Document (#35921)

Author

Jötten, F.

Title

Auf der Suche nach der göttlichen Zahl : Wie ein Spielzeug einen Darmstädter Mathematiker ein Erwachsenenleben lang nicht mehr losließ

Source

Frankfurter Rundschau. Nr.191 vom 19.8.2010, S.12

Year

2010

Series

Wissen & Bildung

Abstract

Noch 30 Jahre nach seiner Markteinführung beschäftigen sich Forscher täglich mit Rubiks Würfel.

Content

"Ein kleiner Junge reicht einem Roboter einen verdrehten Zauberwürfel. Der hebt den Würfel vor sein Blechgesicht, wendet ihn hin und her - und beginnt dann blitzschnell mit seinen Metallarmen zu drehen, bis nur noch eine Farbe pro Seite zu sehen ist. Das Internet ist voller solcher Videos von Menschen und Maschinen, die einen Zauberwürfel wieder in die Ausgangsposition bringen. Ein dreijähriges Kind löst die Aufgabe unter zwei Minuten, ein 18-jähriger Niederländer schafft es in sieben Sekunden, ein Roboter aus Lego in zehn, ein Franzose mit verbundenen Augen in 23.
Forschen nach der Formel Die Wissenschaft tüftelte seit 30 Jahren an seinem Rätsel - jetzt ist es gelöst. Die so genannte Gotteszahl ist gefunden. So nennen die Wissenschaftler die kleinstmögliche Anzahl von Zügen, die es braucht, um einen Würfel aus jeder denkbaren Position in den Ausgangszustand zu drehen. Das Zentrum der europäischen Zauberwürfelforschung ist ein Arbeitszimmer in Darmstadt. Herbert Kociemba, 56, Lehrer für Physik und Mathematik und einer derjenigen, die an dem jüngsten Forschungserfolg beteiligt waren, sitzt an seinem Schreibtisch. Neben ihm steht seine Zauberwürfel-Sammlung, daneben eine Plastiktüte mit winzigen, bunten Kacheln - damit ersetzt er die Aufkleber auf seinen Würfeln: Das sieht besser aus und ist haltbarer. Wenn es um Rubik's Cube geht, merkt man, dass der für ihn mehr ist, als nüchterne Mathematik. "Der Würfel knarrt so schön, wenn man ihn dreht", sagt er und lächelt verzückt. "Er wird nie vergessen, weil er einfach genial ist." Bei der Markteinführung hatte Kociemba gerade begonnen als Lehrer zu arbeiten. "In den Noten-Konferenzen strickten die Frauen - und männliche Kollegen drehten am Zauberwürfel", erinnert er sich. Heute sitzt Kociemba vor seinem Computer, auf dem Bildschirm bunte Quadrate und graue Schaltflächen: das ist "Cube Explorer", ein Computerprogramm, das Kociemba 1992 erfand. Mit der neuen Version kann der Benutzer per Webcam jede Würfel-Position einlesen und sich berechnen lassen, mit welchen Drehungen man ihn in die Ausgangsposition (alle Seiten des Würfels einfarbig) zurückbringen kann.
"Im Durchschnitt schafft das Programm das mit 19 Zügen", sagt Kociemba. Für Würfelfans ist das Programm essenziell, sie dankt dem Mathematiker frenetisch in Internetforen - die meisten Speedcuber, diejenigen, die den Würfel in möglichst kurzer Zeit lösen wollen, berechnen sich mit Cube Explorer die optimalen Drehkombinationen. "Aber eigentlich hat mich das zuletzt nicht mehr interessiert", sagt Kociemba. Gemeinsam mit dem kalifornischen Informatiker Tom Rokicki und dem Mathematiker Morley Davidson von der Kent State University in Ohio wollte er "Gottes Zahl" finden - den optimalen Weg mit möglichst wenigen Schritten um den Zauberwürfel zu lösen. Der Cube kann 43 Trillionen Positionen einnehmen. Für jede Stellung gibt es 18 Möglichkeiten für den ersten Zug - und dann wieder 18 für jeden folgenden. Wollte man die Gotteszahl so berechnen, dass man für jede Würfelstellung die optimalen Züge berechnet, müssten fünf Millionen Computer fünf Millionen Jahre lang rechnen - unmöglich. 1992 kam für Kociemba der erste Durchbruch bei der Suche nach der Gotteszahl. Er schrieb einen Zwei-Phasen-Algorithmus. Der Trick: Der Würfel wird aus einer beliebigen Anfangsstellung in maximal zwölf Zügen in eine Zwischenformation gebracht, das schränkt die Anzahl der verbleibenden Möglichkeiten auf 20 Milliarden ein, was Computer heute gut bewältigen. In einer zweiten Phase wird er dann in die Zielposition (alle Seiten des Würfels einfarbig) gebracht. Dazu braucht es höchstens 18 Drehungen, in der Summe sind also nach diesem Modell höchstens 30 notwendig. In den vergangenen 18 Jahren reduzierten die Forscher die Zahl. 2008 zeigte Rokicki, dass sie nicht größer als 25 sein kann. Er nutzte Kociembas Weg, unterteilte die Würfelpositionen aber in Gruppen, so dass er nicht jede einzeln berechnen musste. Dann fehlte ihm nur noch Rechnerleistung. Zunächst stellte Sony Pictures nachts die Computer zur Verfügung, auf denen sonst Trickfilme entstehen. Dann half Google mit seiner riesigen Rechner-Kapazität. Jetzt steht fest: Der Zauberwürfel kann, egal wie er verdreht ist, in 20 Zügen in die Zielposition gebracht werden. "Ein moderner Desktop-PC hätte für die Rechenarbeit 35 Jahre gebraucht", sagt Rokicki."

Footnote

Vgl.: http://www.fr-online.de/wissenschaft/suche-nach-der-goettlichen-zahl/-/1472788/4569368/-/index.html.

Field

Mathematik

Object

Rubik Cube

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5. Blittkowsky, R.: ¬Das World Wide Web gleicht einer Fliege : Studien versuchen zu erklären, warum Suchmaschinen nicht immer fündig werden (2001) 0.28

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