## The Pleasures of CountingIn this engaging and readable book, Dr. Körner describes a variety of lively topics that continue to intrigue professional mathematicians. The topics range from the design of anchors and the Battle of the Atlantic to the outbreak of cholera in Victorian Soho. The author uses relatively simple terms and ideas, yet explains difficulties and avoids condescension. If you are a mathematician who wants to explain to others how you spend your working days, then seek inspiration here. This book will appeal to everyone interested in the uses of mathematics. |

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### Contents

Unfeeling statistics | 3 |

12 An altar of pedantry | 14 |

Prelude to a battle | 21 |

22 The coming of convoy | 25 |

23 The second submarine war | 32 |

Blackett | 38 |

32 Tizard and radar | 44 |

33 The shortest wavelength will win the war | 50 |

114 How fast can we sort? | 282 |

115 A letter of Lord Chesterfield | 292 |

Deeper matters | 298 |

122 The problems of infinity | 305 |

123 Turings theorem | 311 |

Enigma variations | 317 |

Enigma | 319 |

132 Simple Enigmas | 331 |

34 Blacketts circus | 57 |

Aircraft versus submarine | 62 |

42 Lets try the sliderule for a change | 73 |

43 The area rule | 79 |

44 What can we learn? | 87 |

45 Some problems | 93 |

Meditations on measurement | 99 |

Biology in a darkened room | 101 |

52 The long and the short and the tall | 105 |

Physics in a darkened room | 116 |

62 A different age | 127 |

Subtle is the Lord | 137 |

72 The Lorentz transformation | 141 |

73 What happened next? | 149 |

74 Does the earth rotate? | 154 |

A Quaker mathematician | 159 |

82 Richardsons deferred approach to the limit | 164 |

83 Does the wind have a velocity? | 176 |

84 The fourthirds rule | 186 |

Richardson on war | 194 |

92 Statistics of deadly quarrels | 198 |

93 Richardson on frontiers | 208 |

94 Why does a tree look like a tree? | 215 |

The pleasures of computation | 229 |

Some classic algorithms | 231 |

102 The good old days | 237 |

103 Euclids algorithm | 242 |

104 How to count rabbits | 250 |

Some modern algorithms | 258 |

112 Braesss paradox | 268 |

113 Finding the largest | 275 |

133 The plugboard | 338 |

The Poles | 348 |

142 Beautiful Polish females | 353 |

143 Passing the torch | 362 |

Bletchley | 368 |

152 The bombes at work | 377 |

153 SHARK | 381 |

Echoes | 391 |

162 Shannons theorem | 398 |

The pleasures of thought | 411 |

Time and chance | 413 |

172 Growth and decay | 422 |

173 Species and speculation | 433 |

174 Of microorganisms and men | 444 |

Two mathematics lessons | 452 |

182 A modern mathematics lesson I | 459 |

183 A modern mathematics lesson II | 464 |

184 A modern mathematics lesson III | 471 |

185 A modern mathematics lesson IV | 477 |

186 Epilogue | 481 |

Last thoughts | 488 |

192 The pleasures of counting | 492 |

Further reading | 494 |

A12 Some hard but interesting books | 501 |

Some notations | 508 |

Sources | 511 |

522 | |

529 | |

Acknowledgements | 534 |

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### Common terms and phrases

aircraft argument attack average number axioms Blackett bombes BOY Yes British calculations called Chapter cholera cipher Coastal Command code-breakers consider convoy cycle decodes deduce depth charges discussion disease Donitz effect ELEANOR enciphered encipherment Enigma Enigma machine epidemic equation escorts Euclid's algorithm example Exercise expect experiment Figure Ford-Fulkerson algorithm formula G. I. Taylor German give given greatest common divisor hour increase integers interest kilometres per hour knock-out large number Lemma length less letter look machine mathematicians mathematics merchant ships method naval Navy observe obtain plugboard population positive integers possible probability problem produce proof radar reader result Richardson rotors sequence side simple SOCRATES speed square step streptokinase STUART submarine substitution code Suppose Table TEACHER teams theorem theory things trapezium rule Turing U-boat unit velocity write