Serendipity35

I inherited a copy of Douglas Hofstadter's book, Godel, Escher, Bach: an Eternal Golden Braid, when I started working at NJIT in 2000. It was my lunch reading. I read it in almost daily spurts. I often had to reread because it is not light reading.

It was published in 1979 and won the 1980 Pulitzer Prize for general non-fiction. It is said to have inspired many a student to pursue computer science, though it's not really a CS book. It was further described on its cover as a "metaphorical fugue on minds and machines in the spirit of Lewis Carroll." In the book itself, he says, "I realized that to me, Godel and Escher and Bach were only shadows cast in different directions by some central solid essence. I tried to reconstruct the central object and came up with this book."

I had not finished the book when I left NJIT, and it went on a shelf at home. This past summer I was trying to thin out my too-many books and I came upon it again with its bookmark glowering at me from just past the halfway point of the book. So, I went back to reading it. Still, tough going, though very interesting.

I remembered writing a post here about the book (it turned out to be from 2007) when I came upon a new book by Hofstadter titled I Am a Strange Loop. That "strange loop" was something he originally proposed in the 1979 book.

The earlier book is a meditation on human thought and creativity. It mixes the music of Bach, the artwork of Escher, and the mathematics of Gödel. In the late 1970s, when he was writing, interest in computers was high, and artificial intelligence (AI) was still more of an idea than a reality. Reading Godel, Escher, Bach exposed me to some abstruse math (like undecidability, recursion, and those strange loops) but (here's where Lewis Carroll's "What the Tortoise Said to Achilles" gets referenced though some of you will say it's really a Socratic dialogue as in Xeno's fable, Achilles and the Tortoise) each chapter has a dialogue between the Tortoise and Achilles and other characters to dramatize concepts. Allusions to Bach's music and Escher's art (that loves paradox) are used, as well as other mathematicians, artists, and thinkers. Godel's Incompleteness Theorem serves as his example of describing the unique properties of minds.

From what I read about the author, he was disappointed with how Godel, Escher, Bach (GEB) was received. It certainly got good reviews - and a Pulitzer Prize - but he felt that readers and reviewers missed what he saw as the central theme. I have an older edition, but in a newer edition, he added that the theme was "a very personal attempt to say how it is that animate beings can come out of inanimate matter. What is a self, and how can a self come out of stuff that is as selfless as a stone or a puddle?" I Am a Strange Loop focuses on that theme. In both books, he addresses "self-referential systems." (see link at bottom)

The image at the top of this essay is The Treachery of Images by René Magritte. It says that "This is not a pipe." That is a strange loop.

One thing that stuck with me from my first attempt at GEB is his using "meta" and defining it as meaning "about." Some people might say that it means "containing." Back in the early part of this century, I thought about that when I first began using Moodle as a learning management system. When you set up a new course in Moodle (and in other LMSs since then), it asks if this is a "metacourse." In Moodle, that means that it is a course that "automatically enrolls participants from other 'child' courses." Metacourses (AKA "master courses") feature all or part of the same content but customized to the enrollments of other sections. 

This was a feature used in big courses like English or Chemistry 101. In my courses, I thought more about having things like meta-discussions or discussions about discussions. My metacourse might be a course about the course. Quite self-referential.

I suppose it can get loopy when you start saying that if we have a course x, the metacourse X could be a course to talk about course x but would not include course x within itself. Though I suppose that it could.

Have I lost you?

Certainly, metatags are quite common on web pages, photos, and for cataloging, categorizing and characterizing content objects. Each post on Serendipity35 is tagged with one or more categories and a string of keyword tags that help readers find similar content and help search engines make the post searchable.

A brief Q&A with Hofstadter published in Wired  in March 2007 about the newer book says that he considers the central question for him to be "What am I?."

His examples of "strange loops" include M.C. Escher's piece, "Drawing Hands," which shows two hands drawing each other, and the sentence, "I am lying."

Hofstadter gets spiritual in his further thinking, and he finds at the core of each person a soul. He feels the "soul is an abstract pattern." Because he felt the soul is strong in mammals (weaker in insects), it brought him to vegetarianism.

He was considered to be an AI researcher, but he now thought of himself as a cognitive scientist.

Reconsidering GED, he decides that another mistake in that book's approach may have been not seeing that the human mind and smarter machines are fundamentally different. He has less of an interest in computers and claims that he always thought that his writing would "resonate with people who love literature, art, and music" more than the tech people.

If it has taken me much longer to finish Godel, Escher, Bach than it should, that makes sense if we follow the strange loop of Hofstadter's Law. ("It always takes longer than you expect, even when you take into account Hofstadter's Law.)

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End Note: 
A self-referential situation is one in which the forecasts made by the human agents involved serve to create the world they are trying to forecast. http://epress.anu.edu.au/cs/mobile_devices/ch04s03.html. Social systems are self-referential systems based on meaningful communication. http://www.n4bz.org/gst/gst12.htm.

The notion of talking to oneself, often dismissed as a mere quirky habit or a sign of preoccupation, is, in fact, a powerful, evidence-based cognitive tool essential for learning, problem-solving, and achieving self-regulation. For educators, understanding and deliberately integrating this "verbal thinking"—known in psychological literature as private speech, self-talk, or self-explanation—into pedagogical practice can unlock deeper comprehension and foster truly independent learners. 

The psychological roots of verbal thinking's benefit trace back most prominently to the work of Soviet psychologist Lev Vygotsky. His socio-cultural theory identifies a critical stage in a child's cognitive development where social communication turns inward to become a robust tool for thinking. Vygotsky outlined a three-stage developmental framework for language: beginning with Social Speech in young children, where language is purely external and used for communicating with others; progressing to Private Speech during the preschool years (ages 3-7), where the child begins to speak aloud to themselves, often in a whisper or mumble, utilizing this overt language as a self-guiding tool for planning, regulating, and controlling their own behavior and problem-solving attempts.

For example, a child engaged in a puzzle might audibly walk themselves through the steps: "First, put the red block here, then the blue block goes on top." This transitional phase ultimately leads to Inner Speech (age 7+), which is the fully internalized, silent verbal thought that most adults use for abstract reasoning, reflection, and sophisticated problem-solving. For educators, the key takeaway from Vygotsky’s work is that overt verbal thinking, or private speech, represents the crucial bridge from externally guided learning—where an adult or peer provides the instruction—to true self-regulation and independent, complex thought. By encouraging students to verbalize their process, teachers are helping them build the necessary internal scaffolding for later, silent, and more sophisticated thinking.

Crucially, verbal thinking doesn't just manage behavior; it fundamentally alters how information is encoded and understood by the brain, supporting both memory and comprehension. Research in memory retrieval highlights a phenomenon known as the Production Effect, which demonstrates that reading or generating information aloud significantly improves its memory retention compared to reading it silently. This memory boost occurs because speaking information aloud engages a greater number of sensory channels simultaneously. The learner uses visual input (seeing the text), verbal/motor input (the physical articulation of the words), and auditory input (hearing the words being spoken). This richer, multi-modal encoding creates a more distinctive and robust memory trace in the brain, making the information much easier to recall later. This distinctiveness is vital: when a learner produces a word aloud, it stands out against the background of other silently read words, making the item unique in memory. Therefore, simply having students read key definitions, summaries, or steps aloud in a low-stakes environment is a simple, yet highly effective, way for educators to leverage this proven physiological mechanism to strengthen long-term memory.

Perhaps the most powerful cognitive benefit, particularly for complex material, is the deep processing that occurs through self-explanation. This process is not mere repetition; it is the active, conscious act of trying to explain new information by relating it to what one already knows, making necessary inferences, and proactively clarifying any ambiguities. The first benefit here is powerful metacognitive monitoring: when a learner verbalizes a concept, the very act of articulation immediately exposes areas of confusion or "knowledge gaps." If a student struggles to explain a step in a math proof or a scientific concept, the flaw in their understanding is instantly revealed, prompting them to go back and refine their knowledge. This is a critical act of metacognition—the vital process of thinking about one's own thinking. Secondly, self-explanation drives coherence building. Verbalizing forces the student to translate disparate, often fragmented, pieces of information into a coherent, logical structure. They are not just recalling isolated facts but actively constructing a unified mental model of how the concepts interact. This principle is famously embodied by the Feynman Technique—explaining a concept simply as if teaching it to a novice—which serves as a form of high-level, deliberate verbal thinking that ruthlessly exposes the limits of a learner's comprehension.

The idea that talking to yourself out loud is not only "okay" but also an excellent learning technique is satisfying, but as I dug into this research, I recognized things from my college and grad school education courses. Other than the idea that it's not abnormal behavior to talk to yourself, this research is not completely new. I used several of these pedagogies in my teaching.

The challenge for educators, then, is to move verbal thinking from an accidental occurrence to a deliberate, scaffolded learning strategy within the classroom environment. One highly effective technique is the Think-Aloud Strategy, which focuses on teacher modeling. This strategy is used to make the invisible thought process of an expert visible and accessible to students, thereby explicitly teaching them how to engage in effective self-talk. To implement this, the teacher must first explicitly state the goal: "I’m going to show you how a skilled reader or problem-solver thinks by saying my thoughts out loud." Then, as the teacher reads a complex passage, works through a mathematical equation, or analyzes a primary source, they must stop frequently to verbalize their internal dialogue. This might involve using strategic planning language like, "I'm thinking I should use the quadratic formula here because the equation is set to zero," or demonstrating monitoring and correction by saying, "That word, 'ephemeral,' sounds like it means brief, so I’m going to pause and look that up to make sure I understand the context," or making connections: "The author just described the main character as restless. That connects to the idea I read earlier about his lack of a stable job. I wonder if this will lead to him leaving town." Once modeled, the teacher must transition students to practicing the strategy, perhaps through paired activities known as Reciprocal Think-Alouds, before expecting independent use.

A second practical technique is the Self-Explanation Prompt. This method strategically inserts verbalization breaks into a learning task to force metacognitive reflection and is particularly useful in technical subjects. Implementation begins by identifying key moments in a text, problem set, or lab procedure where a deeper understanding is absolutely necessary before the student can proceed. At these pause points, the teacher provides students with specific open-ended questions they must answer aloud to themselves or in a brief reflection journal. Prompts should be targeted to specific cognitive functions, such as focusing on rationale ("Why did I choose this variable to isolate?"), demanding synthesis ("What is the main idea of this section in my own words?"), or explicitly asking for a connection ("How does this new concept relate to what we learned last week?"). For maximum impact, teachers should then encourage a "Think-Pair-Share" approach where students must first explain their logic to a partner, which solidifies the idea and provides practice in articulation before the whole class moves on.

Finally, the "Teach It Back" Method is a form of high-stakes verbal thinking rooted in the pedagogical principle that to teach a concept is to truly master it. In this strategy, a student is assigned the role of briefly "teaching" a key concept, a section of the reading, or a part of the homework to a small group, to the class, or even to an imaginary audience. The critical instruction given to the student is to explain the topic as simply as possible, perhaps using an analogy, metaphor, or non-technical language if appropriate. The student must translate complex, academic language into straightforward, accessible terms, which serves as the ultimate test of their own comprehension. The teacher should provide specific feedback not only on the accuracy of the content but also on the clarity and logical structure of the explanation, reinforcing the importance of effective verbal articulation as a measure of understanding. By integrating these verbal thinking strategies—modeling, prompting, and teaching back—educators are not just improving a single study skill; they are building the core components of the resilient and self-regulated learner, equipping students with the tools for lifelong, independent cognitive growth.

SOURCES
Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Harvard University Press. (This source is foundational for the concepts of Private Speech and its role in Self-Regulation.)

MacLeod, C. M. (2011). The production effect: Better memory as a consequence of saying aloud during study. Applied Cognitive Psychology, 25(2), 195–204. (This research provides the physiological basis for the Production Effect and memory benefits.)

Chi, M. T. H. (2013). Self-explanation: The effects of talking aloud or writing on learning. Topics in Cognitive Science, 5(1), 1–4. (This source details the mechanism and benefits of Self-Explanation for deep comprehension.)

Berk, L. E. (1992). The role of private speech in the development of mental processes. Psychological Review, 99(4), 779–795. (This provides contemporary developmental research supporting and elaborating on Vygotsky’s observations of private speech.)

I mentioned in an earlier post that everyone in education - students and teachers - says that they use AI in their work, but very few can say they are formally trained or certified in the use of AI.

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The course outline explains that there is a 21x increase in job postings mentioning AI technologies, so this training should give you an edge.

Google AI Essentials can help you discover how you can use AI to assist, empower, and inspire you. Learn how to use generative AI tools to help speed up daily tasks, make more informed decisions, and develop new ideas and content.

A course like this can help you use AI tools to boost your productivity. You can complete the course at your own pace. Zero experience is required

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I see articles and posts about artificial intelligence every day. I have written here about it a lot in the past year. You cannot escape the topic of AI even if you are not involved in education, technology or computer science. It is simply part of the culture and the media today. I see articles about how AI is being used to translate ancient texts at a speed and accuracy that is simply not possible with humans. I also see articles about companies now creating AI software for warfare. The former is a definite plus, but the latter is a good example of why there is so much fear about AI - justifiably so, I believe.

Many educators seem to have had the initial reaction to the generative chatbots that became accessible to the public late last year and were being used by students to write essays and research papers. This spread through K-12 and into colleges and even into academic papers being written by faculty.

A chatbot powered by reams of data from the internet has passed exams at a U.S. law school after writing essays on topics ranging from constitutional law to taxation and torts. Jonathan Choi, a professor at Minnesota University Law School, gave ChatGPT the same test faced by students, consisting of 95 multiple-choice questions and 12 essay questions. In a white paper titled "ChatGPT goes to law school," he and his coauthors reported that the bot scored a C+ overall.

ChatGPT, from the U.S. company OpenAI, got most of the initial attention in the early part of 2023. They received a massive injection of cash from Microsoft. In the second half of this year, we have seen many other AI chatbot players, including Microsoft and Google who incorporated it into their search engines. OpenAI predicted in 2022 that AI will lead to the "greatest tech transformation ever." I don't know if that will prove to be true, but it certainly isn't unreasonable from the view of 2023.

Chatbots use artificial intelligence to generate streams of text from simple or more elaborate prompts. They don't "copy" text from the Internet (so "plagiarism" is hard to claim) but create based on the data they have been given. The results have been so good that educators have warned it could lead to widespread cheating and even signal the end of traditional classroom teaching methods.

Lately, I see more sober articles about the use of AI and more articles about teachers including lessons on the ethical use of AI by students, and on how they are using chatbots to help create their teaching materials. I knew teachers in K-20 who attended faculty workshops this past summer to try to figure out what to do in the fall.

The U.S. Department of Education recently issued a report on its perspective on AI in education. It includes a warning of sorts: Don’t let your imagination run wild. “We especially call upon leaders to avoid romancing the magic of AI or only focusing on promising applications or outcomes, but instead to interrogate with a critical eye how AI-enabled systems and tools function in the educational environment,” the report says.

Some of the ideas are unsurprising. For example, it stresses that humans should be placed “firmly at the center” of AI-enabled edtech. That's also not surprising since an earlier White House “blueprint for AI,” said the same thing. And an approach to pedagogy that has been suggested for several decades - personalized learning - might be well served by AI. Artificial assistants might be able to automate tasks, giving teachers time for interacting with students. AI can give instant feedback to students "tutor-style." 

The report's optimism appears in the idea that AI can help teachers rather than diminish their roles and provide support. Still, where AI will be in education in the next year or next decade is unknown.