Alex's Adventures in Numberland - Alex Bellos [100]
Demaine is tall and skinny, with a fluffy beard and fuzzy dark-blond ponytail. On to a big screen behind him he projected an image of the Haberdasher’s Puzzle. He said that he had recently decided to attack the problem with his PhD students. ‘I didn’t believe it was true,’ he said. Contrary to his expectation, however, he and his students found that you can transform any polygon to any other polygon of equal area through a Haberdasher’s Puzzle-style hinged dissection. The hall started clapping – a rare occurrence in the upper reaches of computational geometry. But in puzzle land this was about as exciting a breakthrough as you can get – the solution to an iconic problem by one of the cleverest minds of his generation.
The Atlanta conference, called the Gathering for Gardner, was the most appreciative audience possible for Demaine’s talk. The Gathering is the world’s premier jamboree for mathematicians, magicians and puzzle people. It is a biannual homage to the man who revolutionized recreational mathematics in the second half of the last century. Martin Gardner, now 93 years old, wrote a monthly maths column in Scientific American between 1957 and 1981. This was a period of great scientific advances – space travel, information technology and genetics – yet it was Gardner’s lively and lucid prose that really caught readers’ imaginations. His column covered subjects from board games to magic tricks, from numerology to early computer games, and often ventured into tangential areas such as linguistics and design. ‘I thought [Gardner] had a playful respect for mathematics that is often lost in mathematical circles,’ Demaine told me when I spoke to him after his talk. ‘People tend to be too serious. My aim is to make everything I do fun.’
As a boy, Demaine was introduced to Gardner’s columns through his father, a glass-blower and sculptor. The Demaines, who often publish mathematical papers together, embody Gardner’s interdisciplinary spirit. Erik is a pioneer of computational origami, a field both mathematical and artistic, and some of the Demaines’ origami models have even been exhibited in New York’s Museum of Modern Art. Demaine considers maths and art parallel activities, which share an ‘aesthetic about simplicity and beauty’.
In Atlanta Demaine didn’t explain the details of his proof of the universality of Haberdasher’s Pzzle-style dissections to the audience, but he did say that dissecting one polygon so it can be rearranged and hinged to form another polygon isn’t always pretty – and will often be completely impracticable. Demaine is now applying his theoretical work on hinged dissections to make robots that can transform from one shape into another through folding – just like the heroes of the comic book and movie franchise Transformers, where robots morph into different types of machine.
The conference was the eighth Gathering for Gardner, or G4G, and its logo, designed by Scott Kim, is known as an inversion, or ambigram.
If you turn it upside-down, it reads exactly the same. Kim, a computer scientist turned puzzle-designer, invented this style of symmetrical calligraphy in the 1970s. Ambigrams do not have to be the same when rotated 180 degrees – any symmetry, or concealed writing, will do.
The writer Isaac Asimov called Kim ‘the Escher of the alphabet’, comparing him to the Dutch artist who played with perspective and symmetries to create self-contradictory images, most famously steps that appear to rise and rise until they reach where they began. Another similarity between Escher and Kim is that their work first reached a mass audience thanks to Martin Gardner.
Ambigrams were independently, and contemporaneously, conceived by the typographer and artist John Langdon. Mathematicians especially love this type of lettering since it is a witty take on their own search for patterns and symmetry. The author Dan Brown was introduced to ambigrams through his father Richard Brown, a maths teacher. Dan Brown commissioned Langdon to design