The Impossible Dream of Fechner and Stevens

Perception ◽  
1981 ◽  
Vol 10 (4) ◽  
pp. 431-434 ◽  
Author(s):  
David J Weiss
Keyword(s):  
Nervous System ◽  
Power Function ◽  
Stimulus Intensity ◽  
Power Law ◽  
Psychophysical Function ◽  
Empirical Function ◽  
Universal Law ◽  
General Truth ◽  
Arbitrary Assumption

The idea that there is a single psychophysical function which describes how the human responds to stimulus intensity is rejected. The form of any empirical function depends upon the buried yet arbitrary assumption about how the stimuli are to be measured. Because psychophysical functions have this arbitrary basis, there can be no universal law, and further, no psychophysical function can reveal a general truth about the nervous system. The power law has been inappropriately reified; the descriptive usefulness of the power function has been incorrectly extended, perhaps because simplicity is appealing.

Subjective Intensity of the Lily-of-the-Valley Scent

1986 ◽  
Vol 63 (2) ◽  
pp. 879-882 ◽  
Author(s):  
Loredana Hvastja ◽  
Lucia Zanuttini
Keyword(s):  
Power Law ◽  
Psychophysical Function ◽  
Subjective Intensity ◽  
Naturalistic Approach

14 blind-folded subjects were requested to give numerical judgments of the perceived intensities of ¼, ½, 1, 2, 4, 8, lily-of-the-valley bunches, according to a naturalistic approach. The psychophysical function conforms to a power law. The exponent, smaller than 1, is in the same range as those commonly found for smell.

Using Psychophysics to Design Speech Warnings

2000 ◽  
Vol 44 (22) ◽  
pp. 698-701
Author(s):  
E. Hellier ◽  
B. Weedon ◽  
J. Edworthy ◽  
K. Walters
Keyword(s):  
Power Function ◽  
Magnitude Estimation ◽  
Power Law ◽  
Warning Signal ◽  
Acoustic Parameter ◽  
Psychophysical Scaling ◽  
The Relationship ◽  
Power Function Exponent

An experiment is reported which applies psychophysical scaling techniques to the design of speech warnings. Participants used magnitude estimation to rate the perceived urgency of computer generated warning signal words (Deadly, Danger, Warning, Caution, Note) that varied systematically in speed. Stevens (1957) Power Law was used to model the relationship between changes in the acoustic parameter and changes in the perceived urgency of a particular signal word. The value for warning designers of the power function exponent, which quantifies and predicts the effect of acoustic changes on perceived urgency, is discussed.

scholarly journals Geography, Trade, and Power-Law Phenomena

2020 ◽  
Author(s):  
Pao-Li Chang ◽  
Wen-Tai Hsu
Keyword(s):  
Empirical Evidence ◽  
Power Function ◽  
Power Law ◽  
Firm Size ◽  
Firm Heterogeneity ◽  
Power Laws ◽  
Tail Probability ◽  
Gravity Equation ◽  
Trade Flows ◽  
City Size

This article reviews interrelated power-law phenomena in geography and trade. Given the empirical evidence on the gravity equation in trade flows across countries and regions, its theoretical underpinnings are reviewed. The gravity equation amounts to saying that trade flows follow a power law in distance (or geographic barriers). It is concluded that in the environment with firm heterogeneity, the power law in firm size is the key condition for the gravity equation to arise. A distribution is said to follow a power law if its tail probability follows a power function in the distribution’s right tail. The second part of this article reviews the literature that provides the microfoundation for the power law in firm size and reviews how this power law (in firm size) may be related to the power laws in other distributions (in incomes, firm productivity and city size).

Psychophysical Relationships Between Perceived Sweetness and Color in Cherry-Flavored Beverages

1982 ◽  
Vol 45 (7) ◽  
pp. 601-606 ◽  
Author(s):  
J. L. JOHNSON ◽  
E. DZENDOLET ◽  
R. DAMON ◽  
M. SAWYER ◽  
F. M. CLYDESDALE
Keyword(s):  
Power Function ◽  
Magnitude Estimation ◽  
Power Law ◽  
Narrow Range ◽  
Sucrose Concentration ◽  
Color Intensity ◽  
Men And Women ◽  
Recording Spectrophotometer ◽  
Highly Correlated ◽  
Power Function Exponent

Sweetness of cherry-flavored and colored beverages, containing 3.2 to 4.8% sucrose, was quantified by a panel of 10 men and women, ages 22–50, using magnitude estimation. Five intensities of cherry colors were formulated using increasing volumes of Red 40 and a constant volume of both Blue 1 and imitation cherry flavoring. Color measurements from the Gardner XL-23 Colorimeter and the G. E. Recording Spectrophotometer were converted to L*, a* and b*. Sweetness was evaluated against sucrose concentration and arctan (a*/b*). Magnitude tests to evaluate color acceptability and pleasantness were also conducted. All magnitude estimates were normalized and subjected to a two-way ANOVA. Sweetness perception was highly correlated with increasing sucrose concentration (r2> .90), producing a power function exponent of 1.98. Sweetness increased approximately 3 to 13% with increasing color intensity in solutions containing 3.96 to 4.4% sucrose. The exponent describing the sweetness-color relationship was less than 1.0, and followed the power law over a narrow range of color intensities. Color 4 was the most acceptable color and color 3 containing 4.6% sucrose had the most pleasant taste. Color might be used to replace some sucrose and can optimize pleasurable taste sensations.

Confined turbulent entrainment across density interfaces

2015 ◽  
Vol 779 ◽  
pp. 116-143 ◽  
Author(s):  
Ajay B. Shrinivas ◽  
Gary R. Hunt
Keyword(s):  
Secondary Flow ◽  
Power Law ◽  
Lower Layer ◽  
Experimental Studies ◽  
Density Interface ◽  
Turbulent Entrainment ◽  
Steady Rate ◽  
Density Interfaces ◽  
Universal Law ◽  
Physical Reasons

In pursuit of a universal law for the rate of entrainment across a density interface driven by the impingement of a localised turbulent flow, the role of the confinement, wherein the environment is within the confines of a box, has to date been overlooked. Seeking to unravel the effects of confinement, we develop a phenomenological model describing the quasi-steady rate at which buoyant fluid is turbulently entrained across a density interface separating two uniform layers within the confines of a box. The upper layer is maintained by a turbulent plume, and the localised impingement of a turbulent fountain with the interface drives entrainment of fluid from the upper layer into the lower layer. The plume and fountain rise from sources at the base of the box and are non-interacting. Guided by previous observations, our model characterises the dynamics of fountain–interface interaction and the steady secondary flow in the environment that is induced by the perpetual cycle of vertical excursions of the interface. We reveal that the dimensionless entrainment flux across the interface $E_{i}$ is governed not only by an interfacial Froude number $\mathit{Fr}_{i}$ but also by a ‘confinement’ parameter ${\it\lambda}_{i}$, which characterises the length scale of interfacial turbulence relative to the depth of the upper layer. By deducing the range of ${\it\lambda}_{i}$ that may be regarded as ‘small’ and ‘large’, we shed new light on the effects of confinement on interfacial entrainment. We establish that for small ${\it\lambda}_{i}$, a weak secondary flow has little influence on $E_{i}$, which follows a quadratic power law $E_{i}\propto \mathit{Fr}_{i}^{2}$. For large ${\it\lambda}_{i}$, a strong secondary flow significantly influences $E_{i}$, which then follows a cubic power law $E_{i}\propto \mathit{Fr}_{i}^{3}$. Drawing on these results, and showing that for previous experimental studies ${\it\lambda}_{i}$ exhibits wide variation, we highlight underlying physical reasons for the significant scatter in the existing measurements of the rate of interfacial entrainment. Finally, we explore the implications of our results for guiding appropriate choices of box geometry for experimentally and numerically examining interfacial entrainment.

Scaling Apparent Distance in a Large Open Field: Presence of a Standard Does Not Increase the Exponent of the Power Function

1982 ◽  
Vol 55 (1) ◽  
pp. 267-274 ◽  
Author(s):  
José Aparecido Da Silva ◽  
Raquel Alves Dos Santos
Keyword(s):  
Open Field ◽  
Power Function ◽  
Magnitude Estimation ◽  
Power Law ◽  
Apparent Distance ◽  
Physical Distance ◽  
Actual Distance ◽  
Standard Distance ◽  
Outdoor Setting

Apparent distance in a large open field was scaled by the method of magnitude estimation with or without a standard distance present. The presence of the standard did not increase the exponent of the power law. The average exponent of the power function relating judged to physical distance was .87. The results are consistent with those of other studies showing that apparent distance is a decelerating function of actual distance in a natural outdoor setting.

When Power Functions Fail: A Theoretical Explanation

1970 ◽  
Vol 30 (2) ◽  
pp. 415-425 ◽  
Author(s):  
John C. Baird ◽  
Timothy Stein
Keyword(s):  
Computer Simulation ◽  
Power Function ◽  
Stimulus Intensity ◽  
Weber Fraction ◽  
Theoretical Explanation ◽  
Power Functions ◽  
Simulation Experiments ◽  
Simple Power ◽  
Simple Power Function

When the simple power function fails to describe psychophysical results, it is necessary to add or subtract a constant from either the stimuli or responses in order to reinstitute a power function. It is suggested here that this failure results from the nonlinearity of the function between the Weber fraction and stimulus intensity. Computer simulation experiments were conducted which supported this contention.

Memory Psychophysics for Areas: Distortion in Natural Memory of a School Campus

1991 ◽  
Vol 73 (3) ◽  
pp. 995-1003 ◽  
Author(s):  
Makiko Naka ◽  
Kuniko Minami
Keyword(s):  
High School ◽  
Power Function ◽  
Power Law ◽  
Junior High School ◽  
Natural Environment ◽  
Junior High ◽  
School Facilities ◽  
Junior High Students ◽  
Visual Areas ◽  
University Undergraduates

As the perceived magnitude of a stimulus is related by power function to the physical magnitude, the remembered visual areas and length are also related by power function to the actual areas and length, The main purpose of this study is to examine whether the power law is also applicable to remembered areas in natural environment, e.g., a school campus, and to its old memory. 31 junior high students and seven university undergraduates who graduated from the same junior high school seven years before were asked to draw a layout of the school campus. The areas of the school facilities and field, and other features of drawings such as the number of recalled facilities and objects, and direction of the sketch were assessed. Analysis showed that the areas remembered by the junior high subjects followed the power law while those remembered by the undergraduates did not. The divergence of exponents observed for undergraduates was accounted for by reconstruction by schema.

Combined Effects of Recovery Period and Stimulus Intensity on the Human Auditory Evoked Vertex Response

1973 ◽  
Vol 16 (2) ◽  
pp. 297-308 ◽  
Author(s):  
David A. Nelson ◽  
Frank M. Lassman
Keyword(s):  
Power Function ◽  
Stimulus Intensity ◽  
Recovery Period ◽  
Normal Hearing ◽  
Response Amplitude ◽  
Evoked Response ◽  
Dual Function ◽  
Combined Effects ◽  
Logarithmic Function ◽  
Recovery Function

Averaged auditory evoked vertex responses were obtained from eight normal-hearing subjects in response to 32 monaural 1000-Hz tone bursts at 30 combinations of recovery period and stimulus intensity. From curves describing N 1 -P 2 peak-to-peak amplitudes, an equation was derived that describes the combined effects of recovery period and stimulus intensity on evoked response amplitude. The results show evoked response amplitude to be a dual function of both recovery period and stimulus intensity. At a given stimulus intensity, evoked response amplitude increases as a logarithmic function of recovery period. At a given recovery period, evoked response amplitude increases as a power function of stimulus intensity. The combined effects of recovery period and stimulus intensity produce equal ratio changes in the slope of the recovery function with equal ratio changes in stimulus intensity.

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