The Weber-Fechner Law: what is it and what does it explain?

One of the most important contributions of psychophysics and the study of perception.

Psychophysical laws establish relationships between physical stimuli and effector responses emitted by subjects; thus, psychophysics establishes the relationship between physical stimuli and perception.

On the other hand, it also studies how external stimuli produce internal responses (subjective experiences), only accessible by the subject himself through introspective processes. In this article we will learn about the Weber-Fechner Law, considered the first law of psychoanalysis.considered the first law of psychophysics.

Background: Weber's Law

Fechner, a German philosopher, physician by training and professor of physics and philosophy, elaborated a law in psychophysics, specifically the first law of psychophysicsThe use of indirect methods was the starting point. For this purpose, he started from Weber's Law and the postulate that establishes the equality of just perceptible differences.

With regard to Weber's Law, he established the concept of DAP (just perceptible difference) as the unit of measurement of the differential threshold. According to Weber the WTP depends on the magnitude or intensity of E (stimulus)and its mathematical formula is as follows:

WTP = k x S (where "k" is a constant and "S" is the intensity of the stimulus.

However, Weber's Law was only true when the stimulus tended to average values; thus, it was true for most of the senses, as long as the intensity of the stimulus was not very close to the threshold..

Weber-Fechner law: characteristics

The Weber-Fechner law establishes a quantitative relationship between the magnitude of a physical stimulus and how it is perceived by the subject. This law was initially proposed by Ernst Heinrich Weber (1795-1878) (German physician and anatomist) and later elaborated to its present form by Gustav Theodor Fechner (1801-1887), mentioned above.

This law states that "the smallest discernible change in the magnitude of a stimulus is proportional to the magnitude of the stimulus." This can be said in many other ways for us to understand; for example, that "the intensity of sensation is proportional to the logarithm of the intensity of the stimulus", or that "if a stimulus grows in geometric progression, perception will evolve in arithmetic progression".

Example

To better understand the Weber-Fechner Law, let us illustrate it with an exampleIf we hold in our hand a ball weighing 100 grams, we may not be able to distinguish it from a ball weighing 105 grams, but we can distinguish it from a ball weighing 110 grams. In this case, the threshold for discerning the change in mass is 10 grams.

But in the case of holding a 1,000-gram ball, 10 grams will not be enough for us to notice the difference, since the threshold is proportional to the magnitude of the stimulus. Instead, we will need to add 100 grams to notice the difference, for example.

Mathematical formulation

The mathematical formulation of the Weber-Fechner Law is as follows:

P = k x log (l) = Fechner's Law

Where "k" is a constant and "l" is the intensity.

Thus, Fechner argues that when the intensity of the stimulus grows according to a geometrical progression the sensation grows according to an arithmetic progression (logarithmically).

Preceding theories

As for the history of psychophysics, and prior to the Weber-Fechner Law, the first theories formulated were oriented to study stimuli that were difficult to detect (of low intensity); for this purpose, two outstanding theories were formulated: the classical threshold theory and the signal detection theory (or response threshold theory). (or response threshold theory).

1. Classical threshold theory

This theory encompasses and defines two types of thresholds:

1.1. Absolute threshold

This is the the minimum amount of energy (E) that an observer can detect..

1.2. Differential threshold

It consists of the smallest difference between two stimuli (EE) that can be detected, or, in other words, the minimum increase in energy necessary for an increase in sensation to be perceived..

2. Signal Detection Theory (SDT) (or response threshold theory)

The SDT dispenses with the concept of threshold and assumes that in the face of any stimulation, the result of the sensory process will consist of a sensation that can adopt multiple values.

This theory considers that the sensory system of people is subject to fluctuations, so that the level of sensation can be, so that the level of the sensation may vary upon the presentation of the same stimulus; for example adopting different values, or, on the contrary, being identical upon the presentation of different experimental conditions.

Bibliographical references:

• Norwich, K. (2003). INFORMATION, SENSATION, and PERCEPTION. Biopsychology, University of Toronto.
• Goldstein, E.B. (2006). Sensation and perception. 6th ed. Debate. Madrid