Laws of Logic

Physicists are translating commonsense principles into strict mathematical constraints on how our universe must have behaved at the beginning of time.  Patterns in the ever-expanding arrangement of galaxies might reveal secrets of the universe’s first moments.

M.C. Escher’s Circle Limit III (1959). M.C. Escher

For over 20 years, physicists have had reason to feel envious of certain fictional fish: specifically, the fish inhabiting the fantastic space of M.C. Escher’s Circle Limit III woodcut, which shrink to points as they approach the circular boundary of their ocean world. If only our universe had the same warped shape, theorists lament, they might have a much easier time understanding it.

Escher’s fish lucked out because their world comes with a cheat sheet — its edge. On the boundary of an Escher-esque ocean, anything complicated happening inside the sea casts a kind of shadow, which can be described in relatively simple terms. In particular, theories addressing the quantum nature of gravity can be reformulated on the edge in well-understood ways. The technique gives researchers a back door for studying otherwise impossibly complicated questions. Physicists have spent decades exploring this tantalizing link.

Inconveniently, the real universe looks more like the Escher world turned inside out. This “de Sitter” space has a positive curvature; it expands continuously everywhere. With no obvious boundary on which to study the straightforward shadow theories, theoretical physicists have been unable to transfer their breakthroughs from the Escher world. orld, the fewer tools we have and the less we understand the rules of the game,” said Daniel Baumann, a cosmologist at the University of Amsterdam.  READ MORE...

MC Escher

Maurits Cornelis Escher (Photo right) 17 June 1898 – 27 March 1972 was a Dutch graphic artist who made mathematically inspired woodcuts, lithographs, and mezzotints. Despite wide popular interest, Escher was for long somewhat neglected in the art world, even in his native Netherlands. He was 70 before a retrospective exhibition was held. In the twenty-first century, he became more widely appreciated, with exhibitions across the world.

His work features mathematical objects and operations including impossible objects, explorations of infinity, reflection, symmetry, perspective, truncated and stellated polyhedra, hyperbolic geometry, and tessellations. Although Escher believed he had no mathematical ability, he interacted with the mathematicians George Pólya, Roger Penrose, Harold Coxeter and crystallographer Friedrich Haag, and conducted his own research into tessellation.

Early in his career, he drew inspiration from nature, making studies of insects, landscapes, and plants such as lichens, all of which he used as details in his artworks. He traveled in Italy and Spain, sketching buildings, townscapes, architecture and the tilings of the Alhambra and the Mezquita of Cordoba, and became steadily more interested in their mathematical structure.

Escher's art became well known among scientists and mathematicians, and in popular culture, especially after it was featured by Martin Gardner in his April 1966 Mathematical Games column in Scientific American. Apart from being used in a variety of technical papers, his work has appeared on the covers of many books and albums. He was one of the major inspirations of Douglas Hofstadter's Pulitzer Prize-winning 1979 book Gödel, Escher, Bach.  SOURCE:  Wikipedia

Some of his illustrations below: