Droesler, Jan (2000) An n-dimensional Weber law and the corresponding Fechner law. JOURNAL OF MATHEMATICAL PSYCHOLOGY, 44 (2). pp. 330-335. ISSN 0022-2496
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Weber's law of 1834, Delta S/S = c for the just noticeable difference (jnd), can be written as S + Delta S = kS, k = 1 + c. It follows that the stimulus decrement required to elicit one jnd of sensation is S - Delta S* = 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 + Delta S-x(0), S-y + Delta S-y(0)] = [k(sin(0))S(x), k(cos(0))S(y)] which determines the stimulus coordinates for all stimuli just noticeably different from the stimulus (S-x, S-y) in all directions 0 less than or equal to theta less than or equal to 2 pi. 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] bar right arrow [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. (C) 2000 Academic Press.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; |
| Subjects: | 100 Philosophy & psychology > 150 Psychology |
| Divisions: | Human Sciences > Institut für Psychologie > Alumni or Retired Professors > Prof. Dr. Jan Drösler |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 26 Apr 2022 14:46 |
| Last Modified: | 26 Apr 2022 14:46 |
| URI: | https://pred.uni-regensburg.de/id/eprint/42447 |
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