Thoughts & Insights

On Puzzles, Ants and the Mathematics of Universal Space

One of the most frequent questions people ask me is what OUBEY was like, as an artist, as a person; how he’d think, how he’d work. Today is OUBEYs birthday and that´s an occasion to give a more specific response to this question by sharing with you a story OUBEY told in his own words.

It forms part of a long conversation that was recorded as part of the preparations for his first and only exhibition in 1992, and it took place ten years previously in 1981/82 at the Institute for Structural Design and Building Construction at the University of Karlsruhe where OUBEY was then studying architecture.

“The year before I went to university, Fritz Haller became director of this institute had been so heavily influenced by Eiermann, which was a great stroke of luck for me. His assignment for those of us in our second semester was that we should design shelving and furniture characterized by a certain variability.

While T.H., with whom I used to work, designed utilitarian furniture, I designed a new mathematical model based on axiomatic reasoning, on what’s known as rotation vectors. This is a mathematics based on vector calculus that doesn’t use the vectorial representation which defines linear structures by points in space, but factors in the movement aspect in space as well.

To put it very simply, the basic building block in a three dimensional grid in vector calculus is an arrow in a coordinate system with a y and a z axis. You can extend it or compress it and you can build a Euclidean solid geometry on it. This all can be transferred to a matrix system. As the rotation vector, the arrow moves in the form of a spiral at the speed of light as a constant of its own rotation, depicts a sphere and returns within a second to its point of departure. It either spins to the left or the right. The sphere describes a line in the form of a spiral, the spiral scans the inside surface of the sphere, and you can move the sphere. The speed you need to move it at is the speed of light because only then is simultaneity assured. And because a sphere can only be depicted when a point in the line scans a space with the highest possible speed known in the universe.

There was no such model in the whole of mathematics. This is what I designed back then. Not bad at all actually. I’m curious to know if it will become important at some point in the twenty first century. Basically it would be a new kind of mathematics. No longer 1+1=2, because the 1 is a form in itself. A universal form which you don’t need to add to other forms.

And it was accepted. Haller accepted it as an outcome for foldable furniture. He told me it was fascinating and that I should continue in this line. That was really the most important thing of all. I came to this model when I set out on calculus for furniture, foldable furniture, but ended up in new descriptions of universal space. But that’s me all over. Somehow I start to puzzle about ants and end up with the weirdest ideas. And I can’t help it. It’s just the way I am.

All I really did was to notice what happens when you try to fold objects in space to bring them into a more compact form, possibly for more efficient storage. Only this practical aspect faded into the background. What interested me was what really happens at these critical points when surfaces or chair legs are rotated. And I found that that I couldn’t get very far with standard mathematics, but that basically each hinge needed its own mathematics to describe its ability to hinge.

And you can only have a general hinge ability when you first define mathematics for this rotation vector. And then this mathematics consists of geometrically limiting this universal possibility. In other words, you’re no longer making mathematics by building something or adding something and creating a formula for it – like a lever principle, for instance “square meters times two, divided by eight” where you describe the load borne by the hinge, the cutting forces, by describing the forces inherent in the carrier – you’re making universal mathematics.”

However, OUBEY didn’t continue his investigations into the rotation vector but turned instead to other interesting questions and, increasingly, to art.

The encounter between a mathematician and OUBEYs art has always been on my list of desiderata for the Encounter Project. And in September 2011 it came about: Professor Karl Sigmund, a mathematician who is a world authority in his own field came face to face with one of OUBEYs paintings in Vienna.


Interestingly, the subject of mathematics was hardly touched on in what he had to say. This video is now online; click here to view it.