This is how the universe is expanding. We know that we can draw a line in a square . Here line is 1dimension and the square is 2dimension. Similarly a square could be drawn on a cube . here square is 2 dimension and the cube is 3dimension. Similarly a point which is 0 dimension could be drawn on a line . Do not confuse between point and a dot . They are two different things. Also, a point could not be drawn on a square . A dot can be drawn . So we conclude that an object can have another object which is one dimension lower.So, if the space is 4d then the universe is 3d.[it is just an example]. So the universe is expanding into the space which is 1 dimension higher to it.

actually the paper is 3 dimensions, it has thickness. you probably mean a plane which is a math concept and doesn't exist in reality.

Well Very well!! you are right that universe in expanding to another dimension.But not 1 dimension. Actually higher dimension. Space is not 4-D,It is 11-D. One dimension of time and 10 spatial dimension.

That's what I would have thought - common sense. Anything that exists must do so in the same number of dimensions. I recall a comprehensive discussion however, several years ago, in Physicsforums, where serious scientists were talking about the real existence of two D objects. Unfortunatley I cannot now find that thread. Anyhow, my question is (though slightly off topic, but it piqued my interest) IS there any object - real object, that science considers two D, or .. what could have I been reading ?

Whatever happened to the "Steady State" universe theory, after all it was the "fact" for many years. Where is it expanding into, aren't there boundaries somewhere that prevent it from forever expanding that we just can't see yet? Just because distances seem to be getting further apart why is it they are expanding, why couldn't they just be moving away from each other like the Earths plates did to form new continents?

I don't know if this will help, but my naive understanding of the 2-D descriptions by experimental physicist is about surface phenomena and the domain confining the energy and particles inside a surface layer so they can't exit, and have all their interactions within that surface layer. So its really a very thin ribbon not 2-D. If around a tube then the ribbon is curved around imbedded in 3-D space but not in the tube material 3-D bulk. Maybe pure mathematics has 2-D structures but they are only hypothetical and just simplifications for mathematical shortcuts ignoring the other dimension for making the maths easier. I haven't read about real 2-D objects, only surface or layers where surface or layer thickness is ignored until it becomes a property which affects the surface layer phenomena of interest. But maybe I haven't read enough. Don't know.

Reply to the above question First, I want to explain two dimensional objects. Actually, a two dimensional object is the edge of a three dimensional object. So, the shape formed by the edges of the base of a cube is 2 dimensional. But for conviencience we take plane figures like square as two dimensional. Now , answering the question which says that whether the space and the universe have boundaries or not. According to me, the space and the universe have boundaries and the universe is still expanding and will expand forever. To explain this I will take the example of a cube and a 2 d object. We know that the cube is 3 d . Now, lets take a small square paper and stick it on the cube . We know that the edges of the paper form a 2d object. For information on time travel see hyperspace.blogspot.in Now, if the side of the square paper is bigger than the side of the cube , it could still be paste on the cube as the extra side of the paper could be folded on the other side of the cube. So, we see that the 3d object could hold 2d object. If we apply this rule to higher dimension , this rule still holds. So, the universe is expanding in a space which is finite. They both have boundaries.