Gödel, Escher, Bach: An Eternal Golden Braid

Douglas Hofstadter (1945) is an American cognitive and computer scientist and the author of Gödel, Escher, Bach: An Eternal Golden Braid. Despite Hofstadter’s use of computers to apply scientific methodology and contributions to the field of artificial intelligence (AI), he claims little interest in technology and is skeptical of AI and the idea of an imminent singularity. In an interview for The Atlantic in November 2013, Hofstadter explained that he is only interested in a narrow definition of AI, one which seeks to understand how human consciousness and cognition function (Somers, James. “The Man Who Would Teach Machines to Think.” The Atlantic, Nov. 2013) When Deep Blue, an IBM supercomputer designed to beat any human chess player, emerged in 1985, Hofstadter questioned the point of AI that does not seek to answer questions about human consciousness and existence. Deep Blue was able to perform a task but not extract meaning from it.

Gödel, Escher, Bach: An Eternal Golden Braid highlights Hofstadter’s deviation from mainstream approaches to AI. In his 2023 article in The Atlantic, Hofstadter asserts that language models like ChatGPT and Google’s Bard pale in comparison to the human mind (Hofstadter, Douglas. “Gödel, Escher, Bach, and AI.” The Atlantic, 8 July 2023). He claims that the distinction between AI and human intelligence is that the former deals in symbols while the latter is concerned with making meaning. Rather than focusing on using AI to solve problems or recreate basic cognitive processing, Hofstadter calls for an approach to studying the nature of consciousness itself, which he argues lies outside the confines of formal systems.

Hofstadter’s interest in the beauty and intricacies of thinking began during childhood, when he was surrounded by creative thinkers. He grew up in New York City, in a house on the Stanford University campus where his father, Robert Hofstadter, worked. Robert Hofstadter won the Nobel Prize for physics in 1961. Hofstadter enjoyed visiting his father’s office and listening to the ideas of his father’s colleagues. Hofstadter graduated with distinction in mathematics from Stanford University. He inherited a strong sense of empathy from his mother, Nancy, who was a political advocate and ethics committee member for the Agnews Developmental Center. In 1975, Hofstadter graduated from the University of Oregon with a Ph.D. in physics. Hofstadter’s butterfly, a spectral graph revealing the self-similar pattern formed by non-interacting two-dimension electrons, was named after an article he wrote, describing and plotting the mathematical structure.

In the summer of 1972, Hofstadter felt frustrated by his doctoral work and decided to pack up and drive across the country. He drove by day and spent his nights in a tent, reading by flashlight. He soon began ruminating on thinking itself. Hofstadter considered the physical properties of cognition and whether it could be expressed through mathematical proofs. Using the work of Kurt Gödel, Hofstadter developed an understanding of consciousness as a self-referential loop.

From his early academic career, Hofstadter was interested in looking at patterns—a passion he carried into all areas of his life. He worked with computer scientist Melanie Mitchell to develop a computer program called “Copycat” that uses analogies to model human cognition. Hofstadter saw that connections could unlock new understandings of the world. His work as a researcher and scientist influences his artwork, poetry, and ethical stance. Hofstadter maintains a vegetarian lifestyle and condemns sexist language. His interest in patterns is reflected in the interdisciplinary approach he applies in his most well-known work. By exploring his ideas across disciplines, Hofstadter emphasizes the pervasive nature of meaning.

Gödel, Escher, Bach, published in 1979 when Hofstadter was 34, compares the relationship between neurons that comprise human consciousness to a colony of ants. Hofstadter asserts that consciousness is derived from strange loops, a pattern that emerges in the work of three thinkers from different disciplines: Kurt Gödel, M.C. Escher, and Johann Sebastian Bach. Hofstadter has been a Distinguished Professor of Cognitive Science and Comparative Literature at Indiana University since 1988. Gödel, Escher, Bach: An Eternal Golden Braid received a Pulitzer Prize and American Book Award in 1980. Following concern that the larger themes of the book were overshadowed, Hofstadter published a follow-up titled I Am a Strange Loop in 2007.

Kurt Gödel (1906-1978) was a 20th-century mathematician, logician, and philosopher. As a young boy in Austria-Hungary, Gödel was nicknamed by his family “Mr. Why” for his inquisitive nature. He received honors in school for his studies in mathematics and languages. When he turned 18, Gödel followed his older brother to the University of Vienna where he studied math, philosophy, and physics. His interest in these fields led him to mathematical logic. He earned his doctorate in mathematics in 1929. In 1930, Gödel presented his findings in his completeness theorems at the Second Conference on the Epistemology of the Exact Sciences. Gödel’s incompleteness theorems catapulted his status as a logician, placing his contribution alongside the offerings of Aristotle.

Gödel’s incompleteness theorems undergird Hofstadter’s work. In these theorems, Gödel uses mathematical logic to deconstruct formal mathematical systems. Each formal system is comprised of basic assumptions, called axioms, which construct specific perimeters. In his first theorem, Gödel shows that, while formal systems support true statements, there are true statements that cannot be proven by the limitations of a formal system. His second theorem shows that the rules of a formal system cannot be used to prove the completeness and consistency of the system itself. Gödel’s theorems are considered among the greatest contributions to mathematical logic of the 20th century.

After he published his incompleteness theorem, Gödel traveled the country, lecturing and developing a friendship with Albert Einstein. Gödel fled Europe at the beginning of World War II to work in the US at the Institute for Advanced Studies, where he worked for the remainder of his life. In 1951, Gödel was awarded the first Albert Einstein Award, and he received the National Medal of Science in 1974. He was inducted into the American Philosophical Society, a prestigious organization recognizing the country’s greatest philosophical thinkers, in 1961.

Maurits Cornelis Escher (1898-1972) was a Dutch artist who used mathematics to inspire and inform his work. During his life, Escher was ignored by his art contemporaries. Escher studied architecture and decorative arts at the Technical College of Delft and the Haarlem School of Architecture and Decorative Arts. While traveling in Italy after leaving school, Escher was struck by the geometrical symmetry of many of the decorative designs he encountered. From then on, Escher focused on blending art and math. Escher created lithographs, woodcuts, paintings, and drawings that employed mathematical optical illusions.

Escher employed multiple mathematical principles and techniques in his art, including impossible objects, symmetry, and perspective. Hofstadter admires Escher’s use of mathematics and calls upon many of Escher’s works to lend visual contextualization of Hofstadter’s ideas. For example, Escher’s use of tessellation, an artistic tiling using one or more repeated geometric shapes, illustrates the self-referential and recursive natures of positive and negative space.

The artist was fascinated by tessellation and referred to his interest as a kind of obsession: “It remains an extremely absorbing activity, a real mania to which I have become addicted” (O'Connor, J. J.; Robertson, E. F. "Maurits Cornelius Escher." Biographies. University of St Andrews, 2000.) A series of drawings called Regular Division of the Plane, which Escher began constructing in 1936, explores a variety of tessellations, including the repeated image of a soldier riding a horse. Other works by Escher, such as Self-Portrait in Spherical Mirror, illustrate ideas like strange loops.