Stage 4 of the journey follows with an example of how implementation of a formal metalanguage helps with, but also hinders, the analysis of meaning of natural-language expressions. In particular, it addresses operations on sentences and introduces the connectives of propositional logic, assessing the degree of fit between them and their natural-language counterparts. In the process, it addesses the question of ambiguity and/or underspecification of the latter and concludes with some ‘food for thought’ on the usefulness of a formal semantic analysis.

This first stage of the journey introduces the concept of meaning in language and discourse, discusses the advantages of studying it at the interfaces of semantics, pragmatics, and philosopy, and moves to the correlates of meaning in the mind and in the world. It also addresses the question of the appropriate unit of study – a flexible type of proposition.

In this chapter we review the basic concepts of digital modulation and demodulation in the absence of noise. Digital modulation is the process of mapping information bits into transmitted waveforms. Demodulation is the process of mapping received signals back into bits. Concepts from signals and systems that are needed in understanding modulation and demodulation are reviewed.

Because sinusoidal signals are fundamental in communication systems, we first review representations of sinusoidal signals. Next, we show how vectors can be mapped into waveforms, as described in Chapter 1. For binary modulation, 1 bit of information (a 0 or a 1) is mapped into one of two vectors. These vectors along with a set of orthonormal waveforms (described below) determine two signals. So 1 bit of information will be mapped into one of two signals that is transmitted.

This stage of the journey offers an explanation of how truth conditions and truth-value judgements can be used in understanding sentence meaning, moving on to the role of a formal metalanguage, possible worlds, and models. As ‘food for thought’, it focuses on the importance of selecting a suitable formal language, introducing some options available in the formal semantic tradition, as well as on the cognitive reality of such approaches to meaning.

This chapter is concerned with error control coding, sometimes called forward error correction (FEC) using block codes. Shannon’s result in Chapter 1 and the cutoff rate theorem in Chapter 6 indicate that performance of communication systems will generally be better if the dimensionality of the signal set is large. Error control codes are used to define large-dimensional signal sets.

Here we discuss inflation, a period of accelerated expansion that occurred in the very early history of the universe. We motivate inflation by describing the flatness and horizon problems, then explain how inflation resolves them. We describe the early history of inflationary ideas, then move on to modern work where we outline the standard scalar-field model for inflation, and define the slow-roll parameters that phenomenologically describe the dynamics of inflation. We briefly outline how inflation leads to the generation of density fluctuations in the universe; we mathematically describe the spectrum of these fluctuations, and confront it with modern observations. We end by discussing more speculative ideas in this area, including eternal inflation and multiverse.

In this chapter we study the primordial process in which nuclei of atoms formed -- the Big Bang nucleosynthesis, or BBN for short. We show that BBN principally leads to the synthesis of hydrogen and helium, along with a trace amount of a few more of the lightest elements. We describe the basic thermodynamical and nuclear-physics conditions in the early universe, and explain how they determine the primordial origin and abundance of nuclei in the universe. Finally, we illustrate how the lightest-element abundances are in spectacularly good agreement with observations, making BBN one of the pillars of the hot Big Bang cosmological model.

In this chapter we review dark matter, whose physical nature remains unknown 90 years after astronomer Fritz Zwicky found the first evidence for it. We go over the historical evidence for dark matter, than review modern indications for the existence of this component. We then review particle candidates for dark matter, outlining the properties that dark matter of each particle candidate would have. Next we go over the direct, indirect, and laboratory searches for dark matter. We end by discussing a dramatically different alternative (to particles) for the nature of dark matter -- that of a modified theory of gravity (MOND).