Cities Mathematical Dances.


C. Farsi, Ph. D.

Department of Mathematics, University of Colorado, Boulder, USA




The aim of this artistic project is to virtually make cities dance.  In particular I present three video clips in where famous buildings, monuments, and everyday objects perform mathematical dances to the music of city sounds. 


1.    The Project


Normally we think of movement in a city as generated by the city’s inhabitants’ daily wanderings and routines. In these clips I creatively imagine that landscape features such as (famous) buildings, monuments, and objects can come alive and dance too. This creates a dream-like world of shifting organic forms and perceptions. Moreover, string theory models the matter as made up of tiny strings and thus predicts a world in perpetual motion. Inspired by this viewpoint, in my project everything becomes a vibrating string. Additionally, I emphasized the use of symmetries to reflect symmetries’ paramount role in mathematical physics.  


The three short video clips I realized for this project are described in detail below.


1.1 The LeaningTowerofPisa Bell Dance. In this clip I describe a left-to-right and right –to-left Tower motion. This work was inspired by the sound of church bells (which are heard daily in all Italian cities) and the realization that, with the help of a modern editing program, the Tower could very well be rendered dancing, in a virtual world, at the tune of those bells. (See Figure 1.)


1.2 The PonteVecchioPouring Dance.  In an up-and-down dancing motion, the Old Bridge waves a partnership with the water of the River Arno. The accompanying sounds of rocks and gravel pouring down from a machine were recorded next to a remodeling site in Florence. The gestures of pouring and weaving are seen as creating dual patterns. (See Figure 1.)


1.3 The WomanMan Single Dance.  This piece was inspired by today’s confusion on men and women’s roles in society and by the quick shifting in roles and traditions. This clip also reflects some of my life experiences as a divorced woman. The mannequins in the photographs were in a Florentine shop window under construction. The images are accompanied by the sounds of an ambulance’s siren, recorded near the Careggi Hospital in Florence. The siren is meant to emphasize the urgent nature of the problems to be addressed. (See Figure 1.)

2. Technical Background

I edited my video clips with Adobe Premiere 1.5. I used a few selected images and symmetries as the clips’ building blocks. (This was inspired by the string-theory view of the world.) I will detail below the generative editing procedures I followed. In all cases, I chose to employ pieces of straight line as opacity functions.


2.1 The LeaningTowerofPisa Bell Dance.  The Tower dance was created by the use of one image (together with its mirror image) and of linear functions that change opacity. The functions’ extreme values reflect the bells sounds’ rhythm, while interpolation is used in between extremes.

2.2 The PonteVecchio Pouring Dance.   The Pouring dance is obtained from three different images, and uses linear functions that change opacity in a moderately smooth way, thus reflecting the act of pouring.


2.3 The WomanMan Single Dance.  The WomanMan dance was created from two images, each one almost the mirror reflection of the other. The opacity function here is crazily jumping up and down, but I still chose it to be continuous.



Figure 1. The LeaningTowerofPisa Bell Dance, The PonteVecchio Pouring Dance and The WomanMan Single Dance: Frames

This work was done while visiting the Mathematics Department of the University of Florence in Italy.