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Is it really that hard for a blind person to intuit geometry? I would have figured one does not require working eyes to understand space.

by Zecc 11y ago

chris_wot 11y ago
I'm genuinely curious how you would think of three dimensional objects without ever being able to see them... I guess you would have to describe them. As a suggestion - and not an attack in any way because I'm not sure how I'd do it! - without reference to anything you can see with your eyes, how would you describe space?
- gchpaco 11y ago
  As a counterpoint it's routine in topological mathematics to work with 8 or 12 or 11 dimensional objects.
  - chris_wot 11y ago
    Good point! But is this done without any reference to 3 dimensional objects, or does it take the principle and not make any assumptions, or describe it in such a way that the concept is explained without any aspects related to sight? Genuinely curious...
    - gchpaco 11y ago
      It is ... difficult for me to describe just how dangerous it is to try to use 3 dimensional intuitions in a higher dimensional space. As the number of dimensions increases the amount of "space" there is for things to get weird get much more complicated; for example any knot that exists in 3 dimensions can be untied trivially in a 4 dimensional space. Suffice to say if you try to use your ordinary everyday life intuitions doing higher dimensional mathematics you will continuously embarrass yourself until you learn not to. Some folks develop the necessary adjustments and have higher dimensional intuitions; I do not and have to do the math anywhere higher than around 4.
- chestervonwinch 11y ago
  You could take a linear algebra approach and explain dimension as the number of possible independent directions of movement. This could be experienced through touch. Start with a pencil, then a piece of paper, then 3-space, and so on.
- andrewchambers 11y ago
  well, you can feel depth and surfaces with your hands, i don't think that is a problem.
- e12e 11y ago
  What? How would you think of three dimensional objects without ever being able to feel them? (I say as a someone that's got reasonable vision, but surely sound and especially touch is much better at spatial positioning that mere faulty "stereoscopic" vision -- there's a reason why you might want to practice martial arts with a blindfold...).
- parham90 11y ago
  The thing with 3 dimensional objects is that you get a lot of those in real life. All it takes to show a blind person what 3 dimensional looks like is to pick up a keyboard, show its different sides, and describe that "This is the height, this is the width, and this is the depth."
- Zecc 11y ago
  > I'm genuinely curious how you would think of three dimensional objects without ever being able to see them... [...] > without reference to anything you can see with your eyes, how would you describe space? But the thing is: I wouldn't have to. People without sight live in space too. What mental models of the universe anyone has inside their head may vary wildly, but at the end of the day a torus is still torus-shaped when the lights are out, and West is to your right when you turn North while upside down.
skywhopper 11y ago
Blind people likely understand space far better than sighted individuals. But computer desktop geometry is something entirely different, and not something that's easy to describe. In any case, it's never a good idea to question someone with a different set of abilities than you have with a "is it really that hard?" Their experience far outweighs your naive intuition about what's easy and hard for them.
- Zecc 11y ago
  > In any case, it's never a good idea to question someone with a different set of abilities than you have with a "is it really that hard?" Their experience far outweighs your naive intuition about what's easy and hard for them. Wise words, certainly. I apologize if my tone came across as condescending. I asked out of genuine curiosity, as I figured that someone who did not rely on their eyes could have a different, but not worse, perhaps even better understanding of space and spatial relations than someone who does (accounting for individuals being unique, and all that). But perhaps I'm being blinded by my own eyes. After reading the article wlesieutre linked to, I believe it might be the case.
wlesieutre 11y ago
http://www.newyorker.com/tech/elements/people-cured-blindness-see http://www.newyorker.com/tech/elements/people-cured-blindnes... might be of interest. One particular point that seems obvious after reading, but would not have occurred to me: If you ask a sighted person to imagine a nearby and distant object (say, a car), the distant object is imagined as smaller than the nearby one. But that distance / visual size relationship is a totally visual thing because you're imagining seeing the objects; a blind person's mental model of the object would be built from touch and is the same regardless of distance. They don't have the visual perspective cues. (If the object make sounds, I suppose it's imagined as quieter?) To take that a bit further, I'd guess that blind people's metal models of geometry, whether it's a small object or navigating within a building, is purely orthographic in nature. They wouldn't have any use for our ideas of visual perspective, field of view, lines of sight, or any of that. Artists didn't work out how to replicate it properly until the renaissance, so it's not as though people have an innate conscious grasp of how it works; we just understand perspective as an innate part of our sight. And on the other hand, the blind probably have a much more developed model of spatial acoustics: changes in reverberation as you pass an open doorway, move from a corridor into a larger space, etc., which our brains for the most part don't learn to build.
- parham90 11y ago
  That is very true. My colleagues had a hard time explaining how one can draw in 3D on a 2D medium, like a board. It was there that I figured sighted people see things differently when it's away from them. It's different than how I hear the sound. At least, it hasn't been researched as widely as there has been research done on sight.

Is it really that hard for a blind person to intuit geometry? I would have figured one does not require working eyes to understand space.

by Zecc 11y ago

Is it really that hard for a blind person to intuit geometry? I would have figured one does not require working eyes to understand space.

chris_wot 11y ago

I'm genuinely curious how you would think of three dimensional objects without ever being able to see them... I guess you would have to describe them. As a suggestion - and not an attack in any way because I'm not sure how I'd do it! - without reference to anything you can see with your eyes, how would you describe space?

gchpaco 11y ago
As a counterpoint it's routine in topological mathematics to work with 8 or 12 or 11 dimensional objects.
- chris_wot 11y ago
  Good point! But is this done without any reference to 3 dimensional objects, or does it take the principle and not make any assumptions, or describe it in such a way that the concept is explained without any aspects related to sight? Genuinely curious...
  - gchpaco 11y ago
    It is ... difficult for me to describe just how dangerous it is to try to use 3 dimensional intuitions in a higher dimensional space. As the number of dimensions increases the amount of "space" there is for things to get weird get much more complicated; for example any knot that exists in 3 dimensions can be untied trivially in a 4 dimensional space. Suffice to say if you try to use your ordinary everyday life intuitions doing higher dimensional mathematics you will continuously embarrass yourself until you learn not to. Some folks develop the necessary adjustments and have higher dimensional intuitions; I do not and have to do the math anywhere higher than around 4.
chestervonwinch 11y ago
You could take a linear algebra approach and explain dimension as the number of possible independent directions of movement. This could be experienced through touch. Start with a pencil, then a piece of paper, then 3-space, and so on.
andrewchambers 11y ago
well, you can feel depth and surfaces with your hands, i don't think that is a problem.
e12e 11y ago
What? How would you think of three dimensional objects without ever being able to feel them? (I say as a someone that's got reasonable vision, but surely sound and especially touch is much better at spatial positioning that mere faulty "stereoscopic" vision -- there's a reason why you might want to practice martial arts with a blindfold...).
parham90 11y ago
The thing with 3 dimensional objects is that you get a lot of those in real life. All it takes to show a blind person what 3 dimensional looks like is to pick up a keyboard, show its different sides, and describe that "This is the height, this is the width, and this is the depth."
Zecc 11y ago
> I'm genuinely curious how you would think of three dimensional objects without ever being able to see them... [...] > without reference to anything you can see with your eyes, how would you describe space? But the thing is: I wouldn't have to. People without sight live in space too. What mental models of the universe anyone has inside their head may vary wildly, but at the end of the day a torus is still torus-shaped when the lights are out, and West is to your right when you turn North while upside down.

skywhopper 11y ago

Blind people likely understand space far better than sighted individuals. But computer desktop geometry is something entirely different, and not something that's easy to describe. In any case, it's never a good idea to question someone with a different set of abilities than you have with a "is it really that hard?" Their experience far outweighs your naive intuition about what's easy and hard for them.

Zecc 11y ago
> In any case, it's never a good idea to question someone with a different set of abilities than you have with a "is it really that hard?" Their experience far outweighs your naive intuition about what's easy and hard for them. Wise words, certainly. I apologize if my tone came across as condescending. I asked out of genuine curiosity, as I figured that someone who did not rely on their eyes could have a different, but not worse, perhaps even better understanding of space and spatial relations than someone who does (accounting for individuals being unique, and all that). But perhaps I'm being blinded by my own eyes. After reading the article wlesieutre linked to, I believe it might be the case.

wlesieutre 11y ago

http://www.newyorker.com/tech/elements/people-cured-blindness-see http://www.newyorker.com/tech/elements/people-cured-blindnes... might be of interest. One particular point that seems obvious after reading, but would not have occurred to me: If you ask a sighted person to imagine a nearby and distant object (say, a car), the distant object is imagined as smaller than the nearby one. But that distance / visual size relationship is a totally visual thing because you're imagining seeing the objects; a blind person's mental model of the object would be built from touch and is the same regardless of distance. They don't have the visual perspective cues. (If the object make sounds, I suppose it's imagined as quieter?) To take that a bit further, I'd guess that blind people's metal models of geometry, whether it's a small object or navigating within a building, is purely orthographic in nature. They wouldn't have any use for our ideas of visual perspective, field of view, lines of sight, or any of that. Artists didn't work out how to replicate it properly until the renaissance, so it's not as though people have an innate conscious grasp of how it works; we just understand perspective as an innate part of our sight. And on the other hand, the blind probably have a much more developed model of spatial acoustics: changes in reverberation as you pass an open doorway, move from a corridor into a larger space, etc., which our brains for the most part don't learn to build.

parham90 11y ago
That is very true. My colleagues had a hard time explaining how one can draw in 3D on a 2D medium, like a board. It was there that I figured sighted people see things differently when it's away from them. It's different than how I hear the sound. At least, it hasn't been researched as widely as there has been research done on sight.