This helped me when I was trying to puzzle this all out for the first time.
Don't think of a point as a 0th dimensional thing. A point IS an 0th dimension, a dimension that has only one attribute, that of position. Then you add
motion. You move the
entire dimension. The act of moving determines the next dimension. We can select an 0th dimension by naming a position in our universe. Moving our 0th dimension in a direction perpendicular to itself gives us a vector of motion, which we can think of as a line drawn along the vector. That direction (both forward and back) is a 1st dimension based on our chosen 0th dimension.
"Perpendicular" does not have a lot of meaning here; you could say it is undefined as it does not describe a direction, yet it describes all possible directions. You can move a point through any dimension, but we have to construct our model in numerical order.
The 1st dimension is not a piece of line. The 1st dimension is something that has only one attribute, that of length. If the 1st dimension is infinite, then its single attribute, length, is infinite. Say we take the
whole 1st dimension (that we have just generated by moving our selected 0th dimension in a selected direction), and we move it perpendicular to itself. This now makes sense. We know what a perpendicular line is. We will pick any of the infinite number of perpendicular directions, and sweep our 1st dimension (forward and back) to create our new 2nd dimensional plane.
Now, we could have picked any one of infinite points in the universe, moved the point in any of infinite directions, and moved the line in any of infinite directions. We might say that all these choices are taking place in the dimension of choice, that is, the 5th dimension. We have not even got to dimensions 3 and 4 yet, but all that we are doing takes place in the 5th dimension of possibilities. All possible 0th-dim point choices, for example, exist in the 5th dimension until we "collapse" things down to our level by designating our starting point.
So then, of course, we can choose a direction perpendicular to that plane we just created. Now, since we can only see in the 3rd dimension, we can no longer see that there are an infinite number of perpendicular directions available. There are, but we just can't see them. We can only see one, and that one leads through our own 3rd dimension. So we choose that perpendicular (collapsing the 5th dimension probability), move our 2nd dimension plane along it, and we get what we call "space."
Now we have to construct our remaining dimensions by choosing a perpendicular to space. We can choose any of infinite possibility perpendiculars (5th dimension directions). If we move space along one of these, we get the 4th dimension, which looks very much as though we have to call it time, because
time is the thing that happens to space in a linear fashion.
I don't know what the next step is. I want to say that you move spacetime to get the 5th dimension, but I don't know how to describe an infinity of optional perpendicular directions in the 6th dimension. This is new and slippery to me too. But maybe I've helped you think farther along the path than before.
OK, I'm trying to get ready for a training class tomorrow morning and I''m trying to conserve some brain power so I'll check back after I've got some sleep.