Watson, Sr., R.I. (1978). The great psychologists. (4th
edition). New York: J.B. Lippincott Co.
CHAPTER 10
FECHNER:
PSYCHOPHYSICS
ENGROSSED as he was in philosophical and mystical interests,
Fechner devoted several periods of his long life to speculation
and investigation of what to him was the most fundamental problem
of life-psychophysics or the scientific investigation of the functional
relations of dependency between body and mind.' We will find in
his work a marked contrast between the "dry-as-dust"
psychophysical studies as
rigorously scientific as anything that had as yet emerged in
psychology and his burning enthusiasm to grapple with the very
nature of the man.
LIFE AND CAREERS OF FECHNER
Gustav Theodor Fechner was born in a small village in the Wendish
country of southeastern Germany in 1801. His father, a preacher
of the Lutheran faith, died when Gustav was but five years old,
but not before he had given his precocious son a grounding in
Latin. After attending a gymnasium, Fechner matriculated at the
University of Leipzig in 1817. This association with the University
was to last for seventy years. He took his degree in medicine
in 1822, but he decided against going into practice.
Even in his youth there were some glimmerings of humanistic interests.
Under the pseudonym of Dr. Mises, he turned the weapon of satire
upona variety of views with which he disagreed. The first of these
satirical pieces appearing in 1821, even before graduation, was
directed against the then current medical fad for the use of iodine-Proof
that Man Is Made of Iodine. For a period of twenty-five years
thereafter, occasional satirical pieces from his pen would appear.
In Germany, earlier in the century, there had been a resurgence
of interest in materialism. To Fechner, materialism was a shallow
theory devoid of any truth. Several of these satires were devoted
to an attack on the view that the universe is inert matter, the
"night view," as he called it, and to a defense of the
position that the universe can be regarded from the point of view
of consciousness, the "day view."
This anti-mechanist position was to be a constant point in what
otherwise appeared to be a series of shifts of interest. Throughout
his life Fechner moved from one field to another, although in
a larger sense these moves formed an integrated whole. The nature
of this unity should become apparent as we move through these
careers. According to Boring, in the productive years between
1817, when he started medical school, and 1887, when he died,
Fechner was successively a physiologist, a physi
cist, a psychophysicist, an experimental estheticist, again a
psychophysicist, and throughout most of the later years, a philosopher.
Following his aim steadfastly through these careers, he happened
to found psychophysics which in turn had so much to do with the
founding of experimental psychology.
After graduation he began his second career by studying physics.
In 1824, after a period without official appointment, he started
to lecture on this subject and to conduct laboratory investigations
in electricity. In 1833, he married. In 1834 he was made a professor
of physics when but thirty-three years of age. His future in academic
work in physics at this time seemed secure and predictable.
During these years sheer economic necessity had led him into
translating various French scientific works which served to add
to his scientific knowledge, however, some of his means of adding
to his income took the form of hack work, such as editing and
writing a considerable share of an encyclopedia of household knowledge
in eight volumes. He broke under the strain of the tremendous
amount of work he carried and became, in the language of the day,
a "nervous invalid." In general it could be characterized
as a neurotic depression with pronounced hypochondriacal features.
In the winter of 1839-40 an eye disorder, involving considerable
pain, developed, and he resigned his chair in physics. Fechner
had studied after-images by staring into the sun, which undoubtedly
aggravated thecondition, if it did not bring it on. Years of suffering
followed. His eyes were so hypersensitive to light that he could
not leave the house without bandaging them, and for the rest of
his life he had to curtail his reading. Sometimes for weeks on
end he could not eat but eventually found that fruit, strongly
spiced raw ham, and wine could be tolerated. He could not talk
for long periods and thought of suicide. Some slight improvement
occurred late in 1843, but it was thought there was no chance
of his regaining his health. In 1844 he received a small pension
from the university, thus establishing officially his position
as an invalid. However, not a one of his remaining forty-four
years went by without some serious contribution from his pen !4
There is no doubt that he really suffered, so it would be unfair,
as well as inaccurate, to apply to him that grand phrase, "he
enjoyed poor health." Nevertheless a defensive component
in his illness was undoubtedly present, but speculation is fruitless
as to whether this was a secondary gain to an organic disorder
or was of primarily psychogenic origin.
His inability to use his eyes meant many hours spent in speculation.
This reinforced his speculative turn of mind which came to the
fore as soon as he was able to resume working. He now entered
the third phase of his career as a psychophysicist with philosophical
leanings. It is in connection with psychophysics that we reach
the reason for his inclusion among the great psychologists. Reserving
details for later systematic discussion, suffice it to say that
he became interested to the point of obsession in demonstrating
that mind and body are identical; the difference that seems to
exist merely being the way they are viewed. Since matter ( body
) is not to be denied any more than is consciousness ( mind ),
the two must be reconciled and made as one.
The solution, he tells us, came with dramatic suddenness on the
morning of October 22, 1850. In bed, "before getting up,"
he realized that the law of the connection between body and mind
is to be found in a statement of the quantitative relation between
mental sensation and bodily stimulus, not in simple proportion,
but such that changes in the former correspond to proportional
changes in the latter.
Ten years later in 1860, when he was fifty-nine years of age,
his Ellmente der Psychaphysik appeared. For this book, Fechner
ranks among the great psychologists. Here he discussed the functional
relations of mind and body and reported investigations of his
own and others on the various senses-sight, sound, and the cutaneous
and muscular senses.
Some conception of Fechner's intent to measure psychological
functions can be gained by turning directly to the next of his
undertakings, the study of experimental esthetics, which is another
field he founded. Fechner had had a long standing and deep interest
in art. His first paper in this new career appeared in 1865 having
to do with the "golden section," the most esthetically
pleasing relation of length to breadth in an object. Here again,
Fechner applied his exact method to a global goal. He rebelled
against the attempt to develop an esthetics "from above down"
by formulating abstract principles of beauty from which to judge
the concrete object, in the manner of the Romanticists. Instead,
he believed one must start with simple figures. In order to find
out what linear proportions the artist had used, he measured endlessly
and patiently the dimensions of pictures, cards, books, snuff
boxes, writing paper, windows, in fact, any object that was purported
to have esthetic appeal. Thus, he sought to develop an experimental
esthetics "from below."
Fechner also became very much involved in a cause celebre of
his day concerning the authenticity of two paintings of the Madonna,
each attributed to Holbein. Although very similar, they differed
in detail, and the authenticity of each was in dispute. Fechner
inclined to the opinion that both were authentic. There was also
a dispute over which was the more beautiful. Taking advantage
of an exhibition in which both of them were exhibited together,
he launched what may be the first public opinion poll. He made
arrangements for the public to be invited to record comments in
a book placed alongside the paintings. Sparseness of returns and
a disproportionate number from art critics, who had already formed
opinions, made this particular venture a failure.
His major book on esthetics, Vorschule der Aesthetik, appeared
in 1876. Its appearance also served to close his participation
in esthetics. Experimental psychology in the person of Wundt,
now also at Leipzig, and the intense interest of many others,
protagonists as well as antagonists, would not leave him in peace
to pursue his still strong philosophical interests. Willy nilly,
he was drawn back to a second career in psychophysics which lasted
until his death in 1887. In this, his last year, he wrote a paper
so well summarizing psychophysical research as to draw from Wundt
the comment that it was the clearest extant summary.
THE AIM OF FECHNER
The careers through which Fechner moved through during his lifetime
did not reflect a change in fundamental interest. His guiding
aim was a search for an answer to an all consuming question-the
nature of the relation between the spiritual and material worlds.
He sought a unified conception of body and soul which, while based
upon mystical speculation, had a scientific basis.
which was romantic, transcendentalist, and vitalistic. A characteristic
tenet was that spiritual influences express themselves through
physical symbols .7 This belief fired the imagination of Fechner
and became an important aspect of what, in a somewhat over-simplified
fashion, can be referred to as the mystical strain in his nature.
And yet the vague symbolism with which the philosophers of nature
pontificated could not escape criticism from that other aspect
of his personality, the scientific. From Herbart he had obtained
both the conception of psychology as a science and the value of
mathematics in this pursuit. However, he could neither go along
with Herbart's metaphysics nor accept his denial of experiment
to psychology. Fechner struggled with both the mystical and scientific
sides of his nature, feeling it necessary to unify them. This
union finds no favor among psychologists today, but it must, nevertheless,
be explored as the background against which Fechner's psychological
contributions were to be made.
In the spirit of Plotinus, his ancestor of seventeen centuries
before, Fechner saw the world as a system of souls appearing to
each other as bodies.8 A mystical strain was most noticeable in
his speculations reflected in the very titles of two of his important
works, Nanna or the Mental Life of Plants and Zend-Avesta or the
Things of Heaven and the Hereafter. In this second book, Fechner
endowed all things with personal souls. The world is made up of
external manifestations, bodies which are correlated with internal
animate realities, the souls. This is panpsychism, a theory of
the world which endows plants as well as animals with some rudimentary
kind of soul. Its relation to primitive animism is direct and
obvious. But Fechner was no simple throwback to primitive times.
He argued these and related problems with verve, subtlety, and
enthusiasm. Since they are peripheral to present major interests,
these arguments must be passed over except to note that Fechner
believed that the soul is related to the body as the inside of
a circle is related to the outside, thus, making his view a double
aspect theory-soul and body are but two aspects of the same fundamental
unity. Since these two aspects were identical, the view is also
referred to as the "identity hypothesis."
Consonant with the two major influences that affected him, Fechner
sought precise confirmation of a metaphysical cosmic speculation.
His was a nature that asked for a relation between a poetical
and speculative world-view, to be demonstrated by means of precise
measurement. He made the mystical aspect his goal, and the scientific
aspect his method. And, actually it was his philosophical, even
mystical, views which led to the first precise measurements in
psychology.
His insightful experience that morning in October 1850 had to
do with the application of measurement of physical stimulus and
mental sensation. The starting point for this measurement he found
in the research of Weber, who was working at the university. He
specifically disclaimed having in mind Weber's work when this
idea occurred to him, although it is reasonably certain he knew
of it before this date. At any rate, shortly thereafter he made
Weber's work the basis of his subsequent investigation. It becomes
necessary to stop to consider the influence of Weber upon his
thinking and research.
THE INFLUENCE OF WEBER
Ernst Heinrich Weber (1795-1878) had been appointed Dozent in
physiology at the University of Leipzig in 1817, the same year
Fechner arrived as a medical student. The next year he was appointed
Professor of Anatomy, and later in his career was made Professor
of Physiology. For many years Weber and Fechner moved in the same
academic circles and lived in the same community.
As a physiologist, Weber was particularly interested in touch
and in the muscle sense, hitherto relatively neglected research
fields.9 At first Weber's research interests will appear to be
a far cry from Fechner's lofty aim. The research, as Weber saw
it, concerned the muscle sense. In investigating the part played
by the muscle sense in relation to touch, he wished to find out
what was the smallest difference between weights, the so-called
"just noticeable difference," that his subjects could
discriminate. Their task was simple. On each trial they lifted
two weights, one a standard weight, the other a comparison weight;
and they reported whether one (and which) felt heavier than the
other. On subsequent trials the same or different comparison and
standard weights were used. Large differences between the weights
were obvious to all subjects and were reported as differences,
but small differences in weight resulted in the subjects' reporting
that the two weights were the same. When Weber studied the results
of many trials and several standard weights in relation to the
weights just noticeably different, he found that for each standard
weight there was a relation between the sheer heaviness of the
weight being compared to the perception of their differences.
This finding was expressed in the form of a ratio of one-fortieth
to each of the standards. Suppose he had used standard weights
of twenty, forty and eighty ounces (actually, relatively lighter
weights were used). He found that a weight of forty ounces could
usually be judged as different if there was one ounce difference
in the comparison weight but that usually no differencewas perceived
when the difference was less than this amount. This gave a ratio
of one-fortieth. This same ratio was found when the standard weight
was cut in half to twenty ounces or doubled to eighty ounces.
It only needed one-half ounce difference at twenty ounces ( one-fortieth
of twenty ounces), while two ounces were required at eighty ounces
( onefortieth of eighty ounces) for a just noticeable difference
to be perceived.
Next Weber asked, suppose instead of being lifted, the weights
were allowed merely to rest upon the skin; what would the ratio
now be? When comparison weights were allowed to rest on the skin
a ratio was found, but now it was one-thirtieth instead of one-fortieth.
In other words, one-thirtieth of the standard weight must be added
to that of comparison weight if a difference just noticeable to
the subject was to be detected. Since smaller differences in weight
could be discriminated when the weights were actively lifted (
one-fortieth ) compared to when they were passively resting on
the skin ( one-thirtieth ), he concluded that this difference
demonstrated the influence of the muscle sense upon discrimination
as compared to the lower degree of discrimination when touch alone
was operative. Adding the muscle sense to touch increased accuracy
of discrimination. Weber also tested capacity to discriminate
length of lines and marshalled evidence on differences in the
pitch of tones and found other constant ratios.
Weber generalized that for each of the senses there is a constant
fraction for which a difference is just noticeable. He10 admitted
that this ratio does not hold without exceptions "at the
end of the tonal series." It was later established, irrespective
of the mode of sensory stimulation, that this ratio does not hold
at the extremes of any range of stimulus, and, in general, that
it is only approximately true.
Weber's second major contribution was the experimental determination
of the accuracy of two-point discrimination of the skin."
This is to say, Weber established the distance apart that two
points must be in order for them to be felt on the skin as two.
With vision eliminated, a subject would be instructed to report
whether he felt one or two points touching the skin. Using an
apparatus resembling a drawing compass, Weber then stimulated
the skin either with one or with two points simultaneously at
varying pre-established distances apart. When the two paints were
a relatively small distance apart, a subject would report a clear
and sharply defined "one"; at relatively great distances,
he would report "two points"; and when in the region
in between these two extremes he would report, "uncertainty
and blurriness." There was a threshold at which two points
could just be discriminated. He showed that this "two-paint
threshold," as it came to be called, varied according to
the part of the body stimulated. On the finger tips the subject
would report discriminating two points as two when they were but
a millimeter apart, but for the same discrimination on the back
of the fingers the points had to be forty to sixty millimeters
apart. His explanation of this difference in sensitivity from
one part of the body to another, rested upon his hypothesis of
"sensory circles," i.e., there are regions of the skin
in which doubleness is not perceived because immediately adjacent
tactile nerve fibers are stimulated. For doubleness to be sensed,
at least one unstimulated fiber must lie between those stimulated.
Regions with large thresholds would thus have touch fibers relatively
sparse; the points stimulated had to be further apart in order
to skip an adjacent fiber.
It can be seen that Weber's studies are experiments in the strict
sense of the term. Varying the intensity of weights and the length
of lines and the distance apart of two points on the skin, under
the control of the experimenter, allowed the experimenter to study
their differential effect upon the perceptual experience of the
subject. These experiments stimulated considerable subsequent
research and helped to lead to the establishment of experimental
psychology as a separate discipline in its own right.
PSYCHOPHYSICS
Weber wrote no specific formula for his results. Without stating
it in the form of an equation, he held that when one distinguishes
between objects, it is not the difference between them that is
perceived, "but the ratio of this difference to the magnitude
of the objects compared:" He made it clear that the magnitude
of stimuli just noticeably different from each other can be stated
as a ratio between the intensities and that this ratio is independent
of the particular intensities used. It was Fechner who grasped
the implications of Weber's statement for his psychophysical problem
and proceeded to develop them.
Fechner believed that Weber's results meant that one could measure
sensation as well as the sensory stimulus and state the relation
between the two in the form of an equation. After years of repeating
and extending Weber's research, he formulated Weber's ratio in
the form of an equation. This formulation may be stated as follows:
p R/R - K, where p R is the just noticeable stimulus increment,
K is a constant, and R is the standard stimulus magnitude. In
other words, a stimulus increment when divided by the magnitude
of the standard stimulus gives a constant value. This, strictly
speaking, is Weber's law, although Fechner in a burst of too great
gratitude, gave Weber's name to the final resultant of several
steps further on in his thinking. Hereafter, this equation with
which Fechner started will be referred to as "Weber's law"
while the final equation will be called "Fechner's law."
Instead of working it through mathematically as did Fechner let
us try to get the general relation clear. As one proceeds arithmetically
by steps of one in the scale of sensation aspect-so Fechner's
law assertsone multiplies the value of the stimulus magnitude
by a constant ratio. Stimuli of twenty, forty, and eighty ounces
should give equal steps of sensation. A long and complicated argument
was offered by Fechner about measuring sensations indirectly from
direct measurement of the stimulus, but, instead of carrying through,
we shall move to discussion of direct measurement that is based
on the assumption that just noticeable differences are equal.
Fechner reasoned that it can be assumed that just noticeable differences,
j.n.d.'s, as they came to be called, are equal through the range
of the sense quality, that these j.n.d.' s are thus equal increments
and measure sensation. Being equal they can be added up to make
magnitudes. There remained only the question of finding a zero
point from which to start so that we can know when we are dealing
with "one," "two," and so on, the number of
units above zero as the j.n.d.'s are cumulated up the scale. This
zero point Fechner took as the threshold stimulus, that value
of the stimulus at which the sensation is just ready to appear.
This value is zero in his scale. The j.n.d. appearing thereafter
is one, the next j.n.d. is two, and so on.
Increase of subjective intensity of a sensation varies directly
with the increase of strength of stimulus, although not proportionally
because the psychic increases arithmetically by a constant difference
when the physical increases geometrically by a constant multiple.
When one series increases arithmetically while the other series
increases geometrically, we are dealing with a logarithmic relation.
This was demonstrated by the mathematical manipulation of Weber's
law, a process by which Fechner emerged with the equation S -
K log R in which S is the sensation's magnitude, K is a constant,
and R is the stimulus' magnitude. A sensation equals a constant
multiplied by the logarithm of the stimulus. This is Fechner's
law. Sensation has been measured, and the identity hypothesis,
so Fechner thought, has been demonstrated. He had found his proof
of his identity hypothesis in a table of logarithms!
To summarize Fechner's research and the researches of those who
have followed Fechner, we may say that the experiments indicate
that Fechner's law holds approximately for the middle range of
stimulus intensity but not with either small or very large intensities.",
Visual brightness has a ratio of about one-hundredth, lifting
weights one-fortieth, and tone one-tenth. For instance, in visual
brightness the ratio just given means that for a change in illumination
to be perceived the total illumination must be increased by one-hundredth
of its amount.
Fechner established what he considered to be the absolute stimulus
threshold or limen, the value of which the subject's sensing of
the stimulus is just ready to appear, as that value of stimulus
which marks the limit of a sensory continuum. Anyone familiar
with the fact that vibrations are heard as sound in the range
between from about sixteen vibrations per second, the lowest audible
tone, to about 20,000 vibrations per second, the highest audible
tone, and knowing that there are vibration rates both higher and
lower not heard as sound, is aware of the existence of thresholds.
(The dog whistle of vibrations beyond 20,000, unheard by humans,
shows that dogs have a higher tonal threshold than humans.) Subject
to qualifications to be given later, one can speak of sixteen
and 20,000 vibrations per second as the stimulus thresholds of
hearing. Lower stimulus thresholds were established by Fechner
and others for weights, brightness, and many other sensory intensities.
No upper thresholds could be established since these were intensities
capable of limitless increase.
Now that the so-called absolute threshold is familiar it can
be seen that when j.n.d.' s were under discussion we were dealing
with something else that can be called the differential threshold.
Fechner believed the differential limen to be the least amount
of change in a stimulus necessary to produce a sensed difference.
Changes below this limen, he held, are not sensed as different.
The addition before the change was below the differential threshold,
the amount necessary to just produce the perceived difference
is the differential limen. The differential threshold resembles
the just noticeable difference enough to be frequently confused
with it. Speaking more accurately than did Fechner, the differential
threshold is a statement of the statistical quantity for the point
between what is sensed as not different and the just noticeable
difference. It is a statistical value representative of the point
where the sensation is just as often not sensed as it is sensed.
In the course of his research, Fechner developed one and systematized
two others of the three fundamental methods of psychophysics.
These three were the method of limits, the method of average error,
and the constant method. The method of average error that Fechner
developed, along with his brother-in-law, is the most fundamental
and will be used as an illustration. The subject, himself, adjusts
a variable stimulus so as to fulfill the instructions given him,
say, to make one line equal to the length of a standard line.
Before him he sees a length of line, the standard. Another line
is to be adjusted by him to be as close to the standard in length
as he can make it. No matter how closely he approximates the line,
however, an error, large or small, will be made. Sometimes he
makes the line too long, sometimes too short, but always he makes
some error. After many trials on his part, the average of his
errors is found, the socalled average error. In an extended form
this procedure is basic to practically all psychological experiments
today, whether conceived as psychophysical or not. An assumption
is made that every psychological value or score for a trial is
in error or only approximate to some degree because we and our
sense organs are perpetually subject to variability. Hence, we
obtain a large number of variable measures which are distributed
in some approximation to a normal probability curve. The average
from these data is taken to be the best single approximation of
the true value. We accept this average as more accurate than any
single measure, since we cannot be certain of the true measure.
Upon publication of the Elemente in 1860, interest in Fechner's
work was immediate, intense, and widespread. Many others, seeing
the value of his work, proceeded to carry out similar experiments,
as will be seen later. Various controversies and objections raged.
One criticism directed against his work, the so-called quantity
objection, is that we are not aware introspectively that sensations
have magnitude. James,16 the phrase maker, said in substance that
our feeling of pink is not a portion of scarlet. Another argument
centered on the question of whether Fechner was really measuring
sensation, since he had assumed the equality of j.n.d.' s. From
the vantage point of today it can be said that Fechner erred methodologically
in the direction of treating psychophysical findings without full
consideration of the various sources of complication present in
the individual and in the conditions of the experiment. As a matter
of fact, sixteen and 20,000 vibrations a second as stimulus thresholds
for hearing are not constant limits for all people. Fechner was
wrong; there are no absolute thresholds. Precise thresholds change
from one individual to another and from one condition to another.
Auditory sensitivity varies widely because of differences in native
acuity, or changes occurring in the ear due to injury or the ageing
process; while conditions, such as the state of the background
noise-level or the precision of the sound source delivering the
particular pitch, also effect the results. These complicating
factors were not as appreciated in Fechner's time as they are
today.
SIGNIFICANCE OF WEBER AND FECHNER
Since Weber's work preceded Fechner, it is plausible to ask why
is not Weber stressed and Fechner merely treated as someone who
later, more or less independently, worked in the same area? Precedence
is given to Fechner because he is an "event-making"
man, while Weber was merely an "eventful" man in the
felicitous terminology that Hook applied in similar circumstances.
Weber, as a physiologist, carried on some research on a problem
which interested him. It was a different problem, to be sure,
from that occupying most of his fellow physiologists, but neither
he nor they saw it as different in spirit. He did not realize
that he had hit upon something that would profoundly effect future
developments in psychology. But he had, and, therefore, in this
sense, he was an "eventful" man. At a propitious time
he worked on research that was to give him a prominent place in
the history of psychology. But its larger significance escaped
him. Fechner, in distinction from Weber, was an event-making man.
He saw what others, including Weber, had not seen-the implications
and consequences of psychophysics. Fechner's insight that October
morning about measuring sensations and relating them to measures
of their stimuli was independent of Weber's researches. It was
related to this prior work on magnitude of stimuli and was recognized
by Fechner as supplying a method, but the insight had to occur
before recognition of the relevance of the method. Weber took
the first step along a fork in the road, but did not realize he
was walking a different road; Fechner realized the road was there,
looked down that road, and in this way created it.
Ironically enough, with all the excitement his findings engendered,
little attention was paid to Fechner's goal for psychophysics.
His attempt to found a philosophy upon exact science was a failure,
but his work was fruitful for the advancement of psychology as
a science.
Sensory psychology was put upon a quantitative basis with the
introduction of Fechnerian psychophysics. No less a person than
Wilhelm Wundt said of him that his was the "first conquest"
in the field of experimental psychology. In all fairness it must
be admitted that not all psychologists have held such a high opinion
of the work of Fechner. William James, 20 for example, some thirty
years after the appearance of Fechner's major work, concluded
that the yield of psychophysics in psychological outcome was precisely
"nothing," and that his findings were "dreadful."
He went on to point out that Fechner's successors, laboring mightily,
could topple over every one of his findings, but invariably they
ended up by praising him for his contribution to the scientific
methodology of psychology. Indeed it is true that his conclusions
have not stood the strain of later criticism; nevertheless his
methods are still not only serviceable and useful, but actually
fundamental in sensory measurement.
