Before entering the theory of Weber’s Law, we must know that one of the most important parts of psychology is the functional analysis that can exist between physical stimuli and effectorial or open responses , since it is what has given rise to to psychophysical laws . The study of the stimuli and the observable responses has allowed the knowledge of the sensorimotor conditioning . Also, it is possible to know how external stimuli produce inferior responses, which would deal with subjective experiences only accessible through an introspective process, as in the case of sensations.

This means that everything has its effect-cause that is caused by an agent, both internal and external and that has a series of visible consequences in the human being, in a clear and sensitive way that not for everyone can be the same, for what minimally the perception can be relative in some cases if the correct formula is not applied, which in that case the evidence in clear and absolute before any example.

What is the Law and what is the Weber-Fechner Law?

The origins of this theory come from the German philosopher Fechner, who was also a trained physician and professor of physics and philosophy . As if that were not enough, I elaborate a psychophysical law , to be exact the first law of psychophysics , from the use of direct methods. To achieve the results of his theory, he started from Weber’s Law establishing a quantitative relationship between the magnitude of a physical stimulus and how it is perceived.

However, it must be clear that it is a shared theory as it was first proposed by Ernst Heinrich Weber in 1860 in his book ‘ Elemente der Psychophysik ‘, and elaborated up to what we know today by Gustav Theodor Fechner , hence the compound name . For his part, Weber established the law of sensation (Weber Law), in which he proposed the mathematical relationship that existed between the intensity of any stimulus and the sensation it produced.

Thanks to these discoveries based on scientific studies related to the field of psychology, it was concluded that all human acts could be explained by physical-chemical principles , which allowed us to consider psychology more specifically psychophysics , as incipient sciences.

Mathematical formulation of the Weber-Fechner Law

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

• P = kx log (l) = Ley de Fechner

The letter ‘k’ is a constant and ‘l’ corresponds to the intensity . In this way, Fechner argues that “when the intensity of the stimulus grows according to a geometric progression, the sensation grows according to an arithmetic progression (logarithmic)”.

Physical example

It must be taken into account that Weber’s Law was only fulfilled when the stimulus tended to mean values . In this way, it was true for most of the senses, but as long as the intensity of that stimulus being analyzed was not very close to the threshold . To understand with an example the Weber-Fechner Law will be understood much better with a simple example.

If we hold an object weighing 100 grams with our hand , it is most likely that it cannot be differentiated from another object that weighs 105 grams, since the difference in weight is minimal. However, if that object weighs 110 grams, the same is already true if we begin to notice more weight in our hand. In this case, the threshold for discerning the change in mass is only 10 grams. In the case of holding an object of about 1,000 grams, 10 grams will not be enough for us to notice the difference, as the threshold is proportional to the magnitude of the stimulus. In this case, we will need to add 100 grams more to be able to notice the odd difference in weight in order to compare .

Theories prior to the Weber-Fechner Law

The history of psychophysics has a long history from the Weber-Fechner Law . The first theories that were formulated were aimed at studying stimuli that are difficult to detect , that is, those that correspond to low intensity , and for this they proposed two theories that stood out . One of them, called the classical threshold theory and on the other hand, the signal detection theory or response threshold theory.

This theory encompasses and defines two types of thresholds:

1. Absolute threshold . This type deals with the minimum amount of energy (E) that an observer can detect.
2. Differential threshold . In this case, this theory consists of detecting the smallest difference of two stimuli (EE) that can be detected. That is, the minimum increase in energy necessary for an increase in the sensation caused by said stimulus to be perceived.