In the analysis of mathematical formulas for anything to do with the physical world, the only thing we would need to know are what the variables are that together interact to affect the results. We must consider how all the factors interact together to affect the results. Are there any patterns that we can spot with the interchangeable values of the variables? With enough experimentation of the different values for the variables in the formula, could we find any patterns of the properties that exist in the physical world that are together used to attain a result in the physical world?
As a simple example with only one variable that we can interact with in the physical world, if we consider the formula to calculate the energy needed to raise the temperature of a known mass a of substance:
Q = m × c × ΔT
Q is the energy transferred in joules, m is the mass of the substances in kg, c is the specific heat capacity in J/kg degrees C, and ΔT is the temperature change in degrees C in the specific heat formula.
This specific formula only has one variable that we can interact with: the variable for the mass of a substance.
If we were to test all the different values in the variable for the mass of a substance in this formula, we would learn that objects with a greater mass heat up slower than objects with a smaller mass. We could also add a note to our understanding of the physical world by paying attention to the physical properties of the many types of substances that exist such as the specific heat capacity for a known substance.
In any study where we are to make a precise determination, we are to consider how all the factors affect the results.
