Wednesday, November 21, 2007

Royal Institution Lecture by Sir Roger Penrose

Attended this evening.

A mind stretching experience.

Managed to get Professor Penrose to sign my copy of The Emperor's New Mind.

Some notes and key words jotted down during the lecture :

  • icosahedral symmetry
  • crystalline patterns can have rotational symmetry as well as translational symmetry
  • n-fold symmetry
  • Penrose tiles are surrounded by rings of 10 pentagons
  • only 3 kinds of polygons are used to create Penrose tiles : star, jester's cap and pentagon
  • Penrose tiles exhibit a "non-repeating quasi 5-fold symmetric pattern"
  • Robert Ammann solids (3-D tiling)
  • J Kepler (1619) in his book Harmonice Mundi shows tiling patterns that anticipate Penrose tiles
  • Penrose tiles exhibit a "hierarchical structure"(?)
  • Penrose tiles have a connection with fractals
  • there seem to be analogies between the formation of quasi crystals and the superposition principle in quantum mechanics ("non-local choice" is present in both)
  • Penrose tiling uses only two structures : kites and darts

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