The sphinx is a good test case illustrating the complexities of studying Greek hybrids. The pronounced sexuality of modern sphinxes (notably those of Moreau and Ingres) sets them apart from Greek examples, which themselves are very different from the sphinxes of Egypt and the Ancient Near East. Common to all is the blurring of human/animal boundaries, a phenomenon going back to the Palaeolithic. Modern comparisons from New Guinea and Africa confirm that there is an animal dimension at the heart of being human. Hybrids, born of this mixing, are polymorphous, polysemic and polyvalent. Around the hybrid there lurks a host of questions: what bits have been mixed, how exactly are the parts combined, and is the mixture taxonomically fitting or anomalous? Each of these questions shapes our response to a hybrid, affirming the power of hybridity to challenge (or affirm) categories and taxonomies. And since taxonomies are the proof of our comprehending the world by classifying phenomena, hybridity represents a culture’s uneasiness with the limits of its epistemology. If such things exist, even if only in our stories and imagination, how certain is certainty?

Problems involving calculations of various properties associated with the density operator and entropies and their relations to more general situations in physics are included.

Born in the year of the liberation Korea from Japanese colonisation, Younghi Pagh-Paan (*1945) grew up during the Korean war and the subsequent division of her homeland. Although she trained in Seoul, her career as a composer properly started with her move to Freiburg in Germany in 1974. The result was a culture shock, and, throughout much of her career, Pagh-Paan struggled with her displacement and endeavoured to reconcile her gender and cultural identity as an Asian woman with Western modernism; vowing, in her own words, ‘[n]ot [to] write music that distances me from what […] I perceive inside me as the root of our culture’. This chapter discusses Pagh-Paan’s career and her aesthetic beliefs, such as her commitment to the student movement and democratic opposition in her country and her syncretistic religiosity that embraces the different spiritual traditions of her country, such as Shamanism and Taoism, as well as her fervent Catholicism. Analysing the reflection of these ideas in her music I conclude that, transcending notions of cultural contrast or ‘East-meets-West fusion’, Pagh-Paan’s work is a response to more than a century of intimate entanglements between Western and Korean culture.

This chapter presents the surprising mathematical result that classical systems can indeed have entanglement. However, the degree to which they can be entangled is strictly limited, while quantum systems have no limit to their amount of entanglement.

This chapter presents some basic calculations that show counterintuitive or unexpected results. First, it is shown that the Planck spectrum of light, which played an important role in the history of quantum mechanics, doesn’t say anything about the existence of indivisible particles. Second, a brief discussion of “chaos theory” shows that jumpy and unpredictable behavior can occur in classical systems. Last, the concept of “entanglement” is introduced as a basic property of quantum systems.

In order to explore translinguistic precarity in greater depth, we need to do three things: First, move towards a sufficiently complex understanding of what precarity means (and does not mean). Is it a general condition of our times, a longstanding effect of capitalist exploitation or an emergent property of unequal social relations? Second, we need to think through ways of relating precarity to language. It is not enough to predefine precarious lives in terms of marginalisation, poverty, struggle or discrimination and then to assume that the language used by or towards such speakers is necessarily precarious or produces precarity. We need instead to understand the co-articulation of translingual practices and lived experiences of precarity, asking how one informs the other. So third, it is important to understand the dynamic interactions among material relations, language ideologies and linguistic resources, where precarity may be an emergent feature as much as a pre-condition, of a local assemblage. Drawing on data from our longitudinal metrolingual project we make a case for understanding translanguaging and precarity in relational terms, entangled with family and friendship support structures, contingencies of the local economy, gender norms, cultural and religious practices, and local language policies and possibilities.

All examples seen in the preceding chapters have dealt with a single particle. In this chapter, the theory is expanded to systems with several identical particles. Here, ‘many’ in practice means two. However, this does allow the introduction of several central aspects. Perhaps the most important one is spin, which is the topic of the first part. Central elements in this context are the Stern–Gerlach experiment and the Pauli matrices. The characteristics of these matrices are studied in some detail as they play crucial roles in the remainder of the book. The concept of entanglement in quantum physics is introduced – exemplified using both the two-particle spin wave function and the combined spin–space wave function for a single particle. Due to the Pauli principle, the importance of spin and exchange symmetry in a many-body context is hard to underestimate. The fact that identical particles are indistinguishable has implications for the symmetry of the wave function. This, in turn, has significant consequences for the structure of the system – including its ground state. This is investigated by performing calculations of energy estimates. Most of these apply the variational principle, but also the notion of self-consistent field and the Hartree–Fock method are introduced.

Contradictions in intellectual history are presented in this chapter regarding: scientific discoveries in physics and biology, Montaigne’s prolific self-investigation, and research on self-complexity. There are also cultural differences: East Asians view the world as being involved in constant flux and are tolerant of contradictions. This tolerance is more problematic for Western individuals, who tend to experience contradiction as a threat to their self-esteem. The Japanese folkloristic figure of yokai is presented as an example representing a coalition of good and bad. Furthermore, utopian ideals are critically discussed as embracing one ultimate end position, with the denial of the fundamentally contradictive nature of human beings. The work of Carl Jung on "shadows" is introduced and compared to the moral middle ground. The process of generative dialogue is proposed as a way to deal with contradictions. Finally, some practical implications are presented: the fostering of self-empathy, stimulating tolerance of uncertainty, and the influence of high-quality listening on the softening of the boundaries of the self.

Building on the analogy from quantum mechanics, we can ask whether certain human rights exist in a shared state. This would mean, for instance, whether the right to privacy exists in a shared state with the right to freedom of expression. Or, whether the right to reputation – leaving aside the issue whether such a self-standing right can be justified – exists in a shared state with the right of access to information. If the premise of such a shared state is correct, then it would follow that change in the scope and meaning of one right (particle) in this shared state leads to a simultaneous change in the opposite direction in the other right (particle). After transposition into a new domain, the features of a human rights idea, or characteristics of some offline traditional right, may appear in a higher spectrum than in the traditional setting. We notice wide variance between the meaning of freedom of expression offline and online, since offline it can rarely be justified as an absolute right, whereas online practice shows a duality: the parallel possibility of relativity and absoluteness.

In Chapter 2, we will review basic facts of quantum measurement that are usually discussed in basic texts on quantum mechanics. These include a motivating experiment – the Stern–Gerlach effect – and discussions of measurement results, statistics, the Born rule, and wavefunction collapse.

In this chapter we discuss the application of entanglement to quantum optical interferometry and to quantum information processing. Quantum random number generation is discussed. Quantum cryptography is discussed, as is quantum computing. The quantum optical realization of some quantum gates is discussed.

Entanglement is one of the most fundamental, and intriguing, properties of quantum mechanics. It is also at the heart of quantum cryptography! In this chapter we start by giving a clear mathematical definition of entanglement. We give two classic applications, to superdense coding and to secret sharing. We then investigate two complementary properties of entanglement that we will use deeply in cryptographic applications. The first is nonlocality, which we investigate through the famous CHSH game. The second is the monogamy of entanglement, which we demonstrate using a three-player version of the CHSH game.

Chapter devoted to the basic quantum properties of entanglement and separability. Introduces the Schmidt decomposition for pure states and the positive partial transpose criterion for mixed states as entanglement witnesses. Introduces the famous Einstein–Podolsky–Rosen paradox and its implementation in terms of qubits, then the Bell inequality, quickly reviewing the experimental demonstrations that quantum mechanics violates this inequality. Gives examples of the use of entanglement in a quantum algorithm to accelerate an information task, namely a database search (Grover algorithm) and the possibility of teleportation of a quantum state.