PART 3 OF SESSION 2 OF COURSE 1

What we are about to discuss is BOUNDEDNESS & SENSE OF DIRECTION. Let's consider a ball in a tube. The ball may move throughout the tube, yet the transversel movement of the ball is limited to the path of the tube. This is because the sides of the balls are touching the inside part of the tube. Through familiarity, it can be perceived that what is termed the sides of the balls is arbitrary and may vary, since if the ball has enough slack to roll throughout the tube, then the ball may roll or spin in multiple directions -- given whatever force is causing that ball to roll.
The ball above is bound in a tube. The physical constraint governing the ball that it cannot roll outside of the tube may be termed a Neumman condition. That is to say, if you were to call the ball being in the tube a function, since Neumman conditions are boundary conditions of a function. Constraints as to the type of motion of the ball in the tube would be the balls Derichlet conditions. Derichlet conditions are the boundaries of a function's gradient, and the types of motion of an object is a gradient of the position of an object. Furthermore, if you were to consider an object's condition during static equilibrium as a function, then its radial and transversely motion of its kinematic component and velocity (directorially here as an acceleration) may be viewed as its gradient. Boundaries show where an object may or may not go, how it may roll or spin, and how it may move along in space transversely with a velocity and/or acceleration. There are boundaries to static objects (you may call any "happening" a function), electric fields, magnetic fields, and moving objects. When different things work together, their boundaries change. Look at synergy. People working together may do more than their summed efforts.
If you know where something is, you've increased your chances of finding it. If you are precise, and the object has detectable size, you may at least surmise with clarity where the object is and what it is giving off at the same time. If you cannot detect something, yet you know it is there, you may use multiple bases to determine with certain probability where the phenomenon is and what it gives off at the same time. The more of a history that you know of something, the better able you tend to be to predict its future outcome.
Mapping an object should not just determine where things are at, yet also how the object changes its boundary conditions each time t hat you are able to detect it. If you can't detect it, you may extrapolate information from phenomena that you can detect, and use this to determine the objects status as both as a phenomenon at a spot, and how this phenomenon's boundaries are changing after each locus of transformation.