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More generic, Can an n-dimensional being ever see an n-dimensional object?. It is my understanding that both of our eyes are capturing projections, and without both of them, we will lose our sense of depth perception. But is sensing depth enough to claim we can see 3D? If humans were 2D beings, then how could we see anything other than straight lines or line-segments? And if we were 4D beings, wouldn't it be only then we can sense 3D?

Image Credit: A two-point perspective illustration created by User:Matticus78 in CorelDRAW

Source: https://en.wikipedia.org/wiki/File:Phantogram_projection_diagram.svg

A two-point perspective illustration

[EDIT]: Before posting this question in PSE, I read about image construction in the retina(s) of a human, so I need to clarify something. By using the word actually, I want to transcend our understanding of seeing beyond reconstruction of a 3D model and have a discussion about how beings in other dimensions are capable of seeing things and how that sense is quantitatively less/more than our (beings in 3D space) capabilities, thus creating a direct relation between the dimension we live in and the way we measure objects by looking at it. Thanks for all your replies.

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  • $\begingroup$ We can't see 3D. Your assertion that n-dimensional beings cannot observe an n-dimensional object is correct; rather they can only observe a projection of it in n-1 dimensions. As for the case of humans and our perception of the 3rd dimension, that is a result of our eyes being accustomed to viewing something smaller as farther away and/or deeper and vice versa. Lighting also significantly impacts how well we can 'see' the 3rd dimension. $\endgroup$
    – d_g
    Commented Apr 22, 2019 at 8:00
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    $\begingroup$ Welcome to Physics SE! This is an interesting question, but it really depends on what you mean by "seeing". If it's just seeing with your eyes then no, because you have an effective 2-D retina, while if you mean seeing "with your brain" (processing images) then of course yes. $\endgroup$
    – Mauro Giliberti
    Commented Apr 22, 2019 at 8:01
  • $\begingroup$ Thanks so much to you both for quick reply. @d_g you mentioned Lighting being a factor for seeing. May be this is not within the scope of this question, can you reflect on that impact for dimension > 3? Simply put, say Light can only travel in 1 direction in 1D, 2 directions in 2D. If I was in 4D space, looking at a 3D object as a 3D human, will it be any different than when I was in 3D space? (considering 4 different directions of Light in 4D) $\endgroup$
    – user86406
    Commented Apr 22, 2019 at 8:14
  • $\begingroup$ @Mauro I'm actually trying to wrap my head around that myself. How can I define 'seeing' in Physical perspective (Biologically, I guess its already established, we have a Retina that works with only 2D projection, so perhaps this question has an already defined limitation, may be I should not have brought up humans :-) ) $\endgroup$
    – user86406
    Commented Apr 22, 2019 at 8:16
  • $\begingroup$ This mathematics sciencedirect.com/science/article/pii/S0010448596000565allows to reconstruct a three dimensional image . The brain is a powerful analogue computer and does it for us, imo $\endgroup$
    – anna v
    Commented Apr 22, 2019 at 8:43

3 Answers 3

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Yes a 3 dimensional being could see in 3 dimensions.

Here is a theoretical example: a being equiped with a bubble chamber (see: bubble chamber) reacting to some wavelength spectrum could get a correct 3D image of a defined spectrum (in term of wavelength) and of a defined region of space. This bubble chamber should be filled with photosensitive cells distributed in 3D in large but finite number and small enough to have the smallest possible shadow. This theoretical would only produce a discrete image and would require a brain to construct an illusion of a continuous image (as human brain does it pretty well: we have a good illusion of continuous environnment).

The natural selection didn't yet reach the bubble chamber complexity of construct. This is the reason why bubble chambers aren't in wide use among different actual forms of life on Earth 😎.

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  • $\begingroup$ Thanks for your reply. This is beyond interesting, but may be the answer is too concentrated for my knowledge. I have one question though, if I do have bubble chambers in place of my eyes, does it have anything to do with my dimensionality? I guess because the Wikipedia article says: Several cameras are mounted around it, allowing a three-dimensional image of an event to be captured. So basically, it comes down to what a camera is capable of doing $\endgroup$
    – user86406
    Commented Apr 23, 2019 at 4:13
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    $\begingroup$ If bubble chambers had evolved for eyes, then evolution would also have added nerves from each of the possible "bubble locations" to the brain's visual cortex - just as it has connected each cell in our retina via a nerve. Hence we would indeed see 3D. $\endgroup$
    – hdhondt
    Commented Apr 23, 2019 at 4:31
  • $\begingroup$ @hdhondt right, with small enough cells or transparent ones to let back plane cells to receive photons too. $\endgroup$
    – athena
    Commented Apr 23, 2019 at 6:14
  • $\begingroup$ @danielAzuelos Yeah, evolution would need to do better than our current setup, with the nerves crossing the front of the retina and the light receptors at the very back ;-) At least it did better with octopuses (octopi, octopussies?) $\endgroup$
    – hdhondt
    Commented Apr 23, 2019 at 9:54
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Our brain builds a 3D model based on 2 dimensional cues, including binocular disparity, shading, relative motion, texture changes, etc. The brain usually succeeds in building the most likely 3D structure based on the available information, however it can be tricked by many visual illusions. Any 2D projection is compatible with an infinite number of possible 3d scenes, however most of these are discarded by our brain as unlikely.

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  • $\begingroup$ Thank you for your reply. So effectively it's the brain, not our eyes that are capable of seeing a 3D object. But then can it also produce 4D models? Or does it come down to comprehensibility of dimensions i.e we are 3D beings, so we won't be able to construct a 4D model? In my question, what I meant by actually is this: We can claim that we understand 3D object by looking at it, but do our eyes exactly capture x, y or z simultaneously. From your answer, I guess not. $\endgroup$
    – user86406
    Commented Apr 23, 2019 at 4:10
  • $\begingroup$ I wanted to add this to discussion 2.5 D, I feel like our brains don't care whether it can construct 2.5D / 3D model. Please correct me if i'm wrong. $\endgroup$
    – user86406
    Commented Apr 23, 2019 at 4:25
  • $\begingroup$ It is still unclear how the brain codes the 3D world, you can read entire books on it. That is not physics though, but neuroscience $\endgroup$
    – user65081
    Commented Apr 23, 2019 at 16:11
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Can we see any object? What happens is that our lenses produce 2D images on the retina. Nature invented optics long before we did. These images are converted into rgb signals in the cones. These signals are used by the visual cortex to construct a 3D image using pattern recognition. The 3D image exists only between our ears. The 2D images can be argued to physically exist on our retina, but even a 2D image, as we finally see it, is reconstructed by our brains.

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  • $\begingroup$ What is transmitted by our retina is a discrete image. The continuous image is a brain constructed object. $\endgroup$
    – athena
    Commented Apr 23, 2019 at 6:17