2. Premodern to Modern Culture

3. Richard Nelson

• Anthropologist
• "The Watchful World," 1983
• Koyukon of Alaska
• Animals as equal subjects
• I and thou

4. Narrative: Homer

• Greece. Ca. 1159 B.C.E.
• Iliad; Odyssey
• Epic poetry, oral tradition; authoritative text by mid-6th century B.C.E.
• Recited every four years.

5. The Naturalists: Thales of Miletos

• Ionian philosopher, fl. 585 B.C.E. Asia Minor.
• What is the world made of? First principles.
• "All is water."
• Universal laws to predict events.
• Earth is a circular disc floating on water.

6. The Naturalists: Anaximenes

• Milesia. fl. 546 B.C.E.
• Ontology: What is the world made of? Air is the basic substance.
• How does change occur? By condensation and rarefaction.
• Uniform natural laws.

7. Process: Heraclitus

• Ephesus. 540-475 B.C.E.
• All is in flux.
• The only constant is the fact of change itself.
• The logos or reason of everything. Order in the harmony of events.
• Dialectics.
• "You cannot step twice into the same river; for fresh waters are ever flowing in upon you."

8. Permanence: Parmenides of Elea

• Elea in S. Italy. fl. 504 B.C.E.
• Being is. Not-being is not.
• Law of identity: a is a. Basis of mathematics.
• Law of non-contradiction: Can't say "a is not-a."
• Logic = thinking
• Opinion = non-thinking

9. Mathematics: Pythagoras

• Samos. fl. 532 B.C.E.
• Cosmos is based on number.
• Numbers are being; substance; matter.
• Numbers are sacred.
• Numbers are eternal.
• Numerical proportions produce music.

10. Triangular and Square Numbers

• Ecstatic contemplation of geometrical forms and mathematical laws.
• Link between humanity and divinity.
• Purges the soul of earthly passion.

11. Spherical Cosmos

• Harmony of the spheres.
• Music: notes are numerical ratios.
• 2:1 = octave; 3:2 = fifth; 4:3 = fourth.
• Planets emit notes.

12. Rational vs. Irrational: Pythagorean Theorem

• Brought from Egypt and/or Mesopotamia by Pythagoras.
• Sum of the squares on the legs of a right triangle is equal to the square on the hypoteneuse.
• But diagonal of a unit square is irrational.

13. Idealism: Socrates and Plato

• Athens. 469-399; 427-347 B.C.E.
• Pure knowledge is of the unchanging. E.g. mathematics.
• The changing, inconstant world of appearances (phenomena) does not lead to knowledge.
• Ideal forms: the pure forms of things; concepts. E.g. the Triangle; the Chair; the Good; Justice; the State.

14. Plato's Academy

• All who enter must study mathematics

15. Five Platonic Solids

• Tetrahedron
• Cube
• Octahedron
• Dodecahedron
• Icosahedron

16. The Atomists: Empedocles

• Akragas in Sicily. fl. 444 B.C.E.
• How to explain identity (Parmenides, Plato) through change (Heraclitus).
• Idealism versus materialism.
• 4 beings (elements): earth, air, fire, water.
• Love and strife act on the 4 elements to create change.

17. The Atomists: Democritus

• Abdera in Thrace. b. 450 B.C.E.
• Quantitative atomism.
• A-tom = not-cuttable.
• Not-being exists. It is space. Nothing is.
• To be: means to be an atom or to be a space.
• Atoms are in ceaseless motion.
• Change is union and separation of atoms.

18. Pliny

• Rome, 23-79 A.D.
• Contrasted beauty and bountifulness of the earth without humans to the imperfections caused by human abuse of the earth.

19. Harmony vs. Discord: Daniel Botkin

• Ecologist.
• Discordant Harmonies (1990); postmodern science; unpredictability.
• Plotinus, A.D. 204-270. Rome.
• The Enneads, trans. S. MacKenna (1956).
• Neoplatonism.

20. Daniel Botkin

• "The true idea of a harmony of nature, which as Plotinus wrote so long ago, is by its very essence discordant, created from the simultaneous movements of many tones, the combination of many processes flowing at the same time along various scales, leading not to a simple melody, but to a symphony at some times harsh and at some times pleasing." (p. 25)

21. David Abram

• The Spell of the Sensuous, 1996.
• Hearing nature's voice.
• "The rustling of leaves in an oak tree or an aspen grove is itself a kind of voice."
• "The rythm and lilt of the local soundscape."