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Our universe has 3 global spatial dimensions - that much I know. I am almost sure, based on an incredibly shoddy knowledge of physics, that there couldn't possibly be a 4th spatial dimension that we simply "can't perceive", because things (including ourselves) would be getting knocked into it all the time.

But what if, in a situation ala Flatland, a human being was transported to a completely different universe in which there were 4 spatial dimensions? Let's leave aside the fact that physics would have to be fundamentally different in such a universe, and assume a 4D analogue, as close as possible, to our own universe.

What would that human experience? Is there some biological/physical limit to our eyes that would prevent us from "perceiving" this 4th dimension, and we would just perceive a 3D slice of it? In my mind, there's no reason why photons coming from a trajectory that intersects this 4th direction couldn't reach our eyes. Would our brain, being used to our 3D world, just process it as multiple 3D spaces stacked on top of each other instead of 3D spaces next to each other in a 4th direction? Would a human being be able to consciously move in the 4th direction?

And if these questions are unanswerable, then why?

I attempted, as one does with dimensions, to analyze the 2D->3D analogue, but didn't get anywhere because a 2D "biology" doesn't really make sense, so talking about what they would perceive doesn't really either.

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    $\begingroup$ I believe the human eye can only see 2D images. We require atleast 2 eyes so that we can process the images and then perceive distance/depth. In a 4D world, our eyes can still, only perceive 2D and by combining multiple images, we will still only achieve 3D dimensions. We simply cannot perceive 4D. $\endgroup$ – Shadowzee Aug 6 at 2:46
  • $\begingroup$ @Shadowzee That’s an interesting point! I think you’re right. It brings up an interesting question, however, of what that 3D perception would be like. Would we see a 3D slice or would everything from the fourth dimension get “mushed in” with it? $\endgroup$ – TreFox Aug 6 at 2:48
  • $\begingroup$ The first thing you'll notice is that your shoelaces won't stay tied. $\endgroup$ – Ray Butterworth Aug 6 at 12:25
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    $\begingroup$ "I am almost sure, based on an incredibly shoddy knowledge of physics, that there couldn't possibly be a 4th spatial dimension that we simply "can't perceive", because things (including ourselves) would be getting knocked into it all the time." - I have a quick experiment for you. Take 3 or 4 matching coins, and place them on a flat surface like a table. Place fingers on all but 1 of the coins. Sliding the coins under your fingers around (as 2D objects moving in 2D space), try to push the last coin up off the surface (into 3D space), without sliding it off the edge of the surface. $\endgroup$ – Chronocidal Aug 6 at 15:14
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2D biology makes plenty of sense. The definitive popular work on the subject is The Planiverse, although there are also other models (some of which have been discussed here before). But, that is a digression. So...

Assuming your body didn't just fall apart on arrival, you wouldn't perceive much of anything. Light would be able to hit your retina from multiple directions without being filtered by the iris or focused by the cornea and lense, making your eyes little more useful than a simple light/dark sensor.

An unaltered human being would not be able to move in the extra dimension, because you have no muscles arranged to pull that way--at least, until bits of you start folding up, re-arranging your muscle vectors in largely random ways.

But suppose you are equipped with 4D blinders. Then you would perceive a single 3D hyperplane of the world projected onto your 2D retina. In order to perceive the full 4D world, you would need to upgrade to a 3D retina, with a 3D lense and pupil. Alternatively, if you are provided with 4D blinders anyway, perhaps you are also provided with 4D glasses which will take care of projecting 4 dimensions down to a 3D image, which your eyes can then reproject down to 2D for your unaltered retinas.

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The 3D man in 4D world would experience an instant death. Brain, organs, blood would just leak or fall of in 4th "side" - there would be no barrier to hold 3D body as a whole thing. To survive human must be put between closly squeezed pieces of 4D glass. And even this will not help much - 3D body would just fall between 4D atoms.

If we had some 4D-scope, then other answers apply. Generely we would see a lot of changing, appearing and disappearing forms. Or just nothing if 4d photons would not be able to excite our 3D ions in retina. This depends on this 4D-scope disign.

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  • $\begingroup$ That's a good point, but in the spirit of the question, lets say the powers that be that bring the dude into the 4th dimension also have am inter-dimensional suit custom made for him so he survives. $\endgroup$ – userLTK Aug 9 at 14:42
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    $\begingroup$ Then it depends on how exaclty this suit is doing it's job. Can it rotate and band in 4D? Or is it firmly attached to some 3D plane like we are now (I am talking about 4D space-time)? How exactly it prevents blood from spillig out of a body? There are a lot of variants, that can greatly change experience. $\endgroup$ – ksbes Aug 12 at 7:16
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I recommend you read Liu Cixin: Death's End. There is a passage there, where the characters first experience multidimensional space - I only found this online.

A person looking back upon the three-dimensional world from four-dimensional space for the first time realized this right away: He had never seen the world while he was in it. If the three-dimensional world were likened to a picture, all he had seen before was just a narrow view from the side: a line. Only from four-dimensional space could he see the picture as a whole. He would describe it this way: Nothing blocked whatever was placed behind it. Even the interiors of sealed spaces were laid open. This seemed a simple change, but when the world was displayed this way, the visual effect was utterly stunning. When all barriers and concealments were stripped away, and everything was exposed, the amount of information entering the viewer’s eyes was hundreds of millions times greater than when he was in three-dimensional space. The brain could not even process so much information right away.

In Morovich and Guan’s eyes, Blue Space was a magnificent, immense painting that had just been unrolled. They could see all the way to the stern, and all the way to the bow; they could see the inside of every cabin and every sealed container in the ship; they could see the liquid flowing through the maze of tubes, and the fiery ball of fusion in the reactor at the stern.... Of course, the rules of perspective remained in operation, and objects far away appeared indistinct, but everything was visible.

Given this description, those who had never experienced four-dimensional space might get the wrong impression that they were seeing everything “through” the hull. But no, they were not seeing “through” anything. Everything was laid out in the open, just like when we look at a circle drawn on a piece of paper, we can see the inside of the circle without looking “through” anything. This kind of openness extended to every level, and the hardest part was describing how it applied to solid objects. One could see the interior of solids, such as the bulkheads or a piece of metal or a rock—one could see all the cross sections at once! Morovich and Guan were drowning in a sea of information—all the details of the universe were gathered around them and fighting for their attention in vivid colors.

Morovich and Guan had to learn to deal with an entirely novel visual phenomenon: unlimited details. In three-dimensional space, the human visual system dealt with limited details. No matter how complicated the environment or the object, the visible elements were limited. Given enough time, it was always possible to take in most of the details one by one. But when one viewed the three-dimensional world from four-dimensional space, all concealed and hidden details were revealed simultaneously, since three-dimensional objects were laid open at every level. Take a sealed container as an example: One could see not only what was inside, but also the interiors of the objects inside. This boundless disclosure and exposure led to the unlimited details on display.

Everything in the ship lay exposed before Morovich and Guan, but even when observing some specific object, such as a cup or a pen, they saw infinite details, and the information received by their visual systems was incalculable. Even a lifetime would not be enough to take in the shape of any one of these objects in four-dimensional space. When an object was revealed at all levels in four-dimensional space, it created in the viewer a vertigo-inducing sensation of depth, like a set of Russian nesting dolls that went on without end. Bounded in a nutshell but counting oneself a king of infinite space was no longer merely a metaphor.

Also there is a part in the book, where some weapon is used that renders the 3 dimensional space in 2 dimension. Also interesting...

I found also

  • this on the representation of 4D objects
  • this on the 4th dimension
  • and the source of the above 2 links
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Since my answer isn't getting any upvotes (perhaps to long), let me give it a little bit of an edit, cause I thought I made some good points.

And, I'm going to skip the very possible "you would most certainly die". If a 4th dimension opens up, our blood, which pumps under considerable pressure, about 1/10th of an ATM or more, which, if an open dimension just appears, our blood would fly out in all directions and we wouldn't live long. There's also the possible that the gravity or the atmospheric pressure of a 4D world would crush us as well, or the wind would tear us apart or stretch us painfully. New dimensions are like that. You never know how the laws of physics will feel to our somewhat delicate bodies, so yes - instant death is a very possible outcome, but lets pretend we have a inter-dimensional suit that protects us and we can go to the 4th dimension and take a look around.

Our brains are also well designed to orient what we seen. In my room there's a lamp a few feet ahead of me. If I turn my head, the lamp still appears upright, not sideways. Our brains in combination with our inner ear, tell us which was is up.

The "screens" in the back of our eyes get the images upside down but our brains re-orient them to right side up and give us a sense of depth. We see up-down and left-right but also, partially interpret them and we interpret depth.

There's no right way to do it, as there's no clear cut laws of physics for a 4D world, but if we imagine things behave similarly. Light is a wave that becomes a particle upon interaction. Gravity is a field, we can assume that in 4D, light emits from light sources, dropping off by the inverse cube (not inverse square) in brightness. It's possible that a 3D being would be effectively weightless in a 4D world and immune to gravity.

How the receptors in our eyes would respond to 4D photons is more open to interpretation. If the photons start out as waves, which is basically what quantum mechanics tells us, the waves through 4D space interact with charges, it's theoretically possible that we D light could interact with our receptors. It's also possible that 4D light would pass right through a 3D being and wouldn't interact at all, so we might not see a thing. That's a perfectly valid and perhaps even probable answer to this question. But it's more fun to imagine what it would be like if we could see, so lets go with that.

So, would would the 2D screens in our eyes see in a 4D world?

From the point of view of the viewer, there's always just one depth dimension, and polar coordinates work better to understand what one sees than Cartesian coordinates do.

So in the 4D world, there's a depth dimension (which we interpret more than we see), there's up-down (which would be thrown off if we don't see gravity), there's left-right and there's Other left and other right.

A 2D person wouldn't be able to turn other-left or other-right, but they could be turned by a 4D being, and the 2 D screens in their brain would only see 2 dimensions out of the 3. They'd never see more than a single slice, plus any depth they could interpret.

In the 3D world, solid objects have shapes. In the 4D world, objects would appear to change shape simply by the person being turned.

If there was a singular light source which cast shadows, the shadows cast would be 3 dimensional. You could walk inside of a shadow, or walk around it and observe it's volume.

If there was gravity, and the person had a sense of up and down, the 3D person could see objects hovering in the air, as if by magic, because they wouldn't see how they connected to the ground and were supported, because we only see a slice of all there is at any one time.

Not unlike a single, unmoving Borg Polaron Beam Imagine if the beam is all you could see, you could interpret distance and get one slice at a time.

If you were correctly oriented, you could turn your head and see things disapear, not just turn out of view, but objects would change size as you turn or move in the 4th dimension.

Objects would also be so complicated they'd be hard to interpret. A 4D Square is confusing enough. Imagine a 4D chair or a 4D desk or a 4 dimensional book with 3 dimensional pages. Just dwelling on a 4 dimensional book or 3 dimensional shadows should provide some idea of how ridiculously difficult to interpret the 4D world would be.

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I would argue the human mind would adapt. It's an incredibly adaptable organ, we've simply never had any need to explore 4D space.

Of course, we do regularly explore 4 dimensional problems. Any moving machine with 4 degrees of freedom operates in such domains. We have many people who are intuitively aware of how such machines operate. It's just, for the purposes of motion, 3 seems sufficient for us.

There is some fascinating research going on in the hippocampus. It is starting to suggest that we actually map the world as a 2 dimensional grid of hexagons, and our concepts of 3 dimensions is layered on top by using multiple grids at once. If it turns out that this is an accurate model of how the hippocampus works, a 4th dimension would just be one more grid to track.

Of course, there's no guarantee that we visualize all 4 dimensions. We may also find ourselves visualizing a 3 dimensional manifold in 4 dimensional space. This would be much akin to how we think of the earth as the surface of a sphere, when it is actually a 3d filled sphere.

The more interesting question, to me, would be what are the equations of motion in your 4 dimensional world? That would have a marked effect on our ability to perceive things.

Food for thought: Our body is a 3 dimensional structure. We have kinesthetic sensors throughout. But all of that information must be flowed through any given 2 dimensional cross section of our spinal column.

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