The concept of self-reference has been a topic of interest for centuries, with its roots in ancient Greece and the famous paradox of Epimenides, who stated that ‘all Cretans are liars.’ This paradox is a classic example of a statement that refers to itself, creating a loop that never fully resolves. The idea has since been explored in mathematics, particularly in the work of Kurt Gödel, who in 1931 published the incompleteness theorems, changing the way mathematicians understood the limits of systems.

Source: cdn2.psychologytoday.com

From Gödel to Hofstadter

In 1979, Douglas Hofstadter gave this broader pattern a memorable vocabulary in his book ‘Gödel, Escher, Bach.’ He explored what he called ‘strange loops,’ systems that move through different levels and somehow return to themselves. These loops can be found in various fields, including math, art, music, and the way we think.

The concept of strange loops is closely related to the idea of self-reference, where a system or statement refers to itself, creating a loop that never fully resolves. This idea has been explored in various fields, including mathematics, philosophy, and cognitive science.

AI and the Cognitive Loop

Today, we have another participant in the loop: artificial intelligence (AI). We use AI to think, ask questions, and increasingly use its responses back. But when we work iteratively with a large language model, something more complex begins to happen. The response changes how we understand the problem, which changes what we ask next. A few rounds later, we may find ourselves somewhere new and unexpected with no obvious relationship to our initial intent.

This is where the concept of recursive participation comes in. The human mind can now examine its own thinking through a computational system that is also participating in that thinking. The process continues, but it never quite returns to where it started.

The story takes another curious turn when we begin using AI to understand what AI is doing to us. Researchers can use AI to study AI, and students can ask AI how it might be changing learning. More broadly, any of us can turn to AI to explore if and how technology is changing the way we think. At that point, the instrument has entered the loop—Hofstadter’s ‘eternal golden braid.’

This creates an unusual problem of cognitive self-examination. The technology we are trying to understand can now participate in the process through which we understand it. There is almost something Bach-like and contrapuntal about the exchange where one voice changes what the other encounters next and the idea that returns is never quite the idea that entered.

Because each exchange alters what comes next, there may be no completely neutral or unbiased position from which to observe the loop once we are acting within it. Perhaps ‘recursive participation’ is a useful name to capture this condition.

So, for now, we humans remain the agent and ultimately decide what to accept or reject. But agency doesn’t remove the deeper problem. There’s even an echo here of the observer problem in physics. This is when the act of measurement cannot be completely separated from the system being measured. With AI, the parallel is only metaphorical, but the twisting braid (Hofstadter’s line) is interesting.

The act of examining AI’s influence on our thinking may itself become another instance of that influence. To examine the loop, we may have to enter it.