Mathematical psychology1- webner fechner law

weber law of proportionate perception

1. Mathematical Psychology
Weber–Fechner law
Dr Pratyush Chaudhuri
Nirmal Hospitals and clinics

2. •The Weber–Fechner law attempts to
describe the relationship between the
physical magnitudes of stimuli and the
perceived intensity of the stimuli.

3. •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.

4. 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.

5. •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.

6. •Integrating the above equation gives
where C is the constant of integration, ln is the natural logarithm.

7. •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:
•

8. •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).

9. 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.

10. 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.

11. •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

12. 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.

13. Thank You.