TheoriginalDominoProblemaskedifthereexistsanalgorithm/computerprogramthat,whengivenasinputafinitesetofdominoeswithvaryingcolorcombinationsfortheedges,canoutputabinaryanswer,`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 <span class="italic">does not</span> exist. However, in 1964, 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'soriginalquestionledtonewquestionsandmathematicianstookonthechallengeoffindingthesmallestsetofdominoesthatwouldconstructaninfiniteaperiodictiling.Overthepast60years,thisnumberhasbeencontinuallyreducedwiththecontributionsofmanydifferentmathematiciansuntilthemostrecentdiscoveryofasetof11dominoesalongwithaproofthatnosmallersetsexist.Itisaremarkablenarrative/historyofaparticularepistemologicalproblemthatchallengedagroupofpeoplenotonlytosolveit,buttounderstandittotheextentpossible.
TheoriginalDominoProblemaskedifthereexistsanalgorithm/computerprogramthat,whengivenasinputafinitesetofdominoeswithvaryingcolorcombinationsfortheedges,canoutputabinaryanswer,`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 <span class="italic">does not</span> exist. However, in 1964, 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'soriginalquestionledtonewquestionsandmathematicianstookonthechallengeoffindingthesmallestsetofdominoesthatwouldconstructaninfiniteaperiodictiling.Overthepast60years,thisnumberhasbeencontinuallyreducedwiththecontributionsofmanydifferentmathematiciansuntilthemostrecentdiscoveryofasetof11dominoesalongwithaproofthatnosmallersetsexist.Itisaremarkablenarrative/historyofaparticularepistemologicalproblemthatchallengedagroupofpeoplenotonlytosolveit,buttounderstandittotheextentpossible.
TheexhibitionwillfeatureindividualandcollaborativeworksbyMichaelWinterandMareikeYin-YeeLeeinaconstellationdesignedspecificallyfortheLichthofOstexhibitionroomoftheHumboldtUniversity.TheoriginalkineticsculptureWintercreatedtovisualizetheaperiodictilingsofthehistoryofthedominoproblemwillbejuxtaposedwithrecentworksbyYin-YeeLeeaswellascollaborativelycreatedrealizationsofthetilings.TheworksondisplaybyYin-YeeLeewillhighlightselectionsfromherHiddenLakesandMissingPiecesseriesinwhichenigmaticoutlinesoflakesandvariousshapesencourageobserverstoperceivesimilaritiesanddifferencesinform,pattern,andrepetitionbetweenthepiecesandtomentallyfillinblankspace.ThecollaborativerealizationsofthetilingswillincludeprintsgeneratedbyWinterwiththeaidofacomputerthatincorporateimagesandcolorschemesbyYin-YeeLeeaswellasafloormosaicofdrawingsonmirrors.Theexhibitionplaysonthemacroversusthemicro,transformation,andhowtopologiesofvariouscolorcombinations,relationshipsbetweenshapesandgradientsreflectinspaceinordertoilluminate"a few thoughts on how things fit together..."
TheexhibitionwillfeatureindividualandcollaborativeworksbyMichaelWinterandMareikeYin-YeeLeeinaconstellationdesignedspecificallyfortheLichthofOstexhibitionroomoftheHumboldtUniversity.TheoriginalkineticsculptureWintercreatedtovisualizetheaperiodictilingsofthehistoryofthedominoproblemwillbejuxtaposedwithrecentworksbyYin-YeeLeeaswellascollaborativelycreatedrealizationsofthetilings.TheworksondisplaybyYin-YeeLeewillhighlightselectionsfromherHiddenLakesandMissingPiecesseriesinwhichenigmaticoutlinesoflakesandvariousshapesencourageobserverstoperceivesimilaritiesanddifferencesinform,pattern,andrepetitionbetweenthepiecesandtomentallyfillinblankspace.ThecollaborativerealizationsofthetilingswillincludeprintsgeneratedbyWinterwiththeaidofacomputerthatincorporateimagesandcolorschemesbyYin-YeeLeeaswellasafloormosaicofdrawingsonmirrors.Theexhibitionplaysonthemacroversusthemicro,transformation,andhowtopologiesofvariouscolorcombinations,relationshipsbetweenshapesandgradientsreflectinspaceinordertoilluminate"a few thoughts on how things fit together..."