ABSTRACT
If, though, we had assumed one edge of the flat as the origin, just temporarily, then our two measurements of lengths from origin to edges would always include one measurement of zero. This has two benefits. We do not need to measure anything from the center of town, and performing the same absolute value of the result of the subtraction of two measurements would now be trivial because of the one zero value measure. Of course when using a tape measure, the act of defining an origin by placing the tape end on an edge is rarely considered, we just do it. Origins for length measurements can be points, the center of a spherically shaped dome, lines, the plaster line of the stage, or planes, the stage floor with respect to the height of battens. In all three cases, measurements of position must involve more than a length specification alone. This is because the expression of position by length alone does not resolve the ambiguity of what direction from the origin the measurement is being made. This ambiguity is commonly eliminated by direction indicating specifiers. For instance, in the case of one dimensional, or straight line movement systems, say a flysystem, position is indicated both by a length between object and origin, and a direction specified by any two-state indicator: up, down, in, out, +, –, etc. Because quantities, like position, that require both direction and size are common in physics, a special set of mathematical rules and notations has developed. Any quantity that requires a size, or magnitude, component and a directional component is called a vector. Position is therefore a vector. In most texts a vector quantity is, by convention, indicated by a bold letter: . The magnitude, or the size component of a vector, is notated: x. In a one-dimensional system, a system where all movement occurs along a straight line, the magnitude of a position vector is simply the distance from the origin in the units being used (meters, feet, or inches for instance), and the direction is indicated with a + or – sign. Assigning a sign of + or – to a position is an arbitrary choice that needs to be made once for a given situation, and then followed consistently from then on. Some choices seem obvious, assume the stage floor is the origin or zero point, and then straight up into the flytower is positive, and down into the trap room is negative, but the opposite assumption is just as valid. In other situations there may be no clear convention. Is stage right + or – relative to the centerline? Ultimately it does not matter what you choose, just pick one and stick with it.
