This post continues the previous post *here* on independent and dependent variables.

The selection of a physical independent variable (or variables) applies to a context such as an experiment. Within that context all other variables are, at least potentially, dependent on the independent variable(s) selected. Functions with the physical independent variable as a functional independent variable have a common independent variable and form a kind of closed system.

Nevertheless, an independent variable in one context may be the same as a dependent variable in another context. The functions in both of these contexts may be related. That is, there may be relations between the functions of one independent variable in one context and the functions of another independent variable in another context.

For example, *speed* (the *time speed*) is defined as the change in distance per unit of time with time as the independent variable. This appears to be equal to the reciprocal of the pace, that is, the change in distance per unit of time with distance as the independent variable. This is called the *space speed*, *spot speed*, or *inverse speed*. We could call the space speed the *quasi-speed*, since it seems like the speed (the time speed).

However, these two speeds are not the same. One difference is how the speeds are aggregated or averaged: the speed uses arithmetic addition and averaging but the quasi-speed uses subcontrary (or harmonic) addition and averaging. The average of speeds *v*_{1} and *v*_{2} is (*v*_{1} + *v*_{2})/2. The average of quasi-speeds *v*_{1} and *v*_{2} is 2/(1/*v*_{1} + 1/*v*_{2}).

A quasi variable is a dependent variable in the denominator as if it were an independent variable. If it is a first-order variable, one can take the reciprocal to put it into its proper dependent position, the numerator. Second and higher order variables need to use their inter-functional relation.