4 dimensional space?

Do you believe it exists. Something like a Tesseract would give off the concept of what 4 dimensional space maybe be like. But we ourselves may not ever be able to see what 4-D looks like because no one knows exactly what it looks like. We can all see, in 3-D. Just by looking at our arms, legs, space around us, and everything else. But what does 4-D provide beyond the X,Y, and Z plane? Does it involve another coordinate that we could call "n"? That anyone who's from 4-D space would have complete advantage over 3-D space and they could walk, run, and jump in ways that we could not understand. Is the 4-D the altering and maneuvering or spacetime itself? If someone from the 4-D came her to the 3-D they could alter time and space around them to maybe teleport to any location that would want. They could make time appear to run slower or faster around them. We humans regularly interact with "n" but we can only perceive X,Y, and Z. A 4-D would have complete control over "n" (of the 4-D) and they would comprehend its ability and use it to their advantage. My point is- We'll never know what 4-D is, just the concept. But I want to know what you people think it is. This is a 3-D projection of a Tesseract. Close but not there. -