Douglas Hofstadter’s perpetual search for beauty

Hofstadter’s butterfly, showing the energy levels, E, of Bloch electrons in a magnetic field.In the limit of weak modulation, shown here, the inverse magnetic flux ratio Φ0/Φ determines the internal structure of a Landau band. For example, at Φo/Φ = 1/3, a Landau band splits into three sub-bands.” 

Rarely do you find people so influential across disparate fields who would rather explore those interests with alacrity, celerity, vim, vigor, and vitality than the typical duties of a professor.

Douglas Hofstadter, Professor of Cognitive Science and Comparative Literature at IU, has his own way of characterizing his personal style and his personal goals runs as follows: “perpetually in search of beauty.”  After completing his undergraduate degree in Mathematics at Stanford, Hofstadter’s serendipitous life drove him towards Physics research and, later on, work on consciousness, cognition, and perception. His entire work spans the fields of music, the mind, creativity, self-reference, and mathematics. Many know him for his Pulitzer-winning book “Gödel, Escher, and Bach” that explores cognition through mathematics and physics.

Hofstadter’s Butterfly is an example of mathematical beauty in theoretical numbers, but later empirically discovered in imaging of graphene electrons.

The other day, Dr. Hofstadter returned to IU to share an autobiographical story of his work. It was incredibly mind-blowing to hear how he had cultivated his passions for thinking, numbers, and everything in-between. The most striking of his love for elegance shone through his explanation of patterns among numbers.

Hofstadter’s talk began of the physics in the exciting 1950s, in the challenging arena of Bloch electrons, the charges found in crystallized structures, the field was shrouded in mystery and awe. While the most powerful computer at Stanford at University was only as powerful as today’s watches, Hofstadter learned how to program the earliest calculators and graphing tools to explore the field. But, before he serendipitously tumbled into the invisible force-lines of a magnetic field, Hofstadter’s butterfly path lead him through the wonderfully creative number theory. After struggles of failing a physics course as an undergraduate and dropping out of his theoretical mathematics PhD in the 1970’s, Hofstadter meandered into Particle Physics before falling into Solid State Physics. The Brownian drunk walk mirrored his love of the subtle interplay of continuous and discrete mathematics: the theory and wonder that create magically to a one-dimensional Fibonacci-like difference equation playing the role of Schrödinger’s differential wave equation. Through a great stroke of luck, wound up being almost magically parlayed into the empirical discovery of a mysterious, surprising, and visually riveting new type of quantum-mechanical energy spectrum.

A recursion error during Hofstadter’s presentation. (But maybe it wasn’t so much of an “error.”)

His story plays unfolds recursively, or self-referentially, as his spontaneous ideas from his college notebooks would later guide his work as a professor. His work would fold in on itself, more and more, until he would find ideas of what human consciousness is. The mind is clearly not a recursive algorithm, nor it is a fractal picture, but the way he explored the beauty of logic and language would lead him to cognitive science. Now, Hofstadter critiques artificial intelligence, technology, and nerd culture.

My friends who have met and taken classes with Dr. Hofstadter have only expressed mind-blowingly positive experiences, whether the courses are in the sciences or the humanities.

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