At virtually the same time as the rise in cross-cultural studies of development, there has been a dramatic increase in interest in life span development, which covers not only the period from birth to maturity, but also continues through maturity to eventual demise (Baltes, Lindenberger and Staudinger, 2006). In this chapter, we examine cross-cultural variations in the developmental stages beyond the ones that were discussed in Chapter 2; these are childhood, adolescence and adulthood. After discussing cultural notions of childhood and adolescence, we will present evidence on how childhood experiences can explain cross-cultural variations in adulthood. In the section on adulthood, we will deal with mating, partnership and parenting across cultures. In the final section, we will discuss life span developmental and evolutionary approaches to late adulthood. The chapter concludes with reflections on the cross-cultural applicability of the developmental issues raised in the last two chapters.

Childhood and adolescence

As we have seen in the previous chapter, human development can be described in stages. There, we dealt with the first decade of life, comprising the two earliest stages, infancy and early childhood. While infancy is the period from birth to two years, childhood is mainly defined as the period after infancy and before sexual maturation.

In the previous chapter the solution of both homogeneous and non-homogeneous linear ODEs of order ≥ 2 was discussed. In particular we developed methods for solving some equations in which the coefficients were not constant but functions of the independent variable x. In each case we were able to write the solutions to such equations in terms of elementary functions, or as integrals. In general, however, the solutions of equations with variable coefficients cannot be written in this way, and we must consider alternative approaches.

In this chapter we discuss a method for obtaining solutions to linear ODEs in the form of convergent series. Such series can be evaluated numerically, and those occurring most commonly are named and tabulated. There is in fact no distinct borderline between this and the previous chapter, since solutions in terms of elementary functions may equally well be written as convergent series (i.e. the relevant Taylor series). Indeed, it is partly because some series occur so frequently that they are given special names such as sin x, cos x or exp x.

Since, in this chapter, we shall be concerned principally with second-order linear ODEs we begin with a discussion of this type of equation, and obtain some general results that will prove useful when we come to discuss series solutions.

It is not unusual in the analysis of a physical system to encounter an equation in which an unknown but required function y(x), say, appears under an integral sign. Such an equation is called an integral equation, and in this chapter we discuss several methods for solving the more straightforward examples of such equations.

Before embarking on our discussion of methods for solving various integral equations, we begin with a warning that many of the integral equations met in practice cannot be solved by the elementary methods presented here but must instead be solved numerically, usually on a computer. Nevertheless, the regular occurrence of several simple types of integral equation that may be solved analytically is sufficient reason to explore these equations more fully.

We begin this chapter by discussing how a differential equation can be transformed into an integral equation and by considering the most common types of linear integral equation. After introducing the operator notation and considering the existence of solutions for various types of equation, we go on to discuss elementary methods of obtaining closed-form solutions of simple integral equations. We then consider the solution of integral equations in terms of infinite series and conclude by discussing the properties of integral equations with Hermitian kernels, i.e. those in which the integrands have particular symmetry properties.

The reader will have realized that this book offers a selective presentation of a diverse field. Necessarily many important points of view, empirical research studies and programs of application have not been mentioned, never mind given substantive treatment. Our attention, however, has not been random, but was guided by major themes and debates on the relationship between behavior and culture.

We have also taken the position that psychological processes are shared, species-wide characteristics. These common psychological qualities are nurtured, and shaped by enculturation and socialization, sometimes further affected by acculturation, and ultimately expressed as overt human behaviors. While set on course by these transmission processes relatively early in life, behaviors continue to be guided in later life by direct influence from ecological, cultural and sociopolitical factors. In short, we have considered culture, in its broadest sense, to be a major source of human behavioral diversity producing variations on underlying themes. It is the common qualities that make comparisons possible, and the variations that make comparisons interesting.

Our enterprise has some clearly articulated goals, and it is reasonable to ask whether the field of cross-cultural psychology generally, and this book in particular, has met them. In our view, one of the goals, as expressed in Chapter 1, has not been achieved: we are nowhere close to producing a universal psychology through the comprehensive integration of results of comparative psychological studies.

In this chapter we examine the relationship between the science and practice of psychology as it has developed in the western world, and the need for a culturally informed, relevant and appropriate psychology for all the world's peoples. Psychological knowledge in the west (hereafter referred to as western psychology) is often of little relevance to the majority world (a term used, for example, by Kağitçibaşi, 2007, in preference to “developing” or “Third” World). We accept and applaud the goal of advancing the development of a global psychology, one that is both valid and useful for all cultural populations. There are a number of possible paths toward this goal, including: an examination of the impact of the presence of western psychology on the psychology done in other societies; the development of indigenous psychologies in many distinct societies; and the pulling together of all of these psychologies into a universal psychology that is global in scope.

This move toward an international perspective has been increasingly important in recent years, including for the history of psychology (Brock, 2006), for the teaching of psychology (Karandashev and McCarthy, 2006) and for the practice of psychology (Stevens and Gielen, 2007).

In this chapter we focus on various lines of research that have been developed in order to answer the question to what extent emotions are similar or different across cultures. First, we focus on dimensional approaches. Similar to what has been done in cross-cultural research on personality (Chapter 5) and cognition (Chapter 6), some emotion researchers have tried to reveal common dimensions underlying the many emotions that we experience in daily life and to see whether these dimensions are the same (equivalent) across cultures. The second section addresses research on emotion words. In the absence of a clear definition of emotion terms, the words that people use in daily language have become important tools for cross-cultural researchers. The central question here is whether linguistic differences (differences in words) can be used to infer psychological differences (differences in experience; see also Chapter 8). The third section focusses on studies of specific aspects of emotions. Many contemporary researchers no longer try to define emotion in terms of a single criterion. Rather they use a componential approach, which assumes that emotions can be defined in many different emotion components (e.g., thoughts, feelings, action tendencies, psychophysiological experiences). An important feature of this approach is that cross-cultural differences are assumed to be independent for each component (Mesquita, Frijda and Scherer, 1997).

Preface to book 2

Epistolary prose prefaces were a Hellenistic development, beginning possibly with the letters that Archimedes attached to most of his scientific works (Janson 1964: 19–21). Parthenius' prose Ἐρωτικὰ παθήματα provides the first extant epistolary preface attached to a non-scientific work; by honouring the poet Gallus as dedicatee, it thus promotes the value of the book (Lightfoot 222–4). The practice of putting an epistolary prose preface at the start of a Roman poetry book seems however to have been a Flavian innovation (Janson 1964: 107–12). Martial does this selectively (books 1, 2, 8, 9, 12), St. with all four books of the Siluae published in his lifetime; the posthumous book 5 has a prefatory letter for 5.1 only. The preface to book 2 is in the conventional form of a letter to the dedicatee (cf. 4 epistula), with a salutary phrase at the start (Statius Meliori suo salutem); the prefaces for books 3 and 4 have both opening salutation and concluding uale.

This preface dedicates the book to Atedius Melior, who receives the presentation copy. The preface has many functions beyond summarising the book's contents (thus Van Dam 55): it honours Melior and publicly affirms his friendship with St.; it also honours the addressees of the individual poems and, in keeping with the book's generally domestic character, it emphasises their emotional ties with St. (Johannsen 2006: 268–71).

With growing migration, globalization and internationalization comes an increased need for an understanding of intercultural communication, as well as the use of this information for training people in order to make them more competent in dealing with intercultural issues. The field is very diverse, with publications from a wide variety of scientific and applied disciplines. For example, there is research in linguistics (especially sociolinguistics), sociology, cultural anthropology and cross-cultural psychology. Much of this variety can be surveyed in a handbook edited by Landis, Bennett and Bennett (2004). In this chapter, we mainly focus on the psychological aspects of intercultural communication and training, and point out important issues and studies from a psychological perspective.

This chapter contains three main sections, each representing a distinct area of intercultural communication and training. The first, on intercultural communication, describes the attempts of researchers to delineate which elements of communication are the sources of communication problems during intercultural encounters. This section is somewhat more theoretical than later sections because the main questions focus on the nature of intercultural communication rather than on the application of this knowledge. The second section concerns sojourners, those people who stay in another culture mostly for purposes of work or study (e.g., international exchange students). This is a special group of acculturating people that has already been discussed in Chapter 13.

In Section A.9 of Appendix A we review the algebra of vectors, and in Chapter 1 we considered how to transform one vector into another using a linear operator. In this chapter and the next we discuss the calculus of vectors, i.e. the differentiation and integration both of vectors describing particular bodies, such as the velocity of a particle, and of vector fields, in which a vector is defined as a function of the coordinates throughout some volume (one-, two- or three-dimensional). Since the aim of this chapter is to develop methods for handling multi-dimensional physical situations, we will assume throughout that the functions with which we have to deal have sufficiently amenable mathematical properties, in particular that they are continuous and differentiable.

Differentiation of vectors

Let us consider a vector a that is a function of a scalar variable u. By this we mean that with each value of u we associate a vector a(u). For example, in Cartesian coordinates a(u) = ax(u)i + ay(u)j + az(u)k, where ax(u), ay(u) and az(u) are scalar functions of u and are the components of the vector a(u) in the x-, y- and z-directions respectively. We note that if a(u) is continuous at some point u = u0 then this implies that each of the Cartesian components ax(u), ay(u) and az(u) is also continuous there.