- a history of the domino problem is a performance-installation that traces the history of an epistemological problem in mathematics about how things that one could never imagine fitting together, actually come together and unify in unexpected ways. The work comprises a set of musical compositions and a kinetic sculpture that sonify and visualize rare tilings (more commonly known as mosaics) constructed from dominoes. The dominoes in these tilings are similar yet slightly different than those used in the popular game of the same name. As opposed to rectangles, they are squares with various color combinations along the edges (which can alternatively also be represented by numbers or patterns) called
- The tilings sonified and visualized in a history of the domino problem are rare because there is no systematic way to find them. This is due to the fact that they are
- The original Domino Problem asked if there exists an algorithm/computer program that, when given as input a finite set of dominoes with varying color combinations for the edges, can output a binary answer, `yes' or `no', whether or not copies of that set can form an infinite tiling. The problem was first posed by Hao Wang in 1961, who conjectured that the answer is positive and that such an algorithm does exist. The reason why the Domino Problem is inextricably linked to whether or not aperiodic tilings exist is the following. The existence of aperiodic tilings would mean that such an algorithm does not exist. However, in 1966, his student, Robert Berger, proved him wrong by discovering an infinite, aperiodic tiling constructed with copies of a set of 20,426 dominoes. With the original problem solved, mathematicians then took on the challenge of finding the smallest set of dominoes that would construct an infinite aperiodic tiling. Over the past 60 years, this number has been continually reduced with the contributions of many different mathematicians until the most recent discovery of a set of 11 dominoes along with a proof that no smaller sets exist. It is a remarkable narrative/history of a particular epistemological problem that challenged a group of people not only to solve it, but to understand it to the extent possible. + The original Domino Problem asked if there exists an algorithm/computer program that, when given as input a finite set of dominoes with varying color combinations for the edges, can output a binary answer, `yes' or `no', whether or not copies of that set can form an infinite tiling. The problem was first posed by Hao Wang in 1961, who conjectured that the answer is positive and that such an algorithm does exist. The existence of aperiodic tilings would mean that such an algorithm does not exist. However, in 1966, his student, Robert Berger, proved him wrong by discovering an infinite, aperiodic tiling constructed with copies of a set of 20,426 dominoes. The resolution of Wang's original question led to new questions and mathematicians took on the challenge of finding the smallest set of dominoes that would construct an infinite aperiodic tiling. Over the past 60 years, this number has been continually reduced with the contributions of many different mathematicians until the most recent discovery of a set of 11 dominoes along with a proof that no smaller sets exist. It is a remarkable narrative/history of a particular epistemological problem that challenged a group of people not only to solve it, but to understand it to the extent possible.