This chapter classifies all one-dimensional smooth manifolds, showing that every connected smooth one-manifold is diffeomorphic to one of four basic examples. The proof employs parametrisation by arc length. Using this classification, we demonstrate that smooth manifolds with boundary do not admit a retraction onto their boundary. As an application, we prove Brouwer’s Fixed Point Theorem, first for smooth self-maps of a closed disc in Euclidean space, then for continuous maps, and show by example that the result fails for self-maps of an open ball. Exercises include using Brouwer’s theorem to prove the Perron—Frobenius theorem on the existence of non-negative eigenvalues for matrices with non-negative entries, and showing that the circle is not simply connected.

Discontinuance of innovation is the first decision in the innovation post-adoption process. This chapter scrutinizes subsequent decisions that may follow discontinuance decision. The conventional view is that the discontinued innovation is replaced with another innovation new to the organization. Chapter 6 delineates that replacement is not the sole substitute of a discontinued innovation; rather, it is a choice against alternative substitutes that is made contingent on environmental and organizational circumstances. Additional post-adoption decisions including retraction, reinvention, re-innovation, and readoption are defined and exemplified. In the tradition of the diffusion of innovation, the post-adoption decisions have been studied mostly at the level of individual adopters. Chapter 6 focuses on organizational adopters and confers why and how organizations may choose between alternative substitutes of discontinued innovations. Two empirical studies are illustrated. Similar to the study of innovation discontinuance exemplified in Chapter 5, these studies rely on the dual explanations of rational and institutional perspectives for examining the drivers of replacement, retraction, and readoption of innovation. In combination, the studies exemplified in Chapters 5 and 6 provide a template for investigating the post-adoption process of innovation at the organization level. A process model to guide further studies is proposed.

In this chapter, I want to take a close look at two distinct but related phenomena in the humanities, each of which marks a stark contrast with the natural sciences for reasons that are not altogether clear. The first involves a recent episode in which several deliberately nonsensical articles were published as part of an effort to expose a certain family of humanities disciplines as intellectually hollow. I will argue that the general phenomenon it illustrates does in fact represent a serious problem in the humanities. The second phenomena is the general absence of article retraction in the humanities. Retraction plays an important epistemic role in science. Now, why is the retraction rate in the humanities holding steady at around 0%? Is this cause for celebration, cause for concern, or an insignificant byproduct of the fundamental difference between scientific knowledge and humanistic knowledge?

This chapter demonstrates the influential role of printed books in defining Chaucer’s canon and the implications of that newly formed canon for older books. It considers a series of texts which early modern readers added to manuscripts (and some early printed books) to update and improve them: short poems including Prophecy, Words to Adam, and Bon counsail; Robert Henryson’s Testament of Cresseid; various Plowman-themed texts; the Tale of Gamelyn; and the Retraction. The chapter argues that print made available an array of genuine and apocryphal works which readers could extract, assemble, and reconfigure in line with their own tastes and understanding of the Chaucer canon. The evidence collected in the chapter shows the persistence of particular narratives about Chaucer’s works which were promoted in print: that he was a poet of fin amour, that he condemned Criseyde to a wretched death, that he assigned his Plowman an anticlerical tale, and that the Retraction was a later monkish forgery. The changeability of the manuscript books chronicled in this chapter reflects a concurrent reshaping of Chaucer’s reputation in the period and the variability of his literary canon itself.