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For the Lecture - Concert on 22 Nov 2023 , priority will be given to those who RSVP . Sign up < NuxtLink class = "text-2xl font-bold" to = 'https://www.surveymonkey.de/r/FDL8XW3' > HERE < / NuxtLink > .
For the Lecture - Concert on 22 Nov 2023 , Registration recommended . Sign up < NuxtLink class = "text-2xl font-bold" to = 'https://www.surveymonkey.de/r/FDL8XW3' > HERE < / NuxtLink > .
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< span class = "italic" > a history of the domino problem < / span > 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 mosaics constructed from dominoes . The dominoes in these mosaics 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 < NuxtLink to = 'https://en.wikipedia.org/wiki/Wang_tile' > wang tiles < / NuxtLink > . Like in the game , the rule is that edges of adjacent dominoes in a mosaic must match .
< span class = "italic" > a history of the domino problem < / span > 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 < NuxtLink to = 'https://en.wikipedia.org/wiki/Wang_tile' > wang tiles < / NuxtLink > . Like in the game , the rule is that edges of adjacent dominoes in a tiling must match .
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The tilings sonified and visualized in < span class = "italic" > a history of the domino problem < / span > are rare because there is no systematic way to find them . This is due to the fact that they are < NuxtLink to = 'https://en.wikipedia.org/wiki/Aperiodic_tiling' > < span class = "italic" > aperiodic < / span > < / NuxtLink > . One can think of an aperiodic tiling like an infinite puzzle with a peculiar characteristic . Given unlimited copies of dominoes with a finite set of color / pattern combinations for the edges , there is a solution that will result in a tiling that expands infinitely . However , in that solution , any periodic / repeating structure in the tiling will eventually be interrupted . This phenomenon is one of the most intriguing aspects of the work . As the music and the visuals are derived from the tilings , the resulting textures are always shifting ever so slightly .
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The mosaics sonified and visualized in < span class = "italic" > a history of the domino problem < / span > are rare because there is no systematic way to find them . This is due to the fact that they are < NuxtLink to = 'https://en.wikipedia.org/wiki/Aperiodic_tiling' > < span class = "italic" > aperiodic < / span > < / NuxtLink > . One can think of an aperiodic mosaic like an infinite puzzle with a peculiar characteristic . Given unlimited copies of dominoes with a finite set of color / pattern combinations for the edges , there is a solution that will result in a mosaic that expands infinitely . However , in that solution , any periodic / repeating structure in the mosaic will eventually be interrupted . This phenomenon is one of the most intriguing aspects of the work . As the music and the visuals are derived from the mosaics , the resulting textures are always shifting ever so slightly .
The Domino Problem and its corresponding history are somewhat vexing and difficult to describe . The original 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 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 < span class = "italic" > does not < / span > exist . The problem was first posed by Hao Wang in 1961. He actually conjectured that aperiodic tilings do 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 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 .
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Nov . - Exact dates and exhibition opening hours TBA soon !
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Lichthof ( Ost ) Ausstellungsraum der Humboldt - Universität
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Hauptgebäude , Erdgeschoss , Unter den Linden 6 , 10117 Berlin
Lichthof Ost , HU Berlin , Campus Mitte , Unter den Linden 6 , U Bahn Unter den Linden oder Museuminsel
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22 Nov 2023 | 19 Uhr
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Senatssal der Humboldt - Universität
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Hauptgebäude , 1. Obergeschoss , Unter den Linden 6 , 10117 Berlin
Senatssal , HU Berlin , Campus Mitte , Unter den Linden 6 , U Bahn Unter den Linden oder Museuminsel
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Concert
