

"Long
before it's in the papers" RETURN TO THE WORLD SCIENCE HOME PAGE From cracks to catastrophes, “singularity theory” could shed light June 5, 2008 There’s often more to everyday events than meets the eye. The folding of paper, or dripping of water from a tap, are two examples: they both involve the creation of
points known as singularities.
A workshop organised by the European Science Foundation in Paris in January was one of the first attempts to unify the field of singularities by bringing together experts in the different fields from astronomy to nanoscience—the study of atomicscale structures. The meeting was aimed at developing common mathematical approaches to singularities. Improved understanding of the underlying math would have many benefits, for example in making materials more resistant to breaking, researchers say. The event was a success and and paved the way for further research with greater crosspollination of ideas, said the convenor, Jens Eggers of the foundation. The workshop confirmed, scientists said, that most or all singularities, from microscopic cracks to the Big Bang, share a key property known as selfsimilarity. This means that under magnification the event looks almost the same. For example a crack in a piece of plastic exhibits the same jagged structure when magnified, say, 100 times. This means common mathematical approaches can be applied. But the devil is in the details when it comes to comparing different types of singularities, workshop participants cautioned. Different systems might have some common features such as selfsimilarity, but also unique aspects that require specialised study. One aim of the workshop was to identify the common methods that could be applied as a foundation for more detailed specific study. Jay Fineberg of Hebrew University in Jerusalem, for example, presented investigations of cracks in structures or rock formations. Fineberg discussed new experiments involving gels, allowing the crack’s structure to be determined in great detail down to microscopic dimensions, yielding some unexpected findings. Cracks are often surprisingly complex, Eggers noted, with “many small side branches, which appear to have complicated, if not fractal, structure.” Fractal structure here means much the same as selfsimilarity, involving a geometric pattern that looks unchanged under magnification or reduction. Another example concerned the singularities of crumpling in paper, presented by Tom Witten of the James Franck Institute in Chicago. Crumpled paper comprises many ridges and tips that defy simple analysis. There are many unanswered questions even in describing each individual coneshaped tip, Eggers said; figuring out the underlying math would not just help understand what happens when we crumple paper, but also other physical systems involving ridges and tips, such as the way biological molecules fold into their characteristic forms. One branch of singularity theory is “catastrophe theory,” which rose to prominence in the 1970s, initially developed by French mathematic René Thom and expanded by U.K. mathematic Erik Zeeman. Catastrophe theory deals with events with spaceandtime components, such as collisions between wave fronts, Eggers said. “In that case, a problem that takes place in all of space can be reduced to a problem that takes place along certain lines,” known as caustics, “which can be classified according to catastrophe theory.” But not all singularity problems are amenable to this simplification. The subject “cuts across disciplines and specializations, such as experimental physics, theoretical physics, and rigorous mathematical proofs,” Eggers said. “This workshop very much reflected this fact, as we had speakers from very different backgrounds.” * * * Send us a comment on this story, or send it to a friend




There’s often more to everyday events than meets the eye. The folding of paper, or drip of water from a tap, are two examples: they both involve the creation of “singularities.” Singularities occur at a point of cutoff or of sudden change, as in formation of cracks, lightning strikes, creation of ink drops in printers, and the breaking of a cup when it drops. These points require sophisticated mathematical techniques to describe, analyse and predict. Scientists say many singularities have much in common at all size scales—from microscopic interactions to the formation of the universe itself during the socalled Big Bang. But these seemingly disparate events are usually studied in isolation by different scientists with little interaction. A workshop organised by the European Science Foundation in Paris in January was one of the first attempts to unify the field of singularities by bringing together experts in the different fields of application from astronomy to nanoscience, the investigation of atomicscale structures. The meeting was aimed at developing common mathematical approaches to singularities. Improved understanding of the underlying math would have many benefits, for example in making materials more resistant to breaking, researchers say. The event was a success and and paved the way for further research with greater crosspollination of ideas, said the convenor, Jens Eggers of the foundation. The workshop confirmed, scientists said, that most or all singularities, from microscopic cracks to the Big Bang, share a key property known as selfsimilarity. This means that under magnification the event looks almost the same. For example a crack in a piece of plastic exhibits the same jagged structure when magnified, say, 100 times. This means common mathematical approaches can be applied. But “the devil is in the details” when it comes to comparing different types of singularities, organizers of the workshop cautioned. In other words different systems might have some common features such as selfsimilarity, but also unique aspects that require specialised study. One aim of the workshop was to identify the common methods that could be applied as a foundation for more detailed specific study of particular singularities. Jay Fineberg from the Hebrew University in Jerusalem, for example, presented investigations of cracks in structures or rock formations. Fineberg talked about new experiments involving gels, allowing the crack’s structure to be determined in great detail down to microscopic dimensions, yielding some unexpected findings. Cracks are often surprisingly complex, Eggers noted, with “many small side branches, which appear to have complicated, if not fractal, structure.” Fractal structure here means much the same as selfsimilarity, involving a geometrical pattern that looks unchanged under magnification or reduction. Another example concerned the singularities of crumpling in paper, presented by Tom Witten of the James Franck Institute in Chicago. Crumpled paper comprises many ridges and tips that defy simple analysis. There are many unanswered questions even in describing each individual coneshaped tip, Eggers said; figuring out the underlying math would not just help understand what happens when we crumple paper, but also other physical systems involving ridges and tips, such as the way biological molecules fold into their characteristic forms. One branch of singularity theory is “catastrophe theory,” which rose to prominence in the 1970s, initially developed by French mathematician René Thom and expanded by U.K. mathematician Erik Zeeman. Catastrophe theory deals with events with spaceandtime components, such as collisions between wave fronts, Eggers said. “In that case, a problem that takes place in all of space can be reduced to a problem that takes place along certain lines,” known as caustics, “which can be classified according to catastrophe theory.” But not all singularity problems are amenable to this simplification. The subject “cuts across disciplines and specializations, such as experimental physics, theoretical physics, and rigorous mathematical proofs,” Eggers said. “This workshop very much reflected this fact, as we had speakers from very different backgrounds.” 