Trans people who transition medically are typically hoping to live their lives simply as members of the sex with which their gender corresponds but may wish to make full use of the capabilities of their physical bodies, which may differ from typical male or female bodies. This chapter, co-authored by a trans man who is a transgender health advocate and a trans woman who is a physician, provides an overview of the kind of physical changes that are experienced by trans people, both those who transition from female to or toward male and those from male to or toward female, and alerts gynecologists and other medical healthcare professionals to the trans person’s perspective in clinical encounters.

Chapter 8 presents a de Branges–Rovnyak-type model theory for a given operator-tuple in an appropriate class (indexed by an admissible weight ?) of hypercontractive operator tuples. Application of results from Chapter 4 leads to a shift-type model-operator-tuple acting on a backward-shift-invariant contractively included subspace of a ?-weighted Hardy–Fock space. In the nicest case one can use results of Chapter 5 to define a characteristic operator function from which one can recover in the model the original ?-hypercontractive operator tuple up to unitary equivalence. A particular instance of this nice situation is the case where the ?-hypercontractive operator tuple is pure, or equivalently, when the backward-shift-invariant subspace is isometrically included in the ambient weighted Hardy–Fock space. In this case, there is also an alternative model theory based on a characteristic Bergman-inner family which makes use of results from Chapter 7. In this case, there is also a Bergman-inner characteristic function which is a partial unitary invariant and relates to the work on the Bergman shift from the 1990s.

After a brief discussion of invariant measures and entropy, we introduce semidynamical and dynamical systems. We use Koopmanism to show how to obtain semigroups/groups of linear operators on function spaces, when we have a quasi-invariant measure. Applications are given to solution flows of differential equations. In the last part we discuss “dilations” as a mathematical approach to the origins of irreversibility.

Chapter 3 examines the formal realism of “reverent natural history,” describing the formal properties of natural histories in ways that we have assumed were the sole province of the realist novel’s descriptive operations. The focus is on P. H.Gosse’s seashore trilogy, including A Naturalist’s Rambles on the Devonshire Coast, The Aquarium, and Tenby. These formal properties include: the prevalence of detail that the inductive process and theological orientation that the texts encourage; the quality of dilation as a function of reverence; and how detail, dilation, and minuteness are formal and thematic attributes of these natural histories, which reflect a religiosity that goes beyond the overt references to design arguments. The chapter’s second half focuses on two natural environments of the seashore naturalist: the aquarium and the tide-pool. These environments are read as literary figures, as heightened sites of metonymic display.