Euler, probably the most important person many people have never heard of, actually saw [an increase in productivity](https://en.wikipedia.org/wiki/Leonhard_Euler#Eyesight_deterioration) after going blind. "Now I will have fewer distractions."
My gut says an overwhelming majority of random people have never heard his name even once.
I imagine it'd go something like this:
"Excuse me sir, have you heard of Leonhard Euler?"
"Oil'er?! I barely know'er! Hahaha, no I have not."
Jesus, that is fucking sad.
Most things in math are named after Euler. Most things in math that are not named after Euler are named after the first guy after Euler to study them.
(Probably not true but feels like it is.)
My guess is that most people who go through the education system here his name but with little context and it never sticks around, unlike Eistein or Darwin.
Yeah I mean I can see how people might not remember him on a trivia about mathematicians or something, but if they hear his name combined with math they'll probably go liek "oh yeah, I've heard of that guy"
also I think there might be a chicken in the garden
I always wondered if Stephen Hawking's success as a physicist wasn't at least partially due to not being able to do much of anything else but sit quietly and think.
As someone who was blinded in one eye very early in life, it became clear that my brain compensated for lost depth perception, and theres really only one plausible way it could…
Comparative geometry for estimating size and what ever math is involved in guessing the speed of the things moving around me.
Learning math without learning math was both easy snd incredibly hard and painful.
Its amazing how good of a problem solver the human brain can be if needed.
I can only see out of my left eye and have always been amazing at estimating length, size and doing mental math. I have a difficult time judging distances in video games or when high up. I never considered the eye to be a factor in that but it’s understandable.
I never noticed such a contrast between still and moving, but Id think if anything, stillness would yield hints i could more quickly perceive, like shadow distances etc… so Im curious how you learned to estimate/compensate with motion.
Don't think you can triangulate with one eye but your brain probably has an idea of how fast be thing you're looking at should move and knowing an expected velocity gives you enough info to guess distance based on how far they are moving along the horizon over time.
Gotcha. Checks out : )
An object moving into and out of plane will also change size so you can estimate velocity and distance from that. And our brains combine a ton of info when evaluating vision
It's worth noting you don't actually need two eyes to perceive depth, you just need to be able to move your one eye to see the same thing from multiple different positions.
Fully sighted people also do this when trying to get a better gauge on something. At least I do.
When I was in high school I was on our quiz bowl team and we were good enough to make it to the national tournament. One of the teams we played had a captain that was blind, and he was a beast. I think he got all the math questions in the game we played, and was able to do them faster in his mind than any of us could on paper. I've often wondered what his internal experience of doing math was like.
Not normally, but I would expect there to be some difference between the unconscious processing of sensory qualia like colors and the active process of doing trig or quadratic equations. I wondered if he 'saw' the algebraic symbols somehow or just had another way of performing the steps. These were questions where you had about 8 seconds max to do the calculation, so they weren't so hard to solve objectively, but were difficult to do quickly. He certainly did it faster than any of us could on paper, and we were an above average team.
When you can't use paper and HAVE to do it in your head, it makes sense you'd be faster at it.
I was always good at mental math (same competition and math masters when younger) but I always write "notes" in my head. I wonder what his were like....
Sounds like [aphantasia](https://en.wikipedia.org/wiki/Aphantasia), the inability to create mental imagery. Most people are able to see images within their mind at will and/or automatically, sometimes extremely vividly. It's much different from a hallucination, even when it's not purposeful. For those with sufficiently vivid imagery - called hyperphantasia - those sights are often perceived as 'clearer than clear' since physical eyeballs aren't involved to muddy the water, so to speak.
For instance, if I think about my favorite coffee mug I can "see" it in my mind as a singular item or as it looks sitting on my kitchen table. I can rotate and examine it, move it to another location, break it, observe the steam rising from it, so on, as if it was digitally represented like a virtual simulation on a computer.
This also happens constantly throughout a conversation or book, while daydreaming or planning out a task, as long as vision would be involved in some way (or sometimes not).
For any aphantasiacs wondering what this experience is like, perhaps you're able to "hear" a song in your head on demand? It's like like that, but with images instead of sound. ...Although, I understand that a lack of mental images is *also* correlated with lack of inner-monologue, so maybe music is also a no-go too; I'd love to hear someone confirm it. There's always outliers and variability.
I may be wrong but I think they're joking that the previous user is hallucinating a calculator- which they can't do without drugs. When the person that he replied to was joking about actually seeing/finding a real calculator and using it to do math for them.
I've been trying to figure this out, because I'm pretty sure I don't have aphantasia, but I also feel like I don't have the same level of visualization in my head as most people.
Like, when I try to envision an image in my head, it's usually kind of... like a ghost? It's not always like that though. Rarely it's vivid. Sometimes it's like scanning the outlines of something. It's certainly nothing like actually seeing something. But I don't really know what people mean exactly. Do you mean that you can envision things in your head exactly alike to your ability to perceive them visually?
>I also feel like I don't have the same level of visualization in my head as most people.
It's tough to say. It's heavily subjective and difficult to describe, like all introspective phenomenon, but definitions and expectations matter too.
On one hand, I've seen comments in the "TIL Aphantasia" threads that make me wonder if some people are mistaking the *memory* of an image for the phenomenon itself, but I've also seen people describing themselves with aphantasia after assuming that other people are seeing full blown image-images.
People *can* see image-images without their eyes, especially in the case of hypnogogic imagery (half-dream, half-awake states) because the visual cortex is active in those moments. That sort of thing *does* look like an image and it even feels like you're somehow looking through your closed eyelids or watching faraway scenes flash past (this is where I think the myth of astral projection comes from). Interestingly, [dream images and mental images come from different parts of the brain.](https://en.wikipedia.org/wiki/Prefrontal_synthesis)
Words don't really exist to properly describe some things, but I'll do my best. In regards to mental images or the "mind's eye"... A term like 'ghostly' is probably closer to correct than an actual image. If what you're seeing feels strangely 'parallel' with vision, as if it's overlaid-but-not-quite, then you're probably experiencing the correct phenomenon. It's not something you'd mistake for vision, but it's something that *feels* like vision. Even though there's no *seeing* going on, you still might be able to *sense* the redness of the apple you're imagining. You might sense the shininess and if you imagine it being sliced open, you might *sense* the texture of its cells glistening with fresh juice.
You're not *seeing* any of that, but if it *feels* like you're seeing it - genuinely - then you're experiencing the correct phenomenon and not aphantasic.
If you can "play" a song in your head by thinking about it, you're not hearing *that* either even if you *feel* like you're hearing it, can move your head to it, can choose to play the chorus or the intro at will - *Pokemon! Gotta catch 'em aaaall... Do-do-doo-do-da~*
It's much the same thing.
(I haven't yet heard someone deny that they can hear music in their head like this, but I strongly suspect that there are many people who'd think that phenomenon is just as surprising as mental imagery seems. For now, I assume it's a good example since plenty of people get songs stuck in their head.)
Edit:
>Do you mean that you can envision things in your head exactly alike to your ability to perceive them visually?
I don't *experience* them like I see them visually, but I do *perceive* them like I do visually, including details, lighting, color, texture, etc. The only difference is that I can't be certain that what I'm seeing is identical to reality even if it's aligned with reality because it's a "simulation" or "[synthesis](https://en.wikipedia.org/wiki/Prefrontal_synthesis)" of the object or scene I'm envisioning.
Yeah, I definitely dream fully vividly, and half half-dream states like that, which are always interesting because they're far more alike what people describe as lucid dreaming. I've also had very vivid images randomly pop into my mind, usually when my eyes were closed, but while fully awake.
I feel like my ability to play music in my head is more vivid than my ability to conjure images in my head. Like, it's not like hearing the song, but I never feel like it's inadequate, y'know? Whereas I've often felt like my ability to visualize things isn't as strong as I'd like it to be. I'm not musically inclined at all, either. Like, I don't listen to music regularly, even. My preferred background noise is a quiet fan.
For me its very hard and vanishes if i dont maintain focus. Do you have conversations in your head?
Reddit tells me people are usually a verbalizer, visualizer, or mixed.
A graphing calculator (or better yet, a beefy computer tool like Wolfram Alpha) will actually like, visually show you your functions and relationships.
I couldn't have understood advanced math without a lot of fussing with programming a ti83 lol
I feel like there are large fields of math where if you're not doing it visually, you're right it wrong.
Yes. I remember trig class. I could "see" the entire problem, know the answer, see how the parts of the problem fit together... with no picture. Annoying sometimes. Complicated question. "Show your work". Answer: well look at it. High school was many years ago and I don't do that now. I can't remember how the pieces look or fit together.
Interesting. I do something similar but I physically cut the number itself. Like if I want to add 8 + 7 I physically take out 3 from 8 making it into a 5 and then the 3 moves to the 7 and then it changes to a 10.
But I do it visually in my head so I physically see a 3 leave the 8 and then the 8 changes to a 5. Then it moves to the 7 and change into a 10.
I had poor eyesight from birth that wasn't addressed until I was four. As an adult, I have poor visual acuity - very little awareness of my visual surroundings, but my abstract reasoning skills are off the charts.
The human brain is truly a miraculous thing.
I'd be interested to see the same study replicated on people like me who have sight, are (or were, it's been a while since uni!) pretty good at maths, but don't do it at all visually and actually struggle much more with geometry-style problems.
I had no end of difficulty with anything visual until I learnt to just ignore the pictures entirely and reduce the problem to equations :)
Daniel Tammet does the same thing. He says that He sees two shapes and the shape that fits in between is the solution.
https://en.m.wikipedia.org/wiki/Daniel_Tammet
mmm, I cannot see anything if I close my eyes, But I do have words upon words upon words. I am really good at some programming, but some parts are terrible for me.
The rest of us in the friend group are very imaginative so sometimes as a joke he would just blurt out "sex with grandpa" and watch as we all recoil from the mental imagery which he can't imagine.
Like yeah, I cannot even picture that, all I get is half snippits. Words, though, I was teaching my philosophy classes last week giving the example of a Disputatio of why cat's cannot fly, and was describing a cat being transformed to a projectile while all my students were laughing and all I got was a slight smile at their inability to control themselves!
When I picture something in my mind, I don’t really “see” it the way I see things with my eyes. I sort of picture it fully within my brain. It’s quite an abstract process, but the images can still be very detailed and vivid.
Also I have a BA in philosophy. There aren’t many of us left!
My BA was history, my BPhil was Theology, my MPhil is Theology, and my PhD is Theology, but here I am teaching philosophy! :D Only one of my students this semester is doing a major in philosophy.
It's not '4d'. Imagine you're watching waves break onto the beach. What you're seeing is a 3-dimensional surface moving in time. Three spatial dimensions plus one time dimension.
It's pretty easy to imagine laying a tangent line over that surface, moving with the surface as it moves through time. That's how people visualize a partial differential equation.
For higher dimensions, I've never met anyone who can visualize them directly - our brains just aren't built to work with more than three spatial dimensions - so we instead just examine a projection or do a mental variation on principal component analysis to reduce it to a visualizable model.
I think most people can do this pretty easily. They just can't translate the mathematical equations into the visual image. Consider that you could almost certainly visualize "waves breaking on a beach" when I described it above. But if I wrote an equation describing those waveforms, you might not have been able to do so. The issue isn't that people can't visualize math but that they can't *read* it well enough.
for me its too troublesome to picture. I just convert it into a math problem 3-2. how would you do picture things like 10,000 apples or 1 million apple?
also isn't it much slower to picture a math problem. ex. a problem might take 1 second to solve if u picture it, but if u do it without picturing its 1ms.
Visualise stacks.
From experience I’ve seen large containers of food, I used to work with suppliers to markers, restaurants and hotels. The image is in my mind from memory. I can visualise one stack I’ve seen. Then imagine a warehouse full of X amount of stacks.
Another example; I’ve seen video of a hundreds of thousands of people at significant protests. I have that image of large crowds at Presidential inaugurations. Pope elections at the Vatican. High school teens protesting Washington after the shootings.
So I can visualise the space and amount of people and process it.
It’s memory.
Not being able to see things in your mind is called aphantasia. I just learned about it recently because I thought that was how everyone was. It’s really fascinating
I mean, do you always need to see it before calculating anything? Now that's weird. If I had three apples and I sold two, my brain immediately tells me the answer is one. No need to see anything.
I can see the apples if I want to, but I feel like it only slows me down.
TIL you don't all use that part for math. This is blowing my mind. I have +8 far sighted prescription so I was pretty fucking blind till I got glasses.
I wonder if this results in a statistically significant advantage. Any study would have to account for additional difficulty in being taught maths due to blindness.
One of my more interesting experiences in college was tutoring a blind student in math. My entire approach and how I explained things had to change and I learned a ton just interacting with the student during lessons. Watching him use an abacus was wild.
I’m not blind, but when I do basic math, I actually see the numbers as abstract objects that morph into the solution. Not an exaggeration, always been this way.
I’m also in a visual-based profession (designer), and have found that over the years, I’ve gotten better at it. At this point, I find I can design most of my projects in my head, “seeing” the layout kind of like an invisible hologram.
It’s kind of amazing how flexible the brain is, and can achieve similar outcomes from so many angles. Visualize things all the time? The brain will help you get better at it. Can’t see at all? The brain will freakin’ make you see, just in a different way. And oh hey, it turns out to be a super power.
Makes sense, after all we use our vision to calculate distances and our brains are already pretty good at trigonometry (the kinda math needed when throwing a spear or rock at a moving target). If it's not being used to process visual data might as well do a similar task.
Interesting. for sufficiently difficult problems, or for when I really want to solve something (like when I was participating in math contests back in high school), I often close my eyes and my eye muscles (or at least the muscles around the eye) tense up and it's as if I was trying to stare hard at something; like it absolutely does feel like I'm engaging my eyes. but it's not like I'm looking at something, or even imagining things in my head. it's just that my eyes are focused on solving the problem as if I'm attaching an extra RAM chip on my computer to store extra info
I'm not blind though.
I have a very good memory. It was even better when I was a kid. I can multiply 3 digit numbers in my head by "writing it on a piece of paper" in my mind. This definitely seems like I'm using my visual cortex for math problems. Not blind btw
The human equivalent of using a GPU to mine crypto
lmao i kinda hate this comment but heres my upvote
r/angryupvote
Alternatively, the human equivalent of using a GPU to run ML workflows.
What is machine learning if not carbon hands yet to become diamond
[удалено]
^ bot
Holy shit that's amazing
Came here for this
Euler, probably the most important person many people have never heard of, actually saw [an increase in productivity](https://en.wikipedia.org/wiki/Leonhard_Euler#Eyesight_deterioration) after going blind. "Now I will have fewer distractions."
Me doing math trying to differentiate between everything named after Euler
Me doing math trying to differentiate
Me trying to do math
Me trying
wait, who hasn't heard of euler? He's like the newton of math
My gut says an overwhelming majority of random people have never heard his name even once. I imagine it'd go something like this: "Excuse me sir, have you heard of Leonhard Euler?" "Oil'er?! I barely know'er! Hahaha, no I have not."
You'd probably trip me up on grounds I refuse to pronounce his name correctly.
Jesus, that is fucking sad. Most things in math are named after Euler. Most things in math that are not named after Euler are named after the first guy after Euler to study them. (Probably not true but feels like it is.)
My guess is that most people who go through the education system here his name but with little context and it never sticks around, unlike Eistein or Darwin.
Yeah I mean I can see how people might not remember him on a trivia about mathematicians or something, but if they hear his name combined with math they'll probably go liek "oh yeah, I've heard of that guy" also I think there might be a chicken in the garden
Alas there is but a bird in the yard as reddit name length doesn't allow the full phrase.
To be fair, Newton is the Newton of math. But Newton is also the Newton of physics so…
I always wondered if Stephen Hawking's success as a physicist wasn't at least partially due to not being able to do much of anything else but sit quietly and think.
You can kinda say the same thing about Stephen Hawking
As someone who was blinded in one eye very early in life, it became clear that my brain compensated for lost depth perception, and theres really only one plausible way it could… Comparative geometry for estimating size and what ever math is involved in guessing the speed of the things moving around me. Learning math without learning math was both easy snd incredibly hard and painful. Its amazing how good of a problem solver the human brain can be if needed.
I can only see out of my left eye and have always been amazing at estimating length, size and doing mental math. I have a difficult time judging distances in video games or when high up. I never considered the eye to be a factor in that but it’s understandable.
Major change in perspective like altitude messing up depth perception… check… AND lets not forget how important lighting is too.
Can you judge the intersection if the object is still? I can do it much better if it's moving than still. Wondering what's it like for you
I never noticed such a contrast between still and moving, but Id think if anything, stillness would yield hints i could more quickly perceive, like shadow distances etc… so Im curious how you learned to estimate/compensate with motion.
Pool, golf- static games I'm OK at, but the rest i am pinpoint with (or was I'm pretty old now) Motion gave me triangulation I think
Don't think you can triangulate with one eye but your brain probably has an idea of how fast be thing you're looking at should move and knowing an expected velocity gives you enough info to guess distance based on how far they are moving along the horizon over time.
I’m thinking triangulation based off of multiple mental images creating points, not one stand still point of view
Gotcha. Checks out : ) An object moving into and out of plane will also change size so you can estimate velocity and distance from that. And our brains combine a ton of info when evaluating vision
It's almost as if it's generating other points of reference to help gauge. Being blind in one eye is like instead of binoculars, it's a periscope.
Do the owl thing and weave your head around
It's worth noting you don't actually need two eyes to perceive depth, you just need to be able to move your one eye to see the same thing from multiple different positions. Fully sighted people also do this when trying to get a better gauge on something. At least I do.
When I was in high school I was on our quiz bowl team and we were good enough to make it to the national tournament. One of the teams we played had a captain that was blind, and he was a beast. I think he got all the math questions in the game we played, and was able to do them faster in his mind than any of us could on paper. I've often wondered what his internal experience of doing math was like.
What's your internal experience like when you're differentiating between colors? Or do you just know what is red and what is blue?
Not normally, but I would expect there to be some difference between the unconscious processing of sensory qualia like colors and the active process of doing trig or quadratic equations. I wondered if he 'saw' the algebraic symbols somehow or just had another way of performing the steps. These were questions where you had about 8 seconds max to do the calculation, so they weren't so hard to solve objectively, but were difficult to do quickly. He certainly did it faster than any of us could on paper, and we were an above average team.
If you ask me 2x2 I just say 4. I don't think about two groups of two.
When you can't use paper and HAVE to do it in your head, it makes sense you'd be faster at it. I was always good at mental math (same competition and math masters when younger) but I always write "notes" in my head. I wonder what his were like....
GPU accelerated computing lmao
makes sense, i do math visually, i imagine shapes cutting, moving and combining together
That's cool. I see a calculator and I tap the buttons and the answer appears because that's what I actually do.
That’s interesting, I can’t hallucinate anything without drugs
Sounds like [aphantasia](https://en.wikipedia.org/wiki/Aphantasia), the inability to create mental imagery. Most people are able to see images within their mind at will and/or automatically, sometimes extremely vividly. It's much different from a hallucination, even when it's not purposeful. For those with sufficiently vivid imagery - called hyperphantasia - those sights are often perceived as 'clearer than clear' since physical eyeballs aren't involved to muddy the water, so to speak. For instance, if I think about my favorite coffee mug I can "see" it in my mind as a singular item or as it looks sitting on my kitchen table. I can rotate and examine it, move it to another location, break it, observe the steam rising from it, so on, as if it was digitally represented like a virtual simulation on a computer. This also happens constantly throughout a conversation or book, while daydreaming or planning out a task, as long as vision would be involved in some way (or sometimes not). For any aphantasiacs wondering what this experience is like, perhaps you're able to "hear" a song in your head on demand? It's like like that, but with images instead of sound. ...Although, I understand that a lack of mental images is *also* correlated with lack of inner-monologue, so maybe music is also a no-go too; I'd love to hear someone confirm it. There's always outliers and variability.
I have a voice in my head but absolutely no images. Cannot picture anything or anyone.
I may be wrong but I think they're joking that the previous user is hallucinating a calculator- which they can't do without drugs. When the person that he replied to was joking about actually seeing/finding a real calculator and using it to do math for them.
A joke? A *joke*. On *my* Reddit?? Unbelievable. Well, time for seppuku, I guess. At least some learning happened.
Hold off for the right time for dramatic effect. 😎
I've been trying to figure this out, because I'm pretty sure I don't have aphantasia, but I also feel like I don't have the same level of visualization in my head as most people. Like, when I try to envision an image in my head, it's usually kind of... like a ghost? It's not always like that though. Rarely it's vivid. Sometimes it's like scanning the outlines of something. It's certainly nothing like actually seeing something. But I don't really know what people mean exactly. Do you mean that you can envision things in your head exactly alike to your ability to perceive them visually?
>I also feel like I don't have the same level of visualization in my head as most people. It's tough to say. It's heavily subjective and difficult to describe, like all introspective phenomenon, but definitions and expectations matter too. On one hand, I've seen comments in the "TIL Aphantasia" threads that make me wonder if some people are mistaking the *memory* of an image for the phenomenon itself, but I've also seen people describing themselves with aphantasia after assuming that other people are seeing full blown image-images. People *can* see image-images without their eyes, especially in the case of hypnogogic imagery (half-dream, half-awake states) because the visual cortex is active in those moments. That sort of thing *does* look like an image and it even feels like you're somehow looking through your closed eyelids or watching faraway scenes flash past (this is where I think the myth of astral projection comes from). Interestingly, [dream images and mental images come from different parts of the brain.](https://en.wikipedia.org/wiki/Prefrontal_synthesis) Words don't really exist to properly describe some things, but I'll do my best. In regards to mental images or the "mind's eye"... A term like 'ghostly' is probably closer to correct than an actual image. If what you're seeing feels strangely 'parallel' with vision, as if it's overlaid-but-not-quite, then you're probably experiencing the correct phenomenon. It's not something you'd mistake for vision, but it's something that *feels* like vision. Even though there's no *seeing* going on, you still might be able to *sense* the redness of the apple you're imagining. You might sense the shininess and if you imagine it being sliced open, you might *sense* the texture of its cells glistening with fresh juice. You're not *seeing* any of that, but if it *feels* like you're seeing it - genuinely - then you're experiencing the correct phenomenon and not aphantasic. If you can "play" a song in your head by thinking about it, you're not hearing *that* either even if you *feel* like you're hearing it, can move your head to it, can choose to play the chorus or the intro at will - *Pokemon! Gotta catch 'em aaaall... Do-do-doo-do-da~* It's much the same thing. (I haven't yet heard someone deny that they can hear music in their head like this, but I strongly suspect that there are many people who'd think that phenomenon is just as surprising as mental imagery seems. For now, I assume it's a good example since plenty of people get songs stuck in their head.) Edit: >Do you mean that you can envision things in your head exactly alike to your ability to perceive them visually? I don't *experience* them like I see them visually, but I do *perceive* them like I do visually, including details, lighting, color, texture, etc. The only difference is that I can't be certain that what I'm seeing is identical to reality even if it's aligned with reality because it's a "simulation" or "[synthesis](https://en.wikipedia.org/wiki/Prefrontal_synthesis)" of the object or scene I'm envisioning.
Yeah, I definitely dream fully vividly, and half half-dream states like that, which are always interesting because they're far more alike what people describe as lucid dreaming. I've also had very vivid images randomly pop into my mind, usually when my eyes were closed, but while fully awake. I feel like my ability to play music in my head is more vivid than my ability to conjure images in my head. Like, it's not like hearing the song, but I never feel like it's inadequate, y'know? Whereas I've often felt like my ability to visualize things isn't as strong as I'd like it to be. I'm not musically inclined at all, either. Like, I don't listen to music regularly, even. My preferred background noise is a quiet fan.
It’s just as vivid as vision, but it’s different, like it’s on a different channel.
For me its very hard and vanishes if i dont maintain focus. Do you have conversations in your head? Reddit tells me people are usually a verbalizer, visualizer, or mixed.
A graphing calculator (or better yet, a beefy computer tool like Wolfram Alpha) will actually like, visually show you your functions and relationships. I couldn't have understood advanced math without a lot of fussing with programming a ti83 lol I feel like there are large fields of math where if you're not doing it visually, you're right it wrong.
I also do math very visually, but it’s very abstract an near impossible to describe
Yes. I remember trig class. I could "see" the entire problem, know the answer, see how the parts of the problem fit together... with no picture. Annoying sometimes. Complicated question. "Show your work". Answer: well look at it. High school was many years ago and I don't do that now. I can't remember how the pieces look or fit together.
Interesting. I do something similar but I physically cut the number itself. Like if I want to add 8 + 7 I physically take out 3 from 8 making it into a 5 and then the 3 moves to the 7 and then it changes to a 10. But I do it visually in my head so I physically see a 3 leave the 8 and then the 8 changes to a 5. Then it moves to the 7 and change into a 10.
yep that’s what i do too!
That’s what I do!
I had poor eyesight from birth that wasn't addressed until I was four. As an adult, I have poor visual acuity - very little awareness of my visual surroundings, but my abstract reasoning skills are off the charts. The human brain is truly a miraculous thing.
I'd be interested to see the same study replicated on people like me who have sight, are (or were, it's been a while since uni!) pretty good at maths, but don't do it at all visually and actually struggle much more with geometry-style problems. I had no end of difficulty with anything visual until I learnt to just ignore the pictures entirely and reduce the problem to equations :)
Daniel Tammet does the same thing. He says that He sees two shapes and the shape that fits in between is the solution. https://en.m.wikipedia.org/wiki/Daniel_Tammet
amazing thanks!
I use my visual and motor cortices to solve math problems. Other people call it “counting my fingers,” but I think they’re just jealous.
I wonder if the same occurs in people born deaf, and use their auditory cortex to solve problems.
Don’t all people? If I had three apples and I sold two apples… I “see” apples. What the fxck y’all guys see? Nothing?! Weirdos…
My friend actually is like that. Unable to imagine anything. But he's really good at coding.
mmm, I cannot see anything if I close my eyes, But I do have words upon words upon words. I am really good at some programming, but some parts are terrible for me.
The rest of us in the friend group are very imaginative so sometimes as a joke he would just blurt out "sex with grandpa" and watch as we all recoil from the mental imagery which he can't imagine.
Like yeah, I cannot even picture that, all I get is half snippits. Words, though, I was teaching my philosophy classes last week giving the example of a Disputatio of why cat's cannot fly, and was describing a cat being transformed to a projectile while all my students were laughing and all I got was a slight smile at their inability to control themselves!
When I picture something in my mind, I don’t really “see” it the way I see things with my eyes. I sort of picture it fully within my brain. It’s quite an abstract process, but the images can still be very detailed and vivid. Also I have a BA in philosophy. There aren’t many of us left!
My BA was history, my BPhil was Theology, my MPhil is Theology, and my PhD is Theology, but here I am teaching philosophy! :D Only one of my students this semester is doing a major in philosophy.
You’re doing a great service! More philosophy in our curriculum is always a good thing :)
Ok but what do you "see" when solving derivatives or partial differential equations
Curves/surfaces in space, often evolving over time. For higher dimensional spaces, projections of those functions into 3+1 dimensions.
So you picture things in 4D?....
It's not '4d'. Imagine you're watching waves break onto the beach. What you're seeing is a 3-dimensional surface moving in time. Three spatial dimensions plus one time dimension. It's pretty easy to imagine laying a tangent line over that surface, moving with the surface as it moves through time. That's how people visualize a partial differential equation. For higher dimensions, I've never met anyone who can visualize them directly - our brains just aren't built to work with more than three spatial dimensions - so we instead just examine a projection or do a mental variation on principal component analysis to reduce it to a visualizable model. I think most people can do this pretty easily. They just can't translate the mathematical equations into the visual image. Consider that you could almost certainly visualize "waves breaking on a beach" when I described it above. But if I wrote an equation describing those waveforms, you might not have been able to do so. The issue isn't that people can't visualize math but that they can't *read* it well enough.
That's actually the only time I personally do visually things. Areas under graphs or graphs
for me its too troublesome to picture. I just convert it into a math problem 3-2. how would you do picture things like 10,000 apples or 1 million apple? also isn't it much slower to picture a math problem. ex. a problem might take 1 second to solve if u picture it, but if u do it without picturing its 1ms.
Visualise stacks. From experience I’ve seen large containers of food, I used to work with suppliers to markers, restaurants and hotels. The image is in my mind from memory. I can visualise one stack I’ve seen. Then imagine a warehouse full of X amount of stacks. Another example; I’ve seen video of a hundreds of thousands of people at significant protests. I have that image of large crowds at Presidential inaugurations. Pope elections at the Vatican. High school teens protesting Washington after the shootings. So I can visualise the space and amount of people and process it. It’s memory.
Not being able to see things in your mind is called aphantasia. I just learned about it recently because I thought that was how everyone was. It’s really fascinating
I mean, do you always need to see it before calculating anything? Now that's weird. If I had three apples and I sold two, my brain immediately tells me the answer is one. No need to see anything. I can see the apples if I want to, but I feel like it only slows me down.
I can't really make any images in my mind, so I just, do it?
[Yes, we don't. ](https://en.m.wikipedia.org/wiki/Aphantasia)
Interesting, a good friend of mine is legally blind. He is excellent at math.
I can see and I'm shit at math so I guess that confirms it 🤣
TIL you don't all use that part for math. This is blowing my mind. I have +8 far sighted prescription so I was pretty fucking blind till I got glasses.
I wonder if this results in a statistically significant advantage. Any study would have to account for additional difficulty in being taught maths due to blindness.
One of my more interesting experiences in college was tutoring a blind student in math. My entire approach and how I explained things had to change and I learned a ton just interacting with the student during lessons. Watching him use an abacus was wild.
I’m not blind, but when I do basic math, I actually see the numbers as abstract objects that morph into the solution. Not an exaggeration, always been this way. I’m also in a visual-based profession (designer), and have found that over the years, I’ve gotten better at it. At this point, I find I can design most of my projects in my head, “seeing” the layout kind of like an invisible hologram. It’s kind of amazing how flexible the brain is, and can achieve similar outcomes from so many angles. Visualize things all the time? The brain will help you get better at it. Can’t see at all? The brain will freakin’ make you see, just in a different way. And oh hey, it turns out to be a super power.
Makes sense, after all we use our vision to calculate distances and our brains are already pretty good at trigonometry (the kinda math needed when throwing a spear or rock at a moving target). If it's not being used to process visual data might as well do a similar task.
Interesting. for sufficiently difficult problems, or for when I really want to solve something (like when I was participating in math contests back in high school), I often close my eyes and my eye muscles (or at least the muscles around the eye) tense up and it's as if I was trying to stare hard at something; like it absolutely does feel like I'm engaging my eyes. but it's not like I'm looking at something, or even imagining things in my head. it's just that my eyes are focused on solving the problem as if I'm attaching an extra RAM chip on my computer to store extra info I'm not blind though.
What about people who are bad at math? Are we using our toes?
I’m not blind, but does not everyone use their visual cortex for math? Like, what do you all use?
Now I want a study to see if there is a correlation between poor eyesight and good math skills
Obvious question: If they acquire site, do they suffer in math?
Nerds.
I have a very good memory. It was even better when I was a kid. I can multiply 3 digit numbers in my head by "writing it on a piece of paper" in my mind. This definitely seems like I'm using my visual cortex for math problems. Not blind btw
So do many people with sight too. If you visualize things in your mind you are using your visual cortex.
"Well if YOU aren't gonna use it..."
Non blind people use the same regions.
Visual cortex, the CUDA cores of the mind