Welcome, Jonathan.
Well, yes, higher dimensions offer incredible abilities that defy many of our laws of physics. But there is a flaw. Usually when we refer to the next higher spatial dimension, we use the 5th, accepting time as the 4th. Now, a theory that holds up to date to the superstring theory is that the universe began in 10 dimensions, but some disturbance caused all the matter to flow into and remain in 4 dimensions, space-time. The other 6, without any matter collapsed into a nearly impenetrable size, the Planck length. To probe it, it would require incredible amounts of energy we cannot harvest just yet.
This is from the book hyperspace, imagine a man that lives in 2D, and is somehow exposed to the 3rd dimension and is floating through it. His vision is limited to be able to conceive only 1 dimension. We, as 3 dimensional beings can observe only 2 dimensions at once without rotation. Now, he would be floating through space, and let’s say he encountered an apple. What he would see is a red line, that becomes progressively larger, then smaller, and then it turns brown and disappears. He would be seeing the apple in 1 dimensional cross-sections. Apply that to our 3 dimensions. We can only conceive 2 dimensions at a time, but supposedly a higher being, to visualize a hypercube for example; we should be able to conceive all 3 dimensions at once to be able to visualize higher dimensional movement. But we can’t do so without rotating the figure.
So let’s say we were floating through a higher dimension and we encountered a hyper-sphere or a hyper-apple to suppose. What we would see is a 2D view of the sphere, and as we progress through the cross-sections of the sphere, we would see the sphere appear out of nowhere, get bigger, then smaller, and then disappear.
What you’re speaking of, regarding walking through walls is often used in mystical sciences, to explain the movement of ghosts, spirits, etc. Take the same 2D person, and draw a box around him on a piece of paper. His vision is limited to the paper; he cannot visualize or move up and down as we have it. No matter which way he would move, he would not be able to escape. Now, take a prison cell for example, and place a higher dimensional being into it. Being able to move through a higher spatial dimension, he would be able to move ana or kata, the motions defined for the next spatial dimension, and go around the walls and appear back on the other side by reversing the motion.
Some argue though that we do exist in all dimensions, but being that the dimensions are so microscopically small and looped, if we do move through them, our motion is limited past what we can observe. But that is another idea behind tunneling, where a particle can move from point to point through any barricade under a certain probability. Whether that fits under the Schrödinger wave function or that is up to the rest. But a higher dimensional being will not exist if there isn’t room for it in the shrunken higher dimensions, unless we are actually are those beings.
. How do you pronounce "Ploegman"?