In his book I Want to be a Mathematician, Paul Halmos reveals a secret:

Sink or Float? is actually a collection of examples in the guise of problems. The problems are multiple-choice, challenging you to think through each one. You don't need fancy terminology or familiarity with a mathematical specialty to understand them. They are concrete, and most are understandable to anyone.

The willingness and confidence to apply common sense to the real world can be very rewarding. It's one of the aims of this book to show that it works, that thinking can enlighten us and bring perspective to the world we live in. The range of problems to which common sense applies is almost limitless.

The example is one of the most powerful tools for discovering new things and for sug- gesting how to solve problems. Examples come in different degrees of concreteness and often, the more concrete, the more informative. The following tale provides an example of “concreter can be better,” and is the story of what started this book.

It begins in the dentist's chair. After putting generous amounts of cotton in my mouth, my dentist commences his customary free-wheeling question and answer session.