If variable A is inversely related to variable B and A is linearly related to C, then express an algebraic equation that would reflect these relationships. All of this comparison results is predicated on an important universal assumption, the continuity of the universe. If I, for example, use specific objects made of specific substances in the above investigation, I am assuming that using some other different substance for the objects will lead to the same conclusions. That is called the uniformity or continuity principle of the universe, and is absolutely essential for any deductive or inductive reasoning. Empirical vs intuitive mathematical formulas Most algebraic expressions defining the physical relationships between two or more variables are developed either in an experimental or investigatory manner or they are developed intuitively.
Experimentation involves the controlling of variables within the experimental design.
Some variables are held constant while others are allowed to vary. When investigating the relationship between two variables with other defined variables present in the same physical environment, the other variables must be held by the experimenter fixed so as to get a precise definition on the relationship between the two variables under investigation. Otherwise, one could never quite know if any changes between the values of two variables was due to their relationship toward one another or the relationship of some other variable that was not held fixed during the investigation. When making comparisons as we did earlier in this discussion, the same procedure must be observed. We had to hold one of the three variables constant in order to get a definition of the relationship of the other two variables to one another.