARY NUMBERS REAL?

Guillermo Bleichmar and Peter Pesic
July 5–16 (Two Weeks), 10 a.m.–12 p.m. MT | 12–2 p.m. ET
Online

What does imagination mean in mathematics? We consider “imaginary” quantities, those based on the square roots of negative numbers. In common parlance, these are usually distinguished from “real” numbers. Even today many people are uneasy about imaginary numbers. What do they really mean? Are they only fictitious objects of imagination or mere tools? If they are “real,” what kind of reality do they have? We discuss Barry Mazur’s Imagining Numbers (particularly the square root of minus fifteen) as we read various attempts to understand the imaginary in mathematics, with the help of some philosophical and literary texts. Then we consider the applications of imaginary numbers to the “real” world, especially in relativity and quantum physics.

Text: Barry Mazur, Imagining Numbers. Picador, ISBN-13: 9780312421878

ANCIENT ART OF SKY-WATCHING: PTOLEMY, BRAHE, AND KEPLER

William Donahue and Phil LeCuyer
July 12–16, 10 a.m.–2 p.m. MT | 12–4 p.m. ET

In-person, two meetings daily

For thousands of years, long before the invention of the telescope, people made remarkably accurate observations of stars and planets, observations that led to a view of cosmic order that shaped the entire course of Western science. How did they do it? What were the problems they had to solve? At St. John’s, we have recently installed the world’s only functioning replica of one of the most technologically advanced instruments of the pre-telescopic era: the Tychonic armillary sphere. After testing the older methods of Ptolemy and Levi ben Gerson, we use Tycho Brahe’s instrument and see for ourselves the techniques that made Kepler’s great achievements possible. We do as much observation as weather permits, including a possible visit to a dark-sky site.

Text: Manual of readings provided.

GENERAL RELATIVITY: A TRIP TO THE FOURTH DIMENSION

Peter Pesic and Paola Villa
July 19–30 (Two Weeks), 10 a.m.–12 p.m. MT | 12–2 p.m. ET
Online

Most popular expositions of Albert Einstein’s theory of general relativity avoid dealing with his actual equations; this limits any deeper understanding. In contrast, we study the math involved in his equations, discussing in detail how they are derived and what they mean. If you are comfortable with high school algebra, have taken a beginning calculus course, and are not afraid of equations, you can do it. We go through a concise exposition of Einstein’s field equations by Lillian Lieber, which Einstein himself “warmly recommended” as “clear and vivid.” Her book is a classic that embraces the mathematics other books avoid, highlighting its beauty and intelligibility. In addition, we read sections from Einstein’s 1916 paper that introduced general relativity.

Texts:

  • Lillian R. Lieber, The Einstein Theory of Relativity: A Trip to the Fourth Dimension. Paul Dry Books, ISBN-13: 9781589880443
  • Manual of additional readings provided

About Peter Pesic

Peter Pesic is a writer, pianist, and educator. He is director of the Science Institute at St. John’s College, Santa Fe, New Mexico, where he is Musician-in-Residence and Tutor Emeritus. His writings include five books about the history of science, music, and ideas, six editions, and sixty papers. As a pianist, he has been heard in many places in the United States and in Europe.

He is the author of the following books, all published by the MIT Press:

  • Abel’s Proof: An Essay on the Sources and Meaning of Mathematical Unsolvability
  • Seeing Double: Shared Identities in Physics, Philosophy, and Literature
  • Sky in a Bottle
  • Music and the Making of Modern Science

Peter Pesic’s books are available at the SJC Bookstore.