earlier one, as by our recollection of certain facts about it. Thus I know that the sunshine to-day is less bright than on a certain day last week, because I then said it was quite dazzling, a remark I should not now care to make. Or I know myself to feel better now than I was last summer, because I can now psychologize, and then I could not. We are constantly busy comparing feelings with whose quality our imagination has no sort of _acquaintance_ at the time--pleasures, or pains, for example. It is notoriously hard to conjure up in imagination a lively image of either of these classes of feeling. The associationists may prate of an idea of pleasure being a pleasant idea, of an idea of pain being a painful one, but the unsophisticated sense of mankind is against them, agreeing with Homer that the memory of griefs when past may be a joy, and with Dante that there is no greater sorrow than, in misery, to recollect one's happier time.
Feelings remembered in this imperfect way _must_ be compared with present or recent feelings by the aid of what we know about them. We identify the remote experience in such a case by _conceiving it_. The most perfect way of conceiving it is by defining it in terms of some standard scale. If I know the thermometer to stand at zero to-day and to have stood at 32° last Sunday, I know to-day to be colder, and I know just how much colder, than it was last Sunday. If I know that a certain note was _c_, and that this note is _d_, I know that this note must be the higher of the two.
The inference that two things differ because their concomitants, effects, names, kinds, or--to put it generally--their _signs_, differ, is of course susceptible of unlimited complication. The sciences furnish examples, in the way in which men are led, by noticing differences in effects, to assume new hypothetical causes, differing from any known heretofore. But no matter how many may be the steps by which such inferential discriminations are made, _they all end in a direct intuition of difference somewhere_. The _last_ ground for inferring that A and B differ must be that, whilst A is an _m_, B is an _n_, and that _m_ and _n_ are _seen to differ_. Let us then neglect the complex cases, the A's and the B's, and go back to the study of the unanalyzable perception of difference between their signs, the _m_'s and the _n_'s, when these are seemingly simple terms.
I said that in their immediate succession the shock of their difference was _felt_. It is felt _repeatedly_ when we go back and forth from _m_ to _n_; and we make a point of getting it thus repeatedly (by alternating our attention at least) whenever the shock is so slight as to be with difficulty perceived. But in addition to being felt at the brief instant of transition, the difference also feels as if incorporated and taken up into the second term, which feels 'different-from-the-first' even while it lasts. It is obvious that the 'second term' of the mind in this case is not bald _n_, but a very complex object; and that the sequence is not simply first '_m_,' then '_difference_,' then '_n_'; but first '_m_,' then '_difference_,' then '_n-different-from-m_.' The several thoughts, however, to which these three several objects are revealed, are three ordinary 'segments' of the mental 'stream.'
As our brains and minds are actually made, it is impossible to get certain _m_'s and _n_'s in immediate sequence and to keep them _pure_.
If kept pure, it would mean that they remained uncompared. With us, inevitably, by a mechanism which we as yet fail to understand, the shock of difference is felt between them, and the second object is not _n_ pure, but _n-as-different-from-m_.[417] It is no more a paradox that under these conditions this cognition of _m_ and _n_ in mutual relation should occur, than that under other conditions the cognition of _m_'s or _n_'s simple quality should occur. But as it has been treated as a paradox, and as a spiritual agent, not itself a portion of the stream, has been invoked to account for it, a word of further remark seems desirable.
My account, it will be noted, is merely a description of the facts as they occur: feelings (or thoughts) each knowing something, but the later one knowing, if preceded by a certain earlier one, a more complicated object than it would have known had the earlier one not been there. I offer no _explanation_ of such a sequence of cognitions.
The explanation (I devoutly expect) will be found some day to depend on cerebral conditions. Until it is forthcoming, we can only treat the sequence as a special case of the general law that every experience undergone by the brain leaves in it a modification which is one factor in determining what manner of experiences the following ones shall be (_cf._ pp. 232-236). To anyone who denies the possibility of such a law I have nothing to say, until he brings his proofs.
The sensationalists and the spiritualists meanwhile (filled both of them with their notion that the mind must in some fashion _contain_ what it knows) begin by giving a crooked account of the facts. Both admit that for _m_ and _n_ to be known in any way whatever, little rounded and finished off duplicates of each must be contained in the mind as separate entities. These pure ideas, so called, of _m_ and _n_ respectively, succeed each other there. And since they _are distinct_, say the sensationalists, they are _eo ipso_ distinguished. "To have ideas different and ideas distinguished, are synonymous expressions; different and distinguished meaning exactly the same thing," says James Mill.[418] "Distinguished!" say the spiritualists, "distinguished _by what_, forsooth? Truly the respective ideas of _m_ and of _n_ in the mind are distinct. But for that very reason neither can distinguish itself from the other, for to do that it would have to be aware of the other, and thus for the time being become the other, and that would be to get mixed up with the other and to lose its own distinctness.
Distinctness of ideas and idea of distinctness, are not one thing, but two. This last is a _relation_. Only a _relating principle_, opposed in nature to all facts of feeling, an Ego, Soul, or Subject, is competent, by being present to both of the ideas alike, to hold them together and at the same time to keep them distinct."
But if the plain facts be admitted that the _pure_ idea of '_n_' is _never in the mind at all_, when '_m_' has once gone before; and that the feeling '_n-different-from-m_' is itself an absolutely unique pulse of thought, the bottom of this precious quarrel drops out and neither party is left with anything to fight about. Surely such a consummation ought to be welcomed, especially when brought about, us here, by a formulation of the facts which offers itself so naturally and unsophistically.[419] We may, then, conclude our examination of the manner in which simple involuntary discrimination comes about, by saying, 1) that its vehicle is a thought possessed of a knowledge of both terms compared and of their difference; 2) that the necessary and sufficient condition (as the human mind goes) for arousing this thought is that a thought or feeling of one of the terms discriminated should, as immediately as possible, precede that in which the other term is known; and 3) and that the thought which knows the second term will then also know the difference (or in more difficult cases will be continuously succeeded by one which does know the difference) and both of the terms between which it holds.
This last thought need, however, not _be_ these terms with their difference, nor _contain_ them. A man's thought can know and mean all sorts of things without those things getting bodily into it--the distant, for example, the future, and the past.[420] The vanishing term in the case which occupies us vanishes; but because it is the specific term it is and nothing else, it leaves a specific influence behind it when it vanishes, the effect of which is to determine the succeeding pulse of thought in a perfectly characteristic way. Whatever consciousness comes next must know the vanished term and call it different from the one now there.
Here we are at the end of our tether about involuntary discrimination of successively felt simple things; and must drop the subject, hopeless of seeing any deeper into it for the present, and turn to discriminations of a less simple sort.
THE PROCESS OF ANALYSIS.
And first, of the discrimination of simultaneously felt impressions!
Our first way of looking at a reality is often to suppose it simple, but later we may learn to perceive it as compound. This new way of knowing the same reality may conveniently be called by the name of _Analysis_. It is manifestly one of the most incessantly performed of all our mental processes, so let us examine the conditions under which it occurs.
I think we may safely lay down at the outset this fundamental principle, that _any total impression made on the mind must be unanalyzable, whose elements are never experienced apart_. The components of an absolutely changeless group of not-elsewhere-occurring attributes could never be discriminated. If all cold things were wet and all wet things cold, if all hard things pricked our skin, and no other things did so; is it likely that we should discriminate between coldness and wetness, and hardness and pungency respectively? If all liquids were transparent and no non-liquid were transparent, it would be long before we had separate names for liquidity and transparency. If heat were a function of position above the earth's surface, so that the higher a thing was the hotter it became, one word would serve for hot and high. We have, in fact, a number of sensations whose concomitants are almost invariably the same, and we find it, accordingly, almost impossible to analyze them out from the totals in which they are found.
The contraction of the diaphragm and the expansion of the lungs, the shortening of certain muscles and the rotation of certain joints, are examples. The converging of the eyeballs and the accommodation for near objects are, for each distance of the object (in the common use of the eyes) inseparably linked, and neither can (without a sort of artificial training which shall presently be mentioned) be felt by itself. We learn that the _causes_ of such groups of feelings are multiple, and therefore we frame theories about the composition of the feelings themselves, by 'fusion,' 'integration,' 'synthesis,' or what not. But by direct introspection no analysis of them is ever made. A conspicuous case will come to view when we treat of the emotions. Every emotion has its 'expression,' of quick breathing, palpitating heart, flushed face, or the like. The expression gives rise to bodily feelings; and the emotion is thus necessarily and invariably accompanied by these bodily feelings. The consequence is that it is impossible to apprehend it as a spiritual state by itself, or to analyze it away from the lower feelings in question. It is in fact impossible to prove that it exists as a distinct psychic fact. The present writer strongly doubts that it does so exist. But those who are most firmly persuaded of its existence must wait, to prove their point, until they can quote some as yet unfound pathological case of an individual who shall have emotions in a body in which either complete paralysis will have prevented their expression, or complete anæsthesia will have made the latter unfelt.
In general, then, if an object affects us simultaneously in a number of ways, _abcd_, we get a peculiar integral impression, which thereafter characterizes to our mind the individuality of that object, and becomes the sign of its presence; and which is only resolved into _a, b, c, d,_ respectively by the aid of farther experiences. These we now may turn to consider.
_If any single quality or constituent, a, of such an object, have previously been known by us isolatedly,_ or have in any other manner already become an object of separate acquaintance on our part, so that we have an image of it, distinct or vague, in our mind, disconnected with _bcd, then that constituent a may be analyzed out from the total impression_. Analysis of a thing means separate attention to each of its parts. In Chapter XI we saw that one condition of attending to a thing was the formation from within of a separate image of that thing, which should, as it were, go out to meet the impression received.
Attention being the condition of analysis, and separate imagination being the condition of attention, it follows also that separate imagination is the condition of analysis. _Only such elements as we are acquainted with, and can imagine, separately, can be discriminated within a total sense-impression_. The image seems to welcome its own mate from out of the compound, and to heighten the feeling thereof; whereas it dampens and opposes the feeling of the other constituents; and thus the compound becomes broken for our consciousness into parts.
All the facts cited in Chapter XI, to prove that attention involves inward reproduction, go to prove this point as well. In looking for any object in a room, for a book in a library, for example, we detect it the more readily if, in addition to merely knowing its name, etc., we carry in our mind a distinct image of its appearance. The assafœtida in 'Worcestershire sauce' is not obvious to anyone who has not tasted assafœtida _per se_. In a 'cold' color an artist would never be able to analyze out the pervasive presence of _blue_, unless he had previously made acquaintance with the color blue by itself. All the colors we actually experience are mixtures. Even the purest primaries always come to us with some white. Absolutely pure red or green or violet is never experienced, and so can never be discerned in the so-called primaries with which we have to deal: the latter consequently pass for pure.--The reader will remember how an overtone can only be attended to in the midst of its consorts in the voice of a musical instrument, by sounding it previously alone. The imagination, being then full of it, hears the like of it in the compound tone. Helmholtz, whose account of this observation we formerly quoted, goes on to explain the difficulty of the case in a way which beautifully corroborates the point I now seek to prove. He says: "The ultimate simple elements of the sensation of tone, simple tones themselves, are rarely heard alone. Even those instruments by which they can be produced (as tuning-forks before resonance-chambers), when strongly excited, give rise to weak harmonic upper partials, partly within and partly without the ear...Hence the opportunities are very scanty for impressing on our memory an exact and sure image of these simple elementary tones. But if the constituents are only indefinitely and vaguely known, the analysis of their sum into them must be correspondingly uncertain. If we do not know with certainty how much of the musical tone under consideration is to be attributed to its prime, we cannot but be uncertain as to what belongs to the partials. Consequently we must begin by making the individual elements which have to be distinguished individually audible, so as to obtain an entirely fresh recollection of the corresponding sensation, and the whole business requires undisturbed and concentrated attention. We are even without the ease that can be obtained by frequent repetitions of the experiment, such as we possess in the analysis of musical chords into their individual notes. In that case we hear the individual notes sufficiently often by themselves, whereas we rarely hear simple tones, and may almost be said never to hear the building up of a compound from its simple tones."[421] THE PROCESS OF ABSTRACTION.
Very few elements of reality are experienced by us in absolute isolation. The most that usually happens to a constituent _a_, of a compound phenomenon _abcd_, is that its _strength_ relatively to _bcd_ varies from a maximum to a minimum; or that it appears linked with _other_ qualities, in other compounds, as _aefg_, or _ahik_. Either of these vicissitudes in the mode of our experiencing _a_ may, under favorable circumstances, lead us to feel the difference between it and its concomitants, and to single it out--not absolutely, it is true, but approximately--and so to analyze the compound of which it is a part.
The act of singling out is then called _abstraction_, and the element disengaged is an _abstract_.
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 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,