ASTRONOMY 9: HISTORY OF COSMOLOGY

Handout #9

J. E. Baker
UC Berkeley, Spring 2000

Cosmology in Ancient Greece: Plato and Eudoxus

1.

Socrates (approx. 470-399 BC)

• ``Called down philosophy from the skies.'' (Cicero)
• Emphasis on human, ethical, moral (not just cosmological) issues
• Time of great social turmoil (war, corruption, population decline, ...)
• Preached the need for a new moral philosophy
• Dialogs: unyielding questioning of others' knowledge
• Condemned by parents of ``corrupted youth'', death by poison
• Dialogs survive as written by student Plato

2.

Plato (approx. 428-348 BC)

• Goals:
  • Formulate new moral philosophy based on immutable truths
  • Educate new ``philosopher-kings'' to rule the ``ideal society'' (in fact a very unattractive aristocracy!)
• Founded Academy (perhaps first university), lasted 900 years!
• Division of the cosmos into two realms:

  (a)

  Forms: perfect, true reality, world of Ideas

  (b)

  Physical world: imperfect shadow of ideal reality

  • Cave allegory
  • Line vs. drawing of a line
• Cosmology presented in Timaeus
  • Abstract deity (``demiurge''): principles of reason, order
  • Teleology: belief in cosmic design
  • Pythagorean number mysticism replaced by geometrical mysticism
  • Five elements with shape of five Platonic solids:

    (a)

    Fire -- Tetrahedron (4, triangle)

    (b)

    Earth -- Cube (6, square)

    (c)

    Air -- Octahedron (8, triangle)

    (d)

    Cosmos -- Dodecahedron (12, pentagon)

    (e)

    Water -- Icosahedron (20, triangle)

  • Earth at cosmic center
  • Celestial objects are all perfect spheres
  • All orbits are circular
  • Only one world (only possible likeness of the ideal)
• Challenge to students: ``Save the phenomena''
  • Observational science (astronomy) demoted to secondary role
  • Nevertheless, it can serve as a bridge to the divine mind
  • How can complicated planetary motions (e.g., retrograde) be described as a combination of simple circular motions?

3.

Eudoxus (c. 408-356 BC)

• Devised a ``solution'' to Plato's challenge
• Nested spheres: 4 for each planet, 3 for sun, 3 for moon, 1 for fixed stars $\Rightarrow$ 27 total spheres!
• Four spheres for each planet:
  • Outer: daily rotation
  • Next: ``annual'' motion through Zodiac
  • Inner 2: hippopede (figure-8) motion to explain retrograde motion
  • All spheres are free to rotate about different axes
  • Motion is transferred: Apparent motion given by combined motions of all spheres
  • Spheres are abstract geometrical construction, not thought of as physically real
• Good qualitative description of planetary motions
• Unanswered mysteries:
  • Why is motion transferred between spheres?
  • How to explain variable brightness of planets?

4.

Callippus (about 370-310 BC)

• Extended Eudoxus' model by adding 7 new spheres (total 34)
• Added one each for Mercury, Venus and Mars, and two each for Sun and Moon
• Better description of retrograde motion
  • Hippopede replaced by more complicated, elongated figure

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