raumaan wrote: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But then, this "outer space" image of the coffee with withdrawn cup is wrong.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