Late in his life, Flaubert would insist that he never wanted to hear of Madame Bovary again: ‘the name alone annoys me’ (13 June 1879, RdG). This disaffection, we saw, was part of its very writing as a book undertaken against the grain of Flaubert's desire: ‘don't judge me on it… it was a matter of set purpose, an exercise in composition’ (30 October 1856, RdG). Exasperatingly, his first published novel, cut off from his natural lyricism ('everything I like isn't in it', ibid), achieved a notoriety that fixed him as its author, just'Flaubert, author of Madame Bovary'. And this even as his work continued, as the other novels were published: Salammbo (1862), the purple novel of war and passion in the Carthage of antiquity, begun soon after Madame Bovary; the second Education sentimentale (1869), using the career of its (anti-) hero in Paris in the 1840s and 50s to grasp the historical reality of contemporary society; and those two great extreme projects that sum up his raison d'ecrire: La Tentation de saint Antoine (1874), the book of the unleashing of the imagination through saintly ascesis, and Bouvard et Pecuchet (1881), the posthumous novel of the two clerks who set out to explore human knowledge from geology to literature, agriculture to theology, and who end up back at a desk copying, like Flaubert himself, the compiler of this commonplace book, lost - impersonal - in all the stupidity of the human. Since his death, each of these novels has, in fact, been singled out as centrally - and often exclusively - important: for James, for Sartre, Flaubert was Madame Bovary; for Proust, for Kafka, he was supremely L'Education sentimentale; for Valery, who not unlike Flaubert himself detested Madame Bovary and ‘its ‘'truth'’ of reconstituted mediocrity', the significant book was La Tentation; for Barthes and others in recent years, it has been Bouvard et Pecuchet; and mention must also be made again of the Correspondance which has itself been treated as a major book, a great portrait-novel-document of the modern writer.

Flaubert began writing Madame Bovary on the evening of 19 September 1851; on the last day of May 1856 he sent the final manuscript to his friend Maxime Du Camp for publication in the Revue de Paris. His novel thus represents almost five years of a labour of composition that has become the very example of literary creation, of the vocation of the writer as artist. Two people shared in something of the trials of this labour: Louis Bouilhet, the Rouen schoolfriend, himself a poet, to whom the work in progress was read on Sundays; Louise Colet, the mistress, herself a poet and author, the recipient in Paris of the expression of Flaubert's passion of writing as recorded in more than 180 extant letters from 1851 onwards. When they broke up in 1854 and the letters came to an end, Flaubert was at the episode of the club-foot, the terms of the novel were set. Madame Bovary, indeed, was written to the rhythm of their relationship; or rather, the relationship was carried on to the rhythm of its writing, with meetings as and when this and then that section was completed; ‘We won't see each other before…’ became a constant refrain.

To write to Colet was to write to ‘the eiderdown on which my heart comes to rest and the handy desk on which my mind can open’ (27 February 1853, C). The letters are lengthy, mostly written late at night after the hours of struggle with the novel, as a respite from style: ‘it's so easy to chatter on about the beautiful but to say in good style “close the door” or “he wanted to sleep” requires more genius than giving all the literature courses in the world’ (28 June 1853, C). If in the first three months or so of 1853 Flaubert drafted thirty-nine pages of Madame Bovary, in the same period he wrote some twentythree letters to Colet; that of 27 March, for example, running to well over 4,000 words. Untiringly he set out his ideas on the novel in hand and on art in general: ‘one must esteem a woman, to write her such things as these’ (23 October 1851, C).

This text is based on a course of the same title given at Cambridge for a number of years. It consists of an introduction to information theory and to coding theory at a level appropriate to mathematics undergraduates in their second or later years. Prerequisites needed are a knowledge of discrete probability theory and no more than an acquaintance with continuous probability distributions (including the normal). What is needed in finite-field theory is developed in the course of the text, but some knowledge of group theory and vector spaces is taken for granted.

The two topics treated are traditionally put into mathematical pigeon-holes remote from each other. They do however fit well together in a course, in addressing from different standpoints the same problem, that of communication through noisy channels. The authors hope that undergraduates who have liked algebra courses, or probability courses, will enjoy the otherhalf of the book also, and will feel at the end that their knowledge of how it all fits together is greater than the sum of its parts.

The Cambridge course was invented by Peter Whittle and the debt that particularly the information-theoretic part of the book owes him is unrepayable. Certain features that distinguish the present approach from that found elsewhere are due to him, in particular the conceptual ‘decoupling’ of source and channel, and the definition of channel capacity as a maximized rate of reliable transmission. The usual definition of channel capacity is, from that standpoint, an evaluation,less fundamental than the definition.

In detail, the first four chapters cover the information-theory part of the course. The first, on noiseless coding, also introduces entropy, for use throughout the text. Chapter 2 deals with information sources and gives a careful treatment of the evaluation of rate of information output. Chapters 3 and 4 deal with channels and random coding. An initial approach to the evaluation of channel capacity is taken in Chapter 3 that is not quite sharp, and so yields only bounds, but which seems considerably more direct and illuminating than the usual approach through mutual information. The latter route is taken in Chapter 4, where several channel capacities are exactly calculated.

The aim in this first chapter is to represent a message in as efficient or economical a way as possible, subject to the requirements of the devices that are to deal with it. For instance, computer memory stores information in binary form, essentially as strings of 0s and 1s. Everyone knows that English text contains far fewer letters q or j than e or t. So it is common sense to represent e and t in binary by shorter strings than are used for q and j. It is that common-sense idea that we shall elaborate in this chapter.

We do not consider at this stage any devices that corrupt messages or data. There is no error creation, so no need for error detection or correction. We are thus doing noiseless coding, and decoding. In later chapters we meet ‘noisy’ channels, that introduce occasional errors into messages, and will consider how to protect our messages against them. This will not make what we do in this chapter unnecessary, for we can employ coding and decoding for error correction as well as the noiseless coding and decoding to be met with here.

The first mathematical idea we shall consider about noiseless coding — beyond just setting up notation, though that carries ideas along with it — is that codes should be decipherable. We shall, naturally, insist on that! The mathematical expression of the idea, the Kraft inequality, limits how little code you can get away with to encode your messages. Under this limitation you still have much choice of code, and need therefore a criterion of what makes a code optimal. Now the problem is not to encode a single message, but to set up the method of encoding an indefinitely long stream, stretching into the future, of messages with similar characteristics. The likely characteristics of those prospective messages have to be specified probabilistically. That is, there is a message ‘source’ whose future output from the point of view of having to code it, is random, following a particular probability distribution or distributions which can be ascertained from the physical set-up or estimated statistically.