4D lakes possible?

[raumaan]

Are 4D lakes possible? Ahem, "they" have three dimensions. Problems:

1. They could only exist in outer space in 3D?
2. To exist as 3D objects, you should in 3D standards go to outer space?
3. This all has to do with outer space?
4. How can I imagine this thing without imagining space?


Physicist Michio Kaku said:

Like ostriches with their heads in the sand, we humans have a sense that if we don't see something, it ain't there. But then there is a whole world out there, not just the sand.

Could this have something to do with this? After all, I heard him say this on a TV episode about "Parallel Universes and Higher Dimensions Associated".

Bye!

[dodecahedron]

First off i would like to point out ostriches dont do that.
Secondly the descriptions are the surfaces of lakes theres water "below" them.

[wendy]

4D lakes exist, because it is the product of depth and a 3D surface. If ye are having problems grasping this, then you are not dealing with four dimensions.

[quickfur]

I don't understand what 4D lakes have to do with outer space. There is no relation whatsoever.

All the perceived "problems" are from trying to shoehorn a 4D object into 3D space, which is impossible. 4D lakes can certainly exist -- in their native 4D space. Not in a 3D space, because 3D space can't hold any 4D objects.

[suny]

Nice post. I like it. Thanks for sharing these information. Keep it up.

[Keiji]

I don't understand what 4D lakes have to do with outer space. There is no relation whatsoever.

All the perceived "problems" are from trying to shoehorn a 4D object into 3D space, which is impossible. 4D lakes can certainly exist -- in their native 4D space. Not in a 3D space, because 3D space can't hold any 4D objects.

[Hugh]

3D space can't hold any 4D objects.

Just as 2D space can hold a 2 dimensional slice of a 3D object including length and width, 3D space can hold a 3D slice of a 4D object including length, width and height, can't it?

[quickfur]

3D space can't hold any 4D objects.

Just as 2D space can hold a 2 dimensional slice of a 3D object including length and width, 3D space can hold a 3D slice of a 4D object including length, width and height, can't it?

Yes, but don't expect a 4D object to behave like a 3D one. For example, we can draw a map of a 3D terrain on a 2D piece of paper, which can show lakes, etc.. But don't expect those diagrams of the lake will be subject to 2D gravity, for example. Similarly, you can draw a map of a 4D lake in 3D, but don't expect it to behave like a 3D object "in space" (whatever that means).

[wendy]

One should not treat the propositions given on television as being true. In essence, it's there to make things happen. The idea of going into space is to remove gravity, for those people who can't tell the difference between a photo and a map.

You can easily imagine 4d from 3d, by considering that photos and maps of 3d are 2d, and thus photos and maps in 4d are 3d things. In both cases, they loose a dimension. A lake in 4d would present a 3d solid on a map, but it has a perpendicular depth, just as a lake mapped on 2d has depth in 3d.

The other thing to recall about this image, is that to correctly grasp the concept, you have to suppose access to any point without going through any other point. For example, on a map of a 3d city, (which is a 2d thing), you don't have to go from the edge to get to any part of the map: you can look directly at any part. So is it also in 4d, except that you get a 3d thing which you are supposed to look at the innards direct.

It's similar to looking at a person, and supposing you can see the interior of the heart and lungs and muscles and lunch, without making any cut or x-ray vision. You're not supposed to be looking through the person, you are supposed to be looking from the 4d, like we look at 2d from the 3d.

[Klitzing]

Are 4D lakes possible? Ahem, "they" have three dimensions. Problems:
[b]
1. They could only exist in outer space in 3D?
2. To exist as 3D objects, you should in 3D standards go to outer space?
3. This all has to do with outer space?
4. How can I imagine this thing without imagining space?

...

Lots of replies already.
Just would like to add some point, which seems closer to the questions.
4D clearly is 1 dimension up. So yes, the surface of that lake would be a 3D solid, as Wendy already pointed out: the lake of any dimension is surface x depth. Even so you could not embed 4D things in 3D, you could do so for sections (slices). So first you could consider some section which totally includes the depth dimension. This is what a 3D lake would look like. But you well could use a section which runs completely orthogonal to that depth direction. Then you either would get a section "above" the water, at the surface, or underneath the surface. In the latter 2 cases you would get some connected 3D body as lake section. Which embedded into our normal space is just as cup of coffee within a satelite: you could withdraw the cup, it holds together. This is due to 3D gravity, but also to the surface forces. And that latter could serve for analogy here too: it is a 3D surface of a 4D lake, so surface forces apply indeed! But those surface forces of 4D work within a 3D subspace, thus they could be represented within our 3D world more like our gravity (here also a 3D effect).
But then, this "outer space" image of the coffee with withdrawn cup is wrong. Look again at your section of 4D: that one would not only cut through the water, it would likewise cut through the holding grounds around. And that one surrounds it completely (else it would pouring out.) Accordingly that 3D body of water would be enclosed totally by some rocky shell! Therefore, your 3D section (orthogonal to depth-direction) of a 4D lake rather would look like a geode, a druse!
One more thought onto "outer space": surface forces are there stronger than gravity. Note: it is not the gravity of the coffee itself, whic holds that coffe together. As there are other bodies too: the space ship, the astronaut, the cup. So gravity would not go towards the body center of that coffee! Instead it is just a rather weak one there. It is the surface force, which is the stronger one there. Kind of 2 drops on a plate: getting close enough they will melt together. But on earth the gravity is much stronger. As soon as the lake boundary gets hit, the water would pour out. So too in your 4D case: as soon as the druse would get an opening, the water within would pour out. And this not only within our 3D embedding, but likewise as a mere section of 4D!

--- rk