how is 3d perceived from 4d?

[sondizzle]

ok, this is my first post here, and i am pretty new to this and trying to become smarter, so forgive me if this has been asked already.

in our 3d universe, 2d only exists as an idea. one cannot draw a true 2d line because there is always 3d medium i.e. paper. one can only imagine a 1d point. kind of like plato's world of the forms, the perfect triangle can only exist as an idea.

so in a 4d 'universe', could 3d even be possible, or would 3d exist in idea form only?

does this make sense?

[papernuke]

probably not, and it dosent make sense to me

[PWrong]

so in a 4d 'universe', could 3d even be possible, or would 3d exist in idea form only?

Pretty much. But an idea is all you really need. Drawings on paper are an approximation to a platonic form, as you said, but it's a very good approximation. And when we define a line in terms of maths, it becomes perfect.

[Nick]

Well, seeing as how we know for a fact that there is 3 dimensional life, I don't see how this question is relevant.

[Hugh]

4d beings would see in 3d, and those 3 axes would be orthogonal to each other.

[sondizzle]

ok, thanks. can i ask another question?

i was just watching an episode of cosmos by carl sagan. in it he briefly touches on the 4th dimension. he does a demonstration of a 2 dimensional plane being curved by 3 dimensional space into a sphere. he supposes that he is a 2d creature unaware that it is in fact 3 dimensional, he marks a spot on the plane and sets off in one direction and eventually winds up back where he started.

so my question is, could our expanding universe eventually "curve" back to it's starting point? could all matter eventually come "back" to the point of the big bang?


or if i took off in one direction into the universe, after a long enough period of time, would i wind up where i started?

[PWrong]

he supposes that he is a 2d creature unaware that it is in fact 3 dimensional, he marks a spot on the plane and sets off in one direction and eventually winds up back where he started.

If the space is wrapped around a sphere, the 2D creature will not be entirely unaware. If you were a 2D being who wants to find out if you're living on a sphere, fire two rays of light and try to keep them exactly parallel. If you're living on a sphere, you will find this is impossible. The light rays will eventually diverge, because there are no parallel lines on a sphere (a line on a sphere is always a great circle. Lines of latitude are actually curved).

If we live on a 4D sphere, we could find out with a similar experiment. People have tried this, and the light rays don't diverge. So there's no evidence yet that we live on a 4D sphere.

There is another possibility. Imagine a 2D being living on the surface of a torus (a doughnut). Now his light rays don't diverge, but if he moves far enough he'll end up back where he started. Our situation could be more like this i.e. we live on a 4D torus. The only problem is that there's no way to test this theory without actually going all the way round, AFAIK.

[batmanmg]

thats the topic i asked in another thread ... what shape is the universe? but i don't like the idea of a 4d torus... it seems too complexe to be true...... this also depends on what you consider a 4d torus... i take it to be a sphere rotated around a plain... i am forced to consider the 4 torus to be the only sensical answer becuase i don't have anything else to consider

[PWrong]

thats the topic i asked in another thread ... what shape is the universe? but i don't like the idea of a 4d torus... it seems too complexe to be true......

The actual shape is difficult to visualise, but if you're living on the surfuce, it's much simpler than a sphere. The equations are simpler too.

this also depends on what you consider a 4d torus... i take it to be a sphere rotated around a plain...

By 4D torus, I meant ((21)1), the 3-torus (or tetratorus if you insist on breaking convention). The shape you describe is the toracubinder, (211). That's no good for the shape of the universe, because it's flat in one direction and curved in others.

[prime]

3d can be perceived from 4d in a similar way as 2d can be perceived from 3d.
from the 3d space we can see everything inside the 2d world.If there is a dot inside a circle it cannot be removed from the 2d plane without breaking through the circle.but we can remove the dot by taking it perpendicular to the plane into the 3rd dimension.Similarly if there is a point inside a sphere in 3d space..it cannot be removed outside without cutting through the sphere....but it possibly can be removed by taking it perpendicular from the space into the 4th dimension...So it is possible that a 4d creature would remove a point inside a sphere without cutting through it