Chapter 37

THE LAWS OF ASSOCIATION

AN ATTEMPT TO REDUCE THE LEARNING PROCESS TO ITS ELEMENTS

This is a very serious occasion. What we now have before us is one of the great outstanding problems of psychology, a problem that has come down through the ages, with succeeding generations of psychological thinkers contributing of their best to its solution; and our task is to attack this problem afresh in the light of modern knowledge of the facts of learning and memory. We wish to gather up the threads from the three preceding chapters, which have detailed many facts regarding learned reactions of all sorts, and see whether we cannot summarize our accumulated knowledge in the form of a few great laws. We wish also to relate our laws to what is known of the brain machinery.

The Law of Exercise

Of one law of learning, we are perfectly sure. There is no doubt that the exercise of a reaction strengthens it, makes it more precise and more smooth-running, and gives it an advantage over alternative reactions which have not been exercised. Evidence for these statements began to appear as soon as we turned the corner into this part of our subject, and has accumulated ever since. This law is sometimes called the "law of habit", but might better be called the "law of improvement of a reaction through exercise", or, more briefly, the "law of exercise".

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The law of exercise is very broad in its scope, holding good of life generally and not alone of mental life. Exercise of a muscle develops the muscle, exercise of a gland develops the gland; and, in the same way, exercise of a mental reaction strengthens the machinery used in making that reaction.

Let us restate the law in terms of stimulus and response. _When a given stimulus arouses a certain response, the linkage between that stimulus and that response is improved by the exercise so obtained_, and thereafter the stimulus arouses the response more surely, more promptly, more strongly than before.

Under the law of exercise belong several _sub-laws_ already familiar to us.

1. The law of _frequency_ refers to the cumulative effect of repeated exercise. The practice curve gives a picture of this sub-law, showing how improvement with repeated exercise of a performance is rapid at first and tapers off into the physiological limit, beyond which level more repetition cannot further improve the performance. The superiority of "spaced study" over unspaced means that exercise is more effective when rest periods intervene between the periods of exercise; as this is notoriously true of muscular exercise, it is not surprising to find it true of mental performances as well.

2. The law of _recency_ refers to the gradual weakening of the machinery for executing a reaction when no longer exercised; it is the general biological law of "atrophy through disuse" applied to the special case of learned reactions. As exercise improves the linkage between stimulus and response, so disuse allows the linkage to deteriorate. This law is pictured more completely and quantitatively in the curve of forgetting.

Really, there are two laws of recency, the one being a {391} law of retention, the other a law of momentary warming up through exercise. The law of retention, or of forgetting, is the same as atrophy through disuse. The warming-up effect, well seen in the muscle which is sluggish after a long rest but becomes lively and responsive after a bit of exercise, [Footnote: See p. 73.] appears also in the fact that a skilled act needs to be done a few times in quick succession before it reaches its highest efficiency, and in the fact of "primary memory", the lingering of a sensation or thought for a few moments after the stimulus that aroused it has ceased. Primary memory is not strictly memory, since it does not involve the recall of facts that have dropped out of mind, but just a new emphasis on facts that have not yet completely dropped out. Warming up is not a phenomenon of learning, but it is a form of recency, and is responsible for the very strong "recency value" that is sometimes a help in learning, [Footnote: See p. 345.] and sometimes a hindrance in recall. [Footnote: See p. 356.]

3. The law of _intensity_ simply means that vigorous exercise strengthens a reaction more than weak exercise. This is to be expected, but the question is, in the case of mental performances, how to secure vigorous exercise. Well, by active recitation as compared with passive reception, by close attention, by high level observation. In active recitation, the memorizer strongly exercises the performance that he is trying to master, while in reading the lesson over and over he is giving less intense exercise to the same performance.

The Law of Effect

We come now to a law which has not so accepted a standing as the law of exercise, and which may perhaps be another sub-law under that general law. The "law of effect" may, however, be regarded simply as a generalized statement of {392} the facts of learning by trial and error. The cat, in learning the trick of escaping from a cage by turning the door-button, makes and therefore exercises a variety of reactions; and you might expect, then, in accordance with the law of exercise, that all of these reactions would be more and more firmly linked to the cage-situation, instead of the successful reaction gradually getting the advantage and the unsuccessful being eliminated. The law of effect, stated as objectively as possible, is simply that the successful or unsuccessful outcome or _effect_ of a reaction determines whether it shall become firmly linked with the stimulus, or detached from the stimulus and thus eliminated. _The linkage of a response to a stimulus is strengthened when the response is a success, and weakened when the response is a failure_.

Success here means reaching the goal of an awakened desire or _reaction-tendency_, and failure means being stopped or hindered from reaching the goal. Since success is satisfying and failure unpleasant, the law of effect is often stated in another form: a response that brings satisfaction is more and more firmly attached to the situation and reaction-tendency, while a response that brings pain or dissatisfaction is detached.

The law of effect is a statement of fact, but the question is whether it is an ultimate fact, or whether it can be explained as a special case of the law of exercise. Some have suggested that it is but a special case of the sub-law of frequency; they call attention to the fact that the successful response must be made at every trial, since the trial continues till success is attained, whereas no one unsuccessful response need be made at every trial; therefore in the long run the successful response must gain the frequency advantage. But there is a very ready and serious objection to this argument; for it may and does happen that an unsuccessful response is repeated several times during a single {393} trial, while the successful response is never made more than once in a single trial, since success brings the trial to a close; and thus, as a matter of fact, frequency often favors the unsuccessful response--which, nevertheless, loses out in competition with the successful response.

Can the law of effect be interpreted as an instance of the sub-law of recency? The successful reaction always occurs at the end of a trial, and is the most recent reaction at the beginning of the next trial. This recency might have considerable importance if the next trial began instantly (as in unspaced learning), but can have no importance when so long as interval as a day is left between trials; for evidently the recency of twenty-four hours plus ten seconds is not effectively different from that of an even twenty-four hours. Recency, then, does not explain the law of effect.

Can it be explained as an instance of the sub-law of intensity? An animal, or man, who sees success coming as he is making the reaction that leads directly to success, throws himself unreservedly into this reaction, in contrast with his somewhat hesitant and exploratory behavior up to that time. The dammed-up energy of the reaction-tendency finds a complete outlet into the successful reaction, and therefore the successful reaction is more intensely exercised than the unsuccessful. This seems like a pretty good explanation, though perhaps not a complete explanation.

Limitations of the Law of Exercise

The law of exercise, with all its sub-laws, is certainly fundamental and universal; it is always in operation whenever anything is learned; and yet, just by itself, it goes only halfway towards accounting for learned reactions. For a reaction to be exercised, it must be _made_, and the law of exercise presupposes that it is made, and does not attempt to account for its being made in the first place.

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The law of exercise does not cover the formation of new linkages, but only the strengthening of linkages that are already working. It does not explain the attachment of a response to some other than its natural stimulus, nor the combination, of responses into a higher unit, nor the association of two facts so that one later recalls the other. We learn by doing, but how can we do anything new so as to start to learn? We learn by observing combinations of facts, but how in the first place do we combine the facts in our minds?

How, for example, can we learn to respond to the sight of the person by saying his name? Evidently, by exercising this linkage of stimulus and response. But how did we ever make a start in responding thus, since there is nothing about the person's looks to suggest his name? The name came to us through the ear, and the face by way of the eye; and if we repeated the name, that was a response to the auditory stimulus and not to the visual. How has it come about, then, that we later respond to the visual stimulus by saying the name?

In short, the more seriously we take the law of exercise, the more we feel the need of a supplementary law to provide for the first making of a reaction that then, by virtue of exercise, is strengthened.

This is the problem that occupied the older writers on psychology when they dealt with "association"; and their solution of the problem was formulated in the famous "laws of association". The laws of association were attempts to explain how facts got associated, so that later one could recall another.

These laws have a long history. From Aristotle, the ancient Greek who first wrote books on psychology, there came down to modern times four laws of association. Facts become associated, according to Aristotle, when they are {395} contiguous (or close together) in space, or when they are contiguous in time, or when they resemble each other, or when they contrast with each other. The psychologists of the earlier modern period, in the eighteenth and first part of the nineteenth centuries, labored with very good success to reduce these four laws to one comprehensive law of association. Contiguity in space and in time were combined into a law of association by _contiguity in experience_, since evidently mere physical contiguity between two objects could establish no association between them in any one's mind except as he experienced them together.

Association by Similarity

Continuing their simplification of the laws of association, these older psychologists showed that resemblance and contrast belonged together, since to be similar things must have something in common, and to be contrasted also two things must have something in common. You contrast north with south, a circle and a square, an automobile and a wheelbarrow; but no one thinks of contrasting north with a circle, south with an automobile, or a square and a wheelbarrow, though these pairs are more incongruous than the others. Things that are actually associated as contrasting with each other have something in common; and therefore association by contrast could be included under association by similarity. Thus the four laws had been reduced to two, association by contiguity and association by similarity.

The final step in this reduction was to show that association by similarity was a special case of association by contiguity. To be similar, two things must have something in common, and this common part, being contiguous with the remainder of each of the two things, establishes an indirect contiguity between the two things, a {396} sort of contiguity bridge between them. One thing has the parts or characteristics, A B X Y, and the similar thing has the parts or characteristics, C D X Y; and thus X Y, when seen in the second thing, call up A B, with which they are contiguous in the first thing.

A stranger reminds me of my friend because something in the stranger's face or manner has been met with before in my friend; it has been contiguous with my friend, and recalls him by virtue of this contiguity. The stranger, as a whole individual, has never been contiguous with my friend, but some characteristic of the stranger has been thus contiguous. In association by similarity, it is not the whole present object that arouses recall of the similar object, but some _part_ of the present object. This kind of association is important in thinking, since it brings together facts from different past experiences, and thus assembles data that may be applied to a new problem. If every new object or situation could only be taken as a whole, it could not remind me of anything previously met; and I should be like an inexperienced child in the presence of each new problem; but, taken part by part, the novel situation has been met with before, and can be handled in the light of past experience.

Exactly what there is in common between two similar faces or other objects cannot always be clearly made out; but the common characteristic is there, even if not consciously isolated, and acts as an effective stimulus to recall.

Association by Contiguity

This reduction of all the laws of association to one great law was no mean achievement; and the law of association by contiguity in experience holds good. If one thing recalls another to your mind, you can be sure that the two {397} have been contiguous in your experience, either as wholes or piecemeal. For two things to become associated, they must be experienced together.

Yes, the law holds good, when thus stated--but notice that the statement is virtually negative. It says, in effect, that two things do _not_ become associated _unless_ they are contiguous in experience. If it were turned about to read that two things do become associated if they are contiguous in experience, it would no longer be a true law, for the exceptions would then be extremely numerous.

The memory and testimony experiments have brought many exceptions to light. Show a person twenty pictures in a row, and let him examine each one in turn so closely that he can later recognize every one of them; and still he will not have the adjacent pictures so associated that each one can call up the next in order. To accomplish his last task, he has to observe the order specifically; it is not enough that he simply experiences pictures together. Or, again, read to a person twenty pairs of words, asking him to notice the pairs so that later he can respond by the second word of any pair when the first word is given him; and read the list through three or four times, so that he shall be able to make almost a perfect score in the expected test; still he will have formed few associations between the contiguous pairs, and will make a very low score if you ask him to recite the pairs in order. Many similar experiments have yielded the same general result--contiguity in experience and still no association.

The law of association by contiguity is unsatisfactory from a modern standpoint because it treats only of the stimulus, and says nothing about the response. It states, quite truly, that stimuli must be contiguous in order that an association between them may be formed, but it neglects to state that the association, being something in us, must {398} be formed by our reaction to the stimuli. It is especially necessary to consider the response because, as we have just seen, the response is not always made and the association, therefore, not always formed. Only if the stimuli are contiguous, can the associating response be aroused, but they do not infallibly arouse it even if they are contiguous.

The law of contiguity is incomplete, also, because it is not applicable to the association of two motor acts into a coördinated higher unit, or of the combination of two primary emotions into a higher emotional unit.

In a word, the time-honored law of association is no longer satisfactory because it does not fit into a stimulus-response psychology. It comes down from a time when the motor side of mental performances was largely overlooked by psychology, and when the individual was pictured as being passively "impressed" with the combinations of facts that were presented to his senses.

The Law of Combination

What we need, then, as an improvement on the old law of association by contiguity, and as a supplement to the law of exercise, is some law governing the response to two or more contiguous stimuli. Now we already have such a law, which we put to some use in studying attention, [Footnote: See pp. 268-264.] and called the law of "combination", or of "unitary response to a plurality of stimuli". We had better fetch that law out again and put it in good repair, and see whether it is adequate for the job that we now have on hand. In a very general, abstract form, the law of combination read that "two or more stimuli may arouse a single joint response". Let us add a single word, which had not risen above the horizon when we formulated the law before, and say that {399} _two or more contiguous stimuli may arouse a single joint response_.

That seems very little to say; can we possibly go far with so simple a statement? Well, let us see. In saying that two or more stimuli arouse a single response, we imply that _there is already some rudimentary linkage between each stimulus and their common response, and that this linkage is used in arousing the response_. Now bring in our trusty law of exercise, and we see that the use, or exercise, of such a linkage may strengthen it to such an extent that, _later, a single one of the stimuli may arouse the response which was originally aroused by the whole collection of stimuli_.

Does that promise any better? Probably it requires further discussion and exemplification before its value can be appreciated. Let us, then, first discuss it a bit, and then apply it to the explanation of the chief varieties of learned reaction that have come to our attention.

The law of combination attempts to show how it comes about that a stimulus, originally unable to arouse a certain response, acquires the power of arousing it; and the law states that this occurs only when the originally ineffective stimulus is combined with others which can and do arouse the response. The ineffective stimulus, being one of a combination of stimuli which collectively arouse the response, participates to some slight degree in arousing that response and may thus become effectively linked with the response.

Notice an assumption underlying the law of combination. Evidently a stimulus could not take part in arousing a response unless there were some pre-existing linkage between it and the response. This linkage may however be extremely loose and feeble, and wholly incapable by itself of arousing the response. The assumption of pre-existing loose linkage between almost any stimulus and almost any response is justified by the facts of playful behavior and trial and error {400} behavior. In addition to the close reflex connections provided in the native constitution, and in addition also to the close connections formed in previous training, there are at any time, and especially in childhood and youth, a vast number of loose connections. These are too weak to operate singly, until they have coöperated in producing a response, and thus been individually strengthened, after which they may be able singly to produce the response.

The law of combination, then, as applied to learning, includes four points:

(a) A collection of stimuli may work together and arouse a single response.

(b) This is possible because of pre-existing loose linkage between the separate stimuli and the response.

(c) When any stimulus, working together with others, helps to arouse a response, its linkage with that response is strengthened by exercise.

(d) The linkage may be sufficiently strengthened so that a single stimulus can arouse the response without help from the other stimuli that were originally necessary.

Having now abundantly stated and reiterated the law of combination in the abstract, let us turn to concrete instances of learned reactions, and see how the law takes care of them. We have already classified a large share of all the concrete instances under a few main heads, as substitute stimulus, substitute response, combination (or association) of stimuli, and combination of responses. We shall presently find it possible to reduce these four classes to two, since the association of two objects, by virtue of which one of them later recalls the other, is a rather complicated case of substitute stimulus, while the combination of movements into a higher unit is a complicated case of substitute response.

[Footnote: To distinguish between "substitute stimulus" and "substitute response" is, in strict logic, like distinguishing between "inside out" and "outside in." Whenever there is a substitute stimulus there is also a substitute response, of course, since this stimulus, in being substituted for another, gets that other's response in place of its own original response; and in the same way, you can always find substitute stimulus in any instance of substitute response; for, in being substituted for another, a response gets that other's stimulus in place of its own original stimulus. For all that, the distinction between the two main cases of learning is of some importance, since sometimes the changed stimulus, and sometimes the changed response, is the interesting fact.]

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I. SUBSTITUTE STIMULUS EXPLAINED BY THE LAW OF COMBINATION

Here the response, without being itself essentially changed, becomes attached to a new stimulus. We distinguish two cases under the general head of substitute stimulus. In the one case, the substitute stimulus was originally extraneous, and unnecessary for arousing the response, while in the other case it was originally necessary as part of a team of stimuli that aroused the response.

A. Substitute Stimulus Originally Unnecessary for Arousing the Response

1. Conditioned reflex.

This is the very simplest case belonging under the law of combination. The dog that responded to the bell by a flow of saliva, after the bell plus a tasting substance had acted together on him time after time, is the typical instance; and another good instance is that of the little child who was "taught" to shrink from a rabbit by the sounding of a harsh noise along with the showing of the rabbit. [Footnote: See p. 303.] The explanation of all instances of conditioned reflex is the same. We have an effective stimulus acting, i.e., a stimulus strongly linked with the response; and we also have acting an ineffective stimulus, which gets drawn into the same reaction. The effective stimulus determines what response shall be made, and the other stimulus finds an outlet {402} into that response, being, as it seems, attracted towards the activated response, sucked into it. The weak linkage from the ineffective stimulus to the response, being thus used and strengthened, later enables this stimulus to arouse the response single-handed.

This sort of thing is best presented in a diagram. A full line in the diagram denotes a linkage strong enough to work alone, while a dotted line denotes a weak linkage. Letters stand for stimuli and responses. In the diagram for conditioned reflex, A is the original effective stimulus (the rasping noise in the instance of the child and the rabbit), and B is the ineffective stimulus (the sight of the rabbit). R is the shrinking response, linked strongly to the stimulus A and only weakly to the stimulus B, which has several other linkages fully as good as the linkage B-R. But A arouses the response R; and R, being thus activated, draws on B and brings the linkage B-R into use. After this has occurred a number of times, the linkage B-R has been so strengthened by repeated exercise that it can operate alone, so that the rabbit brings the shrinking response even in the absence of A, the noise.

At first, the child shrinks from the noise, but, the rabbit being before his eyes, he incidentally shrinks from the rabbit as well. He really shrinks in response to all the stimuli acting on him at that moment. He shrinks from the whole situation. He makes a unitary response to the whole collection of contiguous stimuli, and thus exercises the linkage between each stimulus and their joint response. The {403} linkage between rabbit and shrinking is later strong enough to work alone. It is a clear case of the law of combination.

2. Learning the names of things.

A child who can imitate simple words that he hears is shown a penny and the word "penny" is spoken to him. To this combination of stimuli he responds by saying the word. This is primarily a response to the auditory stimulus, since the sight of the penny, though it might probably have aroused some response, and even some vocal response from the child, had no strong linkage with this particular vocal response. But the auditory stimulus determined the response, and attracted the visual stimulus into this particular channel of saying "penny". The linkage from the sight of the penny to the saying of this word being thus strengthened by exercise, the seen penny later gives the right vocal response, without any auditory stimulus to assist.

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B. Substitute Stimulus Originally an Essential Member Of A Team of Stimuli That Aroused the Response

1. Observed grouping or relationship.

"Learning by observation" is a very important human accomplishment, and we found many evidences of its importance in our study of the process of memorizing. The facts observed, which assist memory so greatly, are usually relations or groups.

Evidently the observation of a group of things is a response to a collection of stimuli, and could not originally be aroused by any one of the stimuli alone. The same is true of observing a relationship; the observation is a response to two things taken together, and not, originally, to either of the two things taken alone. In spite of this, a single one of the things may later call to mind the relationship, or the group; that is, it arouses the response originally made to the pair or group of stimuli. The single stimulus has been substituted for the team that originally aroused the response. Its linkage with the response has been so strengthened by exercise as to operate effectively without assistance.

For example, in learning pairs of words in a "paired {405} associates experiment", [Footnote: See p. 336.] the subject is apt to find some relation between the words forming a pair, even though they are supposed to be "unrelated words". When he has thus learned the pair, either of the words in it will recall the observed relation and the other word of the pair. Sometimes, after a long interval especially, the relation is recalled without the other word. One subject fixed the pair, "windy--occupy", by thinking of a sailor occupying a windy perch up in the ropes. Some weeks later, on being given the word "windy", he recalled the sailor on the perch, but could not get the word "occupy". That is, he made the same response to "windy" that he had originally made to "windy--occupy", but did not get the response completely enough to give the second word.

In the typical cases of _association by contiguity_ when one object reminds us of another that was formerly experienced together with it, the law of combination comes in as just described. The two objects were observed to be grouped or related in some way, or some such unitary response was made to the two objects taken together, and this response became so linked to each of the objects that later a single one of them arouses this unitary response and recalls the other object. In the free association test, [Footnote: See p. 380.] the stimulus word "dimple" calls up the previously made response of seeing a dimple in a cheek, and so leads to the word "cheek". In a controlled association test, where opposites are required, the stimulus word "mythical" arouses the previously made observation of the antithesis of mythical and historical, and so leads to the motor response of saying the latter word.

[Footnote: When, however, this indirect linkage between stimulus and motor response is frequently exercised, short-circuiting takes place (see p. 338), and the stimulus word arouses the motor response directly. Short-circuiting follows the law of combination very nicely. Let a stimulus S arouse an idea I and this in turn a motor