The curvature of the universe in the 4th spat. dimension

[RQ]

There was a topic long time ago (like 2.5 years) where someone asked how we knew whether there was a 4th spatial dimension and I answered something like "because we know the universe is finite but has no boundary (i.e. space is like the surface of the Earth but +height)" and jinydu answered that current models explained the universe in 3 spatial dimensions while it is finite...

I guess I'm wondering what the current consensus thinks of the shape of the universe and its relationship with the 4th spatial dimension.

[Keiji]

Well, it would make sense to me if the universe was in the shape of a glome or tritorus in flunespace...

[papernuke]

two things, whats flunespace and whos rq?

[edit] who did he used to be

[RQ]

two things, whats flunespace and whos rq?

[edit] who did he used to be

I think flunespace is space with 5 spatial dimensions. I used to post here 2+ years ago.

Hayate, I know it makes logical sense to assume that the universe must be curved in the 4th spatial dimension, I'm curious as to what the current models are etc.

[Keiji]

Flunespace is the same as tetraspace, just continuing on the "point/line/plane/realm" series rather than the "null/mono/di/tri" series.

[wendy]

Space as we know it is three-dimensional. Exactly what shape the manifold is, is not known, but it is essentially without large-scale curvature over vast distances.

All space, even euclidean, is curved, but curvature is not something that happens in a higher space, but is a property of the space itself. For tech types, curvature is something akin to a point diadic.

One implication of Einstein's theory is that it is pretty easy to follow curvature, since this is the proper motion of a free body at rest, is to follow the greatest gradient of curvature, to space of more negative curvature.