## The Pleasures of CountingWhat is the connection between the outbreak of cholera in Victorian Soho, the Battle of the Atlantic, African Eve and the design of anchors? One answer is that they are all examples chosen by Dr Tom Körner to show how a little mathematics can shed light on the world around us, and deepen our understanding of it. Dr Körner, an experienced author, describes a variety of topics which continue to interest professional mathematicians, like him. He does this using relatively simple terms and ideas, yet confronting difficulties (which are often the starting point for new discoveries) and avoiding condescension. If you have ever wondered what it is that mathematicians do, and how they go about it, then read on. If you are a mathematician wanting to explain to others how you spend your working days (and nights), then seek inspiration here. |

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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 | |

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