The coda draws out the implications of modernist physiognomy for our contemporary moment. As we move from nineteenth-century physiognomy to modernist physiognomy, we encounter more minimalist descriptions of faces – facial sketches, outlines. We encounter faces reduced to a minimalist form. This form is taken up by contemporary facial recognition technologies. Across the scholarly literature on facial recognition technologies, there is a growing awareness of bias: technology is biased because training sets are biased. As Cathy O’Neil writes, “data embeds the dark past.” At the conclusion of this book, the coda frames its contribution to the call issued by Soshana Zuboff in Surveillance Capitalism: “If the digital future is to be our home, then it is we who must make it so.” This book will have aimed to give historicized substance to a fragment of this past: algorithmic data embeds the long history of the face, including elements of modernist physiognomy.

This chapter follows on from the previous chapter in quantum statistical mechanics but specialising on systems with identical particles. Using Gibbs prescritpion on generic states from Chapter 3, the occupation number representation is introduced. Constraints imposed on statistics by irreducible representations of the permutation group are discussed. These group-theoretic considerations are used to justify the use of Gentile’s parastatistics. Fermions and bosons are introduced as special cases of Gentile’s statistics, corresponding to the trivial representation of the permutation group for bosons, and the sign representation of the permutation group for fermions. Basic applications to fermions and bosons is given, including the Fermi–Dirac and Bose–Einstein statistics. A detailed expose of why photons are said to have zero chemical potential is also proposed.

This chapter provides a framework for the reader to describe abnormalities of the electrographic background and foreground. The electrographic background may be described based on symmetry, continuity, voltage, organization, reactivity, and sleep architecture. A waveform or potential abnormality may be described based on its location, occurrence (sporadic or repetitive – rhythmic or periodic), and morphology (slow or sharp wave). Further, this description can be qualified based on modifiers such as prevalence, frequency, duration, and amplitude. When reporting waveforms, the modifiers should precede the key features in your description. [88 words/557 characters]

One of life’s most fundamental revelations is change. Presenting the fascinating view that pattern is the manifestation of change, this unique book explores the science, mathematics, and philosophy of change and the ways in which they have come to inform our understanding of the world. Through discussions on chance and determinism, symmetry and invariance, information and entropy, quantum theory and paradox, the authors trace the history of science and bridge the gaps between mathematical, physical, and philosophical perspectives. Change as a foundational concept is deeply rooted in ancient Chinese thought, and this perspective is integrated into the narrative throughout, providing philosophical counterpoints to customary Western thought. Ultimately, this is a book about ideas. Intended for a wide audience, not so much as a book of answers, but rather an introduction to new ways of viewing the world.

Symmetries are a key idea in physics. In the classical world, they are associated to conservation laws, courtesy of Emmy Noether. The same, and more, is true in the quantum world. In this chapter we explore how symmetries manifest themselves in quantum mechanics. Special attention will be given to time evolution and the role of SU(2) and angular momentum

This appendix gives some examples of presentations of 2-categories by 3-polygraphs. In many examples, the presented 2-categories are in fact monoidal categories and, actually, PROs.

The main aim of Chapter 2 is to develop your understanding of how signs are formed and to help you improve the accuracy of your sign articulation. Section 2.1 contains detailed information related to the five components of signs: handshape, location, movement, orientation and non-manual features, and also includes some description of the arrangement of the hands and how to put signs together with the least influence from English possible. The following section, 2.2, provides examples of common sign articulation errors made in relation to the five components and how to correct them. This includes explanation of the typical errors that are made when learners rely on English words and do not think about the meaning or context of the concept they want to express. This chapter ends with Section 2.3, which provides exercises to improve sign articulation and encourages BSL learners to practice use of both manual and non-manual features of BSL.

This chapter advocates an ethic of “symmetric interpretation” as a solution to the challenges outlined in Chapter 1. To prevent undue politicization of constitutional law, judges should favor, when possible, constitutional understandings that are “symmetric” in the sense of conferring valuable protections across both sides of the nation’s major political and ideological divides. By the same token, they should disfavor understandings that frame constitutional law as a matter of zero-sum competition between rival partisan visions. Favoring symmetric understandings in this sense will not always be possible. When it is possible, however, favoring symmetry may provide a point of common orientation for judges with differing policy preferences and interpretive outlooks. Reflecting this approach's inherent appeal, an inchoate preference for symmetry is already evident in judges’ opinions, oral argument questions, and reasoning.

This chapter advances theoretical reasons to support symmetric interpretation. First, favoring symmetry accords with the Constitution’s character as a comparatively terse, “framework” document focused on establishing democratic procedures rather than definitive policies. Second, an ethic of symmetric interpretation accords with widely accepted features of judicial role-morality. Finally, symmetric interpretation accords with the framers’ own constitutional aspirations and interpretive methods. Multiple widely accepted theoretical considerations in constitutional law thus support preferring symmetric understandings when possible.

Originally established by “we the people,” as its preamble majestically states, the Constitution belongs to us all. But Americans increasingly treat it as the property of one political faction or the other. In keeping with their own preferences, conservatives interpret the Constitution to protect religion, limit gun control, and obstruct administrative governance while allowing state-level regulation of moral questions like abortion. Progressives see a mirror-image constitution that advances social justice, confers broad federal power, and allows flexible administrative regulation while at the same time limiting state and local police authority and guaranteeing sexual and reproductive autonomy. As national politics have grown ever more divided and polarized, preventing either side from implementing its goals through federal legislation, both coalitions have dreamed of capturing the courts and implementing their vision instead through constitutional interpretation. A document that should be a source of unity and shared commitments has become a vehicle for extending political conflict.

In modern physics, symmetries are a powerful tool to constrain the form of equations, namely the Lagrangian that describes the system. Equations are assumed to be invariant under the transformation of a given group, which may be discrete or a continuous Lie group. Classification of the various types of symmetry. The concept of spontaneous symmetry breaking. It will evolve into the Higgs mechanism, which gives origin to the masses of the vector bosons that mediate the weak interactions, of the quarks and of the charged leptons.

The discrete symmetries, in particular the parity and the particle–antiparticle conjugation operations and the corresponding quantum numbers.

An important dynamical symmetry of the hadrons, the invariance of the Lagrangian under rigid rotations in an ‘internal’ space, the isospin space. The unitary group is SU(2).