Described as a laboratory for visual mathematics, the Design Science Studio in Harvard’s Carpenter Center for the Visual Arts was a site for interdisciplinary experimentation and hands-on learning. It was the invention and classroom of Dr. Arthur Lee Loeb (1923-2002), a Dutch crystallographer who taught courses in synergetic geometry in the Department of Visual and Environmental Studies (VES) from 1970-2002. The VES concentration taught students to look, think, and speak about images. The Design Science Studio trained them to engage with spatial complexities. Through the study and making of models, they learned how to recognize patterns and identify generalized spatial principles that could be applied to the built environment.
Inside the Design Science Studio examines Loeb’s approach to teaching and learning through the objects and documents that surrounded him. Comprising course materials, student assignments, geometric models, tessellation prints, natural specimens, and books, the Arthur Loeb Design Science Teaching Collection and Archive at RISD is a material record of Loeb’s influence as a teacher, scientist, artist and collaborator. It documents the intersection of scientific methods and artistic processes within design education. Loeb’s widow and frequent collaborator, Charlotte (Lotje) Aarts Loeb, donated the collection to RISD in 2006, to ensure its continued use for education of artists and designers.
Design Science
Patterns and strategies refined by nature over billions of years of evolution inform the creation of sustainable and efficient design solutions. The approach is rooted in the idea that “universal generalized principles” govern natural and constructed structural systems. Students in the Design Science Studio were encouraged to discover these systems through scientific thinking and creative inquiry, and by thinking beyond the square. While artifacts in the teaching collection capture these processes, they also trace Loeb’s own pathway into Design Science, from his childhood in the Netherlands, to his work with computing and crystallography, and his relationships with artists, scientists, architects, and educators, who were determined to improve the world through design.
Artifacts:
Arthur L. Loeb, Thermal Egg, 1949.
Egg-shaped device used for measuring the thermal conductivity of ceramics.
Arthur L. Loeb, Moduledra, ca. 1960.
Clear plastic tetrahedral- and octahedral-shaped building blocks used to illustrate the molecular structure of close-packed crystals.
Clear Plastic Tetrahedron with Center Ball, date unknown
Sea Urchin, date unknown
M.C. Escher, Icosahedron, 1963.
Limited edition embossed twenty-sided tin created to commemorate the 75th anniversary of the Dutch tin manufacturer N.C. De Vereenidge Bilkfabrieken
Books:
Module, Proportion, Symmetry, Rhythm by György Kepes, 1966
Concept and Images: Visual Mathematics by Arthur Loeb, 1992
Documents:
Harvard Magazine, vol. 84. No. 3. March-April 1982
Courses Guide for Visual and Environmental Studies, date unknown
Photographs of the Design Science Studio at Harvard, ca. 1990s
Posters:
R. Buckminster Fuller Patent for Laminar Geodesic Dome, ca. 1980
Ricardo Barthelemy Photogram of a Dragonfly Wing, date unknown
Color and Symmetry
Symmetry is a fundamental feature of crystals. Their internal structure consists of repetitive arrangements of atoms and molecules that remain unchanged under geometric transformations. When working as a research scientist at Kennecott Copper Company’s Ledgemont Laboratory, Loeb developed a system for describing these symmetries that had applications beyond crystallography. His work caught the attention of Mirko Basaldella, director of the Design Workshop at Harvard, who invited him to lecture and participate in the 1966 exhibition, Symmetry and Transformation. By 1970, Loeb was teaching courses on the subject to architecture, science, and engineering students.
Artifacts:
Golden Rectangle Pillow, date unknown (student model)
Panels from Color and Symmetry Exhibition, date unknown
Hexagonal Tiles, date unknown (student model)
Books:
Color and Symmetry by Arthur Loeb, 1971
Prints:
Holly Compton Alderman, The Symmetry Portfolio, 1983
Silkscreen on posterboard that illustrate different plane symmetry groups outlined in Color and Symmetry.
Structure of Structures
Structure is the arrangement of entities in a pattern, and the study of relationships between structures is the “structure of structures.” Students in the Design Science Studio discovered systems of organization both within and between three-dimensional forms like polyhedra. The hierarchy of form was not limited to geometry, but extended to disciplines like crystallography, architecture, music, dance, and psychology.
Polyhedral Bingo, date unknown
Wooden models that were used to illustrate the relationships between polyhedra.
Synergetic Geometry
Once students were proficient in two-dimensional design, they began learning about three-dimensional spatial order. Arthur Loeb’s VES 176/176b courses addressed topics of sphere packing, Platonic solids, Archimidean solids, truncation, stellation, space fillers, jitterbug transformations, tensegrity, and dome structures.
Every iteration of Loeb’s courses were unique and depended on the interests of students. Students arrived at an understanding of spatial complexities through analysis, intuition, and model making. While many of the models in the teaching collection were created by students, several were commissioned by Loeb as teaching tools that helped visualize geometric principles.
Artifacts:
Andrew Spalding, Polyhedral Arithmetic, ca. 1978
Plastic model commissioned by Loeb to illustrate the nesting of polyhedra.
Cube Showing Hexagonal Layers, date unknown (student model)
John Ehrmann, Cube with ⅙ Tetrahedron and ¼ Octehedron Pieces, 1978
Stackable Cuboctahedron with Embedded Octahedron, date unknown (student model)
Half Cube Paper Models, date unknown (student model)
Fold-Up Triacontrahedron, date unknown (student model)
Books:
Space Structures: Their Harmony and Counterpoint by Arthur Loeb, 1976
Documents:
Arthur L. Loeb & C. Todd Stewart, Unwrapping the Cube, date unknown
A photographic essay that illustrates the many faces and properties of a cube.
Flyer for Philomorphs: The Last Meeting of Spring 1974
Synergetic Geometry Continued
Artifacts:
Partial Tetrahedron, date unknown (student model)
Cuboctahedral Mesh, date unknown (student model)
Suspended Wooden Triangles, date unknown (student model)
Plastic Balls, date unknown
commercial product used to learn about sphere packing
Ecological Pyramid, date unknown (folded paper)
Golden Rectangles with String Outlining Icosahedron, date unknown
plastic and thread
Six-Strut Tensegrity, date unknown
wooden dowels and wire
Twelve-Strut Tensegrity, date unknown
wooden dowels and wire
Dennis Dreher, Octahedral Jitterbug, ca.1980
A stainless steel jitterbug that transforms from one polyhedron into another through a combination of rotation and radial displacement.
Documents:
Artnews, vol. 80. no. 2. February 1982
Photographs of Tensegrities, ca. 1970s
R. Buckminster Fuller
R. Buckminster Fuller (1895-1983) worked across multiple fields of architecture, design, geometry, engineering, science, cartography, and education, with the goal of making the world work for 100% of humanity. He believed that mathematical principles should come from the natural world rather than abstract conventions. Observations of natural phenomena led to generalizations and the development of concepts like tensegrity, isotropic vector matrix, and geodesic domes. Fuller’s conviction that we could solve humanity’s problems by embracing Comprehensive Anticipatory Design Science (CADS) influenced generations of architects and designers to adopt more sustainable and holistic approaches to problem-solving.
Artifacts:
R. Buckminster Fuller, 30-Strut, 3 Frequency, Geodesic Dome Tensegrity, ca. 1980
Wooden dowel and wire tensegrity model.
Documents:
Jim Knighton & BFI, Dymaxion Globe Kit, 2002
A icosahedral map designed according to R. Buckminster Fuller’s 1954 Dymaxion Projection, a flat representation of the entire surface of the earth without obvious distortion or an up and down orientation,
Some Contributions to Synergetics: Explorations in the Geometry of Thinking, Technical Note no.38, by A.L. Loeb, 1967
R. Buckminster Fuller, Complex of Jitterbugs, 1948/1976 (on loan from Abbot Stranahan)
1 of an edition of 25 aluminium, copper and stainless sculptures that Fuller produced in partnership with his gallerist Carl Solway. With a twist of a threaded collar on its tubular steel stem, the closely packed octahedral units open into an array of cuboctahedrons.
Six Great Silver Circles, date unknown (student model)
Silver Cube Showing All Diagonal Faces, date unknown (student model)
Mabel Liang and Tad Paul, Hyperoctahedron, date unknown
Wire Model with Pieces of Map Glued to it, date unknown (student model)
Icosahedron with Colored Edges, date unknown
Nested Pentagonal Dodecahedron and Icosahedron, date unknown (student model)
Geodesic Sphere, date unknown
Collapsing Tetrahelix made of String and Wooden Dowels, date unknown (student model)
Six Strut Tensegrity, date unknown
