The major difference here is that, where Larson refers to the word direction, as if these scalar values had direction, as in "the latter being traversed repeatedly in opposite directions," at the LRC, we make the crucial distinction between "direction" and direction. Direction is a property of vectors, while "direction" is a quite different property of scalars. A scalar quantity increase is in the opposite "direction" of a scalar quantity decrease, but the meaning of the word "direction" has a very different meaning than the word direction, as used in connection with vectorial concepts of motion.
A good example of this difference is found in the financial world, where prices are commonly referred to as "going up," or "going down" like an elevator, but these two opposite "directions" of up and down are understood as simply increases or decreases in the price of a stock or commodity, a scalar value. There is no concept of a literal movement in a linear direction, with respect to scalars.
Likewise, in the case of a spatial concept of scalar, an increase, or decrease, in space is not a literal movement of "space" in a literal direction, but simply an increase, or decrease, of a quantity of space relative to a previous, or subsequent, quantity of space. Thus, the increase in the volume of a balloon, is a "movement" in the "direction" of increasing volume, which is opposite to the "movement" in a decreasing "direction," when its volume is decreased. Nevertheless, this use of the word "direction" has a different meaning than the meaning of the word direction in connection with the vectorial motion of objects.
A good example of this difference is found in the financial world, where prices are commonly referred to as "going up," or "going down" like an elevator, but these two opposite "directions" of up and down are understood as simply increases or decreases in the price of a stock or commodity, a scalar value. There is no concept of a literal movement in a linear direction, with respect to scalars.
Likewise, in the case of a spatial concept of scalar, an increase, or decrease, in space is not a literal movement of "space" in a literal direction, but simply an increase, or decrease, of a quantity of space relative to a previous, or subsequent, quantity of space. Thus, the increase in the volume of a balloon, is a "movement" in the "direction" of increasing volume, which is opposite to the "movement" in a decreasing "direction," when its volume is decreased. Nevertheless, this use of the word "direction" has a different meaning than the meaning of the word direction in connection with the vectorial motion of objects.