1.1 Science and regularity 1/2

1.1 Science and regularity 2/2

1.2 Mathematics and quantification 1/2

» 1.2 Mathematics and quantification 2/2

2 The clockwork Universe

3 The irreversible Universe

4 The intangible Universe

5 The uncertain Universe

6 Closing items

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Other titles in the Physical World series

Describing motion

Predicting motion

Classical physics of matter

Static fields and potentials

Dynamic fields and waves

Quantum physics: an introduction

Quantum physics of matter

1.2 Mathematics and quantification

Part 1 of 2 | Part 2 of 2

For a printable version of '1 The lawful Universe' click here

Mathematics has been an immensely effective part of the scientist’s toolkit throughout history. It was the increased use of mathematics in the sixteenth and seventeenth centuries, in the hands of individuals such as Galileo Galilei (1564–1642) and Isaac Newton (1642–1727), that opened a new era of physics and marked one of the greatest flowerings of science. Galileo and Newton, it should be noted, were both, at key times in their careers, professors of mathematics. In both cases they brought mathematical precision and rigour to the study of science, and in Newton’s case made major breakthroughs in mathematics in the process. The types of mathematics used in physics are extremely varied. Practically every branch of mathematics that has developed over the centuries has been used within physics. Sometimes physics has provided direct inspiration for new mathematical concepts, sometimes abstract mathematical theories have found completely unexpected uses in physics, years after their introduction as products of pure thought.

Despite its power, physics students often find the extensive use of mathematics troublesome and some think of mathematics as providing a barrier to understanding. Do not let this happen to you. From the outset, you should regard mathematics as a friend rather than a foe. As the course progresses, you may meet some mathematical ideas that are new to you, or you may need to improve your ability to use methods you have met before. These are not distractions from trying to understand physics, but are the tools needed to make that understanding possible. It is only through using mathematics that a secure understanding can be achieved. When you see an equation, welcome its concision and clarity and try to ‘read’ the equation just as you would the large number of words it replaces. Learn to get beneath the squiggles and the equals sign and to understand the quantitative assertion that is being made.

Fig 1.2 "I see through your squiggles." Click here for larger image (11.52kb)

Later, you will see how graphs can be used to visualize an equation and how consideration of special cases and trends can help unpack its meaning.

Question 1.1 Answer
When Jesuits first visited China they spoke about the ‘laws of science’. The Chinese thought this was a ridiculous notion: people could be persuaded to obey the laws of the Emperor, but sticks and stones have no intelligence so it is absurd to think of them as ‘obeying laws’. How would you respond to this?

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A note on powers of ten and significant figures

Some highlights of physics

Featured Physicists

Suggestions for further reading

Questions, answers and comments

Acknowledgements

Index