Problem solving is a well-explored field in experimental psychology. TFA is a bit unfocused, making both some generally supported speculations and some traditional ideas that haven't been supported. A very good survey is the edited volume, The Psychology of Problem Solving (Davidson 2003).
Although TFA doesn't refer to it by name, "insight" problem solving is when you are stuck on something and then suddenly realize the solution. The common explanation for being stuck is "fixation" on the wrong things. In agreement with TFA, there is indication that verbalization supports fixation more than visualization.
It's quite frustrating when writers like the author - who seem quite thoughtful and potentially useful to read - appear to pontificate on a field without seemingly being aware of it; using a great mathematician's thoughts on it as a springboard doesn't justify it as its not his field of expertise either.
The essay might be more useful grounded with references to the sort of thing you link to.
Reminds me of the description of Peter Scholze as he was coming up with condensed mathematics. Didn't write a thing until he had it all worked out in his head (which is how he always works). Knew if he didn't get it worked out before the weekend he'd never be able to build it up again. Once he worked it out, he was able to retain it for months until finally writing it down.
But we all know thoughts aren't words, the words come after the thought. The proof is that you can stop your inner words mid-sentence and you still know what you were going to think, because the thought itself takes a few milliseconds, and happens before the words start.
The question reminds me of a quote from Rilke: "There is a depth of thought untouched by words, and deeper still a depth of formless feeling untouched by thought".
I don't have an "inner monologue" and don't think in words, only in images, but I've never experienced what this author is describing in terms of "nonsense words" or "hand vibrations".
I was with some friends that were in a band together, and we got thinking about this topic, and ended up arranging ourselves from least verbal to most verbal. I was on one end, where all of my thoughts appear as emotions or images; on the other end was our bassist, who experienced his thoughts as fully formed sentences. He said when he's getting to a difficult passage in a song the words "better focus here, don't mess up" will ring out in his head. He also said he has fully dictated mental conversations with himself.
I also read very quickly because I look at the shape of paragraphs and assemble the word-shapes into mental images and pick up meaning that way; high speed, but low comprehension. I struggle greatly to read philosophy because it's quite difficult to visualize. My wife reads slowly but hears every word in her head; her comprehension is much higher. I can do high comprehension reading by slowing down and looking at every word, but it feels like holding back an excitable dog.
When making visual art, I don’t think in words. Shapes, colors, shading, perspective together turn into a final drawing; at no point do I translate this to words. I’m not sure what trying to draw by thinking in words would even look like.
Identifying and searching for morel mushrooms in the woods also feels largely nonverbal (although near a dying elm in late spring after a rain captures an essence of the idea, and those words provide a good starting point).
Coding ends in “words”, or at least some form of written language. But when I try to solve problems I do not think in words until it is time to put fingers to keyboard.
Words are useful (I could not convey this comment otherwise), but they’re not everything. It feels extremely difficult to convey my nonverbal thoughts through an inherently verbal medium like an HN comment. Perhaps to make a wordful analogy, the difficulty is like translating an idiom from one language to one of completely different context and origin.
I don’t deny that words do shape some of my thinking, but to me it’s just one part of the whole stream of conscious.
I’m curious if anyone else feels this way about words?
Glad you pointed out Feynman’s experience. The paper and the writing were the work. Oftentimes, I don’t settle on a meaningful, elegant solution until I have tried to explain my thoughts many times. “Eureka!” becomes “oh wait…” and back—a pendulum that eventually settles on a beautiful solution.
This is one of those things that you don't really tend to think about (pun not intended!) until you experience a change in your thinking or meet someone who thinks like you do!
> If we can avoid the compression step, and do the manipulations directly in the high-dimensional, non-linguistic, conceptual space, we can move much faster
With my neurodivergent brain I've always conducted my thoughts in an "uncompressed format" and then eternally struggled to confine it all into words. Only then for people to misinterpret and question it. They might get caught up in the first sentence when the end of the paragraph is where you need to be!
That's why when you meet someone who thinks like you the depth of conversation and thinking you can achieve together is vast and also incredibly liberating! Your no longer limited by words in same way.
Since becoming ill I've suffered badly with brainfog. The cutesy name for a cruel experience. Sometimes there's no memories to draw on when your thinking, the cupboards are bare. You can't leap from thought to thought because they disappear before you get there or after like a cursed platformer. You might be able to grab hold of the thought but you can't reach inside or read it. It's all wrong somehow like when your suddenly convinced a word is spelt wrong even though you know it's right. You can't maintain focus long enough to finish your train of thought.
Even that subconscious processing is affected I used to prime my brain with information all day and instead of waking up with the solution I'll wake up frustrated but not knowing why. Just the vague notion that I failed at something that used to come so easily.
That description really resonates with me, it feels a lot like what I've been experiencing on and off for several months. I sometimes describe it like being able to see and examine an idea sitting in front of me on the table but having a hard time picking up and being able to manipulate it enough to write it out. Or like your fingers are working poorly like when it's very cold and you're not wearing gloves.
It only takes some practice to get better at it even if it doesn’t come naturally to you. I think it’s worth working on our weakest skills, over time it compounds quite nicely.
But what I do not get is how you would convey these thoughts to someone else that thinks the same way as you, seeing as these thoughts don’t neccesarily seem to be contained to words or sentences.
I don't think its the same thing as whats described in the article.
When i talk with someone very aligned with my thinking and knowledge (fellow it collegues/friends with simiiliar skill level) we do not a lot of words to be aligned and convey complex thoughts.
We reference and use words which we both know, we read and reference similiar news stories etc.
But the way they describe it with colors, vibrations etc. is probably somethig you can't just convey.
> I've always conducted my thoughts in an "uncompressed format" and then eternally struggled to confine it all into words. Only then for people to misinterpret and question it.
This resonates so much with me. To a point where I don't write/contribute in public forums out of fear for this misinterpretation.
Strangely, your post has made me push through that exact fear to write this, so any perceived misinterpretation has positively impacted at least one stranger. This is a good reminder for me that focusing only on negative consequences misses the unintended positive ones of still putting something out there, even if its not a perfect representation of the "uncompressed format".
Thank you for sharing, and I wish you a speedy recovery.
I've too often made the experience of having something that feels significant and whole in my head, and in the process of trying to articulate it to another person, it becomes almost completely lost. What comes out is a two-dimensional, crippled shadow of the original idea, and it (this is the worst part) cuts off my connection to the complex form.
I've certainly noticed a bit of a pattern where programmers who can listen to podcasts or lyrics while they code (I can't; I rely too much on my verbal center for coding) can operate much faster and solve more complex problems than your average bear. They're rare, so I don't have enough data to feel certain, but I have a suspicion that sometimes they're forced into it by living in noisy environments where tuning out the words or thinking without them makes more sense.
Been thinking a lot recently about what my thoughts look like. They definitely aren't words (though as I type this, I can imagine hearing myself think ahead to the end of the sentence). The best I can describe it is visualisations - whether that's images of maths notation, 3D rotating models, or a flow/map/block diagram.
One pattern is that I'm a very prolific connection-forming machine.
Exhibit A: The first thing that enters my mind for each word.
(OnePlus One) (android pattern unlock) (Islamic State) (unit vector named t) (ich bin) (emoji-blood-type-A) (Latin etymology word root with verily) (https://prolificusa.com/) (New York Times Connections) (roll-forming, blow moulding, sheet metal stamping...) ("my body is a machine" meme)
My wife was confounded when I told her I don't think in words. For her, it's a one to one correlation.
She had assumed that all people think in this mode. I had assumed that all people think in "thoughts" and went through a separate step to articulate them.
Made both of us aware of a difference in people.
I don't feel vibrations or sensations though, and I definitely don't think in images. I only have a thought level, and it's very independent of any external presentation.
Anecdotally, the degree to which one does certain types of thinking can change over time, too.
Around 2020, I decided to try to learn as much as I could about "higher" mathematics in earnest, having basically no background in the subject. Five years later, I have finally read and suffered enough to be able to pick up texts in any of the abstract branches of mathematics and at least understand most of what's being shown/said at a basic level.
More fascinating to me, though, is that this shift in focus has lead to a definite shift in my thinking. My thinking used to be almost hyperlinguistic. Words were my medium of choice, and I had a strong stream of inner linguistic thought running through my head. Now, that inner voice is mostly quiet. I also find that I tend to think about certain situations in terms of abstract "relationship pictures" rather than a descriptive sentence.
I actually kind of miss the old linguistic tendencies I had at times. I'm hoping a shift back into literature helps reestablish some of that.
And yeah, as with all general proclamations that sound nice because they allow us to seemingly boil complexities down to a singular thing, the whole "wiring is thinking" idea isn't true. The truth in that statement is more akin to "human thought is often tool assisted"—and a manner of tools can aid in elaborating thought. Thought and action are not as severed as we tend to think.
I knew a really great programmer. He was also a classical pianist (and unrelatedly an astronomer). Well anyway he wrote large entire programs with mostly two character variable names. He usually conceives entire programs in his head and would write them out using whatever symbols were still available. Most of the time, I would see him sitting and swaying in his office chair and maybe touching fingertips while looking around at the ceiling or walls. His title back in the 80s before such things became memes was Chief Scientist. He also couldn't care less that another person at the company would write books and take credit for his creations. (Maybe he saw the marketing value in something he had no interest in doing.) Oh and the programming language used didn't have variable scoping--all global. It's kind of like Tesla designing an A/C motor in his minds eye and drawing it out only for purpose of communication.
I would say that this is the intuitive, naive way of starting coding if no one has taught you coding or you haven't had to care about maintainability or other people reading your code.
"Keller would construct an analysis in the form of an analytic score written for the same forces as the work under consideration and structured as a succession of 'analytic interludes' designed to be played between its movements."[1]
On that note! I am an intensely verbal person, with words and narrative as my primary mode of thought. This essay and discussion reminds me of a desire I've felt before to develop the muscles, so to speak, of thinking without words.
Does anyone have any advice or techniques to that end?
Perhaps do activities like manipulating physical objects (carpentry?, Lego, Rubiks cube), games like Tetris, or complex body movements where verbalization won't be of much use. Or standard Quantitative Reasoning problems from entrance exams. A few years back, the wordcel vs shape rotator debate/binary was being discussed online: https://roonscape.ai/p/a-song-of-shapes-and-words?r=53sw
>> the moment when the solution to a problem emerges “in the shower” unexpectedly after a long period of unconscious incubation.
A lot of responses here seem to place this chain-of-thought on a spectrum between verbal and "vibe". I don't think that solving problems pre-verbally is actually at odds with verbal intelligence, or that a person must by definition be better at one than another. The pregnant, mathematical, nonverbal thought in the shower is only really useful if it can be organized and stated rationally at some point later. Likewise, the wordy explanation is useless without a well-reasoned theory it's explaining.
For me, I find that dreams help bridge this gap. Oftentimes I'll be struggling with a difficult mental model of a problem, and thinking of a lot of math in my head in the shower. But when I sleep, I'll have some dream that acts as a metaphor for the problem. Say, e.g. I'm thinking about how to time two independent processes to deconflict some data. I might have a dream about missing a flight because the plane already arrived but was announced at the wrong gate, and I'm running across the airport. Then I wake up and see the answer to the problem. Moreover, I then see how to explain the problem I just solved, using a metaphor that most people can understand.
As far as actually explaining it formally in writing, I usually test the code a zillion ways first and then write the documentation.
61 comments
[ 4.8 ms ] story [ 68.1 ms ] threadAlthough TFA doesn't refer to it by name, "insight" problem solving is when you are stuck on something and then suddenly realize the solution. The common explanation for being stuck is "fixation" on the wrong things. In agreement with TFA, there is indication that verbalization supports fixation more than visualization.
The essay might be more useful grounded with references to the sort of thing you link to.
https://www.quantamagazine.org/lean-computer-program-confirm...
I was with some friends that were in a band together, and we got thinking about this topic, and ended up arranging ourselves from least verbal to most verbal. I was on one end, where all of my thoughts appear as emotions or images; on the other end was our bassist, who experienced his thoughts as fully formed sentences. He said when he's getting to a difficult passage in a song the words "better focus here, don't mess up" will ring out in his head. He also said he has fully dictated mental conversations with himself.
I also read very quickly because I look at the shape of paragraphs and assemble the word-shapes into mental images and pick up meaning that way; high speed, but low comprehension. I struggle greatly to read philosophy because it's quite difficult to visualize. My wife reads slowly but hears every word in her head; her comprehension is much higher. I can do high comprehension reading by slowing down and looking at every word, but it feels like holding back an excitable dog.
Identifying and searching for morel mushrooms in the woods also feels largely nonverbal (although near a dying elm in late spring after a rain captures an essence of the idea, and those words provide a good starting point).
Coding ends in “words”, or at least some form of written language. But when I try to solve problems I do not think in words until it is time to put fingers to keyboard.
Words are useful (I could not convey this comment otherwise), but they’re not everything. It feels extremely difficult to convey my nonverbal thoughts through an inherently verbal medium like an HN comment. Perhaps to make a wordful analogy, the difficulty is like translating an idiom from one language to one of completely different context and origin.
I don’t deny that words do shape some of my thinking, but to me it’s just one part of the whole stream of conscious.
I’m curious if anyone else feels this way about words?
> If we can avoid the compression step, and do the manipulations directly in the high-dimensional, non-linguistic, conceptual space, we can move much faster
With my neurodivergent brain I've always conducted my thoughts in an "uncompressed format" and then eternally struggled to confine it all into words. Only then for people to misinterpret and question it. They might get caught up in the first sentence when the end of the paragraph is where you need to be!
That's why when you meet someone who thinks like you the depth of conversation and thinking you can achieve together is vast and also incredibly liberating! Your no longer limited by words in same way.
Since becoming ill I've suffered badly with brainfog. The cutesy name for a cruel experience. Sometimes there's no memories to draw on when your thinking, the cupboards are bare. You can't leap from thought to thought because they disappear before you get there or after like a cursed platformer. You might be able to grab hold of the thought but you can't reach inside or read it. It's all wrong somehow like when your suddenly convinced a word is spelt wrong even though you know it's right. You can't maintain focus long enough to finish your train of thought.
Even that subconscious processing is affected I used to prime my brain with information all day and instead of waking up with the solution I'll wake up frustrated but not knowing why. Just the vague notion that I failed at something that used to come so easily.
But what I do not get is how you would convey these thoughts to someone else that thinks the same way as you, seeing as these thoughts don’t neccesarily seem to be contained to words or sentences.
When i talk with someone very aligned with my thinking and knowledge (fellow it collegues/friends with simiiliar skill level) we do not a lot of words to be aligned and convey complex thoughts.
We reference and use words which we both know, we read and reference similiar news stories etc.
But the way they describe it with colors, vibrations etc. is probably somethig you can't just convey.
insight often lives in the ability to skip a b c d, then post processing is to allow mortals to understand
sometimes my verbal skills fail me and the steps are missing
this is why i disagree that if you can’t write it, you don’t know it
in another words, i may know the note to sing but not have the voice to sing it
This resonates so much with me. To a point where I don't write/contribute in public forums out of fear for this misinterpretation.
Strangely, your post has made me push through that exact fear to write this, so any perceived misinterpretation has positively impacted at least one stranger. This is a good reminder for me that focusing only on negative consequences misses the unintended positive ones of still putting something out there, even if its not a perfect representation of the "uncompressed format".
Thank you for sharing, and I wish you a speedy recovery.
One pattern is that I'm a very prolific connection-forming machine.
Exhibit A: The first thing that enters my mind for each word. (OnePlus One) (android pattern unlock) (Islamic State) (unit vector named t) (ich bin) (emoji-blood-type-A) (Latin etymology word root with verily) (https://prolificusa.com/) (New York Times Connections) (roll-forming, blow moulding, sheet metal stamping...) ("my body is a machine" meme)
She had assumed that all people think in this mode. I had assumed that all people think in "thoughts" and went through a separate step to articulate them.
Made both of us aware of a difference in people.
I don't feel vibrations or sensations though, and I definitely don't think in images. I only have a thought level, and it's very independent of any external presentation.
Around 2020, I decided to try to learn as much as I could about "higher" mathematics in earnest, having basically no background in the subject. Five years later, I have finally read and suffered enough to be able to pick up texts in any of the abstract branches of mathematics and at least understand most of what's being shown/said at a basic level.
More fascinating to me, though, is that this shift in focus has lead to a definite shift in my thinking. My thinking used to be almost hyperlinguistic. Words were my medium of choice, and I had a strong stream of inner linguistic thought running through my head. Now, that inner voice is mostly quiet. I also find that I tend to think about certain situations in terms of abstract "relationship pictures" rather than a descriptive sentence.
I actually kind of miss the old linguistic tendencies I had at times. I'm hoping a shift back into literature helps reestablish some of that.
And yeah, as with all general proclamations that sound nice because they allow us to seemingly boil complexities down to a singular thing, the whole "wiring is thinking" idea isn't true. The truth in that statement is more akin to "human thought is often tool assisted"—and a manner of tools can aid in elaborating thought. Thought and action are not as severed as we tend to think.
[0] https://news.ycombinator.com/item?id=45800777
Does this suggest most people think in words? Really?
"Keller would construct an analysis in the form of an analytic score written for the same forces as the work under consideration and structured as a succession of 'analytic interludes' designed to be played between its movements."[1]
[1] https://www.artandpopularculture.com/Wordless_functional_ana...
Does anyone have any advice or techniques to that end?
I'd come across this book "Visual Thinking in Mathematics" (https://www.amazon.in/Visual-Thinking-Mathematics-Marcus-Gia...) which goes into some of this.
A lot of responses here seem to place this chain-of-thought on a spectrum between verbal and "vibe". I don't think that solving problems pre-verbally is actually at odds with verbal intelligence, or that a person must by definition be better at one than another. The pregnant, mathematical, nonverbal thought in the shower is only really useful if it can be organized and stated rationally at some point later. Likewise, the wordy explanation is useless without a well-reasoned theory it's explaining.
For me, I find that dreams help bridge this gap. Oftentimes I'll be struggling with a difficult mental model of a problem, and thinking of a lot of math in my head in the shower. But when I sleep, I'll have some dream that acts as a metaphor for the problem. Say, e.g. I'm thinking about how to time two independent processes to deconflict some data. I might have a dream about missing a flight because the plane already arrived but was announced at the wrong gate, and I'm running across the airport. Then I wake up and see the answer to the problem. Moreover, I then see how to explain the problem I just solved, using a metaphor that most people can understand.
As far as actually explaining it formally in writing, I usually test the code a zillion ways first and then write the documentation.
A name that can be named is not The Name
Tao is both Named and Nameless As Nameless, it is the origin of all things As Named, it is the mother of all things
A mind free of thought, merged within itself, beholds the essence of Tao
A mind filled with thought, identified with its own perceptions, beholds the mere forms of this world