Lecture #2 Early Scientific Roots of Cosmology

Dennis PapadopoulosASTR 340Fall 2006

Pythagoras of Samos Everything is number

Numbers and Equations can be used to formulate scientific theories

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

Bridge should divide the string into simple ratios for notes to blend wellCULT OF

PYTHAGORAS

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

=1.618

The chambered nautilus

A BC

AB/AC=AC/CB=(1+x)/x=x, x=1.618…, Never ending never repeating numbers

Irrational numbers

1x

Line cut in extreme and mean ratio

Shapes and numbersPentagram the mystical symbol

Five pointed star

PentagramSelf 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 KepplerDistinction between creator and creations

Cube single angle-Solitude – 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