# Quantum math takes on contemporary art with a VR donut

Virtual Reality - VR - has made a serious entrance into the art scene in recent years. And now the Center for Quantum Mathematics (QM) is putting on its Virtual Reality glasses and participating in a large interactive VR artwork, TORUS (Act 1), by Sophie Hjerl.

Homer Simpson would probably put Sophie Hjerl’s VR artwork on his must-see list. Because the artwork, TORUS (Act 1), with its geometric shape, undeniably looks like a donut. But then all comparisons with the ring-shaped cake and the animated TV series character also end.

”In many ways, mathematics is as much about providing understanding as it is about formulas and numbers, and many forms of understanding involve an aesthetic component. Through that we have the connection to the arts.

Because Sophie Hjerl’s VR artwork is not edible.

Instead, the Danish artist, with the help of professor and head of center Jørgen Ellegaard Andersen and postdoc William Elbæk Mistegaard (both from the Centre for Quantum Mathematics), has created a virtual journey through the abstract universe of mathematics, where, together with several members of the audience, you can simultaneously experience a torus, which is a geometric shape that can be explored, unfolded, and challenged, and which thus resembles a doughnut.

Jørgen Ellegaard Andersen and William Elbæk Mistegaard were consultants on the exhibition, and the artist visited the center twice and had the mathematics she needed thoroughly explained to her. This has now resulted in the VR artwork, TORUS (Act 1).

## Interdisciplinary collaboration

– There are many connections between art and mathematics, and as a mathematician it has been very interesting to help Sophie (the artist behind the exhibition), says William Elbæk Mistegaard.

”We agreed that art could actually be a “common space” where you can experience mathematics with your senses instead of having it explained.

– In many ways, mathematics is as much about providing understanding as it is about formulas and numbers, and many forms of understanding involve an aesthetic component. Through that we have the connection to the arts.

In our daily work with research in quantum mathematics, we work with the mathematics behind modern quantum physics and especially quantum field theory. The precise mathematical description involves geometric quantities called n-manifolds, which are spaces that are locally n-dimensional (where n is a positive integer such as 1,2,3 and so on). For example, 4-manifolds are central to the description of relativity, in which they figure as space-time.

### The ring of rings

Rings appear in many cultures and religions, and life is often represented understood as an Ouroboros, the mythical snake that bites its own tail and unites beginning and end.

A torus is the product of two circles or "rings of rings" that loop around themselves in multiple dimensions. The shape plays a central role in topology, the mathematical study of continuous spaces and surfaces.

Torus is the first work in a series of three, all exploring the torus shape, which can seem both simple and complex at the same time.

In computer graphics, Torus is known as a primitive - a simple shape frequently used as a starting point by 3D artists when designing virtual objects, and thus TORUS (Act 1) very appropriately marks the start of the new era of virtual experience spaces.

*Source: Phenomenal Viborg and Wikipedia*

A torus (the exhibition’s central object) is an example of a 2-manifold, so it was an obvious choice to participate in this exhibition, and it was very exciting to hear Sophie’s artistic perspectives on the torus, adds William Elbæk Mistegaard.

Jørgen Ellegaard Andersen finds that more and more researchers and artists are interested in interdisciplinary collaboration.

– Quantum mathematics is characterised by the need to confront complexity, says Jørgen Ellegaard Andersen. It seemed like a serious project, and since we at the Centre for Quantum Mathematics deal with pure theoretical/abstract mathematics, which is quite difficult to communicate, we agreed that art could actually be a “common space” where you can experience mathematics with your senses instead of having it explained, elaborates Jørgen Ellegaard Andersen, who has previously been involved in the art exhibition “Imaginary - Through the Eyes of Mathematics” at the Steno Museum in Aarhus in 2013.

*Still from the VR artwork TORUS (Act 1) by Sophie Hjerl.
CG artist: Andreas Schönau.
© 2022 Sophie Hjerl*

### TORUS (Act 1)

The VR artwork takes up a 250m2 space, offering huge possibilities for free exploration. According to Phenomenal Viborg, an experience centre for animation, art, and XT (extended reality), Sophie Hjerl’s VR artwork is the first place in the world where several people can participate in the same VR experience. This adds a new dimension to the experience, making it more like being in a real museum.

The project is supported by the Danish Arts Council, Viborg Municipality and The Animation Workshop – VIA University College and the Centre for Quantum Mathematics (QM) at the University of Southern Denmark.

*Source: Phenomenal Viborg and Wikipedia*

##### Meet the researcher

Professor Jørgen Ellegaard Andersen is the Founder and Head of the Center for Quantum Mathematics and Professor at the Department of Mathematics and Computer Science (IMADA) at the Faculty of Science, SDU.

##### Meet the researcher

William Elbæk Mistegård has a postdoctoral fellowship at the Center for Quantum Mathematics.