After coming back from a tour of the Ronald and Maxine Linde Hall of Mathematics and Physics at Caltech recently, I realized that there was a common theme running through much of what I saw: lighting in the form of canonical math ideas… or should I say (ner)delights? (you have to say that out loud). I was lead by Gloria Mullendore and Carol Chin, docents from the Caltech History & Architectural Tour Service (CHATS), and all three of us were surprised at the variety of ways in which math themes can be incorporated into lighting.
This building was originally constructed in 1923 to house very high voltage equipment, and its exterior was designed by Bertram Goodhue (of Balboa Park fame, if you’ve been to San Diego). It was completely renovated in 2019 in midcentury modern style, with some quirky touches.
Our first stop was what I call the Pi-light —and perhaps highlight— of the building.
Diffusing the lights on the ceiling is a metal screen representing the decimal expansion of the irrational number π=3.14159265358979323846264338327950288419716939937510… to 433 decimal places. Below is a detailed and annotated view of the first few digits of the expansion, read from right to left.
Each natural number is represented by the corresponding number of dots all next to each other. The vertical bar stands for the decimal point. But what about zero? I will leave that to the reader’s imagination. Zoom in on one of the pictures above and you will see it.
For our next stop we stepped into the adjacent Kellogg Radiation Laboratory, a 1931 building renovated in the same style as the math and physics building. There we saw very modern looking lights with tetrahedral frame accents.
The tetrahedron, also known as a triangular pyramid, is a solid whose faces are 4 triangles. The name comes from Greek: tetra means 4 and hedra means seats, or faces. With 4 vertices, or corners, it is the simplest solid one can build in 3 dimensions. It is the 3-dimensional analogue of a triangle, which is the simplest polygon possible in 2 dimensions.
One thing that was eluding us on this tour was the trefoil knot light which I had glimpsed in a photograph online the day before. After several futile trips up and down the stairs, popping our heads into various classrooms, and asking several maintenance staff, we finally found a member of the math department staff who identified the trefoil knot light as belonging to the faculty workroom. She was kind enough to let us in, and this is a summary what we saw.
The light is directly above the conference room table, so it was difficult to get a picture that shows the symmetry of this knot projection. Fortunately, I was able to place my spherical camera in the middle of the conference table and ultimately get the picture shown above. The nerdy spirit of this blog demands a further explanation. The actual image produced by my spherical camera can be interacted with here. Further software processing of the image by results in an approximately stereographic projection, which is what you see above.
The trefoil knot is the simplest nontrivial (meaning not just a loop of unknotted string) knot one could make with a string. Earlier we saw a tetrahedron, which is the simplest solid one could build. These structures may be simple, but the mathematics that developed around them is anything but. They are aesthetically pleasing as well as conversation starters, which, in my mind, makes them perfect elements of decor for the math and physics building.