1 "Vision under manual operation does not belong to the category of form perception and should not be included in the five-point recording method"
Its main point is: "In statistics, homogeneity is comparable. In the five-point method, there are optotype, finger, palm and light used to measure vision, and accordingly their measured vision is different, that is, optotype and finger are used to check the cone function, that is, central vision. However, the stimulation range of manual and light sense has exceeded the central area of retina and cannot represent central vision [3]. " "The eye chart confuses the sense of light and movement of vision with the sense of form aiming at' E'." And "No light sensation, light sensation and manual operation are beyond the range of' central vision', and set the light sensation, light sensation and manual operation to 0, 1 and 2 respectively. If they are beyond the scope of this idea, it is suggested to delete [7]. "
This view was first put forward by Hu and later praised by some people. However, the author thinks that he has fallen into a misunderstanding of thinking.
As we all know, human vision is divided into shape perception and color perception, that is, the function of distinguishing the shape and outline of an object and distinguishing the color. When the light in the visible spectrum is focused on the retina by human eyes, it will cause the reaction of visual cells. The intensity of light reflected by each point of the observed object is different, and there is a corresponding reaction on the retina, so that people can distinguish the outline and details of the observed object, which is called "form perception". Light waves with different frequencies will cause different reactions, which is called "color vision". Retina is the photoreceptor of human eyes, which is divided into central area and peripheral area. The central area is all sharp cone-shaped cells with fine shape perception and color perception. There are rod-shaped cells and a few cone-shaped cells in the surrounding area, with only a rough sense of light and shape. Therefore, the shape perception of human eyes is completed by the whole retina, that is, the central area and the peripheral area, while the color perception is completed by the central area alone. The central area is responsible for the fine resolution of the small area in the center of the field of vision, while the peripheral area gives people a rough outline impression of the whole field of vision. When people open their eyes, the brain feels a complete image in the whole field of vision, which fully shows that the surrounding areas are also capable of tangible perception and recognition. If the central area is diseased and loses sensory ability (such as macular degeneration), then the shape perception ability can only be completed by the peripheral area. The so-called concept of "motion perception" is because the human eye always looks at the small area in front of the visual axis, which is equivalent to the central area of the retina, and the surrounding things will only attract people's attention when moving. In fact, "motion perception" is the morphological perception ability of the peripheral area of retina. Can the human eye feel the motion of an object without shape discrimination? Similarly, "manual" also belongs to the scope of morphological perception, of course, at this time, the ability of eyes to distinguish the shape of objects is very poor. As for "light perception", it is the time when the sense of form is close to or has been lost.
As the numerical definition of human eye's shape perception ability, that is, the formulation of visual standards, it should undoubtedly cover the whole range of shape perception vision. If we only set standards for central vision, it can only be called "central vision standard" and "central vision chart" In some traditional methods, high vision is expressed by numerical values (such as 0.0 1 ~ 2.0 in decimal), and low vision is expressed by words (such as index, manual and light perception). This "mixed number system" is certainly not a scientific and reasonable method. In fact, not all foreign countries use words to express low vision. For example, in Russia, 0.00 1 indicates manual operation, and 0.0005438+0 indicates light perception. What's more, the so-called "central vision standard" can't determine a scientific and accurate initial vision, because the central retinal area is not a standard circular structure, but a very irregular area. In this way, the maximum viewing angle of a person in the horizontal direction of the central area may be equivalent to decimal 0.0 1, while the vertical direction may reach decimal 0.02. Considering the greater differences among individuals, it is unfounded to artificially set the decimal system of 0.0 1 as the starting point of "central vision standard". To put it bluntly, this is nothing more than nostalgia for the decimal system.
Admittedly, in the case of low vision, because the actual accurate value is of little clinical significance and difficult to accurately test, it is understandable to simply and generally use manual or photosensitive second gear to express it (for example, two patients with clinical actual vision of 0.00 1 and 0.002 will be recorded as "manual"). Therefore, the logarithmic visual acuity chart records these two files as 2 and 1, and there is no decimal point, which means that only a rough definition is made in the low vision area, that is, the visual acuity difference between each file is one order of magnitude (10 times), and it has not been accurately tested. The advantage of this overall digitization is that it gives a quantitative concept of visual changes in the whole range (although the low end is rough). For example, a patient's vision has improved from the light perception index, and it is impossible to know the degree of improvement simply from the text description, but it is obvious that his vision has improved by two orders of magnitude (3.0- 1=2), which is about 100 times.
However, this does not mean that the vision will change by leaps and bounds under low vision, and it must also change continuously, because all the parameter variables in nature, including the human body, are continuously changing, showing a continuous function mathematically and a continuous curve graphically. In fact, if you really need to test specific data in very low vision, you can do it. For example, Table 7 in the standard logarithmic visual acuity chart shows that the variable distance method can be used to test the visual acuity below logarithmic visual acuity 3.0. When the near vision chart is moved to the distances of 20 cm, 15 cm, 12 cm and 10 cm, the original vision corresponding to 3.0 vision is 2.9 cm, 2.8 cm, 2.7 cm and 2.6 cm respectively. As for the test of low vision, you can make a bigger visual target and test it at a closer distance. For example, Professor Luo Wenbin of Sichuan has conceived a plan [8], and those who are interested can further study it.
In fact, there are many ways to test a physical quantity. For the most common temperatures, there are mercury thermometer, thermistor thermometer, thermocouple thermometer, infrared thermometer and so on. Their testing tools, testing principles and testing ranges are completely different, but the test object is "homogeneous" temperature. Similarly, the visual acuity measured by sight mark and shaking finger is "homogeneous".
2. The view that Weber-Fechner rule is not applicable in the field of formal perception, so the theoretical basis of logarithmic visual acuity chart is not established.
Only an article by director Li Changxun [4] holds this view. Although there are few followers, their views are sharp, and the author also expounds his own views here.
Weber-Fechner Law is a famous psychophysical law put forward by German physicist Fechner on the basis of Weber's research in 1860. This law shows that all human senses, including sight, hearing, skin feeling (including pain, itching, touch, temperature), taste, smell, electric shock feeling and so on. , all follow the law of "feeling is not proportional to the intensity of the corresponding physical quantity, but is proportional to the common logarithm of the intensity of the corresponding physical quantity". Since this law was put forward, it has become the basic theory of psychophysics, and later generations have formulated quantitative standards for various human sensory standards, which have been in use ever since. For example:
Measuring the loudness of sound: the intensity of sound emitted by a sound source is called sound intensity, which is an objective index to describe the sound intensity; The human ear's perception of sound intensity is called loudness, and loudness is a subjective index of sound intensity.
According to Weber-Fechner's law, the subjective sensory quantity is directly proportional to the logarithm of the objective quantity, so there is a relationship between sound intensity and loudness: perceived loudness = K LG (objective sound intensity)+C.
Generally, the logarithm of sound intensity is used to measure the strength of sound, which is called sound intensity level (sound intensity is equivalent to the "visual standard" in visual measurement), so the above formula shows that loudness is directly proportional to sound intensity level. The unit of sound intensity level is Bel, and we generally use its110 as the practical unit, that is, "dB". The sound intensity level of talking loudly is 65 dB, which is 6.5 times of the sound intensity level of Sasha Vujacic leaves 10 dB, so the actual intensity difference between them is 10 (6.5- 1) times, which is about 3 16000 times.
Measuring the pitch of sound: Two tones separated by an octave have twice the vibration frequency difference, and the human ear will think that they are separated by an octave. We divide an octave into twelve semitones, so the frequency difference of each semitone is112 (■ ≈1.05946 times) of the logarithm based on 2.
Measure the visual brightness of a star: use the unit "apparent magnitude". The magnitude difference is 5, and the brightness difference is 100 times.
In fact, this law is well understood in mathematics. Is to change the variables in nature into a small number by taking logarithm, in other words, to change the number set arranged by geometric progression into the number set arranged by arithmetic progression. This is not only in line with the degree of psychological feelings, but also convenient for people to remember and communicate. For example, the audio example mentioned above, recording 3 16000 times is definitely not as convenient as the difference of 65- 10=55 dB. Therefore, in some non-psychophysical fields, the quantitative standards of number series are also adopted, such as the internationally accepted earthquake standard Richter scale, which was first proposed by American seismologist Kurt in 1935 and then formulated, and its range is between 1 and 10. Every time the Richter scale increases by one level, it shows that the released heat energy increases by about 32 times.
In Li's article, he mentioned that shinya yamanaka (1940), a Japanese, found that the appearance value of form perception was obviously greater than the disappearance value in the experiment. He thought that "the increase and decrease of sensation are not equal, so his hypothesis (that the intensity of sensation is equal when the minimum sensation is increased and decreased) is not valid, and form perception should not be quoted from his calculation formula [4]. In this respect, it must be emphasized that Weber-Fechner law is an empirical law, and it has its scope of application like all laws. When the stimulus exceeds a certain range, especially in the boundary area of measurement, it is natural to deviate from the law, and nonlinear deviation may occur completely. In hearing measurement, it is generally believed that "the perception of two kinds of sounds by human ears is roughly proportional to the logarithm of the ratio of two kinds of sound intensities", and strict proportional relationship is not emphasized because it does not affect hearing measurement. Considering the phenomenon of "visual residual" in visual function, it may be easier to understand the phenomenon that the appearance value of form perception is greater than the disappearance value (if it really happens).
Director Li Changxun not only doubted the inapplicability of Weber-Fechner rule in the field of formal perception, but actually doubted and denied the scientificity and correctness of Weber-Fechner rule itself. He thinks: "Fechner was a scholar in the heyday of metaphysics in the19th century. His formula has fully proved its mechanical properties. He regards the living and extremely complicated human body as a rigid and simple machine. As can be seen from his calculation formula, the number of stimuli is directly proportional to the number of feelings. In fact, it is impossible to form such a linear relationship between feeling and stimulation. "
Director Li Changxun's point of view seems a little extreme. For more than a century, Weber-Fechner law has been proved and recognized by many scholars, and has been applied to almost all fields of psychophysics and other fields. According to Li, all these standards have to be reinvented.
The history of human science clearly shows that many profound and mysterious natural laws can often be described by very simple formulas, including Newton's and Einstein's formulas. Even in the field of psychophysics, China's pentatonic scale existed thousands of years before Europeans used logarithm to calculate scales, but the ratio between the frequencies of its pentatonic scale almost completely conforms to the modern pentatonic scale calculated by logarithm (of course, two tones are missing), because people are most happy to hear music composed of changing scales with the same frequency difference. The scientificity and correctness of Weber-Fechner law remain unshakable.
The scientific development of nature and human beings is endless, and so is the field of psychophysics. Stevens put forward another theory-power law in 196 1, but it has been known for more than 40 years, and its application is even less. However, throughout the history of science, the theories drawn by later generations often do not overthrow the previous theories, but are often perfected and unified at a higher level. For example, the well-known Euclidean geometry is based on the axiom that a straight line can and can only be drawn from a point outside the straight line. Because it cannot be proved, it is called axiom. Later, someone changed this axiom to: two (actually countless) straight lines parallel to this straight line can be drawn from a point outside a straight line, and on this basis, another complete geometric system was established, which is the so-called non-Euclidean geometry. Both systems are correct under their own axioms and do not deny each other, but their bases are just the opposite. For example, there were only independent laws of conservation of mass and energy in Newton's era, and it was not until Einstein invented the formula of E=MC2 that it was unified into the law of conservation of mass and energy. But the above law is still correct without nuclear change. Einstein's theory of relativity based on dialectics did not deny Newton's mechanism based on metaphysics, but unified it at a higher level.
3 logarithmic visual acuity chart and golden ratio law
The golden ratio φ= 1.6 18 (or 0.6 18) is probably the most mysterious number in nature. It originated from the famous Fibonacci odd number sequence: 1, 2, 3, 5, 8, 13, 2 1, 34, 55, 89, and was naturally propagated by a pair of rabbits.
The golden ratio φ has many magical characteristics:
1.6 18/ 1= 1/0.6 18=0.6 18/( 1-0.6 18);
1+0.618 =1/0.618 (it is the only number that is added with1to get its reciprocal);
1.6 18-0.6 18= 1; 1.6 18×0.6 18= 1; Wait, there are many, many interesting functions.
Thousands of years ago, people found that lines arranged according to the golden ratio had the most aesthetic comfort, and they were widely used in architecture. For example, the pyramid of Giza in ancient Egypt, its inclined height/vertical height = vertical height/half of the bottom =■, so its inclined surface area is exactly equal to φ. The visual beauty of the golden ratio is also a strong evidence that Weber-Fechner rule is applicable to the visual field.
The shadow of the golden ratio can also be seen everywhere in the human body. The ratio of the length below the navel to the height of the human body is close to 0.6 18, and the closer to 0.6 18, the more symmetrical and beautiful it looks. The ratio from throat to top of head to navel is 0.618; The ratio from knee to heel to navel is 0.618; The ratio from elbow joint to shoulder joint to middle fingertip is also 0.6 18. The ratio of the length between every two adjacent segments of a person's three fingers also conforms to the golden ratio relationship, and so on.
The normal body temperature of 37℃ is very close to the golden section point of 38.2℃ between freezing point (0℃) and boiling point (100℃). The most comfortable temperature for human body is around 23℃ (air temperature), which is also the golden section point (23≈37×0.6 18) between 0℃ and 37℃ normal body temperature.
When the ratio of high frequency to low frequency of brain beta wave frequency is the approximate value of 1: 0.6 18 (12.9 Hz and 8 Hz), people are happiest physically and mentally. If you take an exam or a competition at this time, you can better play your level.
The most beautiful music and harmony are 6 degrees higher because the note frequency ratio between them is closest to the golden section ratio of 0.6 18, and the ratio of 6 degrees higher leads to the inner ear cochlea-just the logarithmic spiral organ vibrating harmoniously.
The golden ratio is the best proportional relationship between two static line segments (or data). If we "move" this line segment, we can get a dynamic golden rectangle, that is, a golden spiral (the radius increases by 1.6 18 times every rotation of a fixed angle) or a more generalized logarithmic spiral (the radius increases by ≠ 1. 18). This spiral reveals the subtle mathematical form of the law of natural growth in the universe. From cosmic galaxies (such as the Milky Way and the tail of a comet) to the earth's climate (such as hurricanes and waves), from animals (snail shells, pinecones and ferns) to microorganisms (the growth rate of bacteria), the trajectory of the golden spiral (or logarithmic spiral) can be found wherever there is life.
From a comparative point of view, the logarithmic spiral (including the golden spiral) is based on geometric progression, while the archimedean spiral based on arithmetic progression (the radius increases every certain angle to determine the value) can hardly be found in nature.
Numerous facts have led human beings to come to the conclusion that wherever there is life, its growth process is carried out according to "amplification" In other words, life is not "step by step" (walking the same distance every time), but "jumping" (the same magnification is greater than the last time). When human beings perceive the external world, they are transformed into "arithmetic" changes through the deduction of the highest form products in the evolution of life, so that they can easily perceive the external world. This is the natural truth revealed by Weber-Fechner Law.
I happened to find that the ratio of the length of every other line in the logarithmic visual chart is very close to the golden ratio φ, and the error is only 2% (■×■= 1.5848932, which is only 2% different from 1.6 18). As it happens, the frequency ratio between music and harmony of magnitude 6 is also about 2% different from that of 1.6 18: (■)8= 1.58740 1, that is to say, the scale length ratio is about ■, that is, the ratio of the three sides of the Giza pyramid (■?■ Therefore,
The author thinks that in the field of psychophysics, it not only conforms to Weber-Fechner law, but also conforms to the golden ratio law, that is, if the psychophysical quantity changes according to the golden ratio, it can make people feel the best (it is most likely to cause psychological ringing). In this sense, the eye chart designed directly with the golden ratio constant ■ as the scale constant of the eye chart may be the one that is most in line with visual physiology. What this relationship means in physiology and clinic is still unknown. Interested people might as well try to explore, for example, whether their eyesight will drop or rise two lines at a time (or multiples of two lines) during the process of dropping or improving.
Comparison between decimal representation and logarithmic representation (quintile system)
The development of eye chart in the world gradually converges to Weber-Fechner rule in the arrangement of eye chart, that is, the size of eye chart is arranged in equal scale series, and the scale factor is mostly the value of Muir eye chart ■≈ 1.2589, but the record of eye chart data still stays in decimal system (or fractional system), or the designed logarithmic value is not reasonable enough, so up to now, the number system indication method can not be widely used. According to the author's shallow analysis, the main reasons are as follows:
① The visual data range is not large, and the decimal system can barely cope: we know that the numerical range of sound intensity level is 0~ 130 dB, that is, the dynamic range is 13 to the power of 10, and the earthquake magnitude range is more than 10. Such a large data range will be extremely difficult if it is used directly without logarithmic compression. The range of visual acuity is only five orders of magnitude, and the visual acuity of most normal people is between1.5 and 0.01,only two or three orders of magnitude. Such a numerical range is not inconvenient to use.
② Intuitive reason: The decimal design sets the vision of 1 to 1.0 and 10 to 0. 1. This is intuitive and easy to remember. So the love of decimal system is understandable.
Hey? Some definitions of logarithmic visual acuity charts in the world are unreasonable: for example, the draft international standard drawn up by ISO (International Organization for Standardization) is in 198 1, and its design value ranges from 1.3 to -0.3, which is difficult to accept.
But none of this proves the superiority of decimal system. On the contrary, the visual decimal system is a primitive and unscientific number system and should be abandoned.
First of all, because it is the data obtained directly from the reciprocal of the viewing angle, without reasonable mathematical transformation, it is a primitive number system similar to the ancient people tying knots on a rope to count. One of its manifestations is the unequal length of values: there is a decimal place above 0. 1; Those with two decimal places are between 0. 1 and 0.0 1; Further down, there will be more decimals. Perhaps it is precisely because the value below 0.0 1 is not easy to remember and use, so it is often necessary to use uncertain text descriptions such as "counting fingers, manual operation, and light perception" to supplement the expression. Looking at all the physiological and biochemical indicators (just look at the physical examination table), their numerical ranges are mostly between 1 and 100, some are complete integers, and some have one or two decimal places. This is because it is most convenient for people to remember integers, and generally they only use two digits to remember decimals at most (so we will use millimeter mercury instead of meter mercury as the unit of blood pressure, so the measured data is 75/ 120 instead of 0.075/0. 12. Obviously, the former is easier to remember and understand. )。 However, the parameters with decimals, regardless of the numerical value, must have the same number of decimals (for example, the normal reference value range of serum total bilirubin is 3.4~2 1. 1). Visible, in all physiological and biochemical indicators, visual decimal is the most irregular numerical standard.
Secondly, more importantly, the visual decimal system has no reference unit (or minimum resolution), and its data are not related to each other, so it is impossible to carry out various mathematical statistical analysis on the visual decimal system. We know that all physiological and biochemical indicators (broadly speaking, any parameter in nature) have a reference unit (or the lowest resolution). According to the increase or decrease of the reference unit, it constitutes the whole data interval. For example, the reference unit of blood pressure is 1 mmHg, and the reference unit of sound intensity level of hearing is 1 dB. However, the visual decimal system has no reference unit, and its numerical arrangement interval is not uniform and equidistant. The essential reason of this unreasonable phenomenon just shows the necessity and correctness of Weber-Fechner principle. According to Weber-Fechner principle, in the field of physiological psychology, the minimum perceptible difference (continuous just perceptible difference) is taken as the unit of sensory quantity, that is, each additional just perceptible difference increases the psychological quantity by one unit. It is expressed by a formula, that is, △I/I=K (where I is the original stimulus, △I is the difference that can be just detected at this time, and k is a constant, also known as Weber rate). Therefore, Weber's rate k (or some multiple of k) is the reference unit (or the lowest resolution) of physiological and psychological quantities. In the field of physiological psychology, only according to Weber-Fechner principle, the designed number system standard is correct and reasonable. In the five-point vision system, the reference unit (or the lowest resolution) is 0. 1, which means that the size (and viewing angle) of the visual object has changed by ■≈ 1.2589 times on the original basis. With the correct data, it is possible to carry out mathematical statistics of vision, such as the comparison of the amplitude of increasing and decreasing vision, the average value of vision, the normal distribution curve of vision and so on.
5 conclusion
In the field of psychophysics, Weber-Fechner rule is still the authoritative guiding theory. Based on this principle, the logarithmic visual acuity chart and five-point recording method define the whole range of standard values of human vision, which can reasonably reflect the feeling degree of visual psychology and provide basic conditions for comparison, statistics and analysis of visual data. It is undoubtedly a great progress in visual inspection technology to replace decimal visual acuity chart with logarithmic visual acuity chart. However, some people in the industry are still obsessed with the decimal system, which has both cognitive and customary reasons. This study attempts to analyze and compare this from the perspective of "layman looking at expert" in order to attract more attention. If there are any improper or even fallacies, please criticize and advise.
Acknowledgement: The publication of this article has been strongly supported by Professor Qu Jia. Dr. Bao and Professor Xu carefully reviewed this article and put forward suggestions for revision. I would like to express my heartfelt thanks here!