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An n-dimensional Weber Law and the Corresponding Fechner Law.
MedLine Citation:
PMID:  10831375     Owner:  NLM     Status:  Publisher    
Abstract/OtherAbstract:
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.
Authors:
Drösler
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Publication Detail:
Type:  JOURNAL ARTICLE; JOURNAL ARTICLE    
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:  -    
Affiliation:
Universität Regensburg
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