It is particularly challenging but interesting to consider other dimensions of space and time. Physicists became interested in the idea of additional dimensions upon developing string theory, which despite being somewhat controversial, as there are few conceivable ways to test such a theory, is currently our best prospect for a complete physical theory --it would make sense on both small scales and large scales, would unify the fundamental forces, and would actually predict gravity instead of just observing it-- and happens to make the most sense in 10 or 11 dimensions. Regardless of whether string theory proves to be accurate, many physicists see no reason as to why our universe should not have more dimensions than we can perceive. A line exists in one dimensional space, but it also exists in 2-D space, 3-D space, 4-D space, and so on.
Studying extra dimensions has spawned additional theories of wormholes, parallel universes, and the multiverse. Higher dimensions make up what is typically called hyperspace.
Almost any physicist or mathematician working in this field will reference "Flatland," a book written in 1884 by Edwin A. Abbot, when trying to explain their work to the public. I still haven't read Flatland but I've become very familiar with the story. It takes place in a two dimensional world called Flatland and is narrated by a character named "A. Square" who presents to the reader life in a two dimensional world. The story is designed to provoke thought concerning dimensions other than the ones with which we are familiar, and A. Square himself is forced to do the same. First when he visits a one dimensional world in a dream, and then when he is visited by a three dimensional sphere who appears to him as a circle increasing and then decreasing in size.
Flatland is so frequently referenced because the idea extends easily to our own perception. It raises questions of what a 4-dimensional object would look like, and to the true nature of reality. Similar to A. Square's perception of a sphere, a four dimensional object would appear to us in 3-dimensional cross sections. A 4-D sphere, or hypersphere would appear to be a sequence of spheres increasing in size and then decreasing, finally vanishing into a point. We would only be able to see the object in its entirety throughout time (another dimension) but could never imagine its spatial form.
Recently, in trying to understand multiple dimensions and my own perception, I've been trying to deconstruct my experience as an observer. In a single moment, time has no dimension; it is only a point. Space should have three dimensions but without time, I can only perceive two dimensions. Therefore it is my memory and my mind which allow me to assemble these splices to create three spatial dimensions and one time dimension; a succession of moments in space.
I still can't wrap my head around the fact that physical positions are so transient and what it could mean in terms of dimensions. If I move my hand, there is nothing in the space that it occupied. It reminds me again of perceiving only splices of a continuous physical thing. In a video called imagining the tenth dimension which contributed to my early interest in higher dimensions, to help imagine another dimension, the viewer is asked to consider a long "snake" that would correspond to his or her entire life's path. Our experience then consists of cross sections of this 4-dimensional "snake" and if we know we are viewing cross sections, why can we not infer another dimension? If all of our experiences were to persist in physical space, space would become overcrowded. It would require at least another dimension to compensate. If I know that 10 minutes ago I was sitting on my couch and now I am sitting on my bed, I am confident that both are part of reality but the self that was on the couch 10 minutes ago has vanished and will never be again. In every moment time and space are changing and all of experience is piecing together traces. If these moments are not in fact connected, we would not be able to experience them sequentially as we do. Time would never pass. I have read in several books on some of the subjects I have been discussing that we could stack two dimensional surfaces on top of one another to obtain a 3-dimensional object, but that is not true! If the surfaces are in fact two dimensional, they have no thickness and we can stack as many on top of one another as we'd like, we will still have a two dimensional surface. Many theories permit the existence of multiple dimensions by deducing that they must be so small that they are invisible to us. I feel like there must be some "thickness" to our moments; another very small dimension; something that allows time to pass. It has confused me for a while that even though there are an infinite number of numbers between 0 and 1, we can in fact go from 0 to 1. For me it is proof that space and time are not in fact continuous but discrete, but it's something I'm still thinking about.
As I said earlier, these are just ideas. Often when I write things of this nature it is out of confusion. It's possible that in a couple days I will understand why this can't be so. Or come to another understanding of what may be going on. In the meantime it's interesting to think about. I was originally attracted to science and math because of the certainty involved, particularly in math. If you accept very basic and obvious statements to be true you can use these statements to build more complicated ones that eventually build off of each other to create advanced and beautiful theorems whose validity becomes unquestionable. It has always seemed a waste of time to me to learn things that may not be true. Yet I find myself infatuated with theoretical physics, a science which was once undoubtedly a science, but now will more closely resemble philosophy or science fiction at times. Theories by some of the most respected physicists can seem too far out to believe, and it can be hard to know what to take seriously. The idea that so much is unknown leaves a lot of possibility and people are starting to get creative.