The Weber-Fechner Law: what it is and what it explains

The psychophysical laws establish relationships between physical stimuli and effector responses emitted by the 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 psychophysics.

• Related article: "Gustav Theodor Fechner: biography of the father of psychophysics"

Background: Weber's Law

Fechner, a German philosopher, physician by training, and professor of physics and philosophy, drew up a law in psychophysics, specifically the first law of psychophysics, from the use of indirect methods. To do this, he started from Weber's Law and the postulate that establishes the equality of justly perceptible differences.

As for Weber's Law, he established the concept of DAP (barely perceptible difference), as the unit of measurement of the differential threshold. According to Weber,

the DAP depends on the magnitude or intensity of the E (stimulus), and its mathematical formula is as follows:

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

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

• You may be interested in: "Psychophysics: the beginnings of Psychology"

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 into its current form by Gustav Theodor Fechner (1801-1887), already 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 the 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 geometric progression arithmetic".

Example

To better understand the Weber-Fechner Law, let's illustrate it with an example: if we hold a 100-gram ball in our hand, we may not be able to distinguish it from another 105-gram ball, but we can distinguish it from a 110-gram ball. In this case, the threshold for discerning the mass change 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 defends that when the intensity of the stimulus increases according to a geometric progression the sensation grows according to an arithmetic progression (in logarithmic form).

Preceding theories

Regarding the history of psychophysics, and prior to the Weber-Fechner Law, the first Formulated theories were aimed at studying difficult-to-detect stimuli (of low intensity); For this, two notable theories were formulated: classical threshold theory and signal detection theory (or response threshold theory).

1. classical threshold theory

This theory encompasses and defines two types of thresholds:

1.1. absolute threshold

Is about 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 (TDS) (or Threshold Response Theory)

The TDS dispenses with the concept of threshold and assumes that before any stimulation, the result of the sensory process will consist of a sensation that can take on multiple values.

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

Bibliographic references:

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