22A Page 45

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22 STATISTICAL FOUNDATIONS

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22A | Introductory |

22B | The Chi Stream |

22C | The Motor Stream |

22D | The Psi Stream |

22E | The Sum of Two Streams |

22F | The Key Stream |

22G | The Plain Language Stream |

22H | The De-chi Stream |

22J | The Cipher Stream |

22K | Sampling Errors in Alphabetical Counts |

22W | Some further Streams |

22X | The Algebra of Proportional Bulges |

22Y | The Amount of Evidence derived from a Letter Count |

__22A INTRODUCTORY__

Statistical methods of Tunny breaking are possible because (and only because) cipher, plain, key, chi, extended psi, de-chi and motor streams can - with suitable treatment - be made to exhibit marked characteristics which will distinguish them from a random sequence of letters. In this chapter we analyse these characteristics, and in subsequent chapters we show how they are exhibited.

(a) __Notation__.

The letters Z, P, K, Χ, Ψ', D are used to denote the operative letters of the Cipher, Plain, Key, Chi, Extended psi and de-chi Streams at any given ciphering position. They are connected by the equations:

Z | = | P | + | K | ||||

K | = | Χ | + | Ψ' | ||||

D | = | Z | + | Χ | = | P | + | Ψ' |

The suffixes 1, 2, 3, 4, 5 are used when a particular impulse is specified so that (using a generalised form) U_{i} denotes the operative

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