Session 6 of Course 1, Jointedness‏

Picture the frame of a warehouse as it is being built. Certainly, all of the materials used to build the building are not going in the same direction. If this were to happen, the pieces used to make this building would either be laying on top of each other and/or laying side by side and/or connected in a long line that would not be able to form a building. Some parts of the building would need to be connected at the side of other parts.
If you are going down a road, and you come to a stop, after which immediately turning right, you would have made a ninety degree turn. The same would be true in such a case if you were to turn left. Ninety-Degrees looks like an "L" or a backwards "L." Ninety-Degrees is also the change from the side of a circle to its top, and is the phase difference between sine and cosine. When you draw a sine wave correctly, it is a smooth curve. When you draw a cosine wave correctly, it is a smooth curve. If you draw a terraced structure correctly, it makes some immediate direction changes either when going from up to across and from across to up or when going from across to down and from down to across.
Let us examine a curve that is smooth from our perception. Its change in direction has no erratic differences along the swipe of the curve. You can't draw any lines between any three points of the curve from the perspective at which the curve is smooth. Yet, if you were to observe the curve from a smaller scale -- perhaps down to individual molecules that make up the writing that formed the drawing of that curve, you would notice jointedness at this or some smaller level. Likewise, if you took monkey bars at an elementary school, and you looked at these at some smaller level, there would be a point where you could see a smoothness to the curvature. This would be a perspective of the apparently jointal object to where it would no longer appear jointal, yet smoothly curved.
So, jointedness is a function of all phenomena, as well as smooth curvature is a function of all phenomena. If you look at phenomena at a small enough basis, any change in position is a ninety-degree alteration of space relative to some other phenomenon. Yet, if you look at things from a large enough or a small enough basis, all curvature has some smoothness. For instance, with the monkey bars, if you make a one sided map of the area of the monkey bars at a distance, and localized these, the monkey bars would appear as a thin structure of lines, or, if observed from a further distance, these may appear as a dot or a thin line. It would not appear as a jointal composite here, yet as a smooth and tiny structure. Yet, if you observed certain molecule's curvature from within the monkey bars themselves, again, the monkey bars would appear as a smooth structure and not as jointal. Certainly, observing the monkey bars for their intended purpose would make them appear quite jointal.
Ninety-Degrees means immediate change in direction. In order for anything to happen in space, direction must change immediately from some perspective. Yet, in order for change to have any organization, there must be smoothness. Thus, jointedness and smooth curvedness.