Higher Dimensional Space
Roughly speaking, higher dimensional space is another volume of space located outside of our three dimensional universe. This volume of space has a unique perspective: an observer in three dimensional space cannot see anything existing in higher dimensional space, however, from higher dimensional space, an observer can seeeverything existing in three dimensional space.
The entrance into higher dimensional space is a most unique motion - unlike any other motion in our three dimensional universe. It is difficult to imagine because there is nothing to compare it to. To enter into higher dimensional space, one has to travel at right angles to all three dimensions of space simultaneously. If that doesn't seem to make much sense, the only way to explain this direction is the use of the word "within": within space itself. Or, when matter is used as the reference point, "within" matter itself - in a direction towards the geometric center of matter.
If you seem a little confused, don't feel bad. Since we think and reason in terms of three dimensional space, higher dimensional space is almost impossible to visualize. This problem occurs because of the way higher dimensional space is constructed. Higher dimensional space is a volume of space at right angles to the volume of three dimensional space we inhabit.
Another way to understand this construction is to look up at a corner of the room you are sitting in. Observe the point where the ceiling and the two walls meet. The ceiling and the two walls represent the three dimensions of space we live in: length, width, and height. Now observe how the ceiling is at right angles to both walls, while both walls are at right angles to the ceiling and the opposite wall. This relationship allows us to observe the fact that each dimension is at right angles to the other two dimensions simultaneously.
Although this three dimensional relationship is easy to see, the relationship between these three lower dimensions and higher dimensional space is not. It is easy to say the fourth dimension is at right angles to the first three dimensions, and fifth dimensional space is at right angles to the first four dimensions and so on, but it is impossible to visualize this relationship.
What we can visualize is movement into or out of the fourth dimension. To do this, again look up at the same corner of the room and observe the tiny point where the ceiling and the two walls meet. To reach the fourth dimension we must travel within this point, towards its geometric center, and then outward, into the fourth dimension.
Although this doesn't seem to make too much sense, it does when we realize every invisible point of space within the room you are sitting in is exactly like the point you are looking at. Hence, to reach higher dimensional space, one has to travel within space itself. Or, since every object is made up of an infinite number of such geometric points, a way to describe the location of higher dimensional space to someone who does not comprehend what you are talking about is to use the word "WITHIN".
As a demonstration, you can hold up a small pebble and say to a group of children that the location of higher dimensional space is "within" this very pebble. However, even though this is a dramatic demonstration, it is a poor illustration. Although what you said was true, the children might misunderstand what you are saying and think higher dimensional space is located within this particular rock. So, an even better way to describe the location of higher dimensional space is to use another illustration. For example, you could say higher dimensional space was not only within them, it is also within each and every one of us. By using the matter out of which our bodies are constructed as a reference point, we must travel within - within our own selves: towards the geometric center of our own physical body.