Aug 082013
 

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Today is the birthday (1931) of Roger Penrose, mathematician, philosopher, and artist.  I am a big fan.  Some of you who read this blog regularly may wonder why I admire so many mathematicians; maybe this post will solve that puzzle.

Penrose was born in Colchester on the east coast of England, and is the brother of mathematician Oliver Penrose and of chess Grandmaster Jonathan Penrose. Penrose attended University College School and University College, London, where he graduated with a first class degree in mathematics. While an undergraduate he was already doing original research which he continued at Cambridge, taking his Ph.D. in 1958.

As a student in 1954, Penrose was attending a conference in Amsterdam when by chance he came across an exhibition of M.C. Escher’s work. Soon he was trying to conjure up impossible figures of his own and discovered the tri-bar – a triangle that looks like a real, solid three-dimensional object, but isn’t.

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Together with his father, a physicist and mathematician, Penrose went on to design a staircase that simultaneously loops up and down. An article followed and a copy was sent to Escher. Completing a cyclical flow of creativity, the Dutch master of geometrical illusions was inspired to produce his two masterpieces.

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In 1965, at Cambridge, Penrose proved that singularities (such as black holes) could be formed from the gravitational collapse of immense, dying stars. This work was extended by Stephen Hawking to create the Penrose–Hawking singularity theorems.  In 1969, he conjectured the cosmic censorship hypothesis. This proposes (rather informally) that the universe protects us from the inherent unpredictability of singularities (such as the one in the center of a black hole) by hiding them from our view behind an event horizon. Black holes have intense gravitational pull, constantly attracting matter towards their centers.  The event horizon is the boundary point beyond which nothing can escape this gravitational force. Hence we cannot know anything about what exists beyond this horizon because nothing, not even light, can escape to give us information. Proving this conjecture, and a stronger version which Penrose proposed 10 years later, are major outstanding problems within the field of general relativity.  Although the mathematics of these conjectures is beyond the comprehension of all but a few specialists, the general implications are easy enough to understand and have become part of popular culture.

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Penrose is well known for his 1974 discovery of Penrose tilings. A tiling is a pattern of “tiles” (2-dimensional shapes) that can be arranged so that there are no spaces or overlaps on a flat surface. Squares and certain triangles are the simplest form of tiling (as you know from the tiles in your shower stall). Quilt patterns and tile patterns in mosques are more complicated tilings. Penrose tilings have two properties. (1) They are formed using only two different shapes of tiles. (2) They are aperiodic, meaning that you cannot copy an area of the tiling on to tracing paper and then shift the paper to another area of the tiling and have it match.  In simple, slightly inaccurate, layman’s terms, the local patterns do not repeat. They appear in nature in what are known as quasicrystals, and have become the inspiration for graphic design artists.

First Penrose Tiling

First Penrose Tiling

Quilt

Quilt

Mosque Tiles

Mosque Tiles

Quasicrystal

Quasicrystal

He was influential in popular