As you read on, you'll possibly think that I've been smoking something good or drinking way too much. Well the scary fact is that I've never done drugs and my thoughts are still weird (many of my friends believe that if I did drugs or drank I'd be normal, and that's not something I'm willing to play with).
Flatland
As a young college student interested in Mathematics, my oldest brother, who I call Marcos, but others call Jim (I kind of wonder if he has two personalities to go with his two names), gave me a book called "Flatland".
Flatland is an interesting book (though very sexist, I'll get to that later, but if you read it, be prepared to put your distaste to sexist talk on the side).The book is about a square who lives in a flatland (2-space), as a square he is considered part of the working class. In this world as you get brighter and more evolved you get more sides, so a circle (which can be though of as a polygon with infinite sides) is considered the highest form you can achieve, while a triangle (a woman) is the lowest (down, it's a good book to show the 4th Dimension exists, it proves it via mathematical induction). In this book the citizens of 2-space are aware of 0-space (which is a point) and 1-space (line). When the square interacts with someone in 0-space, that point doesn't see anyone, but can hear the conversation. When he passes through 1-space, the point in a line all of a sudden sees a new point in front of him, he's confused by this, since he's only known 1-space. To both 0-space and 1-space the interference of a citizen from 2-space was like a ghost.
One day the square from 2-space is visited by a sphere from 3-space (which has been observing 2-space). This sphere can see inside the walls of the square's house, tell what's in the cabinets or any safes that the square has, this is because what is solid to the square isn't solid to the sphere (look at the blueprint of a house, imagine if you were living in 2-space, all those walls would be real, but as a citizen of 3-space you can see into those walls). The sphere has to prove his existence to the square, but by appearing and disappearing, he manages to convince the square that 3-space exists.
When the square brought this meeting up to the circles in his world, he was labeled as a heretic (oh I forgot to mention, circles were also religious leaders) and locked up (boy doesn't that sound familiar, religious leaders locking up philosophers and scientists). Despite the circles objections the square not only believed in 3-space, but was able, through pure faith in 3-space, be able to experience 3-space. Now when he brought up the idea of 4-space to the sphere, he was told that such talk was that of a heretic.
I don't do it justice, get the book and read it (it's only 100 pages), I believe someone made it into a movie.
Real Life
OK, how does this relate to real life? Well I can't prove that the 4th Dimension exists as a spacial dimension (people tend to talk about time as THE 4th Dimension, but time is just A dimension). It would be helpful if it could be shown and exploited. It could make it very easy to move around, nothing "magical" would happen, but you might be able to make shortcuts when going outside or into the kitchen (maybe Merlin or Houdini understood the use of the 4th Dimension).
It could explain the existence of ghosts, which I don't see as being supernatural beings, I see them as 4th Dimensional beings that happen to be passing through our 3-Dimensional plane, they appear to be passing through walls (they are going around them in 4-space) and we can see through them (because we are only seeing a cross-section of them in 3-space, in 4-space they are quite solid).
I'm sure right beside every clothes drier in the world there is a collection of socks and left handed gloves (I always loose the left hand), they are sitting there, but we can't get them. Hide and seek would also be cool in 4-space (well assuming you had access to it and others didn't). In my house I've found a portal for the 4th Dimension, it's under my recliner. I'll have my army knife, alarm fob or something else in my pocket, I'll loose the knife, look all over the house to find it and then finally go and look under my chair, and there is the item I lost. My wife says that the knife is slipping out of my pocket, down through the chair and onto the floor, but I think that the knife falls off my bedside table, through two floors and ends up under my chair (OK she might be right with this one, but I still like my idea better).
It would be great for spies, thieves or anyone else wanting to look or be where they shouldn't. Hmm, I wonder if Homeland Security knows about this, I'd tell them, but they'd probably say that my talk was crazy and that of a heretic.