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) Ui denotes the operative
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