1. Lecture #2 Early Scientific Roots of Cosmology Dennis Papadopoulos ASTR 340 Fall 2006

2. 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 well CULT OF PYTHAGORAS

3. 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

4. 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 AB C AB/AC=AC/CB=(1+x)/x=x, x=1.618…, Never ending never repeating numbers Irrational numbers 1 x Line cut in extreme and mean ratio

5. Shapes and numbers Pentagram the mystical symbol Five pointed star

6. Pentagram Self replication – the golden ratio

7. Sacrament of last supper Dali Floating dodecaedron – Solids enclosed by spheres relate to golden ratio Communion must be symetrical

8. Plato’s Universe 427-347 BC

9. Mysterium Cosmographicum Ordering of planets by Keppler Distinction 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

10. Aristotle’s Universe 384-322 BC

11. Aristotle’s Universe Universe finite – No zeros or infinities – Universe small smaller than 1 AU

12. Eratosthenes Earth and Moon size

13. Measuring Distances Triangulation

14. Earth-Sun Distance

15. Parallax

17. Enter Ptolemy Epicycles

19. Epicycles upon epicycles Rube-Goldberg Universe

20. 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

21. Retrograde motion Geocentric puzzle of puzzles