Document Detail

An n-dimensional Weber Law and the Corresponding Fechner Law.
MedLine Citation:
PMID:  10831375     Owner:  NLM     Status:  Publisher    
Weber's law of 1834, DeltaS/S=c for the just noticeable difference (jnd), can be written as S+DeltaS=kS, k=1+c. It follows that the stimulus decrement required to elicit one jnd of sensation is S-DeltaS*=k(-1)S. If generalized for two stimulus dimensions and two corresponding response dimensions, Weber's law would have to state such equations for all directions of change in the plane. A two-dimensional Weber law with exactly these properties is realized by [S(x)+DeltaS(x)(straight theta), S(y)+DeltaS(y)(straight theta)]=[k(sin(straight theta))S(x), k(cos(straight theta))S(y)] which determines the stimulus coordinates for all stimuli just noticeably different from the stimulus (S(x), S(y)) in all directions 0</=straight theta</=2pi. Fechner's problem now is understood as finding a transformation of the plane which maps the set of stimuli one jnd apart from the standard stimulus onto a unit circle around the standard stimulus' image. This transformation (R(2)(+)-->R(2)) is [x, y]mapsto[log(k)(x), log(k)(y)]. The solution is generalized to arbitrarily many dimensions by substituting the sin and cos in the generalized Weber law by the standard coordinates of a unit vector. Copyright 2000 Academic Press.
Related Documents :
16812585 - Nonhumans have not yet shown stimulus equivalence.
17376705 - Continuous carry-over designs for fmri.
1940765 - Stimulus generalization, discrimination learning, and peak shift in horses.
8335075 - Three-dimensional kinematic analysis of frog hindlimb movement in reflex wiping.
1237825 - Quantitative measurement of saccade amplitude, duration, and velocity.
19111905 - Rod-cone dystrophy with maculopathy in genetic glutathione synthetase deficiency: a mor...
Publication Detail:
Journal Detail:
Title:  Journal of mathematical psychology     Volume:  44     ISSN:  -     ISO Abbreviation:  J Math Psychol     Publication Date:  2000 Jun 
Date Detail:
Created Date:  2000-05-31     Completed Date:  -     Revised Date:  -    
Medline Journal Info:
Nlm Unique ID:  2985082R     Medline TA:  J Math Psychol     Country:  -    
Other Details:
Languages:  ENG     Pagination:  330-335     Citation Subset:  -    
Universität Regensburg
Export Citation:
APA/MLA Format     Download EndNote     Download BibTex
MeSH Terms

From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine

Previous Document:  A Stochastic Version of General Recognition Theory.
Next Document:  Taenia solium: a cysteine protease secreted by metacestodes depletes human CD4 lymphocytes in vitro.