Back when I was studying STEM subjects for my A-Levels, this mindset of not accepting anything until I've understood it was really rewarding.
But I went on to study law and jesus fucking christ did I find myself in a rabbit-hole from which I have yet to emerge. I couldn't even convince myself that central governments and legislatures were necessary for order, although I probably should've satisfied myself with Hobbes' argument and moved on. I thought legal concepts were "transcendental nonsense". Reasoning from precedent seemed extremely shoddy. Judges seemed all too human, value judgments abound disguised in "legal reasoning". There were hardly any "first principles" one could speak of. These were, in short, massive obstacles I had to overcome (or bracket off) before I could justifiably move on to actual doctrinal study.
But a deep understanding of law really requires understanding so many things, such that I could never reach that point where I could say, "Okay, I've got it, now let's use this groundwork to start thinking about legal doctrine". Examples: What even is law? Legal philosophy. Indeterminacy of language and interpretation? Philosophy of language. Distinguishing right and wrong? Moral philosophy, then moral psychology once it became clear to me that morals have to do with groups and emotions. How about understanding society, the realm of law's application and origin? Sociology/Social theory. Not to mention the huge body of "postmodern" work that has grown up around it which sees everything as a social construct, an effect of discourse/power, humans themselves as lacking the kind of agency assumed in law and liberal political philosophy.
And despite everything I have written, I don't feel like I've gotten a grasp on things. (Social) reality is such a massive, incomprehensible beast where everything is chaotically intertwined, arguably unlike mathematics where you can advance your understanding in little, isolated chunks at a time, with reasonable confidence that you've made sense of it. Some days I feel like I've wasted all my energy trying to analyse all these underlying dynamics of law and society, that I've entered a field where the "will to know" never pays off (you never see the full picture) and simply rips your common sense worldview apart without offering anything in return.
Thanks for the essay, it allowed me to explore my thoughts in the preceding paragraphs :)
“At the time, I was infuriated by these inadequate proofs, but I was under time pressure to just learn the operations so that I could answer exam questions because the class needed to move onto the next thing.
And since you actually can answer the exam questions and mechanically perform calculus operations without ever deeply understanding calculus, it’s much easier to just get by and do the exam without really questioning the concepts deeply -- which is in fact what happens for most people. (See my essay on education.)
How many people actually go back and try and understand this, or other such topics, in a deeper way? Very few. Moreover, the ‘meta’ lesson is: don’t question it too deeply, you’ll fall behind. Just learn the algorithm, plug in the numbers, and pass your exams. Speed is of the essence. In this way, school kills the “will to understanding” in people. “
Great insight. I’ve said similar before and people don’t often understand how there could be a difference between acing a Calc III exam and having a conceptual understanding of it. Many people understand math only through the lens of rote algorithms and techniques; some people understand other subjects through this perspective as well.
Even if you try to understand them , in todays real world you will be lagging behind in the workplace and you would be stuck like the others. Also when money is involved you would be unable to pay for anything
Thank you! I think it's worthwhile for both -- some of the very best non-fiction I've read has unforgettable specifics (see John McPhee's book on Oranges, for example...)
That said, non-fiction often deals in abstractions and concepts, where this is maybe less important overall.
I love how you reframe intelligence as more about habits and character - the willingness to look stupid by asking questions, the drive to really understand rather than just get the "right answer," and the patience to examine things from multiple angles. The contrast between stopping at the first proof versus finding multiple approaches is such a clear illustration of this. Your examples of the equals sign and the brick story are perfect reminders that even seemingly simple things contain depths when we're willing to look closer and think longer. It's a refreshing perspective on what real understanding requires.
My wife says she was the top of her class for Calculus and 10 years later couldn't tell you a single thing about it. She excelled at school because she was good at memorizing, not because she understood things well -- she had good hardware, but never learned to load in the software she really needed to be an expert. I guess it doesn't matter. Her field doesn't require Calculus. Makes me wonder if we're wasting people's time on subjects that don't actually matter instead of doubling down on the ones that will for them.
Truly fantastic read. I feel like it has put into words many thoughts I’ve had for so long.
I would like to add that, even though I agree that first-hand experience is an amazing vehicle for understanding, it is inherently limited and should be taken with a grain of salt. Besides the concern that human senses can fool us, I think it is even more concerning that our own human experience is very limited in size, speeds, and time scales. We humans are unable to experience first-hand the very small, the very fast, and processes that take several millions of years to happen. Hence this empirical-data approach can sometimes limit us to exclusively think about concepts that are inherently tied to the human experience.
I would imagine that a being that is several orders of magnitude larger than us and lives over many millions of years instead of mere decades will be inclined to think about physical systems that operate on these scales.
You seem stuck in the depths of left hemisphere reasoning, a very worthy and fine example of it I think, thank you. If you can now move on to right hemisphere thinking, and perhaps how to synthesise the two modes of intelligence, then with your obvious talent as a writer, you could produce something wonderful indeed. I recommend reading The Matter With Things by Iain McGilchrist if you haven’t already done so, I really think you could produce something magnificent.
In true spirit of the article I thought about it and wrote about it in my own way. It helped me understand it more. It proved the words you write, to me.
Cultivating Depth in a Distracted World
In an age of rapid information, the true challenge is not just acquiring knowledge but thinking deeply about it. The ability to think—to truly engage with an idea—requires three key elements: the will to think, the time to think, and the energy to think. Without all three, intellectual progress is stifled, and clarity remains elusive.
The Will to Think
Thinking is not a passive act; it is an intentional pursuit. The will to think is the commitment to engage with difficult concepts, to seek understanding beyond surface-level interpretations. It requires the courage to confront complexity, the discipline to resist easy answers, and the humility to accept that learning is a continuous process.
The Time to Think
Modern life is filled with distractions, demanding our attention in countless ways. Yet, thinking cannot be rushed. Understanding a concept deeply means allowing ideas to marinate, questions to arise, and connections to form. Creating dedicated time for thinking—free from interruptions—fosters clarity and insight.
The Energy to Think
Just as physical energy is required for movement, mental energy is necessary for deep thinking. This means prioritizing sleep, nutrition, and mental well-being. Fatigue breeds complacency; alertness fuels curiosity. A well-rested mind is far better equipped to wrestle with complexity.
Intellectual Honesty: The First Rule of Science
'The first rule of science is that you do not fool yourself—and you are the easiest person to fool.' Intellectual rigor demands honesty, a willingness to challenge one’s own biases, and a readiness to accept when one is wrong. To think well, we must be vigilant against self-deception and remain open to evidence that contradicts our assumptions.
Writing Forces Clarity
If you cannot explain an idea clearly, you do not understand it well enough. Writing is a tool for refining thought, forcing us to articulate what we think we know. It exposes gaps in understanding and compels us to think more deeply. The process of writing is not just about recording thoughts—it is about shaping them.
The Power of Asking Questions
Never let intellectual insecurities prevent you from asking when you do not know. True learners embrace curiosity and discard the fear of appearing uninformed. Every expert was once a beginner, and every insightful thought begins with a question.
The Art of Slow Thinking
Speed is often mistaken for intelligence, but real understanding comes from patience. Read slow. Think slow. Dwell on questions rather than rushing to answers. The more time you spend with a problem, the clearer it becomes. Zoom in, then zoom in again, then once more. The deeper you go, the more profound the insights.
The Discipline of Focus
In a world of endless notifications and fleeting distractions, the ability to focus is a superpower. Cut out unwanted and unneeded distractions. The mind cannot hold multiple complex thoughts simultaneously—depth requires singular attention. The deeper the focus, the greater the clarity.
When in Doubt, Go Closer
Confusion is not a dead end but an invitation to look more closely. If something does not make sense, break it down further. Examine the details. Reconstruct the argument. Clarity emerges not from avoiding difficulty but from engaging with it at a granular level.
Conclusion: Thinking as a Discipline
Thinking well is a deliberate practice. It requires will, time, and energy. It demands honesty, clarity, patience, and focus. In a world driven by speed and superficiality, deep thinking remains a radical act—one that leads to genuine understanding, original thought, and intellectual growth. The challenge, then, is simple: cultivate the will to think, and the rest will follow.
So related to the calculus notation confusion - This annoyed me for years!
and, as a fun coincidence, i’ve been thinking about the brick example for months as part of a creativity framework I’ve been working on (read about it in art of learning).
Intelligence is raw processing ability regardless of how it's used. It is not malleable in the intentionally directed way everyone wishes and some believe.
Back when I was studying STEM subjects for my A-Levels, this mindset of not accepting anything until I've understood it was really rewarding.
But I went on to study law and jesus fucking christ did I find myself in a rabbit-hole from which I have yet to emerge. I couldn't even convince myself that central governments and legislatures were necessary for order, although I probably should've satisfied myself with Hobbes' argument and moved on. I thought legal concepts were "transcendental nonsense". Reasoning from precedent seemed extremely shoddy. Judges seemed all too human, value judgments abound disguised in "legal reasoning". There were hardly any "first principles" one could speak of. These were, in short, massive obstacles I had to overcome (or bracket off) before I could justifiably move on to actual doctrinal study.
But a deep understanding of law really requires understanding so many things, such that I could never reach that point where I could say, "Okay, I've got it, now let's use this groundwork to start thinking about legal doctrine". Examples: What even is law? Legal philosophy. Indeterminacy of language and interpretation? Philosophy of language. Distinguishing right and wrong? Moral philosophy, then moral psychology once it became clear to me that morals have to do with groups and emotions. How about understanding society, the realm of law's application and origin? Sociology/Social theory. Not to mention the huge body of "postmodern" work that has grown up around it which sees everything as a social construct, an effect of discourse/power, humans themselves as lacking the kind of agency assumed in law and liberal political philosophy.
And despite everything I have written, I don't feel like I've gotten a grasp on things. (Social) reality is such a massive, incomprehensible beast where everything is chaotically intertwined, arguably unlike mathematics where you can advance your understanding in little, isolated chunks at a time, with reasonable confidence that you've made sense of it. Some days I feel like I've wasted all my energy trying to analyse all these underlying dynamics of law and society, that I've entered a field where the "will to know" never pays off (you never see the full picture) and simply rips your common sense worldview apart without offering anything in return.
Thanks for the essay, it allowed me to explore my thoughts in the preceding paragraphs :)
“At the time, I was infuriated by these inadequate proofs, but I was under time pressure to just learn the operations so that I could answer exam questions because the class needed to move onto the next thing.
And since you actually can answer the exam questions and mechanically perform calculus operations without ever deeply understanding calculus, it’s much easier to just get by and do the exam without really questioning the concepts deeply -- which is in fact what happens for most people. (See my essay on education.)
How many people actually go back and try and understand this, or other such topics, in a deeper way? Very few. Moreover, the ‘meta’ lesson is: don’t question it too deeply, you’ll fall behind. Just learn the algorithm, plug in the numbers, and pass your exams. Speed is of the essence. In this way, school kills the “will to understanding” in people. “
Great insight. I’ve said similar before and people don’t often understand how there could be a difference between acing a Calc III exam and having a conceptual understanding of it. Many people understand math only through the lens of rote algorithms and techniques; some people understand other subjects through this perspective as well.
Even if you try to understand them , in todays real world you will be lagging behind in the workplace and you would be stuck like the others. Also when money is involved you would be unable to pay for anything
Sometimes, I too feel that we tend to skip a lot of things due to time constraints.
Phenomenal! Thank you so much!
I love this essay so much. Thanks for writing this.
Hi Nabeel,
Enjoyed this!
Question: Why is going closer only good fiction writing advice? How is it different with non-fiction?
Thank you! I think it's worthwhile for both -- some of the very best non-fiction I've read has unforgettable specifics (see John McPhee's book on Oranges, for example...)
That said, non-fiction often deals in abstractions and concepts, where this is maybe less important overall.
I love how you reframe intelligence as more about habits and character - the willingness to look stupid by asking questions, the drive to really understand rather than just get the "right answer," and the patience to examine things from multiple angles. The contrast between stopping at the first proof versus finding multiple approaches is such a clear illustration of this. Your examples of the equals sign and the brick story are perfect reminders that even seemingly simple things contain depths when we're willing to look closer and think longer. It's a refreshing perspective on what real understanding requires.
"People who have not experienced the thing are unlikely to be generating truth. More likely, they’re resurfacing cached thoughts and narratives."
Seems like LLMs. 🙂
That was the case but we're slowly moving away from that paradigm: https://nonint.com/2024/06/03/general-intelligence-2024/
My wife says she was the top of her class for Calculus and 10 years later couldn't tell you a single thing about it. She excelled at school because she was good at memorizing, not because she understood things well -- she had good hardware, but never learned to load in the software she really needed to be an expert. I guess it doesn't matter. Her field doesn't require Calculus. Makes me wonder if we're wasting people's time on subjects that don't actually matter instead of doubling down on the ones that will for them.
Truly fantastic read. I feel like it has put into words many thoughts I’ve had for so long.
I would like to add that, even though I agree that first-hand experience is an amazing vehicle for understanding, it is inherently limited and should be taken with a grain of salt. Besides the concern that human senses can fool us, I think it is even more concerning that our own human experience is very limited in size, speeds, and time scales. We humans are unable to experience first-hand the very small, the very fast, and processes that take several millions of years to happen. Hence this empirical-data approach can sometimes limit us to exclusively think about concepts that are inherently tied to the human experience.
I would imagine that a being that is several orders of magnitude larger than us and lives over many millions of years instead of mere decades will be inclined to think about physical systems that operate on these scales.
You seem stuck in the depths of left hemisphere reasoning, a very worthy and fine example of it I think, thank you. If you can now move on to right hemisphere thinking, and perhaps how to synthesise the two modes of intelligence, then with your obvious talent as a writer, you could produce something wonderful indeed. I recommend reading The Matter With Things by Iain McGilchrist if you haven’t already done so, I really think you could produce something magnificent.
What a nice, warm and welcoming and thoughtful essay. Will check Kolmogorov‘s Essay on the equal sign.. I love stuff like this.
Thank you!
Thank you Nabeel,
In true spirit of the article I thought about it and wrote about it in my own way. It helped me understand it more. It proved the words you write, to me.
Cultivating Depth in a Distracted World
In an age of rapid information, the true challenge is not just acquiring knowledge but thinking deeply about it. The ability to think—to truly engage with an idea—requires three key elements: the will to think, the time to think, and the energy to think. Without all three, intellectual progress is stifled, and clarity remains elusive.
The Will to Think
Thinking is not a passive act; it is an intentional pursuit. The will to think is the commitment to engage with difficult concepts, to seek understanding beyond surface-level interpretations. It requires the courage to confront complexity, the discipline to resist easy answers, and the humility to accept that learning is a continuous process.
The Time to Think
Modern life is filled with distractions, demanding our attention in countless ways. Yet, thinking cannot be rushed. Understanding a concept deeply means allowing ideas to marinate, questions to arise, and connections to form. Creating dedicated time for thinking—free from interruptions—fosters clarity and insight.
The Energy to Think
Just as physical energy is required for movement, mental energy is necessary for deep thinking. This means prioritizing sleep, nutrition, and mental well-being. Fatigue breeds complacency; alertness fuels curiosity. A well-rested mind is far better equipped to wrestle with complexity.
Intellectual Honesty: The First Rule of Science
'The first rule of science is that you do not fool yourself—and you are the easiest person to fool.' Intellectual rigor demands honesty, a willingness to challenge one’s own biases, and a readiness to accept when one is wrong. To think well, we must be vigilant against self-deception and remain open to evidence that contradicts our assumptions.
Writing Forces Clarity
If you cannot explain an idea clearly, you do not understand it well enough. Writing is a tool for refining thought, forcing us to articulate what we think we know. It exposes gaps in understanding and compels us to think more deeply. The process of writing is not just about recording thoughts—it is about shaping them.
The Power of Asking Questions
Never let intellectual insecurities prevent you from asking when you do not know. True learners embrace curiosity and discard the fear of appearing uninformed. Every expert was once a beginner, and every insightful thought begins with a question.
The Art of Slow Thinking
Speed is often mistaken for intelligence, but real understanding comes from patience. Read slow. Think slow. Dwell on questions rather than rushing to answers. The more time you spend with a problem, the clearer it becomes. Zoom in, then zoom in again, then once more. The deeper you go, the more profound the insights.
The Discipline of Focus
In a world of endless notifications and fleeting distractions, the ability to focus is a superpower. Cut out unwanted and unneeded distractions. The mind cannot hold multiple complex thoughts simultaneously—depth requires singular attention. The deeper the focus, the greater the clarity.
When in Doubt, Go Closer
Confusion is not a dead end but an invitation to look more closely. If something does not make sense, break it down further. Examine the details. Reconstruct the argument. Clarity emerges not from avoiding difficulty but from engaging with it at a granular level.
Conclusion: Thinking as a Discipline
Thinking well is a deliberate practice. It requires will, time, and energy. It demands honesty, clarity, patience, and focus. In a world driven by speed and superficiality, deep thinking remains a radical act—one that leads to genuine understanding, original thought, and intellectual growth. The challenge, then, is simple: cultivate the will to think, and the rest will follow.
Profound insights. Thanks for posting.
Crazy good.
So related to the calculus notation confusion - This annoyed me for years!
and, as a fun coincidence, i’ve been thinking about the brick example for months as part of a creativity framework I’ve been working on (read about it in art of learning).
Brilliantly written- Thank you
Intelligence is raw processing ability regardless of how it's used. It is not malleable in the intentionally directed way everyone wishes and some believe.