The Atlantic Monthly just did an interesting piece on Douglas Hofstadter, Pulitzer Prize-winning author of Gödel, Bach and Escher. Hofstadter’s 1979 book investigates the nature of human thought processes by looking at common themes in the work of the mathematician Gödel, the musician Bach and the artist Escher. In particular, it addresses the question of how meaning is born from apparently ‘meaningless’ elements – like the fundamental biological materials of the body and the brain, or the fundamental symbols of mathematics.
While once seen as groundbreaking work in artificial intelligence, the book is not about how to mechanically replicate human thought, but more about what thought ‘is,’ and the emergence of ‘meaning.’ MIT has offered a course on the text for high school students. Lecture videos and lecture notes for these courses can be found here. Early in one of the lectures, the point is made that the premise of Gödel, Bach and Escher is to show how the “I” of our experience, or the event of self-referencing in our experience, corresponds to the the self referencing that happens within mathematics.
James Somers, author of the Atlantic Monthly piece, focuses on an important shift in how Hofstadter’s work is understood.
Hofstadter seemed poised to become an indelible part of the culture. GEB was not just an influential book, it was a book fully of the future. People called it the bible of artificial intelligence, that nascent field at the intersection of computing, cognitive science, neuroscience, and psychology. Hofstadter’s account of computer programs that weren’t just capable but creative, his road map for uncovering the “secret software structures in our minds,” launched an entire generation of eager young students into AI.
But then AI changed, and Hofstadter didn’t change with it, and for that he all but disappeared.
The contrast between the progression of AI efforts and the aim of Hofstadter’s work is particularly relevant to my interests. Hofstadter’s persistence can be seen in the research of what was once called the Fluid Analogies Research Group or FARG at Indiana University. The group has been renamed The Center for Research on Concepts and Cognition. At the end of their research overview, they make the following statement:
We are staunch believers in the idea of using microworlds to study cognition, and the ideas behind our models are informed by many sources, ranging from biological metaphors (the brain is like an ant colony, thinking is like the parallel activity of enzymes in a single cell), to brain research, to the study of error-making, to the careful study of words and their halos, to the observation of our own smallish acts of creativity in various areas of life, to the study of how analogies have pervaded the greatest creative leaps made by physicists and mathematicians.
Lastly, a tiny comment on the philosophy behind FARG computer models. All of them are based on the idea that thinking is an extremely parallel, emergent phenomenon, as opposed to some kind of set of precise computational rules for manipulating abstract meaning-bearing symbols. In other words, we don’t see thinking as any kind of “logic” or “reasoning”, but as a kind of churning, swarming activity in which thousands (if not millions) of microscopic and myopic entities carry out tiny “subcognitive” acts all at the same time, not knowing of each other’s existence, and often contradicting each other and working at cross-purposes. Out of such a random hubbub comes a kind of collective behavior in which connections are made at many levels of sophistication, and larger and larger perceptual structures are gradually built up under the guidance of “pressures” that have been evoked by the situation. None of this activity is seen as being deterministic; rather, our models are all pervaded by randomness or “stochasticity”, to use a fancier term for the same idea. (emphasis added)
This philosophy is usually traced back to a computer program that Hofstadter built called Jumbo. The program was inspired by his interest in understanding what was happening when one solved a newspaper jumble. He had no interest in the program that would quickly solve them. He wanted to understand what was happening when we solved them. As Somers points out:
He had been watching his mind. “I could feel the letters shifting around in my head, by themselves,” he told me, “just kind of jumping around forming little groups, coming apart, forming new groups—flickering clusters. It wasn’t me manipulating anything. It was just them doing things. They would be trying things themselves.”
The architecture Hofstadter developed to model this automatic letter-play was based on the actions inside a biological cell. Letters are combined and broken apart by different types of “enzymes,” as he says, that jiggle around, glomming on to structures where they find them, kicking reactions into gear. Some enzymes are rearrangers (pang-loss becomes pan-gloss or lang-poss), others are builders (g and h become the cluster gh; jum and ble become jumble), and still others are breakers (ight is broken into it and gh). Each reaction in turn produces others, the population of enzymes at any given moment balancing itself to reflect the state of the jumble.
The key for me is the efficacy of what is here referred to as “subcognitive” acts, acts that have some randomness about them, and may even work at cross-purposes. Hofstadter’s philosophy is also evident in his vast collection of speech errors, or his record of instances of swapped syllables, like “hypodeemic nerdle.” Again Somers points out:
Correct speech isn’t very interesting; it’s like a well executed magic trick – effective because it obscures how it works.
The views on ‘thinking’ explored at the research center are provocative and carry large numbers of implications that will likely impact the age-old mind/body debate. They imagine ‘meaningfulness’ within the life of the whole of nature, of which mathematics is very much a part. I plan to spend a lot more time looking at work being done at the Center for Research on Concepts and Cognition and hopefully more time writing about it.