4th dimensionally perpendicular earths

[elpenmaster]

Could there be other earths that are 4th dimensionally perpendicular to this one? for example, take a circle. this is our earth. then rotate this circle 90 degrees about its centre and you have another circle of the same size in the same sphere just like the first one but it is pointed in another direction. then applie this to our 3d earth. you could have other people living on the other earth under the same environmental conditions and be just a few 4d miles away from us. maybe the bermuda triangle is where these two earths intersect :twisted: (somehow). if we found where the two earths intersect, we could cross onto the other one. . .

[Keiji]

That's... interesting.

To think there could be someone watching over my shoulder right now...

[elpenmaster]

well, they wouldnt actualy be able to see us. if the two perpendicular earths are the same size, they would only intersect on the surface in two places, at opposite ends of the globe.. so if you went to one of those points and walked ana or kata or whatever, you would go to the perpendicular earth. but if the other earth was smaller than this one. it would only intersect us inside of the earth. . . and if the other one wass bigger, there would be two walls. . . im not exactly sure what it would look like, though, i find it rather hard to visualize two speres intersecting in 4d!

[Keiji]

Well, I was thinking of having this planet only being the middle slice of a 4D planet, rather than there being another 3D planet. :wink:

[elpenmaster]

actually, i asked this because i am writing a story where the people go from this earth to a fourth dimensionally perpendicular earth that is somewhat bigger than this one. i was wondering if anybody could describe what this would be liike? :?

i think that the two earths would intersect with a circle on the surface of the earth. . .

or something like that. . :?

[PWrong]

if the two perpendicular earths are the same size, they would only intersect on the surface in two places, at opposite ends of the globe..

Wouldn't two perpendicular spheres intersect on a line?

With two perpendicular circles, one circle divides the other in half, so they intersect on a line down the middle, but the line only meets the surface at two points,

Two perpendicular spheres would intersect through a disk, which meets the surface along a line, like the equator. So that rules out the Burmuda triangle

Then again, it is a triangle...
If there were three other perpendicular earths, the three lines might make a small triangle. So no matter which way you enter the bermuda triangle, you can enter one of the other worlds. But then there'd have to be another triangle somewhere else, and three big circles that you can't pass.

[PWrong]

if the two perpendicular earths are the same size, they would only intersect on the surface in two places, at opposite ends of the globe..

Wouldn't two perpendicular spheres intersect on a line?

With two perpendicular circles, one circle divides the other in half, so they intersect on a line down the middle, but the line only meets the surface at two points,

Two perpendicular spheres would intersect through a plane, which meets the surface along a line running round the sphere, like the equator. The intersection would run up into the sky and under the ground as well. So that rules out the Burmuda triangle

Then again, it is a triangle...
If there were three other perpendicular earths, the three lines might make a small triangle. So no matter which way you enter the bermuda triangle, you can enter one of the other worlds. But then there'd have to be another triangle somewhere else, plus three extra lines.

i am writing a story where the people go from this earth to a fourth dimensionally perpendicular earth that is somewhat bigger than this one. i was wondering if anybody could describe what this would be liike?

If the other earth was bigger, dirt would pour out of the intersection onto our earth, until they were both the same size. Come to think of it, no matter where you intersect them, they'll end up becoming the same size, and with the centre in the same place. It's the same reason the earth is a sphere and not a cube. Work it out with circles instead of spheres and see.

The hardest part is deciding how you could turn at the intersection.
The way I see it, you have two options. I quite like the second, but it's your story.

1. Each earth has a small tridth and exists in a 4D universe. In other words, the earth is not a sphere, but a spherinder. We don't notice this because the earth is too tarrow to turn around in. This means we can't get to the other worlds at the intersection, but small objects, gases and liquids can, so the other planet could affect the weather. Alternatively the tridth could get bigger as you approach the intersection, so a human can fit.

2. The universe curves back on itself and intersects with itself across a plane. This plane just happens to pass through the earth and another planet in about the same place. It doesn't matter if the centres of the planets aren't exactly together, because the dirt should all smooth out.

Unfortunately, I have no idea what happens if you walk into the intersection in this case. Objects can handle the curvature of spacetime pretty well, so a 90 degree bend shouldn't be a problem, but the intersection might be confusing. You might as well choose whatever's best for the story.

Oops, I don't know what happened there. I must have submitted while I was writing somehow

[pat]

if the two perpendicular earths are the same size, they would only intersect on the surface in two places, at opposite ends of the globe..

Wouldn't two perpendicular spheres intersect on a line?

Not if they are three-dimensional balls (B³), each in 4-space.

Let one ball be x² + y² + z² ≤ 1, w = 0. Let the other be x = 0, y² + z² + w² ≤ 1. That's as close to perpendicular as one can get for two 3-balls in only 4-dimensions. Those share the disc x = 0, y² + z² ≤ 1, w = 0.

If you're willing to go up to five dimensions, then you can make them "perpendicular" enough to intersect in only a line. If you're willing to go up to six (or any greater number) dimensions, then you can make them "perpendicular" enough to intersect in only a point.

But, perpendicular is a poorly defined concept here. Until you get up to six dimensions, it's not really possible to consider two three-dimensional shapes to be perpendicular/orthogonal.

[PWrong]

Oh, ok. I see what you mean about perpendicular being poorly defined. In this case it doesn't really matter whether they're perpendicular or not.

I should have said disk, rather than a line.
the disk you mentioned is y^2 + z^2 < 1.
so the line I was talking about is actually the circle y^2+z^2 = 1

[RQ]

Umm Pat, it can't get any more perpendicular than a higher dimension, because there would be no reference frame, and not enough dimensions...
(assuming we're talking about flat spaces).

[elpenmaster]

well, the two earths wouldnt have to even out to the same size if there was soolid rock where they intersected. they would intersect in a disk, with a circle, like one of the parrallels, running along each earth. so maybe they intersect at the equator or the 33 pqarallel or something like that.

2 circle in 3d can be perpendicular, so so can 2 spheres in 4d, i think :?

if the earth perpendicular top ours was larger, then maybe we dont run into it because it only exists when it touches certain material (for example)
so characters in my story are climbing up a tree, which contains material to make it touch bigger perpendicular earth and run into it, and characters climb up tree, run into bigger earth, go there, etc.

[swirl gyro]

Ok, it would take a long time for the two planets to become the same size... dirt would just pile out of the bigger one and form a ridge on the smaller planet. Oh, wait... atmosphere, oceans, and magma are all pretty fluid... ok, they'd even out, sorry.

To the person who mentioned size being a factor in making it thru the intersection, that is false. First of all, the concept that they'd be in full 4D space without being able to turn around is false. Now, assume they're on intersecting 3-branes. All things would have the same tridth (ie, none).

...Except that, the only meaningful way to choose which way to go from the intersection is to give the branes curled up micro-dimensions, tridth (am I using tridth properly?). The branes may be of different tridths, and things from the thicker one may not be able to get into the thinner one. But 3D size still makes no difference.

Side note, I think "curled up" is bad terminology, but that seems to be what everyone uses. For those who don't know what I'm talking about, example: A paper towel roll is 1D with a curled up secondary dimension.

RQ, I'll try to explain what Pat was talking about. I guess you could say, there are degrees of perpindicularity. But 3D is too low for us to notice the effect. here in 3D, 2 planes can only be perpindicular along one axis. But in 4D, planes could also be perpindicular along both axii, so that they only intersect at the central point. Am I any help?

That last paragraph reminded me of knots. Does anyone here think about higher dimensional knots, composed of planes & soforth? I haven't been able to picture such a knot, but I know which types work in whch dimensions. I discovered high-D knots on my own, and I've never seen anyone else talk about them. Sorry for going off-topic.

[PWrong]

You're right, it does sound like bad terminology. I only use it because that's what Briane Greene uses in the elegant universe.

I was thinking in terms of that too, although it doesn't matter if you take the extra dimensions out. The problem is how to determine whether an object continues forwards, or turns ana/kata into the other earth. Since we haven't noticed anything strange, it's safe to assume that we always go forward.

Although, how would we know the difference if we always turned ana? It's just the space that's bent, nothing else. We'd only notice if it kept changing all the time.

Assuming the planet we're used to is all on the same realm in hyperspace, what about the sun? If we're orbiting the sun normally, then the other earth can't be. Imagine it in 2d. It doesn't really work no matter how you look at it. So we can't have a similar climate. Wow, it's getting complicated now.

[swirl gyro]

Although, how would we know the difference if we always turned ana? It's just the space that's bent, nothing else. We'd only notice if it kept changing all the time.

It would keep changing all the time. walk thru the intersection, ana. try to walk back thru to where you came from: you can't, you turned ana again, so you're back in your realm, but on the other side of the intersection. And looking thru the intersection, you see a different half-realm than the one you'd reach by walking thru it.

Assuming the planet we're used to is all on the same realm in hyperspace, what about the sun? If we're orbiting the sun normally, then the other earth can't be. Imagine it in 2d. It doesn't really work no matter how you look at it. So we can't have a similar climate. Wow, it's getting complicated now.

It would have to be orbiting it's own sun, in it's own realm. It could have a similar climate.

[swirl gyro]

walk thru the intersection, ana. try to walk back thru to where you came from: you can't, you turned ana again

Umm... I hope ana/kata is subjective like left/right, rather than objective like north south, kuz otherwise I messed up If ana was objective, and you always turn ana at the intersection, you'd be stuck in that quadrant forever.

Edit by BobXP: I don't know if alkaline likes profanity or not, but I'll play safe.

[PWrong]

Assuming the planet we're used to is all on the same realm in hyperspace, what about the sun? If we're orbiting the sun normally, then the other earth can't be. Imagine it in 2d. It doesn't really work no matter how you look at it. So we can't have a similar climate. Wow, it's getting complicated now.

It would have to be orbiting it's own sun, in it's own realm. It could have a similar climate.

No, because the other planet is attached to ours, and it has to move around our sun with us. So it can't be orbiting anything in its own realm...

Hmm.
Unless the whole other realm moves around our sun with us, always at 90 degrees to us. But even then, the other planet can't orbit around anything, the other sun would have to orbit around it.

So the other earth is the centre of the other universe! A victory for the other-catholic church against other-Galileo!

[Keiji]

Riiiiiiiight.

Well, I would still imagine that our planet is one slice of a 4D planet, which orbits around its own sun in the same plane as our planet orbits in. :wink:

[PWrong]

Alright, I didn't explain that very well. But imagine it in the 2D example and it all makes sense. I just made an animation of the system, but I figured it out just by visualising it.

C1 exists in the XY plane, C2 in the XZ plane. C1 moves around the sun in a circular orbit. C2 is attached to C1, so it can't move around in its own plane at all. Instead, the other sun moves around the planet itself. It's like the other earth is the centre of it's own solar system.

Using my animation, I found that in some cases the other sun will temporarily move straight through our own. This only happens if the disk where they intersect points towards the sun, so it would probably be about on the equator, and if both planets have similar climates (implying same distance from the sun, and same length of a year). I'm not completely sure if this is true for 3D.

That doesn't really matter though. It's a bit too complicated to allow the other earth to have its own solar system, especially one that's different from ours.

[swirl gyro]

walk thru the intersection, ana. try to walk back thru to where you came from: you can't, you turned ana again

Umm... I hope ana/kata is subjective like left/right, rather than objective like north south, kuz otherwise I messed up If ana was objective, and you always turn ana at the intersection, you'd be stuck in that quadrant forever.

Edit by BobXP: I don't know if alkaline likes profanity or not, but I'll play safe.

I was profane? ah, "messed", right. well, you can go bleep youself you censorous biphole

[swirl gyro]

C1 exists in the XY plane, C2 in the XZ plane. C1 moves around the sun in a circular orbit. C2 is attached to C1, so it can't move around in its own plane at all. Instead, the other sun moves around the planet itself. It's like the other earth is the centre of it's own solar system.

Motion is relative. Earth and Sol both orbit around their combined center of gravity.

That doesn't really matter though. It's a bit too complicated to allow the other earth to have its own solar system, especially one that's different from ours.

No, it's not complicated at all. Anchor them together, and they can both slide around in any direction within their own realms. there is no restriction of movement, and I don't know where you get that idea from.

[Keiji]

walk thru the intersection, ana. try to walk back thru to where you came from: you can't, you turned ana again

Umm... I hope ana/kata is subjective like left/right, rather than objective like north south, kuz otherwise I messed up If ana was objective, and you always turn ana at the intersection, you'd be stuck in that quadrant forever.

Edit by BobXP: I don't know if alkaline likes profanity or not, but I'll play safe.

I was profane? ah, "messed", right. well, you can go bleep youself you censorous biphole

That's what I edited :wink:

[PWrong]

Motion is relative. Earth and Sol both orbit around their combined center of gravity.


No, it's not complicated at all. Anchor them together, and they can both slide around in any direction within their own realms. there is no restriction of movement, and I don't know where you get that idea from.

The only way I can see it is if the realms actually move relative to each other, with the planets sliding around within them. There's no contradiction about that, but the image is a bit ugly. Why should the universe slide around us?

[RQ]

Motions do get more complicated the higher you go. That's why orbits in 4D become more unstable.

I suppose we're talking about two Earths perpendicular to each other in the same space, so here's my thought:

The two Earths are perpendicular to each other in the 4th dimension. They don't really cross each other with observable consequences, so therefore there must be a double space of some sort.

[elpenmaster]

or maybe the other earth does orbit around its own sun, which is perpendicular in the 4d way to our sun. then this second earth would only intersect us twice a year. . . .or maybe once in a long long time, if they orbited different. maybe this causes earthquakes. . .or caused mass extinction 225 mya, and dinosaur extinction. . . :?

[RQ]

How would they interact? If the perpendicular Earth even showed it's "face" around the other one, where would the missing space from the second Earth go to? Simply, they wouldn't interact.

[elpenmaster]

when the two earths hit each other, there would be major damage to both, causing mass extinction. interesting, this could also induce "transgravispermia", where life is sent form one dimension to another

[RQ]

Quite interesting, but for life to get sent to the other planet, it would have to bend in the fourth dimension, so how could the Earths even interact?

[PWrong]

The two planets intersect at a disk. The disk meets the surface of the earth at a line running around the earth, like at the equator.

Supposedly you could simply walk up to this line and simply turn ana or kata, so you'd be on the other planet. I don't know you would go about doing that. If the intersection is deliberate, you could just press a button and make space bend in a different direction. Once on the other planet, you can put it back to normal.

[PWrong]

or maybe the other earth does orbit around its own sun, which is perpendicular in the 4d way to our sun. then this second earth would only intersect us twice a year. . . .or maybe once in a long long time, if they orbited different. maybe this causes earthquakes. . .or caused mass extinction 225 mya, and dinosaur extinction. . . :?

I prefer the original idea of having the two planets connected. I tend to distrust any kind of 4D explanation for mass extinction. Ideally, we want two planets orbiting around the same sun. Maybe we need to curve space around in a particular way to make it all fit together.

[swirl gyro]

I prefer the original idea of having the two planets connected. I tend to distrust any kind of 4D explanation for mass extinction. Ideally, we want two planets orbiting around the same sun. Maybe we need to curve space around in a particular way to make it all fit together.

Why do you want them around the same sun? I'd want them around different suns, so you can travel many light years just by crossing the boundary... make travel easier.