The purpose of the simultaneous measurement of noncommuting quantum observables can be viewed as the joint estimation of parameters of the density operator of the quantum system. Joint estimation involves the application of a multiply parameterized operator-valued measure. An example related to the simultaneous estimation of the position and velocity of a particle is given. Conceptual difficulties attending simultaneous measurement of noncommuting observables are avoided by this formation.

The blood oxygen level dependent effect that provides the contrast in functional magnetic resonance imaging has been demonstrated to affect the linewidth of spectral peaks as measured with magnetic resonance spectroscopy and through this, may be used as an indirect measure of cerebral blood flow related to neural activity. By acquiring MR-spectra interleaved with frames without water suppression, it may be possible to image the BOLD effect and associated metabolic changes simultaneously through changes in the linewidth of the unsuppressed (...) water peak. The purpose of this study was to implement this approach with the MEGA-PRESS sequence, widely considered to be the standard sequence for quantitative measurement of GABA at field strengths of 3 T and lower, to observe how changes in both glutamate and GABA levels may relate to changes due to the BOLD effect. MR-spectra and fMRI were acquired from the occipital cortex of 20 healthy participants whilst undergoing intrascanner visual stimulation in the form of a red and black radial checkerboard, alternating at 8 Hz, in 90 s blocks comprising 30 s of visual stimulation followed by 60 s of rest. Results show very strong agreement between the changes in the linewidth of the unsuppressed water signal and the canonical haemodynamic response function as well as a strong, negative, but not statistically significant, correlation with the Glx signal as measured from the OFF spectra in MEGA-PRESS pairs. Findings from this experiment suggest that the unsuppressed water signal provides a reliable measure of the BOLD effect and that correlations with associated changes in GABA and Glx levels may also be measured. However, discrepancies between metabolite levels as measured from the difference and OFF spectra raise questions regarding the reliability of the respective methods. (shrink)

The problem of simultaneous measurement of incompatible observables in quantum mechanics is studied on the one hand from the viewpoint of an axiomatic treatment of quantum mechanics and on the other hand starting from a theory of measurement. It is argued that it is precisely such a theory of measurement that should provide a meaning to the axiomatically introduced concepts, especially to the concept of observable. Defining an observable as a class of measurement procedures yielding a certain prescribed result for (...) the probability distribution of the set of values of some quantity (to be described by the set of eigenvalues of some Hermitian operator), this notion is extended to joint probability distributions of incompatible observables. It is shown that such an extension is possible on the basis of a theory of measurement, under the proviso that in simultaneously measuring such observables there is a disturbance of the measurement results of the one observable, caused by the presence of the measuring instrument of the other observable. This has as a consequence that the joint probability distribution cannot obey the marginal distribution laws usually imposed. This result is of great importance in exposing quantum mechanics as an axiomatized theory, since overlooking it seems to prohibit an axiomatic description of simultaneous measurement of incompatible observables by quantum mechanics. (shrink)

Single and double meter simultaneous measurements of a harmonic oscillator are reviewed and compared. Naimark extensions are constructed and relevant projection properties are exhibited for both cases. The theory is extended to the simultaneous measurement of squeezed position and momentum measurements.

A reproducibility principle is formulated and adopted as the guiding criterion for the acceptance of an experimental procedure as a simultaneous measurement of several observables. It is pointed out that this criterion can be applied to classical as well as quantum physics, and that it incorporates compatible as well as incompatible observables. The concept of fuzzy probability measure is presented as a possible mathematical tool for the description of statistical processes involving measurements of incompatible observables.

Measurements involving spin-1/2 meters which result in the simultaneous measurement of spin components are described. The spin analoge of the Arthur-Kelly experiment is contrasted with a simultaneous measurement which interacts with the system. Naimark extensions are constructed and Bloch state projection properties are discussed for each case. The theory is extended to squeezed angular momentum measurement.

We report on an “anti-Gleason” phenomenon in classical mechanics: in contrast with the quantum case, the algebra of classical observables can carry a non-linear quasi-state, a monotone functional which is linear on all subspaces generated by Poisson-commuting functions. We present an example of such a quasi-state in the case when the phase space is the 2-sphere. This example lies in the intersection of two seemingly remote mathematical theories—symplectic topology and the theory of topological quasi-states. We use this quasi-state to estimate (...) the error of the simultaneous measurement of non-commuting Hamiltonians. (shrink)

We investigated whether the inferior parietal lobule (IPL) responds in real-time to multisensory inconsistency during movement. The IPL is thought to be involved in both the detection of inconsistencies in multisensory information obtained during movement and that obtained during self-other discrimination. However, because of the limited temporal resolution of conventional neuroimaging techniques, it is difficult to distinguish IPL activity during movement from that during self-other discrimination. We simultaneously conducted electroencephalography (EEG) and near-infrared spectroscopy (NIRS) with the goal of examining (...) IPL activity with a high spatiotemporal resolution during single reaching movements. Under a visual feedback-delay condition, gamma event-related synchronization (γ-ERS), i.e., an increase in gamma (31–47 Hz) EEG power, occurred during reaching movements. This γ-ERS is considered to reflect processing of information about prediction errors. To integrate this temporal information with spatial information from the NIRS signals, we developed a new analysis technique that enabled estimation of the regions that show a hemodynamic response characterized by EEG fluctuation present in the visual feedback-delay condition. As a result, IPL activity was explained by γ-ERS specific to visual feedback delay during movements. Thus, we succeeded in demonstrating real-time activation of the IPL in response to multisensory inconsistency. However, we did not find any correlation between either IPL activity or γ-ERS with the sense of agency. Therefore, our results suggest that while the IPL is influenced by prediction error signals, it does not engage in direct processing underlying the conscious experience of making a movement, which is the foundation of self-other discrimination. (shrink)

The recently established universal uncertainty principle revealed that two nowhere commuting observables can be measured simultaneously in some state, whereas they have no joint probability distribution in any state. Thus, one measuring apparatus can simultaneously measure two observables that have no simultaneous reality. In order to reconcile this discrepancy, an approach based on quantum logic is proposed to establish the relation between quantum reality and measurement. We provide a language speaking of values of observables independent of measurement based (...) on quantum logic and we construct in this language the state-dependent notions of joint determinateness, value identity, and simultaneous measurability. This naturally provides a contextual interpretation, in which we can safely claim such a statement that one measuring apparatus measures one observable in one context and simultaneously it measures another nowhere commuting observable in another incompatible context. (shrink)

Noncommuting quantum observables, if considered asunsharp observables, are simultaneously measurable. This fact is exemplified for complementary observables in two-dimensional state spaces. Two proposals of experimentally feasible joint measurements are presented for pairs of photon or neutron polarization observables and for path and interference observables in a photon split-beam experiment. A recent experiment proposed and performed by Mittelstaedt, Prieur, and Schieder in Cologne is interpreted as a partial version of the latter example.

I discuss the attitude of Jewish law sources from the 2nd–:5th centuries to the imprecision of measurement. I review a problem that the Talmud refers to, somewhat obscurely, as impossible reduction. This problem arises when a legal rule specifies an object by referring to a maximized measurement function, e.g., when a rule applies to the largest part of a divided whole, or to the first incidence that occurs, etc. A problem that is often mentioned is whether there might be hypothetical (...) situations involving more than one maximal value of the relevant measurement and, given such situations, what is the pertinent legal rule. Presumption of simultaneous occurrences or equally measured values are also a source of embarrassment to modern legal systems, in situations exemplified in the paper, where law determines a preference based on measured values. I contend that the Talmudic sources discussing the problem of impossible reduction were guided by primitive insights compatible with fuzzy logic presentation of the inevitable uncertainty involved in measurement. I maintain that fuzzy models of data are compatible with a positivistic epistemology, which refuses to assume any precision in the extra-conscious world that may not be captured by observation and measurement. I therefore propose this view as the preferred interpretation of the Talmudic notion of impossible reduction. Attributing a fuzzy world view to the Talmudic authorities is meant not only to increase our understanding of the Talmud but, in so doing, also to demonstrate that fuzzy notions are entrenched in our practical reasoning. If Talmudic sages did indeed conceive the results of measurements in terms of fuzzy numbers, then equality between the results of measurements had to be more complicated than crisp equations. The problem of impossible reduction could lie in fuzzy sets with an empty core or whose membership functions were only partly congruent. Reduction is impossible may thus be reconstructed as there is no core to the intersection of two measures. I describe Dirichlet maps for fuzzy measurements of distance as a rough partition of the universe, where for any region A there may be a non-empty set of - _A, where the problem of impossible reduction applies. This model may easily be combined with probabilistic extention. The possibility of adopting practical decision standards based on -cuts is discussed in this context. I propose to characterize the uncertainty that was presumably capped by the old sages as U- uncertainty, defined, for a non-empty fuzzy set A on the set of real numbers, whose -cuts are intervals of real numbers, as U = 1/h 0 h log [1+]d, where h is the largest membership value obtained by any element of A and is the measure of the -cut of A defined by the Lebesge integral of its characteristic function. (shrink)

Working in stochastic spin space and using POV measures as in the Davies and Lewis measurement scheme, we construct a formalism to describe the simultaneous measurement of incompatible spin components. The methods are illustrated with a new analysis of the Stern-Gerlach experiment, and with a discussion of spin dynamics in stochastic spin space. We also present a new short proof of a theorem on representations of spin-1/2 systems, find a joint spectral family for (noncommuting) spin components, and indicate the connection (...) of our result with the Riesz extension theorem. (shrink)

The present paper pursues two aims. First to show that the experiment proposed by Stolakis [1986] does not lead to absolute synchronization in a single frame of reference and therefore also to the measurement of one-way velocity of light. Second, by consecutively considering the problems of the conventionality of simultaneity and of existence to show that the simultaneity of distant events can be a matter of convention only in a four-dimensional world. * I am grateful to the anonymous referees for (...) their useful suggestions on an earlier version of this paper. (shrink)

Thick concepts, namely those concepts that describe and evaluate simultaneously, present a challenge to science. Since science does not have a monopoly on value judgments, what is responsible research involving such concepts? Using measurement of wellbeing as an example, we first present the options open to researchers wishing to study phenomena denoted by such concepts. We argue that while it is possible to treat these concepts as technical terms, or to make the relevant value judgment in-house, the responsible thing (...) to do, especially in the context of public policy, is to make this value judgment through a legitimate political process that includes all the stakeholders of this research. We then develop a participatory model of measurement based on the ideal of co-production. To show that this model is feasible and realistic, we illustrate it with a case study of co-production of a concept of thriving conducted by the authors in collaboration with a UK anti-poverty charity Turn2us. (shrink)

In a recent paper, Prugovečki offered a theory of simultaneous measurements based upon an axiomatic description of the measurement act which excludes certain illustrations of simultaneous measurement previously discussed by the present writers. In this article, the fundamental conceptions of state preparation, state determination, and measurement which underlie our research are compared to Prugovečki's interpretations of the analogous constructs in his theory of measurement.

Evaluative conditioning (EC) refers to the change in the valence of a conditioned stimulus (CS) due to its pairing with a positive or negative unconditioned stimulus (US). To the extent that core affect can be characterised by the two dimensions of valence and arousal, EC has important implications for the origin of affective responses. However, the distinction between valence and arousal is rarely considered in research on EC or conditioned responses more generally. Measuring the subjective feelings elicited by a CS, (...) the results from two experiments showed that (1) repeated pairings of a CS with a positive or negative US of either high or low arousal led to corresponding changes in both CS valence and CS arousal, (2) changes in CS arousal, but not changes in CS valence, were significantly related to recollective memory for CS–US pairings, (3) subsequent presentations of the CS without the US reduced the conditioned valence of the CS, with conditioned arousal being less susceptible to extinction and (4) EC effects were stronger for high arousal than low arousal USs. The results indicate that the conditioning of affective responses can occur simultaneously along two independent dimensions, supporting evidence in related areas that calls for a consideration of both valence and arousal. Implications for research on EC and the acquisition of emotional dispositions are discussed. (shrink)

Studies in cognitive psychology have shown that the deployment of visual attention operates under spatial limitations, rendering its assignment to multiple locations difficult or costly. This study explored whether this conventional understanding applies to human metaattention as well. I measured the spatial distribution of metaattention during viewing of natural scenes and found that participants believed they could attend to multiple locations simultaneously. Study 2 tested whether this tendency could be modified by information about the tendency to overestimation. After participants (...) were informed of this tendency toward overestimation with both verbal instruction and demonstrations of attentional blindness and blindness to these phenomena, the selectivity of metaattention increased. Study 3 demonstrated that participants overestimated their attentional abilities by comparing the metaattentional drawings and the actual behavioral performances of the same participants. These results were consistent with recent findings of metaattentional overestimation in change detection and suggested human insensitivity in monitoring attentional limitations. (shrink)

It is far from obvious that outside of highly specialized domains such as commercial agriculture, the methodology of biometrics—quantitative comparisons over groups of organisms—should be of any use in today’s bioinformatically informed biological sciences. The methods in our biometric textbooks, such as regressions and principal components analysis, make assumptions of homogeneity that are incompatible with current understandings of the origins of developmental or evolutionary data in historically contingent processes, processes that might have come out otherwise; the appropriate statistical methods are (...) those suited to random walks, not normal distributions. A valid methodology would further require that especially close attention be paid to the difference between aspects of processes that are plastic, those that encode their own histories or biographies, and the very small fraction of quantifications that can usefully and realistically be modeled as varying by colored noise around a central tendency that itself has some quantitative meaning. This point of view—that only a vanishingly small fraction of the quantitative information borne by any living organism is worth quantifying—is illustrated by some data on a human birth defect, namely, fetal alcohol syndrome. In a suggestive metaphor, the biometrician is like the pilgrim in Friedrich’s painting Der Wanderer über dem Nebelmeer, uncertain as to whether to measure the mountains or the clouds. The mountains stand for contingent history, the clouds for the subset of the data most closely matching controlled experiments suitable for quantitative biometric summary. Biometrics applies to the clouds, not the mountains. The success of statistical methods comes at the expense of all the theories that we simultaneously hold to be true about the biological materials to which they both pertain. Biometrics is thus complementary to all of the emerging reductionist sciences of biological structure. (shrink)

The ability to distinguish between an individual's own actions and those of another person is a requirement for successful joint action, particularly in domains such as group music making where precise interpersonal coordination ensures perceptual overlap in the effects of co-performers' actions. We tested the hypothesis that such coordination benefits from simultaneous integration and segregation of information about ‘self’ and ‘other’ in an experiment using a musical joint action paradigm. Sixteen pairs of individuals with little or no musical training performed (...) a dyadic synchronization task on a pair of electronic music boxes. The relationship between pitches produced by paired participants (same vs. different) and the relationship between movement frequencies required to trigger synchronous tones (congruent vs. incongruent) were varied in a repeated measures design. The results indicate that interpersonal coordination was most accurate when sounds were different in pitch but movement frequency was congruent. Under other conditions, participants often drifted apart, resulting in poor coordination, especially with same sounds and incongruent movements across co-performers. These findings suggest that interpersonal coordination was facilitated when simultaneous self-other integration and segregation occurred across sensory modalities in an asymmetrical manner where pitch relations favoured segregation via auditory streaming while movement congruence favoured integration via visuo-motor coupling. Such self-other representational balance may enable co-performers to maintain autonomous control while attending, anticipating, and adapting to each other's timing when joint action requires precise temporal coordination. (shrink)

In this paper the classical topic of “conventionality” in defining the simultaneity (or synchrony) of distant events is tackled again, and the validity of Reichenbach's view is carefully circumscribed. In particular, the role of “one-way” assumptions in the foundations of special relativity is emphasized. The restriction by the round-trip isotropy condition on the admissible distance functions in inertial frames is studied, and its relevance to several issues (absolute simultaneity, the interpretation of Michelson–Morley type experiments, the self-measured speed of a clock) (...) is shown. Two “clock transport” synchronizations in an inertial frame, using self-measured speed and “proper distance,” are presented in detail, and the agreement of the synchronies so established with standard synchrony is proven to be non- circular. By assuming a reasonable concept of “convention” this result is shown to dissolve several objections by supporters of a strong version of conventionalism. Throughout, a number of common misapprehensions in the literature are pointed out. (shrink)

This essay focuses on the history of psychometry, the science of soul measuring. For its founder, Dr Joseph Rodes Buchanan, the soul was simultaneously an object for anthropological research and a measuring instrument capable of revealing human character, interpreting natural history, and demonstrating the reality of an immortal soul. Psychometry taught that human souls, especially those of women, were capable of acting as instruments because they could feel the mysterious energies that people and objects radiated. Although orthodox male scientists (...) rejected the visions of sensitive women as the antithesis of reliable data, psychometric researchers believed that the feelings of women were both the instruments and information that made their science possible. Psychometry promised to revolutionize science by insisting that sympathy and subjectivity, not detachment and objectivity, ought to undergird research. Yet as male experimenters worked to prove psychometry’s effectiveness, they almost invariably cast themselves as detached observers accurately recording the data provided by their female instruments. Thus, despite pushing for scientific reform, the methods and discourse of male psychometric experimenters eroded their field’s core arguments about connectedness and subjectivity and, instead, reinforced the notion that detachment and objectivity were essential to legitimate science. Challenges to objectivity could prove just how thoroughly it dominated scientific discourse and practice. Still, some psychometers, particularly women who practiced at home, were untroubled by the fact that their research was predicated on subjective feelings, and psychometry remained a viable pursuit among spiritualists even as it faded from the realm of science. Psychometry emerged and, ultimately, fractured amid tensions between widespread enthusiasm for sciences that emphasized spiritual connectedness and the mounting pressure to legitimize scientific knowledge through the language and practices of objectivity. (shrink)

We show that true colors as defined by Chevreul (1839) produce unsuspected simultaneous brightness induction effects on their immediate grey backgrounds when these are placed on a darker (black) general background surrounding two spatially separated configurations. Assimilation and apparent contrast may occur in one and the same stimulus display. We examined the possible link between these effects and the perceived depth of the color patterns which induce them as a function of their luminance contrast. Patterns of square-shaped inducers of a (...) single color (red, green, blue, yellow, or grey) were placed on background fields of a lighter and a darker grey, presented on a darker screen. Inducers were always darker on one side of the display and brighter on the other in a given trial. The intensity of the grey backgrounds varied between trials only. This permitted generating four inducer luminance contrasts, presented in random order, for each color. Background fields were either spatially separated or consisted of a single grey field on the black screen. Experiments were run under three environmental conditions: dark-adaptation, daylight, and rod-saturation after exposure to bright light. In a first task, we measured probabilities of contrast, assimilation, and no effect in a three-alternative forced-choice procedure (background appears brighter on the ‘left’, on the ‘right’ or the ‘same’). Visual adaptation and inducer contrast had no significant influence on the induction effects produced by colored inducers. Achromatic inducers produced significantly stronger contrast effects after dark-adaptation, and significantly stronger assimilation in daylight conditions. Grouping two backgrounds into a single one was found to significantly decrease probabilities of apparent contrast. Under the same conditions, we measured probabilities of the inducers to be perceived as nearer to the observer inducers. These, as predicted by Chevreul’s law of contrast, were determined by the luminance contrast of the inducers only, with significantly higher probabilities of brighter inducers to be seen as nearer, and a marked asymmetry between effects produced by inducers of opposite sign. Implications of these findings for theories which attempt to link simultaneous induction effects to the relative depth of object surfaces in the visual field are discussed. (shrink)

Bergson's central contention is that time is not measurable by any objective standard; in Duration and Simultaneity, that position is tried out against the major movement in physics of the day - Relativity. Bergson argues that Relativity fails to live up to the promise of a truly relative physics, and counter to its own spirit retains some of the objectivist assumptions of previous world views. Duration and Simultaneity was conceived in the desire to make good the new paradigm to (...) which Relativity was bound to lay claim; in the desire to be more Einsteinian than Einstein. (shrink)

Objective: to develop and test the factorial structure of a new self-determination theory-based measure of behavioral regulation in children. Method: 590 (F = 51.7%) children aged 7-11 years completed the Motivation to Exercise and Diet (MED-C) questionnaire, which comprises 16 items (8 for exercise and 8 for diet) grouped into eight-factors (5 motivations and 3 needs). Psychometric testing included confirmatory factor analysis and internal consistency. Measurement invariance analyses were also performed to evaluate whether the factorial structure of the MED-C was (...) equivalent for gender (male vs. female), age ( 10yo) and the perception of having at least one parent with overweight or obesity (yes vs. no). Results: factorial analysis confirmed an acceptable factors solution for the MED-C and a good fit to the data for both the exercise and the diet subscales assessed independently. The Maximal Reliability coefficient revealed good reliability for the exercise and the diet subscales. Moreover, the MED-C factor structure was invariant across group comparisons. Discussion: findings support the construct validity and reliability of the MED-C. Therefore, it represents the first validated instrument simultaneously measuring motivational regulation and psychological need satisfaction in the context of children’s exercise and diet. Considering the goodness of these results, scale percentile ranks of the total score distribution as well as the z-score and the T-score were provided for clinical and research purposes. Conclusion: The MED-C might support the understanding of motivations and needs of children with weight problems and assist their process of behavioural change in primary and secondary prevention programs. Psychological factors represent, in fact, potential targets for interventions to increase children’s motivation to exercise and diet. (shrink)

Because it promises to benefit business and society simultaneously, strategic philanthropy might be characterized as a “happy marriage” of corporate social responsibility behavior and corporate financial performance. However, as evidence so far has been mostly anecdotal, it is important to understand to what extent empirics support the actual practice as well as value of a strategic approach, which creates both business and social impacts through corporate philanthropic activities. Utilizing data from the years 2006 to 2009 for a sample of (...) the Dow Jones Sustainability Index, which monitors the world’s most sustainable companies, the authors test a model of strategic philanthropy in which the dependent variable is evidence that a firm does or does not measure business and social impacts simultaneously. From the DJSI data, the authors find a proposed measure of overall corporate social performance to be the most important explanatory factor for engagement in strategic philanthropy. Moreover, this measure of CSP has a mediating effect on the relations between certain independent variables and strategic philanthropy. Other important findings provide support for the influence of the institutional factors industry and region on the likelihood that companies are practicing strategic philanthropy, but little effect of the business characteristics company size and profitability on that likelihood. (shrink)

Electroencephalographic correlates of movement have been studied extensively over many years. In the present work, we focus on investigating neural correlates that originate from the spine and study their connectivity to corresponding signals from the sensorimotor cortex using multivariate autoregressive models. To study cortico-spinal interactions, we simultaneously measured spinal cord potentials and somatosensory evoked potentials of wrist movements elicited by neuromuscular electrical stimulation. We identified directional connections between spine and cortex during both the extension and flexion of the wrist (...) using only non-invasive recording techniques. Our connectivity estimation results are in alignment with various studies investigating correlates of movement, i.e., we found the contralateral side of the sensorimotor cortex to be the main sink of information as well as the spine to be the main source of it. Both types of movement could also be clearly identified in the time-domain signals. (shrink)

In this paper, we show that a restricted form of time travel both accords with special relativity kinematics and avoids several prima facie objections. We argue that such time travel provides a reasonable way to interpret certain phenomena which can readily be described, and the analogues of which have already been observed at the level of elementary particle reactions. We then describe how a time-traveling object could measure itself, and demonstrate how, in the appropriate circumstances, such an experiment could convince (...) a theorist who insisted on a single criterion for length measurements that his standard had itself changed in length. The same experiment can shed light on the possibility of detecting a universal expansion; and we show that, given certain experimental results, one must conclude that every member of a class of time travelers has changed in length simultaneously, though perhaps only while going backwards in time. (shrink)

It will be shown that the Peres–Mermin square admits value-definite noncontextual hidden-variable models if the observables associated with the operators can be measured only sequentially but not simultaneously. Namely, sequential measurements allow for noncontextual models in which hidden states update between consecutive measurements. Two recent experiments realizing the Peres–Mermin square by sequential measurements will also be analyzed along with other hidden-variable models accounting for these experiments.

The paper defends the thesis of conventionality in distant simultaneity within the special theory of relativity. The thesis can be expressed in the following way: There is no method independent of standard synchronization by which the one-way velocity of light can be measured if all empirical consequences of the special theory of relativity are to be accepted. Three methods which have recently been suggested are investigated. It is shown that they all depend on the method of standard synchronization. It is (...) finally claimed that nobody has suggested a method which cannot be shown to depend on the method of standard synchronization. (shrink)

The disk that rotates in an inertial frame in special relativity has long been analysed by assuming a Lorentz contraction of its peripheral elements in that frame, which has produced widely varying views in the literature. We show that this assumption is unnecessary for a disk that corresponds to the simplest form of rotation in special relativity. After constructing such a disk and showing that observers at rest on it do not constitute a true rotating frame, we choose a “master” (...) observer and calculate a set of disk coordinates and spacetime metric pertinent to that observer. We use this formalism to resolve the “circular twin paradox”, then calculate the speed of light sent around the periphery as measured by the master observer, to show that this speed is a function of sent-direction and disk angle traversed. This result is consistent with the Sagnac Effect, but constitutes a finer analysis of that effect, which is normally expressed using an average speed for a full trip of the periphery. We also use the formalism to give a resolution of “Selleri’s paradox”. (shrink)

Rapid individual cognitive phenotyping holds the potential to revolutionize domains as wide‐ranging as personalized learning, employment practices, and precision psychiatry. Going beyond limitations imposed by traditional lab‐based experiments, new efforts have been underway toward greater ecological validity and participant diversity to capture the full range of individual differences in cognitive abilities and behaviors across the general population. Building on this, we developed Skill Lab, a novel game‐based tool that simultaneously assesses a broad suite of cognitive abilities while providing an (...) engaging narrative. Skill Lab consists of six mini‐games as well as 14 established cognitive ability tasks. Using a popular citizen science platform (N = 10,725), we conducted a comprehensive validation in the wild of a game‐based cognitive assessment suite. Based on the game and validation task data, we constructed reliable models to simultaneously predict eight cognitive abilities based on the users’ in‐game behavior. Follow‐up validation tests revealed that the models can discriminate nuances contained within each separate cognitive ability as well as capture a shared main factor of generalized cognitive ability. Our game‐based measures are five times faster to complete than the equivalent task‐based measures and replicate previous findings on the decline of certain cognitive abilities with age in our large cross‐sectional population sample (N = 6369). Taken together, our results demonstrate the feasibility of rapid in‐the‐wild systematic assessment of cognitive abilities as a promising first step toward population‐scale benchmarking and individualized mental health diagnostics. (shrink)

It is routinely assumed that Einstein discovered the relativity of simultaneity by thinking about how clocks can be synchronized by light signals, much in accord with the analysis he gave in his 1905 special relativity paper. Yet that is just supposition. We have no real evidence that it actually happened this way. In later recollections, Einstein stressed the importance of several thought experiments in the thinking that led up to the final theory. They include his chasing a light beam thought (...) experiment and his magnet and conductor thought experiment. They do not include thought experiments on clocks and their synchronization. My goal here is to show that other pathways to the relativity of simultaneity are quite plausible. In several places Einstein stressed the importance in his discovery of special relativity of stellar aberration and Fizeau's measurement of the speed of light in moving water. The results can be seen as direct observational expressions of the relativity of simultaneity, if one knows how to read them. I will suggest that, thanks to his knowledge of Lorentz's 1895 Versuch, Einstein did know how to read them, and that it is quite possible that these observations first led Einstein to the relativity of simultaneity. (shrink)

Simultaneous bimanual movements are not merely the sum of two unimanual movements. Here, we considered the unimanual/bimanual motor system as comprising three components: unimanual-specific, bimanual-specific, and overlapping. If the force-generating system controlling the same limb differs between unimanual and bimanual movements, unimanual exercise would be expected to fatigue the unimanual-specific and overlapping parts in the force-generating system but not the bimanual-specific part. Therefore, we predicted that the decrease in bimanual force generation induced by unimanual neuromuscular fatigue would be smaller than (...) the decrease in unimanual force generation. Sixteen healthy right-handed adults performed unimanual and bimanual maximal handgrip measurements before and after a submaximal fatiguing handgrip task. In the fatigue task, participants were instructed to maintain unimanual handgrip force at 50% of their maximal handgrip force until the time to task failure. Each participant performed this task in a left-hand fatigue condition and a right-hand fatigue condition, in a random order. Although the degree of neuromuscular fatigue was comparable in both conditions, as expected, the decrease in bimanual right handgrip force was significantly smaller than those during unimanual right performance in the RF condition, but not in the LF condition. These results indicate that for the right-hand, neuromuscular fatigue in unimanual handgrip does not completely affect simultaneous bimanual handgrip. Regarding the underlying mechanisms, we propose that although neuromuscular fatigue caused by unimanual handgrip reduces the motor output of unimanual-specific and overlapping parts in the force-generating system, when simultaneous bimanual handgrip is performed, the overlapping part and the bimanual-specific part generate motor output, thus decreasing the force reduction. (shrink)

Data envelopment analysis is a popular mathematical tool for analyzing the relative efficiency of homogenous decision-making units. However, the existing DEA models cannot tackle the newly confronted applications with imprecise and negative data as well as undesirable outputs simultaneously. Thus, we introduce undesirable outputs into modified slack-based measure model and propose an interval-modified slack-based measure model, which extends the application of interval DEA in fields that concern with less undesirable outputs. The novelties of the model are that it considers (...) the undesirable outputs while dealing with imprecise and negative data, and it is slack-based. Furthermore, the model with undesirable outputs is proven translation-invariant and unit-invariant. Moreover, a numerical example is provided to illustrate the changes of the lower and upper bounds of the efficiency score after considering the undesirable outputs. The empirical results show that, without considering undesirable outputs, most of the lower bounds of the efficiency scores will be overestimated when the DMUs are weakly efficient and inefficient. The upper bound will also change after considering undesirable outputs when the DMU is inefficient. Finally, an improved degree of preference approach is introduced to rank the DMUs. (shrink)

This paper shows that the non-Boolean logic of quantum measurements is more naturally represented by a relatively new 4-operation system of Boolean fractions—conditional events—than by the standard representation using Hilbert Space. After the requirements of quantum mechanics and the properties of conditional event algebra are introduced, the quantum concepts of orthogonality, completeness, simultaneous verifiability, logical operations, and deductions are expressed in terms of conditional events thereby demonstrating the adequacy and efficacy of this formulation. Since conditional event algebra is nearly Boolean (...) and consists merely of ordered pairs of standard events or propositions, quantum events and the so-called “superpositions” of states need not be mysterious, and are here fully explicated. Conditional event algebra nicely explains these non-standard “superpositions” of quantum states as conjunctions or disjunctions of conditional events, Boolean fractions, but does not address the so-called “entanglement phenomena” of quantum mechanics, which remain physically mysterious. Nevertheless, separating the latter phenomena from superposition issues adds clarity to the interpretation of quantum entanglement, the phenomenon of influence propagated at faster than light speeds. With such treacherous possibilities present in all quantum situations, an observer has every reason to be completely explicit about the environmental–instrumental configuration, the conditions present when attempting quantum measurements. Conditional event algebra allows such explication without the physical and algebraic remoteness of Hilbert space. (shrink)

Erik Angner has argued that simultaneous endorsement of the representational theory of measurement and psychometrics leads to inconsistency. His claim rests on an implicit assumption: RTM and psychometrics are full-fledged approaches to measurement. I argue that RTM and psychometrics are only partial approaches that deal with different aspects of measurement, and that therefore simultaneous endorsement of the two is not inconsistent. The argument has implications for the improvement of measurement practices.

Theoretical problems concerning concepts of systems and measurement of behavior were encountered during experimental studies of the effects of electrical stimulation of the brain on the social behavior of a monkey colony. General problems involved in the description and measurement of behavior of natural systems, and especially of organisms are discussed. In animals with differentiated brain the general process of stimulation may be divided into four subprocesses: input, throughput, transput and output. Categories of behavior, temporal and spatial units, and logical (...) rules of homogeneity for sorting data and comparing measurements and categories, are discussed. Simple behavioral units are divided into: 1. Individual a. static or postural b. dynamic or gestural 2. Social a. static b. dynamic. Complex behavior is divided into: 1. Simultaneous 2. Sequential 3. Syntactic 4. Roles. The process of interpretation of data by the observer is assumed to be dependent upon actual behavior of the system, techniques of observation and experimentation, theoretical and technical processes of analysis, and synthesis and integration of data. Expression of behavior in mathematical terms insures greater accuracy than descriptive methods and enables data to be processed with computers. (shrink)

I am grateful to Dr William L. Craig for his reply to an earlier article of mine in this journal, on the relationship between God and time. Craig and I agree on most points with respect to the relationship between God and time. What then is there for us to disagree about? The point Craig argues for is, eternity is ‘coincident’ with our history, i.e. the duration of our space–time is simultaneous with some duration of eternity. But I already agree (...) to this point. In fact, I argued that if God sustains the universe, and if the universe and God are temporal, then God's time must be related to our time. We are in God's time, and God's time is our time, when by time we mean ‘ontological time’ or what I call duration, rather than Measured Time. If this is so, where is our disagreement? Our disagreement turns on this question: does history measure eternity? Does the ‘cosmic time’ of our universe give a proper measure to the same duration of God's time in eternity? I say it does not, while Craig says that it does. (shrink)

ArgumentTwo simultaneous episodes in late nineteenth-century mathematical research, one by Karl Hermann Brunn and another by Hermann Minkowski, have been described as the origin of the theory of convex bodies. This article aims to understand and explain how and why the concept of such bodies emerged in these two trajectories of mathematical research; and why Minkowski's – and not Brunn's – strand of thought led to the development of a theory of convexity. Concrete pieces of Brunn's and Minkowski's mathematical work (...) in the two episodes will, from the perspective of the above questions, be presented and analyzed with the use of the methodological framework of epistemic objects, techniques, and configurations as adapted from Hans-Jörg Rheinberger's work on empirical sciences to the historiography of mathematics by Moritz Epple. Based on detailed descriptions and a comparison of the objects and techniques that Brunn and Minkowski studied and used in these pieces it will be concluded that Brunn and Minkowski worked in different epistemic configurations, and it will be argued that this had a significant influence on the mathematics they developed for those bodies, which can provide answers to the two research questions listed above. (shrink)

This article concerns the distinction between memory-time and information-time, which appeared in Wittgenstein’s middle-period lectures and writings, and its relation to Wittgenstein’s career-long reflection about musical understanding. While the idea of “information-time” entails a public frame of reference typically pertaining to objects which persist in physical time, the idea of pure “memory-time” involves the totality of one’s present memories and expectations that do now provide any way of measuring time-spans. I argue that Wittgenstein’s critique of Augustine notion of pure memory-time (...) entails ipso facto a critique of an influential idea of musical motion, which has been recurring in the work of some major philosophers of music up until the present day. The article connects Wittgenstein’s critical remarks on the confused foundations of such “Augustinian Picture of Music” with his emphasis on the notion of phrasing or characterization in language and music. Wittgenstein’s reversal of Augustinian priorities regarding musical time brings to surface the particularity of expression and the aesthetically “right” in music, evoked by Wittgenstein’s remarks on simultaneity and tempo in music and language. Wittgenstein renders musical simultaneity as enabled by a “protocol” which inheres in musizieren, in the aptly collaborative quest for drawing in significance by means of the phrasing and re-phrasing of a passage in order to characterize it, enabling by means of such comparative investigation meaningful distinctions between right and wrong. (shrink)

We establish the consistency of the failure of the diamond principle on a cardinal [Formula: see text] which satisfies a strong simultaneous reflection property. The result is based on an analysis of Radin forcing, and further leads to a characterization of weak compactness of [Formula: see text] in a Radin generic extension.

This article concerns the distinction between memory-time and information-time, which appeared in Wittgenstein’s middle-period lectures and writings, and its relation to Wittgenstein’s career-long reflection about musical understanding. While the idea of “information-time” entails a public frame of reference typically pertaining to objects which persist in physical time, the idea of pure “memory-time” involves the totality of one’s present memories and expectations that do now provide any way of measuring time-spans. I argue that Wittgenstein’s critique of Augustine notion of pure memory-time (...) entails ipso facto a critique of an influential idea of musical motion, which has been recurring in the work of some major philosophers of music up until the present day. The article connects Wittgenstein’s critical remarks on the confused foundations of such “Augustinian Picture of Music” with his emphasis on the notion of phrasing or characterization in language and music. Wittgenstein’s reversal of Augustinian priorities regarding musical time brings to surface the particularity of expression and the aesthetically “right” in music, evoked by Wittgenstein’s remarks on simultaneity and tempo in music and language. Wittgenstein renders musical simultaneity as enabled by a “protocol” which inheres in musizieren, in the aptly collaborative quest for drawing in significance by means of the phrasing and re-phrasing of a passage in order to characterize it, enabling by means of such comparative investigation meaningful distinctions between right and wrong. (shrink)

The picture which one naturally presents of the situation is that which would arise before an observer placed outside the earth, who could watch the light wave starting from the central mirror and pursuing the distant mirror, catching up with it at some distance beyond the point at which it was when the light wave started. In this case the observer is able to locate the points at which the parts of the apparatus were at different moments and to measure (...) the distances between. We could simulate this situation on the earth by assuming an enclosed square car, from some point in which two balls were shot out in directions at right angles to each other to the walls of the car, bounding back to the point at which they started. We will assume that the balls move with uniform velocity going and coming, and we will assume that the car is moving. An observer outside the car who marked the point on the rail directly over the starting point and the points reached by the balls when they struck the sides of the car, and then measured the distances which the balls travelled, would find that the ball which travelled with the car covered a greater distance than that traversed by the ball which went at right angles to the direction of the train, and yet the balls would return to the starting point at the same moment, provided they travelled over both their paths at the same velocity during their entire trajects, i.e., the same velocity measured within the car. The observer would be at no difficulty to explain this, for he would see that the velocity in the direction of its motion of the car had to be added to that of balls within the car. That is not the case of the light wave. The velocity of a moving shining body is not added to that of the light wave. The wave motion being set up in ether travels with its own uniform velocity of approximately 300,000 kilometers a second. The light waves then, from the standpoint of the observer outside the earth, traverse through the stagnant ether different distances at a uniform velocity and yet the ether waves exhibit on their return none of the evidence which they should exhibit in the interferometer. (shrink)