When looking into the concept of other dimensions, many older scientific models deal in terms of symbols and representations that seem to follow a central paradigm or belief system, but those studying quantum physics suggest that other dimensions may work in ways entirely alien to the laws of this universe. But just because something seems unfathomable, that doesn't mean there won't be inquiring minds that attempt to punch through this rift and see into worlds far beyond what we are considered capable of understanding.
An exercise in studying the realities of other dimensions could be to look at a drawing of an object, like a cat and trying to compare the two. Remember in doing this that you're not actually comparing the idea the drawing represents, but the drawing itself. A two dimensional object can only exist on an x and y axis, with no way of moving left, right, forward, or backward. There is no way of moving up from this dimension and "ascending." This word "ascend" may be familiar to us as it is used in several mystical traditions. Perhaps this is not mere coincidence, but that ascend does not mean "move into the sky" but rather a sort of ascent similar to that of a two dimensional object moving into three dimensional space. And perhaps the fact that quantum physics seems to share much with mysticism isn't a coincidence either.
A look into what another dimension would look like may actually be possible if we look at one simple object. Imagine a person floating in a void for the sake of simplicity. If the person decides to raise his hand, now imagine suddenly there are an infinite number of him floating nearby in a line and stretching in either direction, each of them raising their hand to varying degrees and at different speeds. Each of these "parallel" people are not merely facsimiles of the original person, but rather actually the same person. Now let's say one of these infinite people who are raising their hands decides to raise his other hand. As he raises his other hand, an infinite number of him suddenly appear in an intersection, where he is displaying every possible variation of either raising or lowering his hand. This is the most simple way of looking at it, and yet it gets even more complex. Not only are the dimensions creating an infinite number of him depending on the action he takes, but an infinite number stretching in every direction for the decision every cell in his body takes. And of course each of those cells, composed of atoms, creates an infinite number of possibilities for every movement they make. The components of the atoms may be yet a smaller unit, such as the vibrating strings in string theory. These strings, millions of which would go into each atom, would each get their own dimensions based on their action or inaction. And assuming this was the absolute smallest unit of measurement possible this would be where it would end. So even with a single human being, an infinite number of possibilities would quickly expand from this central point with each slice of time. And each of these would then progress in their own way, spawning new dimensions until the equation quickly became far too complex to comprehend. When we are able to comprehend a universe such as this we may get some inkling into the complexity of the next dimension. And yet it seems incalculable from our position on a flat piece of paper.