Given that the world as we perceive it appears to be predominantly classical, how can we stabilize quantum effects? Given the fundamental description of our world is quantum mechanical, how do classical phenomena emerge? Answers can be found from the analysis of the scaling properties of modular quantum systems with respect to a given level of description. It is argued that, depending on design, such partitioned quantum systems may support various functions. Despite their local appearance these functions are emergent properties (...) of the system as a whole. With respect to the separation of subject and object such functions of interest are control, simulation, and observation. They are interpreted in close analogy with more basic physical behavior. (shrink)

A theoretical physicist and feminist theorist, Karen Barad elaborates her theory of agential realism, a schema that is at once a new epistemology, ontology, and ethics.

"In Entangled Empathy, scholar and activist Lori Gruen argues that rather than focusing on animal rights, we ought to work to make our relationships with animals right by empathetically responding to their needs, interests, desires, vulnerabilities, hopes, and unique perspectives. Pointing out that we are already entangled in complex and life-altering relationships with other animals, Gruen guides readers through a new way of thinking about and practicing animal ethics. Lori Gruen is Professor of Philosophy and Coordinator of Wesleyan Animal Studies (...) at Wesleyan University. She is the author of Ethics and Animals and co-editor, with Carol Adams, of Ecofeminism: Feminist Intersections with Animals and the Earth."--Back cover. (shrink)

The fateful entanglements of psychoanalysis, cybernetics and digital media Content Type Journal Article Pages 1-4 DOI 10.1007/s11016-011-9570-0 Authors Leon Antonio Rocha, Department of History and Philosophy of Science, University of Cambridge, Free School Lane, Cambridge, CB2 3RH UK Journal Metascience Online ISSN 1467-9981 Print ISSN 0815-0796.

First philosophy: reality, truth, and knowledge -- The universe in brief -- Ontology -- Theory of truth -- Epistemology -- Axiology: goodness, beauty, and liberty -- Values as situations -- Ethics -- Aesthetics -- Political philosophy.

What do we mean by theory in the arts, and what role does it play in that sense? Theory appears as an active, transformative, fluid, and communicative element of art practices, and research in the arts in particular. Theory is the fluid that perfuses and connects the territory of fine art and design, as well as other art forms such as music, architecture, writing, moving images, dance, and theatre. At the heart of this publication is the new field of research (...) in theory and the way the ArtEZ Theory in the Arts research group investigates its possibilities and extends its boundaries. Editor Peter Sonderen currently chairs the professorship Theory in the Arts at ArtEZ University of the Arts. (shrink)

ABSTRACT Theories of sets such as Zermelo Fraenkel set theory are usually presented as the combination of two distinct kinds of principles: logical and set-theoretic principles. The set-theoretic principles are imposed ‘on top’ of first-order logic. This is in agreement with a traditional view of logic as universally applicable and topic neutral. Such a view of logic has been rejected by the intuitionists, on the ground that quantification over infinite domains requires the use of intuitionistic rather than classical logic. In (...) the following, I consider constructive set theories, which use intuitionistic rather than classical logic, and argue that they manifest a distinctive interdependence or an entanglement between sets and logic. In fact, Martin-Löf type theory identifies fundamental logical and set-theoretic notions. Remarkably, one of the motivations for this identification is the thought that classical quantification over infinite domains is problematic, while intuitionistic quantification is not. The approach to quantification adopted in Martin-Löf’s type theory is subtly interconnected with its predicativity. I conclude by recalling key aspects of an approach to predicativity inspired by Poincaré, which focuses on the issue of correct quantification over infinite domains and relate it back to Martin-Löf type theory. (shrink)

Squashed entanglement :829–840, 2004) is a monogamous entanglement measure, which implies that highly extendible states have small value of the squashed entanglement. Here, invoking a recent inequality for the quantum conditional mutual information :575–611, 2015) greatly extended and simplified in various work since, we show the converse, that a small value of squashed entanglement implies that the state is close to a highly extendible state. As a corollary, we establish an alternative proof of the faithfulness of (...) squashed entanglement. We briefly discuss the previous and subsequent history of the Fawzi–Renner bound and related conjectures, and close by advertising a potentially far-reaching generalization to universal and functorial recovery maps for the monotonicity of the relative entropy. (shrink)

The circulation and entanglements of human beings, data, and goods have not necessarily and by themselves generated a universalising consciousness. The "global" and the "universal", in other words, are not the same. The idea of a world-society remains highly contested. Our times are marked by the fragmentation of a double relativistic character: the inevitable critique of Western universalism on the one hand, and resurgent identitarian and neo-nationalistic claims to identity on the other. Sources of an argumentation for a strong (...) universalism brought forward by Western traditions such as Christianity, Marxism, and Liberalism have largely lost their legitimation. All the while, manifold and situated narratives of a common world that re-address the universal are under way of being produced and gain significance. This volume tracks the development and relevance of such cultural and social practices that posit forms of what we call minor universality. It asks: Where and how do contemporary practices open up concrete settings so as to create experiences, reflections and agencies of a shared humanity? With contributions by Isaac Bazié, Anil Bhatti, Jean-Luc Chappey, Elsie Cohen, Leyla Dakhli, Souleymane Bachir Diagne, Nicole Fischer, Albert Gouaffo, Stefan Helgesson, Fatma Hotait, Tammy Lai-Ming Ho, Christopher M. Hutton, Ananya Jahanara Kabir, Mario Laarmann, Rukmini Bhaya Nair, Olivier Remaud, Gisèle Sapiro, Bénédicte Savoy, Maria-Anna Schiffers, Laurens Schlicht, Sergio Ugalde, Hélène Thierard, Khadija von Zinnenburg Carroll. (shrink)

This book shines bright light into the dim recesses of quantum theory, where the mysteries of entanglement, nonlocality, and wave collapse have motivated some to conjure up multiple universes, and others to adopt a "shut up and calculate" mentality. After an extensive and accessible introduction to quantum mechanics and its history, the author turns attention to his transactional model. Using a quantum handshake between normal and time-reversed waves, this model provides a clear visual picture explaining the baffling experimental results (...) that flow daily from the quantum physics laboratories of the world. To demonstrate its powerful simplicity, the transactional model is applied to a collection of counter-intuitive experiments and conceptual problems. (shrink)

This article develops some of the many ways in which Leonardo and Descartes, throughout the prolific period of human valuation from the fifteenth to the seventeenth centuries, seem to have approached and anchored their seminal contributions on the Cartesian body and metaphysical mind. While Leonardo masterfully developed an iterative thinking system of visual design applied to nature and artifacts, Descartes laid the groundwork for methodical critical thinking in dimensions that ironically ranged from dreams to the controlled narrative, from a deceptive (...) body to a rational man. In an interdisciplinary articulation of historical and neurobiological leanings, contemporary concepts of the cognitive emotional brain, led by Damasio as the basis for his conclusions about the "Descartes Error", as well as a torrent of growing evidence that supports high cognitive abilities in associative processes mediated by action/body lead us to a re-evaluation today of the legacies of Leonardo and Descartes, rescuing a scientific mind/brain/body process that underlies the human mastering of a universal technology of discourse that would revolutionize science. (shrink)

We study the entanglement properties of the output state of a universal cloning machine. We analyse in particular bipartite and tripartite entanglement of the clones, and discuss the “classical limit” of infinitely many output copies.

This book provides an interdisciplinary perspective on one of the most fascinating and important open questions in science: What is quantum mechanics talking about? Quantum theory is perhaps our best confirmed physical theory. However, despite its great empirical effectiveness and the subsequent technological developments that it gave rise to in the 20th century, from the interpretation of the periodic table of elements to CD players, holograms and quantum state teleportation, it stands even today without a universally accepted interpretation. The novelty (...) of the book comes from the multiple viewpoints and subjects investigated by a group of researchers from Europe and North and South America. (shrink)

A generalized and unifying viewpoint to both general relativity and quantum mechanics and information is investigated. It may be described as a generaliztion of the concept of reference frame from mechanics to thermodynamics, or from a reference frame linked to an element of a system, and thus, within it, to another reference frame linked to the whole of the system or to any of other similar systems, and thus, out of it. Furthermore, the former is the viewpoint of general relativity, (...) the latter is that of quantum mechanics and information. Ciclicity in the manner of Nicolas Cusanus (Nicolas of Cusa) is complemented as a fundamental and definitive property of any totality, e.g. physically, that of the universe. It has to contain its externality within it somehow being namely the totality. This implies a seemingly paradoxical (in fact, only to common sense rather logically and mathematically) viewpoint for the universe to be repesented within it as each one quant of action according to the fundamental Planck constant. That approach implies the unification of gravity and entanglement correspondiing to the former or latter class of reference frames. An invariance, more general than Einstein's general covariance is to be involved as to both classes of reference frames unifying them. Its essence is the unification of the discrete and cotnitinuous (smooth). That idea underlies implicitly quantum mechanics for Bohr's principle that it study the system of quantum microscopic entities and the macroscopic apparatus desribed uniformly by the smmoth equations of classical physics. (shrink)

In his own words, Herbert Gintis’s latest book is “an analysis of human nature and a tribute to its wonders” (3).1More prosaically, it is a collection of essays, some of which are original and others published elsewhere. Instead of being structured around topics in decision and game theory,like his previous book (2009), this book develops interrelated themes, such as the evolutionary origins of moral sense, its central role in political games, and the socially entangled nature of human rationality and individuality. (...) Some chapters develop Gintis’svision of the unified behavioral sciences by model-building demonstrations; others do so by reflecting on history and methodology. (shrink)

Two of the most difficult problems in the foundations of physics are (1) what gives rise to the arrow of time and (2) what the ontology of quantum mechanics is. I propose a unified 'Humean' solution to the two problems. Humeanism allows us to incorporate the Past Hypothesis and the Statistical Postulate into the best system, which we then use to simplify the quantum state of the universe. This enables us to confer the nomological status to the quantum state in (...) a way that adds no significant complexity to the best system and solves the ''supervenient-kind problem'' facing the original version of the Past Hypothesis. We call the resultant theory the Humean unification. It provides a unified explanation of time asymmetry and quantum entanglement. On this theory, what gives rise to time's arrow is also responsible for quantum phenomena. The new theory has a separable mosaic, a best system that is simple and non-vague, less tension between quantum mechanics and special relativity, and a higher degree of theoretical and dynamical unity. The Humean unification leads to new insights that can be useful to Humeans and non-Humeans alike. (shrink)

This is an extended essay review of Tanya and Jeffrey Bub’s Totally Random: Why Nobody Understands Quantum Mechanics: A serious comic on entanglement. We review the philosophical aspects of the book, provide suggestions for instructors on how to use the book in a class setting, and evaluate the authors’ artistic choices in the context of comics theory. Although Totally Random does not defend any particular interpretation of quantum mechanics, we find that, in its mode of presentation, Totally Random is (...) a beautiful expression and illustration of the information-theoretic interpretation and its value. (shrink)

Despite the entangled universe cannot be considered merely as an enormously complex system, as it is reactive to actions and observations, references on quantum entanglement in living systems may help find ways in which quantum effects can move from the microscopic to the macroscopic, in realms where the mind/brain behave as a quantum object and is sensitive to the dynamic state of the entire universe. Taking up vision from a synaesthetic perspective as a perfusion of senses, and putting together (...) a myriad of references around this perception phenomenon, the idea is to work in the building of artistic experiences where vision takes up a tactile function, emerging from a tension between the movements governed by the interaction of the attractors. (shrink)

Abstract‘We just do not have enough time’. A statement uttered too often in the field of education. Having taught in K-12 schools, universities, and accelerated K-12 and higher education classes, I am no stranger to the myriad of conversations on time that swirl in these spaces. All too frequently, I heard statements like: ‘there is not enough time in the schedule to do this work’, ‘time is our enemy’, ‘do the best you can with the limited time you have’, and (...) witnessed many discussions of entanglements with time, be they individual, institutional, or structural. This article explores issues of time within hybrid/third-space working groups embedded within a teacher residency in an urban Southeastern city of the United States. In exploring the question: what role does time play in hybrid teacher residency work? This article demonstrates how time operates as a structural constraint, as a nonhuman agent, and/or is mobilized to escape/evade the nuanced and complex work of doing/thinking anti-racist abolitionist residency work across practice and theory. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Journal of the History of Philosophy 39.2 (2003) 289-290 [Access article in PDF] Monoson, S. Sara. Plato's Democratic Entanglements: Athenian Politics and the Practice of Philosophy. Princeton: Princeton University Press, 2000. Pp. 256. Cloth, $39.50. Sara Monoson is that rare exception to the rule that political theorists cannot sustain the interest of political philosophers: her training in ancient history and classical Greek gives her treatment of Plato's complicated relationship (...) to democracy a depth and richness that will repay the efforts of the most exacting of critics. The book under review has much to offer philosophers as well as historians of philosophy. Notably, Monoson answers the question, "What is democracy?" with attention to a whole constellation of "cultural practices and normative imagery" (237) constitutive of the Athenian polis, on which the narrow conception of democracy qua system of government depends. The experience of festival participation, including processions, theater, and funeral orations; multifarious opposition to tyranny; and parrhe sia, frank speech, were practices that contributed to the Athenian citizen's confidence and expectation that he should and could participate actively in the governing of his polis. One of Monoson's implicit arguments is that Platonic political philosophy is inextricably bound up with its context; thus, when we excise a Platonic "position" or argument and test its soundness, we are doing philosophy, not the history of philosophy.Monoson details the democratic practices and images that are woven into the dialogues, and she features passages others have neglected or treated as anomalous (e.g., Statesman 303a-d, Letter 7 342d), arguing convincingly that it is an unfair oversimplification to view Plato as anti-democratic, or indeed as a doctrinaire writer in any sense (133-137). Thus she does not describe Plato as simple-mindedly pro-democratic either. Rather, she does an impressive job of demonstrating just how very deeply ambivalence toward democracy runs in the dialogues, most markedly in the Republic and Gorgias,but even in the Laws. Plato was as attracted to democracy as he was wary of it, as committed to its institutions as he was apprehensive of their untoward effects.The parts of Monoson's book devoted to theater participation, frank speech, and opposition to tyranny—in relation to democracy and in Plato—are especially fine and contain a wealth of evidence that withstands scrutiny admirably. Her treatment of the funeral oration, including an interpretation of Plato's Menexenus, is less successful, but because her thesis is demonstrated without it, I need not digress from the book's virtues. Monoson's historical sections on the tyrannicides, the early Academy, and Plato's Sicilian involvement are lucid and compelling. All along in this book, one notes passages that serendipitously bear on contemporary debates and on widely shared—but controversial—interpretations of the dialogues. To take but one example from [End Page 289] what I think of as the centerpiece of the book on the realizability of the Republic's ideal city (130-133), consider the well known and variously interpreted passage suggesting how to realize the ideal the "quick and easy way": send away everyone over ten, and let the philosophers educate the remaining children (541a). The conclusion and crux of Monoson's thoughtful reply is, "I suggest we see in this passage an indication that Plato acknowledged that all governing regimes can be supported or unsettled by cultural formations. He is deeply involved here with the question of how it is that a person or people can imagine themselves out of a dominant discourse." (I should add that the book is remarkably free of jargon.) Although Monoson has given us so much so well, I am greedy to know what she makes of democracy in the Protagoras,how she views the success of sycophants after the Peloponnesian War, and how she would incorporate deme politics into her account.The deficiencies of the work as a whole are few and minor: the sole structural weakness of this excellent book is that Monoson sometimes cites, instead of evidence or argument, the judgments of others whose work... (shrink)

The paper discusses this year’s Nobel Prize in physics for experiments of entanglement “establishing the violation of Bell inequalities and pioneering quantum information science” in a much wider, including philosophical context legitimizing by the authority of the Nobel Prize a new scientific area out of “classical” quantum mechanics relevant to Pauli’s “particle” paradigm of energy conservation and thus to the Standard model obeying it. One justifies the eventual future theory of quantum gravitation as belonging to the newly established quantum (...) information science. Entanglement, involving non-Hermitian operators for its rigorous description, non-unitarity as well as nonlocal and superluminal physical signals “spookily” (by Einstein’s flowery epithet) synchronizing and transferring some nonzero action at a distance, can be considered to be quantum gravity so that its local counterpart to be Einstein’s gravitation according to general relativity therefore pioneering an alternative pathway to quantum gravitation different from the “secondary quantization” of the Standard model. So, the experiments of entanglement once they have been awarded by the Nobel Prize launch particularly the relevant theory of quantum gravitation grounded on “quantum information science” thus granted to be nonclassical quantum mechanics in the shared framework of the generalized quantum mechanics obeying rather quantum-information conservation than only energy conservation. The concept of “dark phase” of the universe naturally linked to the very well confirmed “dark matter” and “dark energy” and opposed to its “light phase” inherent to classical quantum mechanics and the Standard model obeys quantum-information conservation, after which reversible causality or the mutual transformation of energy and information are valid. The mythical Big Bang after which energy conservation holds universally is to be replaced by an omnipresent and omnitemporal medium of decoherence of the dark and nonlocal phase into the light and local phase. The former is only an integral image of the latter and borrowed in fact rather from religion than from science. Physical, methodological and proper philosophical conclusions follow from that paradigm shift heralded by this year’s Nobel Prize in physics. For example, the scientific theory of thinking should originate from the dark phase of the universe, as well: probably only approximately modeled by neural networks physically belonging to the light phase thoroughly. A few crucial philosophical sequences follow from the break of Pauli’s paradigm: (1) the establishment of the “dark” phase of the universe as opposed to its “light” phase, only to which the Cartesian dichotomy of “body” and “mind” is valid; (2) quantum information conservation as relevant to the dark phase, furthermore generalizing energy conservation as to its light phase, productively allowing for physical entities to appear “ex nihilo”, i.e., from the dark phase, in which energy and time are yet inseparable from each other; (3) reversible causality as inherent to the dark phase; (4) the interpretation of gravitation only mathematically: as an interpretation of the incompleteness of finiteness to infinity, for example, following the Gödel dichotomy (“either contradiction or incompleteness”) about the relation of arithmetic to set theory; (5) the restriction of the concept of hierarchy only to the light phase; (6) the commensurability of both physical extremes of a quantum and the universe as a whole in the dark phase obeying quantum information conservation and akin to Nicholas of Cusa’s philosophical and theological worldview. (shrink)

Although coherence has become one of the key concepts in contemporary legal theory, its meaning is taken almost universally to be elusive, complex and controversial. However, these difficulties are due just to the failure of commentators to distinguish the intension of the notion from other features of its (many) referents in extension. The oversight has caused qualities to be ascribed routinely to coherence that properly attach to various object(s) of which coherence is predicated, and which a theorist happens to have (...) in mind when bringing coherence into view. This conceptual error has significance for the substance of present claims made for the use of the notion in law. Freed from the entanglement, coherence emerges thinner and fitter, better able to be deployed with confidence in legal application. (shrink)

Unifying the Universe: The Physics of Heaven and Earth presents a non-technical approach to physics for the lay-science enthusiast. This popular textbook, which evolved from a conceptual course at Cornell University, is intended for non-science undergraduate students taking their first physics module. This second edition maintains its unique approach in crossing boundaries between physics and humanities, with connections to art, poetry, history, and philosophy. It explores how the process of scientific thought is inextricably linked with cultural, creative, and aesthetic aspects (...) of human endeavor, opening the readers up to new ways of looking at the world. The text has been fully updated throughout to address current and exciting new topics in the field, such as exo-planets, the accelerating Universe, dark matter, dark energy, gravitational waves, super-symmetry, string theory, big bang cosmology, and the Higgs boson. There is also an entirely new chapter on the Quantum World, which connects the fascinating topics of quantum entanglement and quantum computing. Key Features: Provides a solid, yet accessible, background to basic physics without complex mathematics Uses a human interest approach to show how science is significant for more than its technological consequences Discusses the arts and philosophies of historical periods that are pertinent to the subject. (shrink)

The experience of the impossible churns up in our epoch whenever a collective dream turns to trauma: politically, sexually, economically, and with a certain ultimacy, ecologically. Out of an ancient theological lineage, the figure of the cloud comes to convey possibility in the face of the impossible. An old mystical nonknowing of God now hosts a current knowledge of uncertainty, of indeterminate and interdependent outcomes, possibly catastrophic. Yet the connectivity and collectivity of social movements, of the fragile, unlikely webs of (...) an alternative notion of existence, keep materializing--a haunting hope, densely entangled, suggesting a more convivial, relational world. Catherine Keller brings process, feminist, and ecopolitical theologies into transdisciplinary conversation with continental philosophy, the quantum entanglements of a "participatory universe," and the writings of Nicholas of Cusa, Walt Whitman, A. N. Whitehead, Gilles Deleuze, and Judith Butler, to develop a "theopoetics of nonseparable difference." Global movements, personal embroilments, religious diversity, the inextricable relations of humans and nonhumans--these phenomena, in their unsettling togetherness, are exceeding our capacity to know and manage. By staging a series of encounters between the nonseparable and the nonknowable, Keller shows what can be born from our cloudiest entanglement. (shrink)

In a quantum universe with a strong arrow of time, we postulate a low-entropy boundary condition to account for the temporal asymmetry. In this paper, I show that the Past Hypothesis also contains enough information to simplify the quantum ontology and define a unique initial condition in such a world. First, I introduce Density Matrix Realism, the thesis that the quantum universe is described by a fundamental density matrix that represents something objective. This stands in sharp contrast to Wave Function (...) Realism, the thesis that the quantum universe is described by a wave function that represents something objective. Second, I suggest that the Past Hypothesis is sufficient to determine a unique and simple density matrix. This is achieved by what I call the Initial Projection Hypothesis: the initial density matrix of the universe is the normalized projection onto the special low-dimensional Hilbert space. Third, because the initial quantum state is unique and simple, we have a strong case for the \emph{Nomological Thesis}: the initial quantum state of the universe is on a par with laws of nature. This new package of ideas has several interesting implications, including on the harmony between statistical mechanics and quantum mechanics, the dynamic unity of the universe and the subsystems, and the alleged conflict between Humean supervenience and quantum entanglement. (shrink)

The book addresses for the first time the dynamics associated with the modernization of mathematics in China from the nineteenth to the mid-twentieth century from a transcultural global historical perspective. Rather than depict the transformations of mathematical knowledge in terms of a process of westernization, the book analyzes the complex interactions between different scientific communities and the ways in which the past, modernity, language, and mathematics were negotiated in a global context. In each chapter, Andrea Bréard provides vivid portraits of (...) a series of go-betweens based on a vast array of translated primary sources hitherto unavailable to a non-Chinese readership. They not only illustrate how Chinese scholars mediated between new mathematical objects and discursive modes, but also how they instrumentalized their autochthonous scientific roots in specific political and intellectual contexts. While sometimes technical in style, the book addresses all readers who are interested in the global and cultural history of science and the complexities involved in the making of universal mathematics. “While the pursuit of modernity is in the title, entanglement is of as much interest. Using the famous ‘Nine Chapters’ as a framework, Bréard considers a wide range of that entanglement from divination to data management. Bréard’s analysis and thought-provoking insights show once again how much we can learn when two cultures intersect. A fascinating read!”. (shrink)

One can often encounter claims that classical (Kolmogorovian) probability theory cannot handle, or even is contradicted by, certain empirical findings or substantive theories. This note joins several previous attempts to explain that these claims are unjustified, illustrating this on the issues of (non)existence of joint distributions, probabilities of ordered events, and additivity of probabilities. The specific focus of this note is on showing that the mistakes underlying these claims can be precluded by labeling all random variables involved contextually. Moreover, contextual (...) labeling also enables a valuable additional way of analyzing probabilistic aspects of empirical situations: determining whether the random variables involved form a contextual system, in the sense generalized from quantum mechanics. Thus, to the extent the Wang-Busemeyer QQ equality for the question order effect holds, the system describing them is noncontextual. The double-slit experiment and its behavioral analogues also turn out to form a noncontextual system, having the same probabilistic format (cyclic system of rank 4) as the one describing spins of two entangled electrons. (shrink)

A geometric model previously developed to analyze the quantum structure of Hardy’s paradox and explore the generic structure of universal states is applied to the Moebius band. The Moebius band’s conformity to the model strengthens its hypothesis. The claim made is that universal states cannot be represented as singular structures without reference to a partition of entangled parts that do not share property with each other. In other words, universal states categorically incorporate a systemic feature of inconsistency (...) within their frameworks. In logic and mathematics, this is the prohibition to forming theoretical principles that are singularly fundamental as absolute truths. The Moebius band contains a dualism of two categorically separate formats. It has, firstly, two discrete and observable sides and secondly, a unitary path, in which the sides are entangled and indistinguishable. Quantum structures display a similar attribute of duality. However, unlike quantum structure, the Moebius band displays the full duality of its structure at the classical level. The geometric model demonstrates the common structural basis shared in the Moebius band and quantum structure. (shrink)