godel escher bach
120748014
Godel, Escher, Bach: An Eternal Golden Braid
From the Publisher: Winner of the Pulitzer Prize, this book applies Godel's seminal contribution to modern mathematics to the study of the human mind and the development of artificial intelligence.
Douglas Richard Hofstadter
59498273
Godel, Escher, Bach: Just Another Braid
This paper describes the synthesis of two completely different minimal art techniques applied in a new type of mathematical art. The portraits of Godel, Escher and Bach are chosen to demonstrate this. The combined techniques are minimal art objects and optical minimal art graphics. Minimal Art Objects Our earlier contributions in creating minimal art objects are described in [1] and [3] An example is shown in Figure 1. Figure 1: Minimal Art Object. Such a minimal art object consists of n x n elements (cubelets) filling a n x n x n space in such a way that it has 3 projections of n x n squares. These 3 projections are perpendicular to each other. The design rules to create such an object obey the rules of the Latin square. A Latin square is a n x n array filled with n different numbers, each occurring exactly once in each row and exactly once in each column. In our object each number is represented by a cubelet, which position in space is determined by its position in the Latin square (in x and y) and the number itself representing the height level (z) The cubelets are connected on the edges into one object. This connectivity of the cubelets asks for further constraints of the Latin square. For this project we use an object with 256 connected cubelets in a 16 x 16 x 16 space, based on the 16 x 16 Latin square of Figure 2. Bridges Finland Conference Proceedings
Hans Kuiper and Walt van Ballegooijen
164863403
Godel, Escher, Bach: An Eternal Golden Braid
Paul Miers Douglas Richard Hofstadter
125327733
Some strategies for teaching a course based on Godel, Escher, Bach
In 1979, Douglas Hofstadter published a Pulitzer prizewinning classic, Godel, Escher, Bach: an eternal golden braid [1] henceforward referred to as GEB. I have presented a course at La Salle University based on GEB eleven times during the last twenty one years. From these experiences, I present below some useful strategies for instructors who are interested in teaching a course where at least half of GEB is covered in some depth.
The Mathematical Gazette
Stephen Andrilli
61272762
Godel, Escher, Bach: An Eternal Golden Braid
Stephen W Smoliar Douglas Richard Hofstadter
86695510
Godel, Escher, Bach
Douglas Richard Hofstadter
171586111
Godel, Escher, Bach: An Eternal Golden Braid.
Jonathan Lieberson Douglas Richard Hofstadter
190432651
Godel, Escher, Bach Les brins d'une guirlande eternelle
Fugue metaphorique sur les esprits et les machines inspiree de Lewis Carroll. Il est bien rare de decouvrir un livre qui nous transporte litteralement dans des mondes nouveaux grace a l'ampleur de son erudition, a la joie creatrice de son style et, surtout, grace a son pouvoir de relier des domaines de connaissances apparemment totalement etrangers les uns aux autres. Godel, Escher, Bach est l'un de ces livres. L'auteur etablit des liens entre les gravures d'Escher, la musique de Bach et la logique mathematique. Il nous rend intelligibles des similitudes cachees entre des domaines aussi varies que la biologie, la psychologie, la physique, l'informatique, la linguistique. et eclaire l'un des mysteres de la philosophie notre apparente inaptitude a comprendre la nature de nos propres processus de pensee. Plus de vingt ans apres sa premiere parution, ce livre culte a garde toute sa magie.
Douglas R Hofstadter Jacqueline Henry Robert M French
193093748
Godel, Escher, Bach: An Eternal Golden Braid@@Godel, Escher, Bach: An Eternal Golden Braid
Stephen W Smoliar Douglas Richard Hofstadter
126005759
Godel, Escher, Bach: An Eternal Golden Braid.
Irvin David Hill Douglas Richard Hofstadter