Download Lecture #2 - University of Maryland Department of Astronomy

Lecture #2
Early Scientific Roots of
Cosmology
Dennis Papadopoulos
ASTR 340
Fall 2006
Pythagoras of Samos
Everything is number

Numbers and Equations can be used to formulate
scientific theories

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Explain harmony of music through harmony of numbers
Harmonious 3:2 ratio perfect fifth; discord e.g. 15:37
Not all notes are allowed
Only certain notes can be played
on a string of fixed length; most
are excluded
CULT OF
PYTHAGORAS
Bridge should divide the string
into simple ratios for notes to
blend well
Monochord
Harmony of Universe
Constantly bathed by his hypothetical
music but cannot perceived because
we have been habituated to it – poor
theory
Keppler developed
little tunes for various
planets
All is a number –Ratios
The golden ratio
Ten classes of harmonic means – Most
sacred and beautiful the golden ratio
F=1.618
x
A
1
C
B
AB/AC=AC/CB=(1+x)/x=x, x=1.618…,
Never ending never repeating numbers
Irrational numbers
Line cut in extreme and mean ratio
The chambered nautilus
Shapes and numbers
Pentagram the mystical symbol
Five pointed star
Pentagram
Self replication – the golden ratio
Sacrament of last supper
Dali
Floating dodecaedron – Solids enclosed by spheres relate to golden ratio
Communion must be symetrical
Plato’s Universe
427-347 BC
Mysterium Cosmographicum
Ordering of planets by
Keppler
Distinction between
creator and creations
Cube single angleSolitude – Saturn
Earth’s position
separates solids that
can stand upright, e.g
cube, tetraedron,
dodecaedron to those
that float e.g.
octaedron, icosaedron
Aristotle’s Universe
384-322 BC
Aristotle’s Universe
Universe finite – No zeros or infinities – Universe small smaller than 1 AU
Eratosthenes
Earth and Moon size
Measuring Distances
Triangulation
Earth-Sun Distance
Parallax
Parallax
Enter Ptolemy
Epicycles
Epicycles upon epicycles
Rube-Goldberg Universe
Aristarchos 310 BC
Geocentric vs. heliocentric
Common sense rejected heliocentric model
why ?
1. If earth moved a constant wind will
flow against us (why don’t we see it?)
2. Incompatible with Greek understanding
of gravity. Everything tended to move
towards the center of universe. Apples,
rocks fell towards earth ->geocentric
3. Apparent lack of shift in positions of
stars. No parallax.
Einstein -> Common sense is a collection
of prejudices acquired at age eighteen
Retrograde motion
Geocentric puzzle of puzzles