GRADE ELEVEN: the required elements

Theory: If in the Ninth Grade, the archetypal idea is Space--the expansion and articulation of the new world space in the voyages of discovery; and if in the Tenth Grade, the archetypal idea is Time-- the story of the individual's rise from rags to riches, from Old World to New, from oppression to revolutionary liberation, then in the Eleventh Grade, the archetypal ideas are Speed and Transformation -- the wedding of time to space in the acceleration of culture in modernization through the instrumentalities of the new cultural vehicles of the world-city and the world war. In both of these large scale organizations of culture, the new transportational vehicles of railroad, automobile, truck, tank, airplane, jet, and rocket have enormous impact on traditional cultures and religious world views, and these react to modernization in visionary movements of mythopoeic prophecy and resacralization that affirm the validity of consciousness and non-rational experience. This conflict between the Mechanists and the Mystics in the articulation of values for a new world civilization continues to this day. This period is also characterized by the shift from Galilean dynamics with their linear systems of causation and reductionist emphasis to Complex Dynamical Systems, Chaos, Uncertainty, and bottom-up systems of self organization that express new appreciations of emergence, as exemplified in ideas about the origins of the life, the culture of the Internet, and the Earth as a self-regulating system (Gaia).

Practice: The explication of the relationships between art, mathematics, and science in configurations such as Cubism and Special Relativity, or chaos dynamics in Poincare and Kupka, as well as the relationships between media such as photography, cinema, painting, and the construction of the past in Haussmann's urban planning, Bergson's philosophy of memory, and Proust's recapture of past time.

Integrative Studies Projects:

• Nativistic Movements and the Psychology of the Prophetic leader;
• Paris and the Reconstruction of Past Time.
• Choose one:
  1. Time and Space in Cubism and Special Relativity, or
  2. Chaos Dynamics in Math, Music, and Painting: the example of Poincare-Satie-Kupka; or
  3. Myth, Ritual, and Riot: the Case of Stravinsky's Rite of Spring.

Math Units:

• Topics:
  • Chaos theory
  • Cantor sets
  • Fractals
  • Noneuclidean geometry
  • Complex numbers
  • Vectors, matrices
• Practice:
  • Computer simulations
• Suggested Integrative Projects (one required):
  • Foundations of Calculus, Dedekind's real numbers
  • Flatland, differential geometry of curves and surfaces
  • German vs. French math styles of thought, Hilbert's program, Godel's Proof, Carnap and the Vienna Circle.
  • Hertz, radio waves, the field concept, vectors, Maxwell's equations
  • Hamilton, quaternions, Minkowski, Poincare, Einstein, and the ether
  • Vibrating strings and quantum mechanics, particles vs. waves
  • Math and War: Lewis Frye Richardson, the birth of politicometrics, Gregory Bateson, cybernetics
  • Cybernetics, Von Neuman, game theory, the prisoner's dilemma, the atomic bomb
  • The shape of the Earth