For generations, field guides to plants and animals have sharpened the pleasure of seeing by opening our minds to understanding. Now John Adam has filled a gap in that venerable genre with his painstaking but simple mathematical descriptions of familiar, mundane physical phenomena. This is nothing less than a mathematical field guide to inanimate nature.

If quantum communication and quantum computation are to flourish, a new information theory will have to be developed.

To put it one way, a collection of Shakespeare's plays is richer than a phone book that uses the same number of letters; to put it another, the essence of information lies in the relationships among bits, not their sheer number.

Claude Shannon, the founder of information theory, invented a way to measure 'the amount of information' in a message without defining the word 'information' itself, nor even addressing the question of the meaning of the message.

An electron is real; a probability is not.

Underneath the shifting appearances of the world as perceived by our unreliable senses, is there, or is there not, a bedrock of objective reality?

As every bookie knows instinctively, a number such as reliability - a qualitative rather than a quantitative measure - is needed to make the valuation of information practically useful.