Leibniz’s main thesis regarding the nature of space is that space is relational. This means that space is not an independent object or existent in itself, but rather a set of relations between objects existing at the same time. The reality of space, therefore, is derived from objects and their relations. For Leibniz and his successors, this view of space was intimately connected with the understanding of the composite nature of material objects. The nature of (...) the relation between space and matter was crucial to the conceptualization of both space and matter. In this paper, I discuss Leibniz’s account of relational space and examine its novel elaborations by two of his successors, namely, the young Immanuel Kant and the Croat natural philosopher Roger Boscovich. Kant’s and Boscovich’s studies of Leibniz’s account lead them to original versions of the relational view of space. Thus, Leibniz’s relational space proved to be a philosophically fruitful notion, as it yielded bold and intriguing attempts to decipher the nature of space and was a key part in innovative scientific ideas. (shrink)

Recently we have studied quantum mechanics of bounded operators with a discrete spectrum. In particular, we derived an expression for the commutator[Q, P] of two bounded operators whose spectrum is discrete, and we showed that in the limit of a continuous spectrum the commutator becomes the standard one of Heisenberg. In this paper we show that the angular momentum operator and the phase operator satisfy the new commutation relation. We also briefly discuss the problem of the canonical phase (...) operator conjugate to the number operator. (shrink)

A new approach to quantum theory is proposed in this paper. The basis is taken to be theoretical variables, variables that may be accessible or inaccessible, i.e., it may be possible or impossible for an observer to assign arbitrarily sharp numerical values to them. In an epistemic process, the accessible variables are just ideal observations connected to an observer or to some communicating observers. Group actions are defined on these variables, and group representation theory is the basis for developing the (...) Hilbert space formalism here. Operators corresponding to accessible theoretical variables are derived, and in the discrete case, it is proved that the possible physical values are the eigenvalues of these operators. The focus of the paper is some mathematical theorems paving the ground for the proposed foundation of quantum theory. It is shown here that the groups and transformations needed in this approach can be constructed explicitly in the case where the accessible variables are finite-dimensional. This simplifies the theory considerably: To reproduce the Hilbert space formulation, it is enough to assume the existence of two complementary variables. The interpretation inferred from the proposed foundation here may be called a general epistemic interpretation of quantum theory. A special case of this interpretation is QBism; it also has a relationship to several other interpretations. (shrink)

If no property of a system of many particles discriminates among the particles, they are said to be indistinguishable. This indistinguishability is equivalent to the requirement that the many-particle distribution function and all of the dynamic functions for the system be symmetric. The indistinguishability defined in terms of the discrete symmetry of many-particle functions cannot change in the continuous classical statistical limit in which the number density n and the reciprocal temperature β become small. Thus, microscopic particles like electrons (...) must remain indistinguishable in the classical statistical limit although their behavior can be calculated as if they move following the classical laws of motion. In the classical mechanical limit in which quantum cells of volume (2πħ)3 are reduced to points in the phase space, the partition functionTr{exp(−βĤ) for N identical bosons (fermions) approaches (2πħ)−3N(N!) ∫ ... ∫ d3r1 d3p1 ... d3rN d3pN exp(−βH). The two factors, (2πħ)−3N and (N!)−1, which are often added in anad hoc manner in many books on statistical mechanics, are thus derived from the first principles. The criterion of the classical statistical approximation is that the thermal de Broglie wavelength be much shorter than the interparticle distance irrespective of any translation-invariant interparticle interaction. A new derivation of the Maxwell velocity distribution from Boltzmann's principle is given with the assumption of indistinguishable classical particles. (shrink)

Given Lewis’s views about recombination and spatial relations, there are possible worlds in which space is discrete and yet the Pythagorean theorem is true – contrary to the so-called Weyl-Tile argument that concluded that the Pythagorean theorem must fail if space is discrete.

In Chapter 1 I discuss the basic problem which made me undertake the issue of human death. That problem was the dualism in the depiction of human nature which has not been fully overcome yet, the dualism which leads to the emergence of new difficulties in contemporary attempts at adequately solving the problem of human death. They include the separation of soul from the body in the moment of death, and the borderline between the moment of death and the moment (...) of resurrection. Chapter 2 is devoted to the presentation of a new anthropological perspective, of an anthropology build “from the bottom up”, that is “from foundations”, and taking into account man’s rooting in the biological environment, and thus also in the genetic heritage taken over from our pre-human ancestors. That anthropology brings new aspects into traditional anthropology by extending it to include new ways of explaining the genesis of the human body and spirit, and new depictions of man’s death. In Chapter 2 I will also present the concept of evolution proposed by P.T. de Chardin, which I appreciate for its comprehensive evolutionary perception of the world. This concept has provoked various responses, but it certainly provides a creative inspiration for further attempts at applying the idea of evolution to various issues. The general framework of the evolutionary model proposed by the French researcher turns out to be useful also when applied to the evolutionary understanding of human death. Chapter 3 contains a discussion of the principal premises of the evolutionary concept of human death taken from analyses carried out by T. Wojciechowski concerning the issue of time, space, and the structure of variable material beings. A being is variable because it has a temporal structure, and the changes that occur are the derivatives of that structure. The temporal structure may be seen as endless, in which a being, even though its existence had a beginning, will exist for ever. Material substance should not be seen statically, but in dynamic and evolutionary terms. In evolution, time becomes a driver of development, an element shaping and directing the evolution of the entire cosmos. Man’s substance has been made capable of two levels of being and acting: the spatial and temporal level, and the endless and immanent level. Together, they form the one essence of man. Thus, the human person is partially immersed in the material cosmos, and partially elevated above it. Chapter 4 presents the evolutionary approach to the moment of man’s death. The views of T. Wojciechowski will be presented in which the moment of death is seen as a moment of transformation and perfection of the structure of the essence of human existence. Furthermore, the issue of the relationship existing, according to T. Wojciechowski, between man’s death and resurrection will be discussed. Understood in evolutionary terms, the moment of death is the time when the structure of human existence is transformed. Death transfers man fully into eternity and enables his life on a higher level of existential being. The element of flesh is retained, but changes its nature. Such view of death allows it to be understood as the moment of resurrection and the culmination of the evolutionary process of life. Death is therefore an “invention” of the evolution and should be seen as a natural and positive phenomenon. At this point, I also propose a solution to the question about reconciliation between temporal and endless existence. In Chapter 5 I take up the issue of consequences flowing from the postulated understanding of human death. They have been pointed to by T. Wojciechowski, but need to be further developed and clarified. He believed two lines in man’s development need to be recognized: that of natural and that of supernatural evolution. Both have the same direction, while occurring on different planes. In each of these lines, death is a natural element of life, pre-planned and, so to say, “encoded” in the cosmic matter. Therefore, the treatment of biological death as the consequence of sin is not only contrary to the evolutionary understanding of life, but in addition artificially combines that which is natural with that which is supernatural. Man’s authentic experience of his own present is a condition of his achieving full existential perfection in the moment of this death. Full engagement in the present is, in a way, a harbinger of the future; thus, the life “here” and “there” may not be inherently inconsistent. In the light of the evolutionary concept, death is not a punishment, but the most positive experience of man’s life in that it enables him to achieve full existential perfection. Chapter 6 is devoted to a substantiation of the possibility of evolutionary transformation of the structure of human existence in the moment of death. An adequate cause needs to be identified which could substantiate that transformation and achievement of perfection. I believe an appropriate substantiation can be found in God’s creative act, interpreted in evolutionary terms. The process of evolution, with its subsequent stages, is only a necessary condition for that “transformation” and “elevation”. The sufficient condition is fulfilled by the continuous creative intervention of God. The concept of God’s creative activity in the moment of man’s death finds its continuation in Chapter 7, where I present a detailed analysis of God’s activity at the time of man’s death. The concept of God’s creative activity extended over the entire process of evolution makes it possible to consider the moment of death as the moment of man’s resurrection. The moment of death is thus a moment of creation in evolutionary terms. Thus, as long as man is related to temporal and spatial elements, his development, or creation, continues. Death is only the completion of the final stage of creation, which may be painful and evoke fear, but in fact should give hope, for it involves resurrection. I also propose that the creative act in the moment of man’s death-resurrection be considered a basic action of God, which explains the manner in which God’s activity is contained within the framework of the creative act, encompassing also the moment of death-resurrection. The final Chapter 8 describes a didactic model illustrating the concept proposed here. I use the analogy of white light dispersion effect in the prism, and compare the incident ray to the creative act, and the dispersed rays going through the prism to the line of man’s natural and supernatural evolution. This model also shows the difference in the perspectives from which the phenomenon of death is seen by God and by man. (shrink)

This essay ties together some main strands of the author’s research spanning the last quarter-century. Because of its broad scope and space limitations, he prescinds from detailed arguments and instead intuitively motivates the general points which are supported more fully in other publications to which he provides references. After an initial delineation of several distinct notions of meaning, the author considers such a notion deriving from the evolutionary biology of communication that he terms ‘organic meaning’, and places it in (...) the context of evolutionary game theory. That provides a framework for a special type of organic meaning found in the phenomenon of expression, of which the author here offers an updated characterization while highlighting its wide philosophical interest. Expression in turn generalizes to a paradigmatic form of human communication—conversation—and section 4 provides a taxonomy of conversation-types while arguing that attention to such types helps to sharpen predictions of what speakers say rather than conversationally implicate. We close with a view of fictional discourse on which authors of fictional works are engaged in conversation with their readers, and can provide them with knowledge in spite of the fictional character of their conversation. Such knowledge includes knowledge of how an emotion feels and is thus a route to empathy. (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’. 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.

The Casimir force between two neutral metallic plates is often considered conclusive evidence for the reality of electromagnetic zero-point fluctuations in ‘empty space’. 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.

From a more physicalistic point of view the paper gives a brief overview of Boscovich’s thought about the bilayer of space and time, real space and time, and mathematical space and time, without going into philosophical analysis in detail. The paper provides examples of possible correspondence between Boscovich’s thought and physicalist concepts in modern physics.

This article states that the concept of time we generally hold is a spatial version of time.However, a spatial time concept creates a series of problems,with unfortunate consequences for education.The problems become particularly obvious when the spatial time concept is used as a basis for the education function that is connected to the individuality of the pupils. In order to examine this problem more closely, the article turns to literature in order to get a new and different insight into education. (...) In part four of the novel Ada or Ardor: A family chronicle (1969) the Russian-American author Vladimir Nabokov claims, by way of the protagonistVanVeen, that a spatial notion of time will lead to a determinate and reduced view of the future. Not only does one in this way sweep the very notion of time under the carpet, but one will moreover hinder the possibility of appearing as a unique and individualised person.Van is preoccupied with a pedagogic question: viz., the question of how one can become individualised through time.This is also the reason he attempts to re-create a time concept that can give him the status of a free and independent individual. With a background in Van’s analysis of time, the article attempts to derive two forms for education. First, formal education, which bases itself on a spatial time concept. Secondly, non-formal education, which bases itself on a time concept that has freed itself in the greatest possible manner from space. Neither of these two solutions is appropriate in regard to education’s individualising function. Therefore, the article draws on Nabokov’s best-known novel, Lolita (1955), so as to broadenVan’s understanding of time. In the end, then, the article articulates a time concept that introduces a notion of education where time occurs through acts of responsibility. Not until education has such a time concept as a basis, can one, so the article argues, attain the education function that has as its goal to individualise and make responsible children and young people. (shrink)

It is shown that the jet mechanism derivable from the Lorentz deformation picture leads to a nearly constant average jet transverse momentum. It is pointed out that this is consistent with the high-energy experimental data. It is pointed out further that this result strengthens the physical basis for the minimal time-energy uncertainty combined covariantly with Heisenberg's space-momentum uncertainty relation.

The Lorentz transformation relates the Einstein-defined measures, associated with two inertial frames, of the space and time coordinates of a body or event. From such information relative velocities and accelerations may be deduced, and their appropriate transformations derived. All other transformations of special relativity are derived from the Lorentz transformation and hence depend on the coordinate measures related by the transformation. In particular, the transformation of forces depends on that for accelerations; hence it may not be appropriately applicable to (...) equilibrium phenomena involving null-acceleration. It is suggested that this is the root of the apparent paradox which arises when the conventional force transformation is applied to the consideration of a right-angled lever in equilibrium in its proper inertial frame. It is shown that this paradox is resolved by the employment of a nonconventional but appropriate special relativistic transformation for forces not associated with corresponding accelerations. (shrink)

Some sufficient conditions on a Symmetric Monoidal Closed category K are obtained such that a diagram in a free SMC category generated by the set A of atoms commutes if and only if all its interpretations in K are commutative. In particular, the category of vector spaces on any field satisfies these conditions . Instead of diagrams, pairs of derivations in Intuitionistic Multiplicative Linear logic can be considered . Two derivations of the same sequent are equivalent if and only if (...) all their interpretations in K are equal. In fact, the assignment of values to atoms is defined constructively for each pair of derivations. Taking into account a mistake in R. Voreadou's proof of the “abstract coherence theorem” found by the author, it was necessary to modify her description of the class of non-commutative diagrams in SMC categories; our proof of S. Mac Lane conjecture also proves the correctness of the modified description. (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 emergence of macroscopic variables can be effected through coarse graining. Despite practical and fundamental benefits conveyed by this partitioning of state space, the apparently subjective nature of the selection of coarse grains has been considered problematic. We provide objective selection methods, deriving from the existence of relatively slow dynamical time scales. Using a framework for nonequilibrium statistical mechanics developed by us, we show the emergence of both spatial variables and order parameters. Although significant objective criteria are introduced in (...) the coarse graining, we do not provide a unique prescription. Most significantly, the grains, and by implication entropy, are only defined modulo a characteristic time scale of observation. (shrink)

The old scholastic principle of the "convertibility" of being and goodness strikes nearly all moderns as either barely comprehensible or plain false. "Convertible" is a term of art meaning "interchangeable" in respect of predication, where the predicates can be exchanged salva veritate albeit not salva sensu: their referents are, as the maxim goes, really the same albeit conceptually different. The principle seems, at first blush, absurd. Did the scholastics literally mean that every being is good? Is that supposed to include (...) a cancer, a malaria parasite, an earthquake that kills millions? If every being is good, then no being is bad—but how can that be? To the contemporary philosophical mind, such bafflement is understandable. It derives from the systematic dismantling of the great scholastic edifice that took place over half a millennium. With the loss of the basic concepts out of which that edifice was built, the space created by those concepts faded out of existence as well. The convertibility principle, like virtually all the other scholastic principles (not all, since some do survive and thrive in analytic philosophy), could not persist in a post-scholastic space wholly alien to it. (shrink)

The well known Bell experiment with two actors Alice and Bob is considered. First the simple deduction leading to the CHSH inequality under local realism is reviewed, and some arguments from the literature are recapitulated. Then I take up certain background themes before I enter a discussion of Alice’s analysis of the situation. An important point is that her mind is limited by the fact that her Hilbert space in this context is two-dimensional. General statements about a mind’s limitation (...) during a decision process are derived from recent results on the reconstruction of quantum theory from conceptual variables. These results apply to any decision situation. Let all the data from the Bell experiment be handed over to a new actor Charlie, who performs a data analysis. But his mind is also limited: He has a four-dimensional Hilbert space in the context determined by the experiment. I show that this implies that neither Alice nor Charlie can have the argument leading to the CHSH inequality as a background for making decisions related to the experiment. Charlie may be any data analyst, and he may communicate with any person. It is argued that no rational person can be convinced by the CHSH argument when making empirical decisions on the Bell situation. (shrink)

This study describes the results of experiments motivated by an attempt to understand spectral processing in the cerebral cortex (DeValois and DeValois, 1988; Pribram, 1971, 1991). This level of inquiry concerns processing within a restricted cortical area rather than that by which spatially separate circuits become synchronized during certain behavioral and experiential processes. We recorded neural responses for 55 locations in the somatosensory (barrel) cortex of the rat to various combinations of spatial frequency (texture) and temporal frequency stimulation of their (...) vibrissae. The recordings obtained from single and multi-unit bursts of spikes were mapped as surface distributions of local dendritic potentials. The distributions showed a variety of patterns that are asymmetric with respect to the spatial and temporal parameters of stimulation, and were, therefore, not simply reflecting whisker flick rate. Next, a simulation of our results showed that these surface distributions of local dendritic potentials can be described by Gabor-like functions much as in the visual system. The results provide support for a model of distributed cortical processing that imposes a physiologically derived frame (the limited extent of a dendritic patch) and an anatomically derived (axonal) sampling of the distributed process. This combination provides a complex Gabor wavelet that encodes phase, which is necessary to processing such details as edges and texture in a scene. The synchronization across cortical areas that make the Gabor wavelet processes within restricted cortical areas available to one another (the binding problem) proceed at a ''higher order'' level of integration. Both levels of distributed processing accomplish computation in the conjoint spacetime and spectral domain. (shrink)

In this work we study the relativistic mechanics of continuous media on a fundamental level using a manifestly covariant proper time procedure. We formulate equations of motion and continuity (and constitutive equations) that are the starting point for any calculations regarding continuous media. In the force free limit, the standard relativistic equations are regained, so that these equations can be regarded as a generalization of the standard procedure. In the case of an inviscid fluid we derive an analogue of the (...) Bernoulli equation. For irrotational flow we prove that the velocity field can be derived from a potential. If in addition, the fluid is incompressible, the potential must obey the d'Alembert equation, and thus the problem is reduced to solving the d'Alembert equation with specific boundary conditions (in both space and time). The solutions indicate the existence of light velocity sound waves in an incompressible fluid (a result known in previous literature (19) ). Relaxing the constraints and allowing the fluid to become linearly compressible one can derive a wave equation, from which the sound velocity can again be computed. For a stationary background flow, it has been demonstrated that the sound velocity attains its correct values for the incompressible and nonrelativistic limits. Finally viscosity is introduced, bulk and shear viscosity constants are defined, and we formulate equations for the motion of a viscous fluid. (shrink)

Propositional attitude verbs, such as think and want, have long held interest for both theoretical linguists and language acquisitionists because their syntactic, semantic, and pragmatic properties display complex interactions that have proven difficult to fully capture from either perspective. This paper explores the granularity with which these verbs’ semantic and pragmatic properties are recoverable from their syntactic distributions, using three behavioral experiments aimed at explicitly quantifying the relationship between these two sets of properties. Experiment 1 gathers a measure of 30 (...) propositional attitude verbs’ syntactic distributions using an acceptability judgment task. Experiments 2a and 2b gather measures of semantic similarity between those same verbs using a generalized semantic discrimination task and an ordinal scale task, respectively. Two kinds of analyses are conducted on the data from these experiments. The first compares both the acceptability judgments and the semantic similarity judgments to previous classifications derived from the syntax and semantics literature. The second kind compares the acceptability judgments to the semantic similarity judgments directly. Through these comparisons, we show that there is quite fine-grained information about propositional attitude verbs’ semantics carried in their syntactic distributions—whether one considers the sorts of discrete qualitative classifications that linguists traditionally work with or the sorts of continuous quantitative classifications that can be derived experimentally. (shrink)

A possible way out of the conundrum of quantum gravity is the proposal that general relativity (GR) emerges from an underlying microscopic description. Despite recent interest in the emergent gravity program within the physics as well as the philosophy community, an assessment of the general motivation for this idea is lacking at the moment. We intend to fill this gap in the literature by discussing the main arguments in favour of the hypothesis that the metric field and its dynamics are (...) emergent. First, we distinguish between microstructure inspired from GR, such as through quantization or discretization, and microstructure that is not directly motivated from GR, such as strings, quantum bits or condensed matter fields. The emergent gravity approach can then be defined as the view that the metric field and its dynamics are derivable from the latter type of microstructure. Subsequently, we assess in how far the following properties of (semi-classical) GR are suggestive of underlying microstructure: (1) the metric's universal coupling to matter fields, (2) perturbative non-renormalizability, (3) black hole thermodynamics, and (4) the holographic principle. In the conclusion we formalize the general structure of the plausibility arguments put forward. (shrink)

A diagram that places two planets in orbit around the sun was inserted into the textual space of a Timaeus manuscript of the late 11th century as well as three more in the 12th century. The diagram derives from a Carolingian tradition of study of Martianus Capella’s astronomy and shows his continued authority into the twelfth century. By way of Capella and through similarly-inspired commentaries on Macrobius’ Commentary on the Dream of Scipio, the idea of circumsolar motion for Mercury (...) and Venus became a well-known and authoritative theme for William of Conches and other scholars in the eleventh and twelfth centuries wo interpreted Plato in terms of current scientific knowledge. (shrink)

The language of entropy is examined for consistency with its mathematics and physics, and for its efficacy as a guide to what entropy means. Do common descriptors such as disorder, missing information, and multiplicity help or hinder understanding? Can the language of entropy be helpful in cases where entropy is not well defined? We argue in favor of the descriptor spreading, which entails space, time, and energy in a fundamental way. This includes spreading of energy spatially during processes and (...) temporal spreading over accessible microstates states in thermodynamic equilibrium. Various examples illustrate the value of the spreading metaphor. To provide further support for this metaphor’s utility, it is shown how a set of reasonable spreading properties can be used to derive the entropy function. A main conclusion is that it is appropriate to view entropy’s symbol S as shorthand for spreading. (shrink)

My aim in this paper is to suggest a new outlook concerning the nature of Zeno’s paradoxes. The attention is directed towards the three famous paradoxes known as “Dichotomy,” “Achilles and the Tortoise,” and “The Arrow.” An analysis of the paradigmatic proposals for a solution shows that an adequate solution has not yet been reached. An answer is provided instead to the question “How Zeno’s paradoxes emerge in their quality of aporiae?,” that is to say in their quality of impasses, (...) of problem situations without an exit, what is the original meaning of the Greek word “aporia.” It is my claim that this is the correct rational approach for solving these conceptual puzzles. In other words, I am not proposing formal solutions by criticizing and/or altering their premises assuming the continuous or discrete nature of space and time, but I try to draw the philosophical attention to the way we possess the phenomenon of motion as a result of the perception of space-time in human experience. (shrink)

Summarya) Bell tries to formulate more explicitly a notion of “local causality”: correlations between physical events in different space‐time regions should be explicable in terms of physical events in the overlap of the backward light cones. It is shown that ordinary relativistic quantum field theory is not locally causal in this sense, and cannot be embedded in a locally causal theory.b) Clauser, Home and Shimony criticize several steps in Bell's argument that any theory of local “beables” is incompatible with (...) quantum mechanics. It is contended that the Clauser‐Horne derivation of a Bell‐type inequality circumvents his weak steps. The Clauser‐Horne derivation must assume that there are no undetected correlations between choices of controllable variables in two space‐like separated regions. Methodological considerations support this assumption.c) In response to criticism by Shimony, Home, and Clauser, Bell tries to clarify the argument of “The theory of local beables”, and to defend as permissible the hypothesis of free variables.d) Bell's reply to an earlier criticism by Shimony, Clauser, and Home is answered. The convergence of Bell's position towards theirs is noted. (shrink)

This case describes an adolescent in a crisis of a chronic medical condition whose situation is complicated by substance abuse and mental illness. D. Micah Hester provides an analytic approach, teasing apart the multiple layers of medical, developmental, and moral issues at hand and describing possible responses and outcomes. Amy T. Campbell examines existing legal guidelines for adolescent decision making, arguing that greater space exists for clinical discretion in these matters than commonly thought. Cheryl D. Lew discusses the development (...) of agency in adolescent patients, the ideal of autonomous decision making in the context of impairment and chronic illness, and the obligation of healthcare teams to examine an adolescent patient’s decisions in relation to her identity. (shrink)

Various aspects of semantic features drive early vocabulary development, but less is known about how the global and local structure of the overall semantic feature space influences language acquisition. A feature network of English words was constructed from a large database of adult feature production norms such that edges in the network represented feature distances between words (i.e., Manhattan distances of probability distributions of features elicited for each pair of words). A word's global feature distinctiveness is measured with respect (...) to all other words in the network and a word's local feature distinctiveness is measured relative to words in sub‐networks derived from clustering analyses. This paper investigates how feature distinctiveness of individual words at local and global scales of the network influences language acquisition. Regression analyses indicate that global feature distinctiveness was associated with earlier age of acquisition ratings, and was a stronger predictor of age of acquisition than local feature distinctiveness. These results suggest that the global structure of the semantic feature network could play an important role in language acquisition, whereby globally distinctive concepts help to structure vocabulary development over the lifespan. (shrink)

We propose that the fine discrete movements of the tongue as used in speech are what account for the extreme lateralization in humans, and that handedness is a mere byproduct of tongue use. With regard to syntax, we support the Armstrong et al. (1995) proposition that syntax derives directly from gestural motor movements as opposed to facial expressions.

A foundation of quantum mechanics based on the concepts of focusing and symmetry is proposed. Focusing is connected to c-variables—inaccessible conceptually derived variables; several examples of such variables are given. The focus is then on a maximal accessible parameter, a function of the common c-variable. Symmetry is introduced via a group acting on the c-variable. From this, the Hilbert space is constructed and state vectors and operators are given a definite interpretation. The Born formula is proved from weak assumptions, (...) and from this the usual rules of quantum mechanics are derived. Several paradoxes and other issues of quantum theory are discussed. (shrink)

Introduces probability theory largely by way of precept. Results of theory are stated, not derived, and then problems are proposed and solved by way of illustration. Although there is a commendable number of such problems, it should be noted that no exercises are concocted and left for the reader. Other topics touched upon besides discrete probability are continuous probability and probability of causes. The treatment lays bare some philosophical issues.—P. S.

Threshold- and signal-detection-based models have dominated theorizing about recognition memory. Building upon these theoretical frameworks, we have argued for a dual-process model in which conscious recollection and familiarity contribute to memory performance. In the current paper we assessed several memory models by examining the effects of levels of processing and the number of presentations on recognition memory receiver operating characteristics . In general, when the ROCs were plotted in probability space they exhibited an inverted U shape; however, when they (...) were plotted inzspace they exhibited a U shape. An examination of the ROCs showed that the dual-process model could account for the observed ROCs, but that models based solely on either threshold or signal-detection processes failed to provide a sufficient account of the data. Furthermore, an examination of subjects' introspective reports using the remember/know procedure showed that subjects were aware of recollection and familiarity and were able to consistently report on their occurrence. The remember/know data were used to accurately predict the shapes of the ROCs, and estimates of recollection and familiarity derived from the ROC data mirrored the subjective reports of these processes. (shrink)

It is shown that both covariant harmonic oscillator formalism and quantum field theory are based on common physical principles which include Poincaré covariance, Heisenberg's space-momentum uncertainty relation, and Dirac's “C-number” time-energy uncertainty relation. It is shown in particular that the oscillator wave functions are derivable from the physical principles which are used in the derivation of the Klein-Nishina formula.

This paper addresses the issues related to designing and estimating the strength of solid-alloy elements in the deforming broaches of significant diameter (exceeding 150 mm) for the developed process of discrete broaching. The tool limit condition was assessed based on two strength criteria: the specific potential energy of shape change and the maximum tangent stresses. Numerical modeling using the finite element method has made it possible to derive the distribution of equivalent stresses in the tool elements and the contact (...) stresses at the surface of the contact between a solid-alloy insert and the body, which enabled the analysis of tool strength under loading. The simulation was performed under a single normal load, which ensured the versatility of the calculation for any contact pressure values. We have derived formulae to calculate the acceptable contact pressure depending on unit load. The effect of the insert protrusion height over the body on the strength of tool elements has been established. We have derived engineering dependences that determine the required magnitude of insert protrusion over the body depending on the ultimate load. An example of calculating the strength of a prefabricated deforming element in the machining of a sleeve made from gray modified cast iron of hardness HB230 has been considered. Our calculations have shown that the deforming element designed for the new technological process corresponds to the conditions of strength, provided the ratio h1/h=0.15 is maintained (where h1 is the insert height above the body, h is the insert height). The results obtained could be used in engineering calculations when designing the prefabricated tool for discrete deformation, as well as to assess the strength of prefabricated tools, such as cutters, core drills, reamers, when refining external loads. (shrink)

The discrete light-cone quantization (DLCQ) of a supersymmetric gauge theory in 1+1 dimensions is discussed, with particular attention given to the inclusion of the gauge zero mode. Interestingly, the notorious “zero-mode” problem is now tractable because of special supersymmetric cancellations. In particular, we show that anomalous zero-mode contributions to the currents are absent, in contrast to what is observed in the nonsupersymmetric case. An analysis of the vacuum structure is provided by deriving the effective quantum mechanical Hamiltonian of the (...) gauge zero mode. It is shown that the inclusion of the zero modes of the adjoint scalars and fermions is crucial for probing the phase properties of the vacua. We find that the ground-state energy is zero and thus consistent with unbroken supersymmetry and conclude that the light-cone Fock vacuum is unchanged with or without the presence of matter fields. (shrink)

We explicitly compute, following the method of Weyl, the commutator [Q, P] of the position operatorQ and the momentum operatorP of a particle when the dimension of the space on which they act is finite with a discrete spectrum; and we show that in the limit of a continuous spectrum with the dimension going to infinity this reduces to the usual relation of Heisenberg.

In this paper, we show that the Kirchhoff equations are derived from the Schrödinger equation by assuming the wave function to be a polynomial like solution. These Kirchhoff equations describe the evolution of n point vortices in hydrodynamics. In two dimensions, Kirchhoff equations are used to demonstrate the solution to single particle Laughlin wave function as complex Hermite polynomials. We also show that the equation for optical vortices, a two dimentional system, is derived from Kirchhoff equation by using paraxial wave (...) approximation. These Kirchhoff equations satisfy a Poisson bracket relationship in phase space which is identical to the Heisenberg uncertainty relationship. Therefore, we conclude that being classical equations, the Kirchhoff equations, describe both a particle and a wave nature of single particle quantum mechanics in two dimensions. (shrink)

The peculiarities of mechanical motion in Minkovski space with three-dimensional time are considered. A variation principle for deriving equations of motion is defined and the vector nature of energy and conservation laws for six-dimensional energy-momentum vector are discussed. Difficulties connected with vacuum instability and the possibility of anomalous nuclear reactions are removed due to the time irreversibility principle. The motion of a charged particle in a constant electric field is studied as an example of multitime processes. Some results concerning (...) planet motion in the multitime gravitation field are presented. (shrink)

A characterisation of a type of weak-operator continuous linear functional on certain linear subsets of B, where H is a Hilbert space, is derived within Bishop-style constructive mathematics.

A Dirac-type equation on R×S 3 topology is derived. It is a generalization of the previously obtained Klein-Gordon-type, Schrödinger-type, and Weyl-type equations, and reduces to the latter in the appropriate limit. The (discrete) energy spectrum is found and the corresponding complete set of solutions is given as expansions in terms of the matrix elements of the irreducible representations of the group SU 2 . Finally, the properties of the solutions are discussed.

De spatio, ac tempore -- De spatio, et tempore, ut a nobis cognoscuntur -- De motu absoluto, an possit a relativo distingui -- De vi inertiae.

Irregularity may occur on the earth’s surface in the form of mountains due to the imperfection of the earth’s crust. To explore the influence of horizontally polarized shear waves on mountains, we considered the fluid-saturated porous medium over an orthotropic semi-infinite medium with rigid and soft mountain surfaces for wave propagation. The mountain surface is defined mathematically as a periodic function of the time domain. The physical interpretation of materials’ structure has been explained in rectangular Cartesian coordinate system originated at (...) the contact interface of layer and half-space. The displacement of the mountains has been derived by solving energy equations analytically. The influence of rigid and soft mountain surfaces on the phase velocity of shear waves has been demonstrated graphically. (shrink)

BackgroundReflexive pitch perturbation experiments are commonly used to investigate the neural mechanisms underlying vocal motor control. In these experiments, the fundamental frequency–the acoustic correlate of pitch–of a speech signal is shifted unexpectedly and played back to the speaker via headphones in near real-time. In response to the shift, speakers increase or decrease their fundamental frequency in the direction opposing the shift so that their perceived pitch is closer to what they intended. The goal of the current work is to develop (...) a quantitative model of responses to reflexive perturbations that can be interpreted in terms of the physiological mechanisms underlying the response and that captures both group-mean data and individual subject responses.MethodsA model framework was established that allowed the specification of several models based on Proportional-Integral-Derivative and State-Space/Directions Into Velocities of Articulators (DIVA) model classes. The performance of 19 models was compared in fitting experimental data from two published studies. The models were evaluated in terms of their ability to capture both population-level responses and individual differences in sensorimotor control processes.ResultsA three-parameter DIVA model performed best when fitting group-mean data from both studies; this model is equivalent to a single-rate state-space model and a first-order low pass filter model. The same model also provided stable estimates of parameters across samples from individual subject data and performed among the best models to differentiate between subjects. The three parameters correspond to gains in the auditory feedback controller’s response to a perceived error, the delay of this response, and the gain of the somatosensory feedback controller’s “resistance” to this correction. Excellent fits were also obtained from a four-parameter model with an additional auditory velocity error term; this model was better able to capture multi-component reflexive responses seen in some individual subjects.ConclusionOur results demonstrate the stereotyped nature of an individual’s responses to pitch perturbations. Further, we identified a model that captures population responses to pitch perturbations and characterizes individual differences in a stable manner with parameters that relate to underlying motor control capabilities. Future work will evaluate the model in characterizing responses from individuals with communication disorders. (shrink)

We examine Paul Halmos’ comments on category theory, Dedekind cuts, devil worship, logic, and Robinson’s infinitesimals. Halmos’ scepticism about category theory derives from his philosophical position of naive set-theoretic realism. In the words of an MAA biography, Halmos thought that mathematics is “certainty” and “architecture” yet 20th century logic teaches us is that mathematics is full of uncertainty or more precisely incompleteness. If the term architecture meant to imply that mathematics is one great solid castle, then modern logic tends to (...) teach us the opposite lesson, namely that the castle is floating in midair. Halmos’ realism tends to color his judgment of purely scientific aspects of logic and the way it is practiced and applied. He often expressed distaste for nonstandard models, and made a sustained effort to eliminate first-order logic, the logicians’ concept of interpretation, and the syntactic vs semantic distinction. He felt that these were vague, and sought to replace them all by his polyadic algebra. Halmos claimed that Robinson’s framework is “unnecessary” but Henson and Keisler argue that Robinson’s framework allows one to dig deeper into set-theoretic resources than is common in Archimedean mathematics. This can potentially prove theorems not accessible by standard methods, undermining Halmos’ criticisms. (shrink)

Mental disorders in university students are very frequent, therefore higher education institutions have established in-campus mental healthcare centres. These clinics have particular characteristics that differ from other mental health centres, as they report to and represent an educational institution, while at the same time looking after the interests and well-being of patients requesting assistance, thus generating unique bioethical conflicts. Ethics Committees are useful tools to offer support to mental health professionals in making ethical decisions. In order to respond to these (...) issues, it was decided that an Ethics Committee would be created in the mental health clinic of a private university in Mexico City. This article describes the implementation process for this Committee, its duties and scope, as well as the case work and review methodology. A list of the most frequent ethical conflicts is attached, jointly with the ethical analysis of the cases treated throughout the year and a half or work by the Committee. (shrink)

In a previous article by two of the present authors Carmeli's group-theoretic method for the formulation of wave equations was applied to the case of the electromagnetic field, and the equations for the vector potential were derived. In the present paper a quantization procedure for these equations is carried out in the Lorentz gauge. It involves two independent variables, corresponding to the number of degrees of freedom of the electromagnetic field in a Hilbert space with a positive-definite metric. Conserved (...) quantities are derived. (shrink)

What are the necessary and jointly sufficient conditions for an object's being a simple (an object without proper parts)? According to one prominent view, The Pointy View of Simples, an object is a simple if and only if the region occupied by that object contains exactly one point in space. According to another prominent view, MaxCon, an object is a simple if and only if it is maximally continuous. In this paper, I argue that both of these views are (...) inconsistent with the possibility of discrete space. I then go on to formulate analogues to these two views that are consistent with this possibility, and argue that if we are willing to grant the possibility of discrete space, we should endorse the analogue to The Pointy View of Simples over the analogue to MaxCon. (shrink)

The editors welcome letters from readers, although we cannot guarantee that all will be published. To ensure timeliness, correspondents must respond to an article within seven weeks and not exceed two double‐spaced pages. Letters become the property of the editors and may be edited and shortened at our discretion.

The editors welcome letters from readers, although we cannot guarantee that all will be published. To ensure timeliness, correspondents must respond to an article within seven weeks and not exceed two double‐spaced pages. Letters become the property of the editors and may be edited and shortened at our discretion.