Reversed dimensional analysis in psychophysics

It is argued that dimensional analysis (from physics) can be applied in psychophysics in the same manner as in physics, provided that the dimensions of sensations are interpreted in the sense of reversed dimensional analysis, which allows for extracting dimensions from data. A dimension obtained by this method, referred to as phenomenological dimension, is similar to a fractal dimension. The examples discussed show that, if the dimension of sensation in Stevens' psychophysical law for time duration (psi = Cphin, n approximately 1.15) is interpreted as a phenomenological dimension, such a dimension can be traced even in short-term memory data. It is suggested that dimensions obtained via reversed dimensional analysis may serve as a link between physical and psychological variables and as a basis for developing the notion of dimension in psychology.     

Magnitude comparisons distort mental representations of magnitude

Many cognitive processes rely on representations of magnitude, yet these representations are often malleable (H. Helson, 1964; J. Huttenlocher, L. V. Hedges, & J. L. Vevea, 2000; A. Parducci, 1965). It is likely that factors that affect these representations in turn affect the psychological processes that rely on them. The authors conducted 4 experiments to investigate whether language-expressible magnitude comparisons distort mental representations of compared magnitudes. Participants compared magnitudes and estimated those magnitudes in a variety of tasks. Experiments 1 through 3 demonstrated systematic comparison-induced distortions. Experiment 4 demonstrated that comparison-induced distortions might account for the asymmetric dominance effect discussed in the decision-making literature. Potential effects of comparison-induced distortions on other psychological processes (e.g., density effects, order effects, body-size estimation, pain estimation, and consumer decision making) are discussed.     

Measurement foundations for multiattribute psychophysical theories based on first order polynomials

The class of first order polynomial measurement representations is defined, and a method for proving the existence of such representations is described. The method is used to prove the existence of first order polynomial generalizations of expected utility theory, difference measurement, and additive conjoint measurement. It is then argued that first order polynomial representations provide a deep and far reaching characterization of psychological invariance for subjective magnitudes of multiattributed stimuli. To substantiate this point, two applications of first order polynomial representation theory to the foundations of psychophysics are described. First, Relation theory, a theory of subjective magnitude proposed by Shepard (Journal of Mathematical Psychology, 1981, 24, 21–57) and Krantz (Journal of Mathematical Psychology, 1972, 9, 168–199), is generalized to a theory of magnitude for multiattributed stimuli. The generalization is based on a postulate of context invariance for the constituent uniattribute magnitudes of a multiattribute magnitude. Second, the power law for subjective magnitude is generalized to a multiattribute version of the power law. Finally, it is argued that a common logical pattern underlies multiattribute generalizations of psychological theories to first order polynomial representations. This abstract pattern suggests a strategy for theory construction in multiattribute psychophysics.     

Psychological relations and psychophysical scales: On the status of “direct” psychophysical measurement

Arguments, originally developed some fifteen years ago, concerning the sort of “direct” psychophysical measurement advocated by S. S. Stevens are reproduced here in order to facilitate access by a wider audience. Considerations of measurement theory, biological adaptation, perceptual invariance, and neurophysiological noise, as well as various empirical results, suggest (a) that it is primarily the relations—particularly the ratios—between stimulus magnitudes and not the individual magnitudes themselves that are represented within the organism and, accordingly, (b) that “direct” psychophysical measurement, by itself, uniquely determines neither a psychological magnitude of any one stimulus nor a psychophysical law relating such psychological magnitudes to corresponding physical magnitudes. What such measurement can uniquely determine, evidently, is a psychological parameter characterizing each sensory continuum.     

BEHAVIOURAL DIMENSION ANALYSIS

H erbst , P. G. Behavioural dimension analysis. A theoretical note. Scand. J. Psychol ., 1972, 13 , 1–4.—The method of dimensional analysis, applied to variables measured by means of ratio scales, leads to laws which take the form of multiplicative power functions. It is shown that the method can be extended to variables measured by means of non-metric scales, and thus applied to a wider range of problems of the type encountered in psychology.     

Interrelations Among Models For The Analysis Of Moment Structures

Factor analysis in several populations, covariance structure models, three-mode factor analysis, structural equation systems with measurement model, and analysis of covariance with measurement model are all shown to be specializations of a general moment structure model published previously in this journal. Some new structured linear models are also described; they may be considered either generalizations or special cases of existing models. Simple representations are developed for complex linear models, and some applications to behavioral data are cited.     

两种数量表征系统

数量表征是人类数学能力的基础,数量表征研究中的一个争论焦点在于是否存在两种不同的数量表征系统：对小数的精确表征系统和对大数的近似表征系统。通过综述不同研究领域对数量表征的研究,总结了支持两种表征系统分离的证据：对1~3范围内小数的表征受数量大小的限制,基于指向物体本身的注意,更依赖于物体的知觉特征,对物体及其数量进行精确表征;而对4以上的数量的近似表征系统则受韦伯定律的限制,基于指向数量的模拟幅度的表征,而不依赖单个物体的知觉特征,是对数量的近似的、心理的表征。fMRI、PET和ERP的脑成像研究结果迄今尚无定论,但认知神经科学研究的深入开展将最终阐明数量表征的机制     

Negative,infinite, and hotter than infinite temperatures

We examine the notions of negative, infinite and hotter than infinite temperatures and show how these unusual concepts gain legitimacy in quantum statistical mechanics. We ask if the existence of an infinite temperature implies the existence of an actual infinity and argue that it does not. Since one can sensibly talk about hotter than infinite temperatures, we ask if one could legitimately speak of other physical quantities, such as length and duration, in analogous terms. That is, could there be longer than infinite lengths or temporal durations? We argue that the answer is surprisingly yes, and we outline the properties of a number system that could be employed to characterize such magnitudes.     

Absolute identification by relative judgment

In unidimensional absolute identification tasks, participants identify stimuli that vary along a single dimension. Performance is surprisingly poor compared with discrimination of the same stimuli. Existing models assume that identification is achieved using long-term representations of absolute magnitudes. The authors propose an alternative relative judgment model (RJM) in which the elemental perceptual units are representations of the differences between current and previous stimuli. These differences are used, together with the previous feedback, to respond. Without using long-term representations of absolute magnitudes, the RJM accounts for (a) information transmission limits, (b) bowed serial position effects, and (c) sequential effects, where responses are biased toward immediately preceding stimuli but away from more distant stimuli (assimilation and contrast).     

Connectionist modelling in psychology: a localist manifesto

Over the last decade, fully distributed models have become dominant in connectionist psychological modelling, whereas the virtues of localist models have been underestimated. This target article illustrates some of the benefits of localist modelling. Localist models are characterized by the presence of localist representations rather than the absence of distributed representations. A generalized localist model is proposed that exhibits many of the properties of fully distributed models. It can be applied to a number of problems that are difficult for fully distributed models, and its applicability can be extended through comparisons with a number of classic mathematical models of behaviour. There are reasons why localist models have been underused, though these often misconstrue the localist position. In particular, many conclusions about connectionist representation, based on neuroscientific observation, can be called into question. There are still some problems inherent in the application of fully distributed systems and some inadequacies in proposed solutions to these problems. In the domain of psychological modelling, localist modelling is to be preferred.     

Perhaps Unidimensional Is Not Unidimensional

Miller (1956) identified his famous limit of 7 ± 2 items based in part on absolute identification—the ability to identify stimuli that differ on a single physical dimension, such as lines of different length. An important aspect of this limit is its independence from perceptual effects and its application across all stimulus types. Recent research, however, has identified several exceptions. We investigate an explanation for these results that reconciles them with Miller’s work. We find support for the hypothesis that the exceptional stimulus types have more complex psychological representations, which can therefore support better identification. Our investigation uses data sets with thousands of observations for each participant, which allows the application of a new technique for identifying psychological representations: the structural forms algorithm of Kemp and Tenenbaum (2008) . This algorithm supports inferences not possible with previous techniques, such as multidimensional scaling.     

Non-symbolic arithmetic in adults and young children

Five experiments investigated whether adults and preschool children can perform simple arithmetic calculations on non-symbolic numerosities. Previous research has demonstrated that human adults, human infants, and non-human animals can process numerical quantities through approximate representations of their magnitudes. Here we consider whether these non-symbolic numerical representations might serve as a building block of uniquely human, learned mathematics. Both adults and children with no training in arithmetic successfully performed approximate arithmetic on large sets of elements. Success at these tasks did not depend on non-numerical continuous quantities, modality-specific quantity information, the adoption of alternative non-arithmetic strategies, or learned symbolic arithmetic knowledge. Abstract numerical quantity representations therefore are computationally functional and may provide a foundation for formal mathematics.     

Automaticity of two-digit numbers

Automatic processing of 2-digit numbers was demonstrated using the size congruency effect (SiCE). The SiCE indicates the processing of the irrelevant (numerical) dimension when 2 digits differing both numerically and physically are compared on the relevant (physical) dimension. The SiCE was affected by the compatibility between unit and decade digits but was unaffected by the global magnitude of the numbers. Together these results suggest automatic processing of the magnitudes of the components of the 2-digit numbers but not of whole numbers. Finally, the SiCE was affected more by the magnitude of the decade digits compared with the unit digits, indicating that the syntactic roles of the digits were represented. The implications of these results for understanding the numerical representations are discussed.     

Tests of multiplicative models in psychology: a case study using the unified theory of implicit attitudes, stereotypes, self-esteem, and self-concept

Theories that posit multiplicative relationships between variables are common in psychology. A. G. Greenwald et al. recently presented a theory that explicated relationships between group identification, group attitudes, and self-esteem. Their theory posits a multiplicative relationship between concepts when predicting a criterion variable. Greenwald et al. suggested analytic strategies to test their multiplicative model that researchers might assume are appropriate for testing multiplicative models more generally. The theory and analytic strategies of Greenwald et al. are used as a case study to show the strong measurement assumptions that underlie certain tests of multiplicative models. It is shown that the approach used by Greenwald et al. can lead to declarations of theoretical support when the theory is wrong as well as rejection of the theory when the theory is correct. A simple strategy for testing multiplicative models that makes weaker measurement assumptions than the strategy proposed by Greenwald et al. is suggested and discussed.     

Representations gone mental

Many philosophers and psychologists have attempted to elucidate the nature of mental representation by appealing to notions like isomorphism or abstract structural resemblance. The ‘structural representations’ that these theorists champion are said to count as representations by virtue of functioning as internal models of distal systems. In his 2007 book, Representation Reconsidered, William Ramsey endorses the structural conception of mental representation, but uses it to develop a novel argument against representationalism, the widespread view that cognition essentially involves the manipulation of mental representations. Ramsey argues that although theories within the ‘classical’ tradition of cognitive science once posited structural representations, these theories are being superseded by newer theories, within the tradition of connectionism and cognitive neuroscience, which rarely if ever appeal to structural representations. Instead, these theories seem to be explaining cognition by invoking so-called ‘receptor representations’, which, Ramsey claims, aren’t genuine representations at all—despite being called representations, these mechanisms function more as triggers or causal relays than as genuine stand-ins for distal systems. I argue that when the notions of structural and receptor representation are properly explicated, there turns out to be no distinction between them. There only appears to be a distinction between receptor and structural representations because the latter are tacitly conflated with the ‘mental models’ ostensibly involved in offline cognitive processes such as episodic memory and mental imagery. While structural representations might count as genuine representations, they aren’t distinctively mental representations, for they can be found in all sorts of non-intentional systems such as plants. Thus to explain the kinds of offline cognitive capacities that have motivated talk of mental models, we must develop richer conceptions of mental representation than those provided by the notions of structural and receptor representation.     

Psychological Science within a Three-Dimensional Ontology

The present paper outlines the nature of a three-dimensional ontology and the place of psychological science within this ontology, in a way that is partly similar to and partly different from that of Pérez-Álvarez. The first dimension is the material realities, and involves different levels (physical, chemical, biological, psychological, etc.), where each level builds on a lower level but also involves the development of new emergent properties, in accordance with Bunge’s emergent materialism. Each level involves systems, with components, structures and mechanisms, and an environment. This dimension can be studied with natural scientific methods. The second dimension is the subjective-experiential realities, and refers to our subjective perspective on the world. In accordance with Husserl’s phenomenology, it is argued that this subjectivity does not exist in the world (i.e., should not be reified as an object among other objects), but represents a perspective on the world that we enter in our capacity as conscious human beings. Essential characteristics of this subjectivity (such as intentionality, temporality, embodiment, and intersubjectivity) can be explored by phenomenological methods. The third dimension is the social-constructional realities, and includes social institutions, norms, categories, theories, and techniques. It is argued that psychological science spans over all three dimensions. Although almost all psychological research by necessity starts from a problem formulation where the subjective-experiential dimension plays an essential role (either explicitly or implicitly), most of present-day psychological research clearly emphasizes the material dimension. It is argued that a mature psychological science needs to integrate all three dimensions.     

Scale-invariance as a unifying psychological principle

How can the classical psychological laws be explained and unified? It is proposed here that scale-invariance is a unifying principle. Distributions of many environmental magnitudes are observed to be scale invariant; that is, the statistical structure of the world remains the same at different measurement scales [Mandelbrot, B., 1982. The Fractal Geometry of Nature (2nd Edn.). W.H. Freeman, San Francisco, CA; Bak, P., 1997. How Nature Works: The Science of Self-organized Criticality. Oxford University Press, Oxford, UK]. We hypothesise that the perceptual-motor system reflects and preserves these scale invariances. This allows derivation of several of the most widely applicable psychological laws governing perception and action across domains and species (Weber's, Stevens', Fitts' and Piéron's Laws). We suggest that these fundamental laws reflect accommodation of the perceptuo-motor system to the scale-invariant physical world and therefore have a common foundation.     

Ordinal representation of numeric quantities by brown capuchin monkeys (Cebus apella)

Using techniques established by E. M. Brannon and H. S. Terrace (2000) with rhesus macaques (Macaca mulatta), the authors tested the ability of brown capuchins (Cebus apella) to order arrays of items ranging in quantity from 1 to 9. Three monkeys were trained on a touch screen to select the quantities 1-4 in ascending order. The monkeys exhibited successful transfer of this ability to novel representations of the quantities 1-4 and to pairs of the novel quantities 5-9. Patterns of responding with respect to numeric distance and magnitude were similar to those seen in human subjects, suggesting the use of similar psychological processes. The capuchins demonstrated an ordinal representation of quantity equivalent to that shown in Old World monkeys.     

Unification of psychophysical phenomena: The complete form of Fechner’s law

Many of the laws and empirical observations of fundamental psychophysics can be unified with a single equation, which has been called the complete form of Fechner’s law. It can be shown that this law embraces both of the commonly used forms: Stevens’s and Fechner’s laws. It assumes one or the other form with appropriate values of the parameters. However, the complete equation confers an advantage beyond simply containing the classical laws. It offers greater flexibility in the representation of experimental data. It is shown that psychophysical phenomena may be represented by any number of triplets of quantities: subjective magnitude of stimulus, subjective just noticeable difference (jnd), and differential threshold. Each of the preceding quantities are functions of the physical magnitude of the stimulus. The investigator has the license to choose two of these quantities in the form he or she thinks is best; the third quantity is determined by the choice of the first two. Thus, for example, different forms of the law of sensation and different forms of the mathematical function for differential threshold may coexist with equal validity.