AI and the Cognitive Loop

Psychology Today published an article on August 20, 2026, exploring how self-referential loops, from Gödel's incompleteness theorems to Hofstadter's strange loops, now include artificial intelligence, arguing that iterative interaction with large language models creates a cognitive loop that changes how we think. The article, reviewed by Michelle Quirk, suggests that understanding AI requires stepping into this loop.

Artificial Intelligence /us/basics/artificial-intelligence AI and the Cognitive Loop From Gödel and Hofstadter to the strange loop we now share with artificial intelligence. Posted August 20, 2026 Reviewed by Michelle Quirk /us/docs/editorial-process Key points - Things that refer to themselves can create loops that never fully resolve. - These loops show up in math, art, music, and the way we think. - AI now joins our thinking, so understanding it means stepping into the loop. “This sentence is false.” Take a moment and think about that. It's a simple sentence that creates a very difficult problem. If the sentence is true, then what it says must be correct, which means it is false. But if it is false, then what it says is incorrect, which makes it true again. Around and around we go. The idea is ancient and commonly associated with Epimenides and his famous statement that “all Cretans are liars.” The modern formulation is cleaner, but the underlying problem is the same. A statement has somehow turned back upon itself. It is making a claim while simultaneously becoming the object of that claim. For centuries, this could remain an intriguing puzzle of language and logic. Then self-reference found its way into mathematics, and things got much more interesting. When Mathematics Looked at Itself In 1931, Kurt Gödel published what is known as the incompleteness theorems, changing how mathematicians understood the limits of systems. Now, this is usually where discussions like this move quickly past some very difficult math and get to the philosophical implications. But Gödel deserves a brief pause—so I beg the indulgence. The incompleteness theorem is often used much more casually than it should be, so here is my simplified version. Gödel showed that any mathematical system will contain statements that cannot be proved within that system. Through his use of encoding , mathematics could make statements about itself. One famous construction amounts roughly to, “This statement cannot be proved within this system.” The actual mathematics is actually beyond me, but the point I want to make is that self-reference had revealed a limit from inside the system itself. That's a long way from “This sentence is false,” but something fascinating to me connects them. What began as a puzzle about language had become something much more consequential. Now the story spins forward. Nearly 50 years later, Douglas Hofstadter gave this broader pattern a memorable vocabulary in Gödel, Escher, Bach https://www.supersummary.com/godel-escher-bach/summary/ . Moving among Gödel’s mathematics, M. C. Escher’s impossible images, and Johann Sebastian Bach’s recursive music, he explored what he called “ strange loops https://loc.closertotruth.com/theory/hofstadter-s-strange-loops ,” systems that move through different levels and somehow return to themselves. That book was published in 1979, a technological lifetime ago. And long before a conversation with a large language model could become part of an ordinary afternoon. Today, it's my contention that the loop has another participant. When AI Entered the Loop I think it's fair to say that we describe artificial intelligence https://www.psychologytoday.com/us/basics/artificial-intelligence AI as something we use to think. We ask it questions and increasingly use its responses back. But spend enough time working iteratively https://www.psychologytoday.com/us/blog/the-digital-self/202409/ai-and-the-emerging-role-of-iterative-intelligence with a large language model and something more complex begins to happen. I ask a question. The machine responds. And the loop begins. The response changes how I understand the problem, which changes what I ask next. A few rounds later, I may find myself somewhere new and unexpected with no obvious relationship to my initial intent. I'm still in control, deciding where the conversation goes and even ends. But it would be incorrect to suggest that the machine had nothing to do with how I got there. Somewhere in that https://www.psychologytoday.com/us/blog/the-digital-self/202409/ai-and-the-emerging-role-of-iterative-intelligence iterative exchange, the nature of the loop itself has changed. A Different Kind of Loop The sentence, or prompt, turns back on itself. Gödel showed that mathematics could do something similar. With AI, I believe that something new is happening. A human mind can now examine its own thinking through a computational system that is also participating in that thinking. I think of this as recursive participation. The human changes the machine's response, and the response changes what the human thinks or asks next. The process continues, but it never quite returns to where it started. A calculator can perform arithmetic for me, but I generally understand the division of labor. Search can retrieve information without becoming deeply involved in what I subsequently think about it. Generative AI is different because its response can become part of the development of the idea itself. At some point, describing the machine as simply providing answers starts to feel, using a term from Gödel, incomplete. Intelligence https://www.psychologytoday.com/us/basics/intelligence Essential Reads When the Instrument Enters the Loop 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 https://www.ethanhein.com/wp/2021/the-art-of-fugue-contrapunctus-i/ 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 https://arxiv.org/pdf/quant-ph/0011086 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.