Science and mathematics intersect in this wonderful idea of a law of science. So what is a law of science?
First, let’s make sure that we do not confuse the word law as used in science with its other uses.
A simple definition of a scientific law is:
A scientific law is mathematical model that describes the generalization of a set of observations about the real world.
Let’s clarify the definition a bit. In the spring experiment above, we wrote down a small set of observations about the length of the spring when a certain weight was attached. Now suppose we use the observation values to create a law in terms of aformula that shows a mathematical relationship between a number representing weight and a number representing spring length. We have now created a generalization of our observations. A generalization means that we can now select a weight number without actually hooking a weight onto the spring, plug it into the formula and produce a spring length number, which should match the spring length as if we actually did the experiment. If the formula give good answers it is an example of a scientific law.
How do we create the formula and verify that it valid? We will discuss this in a later chapter. In the meantime we will show you a formula that works pretty well. You can enter a weight number and the formula will produce a spring length number. You can then verify that the experiment produces roughly what the formula predicts.
Look at the following figure. It shows a formula that computes spring length, symbolized by the letter s, from weight, symbolized by the letter w. You can enter a number that represents a weight and you will see a number computed that represents spring length.
Enter a weight number from one of the observations you made earlier. Look at the spring length number that is computed by the formula. Is it close to the spring length number that you observed for that weight number?