Consider the case of fluctuations of relative strength or intensity

first. Let there be three grades of the compound, as _Abcd, abcd,_ and

_abcD_. In passing between these compounds, the mind will feel shocks

of difference. The differences, moreover, will serially increase, and

their direction will be felt as of a distinct sort. The increase from

_abcd_ to _Abcd_ is on the _a_ side; that to _abcD_ is on the _d_ side.

And these two differences of direction are differently felt. I do not

say that this discernment of the _a_-direction from the _d_-direction

will give us an actual intuition either of _a_ or of _d_ in the

abstract. But it leads us to _conceive_ or _postulate_ each of these

qualities, and to define it as the _extreme_ of a certain direction.

'Dry' wines and 'sweet' wines, for example, differ, and form a series.

It happens that we have an experience of sweetness pure and simple in

the taste of sugar, and this we can analyze out of the wine-taste.

But no one knows what 'dryness' tastes like, all by itself. It must,

however, be something extreme in the dry direction; and we should

probably not fail to recognize it as the original of our abstract

conception, in case we ever did come across it. In some such way we get

to form notions of the flavor of meats, apart from their feeling to the

tongue, or of that of fruits apart from their acidity, etc., and we

abstract the touch of bodies as distinct from their temperature. We may

even apprehend the quality of a muscle's contraction as distinguished

from its extent, or one muscle's contraction from another's, as when,

by practising with prismatic glasses, and varying our eyes' convergence

whilst our accommodation remains the same, we learn the direction

in which our feeling of the convergence differs from that of the

accommodation.

But the fluctuation in a quality's intensity is a less efficient aid

to our abstracting of it than the diversity of the other qualities in

whose company it may appear. _What is associated now with one thing and

now with another tends to become dissociated from either, and to grow

into an object of abstract contemplation by the mind._ One might call

this the _law of dissociation by varying concomitants_. The practical

result of it will be to allow the mind which has thus dissociated and

abstracted a character to analyze it out of a total, whenever it meets

with it again. The law has been frequently recognized by psychologists,

though I know of none who has given it the emphatic prominence in our

mental history which it deserves. Mr. Spencer says:

"If the property A occurs here along with the properties B, C, D,

there along with C, F, H, and again with E, G, B,... it must happen

that by multiplication of experiences the impressions produced by

these properties on the organism will be disconnected and rendered

so far independent in the organism as the properties are in the

environment, whence must eventually result a power to recognize

attributes in themselves, apart from particular bodies."[422]

And still more to the point Dr. Martineau, in the passage I have

already quoted, writes:

"When a red ivory ball, seen for the first time, has been withdrawn,

it will leave a mental representation of itself, in which all that

it simultaneously gave us will indistinguishably coexist. Let a white

ball succeed to it; now, and not before, will an attribute detach

itself, and the _color_, by force of contrast, be shaken out into

the foreground. Let the white ball be replaced by an egg, and this

new difference will bring the _form_ into notice from its previous

slumber, and thus that which began by being simply an object cut out

from the surrounding scene becomes for us first a _red_ object, then a

_red round_ object, and so on."

_Why_ the repetition of the character in combination with different

wholes will cause it thus to break up its adhesion with any one of

them, and roll out, as it were, alone upon the table of consciousness,

is a little of a mystery. One might suppose the nerve-processes of the

various concomitants to neutralize or inhibit each other more or less

and to leave the process of the common term alone distinctly active.

Mr. Spencer appears to think that the mere fact that the common term

is repeated more often than any one of its associates will, of itself,

give it such a degree of intensity that its abstraction must needs

ensue.

This has a plausible sound, but breaks down when examined closely. For

it is not always the often-repeated character which is first noticed

when its concomitants have varied a certain number of times; it is

even more likely to be the most novel of all the concomitants, which

will arrest the attention. If a boy has seen nothing all his life but

sloops and schooners, he will probably never distinctly have singled

out in his notion of 'sail' the character of being hung lengthwise.

When for the first time he sees a square-rigged ship, the opportunity

of extracting the lengthwise mode of hanging as a special accident, and

of dissociating it from the general notion of sail, is offered. But

there are twenty chances to one that that will not be the form of the

boy's consciousness. What he _notices_ will be the new and exceptional

character of being hung crosswise. He will go home and speak of

that, and perhaps never consciously formulate what the more familiar

peculiarity consists in.

This mode of abstraction is realized on a very wide scale, because the

elements of the world in which we find ourselves appear, as a matter of

fact, here, there, and everywhere, and are changing their concomitants

all the while. But on the other hand the abstraction is, so to speak,

never complete, the analysis of a compound never perfect, because

no element is ever given to us absolutely alone, and we can never

therefore approach a compound with the image in our mind of any one of

its components in a perfectly pure form. Colors, sounds, smells, are

just as much entangled with other matter as are more formal elements of

experience, such as extension, intensity, effort, pleasure, difference,

likeness, harmony, badness, strength, and even consciousness itself.

All are embedded in one world. But by the fluctuations and permutations

of which we have spoken, we come to form a pretty good notion of

the _direction_ in which each element differs from the rest, and so

we frame the notion of it as a _terminus_, and continue to mean it

as an individual thing. In the case of many elements, the simple

sensibles, like heat, cold, the colors, smells, etc., the extremes

of the directions are almost touched, and in these instances we have

a comparatively exact perception of what it is we mean to abstract.

But even this is only an approximation; and in literal mathematical

strictness _all_ our abstracts must be confessed to be but imperfectly

imaginable things. At bottom the process is one of _conception_, and is

everywhere, even in the sphere of simple sensible qualities, the same

as that by which we are usually understood to attain to the notions of

abstract goodness, perfect felicity, absolute power, and the like: the

direct perception of a difference between compounds, and the imaginary

prolongation of the direction of the difference to an ideal terminus,

the notion of which we fix and keep as one of our permanent subjects of

discourse.

This is all that I can say usefully about abstraction, or about

analysis, to which it leads.

THE IMPROVEMENT OF DISCRIMINATION BY PRACTICE.

In all the cases considered hitherto I have supposed the differences

involved to be so large as to be flagrant, and the discrimination,

where successive, was treated as involuntary. But, so far from being

always involuntary, discriminations are often difficult in the extreme,

and by most men never performed. Professor de Morgan, thinking, it is

true, rather of conceptual than of perceptive discrimination, wrote,

wittily enough:

"The great bulk of the illogical part of the educated

community--whether majority or minority I know not; perhaps six of one

and half a dozen of the other--have not power to make a distinction,

and of course cannot be made to take a distinction, and of course

never attempt to shake a distinction. With them all such things are

evasions, subterfuges, come-offs, loop-holes, etc. They would hang a

man for horse-stealing under a statute against sheep-stealing; and

would laugh at you if you quibbled about the distinction between a

horse and a sheep."[423]

Any personal or practical interest, however, in the results to be

obtained by distinguishing, makes one's wits amazingly sharp to

detect differences. The culprit himself is not likely to overlook the

difference between a horse and a sheep. And long training and practice

in distinguishing has the same effect as personal interest. Both of

these agencies give to small amounts of objective difference the same

effectiveness upon the mind that, under other circumstances, only large

ones would have. Let us seek to penetrate the _modus operandi_ of their

influence--beginning with that of practice and habit.

That 'practice makes perfect' is notorious in the field of motor

accomplishments. But motor accomplishments depend in part on sensory

discrimination. Billiard-playing, rifle-shooting, tight-rope-dancing,

demand the most delicate appreciation of minute disparities of

sensation, as well as the power to make accurately graduated muscular

response thereto. In the purely sensorial field we have the well-known

virtuosity displayed by the professional buyers and testers of various

kinds of goods. One man will distinguish by taste between the upper

and the lower half of a bottle of old Madeira. Another will recognize,

by feeling the flour in a barrel, whether the wheat was grown in Iowa

or Tennessee. The blind deaf-mute, Laura Bridgman, had so improved her

touch as to recognize, after a year's interval, the hand of a person

who once had shaken hers; and her sister in misfortune, Julia Brace, is

said to have been employed in the Hartford Asylum to sort the linen

of its multitudinous inmates, after it came from the wash, by her

wonderfully educated sense of smell.

The fact is so familiar that few, if any, psychologists have even

recognized it as needing explanation. They have seemed to think that

practice must, in the nature of things, improve the delicacy of

discernment, and have let the matter rest. At most they have said:

"Attention accounts for it; we attend more to habitual things, and what

we attend to we perceive more minutely." This answer is true, but too

general; it seems to me that we can be a little more precise.

* * * * *

_There are at least two distinct causes_ which we can see at work

whenever experience improves discrimination:

First, the _terms_ whose difference comes to be felt contract disparate

associates and these help to drag them apart.

Second, the _difference_ reminds us of larger differences of the same

sort, and these help us to notice it.

Let us study the first cause first, and begin by supposing two

compounds, of ten elements apiece. Suppose no one element of either

compound to differ from the corresponding element of the other compound

enough to be distinguished from it if the two are compared alone, and

let the amount of this imperceptible difference be called equal to 1.

The compounds will differ from each other, however, in ten different

ways; and, although each difference by itself might pass unperceived,

the total difference, equal to 10, may very well be sufficient to

strike the sense. In a word, _increasing the number of 'points'

involved in a difference may excite our discrimination as effectually

as increasing the amount of difference at any one point_. Two men whose

mouth, nose, eyes, cheeks, chin, and hair, all differ slightly, will

be as little confounded by us, as two appearances of the same man one

with, and the other without, a false nose. The only contrast in the

cases is that we can easily name the _point_ of difference in the one,

whilst in the other we cannot.

Two things, then, B and C, indistinguishable when compared together

alone, may each contract adhesions with different associates, and the

compounds thus formed may, as wholes, be judged very distinct. _The

effect of practice in increasing discrimination must then, in part

be due to the reinforcing effect, upon an original slight difference

between the terms, of additional differences between the diverse

associates which they severally affect._ Let B and C be the terms: If

A contract adhesions with B, and C with D, AB may appear very distinct

from CD, though B and C _per se_ might have been almost identical.

To illustrate, how does one learn to distinguish claret from burgundy?

Probably they have been drunk on different occasions. When we first

drank claret we heard it called by that name, we were eating such and

such a dinner, etc. Next time we drink it, a dim reminder of all those

things chimes through us as we get the taste of the wine. When we try

burgundy our first impression is that it is a kind of claret; but

something falls short of full identification, and presently we hear it

called burgundy. During the next few experiences, the discrimination

may still be uncertain--"which," we ask ourselves, "of the two wines is

this present specimen?" But at last the claret-flavor recalls pretty

distinctly its own name, 'claret,' "that wine I drank at So-and-so's

table," etc.; and the burgundy-flavor recalls the name burgundy and

some one else's table. _And only when this different_ SETTING _has

come to each is our discrimination between the two flavors solid and

stable._ After a while the tables and other parts of the setting,

besides the name, grow so multifarious as not to come up distinctly

into consciousness; but _pari passu_ with this, the adhesion of each

wine with its own _name_ becomes more and more inveterate, and at last

each flavor suggests instantly and certainly its own name and nothing

else. The names differ far more than the flavors, and help to stretch

these latter farther apart. Some such process as this must go on in all

our experience. Beef and mutton, strawberries and raspberries, odor of

rose and odor of violet, contract different adhesions which reinforce

the differences already felt in the terms.

The reader may say that this has nothing to do with making us feel the

_difference_ between the two terms. It is merely fixing, identifying,

and so to speak substantializing, the _terms_. But what we feel as

their _difference_, we should feel, even though we were unable to name

or otherwise identify the terms.

To which I reply that I believe that the difference is always concreted

and made to seem _more substantial_ by recognizing the terms. I went

out for instance the other day and found that the snow just fallen

had a very odd look, different from the common appearance of snow. I

presently called it a 'micaceous' look; and it seemed to me as if, the

moment I did so, the difference grew more distinct and fixed than it

was before. The other connotations of the word 'micaceous' dragged the

snow farther away from ordinary snow and seemed even to aggravate the

peculiar look in question. I think some such effect as this on our way

of feeling a difference will be very generally admitted to follow from

naming the terms between which it obtains; although I admit myself that

it is difficult to show coercively that naming or otherwise identifying

any given pair of hardly distinguishable terms is essential to their

being felt as different at _first_.[424]

I offer the explanation only as a partial one: it certainly is

not complete. Take the way in which _practice refines our local

discrimination on the skin_, for example. Two compass-points touching

the palm of the hand must be kept, say, half an inch asunder in order

not to be mistaken for one point. But at the end of an hour or so of

practice with them we can distinguish them as two, even when less than

a quarter of an inch apart. If the same two regions of the skin were

constantly touched, in this experience, the explanation we have been

considering would perfectly apply. Suppose a line _a b c d e f_ of

points upon the skin. Suppose the local difference of feeling between

_a_ and _f_ to be so strong as to be instantly recognized when the

points are simultaneously touched, but suppose that between _c_ and

_d_ to be at first too small for this purpose. If we began by putting

the compasses on _a_ and _f_ and gradually contracted their opening,

the strong doubleness recognized at first would still be _suggested_,

as the compass-points approached the positions _c_ and _d_; for the

point _e_ would be so near _f_, and so like it, as not to be aroused

without _f_ also coming to mind. Similarly _d_ would recall _e_ and,

more remotely, _f_. In such wise _c--d_ would no longer be bare _c--d_,

but something more like _abc--def_,--palpably differing impressions.

But in actual experience the education can take place in a much less

methodical way, and we learn at last to discriminate _c_ and _d_

without any constant adhesion being contracted between one of these

spots and _ab_, and the other and _ef_. Volkmann's experiments show

this. He and Fechner, prompted by Czermak's observation that the skin

of the blind was twice as discriminative as that of seeing folks,

sought by experiment to show the effects of practice upon themselves.

They discovered that even within the limits of a single sitting the

distances at which points were felt double might fall at the end to

considerably less than half of their magnitude at the beginning; and

that some, though not all, of this improved sensibility was retained

next day. But they also found that exercising one part of the skin in

this way improved the discrimination not only of the corresponding part

of the opposite side of the body, but of the neighboring parts as well.

Thus, at the beginning of an experimental sitting, the compass-points

had to be a Paris line asunder, in order to be distinguished by the

little-finger-tip. But after exercising the _other fingers_, it was

found that the little-finger-tip could discriminate points only half a

line apart.[425] The same relation existed betwixt divers points of the

arm and hand.[426]

Here it is clear that the cause which I first suggested fails to apply,

and that we must invoke another.

What are the exact experimental phenomena? The spots, as such, are

not distinctly located, and the difference, as such, between their

feelings, is not distinctly felt, until the interval is greater than

the minimum required for the mere perception of their _doubleness_.

What we first feel is a bluntness, then a suspicion of doubleness,

which presently becomes a distinct doubleness, and at last two

different-feeling and differently placed spots with a definite tract

of space between them. Some of the places we try give us this latest

stage of the perception immediately; some only give us the earliest;

and between them are intermediary places. But as soon as the _image of

the doubleness_ as it is felt in the more discriminative places gets

lodged in our memory, it helps us to find its like in places where

otherwise we might have missed it, much as the recent hearing of an

'overtone' helps us to detect the latter in a compound sound (_supra_,

pp. 439-40). A dim doubleness grows clearer by being assimilated to

the image of a distincter doubleness felt a moment before. It is

interpreted by means of the latter. And so is any difference, like any

other sort of impression, more easily perceived when we carry in our

mind to meet it a distinct image of what sort of a thing we are to look

for, of what its nature is likely to be.[427]

_These two processes_, the reinforcement of the terms by disparate

associates, and the filling of the memory with past differences, of

similar direction with the present one, but of more conspicuous amount,

_are the only explanations I can offer of the effects of education

in this line_. What is accomplished by both processes is essentially

the same thing: they make small differences affect us as if they were

large ones--that large differences should affect us as they do remains

an inexplicable fact. In principle these two processes ought to be

sufficient to account for all possible cases. Whether in fact they are

sufficient, whether there be no residual factor which we have failed to

detect and analyze out, I will not presume to decide.

PRACTICAL INTERESTS LIMIT DISCRIMINATION.

It will be remembered that on page 509 personal interest was named

as a sharpener of discrimination alongside of practice. But personal

interest probably acts through attention and not in any immediate or

specific way. A distinction in which we have a practical stake is one

which we concentrate our minds upon and which we are on the look-out

for. We draw it frequently, and we get all the benefits of so doing,

benefits which have just been explained. Where, on the other hand,

a distinction has no practical interest, where we gain nothing by

analyzing a feature from out of the compound total of which it forms

a part, we contract a habit of leaving it unnoticed, and at last grow

callous to its presence. Helmholtz was the first psychologist who dwelt

on these facts as emphatically as they deserve, and I can do no better

than quote his very words.

"We are accustomed," he says, "in a large number of cases where

sensations of different kinds, or in different parts of the body,

exist simultaneously, to recognize that they are distinct as soon as

they are perceived, and to direct our attention at will to any one of

them separately. Thus at any moment we can be separately conscious of

what we see, of what we hear, of what we feel; and distinguish what we

feel in a finger or in the great toe, whether pressure, gentle touch,

or warmth. So also in the field of vision. Indeed, as I shall endeavor

to show in what follows, we readily distinguish our sensations

from one another _when we have a precise knowledge_ that they are

composite, as, for example, when we have become certain, by frequently

repeated and invariable experience, that our present sensation arises

from the simultaneous action of many independent stimuli, each of

which usually excites an equally well-known individual sensation."

This, it will be observed, is only another statement of our law, that

the only individual components which we can pick out of compounds are

those of which we have independent knowledge in a separate form.

"This induces us to think that nothing can be easier, when a number of

different sensations are simultaneously excited, than to distinguish

them individually from each other, and that this is an innate faculty

of our minds.

"Thus we find, among other things, that it is quite a matter of course

to hear separately the different musical tones which come to our

senses collectively; and we expect that in every case when two of them

occur together, we shall be able to do the like.

"The matter becomes very different when we set to work to investigate

the more unusual cases of perception, and seek more completely to

understand the conditions under which the above-mentioned distinction

can or cannot be made, as is the case in the physiology of the senses.

We then become aware that _two different kinds or grades must be

distinguished in our becoming conscious of a sensation_. The lower

grade of this consciousness is that in which the influence of the

sensation in question makes itself felt only in the conceptions we

form of external things and processes, and assists in determining

them. This can take place without our needing, or indeed being

able, to ascertain to what particular part of our sensations we owe

this or that circumstance in our perceptions. In this case we will

say that the impression of the sensation in question is _perceived

synthetically_. The second higher grade is when we immediately

distinguish the sensation in question as an existing part of the

sum of the sensations excited in us. We will say, then, that the

sensation is _perceived analytically_. The two cases must be carefully

distinguished from each other."[428]

By the sensation being perceived synthetically, Helmholtz means that

it is not discriminated at all, but only felt in a mass with other

simultaneous sensations. That it _is_ felt there he thinks is proved

by the fact that our _judgment_ of the total will change if anything

occurs to alter the _outer cause_ of the sensation.[429] The following

pages from an earlier edition show what the concrete cases of synthetic

perception and what those of analytic perception are wont to be:

"In the use of our senses, practice and experience play a much larger

part than we ordinarily suppose. Our sensations are in the first

instance important only in so far as they enable us to judge rightly

of the world about us; and our practice in discriminating between them

usually goes only just far enough to meet this end. We are, however,

too much disposed to think that we must be immediately conscious of

every ingredient of our sensations. This natural prejudice is due

to the fact that we are indeed conscious, immediately and without

effort, of everything in our sensations which has a bearing upon those

practical purposes, for the sake of which we wish to know the outer

world. Daily and hourly, during our whole life, we keep our senses in

training for this end exclusively, and for its sake our experiences

are accumulated. But even within the sphere of these sensations, which

do correspond to outer things, training and practice make themselves

felt. It is well known how much finer and quicker the painter is in

discriminating colors and illuminations than one whose eye is not

trained in these matters; how the musician and the musical-instrument

maker perceive with ease and certainty differences of pitch and tone

which for the ear of the layman do not exist; and how even in the

inferior realms of cookery and wine-judging it takes a long habit of

comparing to make a master. But more strikingly still is seen the

effect of practice when we pass to sensations which depend only on

inner conditions of our organs, and which, not corresponding at all to

outer things or to their effects upon us, are therefore of no value

in giving us information about the outer world. The physiology of the

sense-organs has, in recent times, made us acquainted with a number

of such phenomena, discovered partly in consequence of theoretic

speculations and questionings, partly by individuals, like Goethe and

Purkinje, specially endowed by nature with talent for this sort of

observation. These so-called subjective phenomena are extraordinarily

hard to find; and when they are once found, special aids for the

attention are almost always required to observe them. It is usually

hard to notice the phenomenon again even when one knows already the

description of the first observer. The reason is that we are not only

unpractised in singling out these subjective sensations, but that

we are, on the contrary, most thoroughly trained in abstracting our

attention from them, because they would only hinder us in observing

the outer world. Only when their intensity is so strong as actually to

hinder us in observing the outer world do we begin to notice them; or

they may sometimes, in dreaming and delirium, form the starting point

of hallucinations.

"Let me give a few well-known cases, taken from physiological optics,

as examples. Every eye probably contains _muscæ volitantes_, so

called; these are fibres, granules, etc., floating in the vitreous

humor, throwing their shadows on the retina, and appearing in the

field of vision as little dark moving spots. They are most easily

detected by looking attentively at a broad, bright, blank surface

like the sky. Most persons who have not had their attention expressly

called to the existence of these figures are apt to notice them for

the first time when some ailment befalls their eyes and attracts

their attention to the subjective state of these organs. The usual

complaint then is that the _muscæ volitantes_ came in with the malady;

and this often makes the patients very anxious about these harmless

things, and attentive to all their peculiarities. It is then hard work

to make them believe that these figures have existed throughout all

their previous life, and that all healthy eyes contain them. I knew

an old gentleman who once had occasion to cover one of his eyes which

had accidentally become diseased, and who was then in no small degree

shocked at finding that his other eye was totally blind; with a sort

of blindness, moreover, which must have lasted years, and yet he never

was aware of it.

"Who, besides, would believe without performing the appropriate

experiments, that when one of his eyes is closed there is a great gap,

the so-called 'blind spot,' not far from the middle of the field of

the open eye, in which he sees nothing at all, but which he fills out

with his imagination? Mariotte, who was led by theoretic speculations

to discover this phenomenon, awakened no small surprise when he

showed it at the court of Charles II. of England. The experiment was

at that time repeated with many variations, and became a fashionable

amusement. The gap is, in fact, so large that seven full moons

alongside of each other would not cover its diameter, and that a

man's face 6 or 7 feet off disappears within it. In our ordinary use

of vision this great hole in the field fails utterly to be noticed;

because our eyes are constantly wandering, and the moment an object

interests us we turn them full upon it. So it follows that the object

which at any actual moment excites our attention never happens to

fall upon this gap, and thus it is that we never grow conscious of

the blind spot in the field. In order to notice it, we must first

purposely rivet our gaze upon one object and then move about a second

object in the neighborhood of the blind spot, striving meanwhile to

_attend_ to this latter without moving the direction of our gaze

from the first object. This runs counter to all our habits, and is

therefore a difficult thing to accomplish. With some people it is

even an impossibility. But only when it is accomplished do we see the

second object vanish and convince ourselves of the existence of this

gap.

"Finally, let me refer to the double images of ordinary binocular

vision. Whenever we look at a point with both eyes, all objects on

this side of it or beyond it appear double. It takes but a moderate

effort of observation to ascertain this fact; and from this we may

conclude that we have been seeing the far greater part of the external

world double all our lives, although numbers of persons are unaware

of it, and are in the highest degree astonished when it is brought

to their attention. As a matter of fact, we never _have_ seen in

this double fashion any particular object upon which our attention

was directed at the time; for upon such objects we always converge

both eyes. In the habitual use of our eyes, our attention is always

withdrawn from such objects as give us double images at the time; this

is the reason why we so seldom learn that these images exist. In order

to find them we must set our attention a new and unusual task; we must

make it explore the lateral parts of the field of vision, not, as

usual, to find what objects are there, but to analyze our sensations.

Then only do we notice this phenomenon.[430]

"The same difficulty which is found in the observation of subjective

sensations to which no external object corresponds is found also in

the analysis of compound sensations which correspond to a single

object. Of this sort are many of our sensations of sound. When the

sound of a violin, no matter how often we hear it, excites over and

over again in our ear the same sum of partial tones, the result is

that our feeling of this sum of tones ends by becoming for our mind a

mere sign for the voice of the violin. Another combination of partial

tones becomes the sensible sign of the voice of a clarionet, etc. And

the oftener any such combination is heard, the more accustomed we grow

to perceiving it as an integral total, and the harder it becomes to

analyze it by immediate observation. I believe that this is one of the

principal reasons why the analysis of the notes of the human voice in

singing is relatively so difficult. Such fusions of many sensations

into what, to conscious perception, seems a simple whole, abound in

all our senses.

"Physiological optics affords other interesting examples. The

perception of the bodily form of a near object comes about through the

combination of two diverse pictures which the eyes severally receive

from it, and whose diversity is due to the different position of each

eye, altering the perspective view of what is before it. Before the

invention of the stereoscope this explanation could only be assumed

hypothetically; but it can now be proved at any moment by the use of

the instrument. Into the stereoscope we insert two flat drawings,

representing the two perspective views of the two eyes, in such a

manner that each eye sees its own view in the proper place; and we

obtain, in consequence, the perception of a single extended solid, as

complete and vivid as if we had the real object before us.

"Now we can, it is true, by shutting one eye after the other and

attending to the point, recognize the difference in the pictures--at

least when it is not too small. But, for the stereoscopic perception

of solidity, pictures suffice whose difference is so extraordinarily

slight as hardly to be recognized by the most careful comparison;

and it is certain that, in our ordinary careless observing of bodily

objects, we never dream that the perception is due to two perspective

views fused into one, because it is an entirely different kind of

perception from that of either flat perspective view by itself. It

is certain, therefore, that two different sensations of our two eyes

fuse into a third perception entirely different from either. Just

as partial tones fuse into the perception of a certain instrument's

voice; and just as we learn to separate the partial tones of a

vibrating string by pinching a nodal point and letting them sound

in isolation; so we learn to separate the images on the two eyes by

opening and closing them alternately.

"There are other much more complex instances of the way in which

many sensations may combine to serve as the basis of a quite simple

perception. When, for example we perceive an object in a certain

_direction_, we must somehow be impressed by the fact that certain

of our optic nerve-fibres, and no others, are impressed by its

light. Furthermore, we must rightly judge the position of our eyes

in our head, and of our head upon our body, by means of feelings in

our eye-muscles and our neck-muscles respectively. If any of these

processes is disturbed we get a false perception of the object's

position. The nerve-fibres can be changed by a prism before the eye;

or the eyeball's position changed by pressing the organ towards one

side; and such experiments show that, for the simple seeing of the

position of an object, sensations of these two sorts must concur. But

it would be quite impossible to gather this directly from the sensible

impression which the object makes. Even when we have made experiments

and convinced ourselves in every possible manner that such must be

the fact, it still remains hidden from our immediate introspective

observation.

"These examples" [of 'synthetic perception,' perception in which each

contributory sensation is felt _in_ the whole, and is a co-determinant

of what the whole shall be, but does not attract the attention to its

separate self] "may suffice to show the vital part which the direction

of attention and practice in observing play in sense-perception. To

apply this now to the ear. The ordinary task which our ear has to

solve when many sounds assail it at once is to discern the voices of

the several sounding bodies or instruments engaged; beyond this it has

no objective interest in analyzing. We wish to know, when many men

are speaking together, what each one says, when many instruments and

voices combine, which melody is executed by each. Any deeper analysis,

such as that of each separate note into its partial tones (although

it might be performed by the same means and faculty of hearing as the

first analysis) would tell us nothing new about the sources of sound

actually present, but might lead us astray as to their number. For

this reason we confine our attention in analyzing a mass of sound to

the several instruments' voices, and expressly abstain, as it were,

from discriminating the elementary components of the latter. In this

last sort of discrimination we are as unpractised as we are, on the

contrary, well trained in the former kind."[431]

After all we have said, no comment seems called for upon these

interesting and important facts and reflections of Helmholtz.

REACTION-TIME AFTER DISCRIMINATION.

The _time required for discrimination_ has been made a subject of

experimental measurement. Wundt calls it _Unterscheidungszeit_. His

subjects (whose simple reaction-time--see p. 85 ff.--had previously

been determined) were required to make a movement, always the same,

the instant they discerned _which_ of two or more signals they

received. The exact time of the signal and that of the movement were

automatically registered by a galvanic chronoscope. The particular

signal to be received was unknown in advance, and the excess of time

occupied by those reactions in which its character had first to be

discerned, over the simple reaction-time, measured, according to Wundt,

the time required for the act of discrimination. It was found longer

when four different signals were irregularly used than when only

two were used. In the former case it averaged, for three observers

respectively (the signals being the sudden appearance of a black or of

a white object),

0.050 sec.;

0.047 sec.

0.079 sec.

In the latter case, a red and a green signal being added to the former

ones, it became, for the same observers,

0.157;

0.073;

0.132.[432]

Later, in Wundt's Laboratory, Herr Tischer made many careful

experiments after the same method, where the facts to be discriminated

were the different degrees of loudness in the sound which served as

a signal. I subjoin Herr Tischer's table of results, explaining that

each vertical column after the first gives the average results obtained

from a distinct individual, and that the figure in the first column

stands for the number of possible loudnesses that might be expected in

the particular series of reactions made. The times are expressed in

thousandths of a second.

2 | 6 | 8.5 | 10.75 | 10.7 | 33 | 53

3 | 10 | 14.4 | 19.9 | 22.7 | 58.5 | 57.8

4 | 16.7 | 20.8 | 29 | 29.1 | 75 | 84

5 | 25.6 | 31 | ... | 40.1 | 95.5 | 138[433]

The interesting points here are the great individual variations, and

the rapid way in which the time for discrimination increases with the

number of possible terms to discriminate. The individual variations are

largely due to want of practice in the particular task set, but partly

also to discrepancies in the psychic process. One gentleman said,

for example, that in the experiments with three sounds, he kept the

image of the middle one ready in his mind, and compared what he heard

as either louder, lower, or the same. His discrimination among three

possibilities became thus very similar to a discrimination between

two.[434]

Mr. J. M. Cattell found he could get no results by this method,[435]

and reverted to one used by observers previous to Wundt and which

Wundt had rejected. This is the _einfache Wahlmethode_, as Wundt calls

it. The reacter awaits the signal and reacts if it is of one sort, but

omits to act if it is of another sort. The reaction thus occurs after

discrimination; the motor impulse cannot be sent to the hand until the

subject knows what the signal is. The nervous impulse, as Mr. Cattell

says, must probably travel to the cortex and excite changes there,

causing in consciousness the perception of the signal. These changes

occupy the time of discrimination (or perception-time, as it is called

by Mr. C.) But _then_ a nervous impulse must descend from the cortex

to the lower motor centre which stands primed and ready to discharge;

and this, as Mr. C. says, gives a will-time as well. The total

reaction-time thus includes both 'will-time' and 'discrimination-time.'

But as the centrifugal and centripetal processes occupying these two

times respectively are probably about the same, and the time used

in the cortex is about equally divided between the perception of

the signal and the preparation of the motor discharge, if we divide

it equally between perception (discrimination) and volition, the

error cannot be great.[436] We can moreover change the nature of the

perception without altering the will-time, and thus investigate with

considerable thoroughness the length of the perception-time.

Guided by these principles, Prof. Cattell found the time required for

distinguishing a white signal from no signal to be, in two observers:

0.030 sec. and 0.050 sec;

that for distinguishing one color from another was similarly:

0.100 and 0.110;

that for distinguishing a certain color from ten other colors:

0.105 and 0.117;

that for distinguishing the letter A in ordinary print from the letter

Z:

0.142 and 0.137;

that for distinguishing a given letter from all the rest of the alphabet

(not reacting until that letter appeared)

0.119 and 0.116;

that for distinguishing a word from any of twenty-five other words, from

0.118 sec. to 0.158 sec.

The difference depending on the length of the words and the familiarity

of the language to which they belonged.

Prof. Cattell calls attention to the fact that the time for

distinguishing a word is often but little more than that for

distinguishing a letter:

"We do not, therefore, distinguish separately the letters of which a

word is composed, but the word as a whole. The application of this in

teaching children to read is evident."

He also finds a great difference in the time with which various letters

are distinguished, E being particularly bad.[437]

I have, in describing these experiments, followed the example of

previous writers and spoken as if the process by which the nature of

the signal determines the reaction were identical with the ordinary

conscious process of discriminative perception and volition. I am

convinced, however, that this is not the case; and that although the

results are the same, the form of consciousness is quite different.

The reader will remember my contention (_supra_, p. 90 ff.) that the

simple reaction-time (usually supposed to include a conscious process

of perceiving) really measures nothing but a reflex act. Anyone who

will perform reactions with discrimination will easily convince

himself that the process here also is far more like a reflex, than

like a deliberate, operation. I have made, with myself and students,

a large number of measurements where the signal expected was in one

series a touch _somewhere_ on the skin of the back and head, and in

another series a spark _somewhere_ in the field of view. The hand

had to move as quickly as possible towards the place of the touch

or the spark. It did so infallibly, and sensibly instantly; whilst

both place and movement seemed to be _perceived_ only a moment

later, in memory. These experiments were undertaken for the express

purpose of ascertaining whether the movement at the sight of the

spark was discharged _immediately_ by the visual perception, or

whether a 'motor-idea' had to intervene between the perception of the

spark and the reaction.[438] The first thing that was manifest to

introspection was that no perception or idea of _any_ sort preceded

the reaction. It jumped of itself, whenever the signal came; and

perception was retrospective. We must suppose, then, that the state of

eager expectancy of a certain definite range of possible discharges,

innervates a whole set of paths in advance, so that when a particular

sensation comes it is drafted into its appropriate motor outlet too

quickly for the perceptive process to be aroused. In the experiments

I describe, the conditions were most favorable for rapidity, for the

connection between the signals and their movements might almost be

called innate. It is instinctive to move the hand towards a thing seen

or a skin-spot touched. But where the movement is _conventionally_

attached to the signal, there would be more chance for delay, and

the amount of practice would then determine the speed. This is well

shown in Tischer's results, quoted on p. 524, where the most practised

observer, Tischer himself, reacted in one eighth of the time needed

by one of the others.[439] But what all investigators have aimed to

determine in these experiments is the _minimum_ time. I trust I have

said enough to convince the student that this minimum time by no means

measures what we consciously know as discrimination. It only measures

something which, under the experimental conditions, leads to a similar

result. But it is the bane of psychology to suppose that where results

are similar, processes must be the same. Psychologists are too apt to

reason as geometers would, if the latter were to say that the diameter

of a circle is the same thing as its semi-circumference, because,

forsooth, they terminate in the same two points.[440]

THE PERCEPTION OF LIKENESS.

The perception of likeness is practically very much bound up with

that of difference. That is to say, the only differences we note _as_

differences, and estimate quantitatively, and arrange along a scale,

are those comparatively limited differences which we find between

members of a common genus. The force of gravity and the color of this

ink are things it never occurred to me to compare until now that I

am casting about for examples of the incomparable. Similarly the

elastic quality of this india-rubber band, the comfort of last night's

sleep, the good that can be done with a legacy, these are things too

discrepant to have ever been compared ere now. Their relation to each

other is less that of difference than of mere logical negativity. To be

found _different_, things must as a rule have some commensurability,

some aspect in common, which suggests the possibility of their

being treated in the same way. This is of course not a theoretic

necessity--for any distinction may be called a 'difference,' if one

likes--but a practical and linguistic remark.

The _same things, then, which arouse the perception of difference

usually arouse that of resemblance also_. And the analysis of them,

so as to define wherein the difference and wherein the resemblance

respectively consists, is called _comparison_. If we start to deal with

the things as simply the same or alike, we are liable to be surprised

by the difference. If we start to treat them as merely different, we

are apt to discover how much they are alike. _Difference, commonly so

called, is thus between species of a genus._ And the faculty by which

we perceive the resemblance upon which the genus is based, is just

as ultimate and inexplicable a mental endowment as that by which we

perceive the differences upon which the species depend. There is a

shock of likeness when we pass from one thing to another which in the

first instance we merely discriminate numerically, but, at the moment

of bringing our attention to bear, perceive to be _similar_ to the

first; just as there is a shock of difference when we pass between two

dissimilars.[441] The objective extent of the likeness, just like that

of the difference, determines the magnitude of the shock. The likeness

may be so evanescent, or the basis of it so habitual and little liable

to be attended to, that it will escape observation altogether. Where,

however, we find it, there we make a genus of the things compared; and

their discrepancies and incommensurabilities in other respects can

then figure as the _differential_ of so many species. As 'thinkables'

or 'existents' even the smoke of a cigarette and the worth of a

dollar-bill are comparable--still more so as 'perishables,' or as

'enjoyables.'

Much, then, of what I have said of difference in the course of this

chapter will apply, with a simple change of language, to resemblance as

well. We go through the world, carrying on the two functions abreast,

discovering differences in the like, and likenesses in the different.

To abstract the _ground_ of either difference or likeness (where it

is not ultimate) demands an analysis of the given objects into their

parts. So that all that was said of the dependence of analysis upon a

preliminary separate acquaintance with the character to be abstracted,

and upon its having varied concomitants, finds a place in the

psychology of resemblance as well as in that of difference.

But when all is said and done about the conditions which favor our

perception of resemblance and our abstraction of its ground, the

crude fact remains, that _some people are far more sensitive to

resemblances, and far more ready to point out wherein they consist,

than others are_. They are the wits, the poets, the inventors, the

scientific men, the practical geniuses. _A native talent for perceiving

analogies_ is reckoned by Prof. Bain, and by others before and after

him, as _the leading fact in genius of every order_. But as this

chapter is already long, and as the question of genius had better wait

till Chapter XXII, where its practical consequences can be discussed at

the same time, I will say nothing more at present either about it or

about the faculty of noting resemblances. If the reader feels that this

faculty is having small justice done it at my hands, and that it ought

to be wondered at and made much more of than has been done in these

last few pages, he will perhaps find some compensation when that later

chapter is reached. I think I emphasize it enough when I call it one of

the ultimate foundation-pillars of the intellectual life, the others

being Discrimination, Retentiveness, and Association.

THE MAGNITUDE OF DIFFERENCES.

On page 489 I spoke of differences being greater or less, and of

certain groups of them being susceptible of a linear arrangement

exhibiting serial _increase_. A series whose terms grow more and more

different from the starting point is one whose terms grow less and

less like it. They grow more and more like it if you read them the

other way. So that likeness and unlikeness to the starting point are

functions inverse to each other, of the position of any term in such a

series.

Professor Stumpf introduces the word _distance_ to denote the position

of a term in any such series. The less like is the term, the more

distant it is from the starting point. The ideally regular series of

this sort would be one in which the distances--the steps of resemblance

or difference--between all pairs of adjacent terms were equal. This

would be an evenly gradated series. And it is an interesting fact in

psychology that we are able, in many departments of our sensibility,

to arrange the terms without difficulty in this evenly gradated way.

Differences, in other words, between diverse pairs of terms, _a_ and

_b_, for example, on the one hand, and _c_ and _d_ on the other,[442]

can be judged equal or diverse in amount. The distances from one term

to another in the series are equal. Linear magnitudes and musical notes

are perhaps the impressions which we easiest arrange in this way.

Next come shades of light or color, which we have little difficulty

in arranging by steps of difference of sensibly equal value. Messrs.

Plateau and Delbœuf have found it fairly easy to determine what shade

of gray will be judged by every one to hit the exact middle between a

darker and a lighter shade.[443]

How now do we so readily recognize the equality of two differences

between different pairs of terms? or, more briefly, how do we recognize

the _magnitude_ of a difference at all? Prof. Stumpf discusses this

question in an interesting way;[444] and comes to the conclusion that

our feeling for the size of a difference, and our perception that

the terms of two diverse pairs are equally or unequally distant from

each other, can be explained by no simpler mental process, but, like

the shock of difference itself, must be regarded as for the present

an unanalyzable endowment of the mind. This acute author rejects in

particular the notion which would make our judgment of the distance

between two sensations depend upon our _mentally traversing the

intermediary steps_. We may of course do so, and may often find it

useful to do so, as in musical intervals, or figured lines, But we need

not do so; and nothing more is really _required_ for a comparative

judgment of the amount of a 'distance' than three or four impressions

belonging to a common kind.

The vanishing of all perceptible difference between two numerically

distinct things makes them _qualitatively the same_ or _equal_.

Equality, or _qualitative_ (as distinguished from numerical)

_identity_, is thus nothing but the _extreme degree of likeness_.[445]

We saw above (p. 492) that some persons consider that the difference

between two objects is constituted of two things, viz., their absolute

identity in certain respects, _plus_ their absolute non-identity in

others. We saw that this theory would not apply to all cases (p. 493).

So here any theory which would base likeness on identity, and not

rather identity on likeness, must fail. It is supposed perhaps, by

most people, that two resembling things owe their resemblance to their

absolute identity in respect of some attribute or attributes, combined

with the absolute non-identity of the rest of their being. This, which

may be true of compound things, breaks down when we come to simple

impressions.

"When we compare a deep, a middle, and a high note, e.g. _C, f_ sharp,

_a'''_, we remark immediately that the first is less like the third

than the second is. The same would be true of _c d e_ in the same

region of the scale. Our very calling one of the notes a 'middle'

note is the expression of a judgment of this sort. But where here is

the identical and where the non-identical part? We cannot think of

the overtones; for the first-named three notes have none in common,

at least not on musical instruments. Moreover, we might take simple

tones, and still our judgment would be unhesitatingly the same,

provided the tones were not chosen too close together.... Neither can

it be said that the identity consists in their all being sounds, and

not a sound, a smell, and a color, respectively. For this identical

attribute comes to each of them in equal measure, whereas the first,

being less like the third than the second is, ought, on the terms

of the theory we are criticising, to have less of the identical

quality.... It thus appears impracticable to define all possible cases

of likeness as partial identity _plus_ partial disparity; and it is

vain to seek in all cases for identical elements."[446]

And as all compound resemblances are based on simple ones like these,

it follows that likeness _überhaupt_ must not be conceived as a special

complication of identity, but rather that identity must be conceived as

a special degree of likeness, according to the proposition expressed at

the outset of the paragraph that precedes. Likeness and difference are

ultimate relations perceived. As a matter of fact, no two sensations,

no two objects of all those we know, are in scientific rigor identical.

We call those of them identical whose difference is unperceived.

Over and above this we have a _conception_ of absolute sameness, it

is true, but this, like so many of our conceptions (cf. p. 508), is

an ideal construction got by following a certain direction of serial

increase to its maximum supposable extreme. It plays an important

part, among other permanent meanings possessed by us, in our ideal

intellectual constructions. But it plays no part whatever in explaining

psychologically how we perceive likenesses between simple things.

THE MEASURE OF DISCRIMINATIVE SENSIBILITY.

In 1860, Professor G. T. Fechner of Leipzig, a man of great learning

and subtlety of mind, published two volumes entitled 'Psychophysik,'

devoted to establishing and explaining a law called by him the

psychophysic law, which he considered to express the deepest and most

elementary relation between the mental and the physical worlds. It is

a formula for the connection between the amount of our sensations and

the amount of their outward causes. Its simplest expression is, that

when we pass from one sensation to a stronger one of the same kind, the

sensations increase proportionally to the logarithms of their exciting

causes. Fechner's book was the starting point of a new department of

literature, which it would be perhaps impossible to match for the

qualities of thoroughness and subtlety, but of which, in the humble

opinion of the present writer, the proper psychological outcome is just

_nothing_. The psychophysic law controversy has prompted a good many

series of observations on sense-discrimination, and has made discussion

of them very rigorous. It has also cleared up our ideas about the best

methods for getting average results, when particular observations vary;

and beyond this it has done nothing; but as it is a chapter in the

history of our science, some account of it is here due to the reader.

Fechner's train of thought has been popularly expounded a great many

times. As I have nothing new to add, it is but just that I should quote

an existing account. I choose the one given by Wundt in his Vorlesungen

über Menschen und Thierseele, 1863, omitting a good deal:

"How much stronger or weaker one sensation is than another, we are

never able to say. Whether the sun be a hundred or a thousand times

brighter than the moon, a cannon a hundred or a thousand times louder

than a pistol, is beyond our power to estimate. The natural measure of

sensation which we possess enables us to judge of the equality, of the

'more' and of the 'less,' but not of 'how many times more or less.'

This natural measure is, therefore, as good as no measure at all,

whenever it becomes a question of accurately ascertaining intensities

in the sensational sphere. Even though it may teach us in a general

way that with the strength of the outward physical stimulus the

strength of the concomitant sensation waxes or wanes, still it leaves

us without the slightest knowledge of whether the sensation varies in

exactly the same proportion as the stimulus itself, or at a slower

or a more rapid rate. In a word, we know by our natural sensibility

nothing of the _law_ that connects the sensation and its outward cause

together. To find this law we must first find an exact measure for the

sensation itself; we must be able to say: A stimulus of strength _one_

begets a sensation of strength _one_; a stimulus of strength _two_

begets a sensation of strength _two_, or _three_, or _four_, etc. But

to do this we must first know what a sensation two, three, or four

times greater than another signifies....

"Space magnitudes we soon learn to determine exactly because we only

measure one space against another. The measure of mental magnitudes

is far more difficult.... But the problem of measuring the magnitude

of _sensations_ is the first step in the bold enterprise of making

mental magnitudes altogether subject to exact measurement.... Were

our whole knowledge limited to the fact that the sensation rises when

the stimulus rises, and falls when the latter falls, much would not

be gained. But even immediate unaided observation teaches us certain

facts which, at least in a general way, suggest the law according to

which the sensations vary with their outward cause.

"Every one knows that in the stilly night we hear things unnoticed in

the noise of day. The gentle ticking of the clock, the air circulating

through the chimney, the cracking of the chairs in the room, and a

thousand other slight noises, impress themselves upon our ear. It is

equally well known that in the confused hubbub of the streets, or the

clamor of a railway, we may lose not only what our neighbor says to

us, but even not hear the sound of our own voice. The stars which are

brightest at night are invisible by day; and although we see the moon

then, she is far paler than at night. Everyone who has had to deal

with weights knows that if to a pound in the hand a second pound be

added, the difference is immediately felt; whilst if it be added to a

hundredweight, we are not aware of the difference at all....

"The sound of the clock, the light of the stars, the pressure of

the pound, these are all _stimuli_ to our senses, and stimuli whose

outward amount remains the same. What then do these experiences teach?

Evidently nothing but this, that one and the same stimulus, according

to the circumstances under which it operates, will be felt either

more or less intensely, or not felt at all. Of what sort now is the

alteration in the circumstances, upon which this alteration in the

feeling may depend? On considering the matter closely we see that it

is everywhere of one and the same kind. The tick of the clock is a

feeble stimulus for our auditory nerve, which we hear plainly when

it is alone, but not when it is added to the strong stimulus of the

carriage-wheels and other noises of the day. The light of the stars is

a stimulus to the eye. But if the stimulation which this light exerts

be added to the strong stimulus of daylight, we feel nothing of it,

although we feel it distinctly when it unites itself with the feebler

stimulation of the twilight. The pound-weight is a stimulus to our

skin, which we feel when it joins itself to a preceding stimulus of

equal strength, but which vanishes when it is combined with a stimulus

a thousand times greater in amount.

"We may therefore lay it down as a general rule that a stimulus,

in order to be felt, may be so much the smaller if the already

pre-existing stimulation of the organ is small, but must be so much

the larger, the greater the pre-existing stimulation is. From

this in a general way we can perceive the connection between the

stimulus and the feeling it excites. At least thus much appears,

that the law of dependence is not as simple a one as might have been

expected beforehand. The simplest relation would obviously be that

the sensation should increase in identically the same ratio as the

stimulus, thus that if a stimulus of strength _one_ occasioned a

sensation _one_, a stimulus of _two_ should occasion sensation _two_,

stimulus _three_, sensation _three_, etc. But if this simplest of

all relations prevailed, a stimulus added to a pre-existing strong

stimulus ought to provoke as great an increase of feeling as if it

were added to a pre-existing weak stimulus; the light of the stars

e.g., ought to make as great an addition to the daylight as it does

to the darkness of the nocturnal sky. This we know not to be the

case: the stars are invisible by day, the addition they make to our

sensation then is unnoticeable, whereas the same addition to our

feeling of the twilight is very considerable indeed. So it is clear

that the strength of the sensations does not increase in proportion

to the amount of the stimuli, but more slowly. And now comes the

question, in what proportion does the increase of the sensation

grow less as the increase of the stimulus grows greater. To answer

this question, every-day experiences do not suffice. We need exact

measurements both of the amounts of the various stimuli, and of the

intensity of the sensations themselves.

"How to execute these measurements, however, is something which daily

experience suggests. To measure the strength of sensations is, as we

saw, impossible; we can only measure the difference of sensations.

Experience showed us what very unequal differences of sensation

might come from equal differences of outward stimulus. But all these

experiences expressed themselves in one kind of fact, that the same

difference of stimulus could in one case be felt, and in another

case not felt at all--a pound felt if added to another pound, but

not if added to a hundred-weight.... We can quickest reach a result

with our observations if we start with an arbitrary strength of

stimulus, notice what sensation it gives us, and then _see how much

we can increase the stimulus without making the sensation seem to

change_. If we carry out such observations with stimuli of varying

absolute amounts, we shall be forced to choose in an equally varying

way the amounts of addition to the stimulus which are capable of

giving us a just barely perceptible feeling of _more_. A light, to be

just perceptible in the twilight need not be near as bright as the

starlight; it must be far brighter to be just perceived during the

day. If now we institute such observations for all possible strengths

of the various stimuli, and note for each strength the amount of

addition of the latter required to produce a barely perceptible

alteration of sensation, we shall have a series of figures in which is

immediately expressed the law according to which the sensation alters

when the stimulation is increased...."

Observations according to this method are particularly easy to make

in the spheres of light-, sound-, and pressure-sensation.... Beginning

with the latter case,

"We find a surprisingly simple result. The barely sensible addition to

the original weight _must stand exactly in the same proportion to it_,

be the _same fraction_ of it, no matter what the absolute value may be

of the weights on which the experiment is made.... As the average of

a number of experiments, this fraction is found to be about 1/3; that

is, no matter what pressure there may already be made upon the skin,

an increase or a diminution of the pressure will be _felt_, as soon

as the added or subtracted weight amounts to one third of the weight

originally there."

Wundt then describes how differences may be observed in the muscular

feelings, in the feelings of heat, in those of light, and in those of

sound; and he concludes his seventh lecture (from which our extracts

have been made) thus:

"So we have found that all the senses whose stimuli we are enabled to

measure accurately, obey a uniform law. However various may be their

several delicacies of discrimination, _this_ holds true of all, that

_the increase of the stimulus necessary to produce an increase of the

sensation bears a constant ratio to the total stimulus_. The figures

which express this ratio in the several senses may be shown thus in

tabular form:

Sensation of light, 1/100

Muscular sensation, 1/17

Feeling of pressure, 1/3

Feeling of warmth, 1/3

Feeling of sound, 1/3

"These figures are far from giving as accurate a measure as might be

desired. But at least they are fit to convey a general notion of the

relative discriminative susceptibility of the different senses....

The important law which gives in so simple a form the relation of the

sensation to the stimulus that calls it forth was first discovered

by the physiologist Ernst Heinrich Weber to obtain in special cases.

Gustav Theodor Fechner first proved it to be a law for all departments

of sensation. Psychology owes to him the first comprehensive

investigation of sensations from a physical point of view, the first

basis of an exact Theory of Sensibility."

So much for a general account of what Fechner calls Weber's law. The

'exactness' of the theory of sensibility to which it leads consists in

the supposed fact that it gives the means of representing sensations

by numbers. The _unit_ of any kind of sensation will be that increment

which, when the stimulus is increased, we can just barely perceive

to be added. The total number of units which any given sensation

contains will consist of the total number of such increments which may

be perceived in passing from no sensation of the kind to a sensation

of the present amount. We cannot get at this number directly, but we

can, now that we know Weber's law, get at it by means of the physical

stimulus of which it is a function. For if we know how much of the

stimulus it will take to give a barely perceptible sensation, and then

what percentage of addition to the stimulus will constantly give a

barely perceptible increment to the sensation, it is at bottom only a

question of compound interest to compute, out of the total amount of

stimulus which we may be employing at any moment, the number of such

increments, or, in other words, of sensational units to which it may

give rise. This number bears the same relation to the total stimulus

which the time elapsed bears to the capital plus the compound interest

accrued.

To take an example: If stimulus A just falls short of producing a

sensation, and if _r_ be the percentage of itself which must be added

to it to get a sensation which is barely perceptible--call this

sensation 1--then we should have the series of sensation-numbers

corresponding to their several stimuli as follows:

Sensation 0 = stimulus A;

Sensation 1 = stimulus A (1 + r);

Sensation 2 = stimulus A (1 + r)^2;

Sensation 3 = stimulus A (1 + r)^3;

.....

Sensation _n_ = stimulus A (1 + r)^_n_.

The sensations here form an arithmetical series, and the stimuli a

geometrical series, and the two series correspond term for term. Now,

of two series corresponding in this way, the terms of the arithmetical

one are called the logarithms of the terms corresponding in rank to

them in the geometrical series. A conventional arithmetical series

beginning with zero has been formed in the ordinary logarithmic tables,

so that we may truly say (assuming our facts to be correct so far)

that the _sensations vary in the same proportion as the logarithms of

their respective stimuli_. And we can thereupon proceed to compute

the number of units in any given sensation (considering the unit of

sensation to be equal to the just perceptible increment above zero,

and the unit of stimulus to be equal to the increment of stimulus

_r_, which brings this about) by multiplying the logarithm of the

stimulus by a constant factor which must vary with the particular kind

of sensation in question. If we call the stimulus R, and the constant

factor C, we get the formula

S = C log R,

which is what Fechner calls the _psychophysischer Maasformel_. This, in

brief, is Fechner's reasoning, as I understand it.

The _Maasformel_ admits of mathematical development in various

directions, and has given rise to arduous discussions into which I

am glad to be exempted from entering here, since their interest is

mathematical and metaphysical and not primarily psychological at

all.[447] I must say a word about them metaphysically a few pages later

on. Meanwhile it should be understood that no human being, in any

investigation into which sensations entered, has ever used the numbers

computed in this or any other way in order to test a theory or to reach

a new result. The whole notion of measuring sensations numerically,

remains in short a mere mathematical speculation about possibilities,

which has never been applied to practice. Incidentally to the

discussion of it, however, a great many particular facts have been

discovered about discrimination which merit a place in this chapter.

In the first place it is found, when the difference of two sensations

approaches the limit of discernibility, that at one moment we discern

it and at the next we do not. There are accidental fluctuations in

our inner sensibility which make it impossible to tell just what the

least discernible increment of the sensation is without taking the

average of a large number of appreciations. These _accidental errors_

are as likely to increase as to diminish our sensibility, and are

eliminated in such an average, for those above and those below the line

then neutralize each other in the sum, and the normal sensibility,

if there be one (that is, the sensibility due to constant causes as

distinguished from these accidental ones), stands revealed. The best

way of getting at the average sensibility has been very minutely worked

over. Fechner discussed three methods, as follows:

(1) _The Method of just-discernible Differences._ Take a standard

sensation _S_, and add to it until you distinctly feel the addition

_d_; then subtract from _S_ + _d_ until you distinctly feel the effect

of the subtraction;[448] call the difference here _d'_. The least

discernible difference sought is _d_ + _d'_/2; and the ratio of this

quantity to the original _S_ (or rather to _S_ + _d_ - _d'_) is what

Fechner calls the difference-threshold. _This difference-threshold

should be a constant fraction_ (no matter what is the size of _S_) _if

Weber's law holds universally true._ The difficulty in applying this

method is that we are _so often in doubt_ whether anything has been

added to _S_ or not. Furthermore, if we simply take the smallest _d_

about which we are _never_ in doubt or in error, we certainly get our

least discernible difference larger than it ought theoretically to

be.[449]

Of course the _sensibility_ is small when the least discernible

difference is large, and _vice versâ_; in other words, it and the

difference-threshold are inversely related to each other.

(2) _The Method of True and False Cases._ A sensation which is barely

greater than another will, on account of accidental errors in a long

series of experiments, sometimes be judged equal, and sometimes

smaller; i.e., we shall make a certain number of false and a certain

number of true judgments about the difference between the two

sensations which we are comparing.

"But the larger this difference is, the more the number of the

true judgments will increase at the expense of the false ones; or,

otherwise expressed, the nearer to unity will be the fraction whose

denominator represents the whole number of judgments, and whose

numerator represents those which are true. If _m_ is a ratio of this

nature, obtained by comparison of two stimuli, _A_ and _B_, we may

seek another couple of stimuli, _a_ and _b_, which when compared will

give the same ratio of true to false cases."[450]

If this were done, and the ratio of _a_ to _b_ then proved to be equal

to that of _A_ to _B_, that would prove that pairs of small stimuli

and pairs of large stimuli may affect our discriminative sensibility

similarly so long as the ratio of the components to each other within

each pair is the same. In other words, it would in so far forth prove

the Weberian law. Fechner made use of this method to ascertain his

own power of discriminating differences of weight, recording no less

than 24,576 separate judgments, and computing as a result that his

discrimination for the same relative increase of weight was less good

in the neighborhood of 500 than of 300 grams, but that after 500 grams

it improved up to 3000, which was the highest weight he experimented

with.

(3) _The Method of Average Errors_ consists in taking a standard

stimulus and then trying to make another one of the same sort exactly

equal to it. There will in general be an error whose amount is large

when the discriminative sensibility called in play is small, and _vice

versâ_. The sum of the errors, no matter whether they be positive or

negative, divided by their number, gives the average error. This,

when certain corrections are made, is assumed by Fechner to be the

'reciprocal' of the discriminative sensibility in question. It should

bear a constant proportion to the stimulus, no matter what the absolute

size of the latter may be, if Weber's law hold true.

* * * * *

These methods deal with just perceptible differences. Delbœuf and Wundt

have experimented with larger differences by means of what Wundt calls

the _Méthode der mittleren Abstufungen_, and what we may call

(4) _The Method of Equal-appearing Intervals._ This consists in so

arranging three stimuli in a series that the intervals between the

first and the second shall appear equal to that between the second

and the third. At first sight there seems to be no direct logical

connection between this method and the preceding ones. By them we

compare equally _perceptible_ increments of stimulus in different

regions of the latter's scale; but by the fourth method we compare

increments which strike us as equally _big_. But what we can but just

notice as an increment need not appear always of the same bigness after

it is noticed. On the contrary, it will appear much bigger when we are

dealing with stimuli that are already large.

(5) The method of doubling the _stimulus_ has been employed by Wundt's

collaborator, Merkel, who tried to make one stimulus seem just double

the other, and then measured the objective relation of the two. The

remarks just made apply also to this case.

* * * * *

So much for the methods. The results differ in the hands of different

observers. I will add a few of them, and will take first the

_discriminative sensibility to light_.

By the first method, Volkmann, Aubert, Masson, Helmholtz, and Kräpelin

find figures varying from 1/3 or 1/4 to 1/195 of the original

stimulus. The smaller fractional increments are discriminated when the

light is already fairly strong, the larger ones when it is weak or

intense. That is, the discriminative sensibility is low when weak or

overstrong lights are compared, and at its best with a certain medium

illumination. It is thus a function of the light's intensity; but

throughout a certain range of the latter it keeps constant, and _in so

far forth_ Weber's law is verified for light. Absolute figures cannot

be given, but Merkel, by method 1, found that Weber's law held good for

stimuli (measured by his arbitrary unit) between 96 and 4096, beyond

which intensity no experiments were made.[451] König and Brodhun

have given measurements by method 1 which cover the most extensive

series, and moreover apply to six different colors of light. These

experiments (performed in Helmholtz's laboratory, apparently,) ran from

an intensity called 1 to one which was 100,000 times as great. From

intensity 2000 to 20,000 Weber's law held good; below and above this

range discriminative sensibility declined. The increment discriminated

here was the same for all colors of light, and lay (according to the

tables) between 1 and 2 per cent of the stimulus.[452] Delbœuf had

verified Weber's law for a certain range of luminous intensities by

method 4; that is, he had found that the objective intensity of a light

which appeared midway between two others was really the geometrical

mean of the latter's intensities. But A. Lehmann and afterwards

Neiglick, in Wundt's laboratory, found that effects of contrast played

so large a part in experiments performed in this way that Delbœuf's

results could not be held conclusive. Merkel, repeating the experiments

still later, found that the objective intensity of the light which we

judge to stand midway between two others neither stands midway nor is

a geometric mean. The discrepancy from both figures is enormous, but

is least large from the midway figure or arithmetical mean of the two

extreme intensities.[453] Finally, the stars have from time immemorial

been arranged in 'magnitudes' supposed to differ by equal-seeming

intervals. Lately their intensities have been gauged photometrically,

and the comparison of the subjective with the objective series has been

made. Prof. J. Jastrow is the latest worker in this field. He finds,

taking Pickering's Harvard photometric tables as a basis, that the

ratio of the average intensity of each 'magnitude' to that below it

decreases as we pass from lower to higher magnitudes, showing a uniform

departure from Weber's law, if the method of equal-appearing intervals

be held to have any direct relevance to the latter.[454]

_Sounds_ are less delicately discriminated in intensity than lights.

A certain difficulty has come from disputes as to the measurement of

the objective intensity of the stimulus. Earlier inquiries made the

perceptible increase of the stimulus to be about 1/3 of the latter.

Merkel's latest results of the method of just perceptible differences

make it about 3/10 for that part of the scale of intensities during

which Weber's law holds good, which is from 20 to 5000 of M.'s

arbitrary unit.[455] Below this the fractional increment must be

larger. Above it no measurements were made.

For _pressure and muscular sense_ we have rather divergent results.

Weber found by the method of just-perceptible differences that persons

could distinguish an increase of weight of 1/40 when the two weights

were successively lifted by the same hand. It took a much larger

fraction to be discerned when the weights were laid on a hand which

rested on the table. He seems to have verified his results for only

two pairs of differing weights,[456] and on this founded his 'law.'

Experiments in Hering's laboratory on lifting 11 weights, running

from 250 to 2750 grams showed that the least perceptible increment

varied from 1/21 for 250 grams to 1/114 for 2500. For 2750 it rose to

1/98 again. Merkel's recent and very careful experiments, in which

the finger pressed down the beam of a balance counterweighted by from

25 to 8020 grams, showed that between 200 and 2000 grams a constant

fractional increase of about 1/13 was felt when there was no movement

of the finger, and of about 1/19 when there was movement. Above and

below these limits the discriminative power grew less. It was greater

when the pressure was upon one square millimeter of surface than when

it was upon seven.[457]

_Warmth and taste_ have been made the subject of similar investigations

with the result of verifying something like Weber's law. The

determination of the unit of stimulus is, however, so hard here

that I will give no figures. The results may be found in Wundt's

Physiologische Psychologie, 3d Ed. i, 370-2.

_The discrimination of lengths by the eye_ has been found also to obey

to a certain extent Weber's law. The figures will all be found in G. E.

Müller, _op. cit._ part ii, chap. x, to which the reader is referred.

Professor Jastrow has published some experiments, made by what may be

called a modification of the method of equal-appearing differences,

on our estimation of the length of sticks, by which it would seem

that the estimated intervals and the real ones are directly and not

logarithmically proportionate to each other. This resembles Merkel's

results by that method for weights, lights, and sounds, and differs

from Jastrow's own finding about star-magnitudes.[458]

* * * * *

If we look back over these facts as a whole, we see that it is not any

fixed amount added to an impression that makes us notice an increase

in the latter, but that the amount depends on how large the impression

already is. The amount is expressible as a certain fraction of the

entire impression to which it is added; and it is found that the

fraction is a well-nigh constant figure throughout an entire region

of the scale of intensities of the impression in question. Above and

below this region the fraction increases in value. This is _Weber's

law_, which in so far forth expresses an empirical generalization of

practical importance, without involving any theory whatever or seeking

any absolute measure of the sensations themselves. It is in the

_Theoretic Interpretation of Weber's Law_

that Fechner's originality exclusively consists, in his assumptions,

namely, 1) that the just-perceptible increment is the _sensation-unit_,

and is in all parts of the scale the same (mathematically expressed,

Δ_s_= const.); 2) that all our sensations consist of sums of these

units; and finally, 3) that the reason why it takes a constant

fractional increase of the stimulus to awaken this unit lies in

an ultimate law of the connection of mind with matter, whereby

the quantities of our feelings are related logarithmically to

the quantities of their objects. Fechner seems to find something

inscrutably sublime in the existence of an ultimate 'psychophysic' law

of this form.

These assumptions are all peculiarly fragile. To begin with, the

_mental fact_ which in the experiments corresponds to the increase

of the stimulus is not an _enlarged sensation_, but a _judgment that

the sensation is enlarged_. What Fechner calls the 'sensation' is

what appears to the mind as the _objective phenomenon_ of light,

warmth, weight, sound, impressed part of body, etc. Fechner tacitly

if not openly assumes that such a _judgment of increase_ consists

in the simple fact that an _increased number_ of sensation-units

are present to the mind; and that the judgment is thus itself a

quantitatively bigger mental thing when it judges large differences,

or differences between large terms, than when it judges small ones.

But these ideas are really absurd. The hardest sort of judgment, the

judgment which strains the attention most (if _that_ be any criterion

of the judgment's 'size'), is that about the _smallest_ things and

differences. But really it has no meaning to talk about one judgment

being bigger than another. And even if we leave out judgments and

talk of sensations only, we have already found ourselves (in Chapter

VI) quite unable to read any clear meaning into the notion that they

are masses of units combined. To introspection, our feeling of pink

is surely not a portion of our feeling of scarlet; nor does the light

of an electric arc seem to contain that of a tallow-candle in itself.

Compound _things_ contain parts; and one such thing may have twice

or three times as many parts as another. But when we take a simple

sensible quality like light or sound, and say that there is now twice

or thrice as much of it present as there was a moment ago, although

we seem to mean the same thing as if we were talking of compound

objects, we really mean something different. We mean that if we were

to arrange the various possible degrees of the quality in a scale of

serial increase, the _distance, interval_, or _difference_ between the

stronger and the weaker specimen before us would seem about as great

as that between the weaker one and the beginning of the scale. _It is

these_ RELATIONS, _these_ DISTANCES, _which we are measuring and not

the composition of the qualities themselves_, as Fechner thinks. Whilst

if we turn to objects which _are_ divisible, surely a big object may be

known in a little thought. Introspection shows moreover that in most

sensations a new _kind_ of feeling invariably accompanies our judgment

of an increased impression; and this is a fact which Fechner's formula

disregards.[459]

But apart from these _a priori_ difficulties, and even supposing that

sensations did consist of added units, Fechner's assumption that all

_equally perceptible_ additions are _equally great_ additions is

entirely arbitrary. Why might not a small addition to a small sensation

be as _perceptible_ as a large addition to a large one? In this case

Weber's law would apply not to the additions themselves, but only to

their perceptibility. Our _noticing_ of a difference of units in two

sensations would depend on the latter being in a fixed ratio. But

the _difference itself_ would depend directly on that between their

respective stimuli. So many units added to the stimulus, so many

added to the sensation, and if the stimulus grew in a certain ratio,

in exactly the same ratio would the sensation also grow, though its

_perceptibility_ grew according to the logarithmic law.[460]

If _A_ stand for the smallest difference which _we perceive_, then we

should have, instead of the formula Δ_s_ = const., which is Fechner's,

the formula Δ_s_/_s_ = const., a formula which interprets all the

_facts_ of Weber's law, in an entirely different theoretic way from

that adopted by Fechner.[461]

The entire superstructure which Fechner rears upon the facts is thus

not only seen to be arbitrary and subjective, but in the highest degree

improbable as well. The departures from Weber's law in regions where

it does not obtain, he explains by the compounding with it of other

unknown laws which mask its effects. As if _any_ law could not be

found in _any_ set of phenomena, provided one have the wit to invent

enough other coexisting laws to overlap and neutralize it! The whole

outcome of the discussion, so far as Fechner's theories are concerned,

is indeed _nil. Weber's law alone remains true, as an empirical

generalization of fair extent:_ What we add to a large stimulus

we notice less than what we add to a small one, unless it happen

_relatively to the stimulus_ to be as great.

_Weber's law is probably purely physiological._

One can express this state of things otherwise by saying that the

whole of the stimulus does not seem to be effective in giving us the

perception of 'more,' and the simplest interpretation of such a state

of things would be _physical_. The loss of effect would take place in

the nervous system. If our feelings resulted from a condition of the

nerve-molecules which it grew ever more difficult for the stimulus

to increase, our feelings would naturally grow at a slower rate than

the stimulus itself. An ever larger part of the latter's work would

go to overcoming the resistances, and an ever smaller part to the

realization of the feeling-bringing state. Weber's law would thus be a

sort of _law of friction_ in the neural machine.[462] Just how these

inner resistances and frictions are to be conceived is a speculative

question. Delbœuf has formulated them as fatigue; Bernstein and Ward,

as irradiations. The latest, and probably the most 'real,' hypothesis

is that of Ebbinghaus, who supposes that the intensity of sensation

depends on the _number_ of neural molecules which are disintegrated in

the unit of time. There are only a certain number at any time which are

_capable_ of disintegrating; and whilst most of these are in an average

condition of instability, some are almost stable and some already near

to decomposition. The smallest stimuli affect these latter molecules

only; and as they are but few, the sensational effect from adding a

given quantity of stimulus _at first_ is relatively small. Medium

stimuli affect the majority of the molecules, but affect fewer and

fewer in proportion as they have already diminished their number. The

latest additions to the stimuli find all the medium molecules already

disintegrated, and only affect the small relatively indecomposable

remainder, thus giving rise to increments of feeling which are

correspondingly small. (Pflüger's Archiv, 45, 113.)

It is surely in some such way as this that Weber's law is to be

interpreted, if it ever is. The Fechnerian _Maasformel_ and the

conception of it as an ultimate 'psychophysic law' will remain an 'idol

of the den,' if ever there was one. Fechner himself indeed was a German

_Gelehrter_ of the ideal type, at once simple and shrewd, a mystic and

an experimentalist, homely and daring, and as loyal to facts as to his

theories. But it would be terrible if even such a dear old man as this

could saddle our Science forever with his patient whimsies, and, in

a world so full of more nutritious objects of attention, compel all

future students to plough through the difficulties, not only of his own

works, but of the still drier ones written in his refutation. Those who

desire this dreadful literature can find it; it has a 'disciplinary

value;' but I will not even enumerate it in a foot-note. The only

amusing part of it is that Fechner's critics should always feel bound,

after smiting his theories hip and thigh and leaving not a stick of

them standing, to wind up by saying that nevertheless to him belongs

the _imperishable glory_, of first formulating them and thereby turning

psychology into an _exact science_,

"'And everybody praised the duke

Who this great fight did win.'

'But what good came of it at last?'

Quoth little Peterkin.

'Why, that I cannot tell,' said he,

'But 'twas a famous victory!'"

FOOTNOTES:

[406] Human Understanding, ii, xi, 1, 2.

[407] Analysis, vol. i, p. 71.

[408] The Senses and the Intellect, page 411.

[409] Essays Philosophical and Theological: First Series, pp. 268-273.

[410] Montgomery in 'Mind,' x, 527. Cf. also Lipps: Grundtatsachen des

Seelenlebens, p. 579 ff.; and see below, Chapter XIX.

[411] Stumpf (Tonpsychologie, i, 116 ff.) tries to prove that the

theory that all differences are differences of composition leads

necessarily to an infinite regression when we try to determine the

unit. It seems to me that in his particular reasoning he forgets the

ultimate units of the mind-stuff theory. I cannot find the completed

infinite to be one of the obstacles to belief in this theory, although

I fully accept Stumpf's general reasoning, and am only too happy to

find myself on the same side with such an exceptionally clear thinker.

The strictures by Wahle in the Vierteljsch. f. wiss. Phil. seem to

me to have no force, since the writer does not discriminate between

resemblance of things obviously compound and that of things sensibly

simple.

[412] The _belief that the causes_ of effects felt by us to differ

qualitatively are facts which differ only in quantity (e.g. that blue

is caused by so many ether-waves, and yellow by a smaller number)

must not be confounded with the feeling that the effects differ

quantitatively themselves.

[413] Herr G. H. Schneider, in his youthful pamphlet (Die

Unterscheidung, 1877) has tried to show that there are no

positively existent elements of sensibility, no substantive

qualities between which differences obtain, but that the terms

we call such, the sensations, are but sums of differences, loci

or starting points whence many directions of difference proceed.

'_Unterschiedsempfindungs-Complexe_' are what he calls them. This

absurd carrying out of that 'principle of relativity' which we shall

have to mention in Chapter XVII may serve as a counterpoise to the

mind-stuff theory, which says that there are nothing but substantive

sensations, and denies the existence of relations of difference between

them at all.

[414] Cf. Stumpf, Tonpsychologie, i, 121, and James Ward, Mind, i, 464.

[415] The ordinary treatment of this is to call it the result of the

_fusion_ of a lot of sensations, in themselves separate. This is pure

mythology, as the sequel will abundantly show.

[416] "We often begin to be dimly aware of a difference in a sensation

or group of sensations, before we can assign any definite character

to that which differs. Thus we detect a strange or foreign ingredient

or flavor in a familiar dish, or of tone in a familiar tune, and

yet are wholly unable for a while to say what the intruder is like.

Hence perhaps discrimination may be regarded as the earliest and

most primordial mode of intellectual activity." (Sully: Outlines of

Psychology, p. 142. _Cf._ also G. H. Schneider: Die Unterscheidung, pp.

9-10.)

[417] In cases where the difference is slight, we may need, as

previously remarked, to get the dying phase of _n_ as well as of _m_

before _n-different-from-m_ is distinctly felt. In that case the

inevitably successive feelings (as far as we can sever what is so

continuous) would be four, _m, difference, n, n-different-from-m_. This

slight additional complication alters not a whit the essential features

of the case.

[418] Analysis. J. S. Mill's ed., ii, 17. Cf. also pp. 12, 14.

[419] There is only one obstacle, and that is our inveterate tendency

to believe that where two things or qualities are compared, it

_must_ be that exact duplicates of both have got into the mind and

have matched themselves against each other there. To which the first

reply is the empirical one of "Look into the mind and see." When I

recognize a weight which I now lift as _inferior_ to the one I just

lifted; when, with my tooth now aching, I perceive the pain to be

_less_ intense than it was a minute ago; the two things in the mind

which are compared would, by the authors I criticise, be admitted to

be an actual sensation and an image in the memory. An image in the

memory, by general consent of these same authors, is admitted to be a

weaker thing than a sensation. Nevertheless it is in these instances

judged stronger; that is, an object supposed to be known only in so

far forth as this image represents it, is judged stronger. Ought not

this to shake one's belief in the notion of separate representative

'ideas' weighing themselves, or being weighed by the Ego, against each

other in the mind? And let it not be said that what makes us judge the

felt pain to be weaker than the imagined one of a moment since is our

recollection of the _downward nature of the shock of difference_ which

we felt as we passed to the present moment from the one before it. That

shock does undoubtedly have a different character according as it comes

between terms of which the second diminishes or increases; and it may

be admitted that in cases Where the past term is doubtfully remembered,

the memory of the shock as _plus_ or _minus_, might sometimes enable us

to establish a relation which otherwise we should not perceive. But one

could hardly expect the memory of this shock to overpower our actual

comparison of terms, both of which are _present_ (as are the image

and the sensation in the case supposed), and make us judge the weaker

one to be the stronger.--And hereupon comes the second reply: Suppose

the mind does compare two realities by comparing two ideas of its own

which represent them--what is gained? The same mystery is still there.

The ideas must still be _known_; and, as the attention in comparing

oscillates from one to the other, past must be known with present just

as before. If you must end by simply saying that your 'Ego,' whilst

_being_ neither the idea of _m_ nor the idea of _n_, yet knows and

compares both, why not allow your pulse of thought, which _is_ neither

the thing _m_ nor the thing _n_, to know and compare both directly?

'Tis but a question of how to _name_ the facts least artificially.

The egoist _explains_ them, by naming them as an Ego 'combining' or

'synthetizing' two ideas, no more than we do by naming them a pulse of

thought knowing two facts.

[420] I fear that few will be converted by my words, so obstinately

do thinkers of all schools refuse to admit the unmediated function of

_knowing a thing_, and so incorrigibly do they substitute _being the

thing_ for it. E.g., in the latest utterance of the spiritualistic

philosophy (Bowne's Introduction to Psychological Theory, 1887,

published only three days before this writing) one of the first

sentences which catch my eye is this: "What remembers? The spiritualist

says, the soul remembers; it abides across the years and the flow of

the body, and _gathering up its past, carries it with it_" (p. 28).

Why, for heaven's sake, O Bowne, cannot you say '_knows it_'? If there

is anything our soul does _not_ do to its past, it is to carry it with

it.

[421] Sensations of Tone, 2d English Ed., p. 65.

[422] Psychology, i, 345.

[423] A Budget of Paradoxes, p. 380.

[424] The explanation I offer presupposes that a difference too faint

to have any direct effect in the way of making the mind notice it _per

se_ will nevertheless be strong enough to keep its 'terms' from calling

up identical associates. It seems probable from many observations that

this is the case. All the facts of 'unconscious' inference are proofs

of it. We say a painting 'looks' like the work of a certain artist,

though we cannot name the characteristic differentiæ. We see by a

man's face that he is sincere, though we can give no definite reason

for our faith. The facts of sense-perception quoted from Helmholtz

a few pages below will be additional examples. Here is another good

one, though it will perhaps be easier understood after reading the

chapter on Space-perception than now. Take two stereoscopic slides and

represent on each half-slide a pair of spots, _a_ and _b_, but make

their distances such that the _a_'s are equidistant on both slides,

whilst the _b_'s are nearer together on slide 1 than on slide 2. Make

moreover the distance _ab = ab'''_ and the distance _ab' = ab''_. Then

look successively at the two slides stereoscopically, so that the

_a_'s in both are directly fixated (that is fall on the two foveæ, or

centres of distinctest vision). The _a_'s will then appear single, and

so probably will the _b_'s. But the now single-seeming _b_ on slide 1

will look nearer, whilst that on slide 2 will look farther than the

_a_. But, if the diagrams are rightly drawn, _b_ and _b'''_ must affect

'identical' spots, spots equally far to the right of the fovea, _b_ in

the left eye and _b'''_ in the right eye. The same is true of _b'_ and

_b''_. Identical spots are spots whose sensations cannot possibly be

discriminated as such. Since in these two observations, however, they

give rise to such opposite perceptions of distance, and prompt such

opposite tendencies to movement (since in slide 1 we _converge_ in

looking from _a_ to _b_, whilst in slide 2 we _diverge_), it follows

that two processes which occasion feelings quite indistinguishable to

direct consciousness may nevertheless be each allied with disparate

associates both of a sensorial and of a motor kind. Cf. Donders, Archiv

f. Ophthalmologie, Bd. 13 (1867). The basis of his essay is that we

cannot _feel_ on which eye any particular element of a compound picture

falls, but its effects on our total perception differ in the two eyes.

_a b_ _a b'_

_Slide_ 1. . . . .

_a b''_ _a b'''_

_Slide_ 2. . . . .

[425] A. W. Volkmann: Ueber den Einfluss der Uebung, etc., Leipzig

Berichte, Math.-phys. Classe. x, 1858, p. 67.

[426] _Ibid._ Tabelle 1, p. 43.

[427] Professor Lipps accounts for the tactile discrimination of the

blind in a way which (divested of its 'mythological' assumptions) seems

to me essentially to agree with this. Stronger ideas are supposed to

raise weaker ones over the threshold of consciousness by fusing with

them, the tendency to fuse being proportional to the similarity of the

ideas _Cf._ Grundtatsachen, etc., pp. 232-3; also pp. 118, 492, 526-7.

[428] Sensations of Tone, 2d. English Edition, p. 62.

[429] Compare as to this, however, what I said above, Chapter V, pp.

172-176.

[430] When a person squints, double images are formed in the centre

of the field. As a matter of fact, most squinters are found blind

of one eye, or almost so; and it has long been supposed amongst

ophthalmologists that the blindness is a secondary affection

superinduced by the voluntary suppression of one of the sets of double

images, in other words by the positive and persistent refusal to use

one of the eyes. This explanation of the blindness has, however, been

called in question of late years. See, for a brief account of the

matter, O. F. Wadsworth in Boston Med. and Surg. Journ., cxvi, 49 (Jan.

20, '87), and the replies by Derby and others a little later.--W. J.

[431] Tonempfindungen, Dritte Auflage, pp. 102-107.--The reader who

has assimilated the contents of our Chapter V, above, will doubtless

have remarked that the illustrious physiologist has fallen, in these

paragraphs, into that sort of interpretation of the facts which

we there tried to prove erroneous. Helmholtz, however, is no more

careless than most psychologists in confounding together the object

perceived, the organic conditions of the perception, and the sensations

which _would_ be excited by the several parts of the object, or by

the several organic conditions, _provided_ they came into action

separately or were separately attended to, and in assuming that

what is true of any one of these sorts of fact must be true of the

other sorts also. If each organic condition or part of the object

is there, its sensation, he thinks, must be there also, only in a

'synthetic'--which is indistinguishable from what the authors whom we

formerly reviewed called an 'unconscious'--state. I will not repeat

arguments sufficiently detailed in the earlier chapter (see especially

pp. 170-176), but simply say that what he calls the 'fusion of many

_sensations_ into one' is really the production of one sensation by the

co-operation of many _organic conditions_; and that what perception

fails to discriminate (when it is 'synthetic') is not _sensations_

already existent but not singled out, but new objective _facts_, judged

truer than the facts already synthetically perceived--two views of the

solid body, many harmonic tones, instead of one view and one tone,

states of the eyeball-muscles thitherto unknown, and the like. These

new facts, when first discovered, are known in states of consciousness

never till that moment exactly realized before, states of consciousness

which at the same time judge them to be determinations of the same

_matter of fact_ which was previously realized. All that Helmholtz

says of the conditions which hinder and further analysis applies just

as naturally to the analysis, through the advent of _new_ feelings, of

_objects_ into their elements, as to the analysis of aggregate feelings

into elementary feelings supposed to have been hidden in them all the

while.

The reader can himself apply this criticism to the following passages

from Lotze and Stumpf respectively, which I quote because they are the

ablest expressions of the view opposed to my own. Both authors, it

seems to me, commit the psychologist's fallacy, and allow their later

knowledge of the things felt to be foisted into their account of the

primitive way of feeling them.

Lotze says: "It is indubitable that the simultaneous assault of a

variety of different stimuli on different senses, or even on the same

sense, puts us into a state of confused general feeling in which we

are certainly not conscious of clearly distinguishing the different

impressions. Still it does not follow that in such a case we have a

positive perception of an actual unity of the contents of our ideas,

arising from their mixture; our state of mind seems rather to consist

in (1) the consciousness of our inability to separate what really has

remained diverse, and (2) in the general feeling of the disturbance

produced in the economy of our body by the simultaneous assault of

the stimuli.... Not that the sensations melt into one another, but

simply that the act of distinguishing them is absent; and this again

certainly not so far that the fact of the difference remains entirely

unperceived, but only so far as to prevent us from determining the

amount of the difference, and from apprehending other relations between

the different impressions. Anyone who is annoyed at one and the same

time by glowing heat, dazzling light, deafening noise, and an offensive

smell, will certainly not fuse these disparate sensations into a single

one with a single content which could be sensuously perceived; they

remain for him in separation, and he merely finds it impossible to be

conscious of one of them apart from the others. But, further, he will

have a feeling of discomfort--what I mentioned above as the _second_

constituent of his whole state. For every stimulus which produces in

consciousness a definite content of sensation is also a definite degree

of disturbance, and therefore makes a call upon the forces of the

nerves; and the sum of these little changes, which in their character

as disturbances are not so diverse as the contents of consciousness

they give rise to, produce the general feeling which, added to the

inability to distinguish, deludes us into the belief in an actual

absence of diversity in our sensations. It is only in some such way as

this, again, that I can imagine that state which is sometimes described

as the beginning of our whole education, a state which in itself is

supposed to be simple, and to be afterwards divided into different

sensations by an activity of separation. No activity of separation

in the world could establish differences where no real diversity

existed; for it would have nothing to guide it to the places where it

was to establish them, or to indicate the width it was to give them."

(Metaphysic, § 260, English translation.)

Stumpf writes as follows: "Of coexistent sensations there are always

a large number undiscriminated in consciousness, or (if one prefer

to call what is undiscriminated unconscious) in the soul. They

are, however, not fused into a simple quality. When, on entering a

room, we receive sensations of odor and warmth together, without

expressly attending to either, the two qualities of sensation are

not, as it were, an entirely new simple quality, which first at the

moment in which attention analytically steps in _changes into_ smell

and warmth.... In such cases we find ourselves in presence of an

indefinable, unnamable total of feeling. And when, after successfully

analyzing this total, we call it back to memory, as it was in its

unanalyzed state, and compare it with the elements we have found, the

latter (as it seems to me) may be recognized as real parts contained

in the former, and the former seen to be their sum. So, for example,

when we clearly perceive that the content of our sensation of oil

of peppermint is partly a sensation of taste and partly one of

temperature." (Tonpsychologie, i, 107.)

I should prefer to say that we perceive that objective fact, known to

us as the peppermint taste, to contain those other objective facts

known as aromatic or sapid quality, and coldness, respectively. No

ground to suppose that the vehicle of this last very complex perception

has any identity with the earlier psychosis--least of all is contained

in it.

[432] Physiol. Psych., ii, 248.

[433] Wundt's Philos. Studien, i, 527.

[434] _Ibid._ p. 530.

[435] Mind, xi, 377 ff. He says: "I apparently either distinguished

the impression and made the motion simultaneously, or if I tried to

avoid this by waiting until I had formed a distinct impression before

I began to make the motion, I added to the simple reaction, not only a

perception, but a volition."--Which remark may well confirm our doubts

as to the strict _psychologic_ worth of any of these measurements.

[436] Mind, xi, 379.

[437] For other determinations of discrimination-time by this method

cf. v. Kries and Auerbach, Archiv f. Physiologie, Bd. i, p. 297 ff.

(these authors get much smaller figures); Friedrich, Psychologische

Studien, i, 39. Chapter ix of Buccola's book, Le Legge del tempo, etc.,

gives a full account of the subject.

[438] If so, the reactions upon the spark would have to be slower than

those upon the touch. The investigation was abandoned because it was

found impossible to narrow down the difference between the conditions

of the sight-series and those of the touch-series, to nothing more than

the possible presence in the latter of the intervening motor-idea.

Other disparities could not be excluded.

[439] Tischer gives figures from quite unpractised individuals, which

I have not quoted. The discrimination-time of one of them is 22 times

longer than Tischer's own! (Psychol. Studien, i, 527.)

[440] Compare Lipps's excellent passage to the same critical effect

in his Grundtatsachen des Seelenlebens, pp. 390-393.--I leave my

text just as it was written before the publication of Lange's and

Münsterberg's results cited on pp. 92 and 432. Their 'shortened' or

'muscular' times, got when the expectant attention was addressed to the

possible reactions rather than to the stimulus, constitute the minimal

reaction-time of which I speak, and all that I say in the text falls

beautifully into line with their results.

[441] Cf. Sully: Mind, x, 494-5; Bradley: _ibid._ xi, 83; Bosanquet:

_ibid._ xi, 405.

[442] The judgment becomes easier if the two couples of terms have one

member in common, if _a--b_ and _b--c_, for example, are compared.

This, as Stumpf says (Tonpsychologie, i, 131), is probably because the

introduction of the fourth term brings involuntary cross-comparisons

with it, _a_ and _b_ with _d, b_ with _c_, etc., which confuses us

by withdrawing our attention from the relations we ought alone to be

estimating.

[443] J. Delbœuf: Éléments de Psychophysique (Paris, 1883), p. 64.

Plateau in Stumpf, Tonpsych., i, 125. I have noticed a curious

enlargement of certain 'distances' of difference under the influence

of chloroform. The jingling of the bells on the horses of a horse-car

passing the door, for example, and the rumbling of the vehicle itself,

which to our ordinary hearing merge together very readily into a

_quasi_-continuous body of sound, have seemed so far apart as to

require a sort of mental facing in opposite directions to get from one

to the other, as if they belonged in different worlds. I am inclined to

suspect, from certain data, that the ultimate philosophy of difference

and likeness will have to be built upon experiences of intoxication,

especially by nitrous oxide gas, which lets us into intuitions the

subtlety whereof is denied to the waking state. Cf. B. P. Blood: The

Anæsthetic Revelation, and the Gist of Philosophy (Amsterdam, N. Y.,

1874). Cf. also Mind, vii, 200.

[444] _Op. cit._ p. 126 ff.

[445] Stumpf, pp. 111-121.

[446] Stumpf, pp. 116-7. I have omitted, so as not to make my text

too intricate, an extremely acute and conclusive paragraph, which I

reproduce here: "We may generalize: Wherever a number of sensible

impressions are apprehended _as a series_, there in the last instance

must perceptions of simple likeness be found. _Proof:_ Assume that

all the terms of a series, e.g. the qualities of tone, _c d e f g_,

have something in common,--_no matter what it is_, call it _X_; then I

say that the differing parts of each of these terms must not only be

differently constituted in each, but must _themselves form a series_,

whose existence is the ground for our apprehending the original terms

in serial form. We thus get instead of the original series _a b c d

ef_ ... the equivalent series _Xɑ, Xβ, Xɣ_,... etc. What is gained?

The question immediately arises: How is _ɑ β ɣ_ known as a series?

According to the theory, these elements must themselves be made up of a

part common to all, and of parts differing in each, which latter parts

form a new series, and so on _ad infinitum_, which is absurd."

[447] The most important ameliorations of Fechner's formula are

Delbœuf's in his Recherches sur la Mesure des Sensations (1873), p. 35,

and Elsas's in his pamphlet Über die Psychophysik (1886) p. 16.

[448] Reversing the order is for the sake of letting the opposite

accidental errors due to 'contrast' neutralize each other.

[449] Theoretically it would seem that it ought to be equal to the sum

of all the additions which we judge to be increases divided by the

total number of judgments made.

[450] J. Delbœuf, Éléments de Psychophysique (1883), p. 9.

[451] Philos. Studien, iv, 588.

[452] Berlin Acad. Sitzungsberichte, 1888, p. 917. Other observers

(Dobrowolsky, Lamausky) found great differences in different colors.

[453] See Merkel's tables, _loc. cit._ p. 568.

[454] American Journal of Psychology, i, 125. The rate of decrease is

small but steady, and I cannot well understand what Professor J. means

by saying that his figures verify Weber's law.