Our last chapter is devoted to entropy. With this excuse we first present Shannon’s information theory, including the derivation of his entropy, and the enunciations and proofs of the source coding theorem and of the noisy-channel coding theorem. Then, we consider dynamical systems and the production of entropy in chaotic systems, termed Kolmogorov–Sinai entropy. For non-experts or readers who require a memory jog, we make a short recap of statistical mechanics. That is just enough to tie up some knots left untied in Chapter 4, when we developed large deviations theory for independent variables. Here we generalize to correlated variables and make one application to statistical mechanics. In particular, we find out that entropy is a large deviations function, apart from constants. We end with a lightning fast introduction to configurational entropy in disordered complex systems. Just to give a tiny glimpse of … what we do for a living!

Chapter 4 takes up the question of book size, including format (folio, quarto, etc.) as well as the adjectives applied to books (big, large, little, etc.). The rhetoric of book size gave people a way to talk about information.

Chapter 8 explores the asymptotic regime of quantum information processing, beginning with quantum typicality, which illustrates the convergence of quantum states toward a typical form with increasing copies. This leads to the asymptotic equipartition property (AEP), indicating that with a high number of copies, probability vectors become uniformly distributed. The method of types is introduced next, a tool from classical information theory that classifies sequences based on their statistical properties. This is crucial for understanding the behavior of large quantum systems and has implications for quantum data compression. Advancing to quantum hypothesis testing, the chapter outlines efficient strategies for distinguishing between two quantum states through repeated measurements. Central to this is the Quantum Stein’s lemma, which asserts the exponential decline in the error probability of hypothesis testing as the sample size of quantum systems increases. The chapter highlights the deep interplay between typicality, statistical methods, and hypothesis testing, laying the groundwork for asymptotic interconversion of quantum resources.

Information processing is a process of uncertainty resolution. Information-theoretic constructs such as surprisal and entropy reflect the fine-grained probabilistic knowledge which people have accumulated over time. The information-theoretic constructs explain the extent of processing difficulty that people encounter, for example when comprehending language. Processing difficulty and cognitive effort in turn are a direct reflection of predictability.

This chapter introduces communication and information theoretical aspects of molecular communication, relating molecular communication to existing techniques and results in communication systems. Communication models are discussed, as well as detection and estimation problems. The information theory of molecular communication is introduced, and calculation of the Shannon capacity is discussed.

This chapter describes new music in Paris in the late 1960s, the period when the young spectral composers were students at the Paris Conservatoire. It opens with an account of Messiaen’s composition class and how elements such as neumes and Messiaen’s analyses of Debussy and Ravel informed Grisey’s, Murail’s, and Levinas’s emerging musical sensibilities. After giving a brief biographical account of those latter composers and Roger Tessier, the chapter touches on serialism’s changing status at a time when it had begun to be taught at the Paris Conservatoire; the effect of May ’68 on the Conservatoire’s pedagogy and on musical mores more generally among young composers; Fifth Republic France’s increased funding for new music festivals in regional cities such as Royan; Boulez and Xenakis’s profiles as the two most influential composers in France; and collectives, aleatoricism, and music theatre in post-1968 composition. The chapter closes with an account of Grisey’s early student works, in particular their creative adaptation of Messiaen’s personnages sonores concept towards the construction of audibly distinct musical figures, which would become a key element in Grisey’s musical style.

The composer-performer collective l’Itinéraire, founded in 1973 by Murail and Tessier, was the de facto platform for spectral music in France. This chapter shows how l’Itinéraire formed with the aim of establishing an organ for the music of the youngest generation of French composers, and how, with the demise of Boulez’s Domaine Musical ahead of the opening of IRCAM, l’Itinéraire fortuitously found itself positioned as the successor to that Parisian new music series, endorsed by Messiaen and recipient of a state subsidy. The chapter details how Grisey composed Périodes, a l’Itinéraire commission and the first work composed from his Les Espaces acoustiques cycle, and how Grisey attended the acoustics laboratory at the Université Paris VI Jussieu, where, alongside lessons in musical acoustics, he absorbed the work of Abraham Moles on the application of information theory to art. The chapter also shows how Murail began to incorporate the models of spectral harmonicity and periodicity into his music from Tigres de verre onwards, and it explores the relationship of these instrumental compositional techniques to the computer sound synthesis work of Risset and Chowning.

The book’s conclusion situates spectral music as a modernist musical movement. It shows how spectral music reprises many of serialism’s concerns, albeit on a more psychoacoustically accurate level. It relates the debates between Levinas and the other spectral composers to an older debate about formalism in art between Flaubert and Sand. Finally, the book concludes by situating Grisey as the founder of spectral music.

Spectral music as a distinct movement began in 1976, when, within a few days of each other, Murail’s Mémoire-érosion and Grisey’s Partiels were both premiered by Ensemble l’Itinéraire. This chapter explores how, driven by the theorist Dufourt, the young composers associated with l’Itinéraire developed a theoretical identity in contradistinction to Boulez and IRCAM. As well as detailing the salient qualities of Grisey and Murail’s music in this period, the chapter explores the diverse spectral music of Dufourt, Levinas, and Tessier. Dufourt’s works Erewhon, La tempesta d’après Giorgione, and Saturne engage with insights regarding sound related to his encounters with Risset and Chowning. Levinas’s works like Appels foregrounded sonic parasitism and a dramatic spectacle far removed from the more reserved forms of Murail, of which the chapter shows Levinas to have been at times a public critic. Tessier’s music in this period was expressionistic and explored electroacoustic resources. As well as detailing these various spectral sub-currents, the chapter explores the role of l’Itinéraire’s performers in helping to develop performing techniques adequate to the spectral writing.

The introductory chapter to Gérard Grisey and Spectral Music: Composition in the Information Age situates the book’s historical narrative by focusing on correspondence between Grisey and Dufourt in 1980 discussing what name they should give their common musical movement:’ spectral music’ or ‘liminal music’. This matter of naming indicates the compositional values the composers prioritised: movement over stasis, thresholds over states, psychoacoustic phenomena over traditional notes and pitches. The chapter then gives an overview of the book’s argument that spectral music developed from serialism through embracing information theory and developments in psychoacoustics and computer sound synthesis. Inasmuch as it arose in France but depended on developments that occurred at Bell Telephone Laboratories in the USA, spectral music was transatlantic in origin and signified a paradigm shift in musical composition.