The significance and use of absence of a thing is highlighted as its presence. The role of absence in various disciplines of mathematics, physics, semi-conductor electronics, computing and cognitive sciences for ease in conceptualizing is discussed. The use of null set, null vector and null matrix are also presented.

We revisit the nonrelativistic problem of a bound, charged particle subject to the random zero-point radiation field, with the purpose of revealing the mechanism that takes it from the initially classical description to the final quantum-mechanical one. The combined effect of the zpf and the radiation reaction force results, after a characteristic time lapse, in the loss of the initial conditions and the concomitant irreversible transition of the dynamics to a stationary regime controlled by the field. In this regime, the (...) canonical variables x, p become expressed in terms of the dipolar response functions to a set of field modes. A proper ordering of the response coefficients leads to the matrix representation of quantum mechanics, as was proposed in the early days of the theory, and to the basic commutator x^,p^=iħ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\left[ {\hat{x}},{\hat{p}}\right] =i\hbar $$\end{document}. Further, the connection with the corresponding Fokker–Planck equation valid in the Markov approximation, allows one to obtain the radiative corrections of qed. These results reaffirm the essentially electrodynamic and stochastic nature of the quantum phenomenon, as proposed by stochastic electrodynamics. (shrink)

In this third paper in a series on stochastic electrodynamics (SED), the nonrelativistic dipole approximation harmonic oscillator-zero-point field system is subjected to an arbitrary classical electromagnetic radiation field. The ensemble-averaged phase-space distribution and the two independent ensemble-averaged Liouville or Fokker-Planck equations that it satisfies are derived in closed form without furtner approximation. One of these Liouville equations is shown to be exactly equivalent to the usual Schrödinger equation supplemented by small radiative corrections and an explicit radiation reaction (RR) vector potential (...) that is similar to the Crisp-Jaynes semiclassical theory (SCT) RR potential. The wave function in this SED Schrödinger equation is shown to have thea priori significance of position probability amplitude. The other Liouville equation has no counterpart in ordinary quantum mechanics, and is shown to restrict initial conditions such that (i) The Wigner-type phase-space distribution is always positive, (ii) in the absence of an applied field, the only allowed solution of both equations is the quantum ground state, and (iii) if a previously applied field is suddenly turned off, then spontaneous transitions occur, with no need for a triggering perturbation as in SCT, until the system is in the ground state. It is also shown that the oscillator energy is a fluctuating quantity that must take on a continuum of values, with average value equal to the quantum ground-state energy plus a contribution due to the applied classical field. (shrink)

This paper will discuss the recent LIGO-Virgo observations of gravitational waves and the binary black hole mergers that produce them. These observations rely on having prior knowledge of the dynamical behaviour of binary black hole systems, as governed by the Einstein Field Equations (EFEs). However, we currently lack any exact, analytic solutions to the EFEs describing such systems. In the absence of such solutions, a range of modelling approaches are used to mediate between the dynamical equations and the (...) experimental data. Models based on post-Newtonian approximation, the effective one-body formalism, and numerical relativity simulations (and combinations of these) bridge the gap between theory and observations and make the LIGO-Virgo experiments possible. In particular, this paper will consider how such models are validated as accurate descriptions of real-world binary black hole mergers (and the resulting gravitational waves) in the face of an epistemic circularity problem: the validity of these models must be assumed to justify claims about gravitational wave sources, but this validity can only be established based on these same observations. (shrink)

The present paper reveals (non-relativistic) quantum mechanics as an emergent property of otherwise classical ergodic systems embedded in a stochastic vacuum or zero-point radiation field (zpf). This result provides a theoretical basis for understanding recent numerical experiments in which a statistical analysis of an atomic electron interacting with the zpf furnishes the quantum distribution for the ground state of the H atom. The action of the zpf on matter is essential within the present approach, but it is the ergodic demand (...) what ultimately leads to the matrix formulation of quantum mechanics. The paper thus represents a step forward in the quest for an elucidation of the fundamentals of quantum mechanics. (shrink)

Organisations that design and deploy artificial intelligence (AI) systems increasingly commit themselves to high-level, ethical principles. However, there still exists a gap between principles and practices in AI ethics. One major obstacle organisations face when attempting to operationalise AI Ethics is the lack of a well-defined material scope. Put differently, the question to which systems and processes AI ethics principles ought to apply remains unanswered. Of course, there exists no universally accepted definition of AI, and different systems pose different ethical (...) challenges. Nevertheless, pragmatic problem-solving demands that things should be sorted so that their grouping will promote successful actions for some specific end. In this article, we review and compare previous attempts to classify AI systems for the purpose of implementing AI governance in practice. We find that attempts to classify AI systems proposed in previous literature use one of three mental models: _the Switch_, i.e., a binary approach according to which systems either are or are not considered AI systems depending on their characteristics; _the Ladder_, i.e., a risk-based approach that classifies systems according to the ethical risks they pose; and _the Matrix_, i.e., a multi-dimensional classification of systems that take various aspects into account, such as context, input data, and decision-model. Each of these models for classifying AI systems comes with its own set of strengths and weaknesses. By conceptualising different ways of classifying AI systems into simple mental models, we hope to provide organisations that design, deploy, or regulate AI systems with the vocabulary needed to demarcate the material scope of their AI governance frameworks. (shrink)

Soonya Vaada, the prime and significant contribution to Indian philosophical thought from Buddhism will be scientifically developed and presented. How this scientific understanding helped to sow seeds of origin of rationalism and its development in Buddhist thought and life will be delineated. Its role in the shaping of Buddhist and other Indian philosophical systems will be discussed. Its relevance and use in the field of cognitive science and development of theories of human consciousness and mind will be put forward. The (...) idea of absence as zero in number system, vacuum in physics and other natural sciences and state of absence of cognition in mind machine modeling will be presented. The use of significance of Soonya Vaada in philosophy, rational social life, natural sciences and technology, mathematics and cognitive science will be comprehensively discussed and a model for human cognition and communication will be arrived at. -/- . (shrink)

The concept of the vacuum in quantum field theory is a subtle one. Vacuum states have a rich and complex set of properties that produce distinctive, though usually exceedingly small, physical effects. Quantum vacuum noise is familiar in optical and electronic devices, but in this paper I wish to consider extending the discussion to systems in which gravitation, or large accelerations, are important. This leads to the prediction of vacuum friction: The quantum vacuum can act in a manner reminiscent of (...) a viscous fluid. One result is that rapidly changing gravitational fields can create particles from the vacuum, and in turn the backreaction on the gravitational dynamics operates like a damping force. I consider such effects in early universe cosmology and the theory of quantum black holes, including the possibility that the large-scale structure of the universe might be produced by quantum vacuum noise in an early inflationary phase. I also discuss the curious phenomenon that an observer who accelerates through a quantum vacuum perceives a bath of thermal radiation closely analogous to Hawking radiation from black holes, even though an inertial observer registers no particles. The effects predicted raise very deep and unresolved issues about the nature of quantum particles, the role of the observer, and the relationship between the quantum vacuum and the concepts of information and entropy. © 2001 American Institute of Physics. (shrink)

I present in detail the case for regarding black hole thermodynamics as having a statistical-mechanical explanation in exact parallel with the statistical-mechanical explanation believed to underly the thermodynamics of other systems. I focus on three lines of argument: zero-loop and one-loop calculations in quantum general relativity understood as a quantum field theory, using the path-integral formalism; calculations in string theory of the leading-order terms, higher-derivative corrections, and quantum corrections, in the black hole entropy formula for extremal and near-extremal black holes; (...) recovery of the qualitative and quantitative structure of black hole statistical mechanics via the AdS/CFT correspondence. In each case I briefly review the content of, and arguments for, the form of quantum gravity being used at a introductory level: the paper is aimed at students and non-specialists and does not presume advanced knowledge of quantum gravity.. My conclusion is that the evidence for black hole statistical mechanics is as solid as we could reasonably expect it to be in the absence of a directly-empirically-verified theory of quantum gravity. (shrink)

To state an important fact about the photon, physicists use such expressions as (1) “the photon has zero (null, vanishing) mass” and (2) “the photon is (a) massless (particle)” interchangeably. Both (1) and (2) express the fact that the photon has no non-zero mass. However, statements (1) and (2) disagree about a further fact: (1) attributes to the photon the property of zero-masshood whereas (2) denies that the photon has any mass at all. But is there really a difference (...) between saying that something has zero mass (charge, spin, etc.) and saying that it has no mass (charge, spin, etc.)? Does the distinction cut any physical or philosophical ice? I argue that the answer to these questions is yes. Put briefly, the claim of this paper is that some zero-value physical quantities are not mere “privations”, “absences” or “holes in being”. They are respectable properties in the same sense in which their non-zero partners are. This, I will show, has implications for the debate between two rival views of the nature of property, dispositionalism and categoricalism. (shrink)

The grounding of semiotics in the finiteness of cognition is extended into constructs and methods for analysis by incorporating the assumption that cognition can be similar within and between agents. After examining and formalizing cognitive similarity as an ontological commitment, the recurrence of cognitive states is examined in terms of a “cognitive set.” In the individual, the cognitive set is seen as evolving under the bidirectional, cyclical determination of thought by the historical environment. At the population level, the distributed “global” (...) cognitive set is argued to be constrained to a manifold in which the cognition of individuals is determined only when their cognitive sets meet certain conditions in the world: a result seen as consistent with Lotman’s semiosphere. With these foundations in place, dimensional modelling of the semiosic field is inaugurated. Firstly, measures of cognitive similarity are formalized as cognitive “distance” and on this basis the concept of a semiotic vector is defined. Secondly, semiotic vectors are seen to shape a general pattern of oscillation in semiosis, and thus to imply zero points in semiosic potential. Thirdly, semiosic oscillation in individual agents is shown to be consistent with a novel diachronic or longitudinal interpretation of Greimas’ semiotic square expanded into a “semiotic pipe” in which cognition traverses an n-dimensional space structured by axes of oscillation. Finally, the expanded theory of finite semiotics is advanced as a useful basis for two new complementary disciplines: a computational, mathematical science of “natural semiotic processing” to trace and model semiotic vectors and oscillation; and an ethical, rhetorical art of “technological influencing” to guide its inputs and applications. (shrink)

We have studied aesthetic field theory in the case where all invariants constructed from Γ jk i and involving g ij are zero. We studied such a “null” theory in 1972, but the cases we cited were plagued with singularities. By introducing complex fields the situation with respect to singularities improved. Complex fields are consistent with the basic “aesthetic principles” we outlined earlier. Within our null theory we see in two-dimensional spacetime a scattering of particles that was more (...) involved than what we had seen before (regardless of dimensions). We see creation and annihilation of particles out of the vacuum. We also see a three-particle system within a small region of spacetime. In three spacetime dimensions we see a bound two-particle system. Another solution suggests a bound three-particle system. As well as we can tell the particles stay together (confinement) and do not give problems with attenuation. We observe in three dimensions one of the bound systems moving along a definite path in time. The four-dimensional spacetime results are not clear at this point. Whether “topological” bound systems of three particles exist has yet to be determined. A map in the four-dimensional case indicates a planar three maxminima confluence and the suggestion of a second such confluence. (shrink)

$${{{\mathcal {F}}}}$$ -systems are useful digraphs to model sentences that predicate the falsity of other sentences. Paradoxes like the Liar and the one of Yablo can be analyzed with that tool to find graph-theoretic patterns. In this paper we studied this general model consisting of a set of sentences and the binary relation ‘ $$\ldots $$ affirms the falsity of $$\ldots $$ ’ among them. The possible existence of non-referential sentences was also considered. To model the sets of all (...) the sentences that can jointly be valued as true we introduced the notion of conglomerate, the existence of which guarantees the absence of paradox. Conglomerates also enabled us to characterize referential contradictions, i.e., sentences that can only be false under a classical valuation due to the interactions with other sentences in the model. A Kripke-style fixed-point characterization of groundedness was offered, and complete (meaning that every sentence is deemed either true or false) and consistent (meaning that no sentence is deemed true and false) fixed points were put in correspondence with conglomerates. Furthermore, argumentation frameworks are special cases of $$\mathcal{F}$$ -systems. We showed the relation between local conglomerates and admissible sets of arguments and argued about the usefulness of the concept for the argumentation theory. (shrink)

Classical electron theory with classical electromagnetic zero-point radiation (stochastic electrodynamics) is the classical theory which most closely approximates quantum electrodynamics. Indeed, in inertial frames, there is a general connection between classical field theories with classical zero-point radiation and quantum field theories. However, this connection does not extend to noninertial frames where the time parameter is not a geodesic coordinate. Quantum field theory applies the canonical quantization procedure (depending on the local time coordinate) to a mirror-walled box, and, in general, each (...) non-inertial coordinate frame has its own vacuum state. In particular, there is a distinction between the “Minkowski vacuum” for a box at rest in an inertial frame and a “Rindler vacuum” for an accelerating box which has fixed spatial coordinates in an (accelerating) Rindler frame. In complete contrast, the spectrum of random classical zero-point radiation is based upon symmetry principles of relativistic spacetime; in empty space, the correlation functions depend upon only the geodesic separations (and their coordinate derivatives) between the spacetime points. The behavior of classical zero-point radiation in a noninertial frame is found by tensor transformations and still depends only upon the geodesic separations, now expressed in the non-inertial coordinates. It makes no difference whether a box of classical zero-point radiation is gradually or suddenly set into uniform acceleration; the radiation in the interior retains the same correlation function except for small end-point (Casimir) corrections. Thus in classical theory where zero-point radiation is defined in terms of geodesic separations, there is nothing physically comparable to the quantum distinction between the Minkowski and Rindler vacuum states. It is also noted that relativistic classical systems with internal potential energy must be spatially extended and can not be point systems. The classical analysis gives no grounds for the “heating effects of acceleration through the vacuum” which appear in the literature of quantum field theory. Thus this distinction provides (in principle) an experimental test to distinguish the two theories. (shrink)

This is the first in a series of papers that present a new classical statistical treatment of the system of a charged harmonic oscillator (HO) immersed in an omnipresent stochastic zero-point (ZP) electromagnetic radiation field. This paper establishes the Gaussian statistical properties of this ZP field using Bourret's postulate that all statistical moments of the stochastic field plane waves at a given space-time point should agree with their corresponding quantized field vacuum expectations. This postulate is more than adequate to derive (...) the Planck spectrum classically via Boyer's and Theimer's methods, but it requires that the stochastic amplitude of each linearly polarized plane wave in the field contain two independent Gaussian random variables, not just a random phase as has sometimes been assumed. In the succeeding papers in the series, the total motion of a charged HO is described by a fully renormalized dipole-approximation Abraham-Lorentz equation. This leads without further approximation to the following major results concerning this stochastic electrodynamics (SED) of the HO: i) The ensemble-average Liouville equation for the oscillator-ZP field system in the presence of an arbitrary applied classical radiation field is exactly equivalent to the usual time-dependent Schrödinger equation supplemented by an explicit radiation reaction vector potential similar to that of the Crisp-Jaynes-Stroud theory; ii) this SED Schrödinger equation for the HO is incomplete, insmuch as there exists a companion equation that restricts initial conditions such that the corresponding Wigner phase-space distribution is always positive; iii) the wave function of the SED Schrödinger equation has thea priori significance of position probability amplitude; iv) first-order transition rates predicted for the HO by this theory agree with those predicted by quantum electrodynamics for resonance absorption and spontaneous emission, which occurs with no triggering necessary; and v) if SED is taken seriously, then the concepts of quantized energies and photons must be abandoned. (shrink)

Les théories linguistiques en général, et plus particulièrement la psychomécanique du langage, dont le modèle est essentiellement binaire, peinent à faire une place à l’absence de déterminant sémiologiquement marqué. Quoique le terme « article zéro » soit communément usité, il n’y a guère de consensus sur le sens à lui donner. Pour le français, où son emploi reste marginal, on observe une fracture entre une posture théorique consistant à l’intégrer au système de l’article et une autre revenant à en nier (...) l’existence. Pour l’anglais, où il est beaucoup plus fréquent, la théorie se heurte à une multiplicité d’emplois difficiles à rassembler sous un même phénomène. Or un examen attentif des occurrences du corpus permet de proposer, dans la continuité de la théorie psychomécanique, un modèle où coexistent d’une part l’absence de tout déterminant et, d’autre part, un article zéro dont on peut montrer qu’il recouvre une véritable opération de détermination définie comme une transition du nom de la langue au discours débouchant sur son aptitude à référer. (shrink)

The Casimir force between two neutral metallic plates is often considered conclusive evidence for the reality of electromagnetic zero-point fluctuations in 'empty space' (i.e. in absence of any boundaries). However, it is not well known that the Casimir force can be derived from many different points of view. The purpose of this note is to supply a conceptually oriented introduction to a representative set of these different interpretations. The different accounts suggest that the Casimir effect reveals nothing conclusive about the (...) nature of the vacuum. (shrink)

The structure of the thermal equilibrium state of a weakly interacting Bose gas is of current interest. We calculate the density matrix of that state in two ways. The most effective method, in terms of yielding a simple, explicit answer, is to construct a generating function within the traditional framework of quantum statistical mechanics. The alternative method, arguably more interesting, is to construct the thermal state as a vector state in an artificial system with twice as many degrees of (...) freedom. It is well known that this construction has an actual physical realization in the quantum thermodynamics of black holes, where the added degrees of freedom correspond to the second sheet of the Kruskal manifold and the thermal vector state is a state of the Unruh or the Hartle–Hawking type. What is unusual about the present work is that the Bogolubov transformation used to construct the thermal state combines in a rather symmetrical way with Bogolubov's original transformation of the same form, used to implement the interaction of the nonideal gas in linear approximation. In addition to providing a density matrix, the method makes it possible to calculate efficiently certain expectation values directly in terms of the thermal vector state of the doubled system. (shrink)

This paper explores the prospects of radical hope for addressing the devastation of the Covid-19 pandemic. Hope is useful for conceptualizing the proper balance between too much fear and too little about our uncertain future. First, I describe the ethical challenge of the pandemic as a wicked problem. Because accepted ethical theories fail to motivate solutions, wicked problems pressure us to develop our value systems, exercise moral imaginations, and discover creative solutions. Second, I develop an Aristotelian account of radical hope, (...) drawing from ancient philosophy, virtue ethics, and recent climate ethics. Radical hope is a novel form of courage, which balances the goal of external success, that something good will emerge from the tragedy, against the goal of living well for its own sake through practical wisdom. I conclude by applying some lessons to our present situation. (shrink)

The aim of the study was to compare the acute effects of traditional resistance training and superset training on training duration, training volume and different perceptive measures. Twenty-nine resistance-trained participants performed a whole-body workout traditionally and as supersets of exercises targeting different muscle groups, in a randomized-crossover design. Each session was separated by 4–7 days, and consisted of eight exercises and three sets to failure. Training duration and number of repetitions lifted were recorded during the sessions. Rate of perceived exertion (...) for effort, rate of perceived exertion for discomfort, session displeasure/pleasure, and exercise enjoyment were measured 15 min after each session. Forty-eight hours after the final session participants reported which session they preferred. The superset session led to significantly higher values for RPE and RPD and tended to be higher for sPDF, i.e., more pleasurable, compared to the traditional session. There was no difference in EES. The traditional session led to significantly increased training volume and lasted 23 min longer than the superset session. Eighteen of the participants preferred the superset session, while 11 preferred the traditional session. In conclusion, performing a whole-body workout as a superset session was more time-efficient, but reduced the training volume and was perceived with greater exertion for effort and discomfort than a traditional workout. (shrink)

Recently, Clifton and Halvorson have tried to salvage a particle phenomenology in the absence of particle ontology within algebraic relativistic quantum field theory. Their idea is that the detection of a particle is the measurement of a local observable which simulates the measurement of an almost local observable that annihilates the vacuum. In this note, we argue that the measurements local particle detections are supposed to simulate probe radically holistic aspects of relativistic quantum fields. We prove that in an axiomatic (...) (Haag-Araki) quantum field theory on Minkowski spacetime, formulated in a Hilbert space $\mathcal{H}$ , there is no positive observable C, with norm less than or equal to 1, satisfying the conditions: (1) the expectation value of C in the vacuum state Ω is zero, (2) there is at least one vector state Ψ in $\mathcal{H}$ in which the expectation value of C is different from zero, and (3) there exists at least one spacetime region $\mathcal{O}$ such that the non-selective measurement of C leaves the expectation values of all observables in the local algebra of that region unaltered regardless of the state the system is in. The result reveals a tension between intuitions regarding localization and intuitions regarding causality: to save “particle phenomena” in the absence of particle ontology, one has to feign “particle” detectors with “good” properties as to locality but “bad” behavior as to causality. (shrink)

This article is a preliminary draft for initiating and commencing a new pioneer dimension of expression. To deal with higher-dimensional data or information flowing in this modern era of information technology and artificial intelligence, some innovative super algebraic structures are essential to be formulated. In this paper, we have introduced such matrices that have multiple layers and clusters of layers to portray multi-dimensional data or massively dispersed information of the plithogenic universe made up of numerous subjects their attributes, and sub-attributes. (...) For grasping that field of parallel information, events, and realities flowing from the micro to the macro level of universes, we have constructed hypersoft and hyper-super-soft matrices in a Plithogenic Fuzzy environment. These Matrices classify the non-physical attributes by accumulating the physical subjects and further sort the physical subjects by accumulating their non-physical attributes. We presented themasPlithogenicAttributiveSubjectivelyWholeHyper-Super-Soft-Matrix(PASWHSS-Matrix)andPlithogenic Subjective Attributively Whole-Hyper-Super-Soft-Matrix (PSAWHSS-Matrix). Several types of views and level-layers of these matrices are described. In addition, some local aggregation operators for Plithogenic Fuzzy Hypersoft Set (PPFHS-Set) are developed. Finally, few applications of these matrices and operators are used as numerical examples of COVID-19 data structures. (shrink)

Bartoszynski, T. and S. Shelah, Closed measure zero sets, Annals of Pure and Applied Logic 58 93–110. We study the relationship between the σ-ideal generated by closed measure zero sets and the ideals of null and meager sets. We show that the additivity of the ideal of closed measure zero sets is not bigger than covering for category. As a consequence we get that the additivity of the ideal of closed measure zero sets is equal to the additivity of (...) the ideal of meager sets. (shrink)

Drawing upon Roland Barthes’ posthumously published notebooks from his 1974 trip to China, in which he remarks upon the ‘complete absence of fashion. Clothing degree zero’, this article offers a ‘late’ reading of Barthes’ interest in fashion, suggested here as a form of writing. In reference to the late works, specifically Barthes’ penultimate lecture course on the Neutral and Travels in China, supplemented by François Jullien’s comments on Barthes’ trip to China, as well as mention of Michelangelo Antonioni’s film Chung (...) Kuo-Cina, it is possible to draw together a reading of fashion as a neutral form. As a final step, reflection is given to Susan Buck-Morss’ reading of ‘history as passing’, as discontinuous moments. Barthes’ writerly mode – which works upon incidental details – is revealed to be a pertinent method. (shrink)

We model a black hole spacetime as a causal set and count, with a certain definition, the number of causal links crossing the horizon in proximity to a spacelike or null hypersurface Σ. We find that this number is proportional to the horizon's area on Σ, thus supporting the interpretation of the links as the “horizon atoms” that account for its entropy. The cases studied include not only equilibrium black holes but ones far from equilibrium.

Motivated by the known mathematical and physical problems arising from the current mathematical formalization of the physical spatio-temporal continuum, as a substantial technical clarification of our earlier attempt (Etesi in Found Sci 25:327–340, 2020), the aim in this paper is twofold. Firstly, by interpreting Chaitin’s variant of Gödel’s first incompleteness theorem as an inherent uncertainty or fuzziness present in the set of real numbers, a set-theoretic entropy is assigned to it using the Kullback–Leibler relative entropy of a pair of Riemannian (...) manifolds. Then exploiting the non-negativity of this relative entropy an abstract Hawking-like area theorem is derived. Secondly, by analyzing Noether’s theorem on symmetries and conserved quantities, we argue that whenever the four dimensional space-time continuum containing a single, stationary, asymptotically flat black hole is modeled by the set of real numbers in the mathematical formulation of general relativity, the hidden set-theoretic entropy of this latter structure reveals itself as the entropy of the black hole (proportional to the area of its “instantaneous” event horizon), indicating that this apparently physical quantity might have a pure set-theoretic origin, too. (shrink)

The explicit history of the “hidden variables” problem is well-known and established. The main events of its chronology are traced. An implicit context of that history is suggested. It links the problem with the “conservation of energy conservation” in quantum mechanics. Bohr, Kramers, and Slaters (1924) admitted its violation being due to the “fourth Heisenberg uncertainty”, that of energy in relation to time. Wolfgang Pauli rejected the conjecture and even forecast the existence of a new and unknown then elementary particle, (...) neutrino, on the ground of energy conservation in quantum mechanics, afterwards confirmed experimentally. Bohr recognized his defeat and Pauli’s truth: the paradigm of elementary particles (furthermore underlying the Standard model) dominates nowadays. However, the reason of energy conservation in quantum mechanics is quite different from that in classical mechanics (the Lie group of all translations in time). Even more, if the reason was the latter, Bohr, Cramers, and Slatters’s argument would be valid. The link between the “conservation of energy conservation” and the problem of hidden variables is the following: the former is equivalent to their absence. The same can be verified historically by the unification of Heisenberg’s matrix mechanics and Schrödinger’s wave mechanics in the contemporary quantum mechanics by means of the separable complex Hilbert space. The Heisenberg version relies on the vector interpretation of Hilbert space, and the Schrödinger one, on the wave-function interpretation. However the both are equivalent to each other only under the additional condition that a certain well-ordering is equivalent to the corresponding ordinal number (as in Neumann’s definition of “ordinal number”). The same condition interpreted in the proper terms of quantum mechanics means its “unitarity”, therefore the “conservation of energy conservation”. In other words, the “conservation of energy conservation” is postulated in the foundations of quantum mechanics by means of the concept of the separable complex Hilbert space, which furthermore is equivalent to postulating the absence of hidden variables in quantum mechanics (directly deducible from the properties of that Hilbert space). Further, the lesson of that unification (of Heisenberg’s approach and Schrödinger’s version) can be directly interpreted in terms of the unification of general relativity and quantum mechanics in the cherished “quantum gravity” as well as a “manual” of how one can do this considering them as isomorphic to each other in a new mathematical structure corresponding to quantum information. Even more, the condition of the unification is analogical to that in the historical precedent of the unifying mathematical structure (namely the separable complex Hilbert space of quantum mechanics) and consists in the class of equivalence of any smooth deformations of the pseudo-Riemannian space of general relativity: each element of that class is a wave function and vice versa as well. Thus, quantum mechanics can be considered as a “thermodynamic version” of general relativity, after which the universe is observed as if “outside” (similarly to a phenomenological thermodynamic system observable only “outside” as a whole). The statistical approach to that “phenomenological thermodynamics” of quantum mechanics implies Gibbs classes of equivalence of all states of the universe, furthermore re-presentable in Boltzmann’s manner implying general relativity properly … The meta-lesson is that the historical lesson can serve for future discoveries. (shrink)

A truth-preservation fallacy is using the concept of truth-preservation where some other concept is needed. For example, in certain contexts saying that consequences can be deduced from premises using truth-preserving deduction rules is a fallacy if it suggests that all truth-preserving rules are consequence-preserving. The arithmetic additive-associativity rule that yields 6 = (3 + (2 + 1)) from 6 = ((3 + 2) + 1) is truth-preserving but not consequence-preserving. As noted in James Gasser’s dissertation, Leibniz has been criticized for (...) using that rule in attempting to show that arithmetic equations are consequences of definitions. -/- A system of deductions is truth-preserving if each of its deductions having true premises has a true conclusion—and consequence-preserving if, for any given set of sentences, each deduction having premises that are consequences of that set has a conclusion that is a consequence of that set. Consequence-preserving amounts to: in each of its deductions the conclusion is a consequence of the premises. The same definitions apply to deduction rules considered as systems of deductions. Every consequence-preserving system is truth-preserving. It is not as well-known that the converse fails: not every truth-preserving system is consequence-preserving. Likewise for rules: not every truth-preserving rule is consequence-preserving. There are many famous examples. In ordinary first-order Peano-Arithmetic, the induction rule yields the conclusion ‘every number x is such that: x is zero or x is a successor’—which is not a consequence of the null set—from two tautological premises, which are consequences of the null set, of course. The arithmetic induction rule is truth-preserving but not consequence-preserving. Truth-preserving rules that are not consequence-preserving are non-logical or extra-logical rules. Such rules are unacceptable to persons espousing traditional truth-and-consequence conceptions of demonstration: a demonstration shows its conclusion is true by showing that its conclusion is a consequence of premises already known to be true. The 1965 Preface in Benson Mates (1972, vii) contains the first occurrence of truth-preservation fallacies in the book. (shrink)

The objective of the study was to investigate the relationship between childhood IQ of parents and characteristics of their adult offspring. It was a prospective family cohort study linked to a mental ability survey of the parents and set in Renfrew and Paisley in Scotland. Participants were 1921-born men and women who took part in the Scottish Mental Survey in 1932 and the Renfrew/Paisley study in the 1970s, and whose offspring took part in the Midspan Family study in 1996. There (...) were 286 offspring from 179 families. Parental IQ was related to some, but not all characteristics of offspring. Greater parental IQ was associated with taller offspring. Parental IQ was inversely related to number of cigarettes smoked by offspring. Higher parental IQ was associated with better education, offspring social class and offspring deprivation category. There were no significant relationships between parental IQ and offspring systolic blood pressure, diastolic blood pressure, cholesterol, glucose, lung function, weight, body mass index, waist hip ratio, housing, alcohol consumption, marital status, car use and exercise. Structural equation modelling showed parental IQ associated with offspring education directly and mediated via parental social class. Offspring education was associated with offspring smoking and social class. The smoking finding may have implications for targeting of health education. (shrink)

Many students feel despair when addressing systemic issues of ethical significance, such as climate change, and student despair has been exacerbated by the circumstances of the Covid-19 pandemic. This creates an unwelcoming space for authentic student engagement. To address the problem, we present an imaginary of radical hope, a pedagogical tool informed by trauma, for developing a brave space for class discussion. It is psychologically beneficial to acknowledge negative emotions, clearing the emotional space for students to engage. Therefore, we frame (...) ethics courses with an uncomfortable discussion, asking students to draw from their positionality and share their feelings of hope and despair, related to course material. In this paper, we explain the problem of despair motivating the project, describe the pedagogical and ethical support of our strategy, share the assignment, activity, and examples, and discuss takeaways. (shrink)

Some belief systems postulate intelligent agents that are deliberately evading detection and thus sabotaging any possible investigation into their existence. These belief systems have the remarkable feature that they predict an absence of evidence in their favor, and even the discovery of counterevidence. Such ‘epistemic black holes’, as I call them, crop up in different guises and in different domains: history, psychology, religion. Because of their radical underdetermination by evidence and their extreme resilience to counterevidence, they develop and evolve in (...) certain predictable ways. Shedding light on how epistemic black holes function can protect us against their allure. (shrink)

Tragedy feels disempowering and the confluence of tragedies since the beginning of 2020 can overwhelm one’s sense of agency. This paper describes how we use a civic engagement (CE) project to nurture radical hope for our students. Radical hope involves a desire for a positive outcome surpassing understanding, as well as an activity to strive to achieve that outcome despite its uncertainty. Our CE project asks students to identify ethical issues they care about and respond in a fitting way, questioning (...) the assumption that their efforts do not matter, and imagining creative ways to make a difference that are in their power. We scaffold our CE project in order to nurture hopeful possibilities for students by offering real-world, feasible pathways for addressing systemic problems. -/- . (shrink)

We propose a method for estimating subjective beliefs, viewed as a subjective probability distribution. The key insight is to characterize beliefs as a parameter to be estimated from observed choices in a well-defined experimental task and to estimate that parameter as a random coefficient. The experimental task consists of a series of standard lottery choices in which the subject is assumed to use conventional risk attitudes to select one lottery or the other and then a series of betting choices in (...) which the subject is presented with a range of bookies offering odds on the outcome of some event that the subject has a belief over. Knowledge of the risk attitudes of subjects conditions the inferences about subjective beliefs. Maximum simulated likelihood methods are used to estimate a structural model in which subjects employ subjective beliefs to make bets. We present evidence that some subjective probabilities are indeed best characterized as probability distributions with non-zero variance. (shrink)

The ternary, not binary, Kripke-type relation on a set of possible worlds is an essential part of the semantics of entailment by Routley-Meyer [2]. The unpopularity of such approach among many logicians is due to its intuitive vague content and complexity. An attempt is made to use not one ternary relation but two binary relations and necessity of bibinarness is demonstrated. It is shown that both semantics are equal hence the soundness and completeness of the system R of (...) entailment can be established with the respect to the bibinary semantics. Furthermore, the ternary semantic with discrete matrix for Lukasiewicz system Lℵ0 , which was proposed in [3], could be transformed into the bibinary one and it leads to the conclusion of the completeness and soundness of Lℵ0 with the respect to the bibinary semantic. The brief consideration of the bibinary semantic intuitive content is added, which further logical study could be based on. (shrink)

In the framework of the rigged Hilbert space, unstable quantum systems associated with first-order poles of the analytically continued S-matrix can be described by Gamow vectors which are generalized vectors with exponential decay and a Breit-Wigner energy distribution. This mathematical formalism can be generalized to quasistationary systems associated with higher-order poles of the S-matrix, which leads to a set of Gamow vectors of higher order with a non-exponential time evolution. One can define a state operator from the set (...) of higher-order Gamow vectors which obeys the exponential decay law. We shall discuss to what extent the requirement of an exponential time evolution determines the form of the state operator for a quasistationary microphysical system associated with a higher-order pole of the S-matrix. (shrink)

We study some properties of the quotient forcing notions \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Q_{tr(I)} = \wp(2^{< \omega})/tr(i)}$$\end{document} and PI = B(2ω)/I in two special cases: when I is the σ-ideal of meager sets or the σ-ideal of null sets on 2ω. We show that the remainder forcing RI = Qtr(I)/PI is σ-closed in these cases. We also study the cardinal invariant of the continuum \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{h}_{\mathbb{Q}}}$$\end{document}, the (...) distributivity number of the quotient \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${Dense(\mathbb{Q})/nwd}$$\end{document}, in order to show that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\wp(\mathbb{Q})/nwd}$$\end{document} collapses \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{c}}$$\end{document} to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathfrak{h}_{\mathbb{Q}}}$$\end{document}, thus answering a question addressed in Balcar et al. (Fundamenta Mathematicae 183:59–80, 2004). (shrink)

The work broadens – to a considerable extent – Z. Pawlak’s original method (1982, 1992) of approximation of sets. The approximation of sets included in a universum U goes on in the contextual approximation space CAS which consists of: 1) a sequence of Pawlak’s approximation spaces (U,Ci), where indexes i from set I are linearly ordered degrees of contexts (I, <), and Ci is the universum partition U, 2) a sequence of binary relations on sets included in U, relations (...) called context relations indexed with degrees of contexts. The introduction of relations of contexts of sets was inspired by the work of W. Ziarnko (1993). Intuitively, set X is the context of set Y to the degree i, when on the basis of knowledge of the elements of set X we can obtain knowledge about the belonging of these elements to set Y to the degree i which is a degree of uncertainty or ambiguity, or inaccuracy. The operations of approximation of sets Ci-, BNi, Ci+, called lower approximation of the degree i, boundary of the degree i, upper approximation of the degree i, are formulated in a way which is analogous with the systems of Pawlak’s approximation, by expanding their formulas accordingly. In the next part of the work, it is shown (in an analogous way to Bryniarski’s work (1989)) that one can define the following operations on contextual rough sets: the union of contextual rough sets, the intersection of contextual rough sets and the complement of contextual rough set. It is proved that the algebra of contextual rough sets is a ditributive lattice with a unit and with a zero. On the basis of the results presented above the problem of defining operations on contextual rough sets by membership relations (Bryniarski 1989) may be formulated analogously to the classical operations on sets. (shrink)

We make a brief review of the Kramers escape rate theory for the probabilistic motion of a particle in a potential well U(x), and under the influence of classical fluctuation forces. The Kramers theory is extended in order to take into account the action of the thermal and zero-point random electromagnetic fields on a charged particle. The result is physically relevant because we get a non-null escape rate over the potential barrier at low temperatures (T → 0). It is (...) found that, even if the mean energy is much smaller than the barrier height, the classical particle can escape from the potential well due to the action of the zero-point fluctuating fields. These stochastic effects can be used to give a classical interpretation to some quantum tunneling phenomena. Relevant experimental data are used to illustrate the theoretical results. (shrink)

A careful examination of the fundamentals of electromagnetic theory shows that due to the underlying mathematical assumptions required for Stokes’ Theorem, global charge conservation cannot be guaranteed in topologically non-trivial spacetimes. However, in order to break the charge conservation mechanism we must also allow the electromagnetic excitation fields \, \ to possess a gauge freedom, just as the electromagnetic scalar and vector potentials \ and \ do. This has implications for the treatment of electromagnetism in spacetimes where black holes both (...) form and then evaporate, as well as extending the possibilities for treating vacuum polarisation. Using this gauge freedom of \, \ we also propose an alternative to the accepted notion that a charge passing through a wormhole necessarily leads to an additional charge on the wormhole’s mouth. (shrink)

This book explains, in lay terms, the surprisingly simple system of mathematical logic used in digital computer circuitry. Anecdotal in its style and often funny, it follows the development of this logic system from its origins in Victorian England to its rediscovery in this century as the foundation of all modern computing machinery. ONES AND ZEROS will be enjoyed by anyone who has a general interest in science and technology.

The gravitational waves from a binary black hole with masses \ can be detected with the Laser Interferometer Space Antenna once their orbital frequency exceeds 10\–10\ Hz. The binary separation at this stage is \R_{\mathrm{g}}\), and the orbital speed is \\). I argue that at this stage, the binary will be producing bright electromagnetic radiation via gas bound to the individual BHs. Both BHs will have their own photospheres in X-ray and possibly also in optical bands. Relativistic (...) Doppler modulations and lensing effects will inevitably imprint periodic variability in the EM light-curve, tracking the phase of the orbital motion, and serving as a template for the GW inspiral waveform. Advanced localization of the source by LISA weeks to months prior to merger will enable a measurement of this EM chirp by wide-field X-ray or optical instruments. A comparison of the phases of the GW and EM chirp signals will help break degeneracies between system parameters, and probe a fractional difference difference \ in the propagation speed of photons and gravitons as low as \. (shrink)

Plastic changes in spinal cord function like neuronal wind-up and increased receptive field are too short-lived to explain chronic pain without structural changes. It is possible that learning could be a mechanism for longlasting changes in nociceptive regulation. A learning process localized to the spinal cord has been shown to be important for the development of tolerance to the analgetic effect of ethanol, suggesting that nociceptive control systems may be changed by learning. Long term potentiation (LTP) is regarded as a (...) useful model of learning and memory. LTP-like changes have been observed in invitro preparations from the spinal cord and in spinal cord field potentials. Recently a long term increase in spinal A-[beta] and C-fibre evoked responses after painful stimulation has been observed. [coderre & katz, dickenson, wiesenfeld-hallin et al.]. (shrink)

This essay offers a set of personal reflections on the relation of creature consciousness to the general philosophical issues of knowledge. morality. and humannature.

This paper describes a method and a practical exercise that offers students a glimpse of everyday enlightenment by using Socrates’ technique of questioning, Plato’s account of the ascent to the form of the good, along with an aspect of Buddha’s Eight Fold Path. The practical exercise prompts students to consider the form of honesty by considering what honesty is for them. The exercise then proceeds to a discussion of how they know they are honest and what rules one must follow (...) to be honest. With this initial account of honesty, the paper then details a set of “proto-philosophical questions” that challenges the student to further articulate their account of honesty, to compare it to dishonesty, and to contextualize it by imagining themselves as the victim of deception or as a deceiver. (shrink)

This paper describes a method and a practical exercise that offers students a glimpse of everyday enlightenment by using Socrates’ technique of questioning, Plato’s account of the ascent to the form of the good, along with an aspect of Buddha’s Eight Fold Path. The practical exercise prompts students to consider the form of honesty by considering what honesty is for them. The exercise then proceeds to a discussion of how they know they are honest and what rules one must follow (...) to be honest. With this initial account of honesty, the paper then details a set of “proto-philosophical questions” that challenges the student to further articulate their account of honesty, to compare it to dishonesty, and to contextualize it by imagining themselves as the victim of deception or as a deceiver. (shrink)

Reproduced with the kind permission of the author. Currently available in the collection I Looked Alive . © 2010 The Brooklyn Rail/Black Square Editions | ISBN 978-1934029-07-7 Originally published 2003 Four Walls Eight Windows. continent. 1.1 (2011): 43-51. Introduction Ben Segal What interests me is instigated language, language dishabituated from its ordinary doings, language startled by itself. I don't know where that sort of interest locates me, or leaves me, but a lot of the books I see in the stores (...) seem to lack language entirely. Gary Lutz (2006). This issue of continent.'s fiction section features a reprint of “This Is Nice of You” from the first edition of Gary Lutz's collection I Looked Alive . That book was originally released by Four Walls Eight Windows in 2003 and has since been reissued in 2010 by The Brooklyn Rail/Black Square Editions. Calamari Press has also reissued Lutz's Stories in the Worst Way (originally published by Knopf, largely forgotten and dismissed, and then re-issued by the too-short-lived 3rd Bed). “This Is Nice of You” was edited for the re-issue of I Looked Alive and, as the original book is out of print, the earlier version of the story has been hard to come by for some time. This initial version is a bit longer than the new version—Lutz is a master of tightening down his texts to their most linguistically intensified cores—but it is in no way sloppy. It is a great privilege for continent. to be able to make available rare texts of (first) aesthetic and (second) scholarly value. For those readers unfamiliar with Gary Lutz, I believe this story will serve as a worthy introduction. Like Raymond Carver, Diane Williams, Christine Schutt, and so many other important twentieth century and contemporary short story writers, Lutz studied with and was edited by Gordon Lish. This connection is apparent in his attention to sound and the sentence as compositional unit, but Lutz's is a unique voice. “This Is Nice of You” bears Lutz's trademark torqued and turning syntax, his sexed-but-nameless characters, his rendering of the human body and its emissions as utterly discomfiting. Lutz's preoccupations with the mundane raise ordinariness, via startling language and observation, to grandiosity and grotesquery. In the fall of 2008, Lutz delivered a lecture entitled “The Sentence is a Lonely Place” to writing students at Columbia University. The lecture was later printed in The Believer (and is linked below). In it, he spoke about the importance of the sentence as a compositional unit, as even the distinguishing formal characteristic of prose. Specifically, Lutz explained that, from Lish, he had developed a "poetics of the sentence." Accordingly, Lutz constructs his stories at the level of the sentence, paying extreme attention to the material of words- their letters and their sounds- and the way they abut one another and interact on this material level even before they are employed in the service of traditional aims of fiction like meaning or story. Lutz often uses a(n almost constraint-related) technique called consecution. Letters or sounds from one word are carried forward into the following, producing drama and movement in the language itself at a level entirely apart from that of plot. For example, you can see how the 't's in the first sentence of “This Is Nice of You” repeat fast and hard through met and then soften into the 'th's of brothers and they. This close attention to the specific material and characteristic conditions of prose means that Gary Lutz's work always involves both a happening in language and of language. “This Is Nice of You” has a richness and depth that is hidden not in symbolism or obscure reference but on the surface of the page, in the language of every sentence. FURTHER READING Lutz, Gary. “ The Sentence Is a Lonely Place. ” The Believer January, 2009. Web. Short stories and excerpts at Web del Sol . Web. Taylor, Justin. “ An Interview with Gary Lutz .” Bookslut. July, 2006. Web. THIS IS NICE OF YOU [156] [1] I was a man dropping already well through my forties, filthy with myself, when, taking a turn at the toilets one afternoon, I met two brothers-they said they were brothers-who swore they had a sister, a schoolteacher, an officer of instruction at the county college, a whirlwind midlife turmoil of everything already put to ruin, who had gone off from a new marriage in an old car, an upkept and ennobling sedan, but had returned now to the apartment and [157] was living there alone with the little runoff there was from the marriage-some outcurved appliances, apparently, and low-posted furniture promoting its own mystery but becoming figurable in certain concentrations of TV light-and, above all, a telephone (on a pedestal, they insisted), the handpiece of which she gripped in lieu of exercise, or in fury, and I thus let out my little, reliable cry that I was in fact a student of the telephone, that it was a debasing apparatus in the main, with its meager economy of bells and tones, and the intimacy of the mouthpiece that sent your breath, tiny aftervapors of it, back toward your lips, so that regardless of the party accepting the outgoing products of your voice, you were, at most, in a further, rivaling exchange with yourself alone, and this is what must have brought the two of them around, the men who proclaimed brotherhood with the woman, because they offered me her phone number, put it at my disposal on a piece of paper one of them had already committed it to, a tearing from a menu, and the looks the men were now giving me had deletions in them, already, of my exact, beanpole shape and size. So off I went to a pay phone, the nearest canopied one I could find. The woman answered after the second ring and said she needed a lift right that very moment into the little, unlevel city close by. She was idling in the doorway of the building when I pulled up in front, and I helped her into the car, then got back in myself. I had always had a way of not having to look at people that nonetheless brought them to me in full, and so I still am certain of the susceptive and impressible comp-[158]lexion, the shimmer on the mouth, a lipstick of low brilliance, a difficulty around the eyes, the hair short and rayed out exclamation ally, skin bagged up over the elbow bone, conflict even in how her arms stayed at her sides—in sum, a spinal loveliness for me, an off-blonde quantity with shadowed, thumbworn hollows that put me out of as much as I might have ever known of women before. I set the two of us into the narrow traffic, and I remember telling her, by way of explaining the little burden which I had shifted, by now, from the shelf of the dashboard and onto my lap, that when you lived in filth, as I then did, a daily newspaper came to count for a lot, although instead of the thick-supplemented local paper I bought a trimmer one from a backlying town—not, of course, for any affluences of native data it carried, but as an article of house ware: a rough immaculacy in four lank sections, a set of fresh, hygienic surfaces to come between the table, say, and whatever I had going for me at the table, if the table was where I was going forward—because what else so cheap comes so clean and far-spreading? The woman told me that her own trouble with paper was that through a modest hole, no larger than a quarter, that had been drilled a foot or so above the floor (the standard height, she had reasoned, of legitimate electrical outlets), and by means of which her faculty office had at last gained communication with the roomier but unoccupied office next door, more and more often shot a single sheet of paper, plain copier paper she had rolled just barely into a tube, [159] so that after landing on the floor of the neighboring office the paper would preserve little if any of the curl, and there would be nothing written or typed on it, of course, and it was always a blank sheet that had been ageing on her desk for some time and had already been moved around, or advanced, from station to station on the desktop, coming into further creaselets and crimps and other infirmities—paper, in short, still too bare and unfraught to be thrown responsibly and forgettably away, and yet too seasoned and beset with irritations of the surface (a molelike blemish, say, or what looked like a tiny hair, an eyelash, sunk into it, or frecklings, or notational pressings of a fingernail), too wrought, in sum, for the paper to be appointed to any secure curricular purpose. Her office, she claimed, was in fact full of such paper, much-handled and singularized sheets of it by the loose, functionless hundred. I had to get it across to the woman that I myself no longer had an office, or any other place to divide me reliably from everybody else, and that for much of the daylight I thus appeared to be among people because I kept putting myself where people came together into even closer-fitting assortments, the viewing areas and showrooms and rotundas and such: I took in the lean-to look of the women, the tongues coming and going in what the men kept thinking of to say—whole families of low knees for me to bark my shins against during the crowded and involving way out. At home afterward, in the one room where my life was packed down, I would keep my nose stuck in the safehold of the phone [160] book, where the names of people suffered reduction to mere episodes of the alphabet and underwent humbling declensions down every column (Lail, Lain, Laine, Lainerd), and he names of streets, of the towns and townships, got docked in crude, heedless abbreviations (the vowels almost always the first to get poked out), and I would run my eyes over the telephone numbers themselves, each sequence of digits another fallible run of the infinite. I thus corrected my feelings for people and assembled myself emotionally into whatever else I had at hand—the obligating arms of the clothes hangers, usually, or the keen-angled understructure, the guardian legginess, of the ironing board. The woman said that in her case, though, it was more a matter of making slow circuits of the classroom where she had to put across the Emporial Sciences, retail theory and methods, to heat-giving and suggestive young women, some of them world cruelties already. There was the cooing of empty stomachs in the hour just before lunch, and the braying and fizzle of loaded stomachs in the low hours of the afternoon. She would recite her notes in a voice barely loyal to anyone octave, a tiny alluvium of slaver hardening at the corners of her mouth on the days she gave the glassy lozenges a slow, warming suck, and she would take lowering notice of how whatever she said succumbed at once to freak spellings and razzing paraphrase in the big, dividered notebooks; and because in midafternoon light the world looked as thorough, as filled in, as it was ever going to get, a better way to set about ruining her eyes was to review how hair had [161] established itself on the arms of the young women, because almost every arm had brought across itself a welcome and diversifying shadow. On one girl it would be a fine, driftless haze afloat above the white of the arm, never seeming to touch down on the skin itself. (An atmosphere, at most, of chestnut brown.) On another, it was as if copper wire, the narrowmost lengthlets of it, had been stuck into the fleshy batter of the thick, freckled forearms. On a third: a field of it–wheat-colored, thin-spun. On a fourth; a differencing, darkish updrift that shaded off as it approached the inner bend of the elbow, then re-emerged at the base of the upper arm as whiskery fringe. On others it was a brassy or rust-colored frizz, or it was as coarse as cornsilk, or it looked fussed on, as if the arm had been slowly stroked with charcoal. But here the woman broke off, or I may well have made an interruption of my own—I think I must have asked whether she was hungry, and she said if I was, and so on one of the lesser streets I parked the car and led her down into a belowstairs eating house I still remembered. Sandwiches were presently lowered in front of us. I watched her remove the festooned toothpick from hers and then play her fingers over the toasted planes before she took a fond first bite. "This is nice of you," she said. I must have looked at her in the way I then had of getting people to speak so they would not seem to be dwelling any longer on my features, because if on the well-set face the mouth and eyes are said to seem frozen in elegant orbit about the til) of the nose, then mine was a face that behold-[162]ers, regarders, could not help trying to round off with greater success, to goad the particulars of it back into the arcs they had wandered away from—the mouth, for instance, having been pursed and pinched suchwise that it seemed resident more on one side of the face than the other—and there were other signs of original strife to be busied with (slapdash eyebrows unbunched, it appeared, from reserves of hair elsewhere on my person; a showing of adult acne, a shrivelly little relevance of it, confined to the declivity of my nose); and so to be polite, the woman thus sank her gaze into her sandwich, and told me, in a voice lowered accordingly, that, one late-childhood summer, she had devoted herself to collecting postage stamps: it was a tongue-involving sideline to early-arriving puberty, and she liked having to lick the pale, gummed hinges instead of the sticky backs of the stamps themselves before entering everything into the hosting album; and once, during some foul weather between her and a brother (the older, thrown-over one, who had already made a habit of fooling the underside of his arm across the top of hers and calling her "pussified"), she reached for the shoe box in which she had let duplicate stamps accumulate—Spanish ones, mostly, of a fading orange—and sent the box slooshing through the lower air so that the stamps showered onto the brother's bare legs with a full, delicate harm. The woman was now touching up the surface of her iced tea with tiny activities, initiatives, of the longspun spoon. I myself was good at getting my touch onto things, although in a way that seemed to mix up the motive atoms inside [163] them, but I was satisfied that for the moment my sandwich, the unbitten-at half of it, was displayable and fit and local to my plate. The woman went on to say that, as a child, she had been bundled off, many an afternoon, to the slope-ceilinged quarters of a bachelor uncle who, when speaking of anybody not immediately present, could not bring himself to use the person's name but instead would say "an acquaintance of mine in ..." and then mention the name of some lapsed homeland, or little-loved rural orchestra, or backset building about to come down; and it was never a riddle, this device of his (not once could the girl have been expected to identify any of the subjects), and no matter how often and aloud he insisted that particularizing persons any further—bringing even a first name down upon anyone of them—would have been indecent, he claimed, much like doing things to people while they slept, the girl accepted all of the uncle's prim and extravagant evasion for what he surely must have intended it to be: a neat, protective trick to space the world out a little further in her favor, to scatter the population so that wherever her hand might at last come down, it would have to be on herself alone. And here I could sense that the woman wanted from my mouth an account of as much as I myself might have ever managed of attachment, so I told her I had once owned a house (a rising, really, of much-fingered, handwrought architecture that amounted to a little family of rooms above garages: a boxlike building with a rattly thorax of downspouts [164] and drainpipes and an unfolded but full-toned fire escape), and I had had for a time a boarder, a student, a high-colored, loose-packed representative of declining girlhood, hung with necklaces and barrettes, a girl of precise but shifting leanings and inclinations; and the afternoon she had come round to ask after the room, I stood in the entranceway, handshaken and asweat, and from what would later be my memory of the girl, I made off with, first, how every pore of her nose seemed to be sheltering within itself a tiny dark seedlet, a grain of something immediately, enormously valuable. And an almost lipless mouth (just a slit, practically), the teeth inside looking wet, watered-it was my life's chore, at that instant, to keep from sending the back of my thumb blotterlike across the line of them (I was later to learn she drank everything cold and through the narrowest of straws). And her hair: it was tea-colored hair she had, long and reachful, an unstopped downcome of it. Tall for a girl, but she managed to stay out of much of her height and put herself across as somebody backward, or behind. I must have told the girl, as best I could, that I of course had a wife, a full-faced, imperishable partner, though for the moment she was gone otherwhere in the marriage, and here the woman, my present companion, my tablemate, whose feet were now parked, in parallel, on the grade of my upper leg, interrupted to say that her husband, too, had been such a liar, and what could I bring up by way of reply other than that a lie is a truth struck through with other, further truth, or that a lie is the present multiplied by the past or that a lie [165] is an outcry of borrowed hope? The woman gave me an allowed look of disgust, her eyes lowered but still popular with me, and on I went with what had now become the girl of my story. For there had been a great, gainful carpet in the room I put the girl into, a matty expanse of coarse, grabby piles, an engrossing affair that took things into itself and held them tight, misered them, and I of course insisted that the girl not bother herself with its upkeep, that I enjoyed weekly access to a prestigious, upstanding vacuum cleaner; but no sooner was the girl out of the house each morning than I would withdraw from my room, where time was unportionable, and loose myself into the ticktock impertinence of the girl's room and get down on my knees, and, going after the carpet first with my fingers, then with a forceps, and finally by unspooling lengths of clear package-sealing tape and pressing them against the tufts in neat rectangles to catch what I might have missed, I brought vast tracts of the carpet to depletion, recovering not simply the girlinesses, the girleries, one would expect (buttons, straight pins, downed jewelry), but flirtier personalia in the form, say, of a stray confetto brought into the world when a page had been wrung with out caution from a spiral-bound notebook, or some pleated paper shells of the chocolates she required, or one of the bargain antihistamines she took to get her naps going, or a trash-bag tie ragged enough to show the kinked line of the wire within (this I would get wound around my finger), or a cough drop enwrapped like a bonbon (I would undo the [166] wings of the wrapper and have to decide whether to suck the drop all down or begin chewing it midway)—I became the following, the public, that these things, these off-faIlings, had come to have; but mostly there was hair, afloat above the uppermost pushings of the fabric of the carpet an almost continuous haziness of loose hairs of all lengths and sources, and I would have to set them out on a fresh sheet of paper and assort them according to the regions of the body they had taken their departure from, and in no time I had nest-like filiations of broken filaments and smaller involvements of the hairs that made me think of hooks, of barbs, of treble clefs, and each pile required a separate envelope, to be filed in a separate shoe box for every sector of the body until, I hoped, the boxes themselves would no longer be enough and I would have raised something semblable, brought up something equal in volume to the comprehensive girl herself. And her wastebasket! For every bit of rubbish, every dreariment she tossed into the thing, I would, in secret, deposit a reciprocal discard of my own, matching a spotted, confessory tissue of hers with a lurid throwaway after my own heart–the cardboard substructions of a fresh parcel of underwear, maybe, or tearings from pantyhose I now and again pressed against a span of my forearm to work onto it the complications of female shading I otherwise made do, choosily, without. I thus built the two of us up together in her trash! One afternoon-it was another of those lifeful, unsam-[167]pled days on which the world humors us each a little differently to keep us nicely on our last legs—I discovered in the wastebasket an inch-deep textbook of hers, a paperback with a celery-colored cover that had come partly unglued, and this dilapidation I paired off, naturally, with a name-your baby guide to whose pages, during my recurrent turnings of them, in bed or at table, I had contributed dried produces of my person, a chemical splendor entirely mine. This coupling sent a sudden spigoty thrill from me that forced an unbuckling and an unzipping and a cleanup with a handkerchief I then ventured responsively into the wastebasket as well. It was in the bathroom afterward that I found a suds-clouded puddle on the unlevel floor of the tub, a little undrained remainder, rimmed with offscum, of the girl's prolonged early-morning soak, and this was as much as I needed to get on my hands; I pressed them flat against the wet porcelain, then flapped them around in the air, and that was when I noticed it—in the amphitheater of the toilet bowl, an orange-yellow tint, or value, to the waters. When the girl arrived home that evening, I told her, of course, that I had discovered fresh, unforeseen trouble within the tank of thelet (a misalignment of the trip lever, a waywardness of the float ball, a ulation of the lift wires, kinks and defects, really, throughout the entire system) and that in fine it was an apparatus now operable only by means of advanced and strenuous equilibrial manipulations that it would be unseemly, inhospitable, of me to pre-[168]sume to burd to burden her with–so that from here on out, following any leak or evacuation she need merely lower the lid and then, before quitting the room, ring the handbell that had been placed on the would seeeverythinghing else. But the bell never rang, not even once, and from my window the next morning I watched the girl carry from the house a little plastic bag distended balloonishly, much like those bags you will remember having seen in the hands of children bearing homeward their solitary carnival-prize goldfish. In fact, I never ran across the likes of the girl again. The man who came to collect her things-not the father, apparently, but an advocate, an upholder-l found to be dull-eared and lax in his speech, and the better part of his face seemed to have already begun making tiny, rotational departures from whatever it was that the eyes, themselves impressively mobile, were just that moment having to take in. (Was there a lamp in the house that was not that night slopping its wattage over everything?) I guess I was waiting for the man to take a laggard, last-minute interest in me, and by now I was pushing everything out into the paired first person–it was, I said, “Our night shot,” and I began including the two of us in whatever it might be doing out, the expected sprinkles and such—but he was no friendship buff, and he paid no heed to my telling him that the only dress of hers I'd ever twidged myself into even part of the way had been the simplest of them all, a large-buttoned wonder of depthless blue, and then only on the principle that one naturally fits whatever one has into whatever somebody else [169] had first, or how else would the world keep getting any taller with people? The man just went about the removal of the girl's things without having to be reminded too noticeably, I guess, of how every dick hangs by a thread. My listener, though, had by this time brought about some becoming slowings of her arm—it was an arm inclinable to langorous diagonals and magicianly swoops through the air above the tabletop—but it no longer was involving itself with her plate, so I suggested we shove off, I made payment for the food, and on our way to the car, and then in the car as I took to following her pointings, the directional tilts of her head, she said that you naturally kept putting more and more of yourself into another person, at first wondering how much she can take, how much of you is accumulable and how much she can hold, and you're letting things out, disbursing yourself, and you've soon got things set up in her, and room is being made for even more of you, and if you bring this off with enough people, even two or three, what you've got is at first a comfort, because you can pass yourself along and move a little more widely through the world and leave it to these others to man your grievances, your disappointments; and what brought this to mind, the woman said, was a term of financial hardship she had contrived for herself a few years back, an unpaid leave of absence from scrupling letter grades onto quiz papers (propped-up As, and upended Bs made to look, rather, like fannies; all As and Bs, no Cs or anything lower, the difference between an A and a B having less to do with the accuracy of whatever facts might [170] have been impounded in provided for an answer than with anything recallable about the way the enrollee ad conformed her body to the confining perpendiculars of her chair and the navel-level writing surface that projected from it, or the way there might one day have been an unignorable blush on the instep of a once-moseying foot, disburdened of its shoe, that had got itself trapped in the grillwork of that cagelike involvement, intended for books, that was welded to, or otherwise schemed into, the underworks of the chair)—this had been a duration, in short, of controlled difficulty when the misexpenditure of even a twenty-dollar bill had set her thrilling, gloating, over everything she would miss out on, and one afternoon she had made an engagement for a haircut, just a trim, and very early in the session the haircutter, a woman ill-defined in the face but otherwise full of conspicuities of emotion, set down the prevailing scissors and pressed the flat of a lukewarm hand against the woman's cheek, held it there for a good minute or longer, while the other hand eventually found its way into a drawer, a shallow treasury of slender specialty scissors, one pair of which the cutter withdrew and began routing deductively through the woman's hair, the other hand staying put on the cheek, longer and longer, and the woman went home and for afterward the bathtub was now a more likely destination than any of the upright furniture, and it got easier to fill the tub with further clarifying volumes than to clear space on the difficult heights of the sofa, and she was hardly claiming to have become a cleaner [171] person in result—she in fact would often discover, voyaging about her body, a browned, fractionary detail of a larger crepe of toilet tissue that must have got itself stuck in some assy crevice and was impossible to get plucked out of the revolving suds—she was saying only that she spent more and more of her time thus immersed, ill off in water, and the haircutter had surely had a hand in it, the woman was doing some of the cutter's life now, coming into some of its wrong, because you sometimes have to look to somebody else's life to get dimensions set back even part of the way around your own, and it should not have to be any less your own life when it comes from somebody else, and you could surely fudge a society out of anyone available person and get this person doubling for the many, so that in the little run of things perpetuable from one person to the next, every loose moment stood to become a complete, active finality. But by now this was a new day, with only an hour or so off it already, and the place the woman had made me bring us to, the man's place, with a promise that the man was elsewhere—this was on a little offshoot of a street, a stewy efficiency apartment the color had long ago gone out of; and when, once in bed, still clothed, I found among the sheets and blankets a spoiling pair of the man's underpants, one of the leg openings of which was puckered into an avid, sloppy mouth, I held myself accountable for redisposing the fabric until I got a befitting featurelessness back onto it; but all the while, I am sure I had to make myself go over again in my mind that if the body is the porter of as many organs of affec-[172]tion as there might one day turn out to be, then the idea was to let the thing carry you to where you would otherwise never have any reason to arrive, because I listened for the unmelodiof the the thede ofthe woman's zipper, and then the woman made me put myself out of my own clothes, the attritional corduroys and overshirt, and got herself up at last onto the topic not of the man whose apartment it was (because his story was scarcely the story of how the boy who decides he is half a girl no sooner starts to worry about where the other half might than he gets careless with where he rests his eyes, or what he gives even the feeblest of fingerholds to, and anything, even a crumbly triangle of pie offered on a saucer instead of on a pie plate proper, comes in easy, ready, wronging answer), but of her husband, and how, no more than a couple of months into the marriage, he had begun snugging away in his undershorts a little source of chanc, reliable frictions to nudge him onward through the workday—anything company-keeping that could be counted on not to slide out of the elasticky leg holes: a half-dollar packet of chocolate tittles, maybe, that was barely noticeable in the baggy surround of the widecut trousers so popular at the time. For by now the woman had at last brought what is usually called the other mouth to within only inches of my lips, but it is not a mouth, obviously, although I let myself go along with the goodwill behind the comparison, the way I will remain loyal to anything deliberately and faithfully misunderstood, and I fussed my tongue against the vital trifles hung inside of her, as much of the curtailed finery as I could find, [173] and gave the whole insimplicity of it a slow-circling, examinational lick, until I was taking a sudden tepid downwash on the tongue. It was a familiar, latrine in dribble that must have tasted, no doubt, like trouble just starting out.p [1] Editor's Note: Original pagination from first edition print denoted with bracketed page numbers. (shrink)