AA,
A dimension is a conceptual device that is entirely related to perception. I realize that someone will likely disagree with me, but I think my argument in favor of that point is very strong. For this post, let D=spacial dimension.
For instance, neither you or I have ever perceived only 2D. Some people point to drawings on paper as an example however, even in this medium, there is an impression on the paper (however slight) and a "thickness" possessed of the medium used to draw. The paper also has thickness and texture. Therefore, the drawing itself is not 2D, although it may contain a conceptually 2D-esque drawing. In other words, even with such clinching proof, we have to conceive of the 2D aspects to see it as proof of 2D.
In this way, we can conceive of 1D although it can never be expressed (even in a drawing) because a 1 dimensional object can never be observed by us.
There is a famous illustration to explain how there could be more than 3 dimensions of space (and even objects that inhabit these). It requires imagination, but a reaches a certain point where it becomes very flawed.
"Imagine," the illustration begins, emphasizing the conceptual requirement, "that you are a 2D being living in a 2D world. A 3D balloon floats overhead in the third dimensional world that exists parallel to yours. How would you experience that balloon, in your 2D world?"
The standard answer is flawed. The standard answer is, "As a shadow." The actual answer is, you would not experience it at all. The reason is simple, to detect a shadow you must have height. In other words, a 2D being cannot see a shadow because of it perceptual limitations. Also, light cannot refract in 2D, so a 2D being would not see anything—not in the sense that we see, anyway. It would only appear as a shadow to a 3D being looking down at a 2D being's universe, but such a 3d being would be able to discern the cause of the shadow as well.
In a similar way, we are limited. We are blind from the perspective of 5D beings or objects. We have no point of reference for how anything in our universe impacts their universe, any more than a 2D being would understand the impacts of its actions on our universe.
There is more in heaven and earth than are dreamt of in our philosphy. Do waves travel through 3 dimensions of space? Yes, as surely as they travel through 2 and 1 dimensions of space. But it could very well be that we are trying to define and codify that which exists beyond our 3D. And, Doryakii, while you gave the textbook answer regarding the fourth dimension, could there not be a fourth SPACIAL dimension that we get hints of, and even "objects" that exist in a 4D universe? If so, aren't we ALSO living in that 4D spacial universe, whether we can perceive it as such or not?
And does our action in our perceptual universe impact the objects in other dimensions as well? Could gravity, for instance, be a manifestation of an object that exists in a higher dimensional "plane" (for lack of a better word, because planes in our concept would technically lose all meaning after 4D)?
We can imagine a 2D universe because we have a frame of reference for it. But, even then, our imagination is crippled by our experience in 3D. We cannot currently imagine a 26D universe. Or even correctly imagine a 4D universe. But, if there are such higher dimensions, it is certain that we ALSO live in them. Simultaneously, we exist in all dimensions. We are crippled by the limitations of our perceptions.
With this thinking in mind, how much room is there in a 1D universe? Dimensions are a conceptual device, a vain attempt to explain the inexplicable. Very useful, in some ways. But they are only concepts.
Respectfully,
AuldSoul