Let no one ignorant of geometry enter. —a phrase engraved at the door of Plato’s Academy
As this admonition indicates, the study of Geometry formed an ideal preparation for higher philosophical studies in the ancient world (cf. Republic, VII, 526c8-527c11). By this alone, the study of Euclid’s Elements would justify geometry’s presence in a course of truly liberal education.
But, when combined with the study of science, it does more.
Since mathematical and scientific reasoning have shaped so much of the modern world, the study of these disciplines form an essential part of liberal education for the postmodern age. These studies enable students to consider the increasingly complex inter-relationships that exist between science, technology, and the human person. To do this, the students acquire scientific literacy in order to comprehend scientific matter intelligently, approach sophisticated technology responsibly, and understand that the human person is a moral agent.
These science tutorials do not seek to cover exhaustively the various sciences or to engage in specialized scientific research. Rather, they seek to assist students in discovering that scientific reasoning is a human activity that involves first principles, fundamental assumptions, and a variety of skills that require careful cultivation. More importantly, the science courses seek to awaken in the students a wonder and love of the natural order, revealing a deeper connectedness of things. Through these courses, students trace both first principles and fundamental assumptions to their roots through the close reading of primary sources.
In the science courses, students learn to observe, experiment, and go into nature for observation. This pedagogical method develops each student’s scientific literacy without divorcing his or her experiences from the apprehension of first principles and fundamental assumptions. Finally, the sequences of readings within the courses integrate the “humanities” with the “sciences” so that the students can begin to see the world as a whole and the human person’s place in it.
Sophomore Year, fall semester, 3 credits +
Through a rigorous study of Books One and Two of Euclid’s Elements (as well as selected propositions from later books), we follow in the steps of this “Master of Geometry,” studying first his definitions, postulates, and common notions, and then immersing ourselves in the beauty of his propositions. Through this course, we come to recognize with a fresh perspective the power of intellectus as it grasps first principles and intuits “the whole” of a proposition. We also come to appreciate the importance of ratio as it leads us from true presuppositions to trustworthy conclusions. In short, we renew—by following Euclid—our own capacity to think mathematically, with rigor and with discipline.
As a counterpoint to the study of Euclid, we also take up Plato’s dialogue, the Meno. Here we encounter fundamental questions about knowledge, opinion, recollection, and many of the epistemological questions that challenge us still today.
In the first half of this course, we make astronomical observations with the unaided eye, identify the major constellations and learn how to determine both latitude and longitude. We examine basic concepts such as the celestial sphere, celestial equator, solar time, sidereal time, and leap year. Through the reading of selections from Ptolemy’s Almagest—placing special emphasis on Ptolemy’s treatment of the sun’s anomaly—we establish the historical and philosophical background against which we will read Copernicus’ On the Revolutions of the Heavenly Spheres.
In the second half of this course, we explore the birth of modern science—in both its philosophical and empirical aspects—and consider two of its most prominent features: the experimental method and the Copernican revolution.
In the first phase of our inquiry, we undertake a close reading of selections from Copernicus’ On the Revolutions of the Heavenly Spheres in relation to corresponding sections from Ptolemy’s Almagest, specifically comparing both astronomers’ treatments of the sun and the planets, with their corresponding anomalies. We also consider how the difficulties in the Copernican heliocentric theory were eliminated by Kepler in his Epitome of Copernican Astronomy. Finally, we examine Galileo’s contributions to astronomy by reading his “Starry Messenger” and studying the moon using the college’s telescope.
Turning to the philosophical origins of modern science, we read Descartes’ Discourse on Method and Bacon’s Great Instauration—while keeping in mind our understanding of the ancient philosophers acquired in previous courses—and compare and contrast the ancient Greek view of the world with that produced by modern science. In this course, we read the following texts in whole or in part:
Copernicus, On the Revolutions of the Heavenly Spheres
In this course we first take up Galileo’s presentation of proto-Newtonian theory, as articulated in his Dialogue Concerning Two New Sciences. Immediately afterward, we examine Isaac Newton’s more complete formulation of the laws governing the mechanical universe. His view of nature is explored (as articulated in his Principia), which lays a foundation for apprehending the first principles of the modern scientific method, as well as for understanding the philosophical outlook of scientific modernity. Through an integrated investigation of both physical problems and their mathematical solutions, we seek to develop a coherent understanding of the application of mathematics, thereby discovering the unity within “science” and “mathematics” and clarifying the mathematical methods discovered by Newton that are still used in physics today. By concentrating on the first principles of motion and their application to matter, we probe beneath the surface of a scientific problem and discover how principles govern mechanical phenomena. In this course we read the following texts in whole or in part:
Galileo: Dialogue Concerning Two New Sciences; “Starry Messenger”
In this second semester, we conclude our examination of classical physics through a careful consideration of fundamental concepts such as mass, motion, force, space, and time by reading selections from Newton’s Principia and through numerous experiments. We observe the laws of motion in concrete phenomena: through the aerodynamics of the boomerang, the motion of billiard balls, fluid dynamics, air flight, and the physics of gymnastics and diving.
In our study of relativity, we take up Einstein’s own account of his theory, the classic Michelson- Morley Experiment, the derivation of the Lorentz transformation, and the latter’s application to sub-atomic particle disintegration. Finally, we investigate the quantum behavior of light by reading Feynman’s classic lectures on the double slit experiment and Heisenberg’s The History of Quantum Theory. In this course, the following texts are read in whole or in part:
Newton, Selected Letters
Feynman, The Feynman Lectures on Physics
Heisenberg, “The History of Quantum Theory” from Physics and Philosophy
In this tutorial we examine the diversity within nature and its classification, availing ourselves of the natural surroundings of autumn in New Hampshire. Next, we investigate the origins and nature of life. Following this we undertake a brief analysis of basic Mendelian genetics, coupled with a study of genes, DNA replication and transcription, and their roles in genetic inheritance. (See the reading list following Biology II.)
During this semester we take up the subjects of ethology (animal behavior), perception, and neurology, studying the contributions of naturalists such as Loren Eiseley, Konrad Lorenz, J. Henri Fabre, Karl von Frisch, and Nikko Tinbergen. We compare the classic neurological writings of Wilder Penfield with the more recent views of Oliver Sacks, Francis Crick and Richard Dawkins.
In the first and second semesters of this course, we read the following texts in whole or in part: Aristotle’s History of Animals, On Generation and Corruption, Parts of Animals, De anima, St. Augustine’s De Genesi ad litteram, Margulis, Darwin, Gould, Eisele, Augros and Stanciu, Mendel, Watson, Lorenz, Frisch, Sacks, Penfield, and others.