Download - Mathematical psychology1- webner fechner law
![Page 1: Mathematical psychology1- webner fechner law](https://reader031.vdocuments.site/reader031/viewer/2022021313/55847a3bd8b42a15768b4ef6/html5/thumbnails/1.jpg)
Mathematical PsychologyWeber–Fechner law
Dr Pratyush Chaudhuri
Nirmal Hospitals and clinics
![Page 2: Mathematical psychology1- webner fechner law](https://reader031.vdocuments.site/reader031/viewer/2022021313/55847a3bd8b42a15768b4ef6/html5/thumbnails/2.jpg)
• The Weber–Fechner law attempts to describe the relationship between the physical magnitudes of stimuli and the perceived intensity of the stimuli.
![Page 3: Mathematical psychology1- webner fechner law](https://reader031.vdocuments.site/reader031/viewer/2022021313/55847a3bd8b42a15768b4ef6/html5/thumbnails/3.jpg)
• Ernst Heinrich Weber (1795–1878) was one of the first people to approach the study of the human response to a physical stimulus in a quantitative fashion.
• Gustav Theodor Fechner (1801–1887) later offered an elaborate theoretical interpretation of Weber's findings, which he called simply Weber's law.
![Page 4: Mathematical psychology1- webner fechner law](https://reader031.vdocuments.site/reader031/viewer/2022021313/55847a3bd8b42a15768b4ef6/html5/thumbnails/4.jpg)
The case of weight
• smallest noticeable difference in weight (the least difference that the test person can still perceive as a difference), was proportional to the starting value of the weight.
![Page 5: Mathematical psychology1- webner fechner law](https://reader031.vdocuments.site/reader031/viewer/2022021313/55847a3bd8b42a15768b4ef6/html5/thumbnails/5.jpg)
• This kind of relationship can be described by a differential equation as,
where dp is the differential change in perception, dS is the differential increase in the stimulus and S is the stimulus at the instant. A constant factor k is to be determined experimentally.
![Page 6: Mathematical psychology1- webner fechner law](https://reader031.vdocuments.site/reader031/viewer/2022021313/55847a3bd8b42a15768b4ef6/html5/thumbnails/6.jpg)
• Integrating the above equation gives
where C is the constant of integration, ln is the natural logarithm.
![Page 7: Mathematical psychology1- webner fechner law](https://reader031.vdocuments.site/reader031/viewer/2022021313/55847a3bd8b42a15768b4ef6/html5/thumbnails/7.jpg)
• To determine C, put p = 0, i.e. no perception; then subtract − klnS0 from both sides and rearrange:•
• where S0 is that threshold of stimulus below which it is not perceived at all.
• Substituting this value in for C above and rearranging, our equation becomes:
•
![Page 8: Mathematical psychology1- webner fechner law](https://reader031.vdocuments.site/reader031/viewer/2022021313/55847a3bd8b42a15768b4ef6/html5/thumbnails/8.jpg)
• The relationship between stimulus and perception is logarithmic.
• This logarithmic relationship means that if a stimulus varies as a geometric progression (i.e. multiplied by a fixed factor), the corresponding perception is altered in an arithmetic progression (i.e. in additive constant amounts).
![Page 9: Mathematical psychology1- webner fechner law](https://reader031.vdocuments.site/reader031/viewer/2022021313/55847a3bd8b42a15768b4ef6/html5/thumbnails/9.jpg)
The case of vision
• The eye senses brightness approximately logarithmically over a fairly broad range.
• Hence stellar magnitude is measured on a logarithmic scale.
• This magnitude scale was invented by the ancient Greek astronomer Hipparchus in about 150 B.C.
![Page 10: Mathematical psychology1- webner fechner law](https://reader031.vdocuments.site/reader031/viewer/2022021313/55847a3bd8b42a15768b4ef6/html5/thumbnails/10.jpg)
The case of sound
• Another logarithmic scale is the decibel scale of sound intensity.
• In the case of perception of pitch, humans hear pitch in a logarithmic or geometric ratio-based fashion.
• For notes spaced equally apart to the human ear, the frequencies are related by a multiplicative factor.
![Page 11: Mathematical psychology1- webner fechner law](https://reader031.vdocuments.site/reader031/viewer/2022021313/55847a3bd8b42a15768b4ef6/html5/thumbnails/11.jpg)
• Notation and theory about music often refers to pitch intervals in an additive way, which makes sense if one considers the logarithms of the frequencies, as
![Page 12: Mathematical psychology1- webner fechner law](https://reader031.vdocuments.site/reader031/viewer/2022021313/55847a3bd8b42a15768b4ef6/html5/thumbnails/12.jpg)
The case of numerical cognition
• Psychological studies show that numbers are thought of as existing along a mental number line.
• Larger entries are on the right and smaller entries on the left.
• It becomes increasingly difficult to discriminate among two places on a number line as the distance between the two places decreases—known as the distance effect.
• This is important in areas of magnitude estimation, such as dealing with large scales and estimating distances.
![Page 13: Mathematical psychology1- webner fechner law](https://reader031.vdocuments.site/reader031/viewer/2022021313/55847a3bd8b42a15768b4ef6/html5/thumbnails/13.jpg)
Thank You.