Chapter 4. Mathematics, Models, and Measurement

The skills you will learn in science are as empowering as they are indispensable. Science can be done by almost anyone who has the curiosity, the persistence, and the training to do the work. The notion that only geniuses do science misses this point.

What is the scientific method? How do scientists define the problems they will study? How do they decide what to do and in what order? How do they protect themselves from error? Science, it is said, has three distinguishing attributes:

1. Science is objective, meaning that no matter who repeats an investigation, the result will always be the same.

2. Science is empirical, meaning that its findings are measurable and that every theory can be tested. No scientific theory can be proved, but a great deal of evidence (including predictions) can be accumulated in its favor.

3. Complicated problems in science are best broken into smaller problems and solved, the assumption being that the whole is the sum of its parts.

This chapter shows you how mathematics, models, and measurement serve science in achieving its goals: to describe and predict the outcome of natural phenomena. Because science is empirical, it begins with observation and measurement. Because measurement is quantitative, science is inevitably mathematical. But observation, no matter how accurate, and measurement, no matter how exact, are not enough. Because scientists need to make sense of their observations and measurements, they construct models: of the structure of matter, of the solar system, of evolution, of the elemental atom...
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