The introduction of the book, .Introduction: A Musico-Logical Offering. begins by quickly
discussing the three main participants in the book, Gvdel, Escher, and Bach. Gvdel was a
mathematician who founded Gvdel.s Incompleteness Theorem, which states, as Hofstadter
paraphrases, .All consistent axiomatic formulations of number theory include undecidable
propositions.. This is what Hofstadter calls the pearl. This is one example of one of the
recurring themes in GEB, strange loops.
Strange loops occur when you move up or down in a hierarchical manner and eventually end up
exactly where you started. The first example of a strange loop comes from Bach.s Endlessly
rising canon. This is a musical piece that continues to rise in key, modulating through the
entire chromatic scale, ending at the same key with which he began. To emphasize the loop Bach
wrote in the margin, .As the modulation rises, so may the King.s Glory..
The third loop in the introduction comes from an artist, Escher. Escher is famous for his
paintings of paradoxes. A good example is his Waterfall; Hofstadter gives many examples of
Escher.s work, which truly exemplify the strange loop phenomenon.
One feature of GEB, which I was particularly fond of, is the .little stories. in between each
chapter of the book. These stories which star Achilles and the Tortoise of Lewis Carroll fame,
are illustrations of the points which Hofstadter brings out in the chapters. They also serve as a
guidepost to the careful reader who finds clues buried inside of these sections. Hofstadter
introduces these stories by reproducing .What the Tortoise Said to Achilles. by Lewis Carroll.
This illustrates Zeno.s paradox, another example of a strange loop.
In GEB Hofstadter comments on the trouble author.s have with people skipping to the end of the
book and reading the ending. He suggests that a solution to this would be to print a series of
blank pages at the end, but then the reader would turn through the blank pages and find the last
one with text on it. So he says to print gibberish throughout those blank pages, again a human
would be smart enough to find the end of the gibberish and read there. He finally suggests that
authors need to write many pages more of text than the book requires just fooling the reader into
having to read the entire book. Perhaps Hofstadter employs this technique.
GEB is in itself a strange loop. It talks about the interconnectedness of things always getting
more and more in depth about the topic at hand. However you are frequently brought back to the
same point, similarly to Escher.s paintings, Bach.s rising canon, and Gvdel.s Incompleteness
theorem. A book, which is filled with puzzles and riddles for the reader to find and answer, GEB,
is a magnificently captivating book.
Written for Math 400
09/26/2000