FYI,

"Origami as the Shape of Things to Come"
New York Times
http://www.nytimes.com/2005/02/15/science/15origami.html

: Three paper shapes cut and pleated by Dr. Erik Demaine, who is
: applying insights from wrinkling and crinkling to questions in
: architecture, robotics and molecular biology.
http://graphics8.nytimes.com/images/2005/02/15/science/15orig.1.583.jp
g

: "Some people don't even think this exists," says Dr. Erik Demaine,
: turning in his hands an elaborately folded paper structure. The
: intricately pleated sail-like form swooshes gracefully in a
: compound curve and certainly looks real enough - if decidedly
: tricky to make.

: Dr. Demaine, an assistant professor of computer science at the
: Massachusetts Institute of Technology, is the leading theoretician
: in the emerging field of origami mathematics, the formal study of
: what can be done with a folded sheet of paper. He believes the form
: he is holding is a hyperbolic parabaloid, a shape well known to
: mathematicians - or something very close to that - but he wants to
: be able to prove this conjecture. "It's not easy to do," he says.

: Dr. Demaine is not a man to be easily defeated by a piece of paper.
: Over the past few years he has published a series of landmark
: results about the theory of folded structures, including solutions
: to the longstanding "single-cut" problem and the "carpenter's rule"
: problem. These days he is applying insights he has gleaned from his
: studies of wrinkling and crinkling and hinging to questions in
: architecture, robotics and molecular biology.

: At 12 years old, after Erik had become intensely interested first
: in computer games, then in computer programming, and finally in
: mathematics, he persuaded the administrators of Dalhousie
: University in Halifax, Nova Scotia, to let him take classes in math
: and computer science. His father sat in as an auditor. Erik Demaine
: received his doctorate at 20 and at the same age became the
: youngest professor ever at M.I.T. In 2003 he was granted a
: MacArthur "genius" fellowship.

: Today, at 23, he has published over 100 academic papers in fields
: as diverse as computational geometry, combinatorial game theory,
: data stuctures and graph theory. Along with his interest in
: folding, Dr. Demaine is also an expert in algorithms. He is also
: one of the computing world's major collaborators, with more than
: 140 co-authors so far.

: "He loves working with other people," says Dr. Joseph O'Rourke, a
: mathematician and computer scientist at Smith College who has been
: collaborating with Erik Demaine since he was 16. "He has a very
: broad understanding of a whole range of topics and he often brings
: in ideas that at first seem off the wall but really help to enrich
: what you are doing."

: Yet for all Dr. Demaine's smarts, the pleated form in front of him
: is not giving up its secrets easily. The perplexing question is
: whether its concertina-like structure can be derived by purely
: mathematical transformations of a flat sheet, or whether the sheet
: must be stretched in places to take on this complex shape.

: As Dr. Demaine explains, stretching would warp the intrinsic
: flatness thereby destroying the underlying geometry. If that were
: the case then, mathematically speaking, it would not exist. "But if
: it doesn't exist mathematically then something else is going on and
: it would be nice to know what that is," he says, setting the model
: down on his desk.

: The model is just one of a whole class of related structures. The
: hyperbolic parabaloid form has four sides, but in theory variations
: can be made with any number of sides. The complexity depends only
: on the patience of the folder.

: Dr. Demaine's office is littered with these models, and a myriad
: other constructions made of paper, plastic, tubing and little
: wooden sticks. The room looks less like a professor's office than
: some kind of geometric playpen. On the windowsill is a collection
: of glass vases and sculptures made by Dr. Demaine and his father,
: who is now a researcher in his son's lab.

: Aside from the mathematical value of the hyperbolic forms, Dr.
: Demaine is interested in them as potential architectural
: structures. At M.I.T. he has also taught courses in the school of
: architecture and imagines being able to computationally generate a
: scaffolding of these shapes over which a flexible skin could be
: draped.

: "If we believe the edges are really straight, which we do, then you
: could 3-D print the skeleton and really build it," he said.

: By his own admission, Dr. Demaine is primarily a theoretician. "I
: love the idea of timeless truths," he remarked over a sushi lunch
: in the cafeteria of M.I.T.'s Stata Center, the lavish new Frank
: Gehry building where Dr. Demaine has his office. But he is also
: deeply interested in relationships between disparate disciplines,
: particularly the sciences and the arts. In this respect his father
: has been a major influence.

: Though Mr. Demaine trained as a glass artist, when his son
: developed a fascination for computing and mathematics he happily
: read the books and attended lectures with him. "I don't really
: think of them as such different activities," he said of this switch
: from art making to mathematical theorizing.

: Today father and son have written 43 papers together. Meanwhile Mr.
: Demaine, who has just been appointed artist in residence in the
: computer science department, also runs the M.I.T. glass blowing
: workshop, where one of his students is his son.

: Among the topics the two have researched together is the "single
: cut" problem, whose roots go back to ancient China and to magic
: tricks. Before Houdini became an escape artist he had a career as a
: magician and supposedly performed a trick in which he folded a
: piece of paper, then cut across the creases to "magically" create a
: five-pointed star. Other examples of single cut magic are sprinkled
: through historical literature. The question that arises is, What
: sorts of shapes can you make this way? In 1998 the two Demaines,
: working with Dr. Anna Lubiw at the University of Waterloo in
: Ontario, proved that you could effectively make any shape just with
: folding and a single cut - a star, a swan or a unicorn.

: You can even create multiple shapes with a single snip of the
: scissors - 2 stars, 10 stars or 50 stars if you like. One set of
: shapes that can be produced this way is the letters of the
: alphabet.

: And since Dr. Demaine's proof shows that you can get as many shapes
: as you want, "in theory you could produce the complete works of
: Shakespeare with a single cut," said Dr. Robert Lang, a former
: laser physicist and professional folder who is collaborating with
: Dr. Demaine on a major origami math project.

: Understanding what you can do with paper is a two-dimensional
: problem, but Dr. Demaine also works with the one-dimensional analog
: or what are known as linkages. A linkage is a set of line segments
: hinged together like the classic carpenter's rule. Though it sounds
: simpler, Dr. Lang noted that the one-dimensional case is often much
: harder to understand and analyze than the two-dimensional case.

: The major part of Dr. Demaine's doctoral thesis was a solution to
: the so-called "carpenter's rule problem," which asks a question
: about how linkages can be unfolded. Put simply: Imagine a
: carpenter's rule arranged on a table in a complicated pattern. Is
: it always possible to unfold the rule, or are there patterns that
: cannot be opened out, that are in what mathematicians call a
: "locked" state?

: Dr. Robert Connelly, a mathematician at Cornell who worked with Dr.
: Demaine on the solution, noted by phone that the problem was a good
: deal subtler than it initially sounded. At first mathematicians
: thought all linkages could be unfolded, but during the 1990's they
: discovered a number of very clever arrangements that looked
: impossible to unfold. "Many people thought a lot of these were
: locked," said Dr. Connelly.

: But he and Dr. Demaine, along with Dr. Günter Rote of the Free
: University of Berlin, proved that all linkage arrangements could be
: unfolded. It turns out that the problem of folding and unfolding
: linkages is applicable to one of the major scientific questions of
: our time: how do proteins fold up? Proteins are made up of long
: strings of amino acids, and as the strings are produced inside a
: cell by the ribosome they fold up into complicated shapes.

: It is this shape that largely determines the biochemical function
: of each protein. Molecular biologists and pharmaceutical companies
: are extremely interested in understanding how protein folding
: occurs, in part because they would like to design specialized
: proteins for use as drugs.

: Recently Dr. Demaine has been working on the question of how
: protein folding occurs. "We think they fold by keeping their
: backbones as linkages," he said. He and Dr. O'Rourke, along with
: Dr. Stefan Langerman at the Free University of Brussels, have
: created a computer model of this process and will report their
: results soon in a paper for the journal Algorithmica. Dr. O'Rourke
: said their model proved that protein linkages could not become
: locked. If their main assumptions hold up, he said, this result
: could help pharmaceutical companies to radically speed up the time
: it takes to find useful proteins.

: Ideally, molecular biologists would like to be able to predict from
: the chemical structure of a protein what shape it would fold into.
: "If you could predict that," said Dr. Demaine, "then you wouldn't
: have to do all the hard work of synthesizing and crystallizing the
: protein to find out what it does."

: Dr. Demaine hope to solve the protein-folding problem completely.
: "I'm an optimist," he said. "I believe it can be done in my
: lifetime."

: Monumental though this challenge is, he is pursuing other equally
: difficult goals. Recently he has begun to work on a branch of
: mathematics called graph theory, a sort of generalized version of
: linkages. Graph theory is known to be fiendishly difficult, but Dr.
: Demaine is confident he can make headway once he immerses himself
: in its arcane lore. In the meantime he has origami models to tame
: and his new hobby of glass blowing to practice.

: In the M.I.T. glass lab, under the encouraging tutelage of his
: father, Dr. Demaine gently turned a piece of red-hot glass on the
: end of long metal blowpipe. He was making a small vase in a shape
: that he had recently learned to craft.

: "We haven't found any mathematics in here yet," he said, before
: blowing into the pipe. "But I'm sure it exists." If anyone can find
: the formalisms in an amorphous molten blob it must surely be he.

Mark Reiff