First-Hand:The Fourth Dimension

Submitted by A. Michael Noll

September 29, 2025

In 1965, while employed as a Member of Technical Staff (MTS) in the Acoustics Research Department at Bell Telephone Laboratories, Incorporated (Bell Labs) in Murray Hill, New Jersey, I programmed a computer-animated film of a rotating four-dimensional hypercube.

The two dimensional projection of the rotating three-dimensional cube looks like 2D squares changing size and shape. Each face of the 3D cube is a 2D square. Not surprisingly, the three dimensional projection of a rotating four-dimensional cube looks like 3D cubes changing size and shape. Each face of the 4D cube is a 3D cube. A four-dimensional cube is called a hypercube, or a tesseract. These are four spatial dimensions, perpendicular to each other.

A system programmer (Doug Eastwood) in the Bell Labs computer center suggested to me that I use my 3D animation to look at the 3D projection of a rotating hypercube. Mohan Sondhi assisted me in understanding the mathematics of four-dimensional projection. This was in1965. The computer-animated film was amazingly fantastic – a three-dimensional cube tuning inside out – magnificently captivating. I programmed the IBM 7094 computer in Fortran, and the Stromberg-Carlson microfilm plotter created the 35 mm and 16 mm film. I noticed, years later, that a rotating hypercube had become a screen saver.

I then placed letters and words in four-space, and the computer animated the stereoscopic projections as they rotated. The words rotated and passed through themselves – it looked fascinatingly beautiful – almost mysterious.

A film producer working making a documentary for AT&T about Bell Labs research using digital computers saw the animated words and asked me to animate the title of the documentary “Incredible Machine.” It was released in 1968, and can be seen on-line. My animated title sequence was placed over Max Mathews sitting at the screen of the DDP laboratory computer, with computer music in the audio. The animation stops at a freeze frame, and conventional animation was used to do a blow out. I have been told that this was a very early example of a computer-animated “flying title.”

I gave many talks and presentations showing my 3D and 4D computer animation. I also wrote published papers describing the computer animation.

A couple of years later, Walt DeFaria of Lee Mendelson Film Productions visited Bell Labs, and I showed him my 4D animations. He was working with Arthur C. Clarke on a TV special to be called “The Unexplained.” Bell Labs’ John R. Pierce (my executive director) knew Clarke because of their interest in artificial satellites for communication. DeFaria asked me to use my 4D animation for the title of the TV special. I was working on other things then, but because of the Pierce/Clarke connection, I worked on the title. I would make a short title sequence and post overnight the 35 mm film to DeFaria, who was working with Clarke in Santa Monica, California. DeFaria would ask me to change the freeze frame at the end, and I would post the result back to him almost immediately. He was amazed by this fast turnaround, which was not possible with conventional animation. The special aired in 1970, and was one of earliest uses of computer animation for a title sequence. As I recall, DeFaria lived in Carmel Valley, CA.

Multi-dimensional physical spaces have been written about. The book Flatland: A Romance of Many Dimensions by Edwin A. Abbott is one example. Another is the paper “Space, Time, and Eternity” by Gustaf Stromberg that appeared in the Journal of the Franklin Institute, in which he suggested that the fourth dimension might involve God.

All my computer animation was great fun. I felt guilty that this was not the research in speech analysis that I was being paid by Bell Labs to perform. But my computer art and animation took little time away from this other “more serious” research. I gave many talks and wrote many papers about computer art and animation – and many artists and others were attracted to it, which was my intention. And I went on to other areas of research and careers.