This is a story of how the impossible became possible. How, for centuries, scientists were absolutely sure that solids (as well as decorative patterns like tiling and quilts) could only have certain symmetries – such as square, hexagonal and triangular – and that most symmetries, including five-fold symmetry in the plane and icosahedral symmetry in three dimensions (the symmetry of a soccer ball), were strictly forbidden. Then, about twenty years ago, a new kind of pattern, known as a “quasicrystal,” was envisaged that shatters the symmetry restrictions and allows for an infinite number of new patterns and structures that had never been seen before, suggesting a whole new class of materials. By chance, solids with five-fold symmetry were discovered in the laboratory at about the same time. Even so, for nearly twenty years, many scientists continued to believe true quasicrystals were impossible because, they argued, such a pattern could only be formed with complex and physically unrealistic inter-atomic forces.
Impossible Crystals is an abstract but ultimately satisfying video lecture by Paul Steinhardt, Albert Einstein Professor of Physics at Princeton University. The presentation is targeted at the layman but realistically, some background in solid state physics/symmetry is necessary to appreciate what Steinhardt is saying. You don’t need a high speed internet connection: you can simply download the PDF and listen to the MP3 of the presentation. There are many other public lectures available for download at Perimeter (see link that follows).
Link to the presentation (look for Impossible Crystals)
Wikipedia entry for Quasicrystal
Wikipedia entry for Aperiodic Tiling
Another teaser image
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