I was lucky enough to have 3 clear examples of this occur during my undergrad physics degree, 35 years ago.
The first came after my second summer, spent building out what would be our small university’s first computer lab (as a means to share costs & own after-hours cycles for my boss’ computational simulations of brown dwarfs & what later became known as Type 1a supernovae — my 1st, 3rd, and 4th year summer jobs).
I was approached by a Sociology professor and asked to TA her “Stats for Jocks” class, using the new lab to introduce computers & SPSS to them. Few ever “got” the concept of data that could be analyzed algorithmically: “what is your favourite food” vs “on a Likert-style scale, rate these foods.”
The second was a counter example: I never could “get” quantum mechanics, though I could, as Neils Bohr put it, “shut up and calculate.”
The last (and most profound) was the day that I “got” statistical mechanics, and was able to produce chemistry’s Boyle’s Law (PV=NkT) from first principles. It was a moment of transcendence, one whose example of emergent properties of complex systems has informed my subsequent career in IT, information security, and risk management — as well as deepening appreciation for Foundation, politics, and, coming full circle, sociology (among many other topics).
Keep helping people learn, and understand understanding 🙏
"Knowing the dependencies and relationships in a process is one of the key features philosophers often point to in theories of what it means to understand." This sums it up for me.
I tend to think of 'understanding' in terms of having a mental map of the relationships between different aspects of the data set. So in my field of psychotherapy, I might represent that as eg a family tree: Freud begat Berne's Transactional Analysis, which would be a cousin of cognitive analytic therapy etc.
I like to think of understanding essentially as when things get simple. It’s difficult as a student because you’re trying to make sense of things that seem complex. It’s only later when you understand (often with enough examples) that things can become simple. This is where enough dots have gotten connected for a coherent picture to emerge. Some day consciousness should also be understood, and so the difference between LLMs and us should be as well. Until such causality gets worked out however, things will seem complex or even magical.
Love this. From my perspective real understanding isn’t about storing more facts, it’s about compressing reality without losing fidelity. That’s what I call semantic fidelity: how well your internal model preserves structure as it simplifies. Cramming builds data; understanding builds recursion. It’s the art of compression that still breathes, where meaning survives the shrink.
What you call "understanding" is close to what I learned to be "wisdom": applying one's experience with some measure of deeper insight into purpose. Takes a journey to get there, and even when you're there, you realize the terrain keeps going.
A shorter version of this essay is a game I play inside my head when faced with a recalcitrant problem. I ask myself "What if..." and then rummage through my current knowledge to see what happens. Sometimes the answer is "I don't know" so I either execute it or go look it up. Either way, I increase my basic fund of knowledge which may or may not lead to a successful resolution. The beauty of it is that it is fast and fun. Sometimes it even works.
It's relevant to the question of whether human understanding is different from AI understanding, which is the ability to produce the appropriate text at the proper moment. My students are skeptical of the value of knowing things, and I think it's partly because they don't see the distinction, so well captured by your examples.
This resonates with Mortimer Adler's distinction that reading is for understanding, not just information nor entertainment.
The point on understanding as compression is fascinating. I wonder if understanding is actually about the constraints during decompression: facing infinite paths to apply supply/demand principles, the econ professor's mental models help narrow down to the most plausible paths. Like how a chess grandmaster's "understanding" instantly sees the few relevant moves among thousands of possibilities?
Also reminds me of Bloom's taxonomy, which places understanding as a sequential progression: remember → understand → apply → analyze → evaluate → create. Is Bloom's framework orthogonal to compression, unification, and mental simulation angles?
As an elementary teacher’s assistant, this resonates with me, but I haven’t found any satisfactory explanations of how these theories apply to K-12 education. I hope you can write articles about it someday if inspiration strikes you. I honestly think most teachers are not truly skilled in teaching since they don’t seem to understand basic cognitive science. To me, it’s been concerning to hear that there is a general consensus that teaching is an art rather than a science, because this means there is no real incentive to develop sound and rigorous explanations for why students do or don’t engage in behavior or do/don’t learn the material. I hear all the time how data-centered teaching is and how much evidence there is waiting to be turned into pedagogy, but I am almost sure that data is not based in child development/cognitive science (and is instead based on the desire to keep funding for funding’s sake). I know I can’t do much as a teacher’s assistant, but can anyone name some resources that might incorporate the claims of this article into something someone in my role can understand?
Great post. I think the point about compression and unification is spot on, and that idea itself compresses and unifies the different modes of explanation/understanding!
There's a couple interesting parallels with a post I wrote a while back. I looked at Plato's Forms and Aristotle's idea of matter as both being different systems of abstraction/data compression, which parallels your comparison of explanation via laws of physics vs biological mechanisms. And where you look at abstraction vs mental simulation, my post considered the concepts as either representing real substructures of the things being studied, or a range of possibilities that might be instantiated. The post is here, if you're interested: https://thinkstrangethoughts.substack.com/p/the-ultimate-abstraction
Excellent piece, Tommy!
I was lucky enough to have 3 clear examples of this occur during my undergrad physics degree, 35 years ago.
The first came after my second summer, spent building out what would be our small university’s first computer lab (as a means to share costs & own after-hours cycles for my boss’ computational simulations of brown dwarfs & what later became known as Type 1a supernovae — my 1st, 3rd, and 4th year summer jobs).
I was approached by a Sociology professor and asked to TA her “Stats for Jocks” class, using the new lab to introduce computers & SPSS to them. Few ever “got” the concept of data that could be analyzed algorithmically: “what is your favourite food” vs “on a Likert-style scale, rate these foods.”
The second was a counter example: I never could “get” quantum mechanics, though I could, as Neils Bohr put it, “shut up and calculate.”
The last (and most profound) was the day that I “got” statistical mechanics, and was able to produce chemistry’s Boyle’s Law (PV=NkT) from first principles. It was a moment of transcendence, one whose example of emergent properties of complex systems has informed my subsequent career in IT, information security, and risk management — as well as deepening appreciation for Foundation, politics, and, coming full circle, sociology (among many other topics).
Keep helping people learn, and understand understanding 🙏
Thanks, Tommy.
"Knowing the dependencies and relationships in a process is one of the key features philosophers often point to in theories of what it means to understand." This sums it up for me.
I tend to think of 'understanding' in terms of having a mental map of the relationships between different aspects of the data set. So in my field of psychotherapy, I might represent that as eg a family tree: Freud begat Berne's Transactional Analysis, which would be a cousin of cognitive analytic therapy etc.
I like to think of understanding essentially as when things get simple. It’s difficult as a student because you’re trying to make sense of things that seem complex. It’s only later when you understand (often with enough examples) that things can become simple. This is where enough dots have gotten connected for a coherent picture to emerge. Some day consciousness should also be understood, and so the difference between LLMs and us should be as well. Until such causality gets worked out however, things will seem complex or even magical.
Nice. Always appreciative of a piece that forces a closer look at our processes. Congrats on the post Tommy
Love this. From my perspective real understanding isn’t about storing more facts, it’s about compressing reality without losing fidelity. That’s what I call semantic fidelity: how well your internal model preserves structure as it simplifies. Cramming builds data; understanding builds recursion. It’s the art of compression that still breathes, where meaning survives the shrink.
Very interesting and fun.
What you call "understanding" is close to what I learned to be "wisdom": applying one's experience with some measure of deeper insight into purpose. Takes a journey to get there, and even when you're there, you realize the terrain keeps going.
A shorter version of this essay is a game I play inside my head when faced with a recalcitrant problem. I ask myself "What if..." and then rummage through my current knowledge to see what happens. Sometimes the answer is "I don't know" so I either execute it or go look it up. Either way, I increase my basic fund of knowledge which may or may not lead to a successful resolution. The beauty of it is that it is fast and fun. Sometimes it even works.
A nice essay, on something I've also considered -- what the nature of understanding is.
https://sermointerruptus.blog/2025/05/25/whats-in-your-consciousness/
It's relevant to the question of whether human understanding is different from AI understanding, which is the ability to produce the appropriate text at the proper moment. My students are skeptical of the value of knowing things, and I think it's partly because they don't see the distinction, so well captured by your examples.
Excellent meta-thinking on "understanding"!
This resonates with Mortimer Adler's distinction that reading is for understanding, not just information nor entertainment.
The point on understanding as compression is fascinating. I wonder if understanding is actually about the constraints during decompression: facing infinite paths to apply supply/demand principles, the econ professor's mental models help narrow down to the most plausible paths. Like how a chess grandmaster's "understanding" instantly sees the few relevant moves among thousands of possibilities?
Also reminds me of Bloom's taxonomy, which places understanding as a sequential progression: remember → understand → apply → analyze → evaluate → create. Is Bloom's framework orthogonal to compression, unification, and mental simulation angles?
Love this piece, inspiring!
As an elementary teacher’s assistant, this resonates with me, but I haven’t found any satisfactory explanations of how these theories apply to K-12 education. I hope you can write articles about it someday if inspiration strikes you. I honestly think most teachers are not truly skilled in teaching since they don’t seem to understand basic cognitive science. To me, it’s been concerning to hear that there is a general consensus that teaching is an art rather than a science, because this means there is no real incentive to develop sound and rigorous explanations for why students do or don’t engage in behavior or do/don’t learn the material. I hear all the time how data-centered teaching is and how much evidence there is waiting to be turned into pedagogy, but I am almost sure that data is not based in child development/cognitive science (and is instead based on the desire to keep funding for funding’s sake). I know I can’t do much as a teacher’s assistant, but can anyone name some resources that might incorporate the claims of this article into something someone in my role can understand?
Great post. I think the point about compression and unification is spot on, and that idea itself compresses and unifies the different modes of explanation/understanding!
There's a couple interesting parallels with a post I wrote a while back. I looked at Plato's Forms and Aristotle's idea of matter as both being different systems of abstraction/data compression, which parallels your comparison of explanation via laws of physics vs biological mechanisms. And where you look at abstraction vs mental simulation, my post considered the concepts as either representing real substructures of the things being studied, or a range of possibilities that might be instantiated. The post is here, if you're interested: https://thinkstrangethoughts.substack.com/p/the-ultimate-abstraction
Lol choose tour own adventure was probably one of the turning points that i learned about AI model memory.