When are semantic targets detected faster than visual or acoustic ones?

Duration-discrimination data from an experiment using empty auditory intervals in a two-alternative forced-choice paradigm are presented. The observed functional relationship between standard deviation of the psychometric density function and stimulus duration is shown to be fit significantly better by a Weber’s law model of duration discrimination than by Creelman’s counter model. Both models fail to predict the rapid rise in the Weber fraction observed for durations longer than about 2 sec. However, the Weber’s law model, based on a generalization of Weber’s law, accurately predicts the initial drop in the Weber fraction for very short durations and the observed constancy of the Weber fraction for durations up to 2 sec.     

A quantal step function in duration discrimination

The difference threshold for duration, for the case of empty time intervals bounded by brief auditory pulses, is an increasing function of base duration. For base durations between 100 and 1,480 msec, Weber’s law describes the function quite well and a Weber ratio of .05 is obtained. These results in the present paper conform closely to results that have been reported by others. However, it is further shown that the function changes as the amount of practice is increased at each specific base duration: steps unfold from the linear function, and these steps are clearly evident after 17 consecutive sessions at each base duration. Expressing threshold in terms of the apparent magnitude of the “time quantum,” it is found that q is about 13 msec when base duration is 100 msec and that it jumps to 25 at 200, to 50 at 400, and to 100 at 800. Between the abrupt risers in this step function, the treads are not quite flat, perhaps because the amount of practice was insufficient. It is concluded that the time quantum can be doubled and halved, at least within the doubles set 13, 25, 50, and 100 msec. It is not restricted to the single value of 50 msec as initially proposed (Kristofferson, 1967).     

Response differentiation: A psychophysical method for response produced stimuli

Twenty-four rats were reinforced for releasing a lever between t and t + .20 sec after pressing it. Response duration differentiation performance decreased monotonically as t was increased in length from .10 sec to 1.60 sec. A response analogue of Weber’s ratio was constant throughout the middle range of duration bandwidth requirements and increased at the ex tremely short bandwidth—a response-differentiation finding analogous to Weber’s law of stimulus discrimination. This finding was interpreted as support for the conceptualization that response differentiation represents a special instance of response discrimination or discrimination based on response-produced stimuli.     

三数值加工系统假说：数值加工机制新探

数值加工的机制是数量认知领域的核心科学问题之一。三数值加工系统假说从新的角度阐释了各种数值加工机制的关系, 它认为认知系统通过三种不同的机制来快速分析非符号刺激的数值：感数(subitizing)机制精确地分析1~4个刺激的数值; 数量(numerosity)机制分析密度适中的刺激点阵的数量, 加工误差正比于被分析的数量, 符合韦伯定律; 当刺激的密度超出一定范围时, 密度(density)机制通过分析刺激密度来推断刺激的数量关系, 加工误差正比于被加工数值的平方根。一系列研究证实, 这三种数值加工机制具有不同的行为规律和脑电特征。未来研究需要探讨数量机制是否分别与感数机制、密度机制存在平行激活, 从而阐明三种数值加工机制的作用关系。     

短时距估计中的标量特性

使用单任务研究程序,采用预期式研究范式和再现时距的研究方法,从心理物理学的视角,通过三个实验系统地考查了人类短时距估计的标量特性、变异源、时距估计中的转换点和韦伯函数的形态等问题。结果表明,刺激物的运动、变化、速度和物理时距是被试进行短时距估计的重要变异源;被试在实验中表现出高估较短时距和低估较长时距的倾向,时距估计的转换点为11.1s;计时过程中得到的韦伯函数是个分段连续函数, 韦伯函数的拐点有两个12s和21s,这两点与本研究得到的时距估计转换点具有部分一致性     

Intensity discrimination for pulsed sinusoids of various frequencies

Studies of pure-tone intensity discrimination have shown that Weber’s law fails for tones in the region of 1 kHz. In this experiment, intensity discrimination of pulsed sinusoids ranging in frequency from 0.15 to 12 kHz is investigated. For each tone in this region, Weber’s law is found to fail. Some theoretical implications of these results are discussed.     

A study of the near-miss involving Weber’s law and pure-tone intensity discrimination

A study of pure-tone intensity discrimination is presented in which amplitude changes are detected in 1000 Hz tone bursts 15–20 msec in duration. The masking function (log detectable increment vs log background intensity) is found to have a slope of 9/10 when calculations are carried out via energy measurements. This near-miss to Weber’s law is in agreement with other data reported in the literature. The masking slope proves to be essentially independent of stimulus duration between 15 msec and 1.5 sec. Our stable slope parameter is interpreted as a detectability restriction generated by “mass-flow” phenomena in the auditory channel. These phenomena are thought to be similar to the fluctuations accompanying a noisy or turbulent stream of events. Pure-tone intensity discrimination is then analyzed as a special case of energy detection.     

Difference threshold for stimulus length under simultaneous and nonsimultaneous viewing conditions

The present study was concerned with Weber’s Law as it is related to the discriminability of the lengths of lines. Experiments were conducted to investigate three questions: (I) Is Weber’s Law equally applicable to simultaneous and nonsimultaneous viewing conditions? (2) Is the relationship between the stimulus sizes and the values ofDLs described more adequately by the function proposed by Weber or a generalized Weber’s Law stated by Miller? and (3) Is Weber’s Law better approximated by proximal or distal size? It was demonstrated that the discriminability of the lengths of lines follows Weber’s Law under the nonsimultaneous viewing condition, but not under the simultaneous viewing condition. Under the nonsimultaneous viewing condition, it was noted that the generalized Weber’s Law as stated by Miller described the relationship between the DL and stimulus size significantly better than the function proposed by Weber. From the results pertaining to the third question, it was not possible to determine whether the proximal or the distal size follows Weber’s Law more closely.     

Bloch’s law and a Poisson counting model for simple reaction time to light

A series of three experiments was conducted with identical design as an earlier series (Hildreth, 1973). Its purpose was (1) to determine whether Bloch’s law holds for simple reaction time (RT) to still lower intensity visual stimuli, and (2) to provide data for testing a stochastic generalization of the temporal integration model (TI-ED) reported earlier. RT means were found to agree with Bloch’s law for durations below 48 msec. By a statistical test, Bloch’s law was shown to hold for both means and standard deviations below about 65 msec. Latency statistics—means and standard deviations—were predicted by a Poisson process counting model. This model assumes that a number of identical, parallel Poisson processes, activated by light, with pulse interarrival times decreasing with light intensity, trigger light detection when a critical number of pulses arrive at a counting center. For the intensities investigated, both the estimated number of Poisson processes and critical number of pulses required for detection range between 8 and 13. The model predicts the Broca-Sulzer effect for mean RTs which is observed in several of these experiments.     

Differential luminance sensitivity of the human visual system

In this paper the differential sensitivity of the visual system is investigated by means of two simultaneously presented stimuli in a yes-no procedure. The sensitivity measure σ_I appears to be proportional to stimulus intensity (i.e., Weber’s law). The curve displaying Weber’s law is little affected by variation of the background intensity or of the adaptation level. An increment threshold experiment using only one stimulus yields a proportionality of σ_I with the square root of the background intensity. An additional experiment shows that the sensitivity measure σ_I for two flashes decreases first, from dark up to a particular background intensity, and increases when the background tends to mask the flashes. So, in general, two background levels exist with the same differential sensitivity. The results cannot easily be explained by the simple quantum fluctuation concept. A model based partially on electrophysiological data from the literature is proposed which encounters a particular adaptation mechanism, a transducer with a limited dynamical range, and a range setting mechanism.     

Ratio scales of sugar sweetness

In a series of 10 experiments, groups of Os judged the sweetness of 16 sugars. The results suggest that, for all sugars except mannose, the intensity of sweetness grows as a power function of concentration, with an exponent of about 1.3. The relative sweetness of sugars was determined using both molarity and per cent by weight. With both measures, sucrose and fructose were the sweetest sugars. The order of the remaining sugars in the sweetness hierarchy was partiy a function of the measure of concentration. The variability of the magnitude estimates of sweetness was roughly proportional to the stimulus concentration, supporting Weber’s law.     

Human Psychophysical Functions,an Update: Methods for Identifying their form; Estimating their Parameters; and Evaluating the Effects of Important Predictors

Stevens’ power law for the judgments of sensation has a long history in psychology and is used in many psychophysical investigations of the effects of predictors such as group or condition. Stevens’ formulation \(\varPsi = {aP}^{n}\), where \(\varPsi \) is the psychological judgment, P is the physical intensity, and \(n\) is the power law exponent, is usually tested by plotting log \((\varPsi )\) against log (P). In some, but by no means all, studies, effects on the scale parameter, \(a\), are also investigated. This two-parameter model is simple but known to be flawed, for at least some modalities. Specifically, three-parameter functions that include a threshold parameter produce a better fit for many data sets. In addition, direct non-linear computation of power laws often fit better than regressions of log-transformed variables. However, such potentially flawed methods continue to be used because of assumptions that the approximations are “close enough” as to not to make any difference to the conclusions drawn (or possibly through ignorance the errors in these assumptions). We investigate two modalities in detail: duration and roughness. We show that a three-parameter power law is the best fitting of several plausible models. Comparison between this model and the prevalent two parameter version of Stevens’ power law shows significant differences for the parameter estimates with at least medium effect sizes for duration.     

Weber laws,the Weber law,and psychophysical analysis

In failing to define the units in which the stimulus is to be measured, the Weber law might seem to make no definite assertion, and indeed, it is shown that any single empirical function, supposed to relate a given stimulus intensity with that intensity which is just noticeably greater, can be put into the Weber form by a suitable change of scale in which the stimulus intensity is to be measured. Nevertheless, it turns out that if different individuals have different Weber functions, when the intensities are measured on a given scale, then it is by no means always possible to transform the scale so that all of the functions can take on the Weber form. Some necessary conditions are given for the possibility of such a transformation when there is at hand a finite number of functions, and when the functions depend upon a single parameter the necessary and sufficient condition is easily derived. The same discussion leads to a generalization of Thurstone's psychophysical scale and shows that such a scale is always possible.     

The Phenomenological Life-World Analysis and the Methodology of the Social Sciences

This Alfred Schutz Memorial Lecture discusses the relationship between the phenomenological life-world analysis and the methodology of the social sciences, which was the central motive of Schutz’s work. I have set two major goals in this lecture. The first is to scrutinize the postulate of adequacy, as this postulate is the most crucial of Schutz’s methodological postulates. Max Weber devised the postulate ‘adequacy of meaning’ in analogy to the postulate of ‘causal adequacy’ (a concept used in jurisprudence) and regarded both as complementary and, in the context of sociological analysis, critical. Schutz extracted the two postulates from the Neokantian epistemology, dismissed the concept of causality, and reduced Weber’s two postulates of adequacy into one, namely, the adequacy of meaning. I discuss the benefits and shortcomings of this reduction. A major problem, in my view, is that Schutz’s reformulation lost the empirical concern that was inherent in Weber’s ‘causal adequacy’. As a result, the models of economics (which shaped Schutz’s conception of social science) are considered to be adequate if they are ‘understandable’ to an everyday actor, even when they are based on the most unrealistic assumptions. To recapture Weber’s empirical orientation I recommend a more restrictive interpretation of the postulate of adequacy that links it to qualitative research and unfolds the critical potential of Schutz’s phenomenological life-world analysis. My second goal is to report on some current developments in German sociology in which a number of approaches explicitly refer to Schutz’s analysis of the life-world and attempt to pursue ‘adequate’ empirical research. This lecture focuses on three approaches: ethnophenomenology, life-world analytic ethnography, and social scientific hermeneutics.     

Semantic congruity effects in judgments of loudness

This research uses comparative judgments of the relative loudness of sounds to make a critical test of one theory of the mental representation of continuous physical attributes. The first two experiments find a semantic congruity effect, which is an interaction such that subjects can pick the louder of two loud sounds faster than the softer, and the softer of two quiet sounds faster than the louder. According to the theory under test, physical quantities are stored as points on a representational continuum, with a variance as well as a mean placement on it. The theory predicts the semantic congruity effect by assuming that the variance of placement of intensities on the representational continuum is a function of the direction of judgment: a soft sound will have less variance than a loud one when judged for softness and more when judged for loudness. Since the speed of making a judgment increases as variance decreases, the theory predicts a semantic congruity effect. However, for loudness, it can be shown that variance does not change in the manner assumed. The finding of a semantic congruity effect therefore disconfirms the theory. Alternative models are discussed. This research was supported by NSF Grant BNS 78-17442.     

Duration discrimination of empty time intervals marked by intermodal pulses

In 1973, Rousseau and Kristofferson reported that short empty intermodal time intervals marked by a light flash and a brief tone were poorly discriminated by subjects, and that AT,5 was constant over a large range of durations. It led them to suggest that short intramodal empty intervals, marked by stimuli from the same sensory modality, might be handled by a “more efficient mechanism” to which intermodal intervals would not have access. Unfortunately, their study lacked the basic evidence needed to make a strong statement: no direct comparison between inter- and intramodal duration discrimination and no within-subject discrimination function were available. To clarify these two issues, three experiments were performed. The data indicate that intermodal time intervals are discriminated more poorly than intramodal ones, and that intermodal duration discrimination functions follow Weber’s law. Analysis of data from different experiments lead to the conclusion that inter- and intramodal intervals are timed by a common timekeeper and that intermodal intervals induce a large noise component in the timekeeping operation.

     

Duration discrimination of acoustically defined intervals in the 1- to 8-sec range

This experiment indicates how one’s ability to distinguish between two acoustically defined durations, differing by .4 sec, diminishes as the shorter duration is increased from 1 to 8 sec. This effect is interpreted with a model in which one’s “subjective temporal estimate” is a random variable whose variance is directly proportional to the actual stimulus duration, the constant of proportionality being about 6 msec² /sec.     

Time and memory: towards a pacemaker-free theory of interval timing

A popular view of interval timing in animals is that it is driven by a discrete pacemaker-accumulator mechanism that yields a linear scale for encoded time. But these mechanisms are fundamentally at odds with the Weber law property of interval timing, and experiments that support linear encoded time can be interpreted in other ways. We argue that the dominant pacemaker-accumulator theory, scalar expectancy theory (SET), fails to explain some basic properties of operant behavior on interval-timing procedures and can only accommodate a number of discrepancies by modifications and elaborations that raise questions about the entire theory. We propose an alternative that is based on principles of memory dynamics derived from the multiple-time-scale (MTS) model of habituation. The MTS timing model can account for data from a wide variety of time-related experiments: proportional and Weber law temporal discrimination, transient as well as persistent effects of reinforcement omission and reinforcement magnitude, bisection, the discrimination of relative as well as absolute duration, and the choose-short effect and its analogue in number-discrimination experiments. Resemblances between timing and counting are an automatic consequence of the model. We also argue that the transient and persistent effects of drugs on time estimates can be interpreted as well within MTS theory as in SET. Recent real-time physiological data conform in surprising detail to the assumptions of the MTS habituation model. Comparisons between the two views suggest a number of novel experiments.     

Information processing limitations as revealed by temporal discrimination

Information processing limit is a fundamental issue in cognitive psychology. One particular way of studying it is to adopt a temporal span perspective. In this experiment, Weber fractions based on thresholds for duration discrimination are used for adopting this perspective. The results showed that, contrary to the constant predicted by Weber's law, the Weber fraction is larger at 2 than at .2 s. This increase is observed in conditions where inter-trial intervals and cognitive load are manipulated, and is argued to be due to the fact that 2 s is beyond a temporal span limit for processing information.