Speculation with portals
Okay here's one for you Paul. If a 4-spacer picked me up and moved me 3 feet in whatever-the-fourth-axis-is-called, what would happen to me then?
Well, unlike speculating about using the fourth axis to leave and return, this question requires we make some assumptions about the environment outside of our own 3-space.
First assumption: Your body remains perfectly rigid and contained along the new axis. This frees us from worrying about your blood all falling out at once, or the 4-spacers accidentally "rolling" you up along the new axis.
Second assumption: We're dealing with one 3-space transition to one 4-space. There aren't any other local 3-spaces that you would be placed in that would seem normal to our 3-dimensional experience. Once out of ours, you would be experiencing the world of the 4-spacers, even if limited by 3-dimensional perception.
Wow, great topic. This whole discussion warms my heart. After reading He Built a Crooked House I tried to make a level in a MUD shaped like a hypercube/tesseract. It took me days to make sure all my exits were lined up correctly and when I tried running through, I got so lost I immediately got a headache and gave up.
A few questions about portals in relation gravity, as to whether they are opaque or transparent.
Situation 1: Both apertures on the floor.
1A: Transparent
You sit there with half your mass out of one portal, half your mass out of the other. You've stepped in gently so after some oscillation you settle in to this position. Since the portals are transparent to gravity (thank God, Cavorite anybody?) the gravitational field of the earth is pulling equally on both halves of your body. You have the Mother-of-All-Stomach-Cramps. I believe this case you would be "bouyant" as if someone tried to pull you out by your hands (or feet) the force of gravity on the other end would pull them into the portal making them easy to pick up, but getting heavier all the time, much like pulling someone out of a pool.
1B: Opaque
I'm not quite sure what to think here, since we are dealing with the backs of the portals. Perhaps you simply have no gravitational pull on either end.
2: Portals on the ceiling.
2a: kind of like being flopped over a bar on your stomach, but more intense. 80 pounds (for an Average Joe)on either end trying to go in opposite directions. Still bouyant, but downwardly so.
2b: This feels like 2a but twice as bad. Since space "be all folded and shit" Earth's gravity is pulling on your entire body. Also Earth is pulling on itself. I'm not sure that it can actually move anywhere since it's a very local effect, but imagine a lot of debris could go crazy. This doesn't seem like a wise situation to put yourself in.
Just some ramblings of mine. Am I off-base in any of these?
Transparent? Opaque? What do you mean?
(Thanks for the qualifications, Shmitz. Good thinking.)
That one's easy. If the 4-spacer lifted you along the W axis (that is, along the axis we don't have in 3-space), then you would disappear from our universe entirely and be detectable to us nevermore unless a 4-spacer brought you back "wdown" to the 3-space where you started. As iamafractal mentioned, because your skin only encloses you in 3D, it is highly likely at this point that all your organs would tumble out "through" (actually around) your skin and you'd die a painful death.
For the sake of argument, if we assume that doesn't happen, perceptually speaking you'd be in a real world of hurt. Once again, the key here is an analogy.
Suppose you could go and pick up Floyd the Flatlander, and rather than rotating him and replacing him in 2-space, you take them right up into 3-space, away from his entire universe/2-space/"piece of paper." Assuming (again, for the sake of argument) that his perceptual faculties still worked at all, he would see a rapidly fluxuating world full of shapes moving, deforming, and growing/shrinking for no apparent reason.
Because, you see, just because you've moved him into the 3rd dimension doesn't mean you've made him 3D. He's still 2D, and his vision is 1D (a line, remember?). So even though Flatlanders are quite adept at using distance/FOV and atmospheric perspective to understand coplanar 2D shapes with that limited vision, they have no prayer of understanding three dimensions.
For the simplest example, consider a ball that exists on our vertical axis, sitting atop the 2-space where Floyd began. Without rotating him at all, you begin to move him straight up. You can imagine what Flloyd can see by extending the XY plane of his body in all directions. Anything intersected by that plane, Floyd could see at that instant (if he looked in its direction). So what Floyd sees as you abduct him from his whole world is, first and foremost, that world blipping away instantly.
Then he would see a single point, the lowest point on the ball. But, contrary to a lifetime of experience, that point wouldn't stay that way. It would immediately jump two dimensions (points are 0D, circles are 2D) and become a circle. To Floyd, this is ludicrous. Points can't become circles on their own. It takes a whole team of engineers, any child knows that. They have to take two points and draw a line, (or ship in a prefab line) and then use that line to describe the circle as its radius. Once they have described the circle's "floor plan," notice that if they want it to be solid/filled-in/have area, they have to start building from the inside out, because once they've built the outside walls they can't reach the space enclosed within anymore. This is analogous to our building the inside parts of the building first, like the steel in skyscraper. If we tried to build from the outside in, not only would the building tumble and fall, we'd look really dumb.
Now he's seeing an object perform this complicated construction process on itself, unbidden, perfectly and smoothly growing. Then it gets worse. Just as his view passes the ball's midpoint, it starts to shrink back down to a point, and then it disappears.
In 2-space, area is analogous to 3-space's volume. So to Floyd's way of thinking, he just saw a point (a 0D object) grow immediately into a 2D object. Floyd naturally would assume that the circle is solid/filled in, that it has area, the same way we assume an object we see has volume -- and to him that would connote "2-mass" (I just made that up), which as far as Floyd is able to tell is as solid as things can ever get). It would look to him as if a huge amount of matter was being created from nothing. And then it shrunk again and disappeared, destroying all the matter that had just been created.
Needless to say, this would make NO sense to Floyd, and that's about the simplest 3D shape we got!
What would you look like to him as you lifted him? Well, he would see the fingers you're lifting him with as circles/ovoids, unconnected to each other as far as he can tell. As he was lifted past your legs he would see two mostly-circular masses whose contours seemed to undulate for no reason. When he got to crotch-level, he would see these two distinct areas merge into one (what the?!), and then that area would wiggle its contours a bit, and he'd start seeing your non-lifting arm in cross-section as a deformed circle, entirely unsure whether that part was or was not connected with your torso. From his POV, it would look completely distinct and unconnected. And so on. He'd be in a nightmare world where objects refused to hold their shape, where they popped into and out of existence, constantly changing their mass and properties.
Now that I've done the "2-spacer lifted through 3-space" account, in some exhaustive detail, does anyone care to take a whack at extending the analogy? Espen?
What would it look like to you if a 4-spacer came along and lifted you "wup" past a hypersphere (a 4-sphere)? (Hint: in this analogy, the entirely of 3-space you can observe is always a "cross section" of the 4-space you're moving through, just like Floyd's 2D universe was a cross-section of our 3-space.)
Hmm sorry. Terminology assumption.
Transparent: It doesn't interact with gravity.
Opaque: Gravity is affected by the portals in the same way matter is.
I'm not sure if those quite fit the definitions, but it was the closest set of antonyms I could come up with without wracking my brain.
How about "immune" and "affected." No special definitions necessary. 
http://uk.youtube.com/watch?v=lwL_zi9JNkE
Simple. Understandable. Perfect.
Hell yes, espen180! Nice link indeed. Carl Sagan was a radical benevolent brainiac.
highly interesting video there espen, loved it and it explained everything we've discussed here really well.
You just keep on trying till you run out of cake!?