Intellectual Heritage - Infinity in the Development of Science

This ten-week component will consist of an in-depth study of how cultural and personal beliefs about infinity influencInfinity in the Development of Scienceed the development of quantitative reasoning and science over the centuries.   Special focus will be given to the antecedents of modern beliefs about infinity.   Emphasis will also be given to the contributions of different cultures.  The beliefs about infinity studied in this component will come from philosophy, religion, literature, science and art and be presented through readings, slides and videos.

Students (individually or in groups of two or three) will be asked to engage in a research project on a topic related to infinity, culminating in the submission of a research paper and presentation of the topic to the class.  Each student will also be required to complete 3 short reaction papers, a midterm exam, a take-home final exam essay, and several in-class discussions/projects.

Outline

1. Primitive and Classical Views of Infinity and their Modern Counterpoint
   -  Zeno
   -  Aristotle
   -  Cantor
2. Infinity in Asia
   -  Hinduism and Bhagavad Gita
3. Infinity in the Middle Ages
   -  Thomas Aquinas
4. Infinity and the Renaissance
   -  Galileo
   -  Descartes
   -  Pascal
5. Infinity and Cosmology
   -  Ptolemy
   -  Copernicus and Galileo
   -  Stephen Hawking
6. Infinity and a Break with Tradition
   -  Non-Euclidean Geometry and Topology
   -  Edward Abbott: "Flatland"
   -  4th Dimension and Beyond
   -  Einstein
7. Influence of Infinity on Contemporary Art and Science
   -  Symmetry and Fractals
   -  Escher