Introduction
Fei Sina's law is also known as Weber-Fisher's law, it is the relationship between psychological and physical quantities The law. It is the law of the number of psychological quantities and physical quantities with German physics, Psychological physics founder G. T. Fisher and E.H. Weber named. This law is developed on the basis of Weber's law.
Weber Law
Basic Introduction
Weber Law, that is, the difference of the sensory threshold varies with the change of the original stimulus, and manifested as a certain regularity The formula is represented by the formula, that is, ΔO / I = K (where i is the original stimulus amount, ΔI is the difference threshold at this time, k is constant, also known as Weber rate).
Character introduction
E.h. Weber is anatomy professor at Leipzig University, Germany, and he has become a founder of psychological physics because of two-point threshold and minimum difference.
Before Weber, French physicist P. Bugr has done an experiment that measured the sensitivity of the eye on the light, he continued to change the relative position between candles and pinh holes, making the light pass The pinhole is in a distant screen, found that in order to create a distinguished shadow in the adjacent shaded zone, the brightness of the two must be at least 64: 1. Buger 's research does not have the principle of the owner of the owner, but this is the idea of "the minimum difference" problem, which has become a tasting research work in Weber.
Research started
Weber's research started from "muscle feelings", what he wants to understand the muscles of muscle can distinguish between the weight different weights. He experimented four trials with three different weights of heavy objects. It is found that the discrimination is not dependent on the absolute value of the weight difference in weight, but is dependent on this absolute value and the standard weight value. Under the optimal conditions, the difference between the weight is approximately 29:30, it can be explicitly recognized. Later, Weber made a similar experiment on other sensations, namely the same result, that is, the identification ability of the two stimuli does not depend on the difference in differences, but depends on the relative value of the difference. He also found in the experiment, "Minimal Identity" can be expressed in a score, although this score varies from the sensation path of the test, but for a certain sense of feelings, it is constant, so He believes that we can determine the uncorrible score of its "minimum touch" for each sensory.
Research Significance
Weber experiments have made the physiologists at the time realized that in the laboratory, it is feasible to discuss some of the purexational problems that have been overlooked. It is also very important. of. Weber's question has attracted a group of talented people like Helmhorn, Fisherna, and he also drilled many such problems and pointed out the system to study these issues.
Later, Wetber's previous student, Physics Professor, Leipzi University, transacted Weber's research results into mathematical form: Δi / i = k, this is what people are now familiar with Weber Law. In this formula, ΔI represents the minimum sensible difference of stimulation (J.N.D.), I represents the strength of standard stimulus, k is the value of a particular sensory track, also called the Weber ratio or Weber score.
Weber's law proposes, providing us with an important indicator of comparative ability. If the standard stimulus used to compare the identification ability of different individuals, the absolute value cannot be compared with the absolute value of the difference threshold, and the Weber ratio is used to compare. On the other hand, due to the countdown 1 / k of the Weber ratio can be used as an indicator of the sensibility, we can also compare the sensibility of different sensations through the Weber ratio.
Fei Sina's law
Basic Introduction
is used by German physicist, psychological physics founder GT Fishernna named by the name The Law of the Quantity and Physical Quantity.
Character introduction
Youth Fener accepted systemic, physics and chemistry training in Leipzig, which made him believe that nature is ordered, you can have nature The study people's spiritual world, but "quantitative science can teach our spirit of cultivating people in the relationship between people. Those precision methods have been successfully applied in natural sciences, how can they help Intrinsic world research? How can we see the soul under the observation of direct and can report? "These issues have plagued Fisherna for a long time. He tried to find a way to determine the relationship between physical and mental activity. . In the morning of October 22, 1850, Fisherna was lying in bed, suddenly there was an idea. He found a quantity relationship in daily life. When the feeling intensity is growing according to the calculation level, the stimulus seems to be geometric Number growth. If a bell is ringing, then adding an impression that the impression of us is more than 10 bells; if the 4-5 candles are glowing, it will only create a minor difference, If it is only 2 candles, the effect it caused is quite large. The effect of stimulation is not absolute, but relative, that is, the existing feeling. Fisherna feels that he may find a simple mathematical relationship in the spiritual world and the material world. So he started a series of brightness experiments, weightlifting experiments and visual, tactile distance experiments to verify that his hypothesis about the relationship between feelings and stimulus. Shortly after the start of the experiment, he accidentally found more than 20 years ago Wayber's work. Weber has proven that there is a relationship between the stimulation strength and the ability to distinguish between two stimuli, which is subject to certain rules: "Minimum Icon" is the constant score of standard stimulus. Fishern's formula mean Δi / i = k summarizes Weber's discovery, and named Weber's law. He noted the relationship between Weber's law with his own hypotheses. He grasped it and fully utilized, and did a lot of experiments to confirm it. However, there is still a big difference between Fisher's hobs and Weber's research. Weber is concerned about "minimum differences", and Fisher is here to obtain a description of the relationship between the material world and spiritual world.
Study starting
Fisher saw the possibility of measuring the measuring threshold from the Weber ratio. In Weber's law Δi / i = k, ΔI represents a differential threshold, and is also the minimum difference. From this, Fisher thinks that each minimum difference can be seen as a minimum change in the feeling and assumes that the subjective amount of each minimum difference is equal. For example, the Weber ratio of weight is 0.03, then any weight, whether a toothpick is still a pack of cement, as long as it is 0.03 times the original weight, the subjective amount of the weight difference is equal. Fisher is proposed a method of calculating a threshold that is the least different from the absolute threshold. If a certain stimulus and absolute threshold are 10 minimum, the amount of sensation caused by this stimulus is 10 units.
Set the minimum sensation of R to R, the above formula is written in the form of differentiation as the sum of the sensations of the assumed threshold is equal to the sum of many minimum feelings, so the above-formula can be obtained. It is R:
this is the logarithm of Fisherna, referred to as Fisher's law. It illustrates that the amount of psychological amount is the logarithmic function of the stimulus, that is, when the irritation is increased in geometric grade, the intensity of the feel increases. The Law of Fishern was once supported by the equilation table of the differential threshold. Putting the data of this equivalent table in half a logarithmic coordinates, you can get a linear psychological measurement function.
Specific content
Fei Sina's law is a simple law, its formula is S = KLGR, where S is sensory intensity, R is stimulating strength, k is constant. Simply, this law indicates all the feelings of people, including visual, auditory, skin, tone, temperature), taste, olfactory, electric shock, etc., compliance is not intensity with corresponding physical quantities. The proportion, but is proportional to the intensity of the corresponding physical quantity. This law was established in the 19th century German heart physicist Fisher, 1801 ~ 1887), established on the law of his brother and teacher Weber, 1795 ~ 1878), which is also known as Weber-Fisher's law is precisely because of this law, psychological physics is established as a new discipline.
Actual examples
We can clearly apply the actual example of the application of Fisher's law.
Measure the sound loudness:
Using the unit "Bel" (BL), we generally use his 1/10 as a utility unit, ie "decibels" (DB). The loud voice is 6.5 dB, which is 6.5 times the loudness of the rock of the leaves of the leaves, so the intensity of the two (6.5-1) times is more than 316000 times, probably 316000 times.
Measuring the sound of the sound:
is separated by two sounds, and the vibration frequency is twice, but the human ear is distinguished, it will be considered an octave. We divide an octave and twelve and a half, so each semi-interval is different to 1/12 of the 2-bottom logarithm.
Measuring the visual brightness of the star:
Using the unit "Vision, etc.". Star is equal to 5, etc., while the brightness is 100 times.
Acoustic Application
Judging different pitch or audio, people's auditory compliance - the sensory rules of the "Weber-Felchner Law". This law clarifies that the amount of increased amount and the ratio of the stimulus are equal. The eight degree of pitch is a frequency ratio of 2: 1. The judgment of sound loudness has two "limit points": listening valve and a painful valve. If the sound intensity is considered to be 1, the limit point of the sound intensity is 1 megaby. According to Weber-Fisher's law, the loudness level used by the acousticist is logarithm, based on the intensity ratio of 10: 1, which is 1 shell (BEL) we know. The sensation range of the loudness is divided into 12 large units, and the amount of increase in 1 shell is divided into a smaller increase amount called decibel, ie 1 shell = 10 decibels. 1 decibel loudness difference is about the minimum change amount of people who can feel about human ear.
About the sense of loudness: the intensity range of human ear, the true numbers between objective strength and subjective loudness (Weber-Fisher's law), for different tones Different intensity on the voter may feel the same loudness (such as loudness curve), the same effect of the homonym, which has accumulated more conclusive data.
Marketing Applied
Weber - Fajina Law is a law in studying the price difference of buyers in marketing. The so-called price difference is to refer to the psychological cognitive level of the purchaser in the face of price adjustment, changing, or different prices. If the consumer can make a rational judgment on the price difference, then when an absolute spread, the same behavior should be produced. However, the results of practice and experiments have shown that the purchaser is not the same for the same difference. Below is an experiment of two different hypothetical conditions:
experiment A: Suppose you are 20 yuan, and someone tells you that other stores is 15 yuan.
experiments B: Suppose you have a price store calculator price of 120 yuan, and someone tells you that other stores are 115 yuan.
So, where you will change to other stores to buy?
The result of the experiment is that about 68% of people in A experiment will change a store to buy About 29% of B experiments will be willing to change a store to buy. What is the special meaning of this experiment? As long as we carefully analyze the difference in the two groups of experiments, it will find that the difference between the two groups of experiments is actually the same (all 5 yuan), so the difference between the experimental results is that if shoppers are rational economists If you have the same economic profit and loss, is there so different? Further analysis, we will find that although the actual savings in the two experiments are 5 yuan, but in A, 5 yuan relative to the price of the price is a small number; in B, 5 yuan relative to the price negligible. This is the famous Weber-Phi Na's law in the marketing student: buyers are related to the level of prices and the level of basic prices, and the purchaser's feelings of prices have more dependent on relative value, rather than absolute value.
According to Weber-Phi Na's law, the purchaser's feelings of price changes will depend on the percentage of changes, rather than the absolute value of the variation; and have a limit on the product prices. . It is easy to be conscious by purchases outside the price to the price, and adjustments within the boundaries are often ignored by the purchaser.