Final draft of review to appear
A Review of the 2006 Bridges Conference
Mathematical Connections in Art, Music, and Science
by B. Lynn Bodner
Since 1998, practicing mathematicians, artists, musicians and scientists have been coming together at the annual Bridges Conference to share ideas and enthusiasm for a commonly held interest in the mathematical connections existing among the fields of mathematics, computer science, science, art, architecture, sculpture, music, dance, theater and education. This year’s conference was hosted by the London Knowledge Lab, an interdisciplinary research lab (http://lkl.ac.uk), and the Institute of Education, a postgraduate institution, both affiliated with the University of London (in the United Kingdom). The six-day conference (from August 4 through August 9, 2006) included invited plenary speaker presentations in the mornings, parallel contributed paper sessions and workshops in the afternoons, a visual art exhibit open throughout the entire day, a musical evening, family day and various excursions. This review will briefly discuss each of these and highlight some of the author’s most memorable experiences.
The plenary speakers, Jacqui Carey, (“Bridging the Gap – a Search for a Braid Language”), Xavier De Kestelier and Brady Peters (“The Work of Foster and Partners Specialist Modeling Group”), Michael Field (“Illuminating Chaos – Art on Average”), Louis Kauffman (“The Borromean Rings – A Tripartite Topological Relationship”), Peter Randall-Page (“Collaborating on the Integration of Sculpture and Architecture in the Eden Project”), Carlo Sequin (“Patterns on the Genus-3 Klein Quartic”), Caroline Series (“Non-Euclidean Symmetry and Indra’s Pearls”), and Simon Thomas (“Love, Understanding and Soap Bubbles”) all gave extraordinarily interesting presentations during the morning sessions of the conference. Picking one as a highlight is extremely difficult, however, having said that, this author found the presentation of Xavier De Kestelier and Brady Peters, members of the Specialist Modeling Group at Fosters and Partners Architects, especially intriguing since some of the structural designs they discussed, including the Swiss Ré Gerkin and the Greater London Authority building, visibly add to the distinctive sky line of central London. The web links of individual plenary speakers may be found at http://www.lkl.ac.uk/bridges/programme.html.
the Swiss Ré Gerkin in the background
Each afternoon, four parallel contributed paper sessions and ‘Bridges for Teachers, Teachers for Bridges’ workshops on a wide range of topics were held concurrently, making for difficult decisions on the part of conference goers as to which event to attend. There were two sessions of seven contributed papers each on the connections between mathematics and music, a session of seven papers on Islamic art, and nine other sessions (consisting of 63 papers in total) on other disparate mathematical art topics. The 80-minute workshops involved various topics for teachers. With so much from which to choose, the author (as was the case for all conference participants) was only able to sample one fifth of the available sessions, and so it is impossible to discuss the highlights of these sessions. Instead, one is encouraged to read the short abstracts which may be found at http://www.lkl.ac.uk/bridges/abstracts.html and the conference Proceedings, containing the full text of the refereed papers, published by and available from Tarquin Publications (www.tarquinbooks.com).
Another major and very popular feature of this year’s conference was the Bridges Art Exhibit, displaying the largest collection of mathematical art (over 150 pieces from 54 contributors) since Bridges’ inception. Robert Fathauer, the Art Exhibit Coordinator, and Anne Burns, who created and maintains the extensive website, also served as jurors of the artwork, along with Nat Friedman, Reza Sarhangi and John Sharp. The collection, which includes sculptures, prints, and quilts, is well worth a look at http://www.bridgesmathart.org/art-exhibits/bridges06/bridges06.html.
On Monday August 7, the Bridges Musical Evening, which was a free event open to the public (thanks in part to the support of Sibelius Software), combined musical performances and short lectures “aiming to illustrate – through music – how mathematics is intertwined with human activity and creativity.” (For more information on most of these presentations, please check the following webpage: http://www.lkl.ac.uk/bridges/musical.html). The most rousing moment of the evening occurred when the audience was invited to join Paco Gomez and Godfried Toussaint in a performance of Steve Reich’s “Clapping Music.” The audience, in concert with Paco, clapped a constant rhythm with their hands while Godfried clapped shifts in the rhythmic pattern by one unit of time after a fixed number of repetitions, until eventually all were clapping in unison again. For those of us musically challenged, this was much harder to do for the entire length of the piece than this description sounds!
The Bridges Family Day on Wednesday August 9, an event for “children of all ages from 5 to 95,” was organized in conjunction with the Royal Institute of Great Britain (www.rigb.org) and planned as “a day to inspire, engage and motivate; to show that Maths really can be ‘fun’, especially when art is involved too.” Two parallel mathematics masterclasses (on perspective, anamorphic art, juggling, and Celtic and African art) and a Zometool workshop were held in the morning and a series of mathematics art “hands on” activities were available in the afternoon. (Please see http://www.lkl.ac.uk/bridges/familyday.html for a description of the program and some of the spontaneous mathematical art activities planned.) To cite just a few, Jacqui Carey, one of the plenary speakers of the conference and a braidmaking specialist, had us creating our own beautiful braids in no time; George Hart and Bradford Hansen-Smith led us in the construction of paper models and sculptures, and David Mitchell had us folding amazing three-dimensional shapes and the regular polyhedra.
Constructing George Hart’s paper model during Family Day
As an adjunct to the conference, participants were given a wide range of excursion choices for Saturday August 5, including an exclusive tour of mathematical sites at Cambridge University, conducted by the distinguished mathematician Michael Longuet-Higgins; a Bloomsbury walking tour led by David Singmaster, mathematician and metagrobologist; a visit to the Hindu temple, Shri Swaminarayan Mandir, led by Phillip Kent, research officer in Mathematics Education of the London Knowledge Lab; an Islamic Kensington tour led by John Sharp, mathematics writer, educator and visiting fellow of the London Knowledge Lab; a walking tour of mathematical and tourist sights in central London, led by Patricia Wackrill, and a walk from Westminster to Trafalgar Square, led by Penelope Woolfitt. Another optional bus excursion on Tuesday August 8 involved visits to the New Art Centre Sculpture Park and Gallery, Roche Court, which contains (among other things) Warp and Weft, a wonderful granite glacial boulder sculpture by Peter Randall-Page, one of the plenary speakers; Salisbury Cathedral, one of England’s great medieval buildings, which contains (among other sights) carved stone polyhedra on the Tomb of Sir Thomas Gorges; and Stonehenge, a key historic site in Britain. For more information and web links on the various excursions, please see http://www.lkl.ac.uk/bridges/excursions.html.
Warp and Weft by Peter Randall-Page at the
New Art Centre Sculpture Park and Gallery, Roche Court
All in all, this year’s Bridges Conference was one of the best ever, with over 200 participants from all over the world, 150 works of art on display at the Art Exhibit, presentations and workshops on a wide variety of topics, and engaging mathematical art activities for all. For information on previous Bridges conferences and also next year’s conference to be held in San Sebastian, Spain, please visit the Bridges home page at http://www.bridgesmathart.org.
B. Lynn Bodner is an associate professor of mathematics at Monmouth University in New Jersey, USA, having taught a wide variety of undergraduate mathematics courses for 23 years. She especially enjoys teaching classes on the geometries, the mathematics of artistic design, and the historical development of mathematics. Her most recent scholarship interest involves the study of medieval geometric Islamic art which incorporates ideas from all three of these areas. Her webpage may be found at http://mathserv.monmouth.edu/coursenotes/bodner/bodner.htm.