According to this video at $1.20$, we, humans, perceive objects in $2$ dimensional.

He also gave an example with a sphere:

"Take a perfect sphere for example... If you're looking at a sphere, it looks just like a regular, two dimensional circle! The only way that you can tell it's an actual sphere instead of a circle is because of the hues of light that it receives..."

But my question is:

Question: What about looking at all the other objects from a different angle?

For a sphere, it is really obvious because a sphere is perfectly round on all sides. So no matter where we look and which angle we look at it, it still looks like a circle!

But how about other objects, such as a cube? If we look at a cube from the front, we essentially see a square! But what about looking at the cube with an angle? We wouldn't see a square anymore, we would see $3$ other faces of the cube.

I need help with this part, I am not quite understanding it. Anything is appreciated!

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    $\begingroup$ What does it have anything to do with "fourth Dimension" in your title? $\endgroup$ – velut luna Nov 17 '16 at 1:51
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    $\begingroup$ "The only way that you can tell [...]" Unless, of course you have stereo vision or interact with it in some manner other than looking at it from only one side (either moving as you suggest or touching it). I'd bet a dollar against a doughnut that the rest of the video is so much hukum just on the basis of that sentence. Each of our eyes images only in two dimensions, but that doesn't restrict our thinking to 2D. $\endgroup$ – dmckee --- ex-moderator kitten Nov 17 '16 at 2:20
  • $\begingroup$ The young man in the video seems pretty sharp, but I don't know if you should take him as an authority on the issue. That being said, to research the issue you are asking about, I recommend looking up "ill posed problems" or "inverse problems". en.wikipedia.org/wiki/Inverse_problem $\endgroup$ – David Elm Nov 17 '16 at 2:21
  • $\begingroup$ @velutluna Well, given that the quote was from the video titled "Fourth dimension explained by a high schooler", I decided to give the title "Fourth Dimension"... I can change it if you want... $\endgroup$ – Frank Nov 17 '16 at 2:22

It's true that our eye sees in 2 dimension. You perceive the three dimension of your cube only when you see from both eyes. The difference of eye position gives perception of the depth. When you look at a sphere, it is completely symmetrical and round (edgeless), so it looks like a circle.

If you looked with only one eye, it would look as if the cube is in a picture. A picture of a cube is 2D, right? You can try it. See a picture of a cube with one eye, then see a real cube with one eye. Then open your second eye. You will immediately realize that perception of depth (the third dimension) is only when both eyes are open. I have checked it similarly, when watching 3D movies.

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