ASTRONOMY 9: HISTORY OF COSMOLOGY

Handout #8

J. E. Baker
UC Berkeley, Spring 2000

Cosmology in Ancient Greece: The Pre-Socratics (c. 620-470 BC)

1.

The Ionians (6th century BC)

• Miletus (city on coast of what is now Turkey)
• Answers to questions about nature sought within nature
  • eg, What is the ``stuff'' that makes up the cosmos?
  • String-pulling deities are discarded
• Roots of scientific thought, though significant differences from modern science:
  • Observation/experiment generally of secondary importance
  • Theories explained the known, but predictive power was not required
• Very few original writings survive
• Emphasis on change, ``becoming''
• Materialistic, optimistic

(a)

Thales (approx. 624-547 BC)

• Probably predicted a solar eclipse (5/28/585 BC?) using Babylonian data
• Difficult: ``to know thyself'', easy: ``to give advice''
• Water as basic substance
• Universe as a biological organism
• Earth as a circular disk floating on water
• Heavens float on upper waters, ``cosmic oyster''

(b)

Anaximander (approx. 610-545 BC)

• Unknown raw material, ``boundless'' substance
• Infinite, eternal, mechanical universe
• Earth surrounded by spheres of mist
• Sun, moon, stars as holes in the rim of moving wheels filled with fire

(c)

Anaximenes (approx. 545 BC)

• Air as basic substance
  • Increasing density: air, fire, water, earth, rock
• Crystalline (invisible) spheres to which heavenly objects are attached
  • This idea dominates astronomical thinking for 2000 years!

(d)

Heraclitus of Ephesus (c. 540-480 BC)

• The ``Dark One'': spoke and wrote in riddles
• Fire as basic substance (transformative power)
• ``You can never step twice in the same river''
• All is change, no stability

2.

The Eleatics (approx. 5th century BC)

• Elea, now southern Italy
• Emphasis on stability, immutability, ``being''
• Change is an illusion, human efforts are in vain

(a)

Xenophanes of Colophon (c. 560-478 BC)

• Founder or precursor of the Eleatic school
• Sun, moon, stars are exhaled daily from earth, with neither permanence nor substance
• Contempt for Olympian gods and mythology

(b)

Parmenides (c. 515-450 BC)

• Spherical, immovable Earth
• Radical monism: one immutable state of being, change is secondary or illusory
• Physics: search for immutable laws of nature

(c)

Zeno (c. 495-430 BC)

• Motion is an illusion
• Book of 40 ingenious paradoxes
• Significance not fully understood even by Plato and Aristotle!
• Three examples:

  i.

  The Dichotomy: How can motion start?

  • ``There is no motion because that which is moved must arrive at the middle of its course before it arrives at the end.'' (Aristotle)
  • To get from A to B, first must reach the midpoint
  • But first must reach 1/4 point
  • But first must reach 1/8 point ...
  • Sum 1/2+1/4+1/8+...=1, but what if you try to do it in reverse order?

  ii.

  The Arrow: Does ``now'' exist?

  • ``If, says Zeno, everything is either at rest or moving when it occupies a space equal to itself, while the object moved is in the instant, the moving arrow is unmoved.''
  • Take snapshots of a flying arrow with smaller and smaller exposure time
  • If motion is continuous, can't think of the arrow at a definite position!
  • If object occupies a particular position on its path, it can't be in motion while there!
  • Note: velocity = distance/time, but what happens as the time considered approaches zero? (Zeno didn't know about calculus, invented in the 17th century.)

  iii.

  The Achilles: Can the rabbit (R) catch up with the tortoise (T)?

  • R must first reach the point where T was when he started (1)
  • But T has now moved ahead to a new point (2)
  • When R gets to (2), T has moved to (3) ...
  • T is always a little bit ahead!

3.

The Pythagoreans (6th-5th centuries BC)

• Mystical understanding of the cosmos using mathematics (key importance in modern physical science)
• All has Form, Forms described by Number $\Rightarrow$ All is Number
• Mathematical abstraction seen as enriching experience, not eliminating meaning and value

(a)

Pythagoras of Samos (c. 580-500 BC)

• Founded Pythagorean Brotherhood
• Great influence on development of philosophy and science
• Numbers as bridge between human and divine mind
• Noticed pitch of musical note depends on string length
  • Pleasing sounds from ratios of whole numbers: 2:1 - octave, 3:2 - fifth (C/G)
  • Beauty (quality) as an expression of mathematics (quantity)!
• Numbers have geometrical form
  • Square numbers obtained by adding odd numbers
  • Proof of Pythagorean theorem: a² + b² = c² (known to Babylonians)
  • 1: point, 2: line, 3: surface, 4: solid; sum = 10 (sacred)
• ``Harmony of the Spheres'': Cosmos as a musical instrument
• Spherical Earth surrounded by air
• Sun, moon, planets move in concentric circles
• Distances in ratios of musical harmonies

(b)

Philolaus of Croton (approx. 475 BC)

• Pupil of Pythagoras
• Idea of the cosmic central fire (not the Sun!)
• Include counter-Earth (to protect uninhabited antipodes from scorching by the fire, to explain some eclipses, and to give 10 total objects!)
• Earth revolves around central fire daily
• Earth moves, and it is not at the center!
• Inhabited portion always faces away from fire

4.

The Atomists (5th-4th century BC)

• All things made of ``atoms'' (indivisible, fundamental)
• Reconciles Ionian change/becoming with Eleatic immutability/being:
  • Change is quantitative, rearrangement of atoms
  • Immutability is qualitative, atoms are unalterable

(a)

Leucippus (approx. 5th century BC)

• Basic idea of atomism: world is composed of small indivisible particles

(b)

Democritus (c. 460-370 BC)

• ``The Laughing Philosopher''
• Detailed formulation of atomism
• All matter is atoms bound together
• Atoms come in infinitely many shapes and numbers
• Move through the Void without purpose
• Note: modern atoms are very different:
  • Divisible into subatomic particles
  • Not infinite in variety
  • Do not behave like billiard balls moving in a void

5.

Other Pre-Socratic Ideas

(a)

Anaxagoras (c. 500-428 BC)

• No single fundamental element, but an infinite variety of them (flesh, bone, bark, leaf, ...)
• Attacked for belief that Sun was a glowing stone, hundreds of miles in size
• Idea of Nous (mind, reason) as the cosmic organizer

(b)

Empedocles (c. 490-430 BC

• Air, earth, fire, water as basic cosmic elements
• Love and strife as primary cosmic forces, causing the elements to mix and separate
• Egg-shaped cosmos

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