In doing science we need to distinguish between the facts and the scientific theories developed to explain them, as sometimes these two ideas are confused. Roughly speaking, facts are what we can observe whereas a theory endeavors to explain what has been observed and why it is so. For example, we may wish to determine a certain theory of migration throughout the Pacific islands that explains certain facts such as language items or items found in burial sites obtained from the various islands. We would like to develop some ideas of closeness or similarity to see if migration connections can be established.
If the use of certain words or artifacts are more “similar” for two islands than for others we can perhaps suspect a migrational connection between the two islands. I have chosen this somewhat unusual example to not only demonstrate the difference between fact and theory, but also to show the variety of scientific theories we can have and to note that mathematics (statistics) is used even here in the definition of “closeness.”
We can set up a measure of “distance” between two islands based on how similar certain items are on both islands. As mathematics plays an important role in scientific theory and people tend to believe that mathematics is truth, we shall look more closely at the role mathematics plays in science. I realize that many readers may not be too excited about mathematics so that they may wish to skip some of the following sections.