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This is nonsense. The human mind cannot visualize more than 3 dimensions. It can perfectly comprehend any number of dimensions as long as they are represented i

by hliyan 15d ago

This is nonsense. The human mind cannot visualize more than 3 dimensions. It can perfectly comprehend any number of dimensions as long as they are represented in a vector space. In fact, that's what linear algebra does.

sublinear 15d ago
Yes. It's worth pointing out that anything with n distinct parameters is just a point in n-dimensional space. We're so used to handling so many dimensions that nobody ever bats an eye until someone brings up the magic word "dimensions". It's quite intuitive actually. The trivial example that comes to mind is the character customization sliders in many video games.
gfody 15d ago
I think the human mind can visualize anything, eg here are some visual descriptions of higher dimensional objects: https://gfody.substack.com/p/mini-hyper-golf https://gfody.substack.com/p/mini-hyper-golf
- Lerc 15d ago
  My aphantasia says your milage may vary on that. On the other hand I deal with higher dimensions better than most, possibly because of my aphantasia.
NitpickLawyer 15d ago
I think you accidentally a word, there. GP is talking about comprehending the capacity of massively multi-dimensional space.
- darig 15d ago
  [dead]
- profsummergig 14d ago
  Correct. I implied nothing about visualizing. I was talking about (information) capacity.
philipswood 15d ago
I think it would be fair to say that at least a few people can do a small amount of 4d visualisation. Agreed, I don't think anyone has a good grasp on, say, 64K D, but we can do a bit better than just 3.
- taneq 15d ago
  I’ve heard people claiming that they can but I’ve never heard compelling evidence that they’re directly visualising 4D objects rather than 3D projections of them, or some symbolic representation (arrays of numbers etc.)
  - Paradigma11 15d ago
    So it is like 3D because you do not visualize the complete 3D models but only 2D projections of them. Or do you really visualize the back and inside of a vase at the same time?
    - taneq 15d ago
      If I visualise a 3D object then it’s in at least pseudo-3D (as in front surface with depth) but I can switch it to a kinda volumetric view. This might be thanks to years worth of 3D modeling and CAD which helped me map between first person and third person cameras and between solid and transparent, though. 4D doesn’t even make sense though, like I can do an animated 3D volume?
  - drdeca 14d ago
    All I’ve been able to do is mentally tag parts of a shape as being at different “depths” (possibly with two parts at the same 3D location but tagged as having different “depths”). Which, yeah, I agree isn’t really visualizing a 4D shape. I think someone better at it than me might be able to use this to leverage one’s visual spatial intuition in a way that is a bit closer to what 4D visualization might be like if it were possible. But I don’t think it is possible for us. At least, for strict senses of visualization. I suspect that the architecture of our brains doesn’t support it. This is rather speculative because I don’t know basically any neuroscience, but I wonder if the whole “the brain is largely a very wrinkled surface (though with several layers to this surface), and the retinas are also surfaces” may have something to do with this. A retina in a eye-4-ball would have a 3D boundary (I.e. hypersurface), and I imagine that the amount of information that it would take in if it had an at all similar angular resolution, would be too great for our visual cortex to be able to represent all of it. Of course, our vision only really has the high resolution it seems to everywhere in the narrow region we’re directly looking at, but still.

by hliyan 15d ago

sublinear 15d ago

Yes. It's worth pointing out that anything with n distinct parameters is just a point in n-dimensional space. We're so used to handling so many dimensions that nobody ever bats an eye until someone brings up the magic word "dimensions". It's quite intuitive actually. The trivial example that comes to mind is the character customization sliders in many video games.

gfody 15d ago

I think the human mind can visualize anything, eg here are some visual descriptions of higher dimensional objects: https://gfody.substack.com/p/mini-hyper-golf https://gfody.substack.com/p/mini-hyper-golf

Lerc 15d ago
My aphantasia says your milage may vary on that. On the other hand I deal with higher dimensions better than most, possibly because of my aphantasia.

NitpickLawyer 15d ago

I think you accidentally a word, there. GP is talking about comprehending the capacity of massively multi-dimensional space.

darig 15d ago
[dead]
profsummergig 14d ago
Correct. I implied nothing about visualizing. I was talking about (information) capacity.

philipswood 15d ago

I think it would be fair to say that at least a few people can do a small amount of 4d visualisation. Agreed, I don't think anyone has a good grasp on, say, 64K D, but we can do a bit better than just 3.

taneq 15d ago
I’ve heard people claiming that they can but I’ve never heard compelling evidence that they’re directly visualising 4D objects rather than 3D projections of them, or some symbolic representation (arrays of numbers etc.)
- Paradigma11 15d ago
  So it is like 3D because you do not visualize the complete 3D models but only 2D projections of them. Or do you really visualize the back and inside of a vase at the same time?
  - taneq 15d ago
    If I visualise a 3D object then it’s in at least pseudo-3D (as in front surface with depth) but I can switch it to a kinda volumetric view. This might be thanks to years worth of 3D modeling and CAD which helped me map between first person and third person cameras and between solid and transparent, though. 4D doesn’t even make sense though, like I can do an animated 3D volume?
- drdeca 14d ago
  All I’ve been able to do is mentally tag parts of a shape as being at different “depths” (possibly with two parts at the same 3D location but tagged as having different “depths”). Which, yeah, I agree isn’t really visualizing a 4D shape. I think someone better at it than me might be able to use this to leverage one’s visual spatial intuition in a way that is a bit closer to what 4D visualization might be like if it were possible. But I don’t think it is possible for us. At least, for strict senses of visualization. I suspect that the architecture of our brains doesn’t support it. This is rather speculative because I don’t know basically any neuroscience, but I wonder if the whole “the brain is largely a very wrinkled surface (though with several layers to this surface), and the retinas are also surfaces” may have something to do with this. A retina in a eye-4-ball would have a 3D boundary (I.e. hypersurface), and I imagine that the amount of information that it would take in if it had an at all similar angular resolution, would be too great for our visual cortex to be able to represent all of it. Of course, our vision only really has the high resolution it seems to everywhere in the narrow region we’re directly looking at, but still.