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CONTACT 2006

CONTACT 2006. Music of the Spheres in More Than 3 Dimensions. Carlo H. S é quin EECS Computer Science Division University of California, Berkeley. The world is a mysterious place !. Astrology  Astronomy  Astrophysics  Cosmology. Pythagoras of Samos ( 569-475 BC ).

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CONTACT 2006

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  1. CONTACT 2006 Music of the Spheresin More Than 3 Dimensions Carlo H. Séquin EECS Computer Science Division University of California, Berkeley

  2. The world is a mysterious place !

  3. Astrology  Astronomy  Astrophysics  Cosmology

  4. Pythagoras of Samos (569-475 BC) “Harmony of the Spheres”

  5. World Model of the Pythagoreans • Earth is at the center. • It is surrounded by 5 crystalline spheres,spanned and held up by the 5 Platonic solids. • The planets and the stars are attached to these. • As they rotate, they created musical harmonies.  Music of the Spheres

  6. Claudius Ptolemy (85-165)

  7. Johannes Kepler (1571-1630)

  8. Kepler – the Scientist Planetary orbits: 1. = ellipses; sun in one focal point. 2. equal areas swept out in equal time. 3. (revolution times)2 ~ (long orbit axes)3

  9. Kepler – the Geometrician • tilings, polyhedra

  10. Kepler – the Mystic The “meaning” of the five Platonic solids Octahedron: Tetrahedron: Dodecahedron: Cube: Icosahedron: Air Fire the Universe Earth Water

  11. Johannes Kepler:“Music of the Worlds” • Diagrams from Kepler’s De Harmonices Mundi (1618), showing the melody “sung” by each heavenly body, and the way in which they join in six-part counterpoint.

  12. Kepler – the Mystic Trying to relate the sizes of the planetary orbits

  13. Kepler’s Mysterium Cosmographicum (1596) • relating the sizes of the planetary orbitsvia the fivePlatonic solids.

  14. Diameters of Inter-Planetery Spheres from the Book of Copernicus • Jup./Sat. = .635 Cube: .577 => -9% • Mars/Jup. = .333 Tetra: .333 => 0% • Earth/Mars = .757 Dodeca: .795 => +5% • Venus/Earth = .794 Icosa: .795 => 0% • Merc./Venus = .723 Octa: .577 => -20% mid-edge radius of Octa: .707 => -2% J. V. Field: "Kepler's Geometrical Cosmology" Univ. of Chicago Press, 1988, page 65.

  15. A Later Table Expressed in Earth Radiiwith corrections by Aiton (1981) • Saturn aph 9.727 --> 10.588 => +9% peri 8.602 --> 9.364 • Jupiter aph 5.492 --> 5.403 => -2% peri 4.999 --> 4.918 • Mars aph 1.648 --> 1.639 => -1% peri 1.393 --> 1.386 • Earth aph 1.042 --> 1.102 => 0% by def. peri 0.958 --> 0.898 • Venus aph 0.721 --> 0.714 => -1% peri 0.717 --> 0.710 • Mercury aph 0.481 --> 0.502 => +4% peri 0.233 --> 0.242 Adding the orbit of the moon to make a thicker shell for the earth; Explanation of errors: Saturn "too far away“, Mercury "too close to sun"

  16. A Problem – More than Six Planets ! • There are only 5 Platonic solids, • but there are more than 5 orbit intervals! • Universe has more than 3 dimensions • Look into higher dimensions for additional “Platonic” solids. • Higher dimensions ... ? ...

  17. Simplest Regular Objects in Any Dimension:Simplex Series • Connect all the dots among D+1 equally spaced vertices:(Find next one abovecentroid). 1D 2D 3D . . . This series goes on indefinitely!

  18. Another Infinite Series:the Hypercube Series • Also called “Measure Polytope” Series • Consecutive perpendicular sweeps: . . . 1D 2D 3D 4D This series also extends to arbitrary dimensions!

  19. The 6 Regular Polytopes in 4D Projections to 3D Space

  20. The Regular 4D 120-Cell (projected to 3D) • 600 vertices, 1200 edges.

  21. The Regular 4D 600-Cell (projected to 3D) • David Richter 120 vertices, 720 edges.

  22. Advantage of Using 4D Polytopes • Four different sphere radii on each polytope: • Through its vertices = Rv • Through its edge-midpoints = Re • Through its face centers = Rf • Through its cell centers = Rc For Hypercube: 2.000 1.732 1.414 1.000 Thus we can form 6 different radius ratios !

  23. Ratios of Sphere Radii of 4D Polytopes Rc/Rv Rc/Re Rc/Rf Rf/Rv Rf/Re Re/Rv Simplex .250 .408 .408 .612 .667 .612 Tesseract .500 .577 .707 .707 .816 .866 Crosspoly .500 .707 .577 .866 .817 .707 24-Cell .707 .816 .817 .866 .943 .866 120-Cell .926 .934 .973 .951 .982 .991 600-Cell .925 .973 .934 .991 .982 .951

  24. How Well Do the New Numbers Fit ? Planet Orbit Ratio Best Fit %Error Mercury 0.39 Venus 0.72 Earth 1.00 Mars 1.53 Asteroids 2.22 Jupiter 5.22 Saturn 9.58 Uranus 19.28 Neptune 30.21 Pluto 39.63 Sedna 70.47 0.537 0.577 7.4 0.725 0.707 -2.5 0.654 0.667 2.1 0.689 0.7072.6 0.425 0.408-4.1 0.545 0.577 5.9 0.497 0.5 0.6 0.638 0.612 -4.1 0.762 0.816 7.1 0.562 0.577 2.6

  25. Johann Daniel Titius (Tietz) (1729-96) • Prussian astronomer, physicist, and biologist whose law (1766) expressing the distances between the planets and the Sun was confirmed by J.E. Bode in 1772. "Titius, Johann Daniel." Encyclopædia Britannica. 2006. Encyclopædia Britannica Premium Service. 12 Mar. 2006 http://www.britannica.com/eb/article-9072653

  26. Table by Johann Titius (1766) • PLANET ORBIT 10R-4 • Mercury 0.39 0 • Venus 0.72 3 • Earth 1.00 6 • Mars 1.53 12 • Jupiter 5.22 48 • Saturn 9.58 96 • “Selene” ? 2.80 24 (missing planet) • Georgian Pl. 19.18 192 (1781: Uranus) • Neptune 30.21 298 (1846)

  27. Table by Johann Titius (revisited) • PLANET ORBIT 10R-4 • Mercury 0.39 0 • Venus 0.72 3 • Earth 1.00 6 • Mars 1.53 11 • (asteroids) - - - • Jupiter 5.22 48 • Saturn 9.58 92 • Uranus 19.18 188 • Neptun 30.06 296

  28. Is the Universea Dodecahedral Poincaré Space? Oct. 2003

  29. Evidence for Dodecahedral Universe ? • Power spectrum of the cosmic microwave background (CMB) radiation. Data from WMAP have extended the accuracy of the spectrum far beyond what was known from earlier measurements. This plot reflects the small differences in the temperature of the CMB across the sky. There are a series of peaks in the spectrum at small angular separations, but at large scales that structure disappears. Standard cosmological models cannot explain this, but Luminet and colleagues’ topological model for a finite universe can (image and text credit: Nature 425 566).

  30. String Concert in 10 Dimensions ? String theory, the current favorite ... • 1200 scientists, mathematicians work on it. • Subatomic particles are resonances of very small (10-35m) loopy strings. • Need to introduce 7 extra dimensions to make numbers work out – sort of ... • These strings are as invisible as Plato’s crystalline spheres.

  31. The Great Pyramidhttp://www.infinitetechnologies.co.za/articles/thegreatpyramid.html • Mean Distance to the Sun: The height of the pyramid times 109 represents the mean radius of the Earth's orbit around the sun. • Mean Distance to the Moon: The length of the Jubilee passage* times 7*107is the mean distance to the moon. ( * Don’t ask ! ) • Tropical Year: The length of the Antechamber used as the diameter of a circle produces a circumference of 365.242 (accurate to 6 digits). • Many more ...

  32. “Adventures in Scienceand Cyclosophy” Cornelis De Jager (astrophysicist), Skeptical Inquirer,Vol 16, No 2, Winter 1992, pp 167 - 172. 

  33. B Dutch Bicycle • W = Wheel diameter(“defines direction of path”)P = Pedal diameter(“gives power, forward dynamics”)L = Lamp diameter(“enlightens the search path”)B = Bell diameter(“means of communication...”) L W P

  34. Amazing Results Mass of Proton Mass of Electron • P2 * ( L B )1/2 = 1823 = • P4 * W2 = 137.0 = Fine Structure Constant • P-5 * ( L / WB )1/3 = 6.67*10-8 = Gravitation Constant • P1/2* B1/3/ L = 1.496 = Distance to Sun (108 km) • W * P2 * L1/3 * B5 = 2.999*105 ~ Speed of Light (km/s) 2.998error of measurement ?

  35. Computerized Search = Aa * Bb * Cc * Dd a, b, c, dcan assume:all integer values from – 5 to + 5,and also the values ± 1/2, ± 1/3, ± . A, B, C, D, are arbitrary assumed constants. Compare (83521 combinations) with databaseof natural constants or simple ratios thereof.

  36. Matching Your Measurements to Your Favorite Theory ... • You can always find good matches, if you look hard enough and ignore measurement uncertainties. • So this seems like a pretty silly game ... • Millions of people are doing it !!

  37. Golden Ratio is Everywhere ...length to width of rectangle = 1.61803 39887 49894 84820

  38. Statistics on Random Rectangles Golden Ratio In range of rectangle ratios from 1.0 to 2.0 • 1/3 of all rectangles fit within 10% (1.45-1.78) • 1/30 fit within 1% (1.602-1.634) of golden ratio. 1:1 1:2

  39. Key Message ! The number-matching game is too easy to play. Most of the found results are meaningless ! MUSIC as Art ...

  40. Music of the SpheresIs it still playing ?? • Let’s look on the Web ... Acknowledgements Thanks to the Internet and to the Google search engine !

  41. “Music of the Spheres” www.spectrummuse.com The Science of Harmonic Energy and Spirit unification of the harmonic languages of color, music, numbers and waves

  42. Sand Mandela by Rosalind Gittings

  43. “Music of the Spheres”by Lisa shukti@techren.com

  44. “Music of the Spheres” by Isabel Rooney

  45. A Novel by Elizabeth Redfern • London, 1795 • Spy story • French astronomersin exile, • sending secret informationhidden in tables of astronomical data. • Describes numbers gameby Johannes Titius ...

  46. “Music of the Spheres” by Bernard Xolotl

  47. Yorkshire Building Society Band

  48. Deutsche Bläserphilharmonie

  49. Wind Chimes

  50. “Music of the Spheres” - John Robinson

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