Space has become a central subject of our time. Astronomers are exploring the far reaches of outer space, probing the birth of our universe; physicists propose that we live in a 10- or 11-dimensional hyperspace and mathematicians are discovering new kinds of geometric and algebraic spaces. Meanwhile, GPS systems help us to navigate urban space, Google Maps allow us to explore geographical space, and spatial representations of data have become critical in fields as diverse as pharmaceutical research and weather prediction. Such tools change the way we understand our world and lead to new ways of solving problems. making space offers a multifaceted exploration of what we mean by the word “space” in its many diverse manifestations, historically and today.
Accompanying this exhibition is a series of lectures, workshops and conversations. In lectures we’ll examine how the modern scientific conception of space evolved as the science of physics matured. What does it mean to say that something has two, three, or ten spatial dimensions? What does relativity tell us about the architecture of space? How do string theorists think about “brane-space”? We’ll also look to artists, writers and mathematicians as we host conversations about visual space, literary space and phase space.
In workshops, visitors will have the chance to construct spatial forms of their own. Hyperbolic planes made from paper strips, platonic solids woven from bamboo sticks, pleated parabaloids and graph-paper tessellations; in each case audiences can engage with key spatial ideas though activities that are at once playful and pedagogically rich.
If you feel like playing, have a seat and fold some of our 60,000 specially designed business cards. Over the next six months we’ll be using them to create geometric, fractal-inspired sculptures. You can design new shapes yourself. The project is an exercise in applied mathematics and participatory aesthetic practice. What happens when art and geometry combine? We invite you to join us in exploring this boundary and in developing a new landscape of form.
This installation continues from December 2012 through May 2013.
The IFF’s business card sculpture project has been inspired by the work of Dr. Jeannine Mosely, an MIT trained engineer and pioneer of business card origami. Dr. Mosely developed her methods as a means to construct models of fractals, geometric objects with intermediate dimensionality. Taking Dr. Mosely’s techniques as our starting point, the IFF and its collaborators are developing an ecology of fractal-like forms. This is an on-going experiment: We invite your input. Feel free to add to the structures on display here, to play with the shapes as shown and adapt the techniques described, or develop new pieces of your own.
Our metaphor here is the evolution of life. Scottish chemist Graham Cairns-Smith has theorized that in the pre-biotic world life catalyzed itself on the crystalline substrate of clays. Complex, self-replicating compounds, clays hold within themselves an intriguing language of form. Somewhere around 3.7 billion years ago, the inorganic geosphere transformed into a zoosphere as the first organisms swirled into being. How did this transition from geo to bio occur?
Cairns-Smith is not the only thinker who has proposed that the structure of crystals played a role in the emergence of life. For Friedrich Froebel, founder of the kindergarten movement, complexification was intrinsically a movement from the simple geometry of regular crystals - the cubic lattice of salt, for example - to ever more complicated assemblies. Along with other Goetherian philosophers, Froebel saw the evolution of form as perhaps the fundamental question of science.
Following on from the success of the Institute’s Crochet Coral Reef project (begun in 2005), with this exhibition we again offer an open-ended exercise in participatory form-making. Join us in developing a business card origami fractal “tree of life.”
exhibition design: Margaret Wertheim core card folders: David Orozco, Christina Simons, Tracy Tynan, Oscar Collins, Margaret + Christine Wertheim card design: Margaret Wertheim + Cindi Kusuda assistant curators: Anna Mayer + Jemima Wyman
Tessellation Chapel
Across the globe, humans have been fascinated by the ways in which a plane can be tiled or tessellated. Deriving from the Latin word tessella – a small cubical piece of stone or glass used for making mosaics – a tessellation is any pattern that fills the plane completely without gaps. Naturally occurring tessellations include the hexagonal structure of honeycombs and the hexagonal fracturing of rock that forms as lava cools in places such as the Giant’s Causeway in Northern Ireland.
In 1618 the mathematician Johannes Kepler wrote one of the first treatises on regular and semi-regular tessellations. Three centuries later, in 1891, the Russian crystallographer E.S. Fedorov proved that every periodic tiling of a plane is one of 17 basic types, known as the “wallpaper groups”. Fedorov’s work is seen as the beginning of the mathematical study of tessellations, which is today a hugely dynamic field of research with application to areas of science and technology as diverse as the creation of new materials, cryptography, sheet metal cutting, quantum mechanics, data compression and CGI animation.
Only three types of regular tessellations exist: those made up of hexagons, squares, and equilateral triangles. A semi-regular tessellation uses two or more regular polygons and every vertex point is the same; there are eight of these types. Other varieties include irregular, periodic, aperiodic, asymmetric and fractal tessellations. Research now extends to tessellations in higher-dimensional and non-Euclidean spaces. The types of tessellation possible in a space are one way of characterizing the space itself.
Artists and craftspeople of many cultures have incorporated tessellations into their designs. The embroidered pieces on display here are traditional works made by women of the Hmong, from the mountainous regions of China, Vietnam, Laos and Thailand. On the video monitor are tessellation patterns underlying Islamic mosaics from the Alhambra Palace in Spain and other Muslim architectural wonders. These tilings, made between the 8th and 14th centuries, are still revealing secrets to mathematicians today.
exhibit curator: Christine Wertheim
Islamic Mosaics
In the classical Islamic world, teams of master craftsmen covered the walls of mosques and palaces with tessellations of dazzling complexity. Multi-pointed stars, often exhibiting 8-fold and 64-fold symmetry, were a favored motif that arose soon after the birth of Islam and quickly spread outward across the Middle East, into Northern Africa and Western Europe. Artisans would carve these designs in wood or stone, build them into latticework, or assemble them from baked terracotta tiles, a style known as Zellij.
All 17 of the possible wallpaper groups, each representing a mathematically distinct pattern, were used by Islamic mosaicists and by ancient Egyptian craftsmen. Designs were often family secrets passed down from father to son. The images on display here are taken from the book Arabesques: Decorative Art in Morocco by Jean-Marc Castera, who has mapped the patterns underlying many Moroccan mosaics and murquanas. These three-dimensional tessellated structures, made from carved blocks of wood, resemble stalactites and were used to adorn ceilings.
It is now known that in the Middle Ages Islamic mosaicists also discovered aperiodic tiling. Western mathematicians long believed such patterns were impossible and discovered them only in the 1960’s. An aperiodic tiling does not repeat itself on any scale and appears at once regular and irregular. Astoundingly, such patterns are present in the structures of quasicrystals, exotic compounds with symmetries that can be understood as projections of regular structures in higher-dimensional space. In 2011, Israeli scientist Daniel Shechtman was awarded the Nobel Prize in chemistry for discovering quasicrystals, after years of ridicule from colleagues. “There are no quasicrystals,” said the great Linus Pauling, “only quasi-scientists.” The Nobel Committee described these materials as “fascinating mosaics of the Arab world reproduced at the level of atoms.”
