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Has mathematics anything in common with music and visual arts? Is it possible to combine in one book the three strands of music, mathematics, and visual arts, and interweave them elegantly into a single braid? As an answer to these queries, Hofstadter has produced an absorbing book of 777 pages, typesetting it himself using a computer system.

Johann Sebastian Bach (1685-1750 } is the famous German composer who also had great ability to improvise on the keyboard. M.C. Escher is a Dutch graphic artist who lived from 1902 to 1972 and produced some of the most intellectually stimulating drawings of our time. Kurt Gödel is a famous mathematician who has established fundamental results about mathematical reasoning using mathematical logic.

The author perceives a common basic element in the compositions of Bach, the drawings of Escher and the theorems of Gödel. In a work called "Musical Offering" Bach has introduced an unending theme which is labelled by the author as the "Endlessly Rising Canon". This unending theme has a potentially infinite aspect which the author calls the Strange Loop. The same idea is also found in Escher's drawings especially in the one called the Waterfall. Water seems to flow downwards in a waterfall  but goes through a criss-cross channel in a natural way and strangely ends up at the head of the waterfall thus creating an illusion of endless flow of water. This idea of infinity which is a product of the Strange Loop is also found in mathematics.

Many profound ideas in computer science, biology, linguistics and artificial intelligence are made simple by the author who adapts the style of conversation between fictional characters like Achilles and the Tortoise, as preludes to some chapters.

Of special interest to our readers are the reference to the famous mathematician Srinivasa Ramanujan who is also represented in a conversation as Najunamar (spelt backwards), and that to Tamil (script) as an elegant curvilinear language!

In the last chapter the author joins the other characters in a dialogue:

Achilles: Suppose I were to write dialogues. 

Who would the author of them be? You, or me?

Author: You, of course. At least in the fictitious world which you inhabit. Whereas in the world I inhabit, perhaps the credit would be given to me...And then ,whoever made me make you write your dialogue would get credit in His world.

This delightful book contains more than 150 illustrations and an annotated bibliography.