Notes

Galileo was a proponent of empirical observations to obtain factual information, and of deductive work to synthesize the observations into laws. Clearly, he did not separate these two major components of doing science.

A few principles set empirical science apart from other kinds of study: testability (empirical verification), operational definition, and controlled observations.

Testability: Empirical science characteristically begins with some observation, which prompts the observer to ask a question. The new question is then subjected to some kind of verification. If the ideas survive the tests, they become part of the body of scientific knowledge, and may give rise to further new ideas, at least until more stringent tests challenge the ideas.

Operational Definition: Any thing or idea that is not operationally definable is not accessible to study by empirical science. All terms used in descriptions or explanations

must be specifically and realistically defined. This makes it possible for someone else to understand explicitly what the facts are, and perhaps carry out further tests of the facts or explanations. Operational definitions make ideas testable.

Controlled Observations: If change in a presumed independent variable leads to change in a dependent variable, we suspect a causal relationship. A convincing test of the effect of a variable on another requires a further result: that we observe the response in the presumed dependent variable when the independent variable does not change. This idea appears at various stages in the history of science; perhaps it was first suggested by Roger Bacon (1214-1294?), a Franciscan monk who taught at Oxford, but clearly by Galileo. Now it is a key concept of empirical science.

Lack of appropriate controls is a common flaw in reasoning. For instance, it has been demonstrated on innumerable occasions that the beating of tom-toms brings an end to eclipses. We too often neglect to ask what happens when no one beats the drums.

Deductive Science:

There are many constructs throughout science that describe logically necessary relationships. These constructs can be used to deductively explore the consequences that are implicit in the axioms used to set up the constructs. Such systems, referred to as tautologies, can be particularly useful when they deal with complex systems, in which the interrelationships may not be immediately obvious. Among the important  tautologies that we commonly use are algebra, euclidean geometry, and computer programs. Such logico-deductive systems organize complicated information and can be made to specify relationships not immediately evident.

Before further discussing models, I should make the point that to truly prove a model, all possible observations about its predictions have to be made; this may be an impossible task. For example, a deductive model could predict that all swans are white. This prediction was corroborated or verified by many, many observations: all over Europe millions of people for centuries saw white swans. In fact, it would be tempting to generalize the observations into a law of nature. Unfortunately, even millions of further observations of white swans would still fail to make this proposition true. The moment that the first European explorer saw the first black swan in Australia, the effort to "prove" the model by corroborating observations

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The role of NPE can be likened to creation of a city map. A city map has two key properties. It is an abstract representation of the real situation in that the distances between any two points on the map are not in geographical proportion, and it is simple because it is uncluttered by unimportant real-world physical details.

The natural urge is to create a NPE "map” adorned with an abundance of physical detail because that would seem to constitute a more faithful representation of the computer system being analyzed. In spite of this urge, you should strive instead to make your NPE models as simple and abstract as a city map. Adding complexity does not guarantee accuracy.

Unfortunately, there is no simple recipe for constructing a city map (or a NPE model).  Einstein reputedly said that things should be as simple as possible, but no simpler. That should certainly be the goal for applying NPE, but like drawing any good map there are aspects that remain more in the realm of art than science.