Everything we understand about our own universe has to come from information gathered through the senses. And while the eyes and ears can have quite abstract concepts ferried to them, it's still impossible to actually observe these complex ideas in everyday life. We can only really observe analogies. So where we have come to understand the three spatial dimensions we exist in, quantum physicists for years have proposed there may be more. And just like the complexity of life is able to be sustained in three dimensions, would it be possible to sustain intelligent beings in more?
Scientists developing the multiverse theory, also known as M-Theory or Meta-Universe Theory have spent considerable time examining what higher dimensions and parallel realities would be like. There are several schools of thought on the subject, but there are several different possible ways higher dimensions could manifest. The easiest way to imagine a higher dimension is to examine them relatively through the lens we already have of seeing lower dimensions.
For example, a being able to only exist in the flat two dimensional would be able to move along its simple plane, but unable to see the hand hovering over it. An ant crawling across its simple world would be a fantastic and magical being only appearing to it as six impossible individuals occasionally shifting in and out of its reality as the bottoms of its feet made contact with the plane. Likewise a simple pencil scratching across the surface of its world could create structures of such complexity the simple two-dimensional being would find it difficult to comprehend, if not impossible.
It's difficult enough to imagine how matter would exist in the fifth dimension, but the first, second, third, and fourth dimensions can all be represented mathematically. The abstract fifth dimension is represented by the symbol N. But before it seems like we'll never understand higher dimensions, consider that our eyes are not actually capable of perceiving true three dimensional space because the retinas collect light in what is essentially a flat (even if slightly curved) plane.
One of the more interesting elements of having binocular vision, as opposed to eyes on the side of the head is the additional illusion of three dimensional vision, which is facilitated through comparative analysis between eyes. This is called in simpler terms depth perception.
So what might a higher dimensional being be like? While there are plenty of theories on what such a being may actually be like, it's difficult to get a firm understanding of something so beyond our own universe. In fact, rather than being super-beings in our own dimension such a being could theoretically actually suffer severe limitations on our own world, and would have to learn to function in an entirely new way.
And our existence, may even seem confining to such an entity to a point where operating within it would feel trivial and perhaps even disturbing. Of course, concepts like triviality would be difficult to translate into higher dimensions as much as the physical being itself. They may operate according to patterns of thought completely beyond what we are capable of on Earth.