Orientation Problems in 2d

[Splatt]

So I read your page on wars in 2 dimensions, and i have a problem with there just being hight and width. i can just as easily see there being only length and width. so if i came acrossed a rock in 2 dimensional space i could go around the right side or the left side but i wouldn't be able to go above or under it.

but as i write this i ask myself the question, what if both exist? you could have one plane that goes throught the y-axis and another plane that goes throught the x-axis and intersect each other as a line.

then it could be taken one step beyond that and say that there can be an intersection similar to the one above in 3 dimensions. But there would be a difference cause then there would be 3 dimensional spaces that intersect. using x, y, and z, to represent our normal axies, and w to represent the extra asis would would need to have the intersections, we could have the 3 dimensional spaces intersect as x-y-w, x-w-z, w-y-z. ok... so maybe we wouldn't have 3 intersecting spaces but we would deffinetly have at least one.

[Aale de Winkel]

curiously I've not seen this adressed yet.

I think however that an n-onian in finding himself in the intersection of 2 n-spaces wouldn't notice the existence of the other n-space, simply since his senses are stuck in his own n-space.
Just in case an funny n+1-onian forces the n-onian into the other n-space he might shift from one n-space into another, but this can also be done of course when the n-spaces don't interact in n+1-space.

This is taken us into the existence of parrallel universae, which might as well intersect. And of course some n-onian might create a passage, the tv-(?)series "sliders" is based upon this idea.

[alkaline]

as far as measurements go, it's not completely simple between height, length, and width - there are some slightly complicated rules for which ones you assign to which dimensions. Height is only used for the vertical measurement. Length is used only if the longest measurement of the object is horizontal, otherwise it's not used. If you are going to use height for describing an object, the first thing you do is assign it to the vertical measurement. Then, you assign length if the longest dimension is horizontal. For the rest, you assign them in order - width, then thickness. In summary:

"tall":
primary - height
secondary - width
tertiary - thickness

"long":
primary - length
secondary - height or width
tertiary - height or thickness

Basically, these terms are only names for measurements, and they don't correlate exactly with the directions or cardinal directions at all. They depend on the orientation of the object.

If you're in tetraspace, all you do is add "trength" in the sequence of width and thickness, and it gets assigned to the fourth measurement (the smallest measurement among the four).

[Jay]

I think that's an interesting idea, but even if these intersections existed, we wouldn't be able to make much use of them.

For a 2-d object travelling across the intersection, they would have to bend at 90 degree angle perpendicular to their universe to get into the other one. For the time being they would have be 3-d.

Just like for us, while crossing an intersection, we have to bend ourselves in a 90 degree angle perpendicular to our universe. And for the time being, we would have to be 4-d.

The again, this may not be so impossible. As Aale de Winkel said, our senses are confined to our dimensions. So the 2-d being might not feel himself being bent in this third dimension because his width and length would remain the same (assuming height is the 3rd dimension). And we would not feel anything because our width, lenth and height would remain the same (as parts of our body moved delta or upsilon).

That brings up an interesting question. Is it possible, that we are being bent into 4-d configurations, but we don't know because we can't feel it?

[Splatt]

yea i like the idea Jay has thinking that we might be more then just a 3 dimensional being but lack the ability to see beyond our 3d existance.

alkaline, i see what your saying about assigning dimensional measurements in a certian order, but what i am suggesting is that there may not be a height dimension in 2d. in your story about 2d war you are looking at it like they live on a wall, i am suggesting that they may live on a table.
Then in our 3d space we have height, length, and width, but there is another axis in 4 dimensions that might be interchanged with one of ours. if it was interchanged it might create a perpendicular space, with a different measurement besides height, length, or width. so using trength as the designation for the other measurement, another 3d space might use width, thickness, and trength, but not height.

[Jay]

The only problem with imagining a 2-d world as a tabletop, with the beings capable of moving left, right, forwards and backwards, is that there would be no gravity pulling them downwards. There would therefore be no friction, and they wouldn't be able to start and stop in conventional ways. That is another flaw in "Flatland".

On a different note, if you can bend a 2-d being into 3 dimensions w/o them noticing, why not their entire universe? Theoretically, you could take two parallel 2-d universes and ruffle them, so that they would intersect at an infinite number of lines. Maybe our universe can be ruffled to do the same with a paralled 3-d universe, intersecting at an infinite number of planes.

[alkaline]

alkaline, i see what your saying about assigning dimensional measurements in a certian order, but what i am suggesting is that there may not be a height dimension in 2d.

Height isn't a dimension. It is the name for a measurement of an object. What you're probably trying to say is that there might not be a y dimension in 2d (the dimension with gravity).

in your story about 2d war you are looking at it like they live on a wall, i am suggesting that they may live on a table.
Then in our 3d space we have height, length, and width, but there is another axis in 4 dimensions that might be interchanged with one of ours. if it was interchanged it might create a perpendicular space, with a different measurement besides height, length, or width. so using trength as the designation for the other measurement, another 3d space might use width, thickness, and trength, but not height.

like i said - these are names for measurements, not dimensions. I think what you mean is that in our 3d space we have x,y, and z. The 4th dimension has another axis, w. Thus you could create a perpendicular space using w and two of the original axes - for example, x,z, and w, but not y. Without gravity, you might rightfully say that there was no height measurement, since height corresponds to the gravity dimension (y). But in 3d, you still have three other names - length, width, and thickness, so you wouldn't use trength.

[alkaline]

The only problem with imagining a 2-d world as a tabletop, with the beings capable of moving left, right, forwards and backwards, is that there would be no gravity pulling them downwards. There would therefore be no friction, and they wouldn't be able to start and stop in conventional ways. That is another flaw in "Flatland".

I think the nature of a 2d world in relation to ours depends on how the dimensions would interact. With a "non-interference" model, then the 2d world would be self-contained, and its gravity would be internal, so it wouldn't matter what orientation it had in relation to our world. The bionians would still be "rooted" to their 2d planet. With an "interference" model, the 2d world would be affected by our gravity, so it would probably be affected by other forces like light & electricity also. The 2d world would probably get torn apart by our forces, which is what bobxp was talking about earlier.

I agree with you that there are problems with flatland's model of a 2d world. I like the model of a 2d world from Planiverse - it is very detailed and fascinating. You really should check out that book.

On a different note, if you can bend a 2-d being into 3 dimensions w/o them noticing, why not their entire universe?

This would be the "non-interference" model, where no forces in 3d affect the 2d world.

[Keiji]

[this post assumes a 2d world omits the z axis]

talking of bending hyperuniverses, if you folded a 2d world into a cylinder along the y axis, a person could travel in a straight line and get back to where they started.

but the interesting thing is this. if you folded it into a cylinder along the x or z axis, a 2d person could fall down the cylinder, but gravity would pull them up the other side of the cylinder. so they would fall ad infinitum, until the cylinder was split back into a flat surface again.

also, if you folded it into a cylinder, then a 2d person went onto the join, and you split it back to a flat surface, would the person a) be split in half or b) be "pushed" to one side of the split?

also, orientation problems would happen if you folded it into a cube - if a 2d person went to one of the joins, the direction of gravity would change. Also, what would happen if you were on a join? you would probably get the same "glitch" as that happens if you try to make a water level in sonic 2 which is wrappable - it will suddenly flicker off and on. **ahem** back to subject, this would mean that with a 2d person, the gravity would disappear when they were on a join.

[alkaline]

This assumes you have a finite 2d world, since you can't fold an infinite 2d world into a cylinder. Thus you have to define what happens at the edges of the universe before you do anything with it. You could just say that it's some kind of solid impassible barrier. Or you could do something altogether different - take an infinite 2d world, cut out a square section and fold that into a cylinder. In either case, you would have to take the two ends that you were joining and seal them together in a seamless fashion. To split apart the cylinder again, you would have to use the same method as you would to cut the square out of planespace in the first place. You would probably want to push the bionians out of the way before you started cutting it apart.

A person would only fall down the cylinder in the fashion you are describing if they were affected by 3d gravity. Gravity swaps at corners of cubes would also only occur if the world was affected by 3d gravity. If 3d gravity did exert force on this world, then a bionian within the top square of a cube sticking his leg into the side square would probably be pulled into the side square and would swing around to the opposite side, just like in the cylinder case.

An interesting thing to think about in these small finite worlds is how light would wrap around infinitely. A bionian in the cylinder looking around the cylinder would basically be staring at his back side.

[Keiji]

*becomes a complete hypocrit by bringing up two and a half year old topic*

Surely, if the 2D world was a cube, it'd be a bit problematic? The top and bottom faces would lack gravity completely, so there would have to be an aether there for anyone to be able to move.

I think a cone might work well. If it was placed so that the flat face was on the bottom, the bottom face of the cone could be used by the bionians as a gravityless swimming pool. And everywhere else, the gravity would be constant.

[bo198214]

Hey you complete hypocrite!
Whats the problem with putting stars on S₂ (or arbitrary shaped 2-manifolds) that have gravity?

[Keiji]

um... What?

[bo198214]

Gravity comes from mass.
And it is no problem to put a mass on a cube-shaped 2d-world. So there is no problem with gravity there.

[Keiji]

We are talking about 3D gravity affecting the 2D world.

[bo198214]

oh, hm, at least you talk about it

[Nick]

I see no problem with 3d gravity effecting 2d space. Isn't that the idea of p-branes? That the extra energy (dark energy) we find in the Universe with apparently no source is from another 3d universe; that the two 3d universes are seperated by 4+ dimensionally space?

[Keiji]

The problem is: suppose 3D gravity DOES affect a 2D world. This 2D world is the surface of a 3D cube. If a bionian decides to move into the top or bottom face of the cube, they are stuck as there is no gravity, so there is nothing for them to move against.

[Hugh]

The problem is: suppose 3D gravity DOES affect a 2D world. This 2D world is the surface of a 3D cube. If a bionian decides to move into the top or bottom face of the cube, they are stuck as there is no gravity, so there is nothing for them to move against.

They could throw objects away from themselves in the opposite direction they want to go, like a rocket in space uses propellant.

The original concept of this thread is fascinating. What if we actually were in 4d space but only saw a 3d slice of it at a time?

For a 2-d object travelling across the intersection, they would have to bend at 90 degree angle perpendicular to their universe to get into the other one. For the time being they would have be 3-d.

Just like for us, while crossing an intersection, we have to bend ourselves in a 90 degree angle perpendicular to our universe. And for the time being, we would have to be 4-d.

What would we see if our viewpoint was bent 90 degrees perpendicular? If we were in another cube viewpoint of a 4d hypercube? We'd see the universe from a different 90 degree direction. Sounds like the VRI to me.

[Nick]

The problem is: suppose 3D gravity DOES affect a 2D world. This 2D world is the surface of a 3D cube. If a bionian decides to move into the top or bottom face of the cube, they are stuck as there is no gravity, so there is nothing for them to move against.

How is "Well the 2d guys would get stuck" have anything to do with mass and gravity? It's not like nature would say "Oh, these poor guys. I think I'll just change all of the laws of physics as we know it for them!".

[Keiji]

I think you misunderstood me. The bionians would be stuck because of the gravity.

[bo198214]

Can you please stop this misleading "bionian"?!

[Keiji]

Misleading?

Bionian means 2D inhabitant.

[thigle]

sorry to pop by, just that it is clear that some people prefer unclear terminology and personal affect over clarity and appropriateness. it was many times well argumented from multiple perspectives that bionian is a misleading term, why, and what's the alternative. so all sane beings if in control of their fates, they srop the misleading terminology and accomodate new.

still some !#%tonians ignore actuality and prefer own constructed solipsistic models that are not optimal.

now i see down the screen how bo is polite ("can you please stop...").
anyway:

BIONIAN IS NOT ETYMOLOGICALY A APPROPRIATE WORD FOR A '2D INHABITANT' :twisted:

love

[bo198214]

Come on Rob! You surely read the discussions about it.
But for the case your memory leaks, there are two reasons to not use it:

• the prefix "bio" suggests that it something biological.
• the prefix "bi" is not greek as for example "tetr" or "pent" is.

[Keiji]

Alkaline has used the term "bionian" ALL the time when writing about 2D space. Why should we change it now when it has been accepted for 3 years already?

[thigle]

now what an argument!

people has been burning so-called witches for almost a century. why has it changed? hmm, was it perhaps inadequate? oh no! it couldn't! so many people were doing it for so long!

just because something was doesn't mean it has to be forever.

let's call you iNVERTED. whatsmore, i propose, you should change your Rob-name back to the old one that you have been using and that was accepted for almost 3 years.

but i've seen in some thread you ask someone to stop calling you inverted?

[bo198214]

Alkaline has used the term "bionian" ALL the time when writing about 2D space. Why should we change it now when it has been accepted for 3 years already?

There I had expected you a bit more authority challenging.
Alkaline used the term anyway before the questioning of it.
So he had no choice to use another name.
And inappropriateness is quite a good reason for change, for my taste.
And "we do it because we always did it" is on the other hand a bad reason for non-change.

[Keiji]

Fair enough, go ahead and call them dionians.

[moonlord]

Now that's a change in the wind.