Puzzlah #20 Puzzlah #20 Why might the Greeks have been more
dependent on astronomy than a tropical culture like the Maya? (A)
More extended empire to keep coordinated (A) More extended empire
to keep coordinated (B) Navigation needed for seafaring (B)
Navigation needed for seafaring (C) Clear weather presented more
astronomical phenomena (C) Clear weather presented more
astronomical phenomena that demanded explanations that demanded
explanations (D) More extremes in weather require better calendars
(D) More extremes in weather require better calendars
Slide 5
Puzzlah #20 Puzzlah #20 Why might the Greeks have been more
dependent on astronomy than a tropical culture like the Maya? (A)
More extended empire to keep coordinated (A) More extended empire
to keep coordinated (B) Navigation needed for seafaring (B)
Navigation needed for seafaring (C) Clear weather presented more
astronomical phenomena (C) Clear weather presented more
astronomical phenomena that demanded explanations that demanded
explanations (D) More extremes in weather require better calendars
(D) More extremes in weather require better calendars
Slide 6
Temple of Poseidon, Sounion
Slide 7
Gateway, Citadel of Mycenae
Slide 8
Parthenon, Athens
Slide 9
Dolphins & Lions of Delos of Delos
Slide 10
The School of Athens (Raphael)
Slide 11
Pythagoras Ptolemy Plato & Aristotle
Slide 12
800 Years of Greek Astronomy: 650 BC 150 AD 650 BC 150 AD
Slide 13
Greek Astronomical Timeline to 250 BC
Slide 14
- Rejects mythological/supernatural explanations of nature
Slide 15
Greek Astronomical Timeline to 250 BC Atomic theory. Plurality
of worlds. Infinite universe.
Slide 16
Greek Astronomical Timeline to 250 BC Physics, biology,
astronomy.
Slide 17
Greek Astronomical Timeline to 250 BC Physics, biology,
astronomy. Mostly erroneous!
Slide 18
Greek Astronomical Timeline to 250 BC
Slide 19
Greek Astronomical Timeline 250 BC 150 AD
Slide 20
First proved for all right triangles by Pythagoras, ca. 530
BC
Slide 21
Irrational numbers a remarkable, even disturbing, discovery of
the Pythagoreans E.g. Square root (2) = 1.41421356... This is not a
"rational" number* It cannot be expressed as the ratio of ANY two
whole numbers. There is an infinity of rational numbers, but the
square root of 2 is NOT among them. * Rational numbers: 2, 5, 2/3,
3/2, 13/17, 129/97, 1489001/747253,.......
Slide 22
Impact of Mathematical Success on Greek Thinking Applied
mathematical logic to thinking in other areas leading to "rational
thinking" leading to "rational thinking" Preference for making
deductions about nature from axioms or abstract principles from
axioms or abstract principles
Slide 23
Impact of Mathematical Success on Greek Thinking Applied
mathematical logic to thinking in other areas leading to "rational
thinking" leading to "rational thinking" Preference for making
deductions about nature from axioms or abstract principles from
axioms or abstract principles Their science based largely on
non-empirical premises Disdained making experiments Great progress
in some areas, but overall success circumscribed by these biases
success circumscribed by these biases x
Slide 24
Puzzlah # 21 You have two objects, A and B, both of which are
the same shape. B weighs twice as much as A. You drop both
simultaneously from a height of 3 feet. What happens? (A) A (the
lighter object) hits the ground first. (A) A (the lighter object)
hits the ground first. (B) B (the heavier object) hits the ground
first. (B) B (the heavier object) hits the ground first. (C) They
hit at the same time. (C) They hit at the same time.
Slide 25
Puzzlah # 21 You have two objects, A and B, both of which are
the same shape. B weighs twice as much as A. You drop both
simultaneously from a height of 3 feet. What happens? (A) A (the
lighter object) hits the ground first. (A) A (the lighter object)
hits the ground first. (B) B (the heavier object) hits the ground
first. (B) B (the heavier object) hits the ground first. (C) They
hit at the same time. (C) They hit at the same time.
Slide 26
You have just done a simple experiment that invalidates
assumptions in Aristotles physics which were accepted for over 1300
years.
Slide 27
Greek Astronomy: Great! Rational, mathematical, logical, mostly
empirical Knew shape and size of Earth and MoonKnew shape and size
of Earth and Moon Understood origin of lunar phasesUnderstood
origin of lunar phases Understood origin of eclipsesUnderstood
origin of eclipses Detected (Hipparchos) polar precessionDetected
(Hipparchos) polar precession Realized (Aristarchus) that Sun is
much more distant (& therefore larger) than MoonRealized
(Aristarchus) that Sun is much more distant (& therefore
larger) than Moon Constructed first cosmological models that
reproduced the dataConstructed first cosmological models that
reproduced the data
Slide 28
Greek Astronomy: Spherical Shape of Earth Curvature of ocean
horizon Curvature of ocean horizon Different stars @ different
latitudes Different stars @ different latitudes Different length of
day @ Different length of day @ Circular Earth shadow during lunar
eclipses Circular Earth shadow during lunar eclipses Shadow lengths
differ at different latitudes and can be used to measure the
diameter of Earth (Eratosthenes) Shadow lengths differ at different
latitudes and can be used to measure the diameter of Earth
(Eratosthenes)
Slide 29
Lunar eclipse
Slide 30
If know size of the Earth, can use shadow to estimate size of
Moon.
Slide 31
Eratosthenes and the shape and size of Earth Syene Alexandria
Sun at noon, June 21: overhead at Syene, but not at Alexandria
Slide 32
Eratosthenes Method (200 BC) Apply plane geometry: Measure d,
H, S. The two (approximate) triangles are congruent. This means
that S/H = d/R so R = dH/S Eratosthenes answer: R = 4025 miles True
value: R = 3950 miles Syene Alexandria S H
Slide 33
Hipparchos, ca 150 BC Star catalogs Magnitude system Precession
Planetary data
Slide 34
Aristarchus Heliocentric Cosmology (ca. 250 BC)
Slide 35
Aristarchus Heliocentric Cosmology (ca. 250 BC) Although
Aristarchus was right, the geocentric cosmology favored by
Aristotle prevailed.
Slide 36
Ultimate Greek Cosmology Cosmic bodies are inanimate, physical
objects, not supernatural beingsCosmic bodies are inanimate,
physical objects, not supernatural beings Model must explain their
known motionsModel must explain their known motions Spherical Earth
at center of universe (geocentric)Spherical Earth at center of
universe (geocentric) Superlunary region pure, eternal,
unchangingSuperlunary region pure, eternal, unchanging In contrast
to corrupted, changeable Earth & sublunar region Only purely
circular (perfect) motions allowedOnly purely circular (perfect)
motions allowed Earth is stationary; universe revolves once per day
around the EarthEarth is stationary; universe revolves once per day
around the Earth
Slide 37
Summary of easily visible motions of celestial objects: an
acceptable model must reproduce ALL