You could try this address, which contains an applet that allows you to see a 4d object using 3d glasses, or just using your own two eyes (like a Magic Eye book).
An American footballer comes across a piece of paper inhabited by flat ants who can only see in 2-D. Cocking his ear close to the paper, he hears the ants talking about the mysterious Third Dimension.
“This will frighten them!” thinks he, and he begins to push the pointed end of the football through the paper. A point suddenly appears in the ant’s world, which grows to become a circle. The ants scream in terror as the circle grows wider and wider as the quarterback pushed the football further through the paper. Then, the circle begins to recede as the midpoint of the football is passed, and finally the ants heave a sigh of relief as it becomes a point, and finally disappears out of their plane altogether.
The footballer laughs. Lucky there’s no Fourth Dimension monster who can do the same to him!
Behind him, a point appeared in mid-air, becoming a rapidly expanding sphere as a 4-D football was pushed through 3-D space.
You’re not really seeing a 4D object. What you are seeing is the 3D projection of a 4D object, a hypercube, into 3D space. It would be like Flatlanders seeing the shadow of a 3D cube, They could see only the 2D shadow of a 3D object. It’s still cool.
I heard this story on NPR, quite some time ago.
This little girl’s father was a beekeeper, who became interested in the dance bees perform in order to tell the other bees where to find nectar. He used diagrams to depict these dances. The little girl liked the diagrams and so her father hung them above her bed.
The girl went to college and became a mathematician. She went into a field of math that dealt with multi-dimensional space. She soon realized that the answers she was getting were expressed in patterns very much like the ones that had hung above her bed, when she was a child.
I’m not sure that this means a damn thing, but it is interesting.
What I think is really neat, is that not only can the higher dimensioned beings see the lower dimensioned objects in full, but they can also see inside them. This should be a prerequisite for a medical degree.
Gee, it is nice to see your continued interest in this.
Yes, it is tempting to imagine that our four-dimensional observers would see objects in the embedded three-dimensional world as flat, but they would see them as merely solid, as opposed to native four-dimensional objects, which would be hypersolid.
Man, some GQ threads go on for months and run into the dozens of pages. Not to blow your ego apart, but this thread really isn’t that unusual.
For an example of a hyperextended GQ thread, look for anything with `.999…’ in its title.*
*Warning: Only look for such threads if you have a hellacious amount of time to kill. 
Oh, and it is absolutely correct that flatlanders would see circles as lines that fade into the distance. We can no more see a complete three-dimensional object than a complete four-dimensional one, after all. (Remember perspective.) I’m guilty of forgetting that sometimes, though I’ve read Flatland in its entirety. (I quite enjoyed it.)
I read a Discover article quite a while back about that too. Here’s a link that talks a bit about her research and hypothesis.
Actually, we can only see in two dimensions; you can never see all of a three dimensional object, just its surface (and only part of that). So if we can fool ourselves into thinking we’re seeing a three dimensional object, maybe we can fool ourselves into thinking we’re seeing a four dimensional object.
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[sup]Thanks! I appreciate the link.[/sup][/ul]
I can’t really contribute much to this thread but for one of my years in math class we had to research the 4th dimension.
If I remember correctly, I learned that if a 4D object were to enter our 3D dimension, we would see it appear as a dot that would expand outwards of all the axes of the 3D dimension and it would shrink back and disappear as it passed through our dimension.
To make sense of that, let’s think of an amoeba living in a 2D world, the surface of a pond. It only knows left, right, front, back… 2 dimensions. It does not know of above or below (which would be a 3rd dimension).
Now, if you pass a 3D object, like a marble, through the pond’s surface (let’s assume that the water will not splash or anything like that), the amoeba will first see the marble as a dot. As the marble passes through the pond surface, the dot will extend in its 2D world and become a line increasing in length, until half the marble has passed and then the line will shrink back into a dot and disappear.
A lot of you probably know that already, but I’ve always found it so incredibly interesting. 
As for people living in higher dimensions, it is said that a person living in 4D can see all there is in our 3D world. This is similar to the amoeba’s pond surface, where we can see everything all around it.
I can’t think of the surface of a pond as a 2D world. My brain won’t let me. What do I have to forget to accept the possibility of a 2D world? Does this world exist only as a mental crutch to facilitate understanding other concepts?
I need to read that book, Flatland, right?
I think there’s a difference between vision and perception that’s being misunderstood. When I look at a cube the light rays being reflected form a two-dimensional image on my retinas. My brain, and me, however, preceive a three-dimensional cube. Part of this perception is through stereoscopic vision and part through learned experience.
I think humans are capable of perceiving four dimensions. The problem isn’t with our brains. The trick is presenting them, over an extended period of time, with visual information that can only be correctly interpreted by invoking a fourth dimension.
You start out so well and end up with such utter nonsense.
Humans cannot experience four spatial dimensions because we only live in three dimensions. We can’t see any more than three mentally, no matter how we try. When we humans try to imagine a cube forming a tesseract, we imagine the cube being pulled along a three-dimensional vector, not along a four-dimensional one perpendicular to all three dimensions.
Derleth, I think you’re being unnecessarily harsh. Not to mention you haven’t addressed The Ryan’s point, which I think is valid.
I’ve spent a lot of time over the years trying to visualize four-dimensional structures. I feel that I’ve succeeded for very simple structures, such as two planes intersecting in a point. More complicated structures, even something as simple as a three-sphere, are another thing, but I intend to keep working on it. I see no reason why a human mind can’t be trained to do such a thing if it can be trained to, say, type.
One trick I’m fond of, although I’m not sure how effective it is in general: imagine a stack of thin glass sheets. Each individual sheet is in fact a flat-screen TV, showing a three-dimensional image in a two-dimensional space. (We’re used to this kind of trickery; most people don’t even think about how a TV image is actually two-dimensional and not three-dimensional.) Then the stack of sheets is showing a four-dimensional image in a three-dimensional space.
True, but they would still be able to see inside us. That is, of course, assuming that the four dimensional observers can see at least in three dimensions and can infer the fourth, as we see in two and infer the third.
Orbifold: I actually addressed The Ryan’s post before he even made it. Look at the last paragraph of my post before jovan’s.
And as for the flat-screen TVs: You still can only see two dimensions, though your mind inferrs the existence of a third automatically. I don’t see how that adds up to seeing four spatial dimensions in any real way. After all, a solid object can still obscure something that’s in the same three-dimensional plane (two-dimensional obscuring).
Ok, now Orbifold claims that photons are 2D.
Bull.
We only see two, but the image (no different than in a mirror) is 3D. Photons have mass. They boink into the receptors in our eyes, causing our brains to perceive them as sight.
I know this discussion is way over my head, but, I remain unconvinced that anything can exist in two dimensions. That’s why our brains add the third. We know better.
Assuming that I’m full of it, please suggest some fairly easy reading that will educate me.
Point taken, although I don’t think that post refutes what The Ryan stated. Perceiving the 3-dimensional world is a matter of performing certain mental computations. I see no reason in principle why the brain can’t perform the same computations for four dimensions.
That’s kind of the point. The thing about the flat-screen TVs is just a way of inferring what the relationships between objects in a four-dimensional space would be, by “squeezing out” one dimension in a familiar way. So you ending seeing three dimensions, but hopefully in a way that allows your mind to infer the existence of the fourth. I didn’t mean to imply that it was anything more than a neat mental exercise.
But I do feel that enough mental exercises of that nature would help train a mind to eventually visualize four dimensions in a more meaningful way. In other words, I agree with MonkeyMensch.
Where the heck did that come from? I’m in no way claiming that photons are 2-d.
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You’re not full of it. But you’re reading a lot more into my post than was there. When I say that a TV image is 2-d, all I mean is that it’s an image on a flat surface; we can’t, for example, look around Bob Barker to see if there’s a $100 bill sticking out of his back pocket. Bob himself is three-dimensional; he has a backside. But the image only has a front.
We just add an extra dimension in our heads when we watch TV, which was my point.