Психофизика заңдары: Вебер мен Фэхнердің қатынастары

Related laws in the field of psychophysics

The Weber–Fechner laws are two related scientific laws in the field of psychophysics, known as Weber's law and Fechner's law. Both relate to human perception, more specifically the relation between the actual change in a physical stimulus and the perceived change. This includes stimuli to all senses: vision, hearing, taste, touch, and smell. Ernst Heinrich Weber states that "the minimum increase of stimulus which will produce a perceptible increase of sensation is proportional to the pre existent stimulus," while Gustav Fechner's law is an inference from Weber's law (with additional assumptions) which states that the intensity of our sensation increases as the logarithm of an increase in energy rather than as rapidly as the increase.

Both Weber's law and Fechner's law were formulated by Gustav Theodor Fechner (1801–1887). They were first published in 1860 in the work Elemente der Psychophysik (Elements of Psychophysics). This publication was the first work ever in this field, and where Fechner coined the term psychophysics to describe the interdisciplinary study of how humans perceive physical magnitudes. He made the claim that " psycho physics is an exact doctrine of the relation of function or dependence between body and soul."

Although Weber's law includes a statement of the proportionality of a perceived change to initial stimuli, Weber only refers to this as a rule of thumb regarding human perception. It was Fechner who formulated this statement as a mathematical expression referred to as Weber contrast. Weber contrast is not part of Weber's law. Since Weber's law fails at low intensity, so does Fechner's law.

Weber's law does not quite hold for loudness. It is a fair approximation for higher intensities, but not for lower amplitudes.

Weber's law does not hold at perception of higher intensities. Intensity discrimination improves at higher intensities. The first demonstration of the phenomena was presented by Riesz in 1928, in Physical Review. This deviation of the Weber's law is known as the "near miss" of the Weber's law. This term was coined by McGill and Goldberg in their paper of 1968 in Perception & Psychophysics. Their study consisted of intensity discrimination in pure tones. Further studies have shown that the near miss is observed in noise stimuli as well. Jesteadt et al. (1977) demonstrated that the near miss holds across all the frequencies, and that the intensity discrimination is not a function of frequency, and that the change in discrimination with level can be represented by a single function across all frequencies: This magnitude scale was invented by the ancient Greek astronomer Hipparchus in about 150 B. C. He ranked the stars he could see in terms of their brightness, with 1 representing the brightest down to 6 representing the faintest, though now the scale has been extended beyond these limits; an increase in 5 magnitudes corresponds to a decrease in brightness by a factor of 100.

Perception of Glass patterns and mirror symmetries in the presence of noise follows Weber's law in the middle range of regularity to noise ratios (S), but in both outer ranges, sensitivity to variations is disproportionally lower. As Maloney, Mitchison, & Barlow (1987) showed for Glass patterns, and as van der Helm (2010) showed for mirror symmetries, perception of these visual regularities in the whole range of regularity to noise ratios follows the law p = g/(2+1/S) with parameter g to be estimated using experimental data.

For vision, Weber's law implies constancy of luminance contrast. Suppose a target object is set against a background luminance In order to be just visible, the target must be brighter or fainter than the background by some small amount The Weber contrast is defined as , and Weber's law says that should be constant for all
Human vision follows Weber's law closely at normal daylight levels (i. e. in the photopic range) but begins to break down at twilight levels (the mesopic range) and is completely inapplicable at low light levels (scotopic vision). This can be seen in data collected by Blackwell and plotted by Crumey, showing threshold increment log versus background luminance log for various targets sizes. At daylight levels, the curves are approximately straight with slope 1, i. e. log = log, implying is constant. At the very darkest background levels ( ≲ 10− 5 cd m−2, approximately 25 mag arcsec−2) showed,
the population distribution of the intrinsic excitability or gain of a neuron is a heavy tail distribution, more precisely a lognormal shape, which is equivalent to a logarithmic coding scheme. Neurons may therefore spike with 5–10 fold different mean rates. Obviously, this increases the dynamic range of a neuronal population, while stimulus derived changes remain small and linear proportional. An analysis of the length of comments in internet discussion boards across several languages shows that comment lengths obey the lognormal distribution with great precision. The authors explain the distribution as a manifestation of the Weber–Fechner law.

The Weber–Fechner law has been applied in other fields of research than just the human senses.

Psychological studies show that it becomes increasingly difficult to discriminate between two numbers as the difference between them decreases. This is called the distance effect. This is important in areas of magnitude estimation, such as dealing with large scales and estimating distances. It may also play a role in explaining why consumers neglect to shop around to save a small percentage on a large purchase, but will shop around to save a large percentage on a small purchase which represents a much smaller absolute dollar amount.

It has been hypothesized that dose response relationships can follow Weber's Law which suggests this law – which is often applied at the sensory level – originates from underlying chemoreceptor responses to cellular signaling dose relationships within the body. Dose response can be related to the Hill equation, which is closer to a power law.

There is a new branch of the literature on public finance hypothesizing that the Weber–Fechner law can explain the increasing levels of public expenditures in mature democracies. Election after election, voters demand more public goods to be effectively impressed; therefore, politicians try to increase the magnitude of this "signal" of competence – the size and composition of public expenditures – in order to collect more votes.

Preliminary research has found that pleasant emotions adhere to Weber’s Law, with accuracy in judging their intensity decreasing as pleasantness increases. However, this pattern wasn't observed for unpleasant emotions, suggesting a survival related need for accurately discerning high intensity negative emotions.