Weber Fechner law is a law that shows the relationship between psychological quantity and physical quantity.German physiologistErnst Heidrich Weber It is found that the difference amount of the same stimulus must reach a certain proportion to cause different feelings.This ratio is a constant, expressed by the formula: Δ I（Difference threshold）/I (standard stimulus intensity)=k (constant/Weber fraction), which isWeber's law。 The minimum perceptible difference (continuous difference threshold) is taken as the unit of sensory quantity, that is, every increase of difference threshold, the psychological quantity increases by one unit.Perception vsphysical quantityThe logarithm of is proportional to the value, that is, the increase of sense quantity lags behind the increase of physical quantity, and the physical quantity isGeometric seriesGrowth, but psychological quantityarithmatic seriesThe empirical formula of growth is called Fichner's law or Weber Fichner's law.Suitable for medium intensity stimulation.
Fichner's law, also known as Weber Fichner's law, is a law that shows the relationship between psychological quantities and physical quantities.German physicistsPsychophysicsFounder GT.fechner And EH. Used to reveal the quantitative relationship between psychological quantities and physical quantitiesLaws。This law isWeber's lawIt is developed on the basis of.
Weber's law
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Basic Introduction
Weber's lawThat is, sensoryDifference thresholdFollow the originalStimulus quantityIt changes with the change of, and shows a certain regularity, which is expressed by the formula: △ I/I=K (where I is the original stimulus amount, △ I is the difference threshold at this time, and K is a constant, also known as Weber's rate).
Profile
E. H. Weber is professor of anatomy at the University of Leipzig, GermanyTwo-point thresholdAnd minimum perceptible errorPsychophysicsFounder of.
Before Weber, French physicist PBugleHe once made an experiment to measure the sensitivity of the eye to light. He constantly changed the relative position between the candle and the pinhole, so that the light could be cast on the distant screen through the pinhole. He found that in order to create a distinguishable shadow in the adjacent dark area, the brightness of the two must be at least 64:1 different.Bugel's research has no principle of special significance, but it is pregnant with“Minimum perceptible error”The idea of question has become a cornerstone of epoch-making research work in Weber's hands.
The whole research
Weber started his research from "muscle sensation". He wanted to know how much muscle sensation can distinguish between different weights.He experimented on four subjects with three sets of weights with different weights, and found that the discrimination was not determined by the absolute value of the weight difference between the two weights, but by the ratio of this absolute value to the standard weight value.Under the optimal conditions, the difference between the weights can be clearly detected at about 29:30.Later, Weber carried out similar experiments on other sensory channels and got the same results, that is, the ability to distinguish two stimuli does not depend on the absolute value of the difference between the two, but depends on the differenceRelative value。In his experiment, he also found that the "minimum perceptible difference" can be expressed by a fraction, although this fractionSubjectsHis sensory channels are different and varied, but they are constant for certain sensory channels. Therefore, he believes that we can determine the constant score of "minimum perceptible difference" for each sense.
research meaning
Weber's experiment made the physiologists at that time realize that it is feasible and important to explore some purely psychological problems that have always been ignored in the laboratory.Weber's question attracted people likeHermann Von Helmholtz 、fechner While waiting for a group of talented people, he also delved into many such problems and pointed out ways to systematically study them.
Later, Weber's former studentsUniversity of LeipzigFishner, a professor of physics at the University of California, transformed Weber's research results into mathematical form: Δ I/I=K, which is now familiar to peopleWeber's law。In this formula, Δ I represents the minimum perceptible difference of stimulus (J.N.D.), I represents the intensity of standard stimulus, and K is specificSensory meatusIs also calledWeber's ratioOr Weber score.
Weber's law provides us with an important indicator of comparative discrimination.If you want to compare the discrimination of a certain sensory tract of different individuals and use different standard stimuli, you cannot useDifference thresholdThe absolute value of is compared with Weber's ratio.On the other hand, since the reciprocal 1/K of Weber's ratio can be used asReceptivitySo we can also compare the receptivity of different sensory channels through Weber's ratio.
Fechner's law
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Basic Introduction
German physicistsPsychophysicsFounder GT.fechner The law named after is used to reveal the quantitative relationship between psychological quantity and physical quantity.
Profile
youthfechner In Leipzig, he received systematic medical, physical and chemical training, which made him believe that nature is orderly and can study the spiritual world of human beings like nature, but "how can quantitative science teach us to study human spirit in the relationship between human spirit and the universe?How can those sophisticated methods that have been successfully applied at the intermediate level of natural science turn to help the study of the inner world?How can we see the soul under direct and reportable observation? "These problems puzzled Fechner for a long time, and he tried to find a way to determine the relationship between physical and mental activities.On the morning of October 22, 1850, Fishner lay in bed and suddenly had an idea. He found that there was a quantitative relationship in daily lifearithmatic seriesWhen growing, the stimulus seems to beGeometric seriesGrowing.If one bell is ringing, adding another one will give us a much stronger impression than adding one more bell to 10 rings;If 4-5 candles are glowing, lighting one more can only make a slight difference, while if only two candles were lit, it will have a considerable impact.The effect of stimulation is not absolute, but relative, that is, it is related to the existing sensory quantity.fechner Feeling that he might be in the spiritual world withMaterial worldA simple mathematical relationship was found in.So he started a series of brightness experiments, weight lifting experiments and visual and tactile distance experiments to verify his hypothesis about the relationship between sensory intensity and stimulus intensity.Shortly after the experiment began, he stumbled upon Weber's work more than 20 years ago.Weber has proved that there is a relationship between stimulus intensity and the ability to distinguish between two stimuli. This relationship is governed by a certain rule: "minimum perceptible difference" is the constant fraction of standard stimulus.Fishner summarized Weber's discovery with formula surface Δ I/I=K and named itWeber's law。He noticed the relationship between Weber's law and his own hypothesis.He grasped it, made full use of it, and did a lot of experiments to confirm it.howeverfechner There is still a big difference between Weber's hypothesis and Weber's research. Weber is concerned about "the minimum perceptible difference", while Fishner is concerned about obtaining aMaterial worldDescription of the relationship with the spiritual world.
The whole research
fechner fromWeber's ratioSee the possibility of measuring suprathreshold sensation in.stayWeber's lawΔ I/I=K, Δ I representsDifference threshold, also called minimum perceptible error.From this point of view, Fechner believes that each minimum perceptible difference can be regarded as a minimum change in sensation, and assumes that the subjective quantities of each minimum perceptible difference are equal.For example, if Weber's ratio of weight lifting is 0.03, the subjective weight difference of any weight, whether a toothpick or a bag of cement, is equal as long as the original weight is increased or decreased by 0.03 times.Fishner proposed a method to calculate suprathreshold sensory quantity, that isAbsolute thresholdThe minimum perceptible error of upward number.If a stimulus is 10 minimum perceptible differences from the absolute threshold, the amount of sensation caused by the stimulus intensity is 10 units.
If R is used to represent the change of minimum sensation, the above formula isdifferentialIt is assumed that the suprathreshold sensory quantity is equal to the sum of many minimum sensory quantities, so integrating the above formula can get that the suprathreshold sensory quantity is R:
Fechner's law is a simple law, whose formula is S=KlgR, where S is the sensory intensity, R is the stimulus intensity, and K is a constant.In short, this law explains all human feelings, including vision, hearingSkin sense(including pain, itching, touch, temperature), taste, smell, electric shock, etc., all follow the principle that feeling is not proportional to the strength of the corresponding physical quantity, but rather to the strength of the corresponding physical quantityCommon logarithmProportional.This law is a 19th century German psychologistfechner (Gustav Theodor Fechner, 1801-1887) was founded on the law of his cousin and teacher Ernst Heinrich Weber (1795-1878), so it is also called Weber Fechner's law,PsychophysicsWas established as a new discipline.
Practical examples
We can give a few practical examples of the application of Fechner's law below.
The unit of use is "Bel" (Bl). We usually use 1/10 of it as the practical unit, that is, "decibel" (dB).The loudness of loud speaking is 6.5dB, which is 6.5 times of the 1dB loudness of rustling leaves, so the intensity difference between the two is 10 times (6.5-1), about 316000 times.
Measure the pitch of the sound:
One apartoctaveThe two tones ofVibration frequencyThe difference is twice, but the human ear will think that the difference is an octave.We divide an octave into twelve half intervals, so each half interval is at the bottom of twologarithm1/12 of.
Measure the visual brightness of stars:
User“Apparent magnitude”。The magnitude difference is 5 and the brightness difference is 100 times.
Acoustic Applications
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To judge different pitches or intervals, human hearing follows a sense rule called Weber Fisher law.This law states that the increase of sensation is equal to the ratio of stimulation.The octave of pitch feels like a 2:1Frequency ratio。To soundloudnessThere are two judgments of“Limit point”: Audible valve andsense of painValve.If the sound intensity at the limit point of the auditory valve is considered as 1, the sound intensity at the limit point of the pain valve is 1 trillion.According to Weber Fechner lawLoudness levelyeslogarithmBased on the strength ratio of 10:1, this is known as 1 bel.The sense range of loudness is divided into 12 large units, and the increase of 1 dB is divided into 10 smaller increases called decibel, that is, 1 dB=10 dB.The difference of 1 decibel loudness is about the smallest change that can be felt by the human ear for our hearing in the middle sound area.
AboutloudnessPerception: the intensity range of audible sounds in the human ear, the true number logarithmic relationship between objective intensity and subjective loudness (Weber Fechner's Law), and the different intensities of sounds in different sound areas may be perceived as the same loudness subjectively（loudness Curve), the influence of homophony continuity on loudness sense, these aspects have accumulated more reliable data.
Marketing Application
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Weber-fechner (Feiler) Law is a law in marketing that studies the buyer's perception of price difference.The so-called sense of price difference refers to the psychological cognition of buyers when facing price adjustment, change or different prices.If consumers can make a rational judgment on the price difference, then when the absolute price difference is the same, the same behavior should occur.However, both practice and experimental results show that buyers have different responses to the same price difference.Here are two experiments under different assumptions:
Experiment A: Suppose that the price of the calculator in the stationery store you visit is 20 yuan, while someone tells you that the price in other stores is 15 yuan.
Experiment B: Suppose that the price of the calculator in the stationery store you visit is 120 yuan, while someone tells you that the price in other stores is 115 yuan.
So, in which case would you change to buy in other stores?
The result of the experiment is that in experiment A, about 68% of the people will buy from another store, and in experiment B, about 29% of the people will be willing to buy from another store.Does the result of this experiment have any special meaning?As long as we carefully analyze the price difference between the two groups of experiments, we will find that the price difference between the two groups of experiments is actually the same (both are 5 yuan), so the difference of the experimental results is that if shoppers are rational economic people, why are their behaviors so different in the face of the same economic losses?Further analysis shows that although the actual savings of shoppers in both experiments are 5 yuan, in A, 5 yuan is a large number relative to the total price;In B, 5 yuan is insignificant relative to the price.This is the famous Weber Fechner's law in marketing: the buyer's perception of price is related to the level of the basic price, and the buyer's perception of price depends more on the relative value than the absolute value.
According to Weber Fechner's law, the buyer's perception of price change depends more on the percentage of change than the absolute value of change;And there is a boundary above and below the product price.Adjusting the price beyond the price is easy to be perceived by buyers, while the adjustment within the boundary is often ignored by buyers.[1]
