Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter

Douglas R. Hofstadter’s 1979 Pulitzer Prize-winning book, Gödel, Escher, Bach: An Eternal Golden Braid, is an exploration into the interconnectedness of mathematics, art, and music that is both entertaining and thought-provoking. It provides a philosophical examination of self-reference and recursion to illustrate notions behind mind, language, and consciousness.

The book begins with a comparison of a self-replicating loop found in Douglas Hofstadter’s version of the ‘Achilles and the Tortoise’ dialogue from Ancient Greek philosopher Zeno of Elea’s dialogue with the infamous Kurt Gödel Incompleteness Theorem. This comparison highlights the self-referential paradox known as ‘strange loops’ and serves to introduce the mutual interplay between the works of Gödel and those of artist M.C. Escher.

Hofstadter moves onto introducing the work of Bach and its relation to algorithmic structure. He specifically applies Bach’s ‘Canon by Intervallic Augmentation’ to illustrate the idea of higher-order ‘embedding’ of patterns within patterns. He uses this analogy to expand his thoughts on artificial intelligence and create a framework for what he calls the ‘Strange Loop’ that would later be used in a variety of contexts related to consciousness and intelligence.

Following this discussion on the mutual applicability of mathematics and music, Hofstadter takes on the challenge of finding intelligence within mechanical artificial structures. This exploration commonly referred to as ‘Hofstadter’s Law’, introduces the notion of ‘cognitive closure’ or ‘the Paradox of Intelligence’ which references the idea of intelligence being potentially self-enclosed within a system. A main example of this concept applied to its context can be seen in Hofstadter’s famous ‘Gold-Bug’ AI experiment that was a literal translation of Edgar Allen Poe’s 1835 short story.

After exploring intelligence through mathematical logic, artificial structures, and language, Hofstadter delves into a discussion of self-reference and the elusive concept of ‘Essence’. In his essay, ‘The Self-Relating Novel’, he addresses the notion of the duality behind the recursion between an entity and its deepest self. He explains that nothing is fundamentally separate from its essence and looks to Gödel’s Incompleteness Theorem as a way to reduce everything to its ‘fundamental infinitely recursive loop’.

Hofstadter concludes his book by summarizing his views on artificial intelligence as something that cannot be defined by a single system or the imitation of the actions of something thought of as intelligent. He introduces the notion of an “artificially intelligent being” or “mentor” and reflects on the idea that “thinking about something that does not think, no matter how deeply and in how many different ways, will never succeed in providing a satisfactory answer”.

Gödel, Escher, Bach: An Eternal Golden Braid offers a unique exploration of the intersection between mathematics, art, and music - a masterpiece overflown with thought provoking philosophical reflections. The book is not only certainly worth a read, but is even better followed up with frequent revisits each of its pages. Douglas R. Hofstadter’s contribution to the development of the understanding of the essence of artificial intelligence is one of the most notable works of the 20th century.