This page is sort of my opinion on labeling dimensions started by MinutePhysics and revisited by 10thdim. Both youtbe account owners.
MinutePhysics made a video on how dimensions aren't labeled: http://www.youtube.com/watch?v=M9sbdrPVfOQ
10thdim made a video explaining that to some extent, dimensions are labeled: http://www.youtube.com/watch?v=RmQqDJwnmAw
I am going to explain why I think that dimensions are clearly labeled.
MinutePhysics made a video on how dimensions aren't labeled: http://www.youtube.com/watch?v=M9sbdrPVfOQ
10thdim made a video explaining that to some extent, dimensions are labeled: http://www.youtube.com/watch?v=RmQqDJwnmAw
I am going to explain why I think that dimensions are clearly labeled.
0 Dimensions
Point
Obviously the only shape that can be made in a 0-Dimensional universe is a point, which would be the only resident. So there are obviously no namable dimensions here.
1st Dimension
Segment on a Line
Obviously the only shape that can be made in a 1-Dimensional universe is a line or segment, but now objects can vary in length. Supposing that the segment was intelligent and had an eye on each end of it's body, it would only be able to see what is before it on it's line and what is after it on it's line. So no matter where we pointed the line in our 3-Dimensional world, it would always seem like the same direction to the segment.
In order for a one dimensional creature to consider the first dimension to be left/right or up/down, then it would have to have an eye on the inside of its body. Then it could see outside its 1-Dimensional line universe and the only ways it could move would be left and right. However, it doesn't make sense to see outside of your universal space, so therefore the first dimension has to be Forward and Backward.
1st-Dimension = Forward and Backward
1st-Dimension = Forward and Backward
2nd Dimension
Square
The second dimension is the first one where we can actually get some diversity in making shapes. Using at least three lines, we can make any 2D shape we want. A world where there is only two dimensions is commonly known as a Flatland. Obviously with adding a demension, it gives the residents of the world two more directions thay can move in. Forward and Backward are already set in stone as the first dimension, but what would the second dimension be? Well, the creatures of Flatland would only be able to see whats to the side of them as well as in front and back, given they have eyes in those places. If not, they could just rotate themselves to view the areas they can't currently see. No matter how the plane they are in is pointed in our 3D universe, the two dimensions will always seem the same to Flatlanders.
In order for a two dimensional creature to see the 2nd dimension as up and down, they would need to have an eye on their inside that was facing up or down. Then, their whole body would rise up and down when they move across their second demension. In order to be able to walk around in a vast world like we do in our world, the second dimension couldn't be up and down and would have to be left and right. Gravity pulls things downward, and it would look silly if the 2D creatures were propped up on their sides.
2nd Dimension = Left and Right
2nd Dimension = Left and Right
3rd Dimension
Cube
The third dimension is easy to figure out because its the only regular dimension left. Up and Down. Unlike the previous dimensions, the third has all three sets of directions, giving us the most freedom of movement.
3rd Dimension = Up and Down
3rd Dimension = Up and Down
4th Dimension
Time
Time is commonly considered the fourth dimension of our universe. However, there are many differences with time than there is with regular dimensions. We constantly move forward in time even though we don't feel it. We also age while we move through time. However, time is not absolute and can be interacted with just as we interact with the first three dimensions our entire lives. Using Time Dilation, we can use high speeds and the Earth's gravity to slow down time. Could a cube that doesn't last for any amount of time at all really exist? That is why time has to be a dimension.
4th Dimension = Time
4th Dimension = Time
Tesseract
Are we just as ignorant as creatures of lower dimensions? Is there a 4th Dimension similar to our first three that we can't interact with? Or, similarly to how a true 2D object can't exist, since our 3D world couldn't exist without at least some thickness in the 4th Dimension, then does that mean there is no 4th Dimension? If there is a 4th Spatial Dimension, is that where God is? If God is there, it would explain how he is everywhere at once and how he got Mary pregnant without you know what. He could have placed the "seed" just as easily as we can place a penny into the center of a square.