Chapter 6 Volume 2 The Founders of the New Science Chapter 4 The Physicalist-2

In the 1830s, at the University of Leipzig, a young bearded professor of physiology was conducting a study quite different from Müller's.His name was Ernest Heinrich Weber.He doesn't use a scalpel, he doesn't cut open a frog's leg, he doesn't saw through a rabbit's head, and instead he uses healthy, intact human volunteers—college students, city folks, friends—and uses some Experiment with mundane tools like small pharmacy weights, lamps, pens, and coarse sweater needles. Coarse sweater needles? Let's take a look at an ordinary day for Webb.He blackened the tip of the needle with magnetic powder, and let the needle fall vertically on the shirtless back of a young man lying prone on the table.The needle left a tiny black spot on the young man's back.Now Weber asked him to point to the black spot with a similarly blackened needle.The young man did so, and Weber carefully measured the distance between the two points when he came across a few inches, and recorded it in his notebook.He repeated the experiment again and again on the young man's back, chest, arms and face.

After doing this for a year, he opened a compasses and pressed the two compasses feet apart on different parts of the body of a blindfolded man to touch the body.When the legs of the compasses were spread far apart, the volunteers knew that both points were touched, but when Weber pulled the legs of the compass closer together, it was difficult for the subjects to tell whether it was one leg or two. The feet touched the body until, at a critical point, he felt two feet as one.This critical distance, Weber discovered, varied according to the different parts of the body.On the tip of the tongue, it's less than one-twentieth of an inch; on the face, it's half an inch; Considerable variation in the relative number of nerve endings in each site is illustrated.

All of Weber's experiments on the sensitivity of the sensory system were relatively simple, but important in the history of psychology.At a time when most mechanists were working only with reflexes and neurotransmission, Weber was looking at the entire sensory system: not just the organs and their corresponding neural responses, but also the conscious interpretation of them.Moreover, the experiments he conducted were some of the first true experiments in psychology; that is, he varied one variable at a time—in this two-point critical-value test, the area of ​​the body—and observed that the area How much variation was induced in the second variable—the critical distance between where the feet of the two compasses landed.

To appreciate the importance of this experiment conducted by Weber in the 1830s, we can consider this period.James Mill was advocating simplistic associationism without leaving his desk; Joan Friedrich Herbart sat on the Kant chair at the University of Göttingen, repeating Kant's claim that psychology cannot It might become an experimental science; Joan Christopher Spotsheim told a crowd of eager supporters at the height of his fame that phrenologists could judge a man's character by the shape of his skull. Weber (1795-1878) was born in Wittenberg, Saxony, and all three brothers became eminent scientists and worked together for a while.Wilhelm, the physicist who helped Webb with his contact studies, and Eduard, the physiologist who, with Webb, discovered the puzzling role of the vagus nerve, which, when stimulated, causes the heart to beat slow down.

Like many other mechanists, Weber trained in medicine and found his specialty in the study of physiology and anatomy.Early in his career, Weber was obsessed with determining the minimum tactile stimulus required to elicit the sensation of touch in different parts of the body, but soon moved on to more complex and interesting problems of sensory sensitivity.Many years ago, the Swiss mathematician Daniel Bernoulli made an astute psychological discovery: a poor man feels luckier when he gets one franc than a rich man; The sense of gain that comes from money depends on one's economic status.This led Webb to formulate a similar inference: the smallest difference we can perceive between two stimuli—say, two yards—is not an objective, fixed quantity, but a subjective one, and varies with the weight of the object.

In order to test this hypothesis, Wei Xiang asked the volunteers to pick up one weight first, then pick up the second one, and then decide which one is heavier.Using a series of weights of varying weights, he succeeded in determining the smallest differences—"merely noticeable differences" (j.n.d.)—that his subjects could feel.As he guessed correctly, the only noticeable difference was not a specific constant weight.The heavier the first size, the more his subjects could perceive the difference before it; the lighter the first size, the more sensitive they felt.He later reported: "The smallest perceivable difference is two weights placed together in a relationship of about 39 to 40, that is to say, one fortieth heavier than the other." One ounce, the smallest perceivable difference in the second weight is a fortieth of an ounce; if it weighs 10 ounces, the smallest perceivable difference in the second weight is a quarter of an ounce.

Weber went on to carry out similar experiments on other sensory systems to determine, among other factors, the smallest possible distance between the lengths of two lines, the temperature of two objects, the brightness of two light sources, the pitch of two tones, etc. Perceive the difference.In each case, Weber found that the size of the smallest perceivable difference varied with the degree of the standard unit stimulus (the one with which the second one was compared), and that the ratio between the two stimuli was a constant.Interestingly, the ratio between the smallest perceivable difference and the norm varies widely across sensory systems.Vision is the most sensitive kind, and can distinguish one sixtieth of the intensity of light.In pain, the smallest perceivable difference is one-thirtieth; in pitch distinction, one-tenth; in smell, one-fourth; in taste, one-third.Weber summed up this law in a simple formula:

δ(R)/R=k, What this formula means is that, in any sensory system, the ratio between the smallest perceivable stimulus (R) and the standard stimulus intensity R is a constant K.This formula, known as Weber's Law, is one of the earliest laws of this kind - the precisely measured interrelationship between the physical and mental worlds.This was the archetype of the kind of generalization that experimental psychologists have been looking for ever since. In 1845, a group of young physiologists initiated a small association, the Berlin Natural Society, to promote their view that all phenomena, including neural and mental processes, can be explained by physical principles.These young men were early pupils of Mill, and one of them, Dubois-Raymond, had earlier advanced the mechanistic dogma mentioned above: "In addition to the usual physical-chemical forces, in organisms There is no other force."

Dubois-Raymond brought a friend to the society in the name of Hermann Helmholtz (1821-1894), surgeon of a regiment stationed at Potsdam.A shy, unsmiling young man with a broad forehead and large, piercing eyes, he seemed an unlikely standard-bearer of the society's radical theory, both in personality and status.However, within a few years, he just became such a person.His research on neurotransmission, colour, vision, hearing, and spatial perception clearly shows that the neurological processes underpinning mental function are physical and can be investigated experimentally. Helmholtz never considered himself a psychologist, his main interest lay in physics.Although the first twenty years of his career were largely devoted to physiology, his aim during this period was to explain perception in terms of the physics of the sensory organs and nervous system; exerted a huge influence.It is ridiculous that in his time, Helmholtz's most famous scientific achievement was something that only took him 8 days, and he himself thought it was not worth mentioning - the invention of the ophthalmoscope. After getting this thing, doctors had the first chance to look at the living retina.

Although Helmholtz became the leading scientist of his time—his achievements earned him the title of nobility (hence the "Von")—he was nothing like the man he most admired. A scientist, the feisty, sullen and reclusive Ithaca Newton.He was polite, generous, and courteous to his fellow scientists, but in private he was a perfectly normal middle-class professor whose biography was unremarkable.His father was a poorly paid philosophy and literature teacher at a specialized school in Potsdam, from whom he inherited a deep foundation in classical literature and philosophy; Surgeon in a regiment served five years; after receiving his first academic post, he married, had two children; became a widower, married again, and had three more.His career has consisted of better and better universities to better and better positions, constant research and writing, and increasing stature and achievement.He has never been involved in a reputation dispute, and has only one scientific controversy.For the record, his only hobbies were classical music and mountaineering.

Helmholtz began his research career while serving in the army.Because it was peacetime and he had a lot of free time, he set up a laboratory in the barracks and conducted frog dissection experiments here, in order to support a mechanistic view of behavior.He measured the energy and heat produced by the frogs and tried to explain it in terms of the oxidation of the food the frogs ingested.Today this sounds very novel, but in 1845 many physiologists were "vitalists" who believed that the processes of life were in part controlled by immaterial and imperceptible "vital energy" and that The vital force is a version of something later called the soul (said to be present in all living things.) Helmholtz firmly opposed this quasi-mystical view, and he wrote a paper called "The Conservation of Forces," based on his frog data and his knowledge of physics, and submitted it in 1847 to of the Physics Society of Berlin.His argument was that all machines obey the law of conservation of energy, so eternal motion is impossible.Then he said that in the organic world it is the same, that the vital force, because it has no source of energy, violates this law, and therefore does not exist.In short, he based his physiology on the standpoint of Newtonian mechanics.This article won him such a high reputation that the Prussian government no longer required him to perform military service, but made him a lecturer in anatomy at the Berlin Academy of Arts and Sciences, and a year later appointed him as a professor of physiology at the University of Königsberg. For the remaining two decades, Helmholtz devoted most of his time to the study of the physiology of sensation and perception. (From then on, he considered himself primarily a physicist at the University of Berlin.) His first historic achievement was the measurement of the speed at which nerve impulses travel along nerve fibers.His teacher Muller, like most physiologists at the time, adopted Galvani's theory of the electrical nature of nerve impulses, thinking that the nervous system is a bit like a coil of continuous wires, and current flows in it at a very high speed-according to a One guess is nearly the speed of light.However, Helmholtz's friend Dubois Raymond had already analyzed nerve fibers chemically, and suggested that these impulses were not necessarily all electrical currents, but electrochemical forms, and if so, their speed was relatively slow . In his laboratory at the University of Königsburg, Helmholtz set out to measure the pulse speed of the frog's motor nerves.Since instantaneous meters were not readily available at the time—the first one was still under development—he had to do some inventions by strapping a galvanometer to a frog's leg (on which the motor nerves rest. ), so that a needle drawing a straight line on the rotating drum would show the time between when the current passed to the upper end of the nerve and when the frog's leg kicked.Knowing the distance between the stimulus and the foot muscle, Helmholtz was able to calculate the velocity of the nerve impulses; experiments have shown that this velocity is rather slow, about 90 feet per second. He also measured the speed of nerve impulses in human subjects.He asks volunteers to raise their hands as soon as they feel a slight electric shock from his toes or thighs.Figures from these experiments ranged from 165 to 330 feet per second, but Helmholtz considered these figures to be less reliable than those derived from frog legs.Something about human testing tends to have a lot of variability. At first, his results, published in 1850, were not widely accepted; they were too hard to believe.Physiologists still believed that what flowed in the nervous system was either immaterial energy or electrical currents, but Helmholtz's data supported a different theory, namely that nerve impulses consisted of complex particle motions.Plus, his findings contradicted common sense.We seem to feel the touch of our fingers or toes. We just want to move our fingers or toes, and they move immediately. However, his evidence was irrefutable, and after an initial period of resistance, his theory eventually won widespread acceptance.If he had done nothing else, that alone would have made him immortal in the history of psychology, for the discovery paved the way, as Edwin Pauling said, "is the future of experimental psychology." All work must be done, such as the chronometry of mental activity and reaction time...it brings the soul back to time, it measures the indescribable things, and actually captures the most basic of the labor of natural science agent of consciousness." Divided in two, here we take a slight detour and look ahead 18 years to an important study in the offshoot of Helmholtz's work: the first attempt to measure the speed of higher thought processes. A Dutch ophthalmologist named Franciscas Konnainias Donders (1818-1889) was inspired by Helmholtz's research.He didn't have any background in psychology, but, he thought, because nerve impulses take time to travel, higher mental operations might take time too.He hypothesized that the delay between stimulus and conscious response was partly due to neurotransmission and partly due to the time taken up by thought processes. Donders devised and conducted an imaginary experiment in 1868 to test his hypotheses and measure mental activity at work.This had the subjects respond to a nonsense word, such as ki, by repeating it as quickly as possible.A pointer recording a track on a rotating drum amplifies the response as a vibration between two ki, and the distance between two micromotions becomes a measure of the time delay. In the simplest case, the subjects knew what sounds to hear and how to respond correctly.The delay between stimulus and response is thus simply reaction time.But what if the subjects were required to engage in some kind of thinking activity?What if the experimenter uttered any of several words, such as ki, ko, ku, and the subjects had to imitate the sounds as quickly as possible?If this takes longer than simple responses, Dondes thought, the difference should be the time between two mental processes: distinction (in the sounds heard) and selection (choosing the correct response). Donders also thought of a way to separate the two mental activities and gain their respective dimensions.If he told the subjects that they might hear ki, ko, or ku, all they had to imitate was ki, and they kept silent about the other sounds.Since there is no need to repeat ko or ku, they may have to differentiate between these sounds and not choose to respond.Subtract the time of difference from the time of difference plus choice, and Donders should get the time of choice. The results were surprising.On average, the difference was 39 milliseconds longer than simple reaction time, and the difference plus choice time was 75 milliseconds longer than reaction alone.So the selection obviously takes 36 ms. Donders optimistically created a series of more complex processes, believing that the time spent on each mental activity added to the time already spent on other activities, and that each activity time could be measured by subtraction.However, the result was not as expected.The difference in time proved unreliable, and only a few times could be added.Subsequent psychologists would greatly improve Donders' methods. He showed, however, beyond doubt that a part of the time spent in the reaction involving cognitive activity is taken up by this activity.More importantly, he sees the time spent as a way of investigating unseen mental activity, which, according to a recent review of his work, "comes along with As a method of measuring the higher mental activities clearly, a new era has begun". Let us go back to Helmholtz in 1852.After determining the speed of transmission of nerve impulses and inventing the ophthalmoscope, he became interested in color vision.Ever since Newton discovered in 1672 that the sun's white light is a mixture of all visible colors, physiologists and psychologists have tried to understand how the eyes and mind perceive color.The most confusing thing is that when all colors of light are mixed together, we see white, however, when two complementary colors, such as a certain shade of red, are mixed with blue-green light, it is also white, and likewise, We see orange when we see pure orange light, but also orange when red and yellow light are mixed together. As a physicist, Helmholtz knew that three particular colors—certain shades of red, blue-violet, and green—when mixed together in the right proportions could reproduce any other color, and these They are all primary colors (the so-called primary colors of pigments are red, blue, and yellow, more precisely, magenta, blue-green, and yellow. Pigments absorb light and reflect light. The result of mixing these primary colors is therefore the same as mixing light results are not the same).He speculated that this meant that human vision could detect all three colors, and hypothesized that the retina must have three different receptor cells, each equipped with a chemical that is sensitive to a certain primary color.He relied on Muller's theory of special neural energy to deduce that the nerves extending from each receptor to the brain not only transmit visual information, but also transmit special color information. A British scientist, Thomas Young, had thought of a similar theory in 1802, but he had no experimental evidence, so it was generally ignored.However, Helmholtz gathered a lot of evidence, including the colors we experience when different colors of light mix together, and the complementary colors we see when we stare at a strong color for a while. Remnants, as well as color blindness in some humans and animals, and the impact of certain brain damage on color vision, etc.He graciously acknowledged Young's discovery first, and his account of color vision has since become known as the Young-Helmholtz theory (or trichromatic theory). The trichromatic theory is a remarkable achievement, a testable mechanistic explanation of how consciousness perceives colors.According to the connection one by one, from the external world to the receptive area of ​​the brain, Helmholtz built a chain of causal phenomena, which replaced some guesses and fantasies of philosophers and physiologists.In its more complex form, it remains by far the most dominant theory of color vision, and overturns the notion that the nerves in each receptor carry different kinds of energy. As to the deep and puzzling question of perception posed by Democritus, Berkeley, Hume, and others—whether what we see is really what the outside world is—Helmholtzby Müller But more mechanistically inclined, he dismissed the question as having no meaning or value: It seems to me impossible to make any sense of talking about whether our thoughts are any other than the actual truth.Our ideas of things cannot be anything but symbols, natural signals of things, which we learn how to use in order to adjust our movements and improve our behaviour.Knowing how to read these symbols correctly, we can use these aids to regulate our actions so as to bring about the desired results, that is, so that the expected new perceptions come. . . . , it is pointless to ask whether vermilion (mercuric sulfide) is really red as we see it, or just an illusion of our senses.The feeling of redness is the normal reaction of the normal eye to the light reflected from the vermilion... It is a different way of saying that the light waves reflected from the vermilion have a certain length. The statement is also completely correct. In this way the mechanistic physiologist becomes a philosopher in psychology, and it is worth seeing him that way. Helmholtz's research on color vision was only one part of his comprehensive exploration of visual perception over many years.His research results, namely "Handbook of Physiological Optics" (1856-1867), are as thick as 500,000 words. In addition to his own research, it also includes all the research results of predecessors in this field.For generations, this work has been the definitive work on the study of the optical and neural properties of the human eye.He also wrote a similar book on listening, but not as thick as this one. In the Handbook of Physiological Optics, Helmholtz dealt primarily with the physics and physiology of vision, with keen observations on the physiological processes by which the mind interprets information from the optic nerve.He made a very valuable distinction between sensation (stimulation of the retina by light of any color, and consequent visual nerve impulses) and perception (consciousness forming meaningful interpretations of received impulses), whereas Previous psychologists have been puzzled by this question.He made the same distinction among inputs to other sensory systems. This distinction is central to Helmholtz's epistemology.He agrees with Kant's view that sensations are interpreted and given meaning by consciousness, but he disagrees with Kant's view that consciousness does not have "categories" and "intuitions" that can provide these meanings.Conversely, he said, consciousness learns to interpret sensations by trial and error—that is, learning which responses to a visual sensation produce an expected result, and which do not. A sense of space is a fitting example.Kant said that the conscious mind innately intuits spatial relationships; Helmholtz said that we perceive space through unconscious references.Little by little, as children, we learn that visual cues such as size, direction, and intensity of color are related to how far away an object is, or whether it is on this side or that side of us, above or below us; Formed a correct judgment on the spatial relationship. (Every parent who has watched a 3-month-old baby try to grasp an object knows this process well.) The English positivist associationists had said similar things, but they lacked the actual evidence to back up their views, whereas Helmholtz, a thorough experimental scientist, backed up his views with research findings. It occurred to him that if he could invert the sense of space that reaches the subject's brain—and if his theory is correct—then the subject should be able to adapt to this inversion of vision and learn to interpret it correctly.In this way, he made a pair of glasses with prisms so that objects appeared to the right of their actual positions.When subjects wearing such glasses tried to touch an object in front of them, they missed it—they reached for the apparent, rather than the actual location. Next, he asked these subjects to wear glasses to continue to grasp objects, and then touch objects; they began to consciously reach out to the left of the objects they saw through the glasses, but after a few minutes, they quickly stopped. He hesitated to grasp the object according to the actual position of the object.They have undergone perceptual adaptation, their consciousness has reinterpreted the information transmitted from the optic nerve, and they can see objects according to the relative relationship of reality. Finally, when they took off their glasses and grabbed the object again, they missed the object again, this time to the left of the actual object.It takes time for their normal sense of spatial orientation to recover. Helmholtz disagreed with Kant on innate abilities, the ability to explain causal relationships.For the rest, he insists that almost all knowledge and thought are the result of conscious interpretations of sensory experience, and that these interpretations, especially those related to the sense of space, are largely the result of unconscious references. This idea was strongly opposed by psychologists of the time, who believed that consciousness inherently explained its perception.A key function they explain in an innate view is that the two images from the eye merge to form a single three-dimensional image.Some say that each point on one retina receives as much information as a corresponding point on the other retina, and that the two optic nerves thus combine the images to form a single image.One opponent of Helmholtz's view said that each retina has innate "signs" that distinguish height, left-right orientation, and depth, thus allowing the nervous system to combine the images before reaching the brain. Helmholtz refuted this view.Nativism, he wrote, is "an inexorable conjecture"; it rests on unprovable assumptions and makes no contribution to the verifiable facts of experimental theories.The strongest evidence he used to demonstrate that experience is something that enables us to perceive pairs of images as a single image is the stereoscope.Invented by Charles Wheatstone in 1833, this instrument allows the observer to see not two identical images but two slightly different images taken from slightly different angles .These images are projected on the retina, so do not form a point-to-point coupling, but if a new observer looks inside the stereoscope for a while, he or she suddenly sees an image—a three-dimensional image.The merging of two images that are not identical yields an image that is different from either image, as a result of experience that takes place in the brain. In the end, Helmholtz didn't quite beat the naysayers, and innateism survived in one cover or another, including Gestalt psychology and more recently the psychology of genes and the analysis of temperament.However, the mainstream of psychology since Helmholtz's time has been largely positivist and experimental.He himself does not consider himself a psychologist, but he will be surprised to find that his profound influence on psychology exceeds his contribution to physics and physiology. Just as the reasonable, normal, young Helmholtz was beginning to accumulate a wealth of evidence for his own mechanistic views on neurological and psychological phenomena, a middle-aged, fanciful and neurotic professor at the University of Leipzig was hard at work, and he wanted to Prove that all people, animals and plants in the universe are composed of matter and soul.The layman Taft Theodor Fechner (1801 -1887) did not achieve this goal, however, in collecting data to show the mathematical relationship between stimuli (the physical world) and the resulting sensations (consciousness or the world of the soul) —He thought this relationship could justify his pan-mind philosophy—but he developed a research method that experimental psychologists since him have used this method to develop the materialistic psychology that he wanted to prove invalid. Fechner was born in a village in southeastern Germany, and his father was the village pastor.The father combined his religious beliefs with an unwavering scientific outlook, just as his son had.He baffled the villagers by preaching in the language of God because he installed a lightning rod on the church steeple, a caution that under the circumstances was a sign of a lack of faith in God.Doesn't God say that he can't even protect himself? Fechner studied medicine at the University of Leipzig, but, after receiving his degree in 1822, his interests turned to physics and mathematics.For several years he supported himself by translating a series of physics and chemistry manuals written in French into German.Within a few years Fechner translated more than nine thousand pages, after which, from 1824 onwards, he taught physics at the university, undertook a large research project on electric currents, and wrote numerous professional articles .This hectic pace earned him a great reputation in physics, but it also came at a great cost: he began to suffer from headaches and bouts of loss of control over his thoughts, which often left him in ecstasy. busy with a lot of trivial things. Although he was only in his early 30s and in the prime of his career—he married in 1833 and received a full professorship in 1834—his health continued to deteriorate. "I couldn't sleep, my body and mind were exhausted, I couldn't think, and it even caused me to lose my confidence in life," he later commented on his life during this period.He went to the spa for treatment, but to no avail.Then, trying to divert his attention by studying afterimages—his first foray into psychology—halfway, he observed the sun for a long time wearing sunglasses.His work on afterimages was recognized—Helmholtz, as we know, used some of his data—but, as a result of his observations, Fechner developed a severe photophobia, with a full range of emotions. collapse. Nearly blind, Fechner shielded himself from light in a darkroom, suffering from pain, emotional depression, overwhelming boredom, and severe digestive problems. (He retired from college and received a pension despite only teaching for a few years.) At the nadir of his three-year ailment, he painted his house black and stayed in it day and night, There was no one to be seen.Various laxatives, surf therapy, hypnosis, two types of shock treatments all to no avail.He was still troubled repeatedly by trifles; besides, he was tormented by the joy of feeling that he was close to discovering the secrets of the world, and the need to prove them scientifically. Worried about the correctness of the secret. Eventually, he got better on his own, and after a while he could see without pain in his eyes, and he could talk to people.When he went for a walk in the garden for the first time in many months, the flowers looked brighter, more colorful, and more beautiful than ever, and he felt that he was giving these things an inner light, and he immediately Captures the meaning of this: I had no doubt that I had discovered the soul of the flower, and thought with my most strange, enchanted emotions: This is the garden hidden behind the partitions of this world.The whole globe and its sphere itself are but a fence around this garden to keep out those still waiting outside. Fechner soon wrote a book on the spiritual life of plants, and spent the remaining years looking for ways to promote his animism, the co-existence of consciousness and matter throughout the world. It was this mystical belief that led Fechner to carry out his historic experimental psychology. On the morning of October 22, 1850, he was lying in bed considering how to prove to the mechanists that consciousness and the body were two aspects of a basic unity, when he had a flash of inspiration: if he could show the power of stimulation If there is a mathematical relationship between them and the intensity of the sensations they produce, then he shows the unity of body and soul. Or so it seemed to Fechner.The logic of this reasoning may escape the non-mystic.Instead, he raises a very valid and important question about the accuracy of conscious perception of the external world: Is there a consistent mathematical relationship between the intensity of a stimulus and the sensation it produces?Intuitively, it might go like this: the brighter the light, the brighter we look.However, if you double the brightness of the light, will the intensity of the perception be doubled?Or is there some other, seemingly real relationship? 费希纳接受过物理学和数学的训练，他感觉到，当刺激的强度增大时，它应该要求更大的差别（绝对值上的差别）来产生一定大小的感觉增大。从数学上来说，刺激在长度上的几何增大会导致感觉的算术增大。一项临时的示意：按照传递到耳朵上的能量，一阵雷声的响声比日常谈话的声音要响好多倍；按分贝——分贝是指人耳能够分辨的最小响度差别——来说，它只是响两倍而已。 为了通过实验确立他的直觉，费希纳得解决一个看上去无法解决的问题：他可以很容易地测量刺激强度，可是感觉是个主观的东西，而且无法测量。可是，他推想，尽管他不能直接地观察和测量感觉，但他可以通过灵敏度的指导而间接地做到。他可以确定在感觉者刚刚能够注意到的、任何水平上最小的刺激力量增大。因为“刚刚能够注意到”在任何水平上都意味着同一个东西，这将是一个感觉的测量单位，借此可以与产生这种意识所必需的刺激的增加进行比较。 费希纳后来说，他不是从韦柏那里得到这个想法的，尽管韦柏是自己以前的老师，他在“刚好能够注意到的差别”上所做的工作几年以前就发表了。可是，他迅速意识到，他会使用到韦柏定律的推广形式。韦柏已经发现两项刚刚能够注意到的差别刺激之间的比率是一个常数，不管这种刺激的大小如何。费希纳却说，尽管两项刺激之间绝对的差别随着刺激的强度增大而增大，可感觉者对一种刚刚可以注意到的差别的感觉却仍然是一样的。 费希纳后来写道，想象一下，你用太阳镜看着天空，并在刚刚可以注意到的天空的背景上挑一片云来看。然后，你戴上一副黑得多的眼镜；云彩没有消失，但几乎只能够注意到：因为，尽管强度的绝对水平在透过黑镜片的过滤后会低得多，但云彩与天空之间的强度比却没有变。 为了表达刺激强度与感觉强度之间的关系，费希纳从数学上转变了韦柏定律，重新加以调整然后写出来： S＝k log R， 这意思是说，在英语中，分段式的感觉强度增大是刺激强度翻倍的结果（乘以某个比率或者系数）。费希纳拼命要把这份荣誉还给他以前的老师，因此，他把这个公式称作韦柏定律——是他本人给韦柏的公式和他自己的公式命名的——可是，后来的心理学家按照这些公式各自的归属把修改后的公式叫作费希纳定律。 费希纳余下的9年花在辛苦的实验工作当中，收集着大量能够确证这个定律的数据。尽管他的性格当中有一些神秘主义者和诗人的气息，可在实验中，他是一位有强制力和严厉的研究者的榜样。他不知疲劳地让受试者们举起重物，注视光源，听各种杂音和音调，观察彩色样本等等，并宣布它们是不同的或是同样的。在这些年里，他对每种刺激的强度进行了范围广泛的实验，使用到了测量这些判断的三种方法。仅在这些方法中的一种里面，他便列出了24576种判断的表格和计算结果。他认为，第一次系统地探索物理和心理学王国之间的数量关系，这是一种新的科学专业，因此命名为“心理物理学”。 在他使用过的三种实验测量方法当中，他从前人那里借来了两种并使之完善，然后自己发明了第三种。直到当时为止，没有人曾使用过这种极仔细、可能准确控制和数量测量方法来探索心理学的反应。他的方法很快就被广泛接受，而且在今天心理学的每一个实验室里还在经常使用着。 一种是极限的方法，费希纳本人管它叫“仅仅可以注意到的差别法”。为了确定一个刺激的临界值，实验者一次提供一个刺激，从最低的量开始逐渐加大强度，直到受试者可以感受到刺激为止为了确定仅仅可以注意到的差别，实验者提供一个“标准的”刺缴和一个“比较用的”刺激，以小幅度增大两种之间的差别，直到受试者说可以感觉到为止。 第二个方法是常量刺激法，费希纳本人叫它“正确和错误情况法”。实验者一次又一次提供等量的刺激——在临界值上的单个刺激或者成对相似的刺激。受试者回答说“有了”（意思是说，他感受到了它，或者两者有了不同），或者说“没有”（表示他没有感觉到，或者两个刺缴没有什么不同。）受试者的回答得出平均值，而这些平均值会指明，在任何指定的刺激水平，或者两个刺激之间的差别上，受试者有没有可能会感觉到这些刺激，或者两个刺激之间的差别。 第三个方法，即费希纳本人的创造性的贡献，叫作调节法，他把它叫做“平均错误法”。实验者或者受试者调节比较刺激，直到它好像（对受试者来说）与标准刺激相等。这边或者那边总是会有一些错误存在的，不管多么微小。每一次错误都记录下来，许多次试验过后，把平均错误加起来，它也是仅仅可以注意到的差别的尺度。这个方法确立了了这个有用的原则，即测量数据可变性可以跟测量集中趋势一样得出信息来。 1860年、费希纳出版了两卷本的《心理物理学纲要》，把他的研究成果公诸于世。他已经59岁了，在这个年纪，科学家一般很少会拿出有创见的东西来的；可是，《心理物理学纲要》的确是富于创见的，并立即产生了很大的影响。兴趣是浓厚而且广泛的——不是对他信奉的泛灵论，而是对它的实验和计量方法学。如波林论及费希纳的成败时曾说过的，“他攻击物质主义的铜墙铁壁，但又因测量了感觉而受到赞美”。确切地说，有些心理学家认为，心理物理学的方法学是一个可怕的话题。许多年以后，伟大的威廉·詹姆斯写道： 如果像他这样一位可敬的老人会用他的怪想使这门科学永久地背上负担，而且，在一个充满各种容易产生成果的。引人注目的事物的世界里，如果迫使未来的学者们在这些繁杂的田地里耕耘，不仅要去研究他的作品，而且得研究那些反对他的更枯燥的作品，那可真是一件要命的事。 可是，很多人并不持这样的看法。尽管对费希纳说仅仅可以注意到的差别都是相等的这个假想的有效性存在激烈的争论，可是，他的方法一般却都认为是天才的突破。对刺激和反应两者之间的关系进行计量研究的时机已经成熟；许多心理学家几乎立即就开始利用费希纳的三个方法了，这三个方法将肉体的生理机构与它们所引起的主观的经验连接起来了。（费希纳本人尽管仍然还在写文章为他的心理物理学辩护，可是；他把漫长余生的大部分都贡献给美学、轻度异常现象。统计学和泛心灵哲学的研究上了。） 后来的心理学家们已经发现有错误，甚至驳倒了他的发现中的每个地方，可是，他的方法不仅仍然有用，而且是感觉测量中最基本的方法。波林总结了费希纳相互矛盾的成就： 没有费希纳……也许仍然会有一种实验心理学……可是，在实验体中，却不可能出现如此广泛的科学范畴，因为，如果测量不能成为科学的工具之一，则我们很难认为某个课题是符合科学的。因为他所做的事情和他做这些事情的时代，费希纳创立了实验计量心理学，并把这门学问从其原来的途径搬回来导入了正轨。人们也许可以称他做实验心理学“之父”，或者，人们也许会把这个称号送给冯特。这没有什么关系。费希纳种下了肥沃的思想之种，它生长起来，并带来了丰硕的成果。