strange that scientifically minded men should have em- ployed it in an explanatory way. It unquestionably is a fact that the animals do resipond positively to certain forms of stimuli and negatively to others, and that in the long run, all things considered, a race of animals has positive tendencies for those stimuli which are harmless to the tis- sue and negative ones for those which are harmful to the tissue. There is a perfectly good reason for this in heredity, viz., those mutants which survived must have had those tendencies to have escaped elimination. One only has to look at the tendencies of young children and those of young animals to see that there are hundreds of misplaced positive and negative tendencies. The child responds positively to a pretty reptile, harmful fluids, fire, swiftly moving but dangerous machinery, etc. Young animals likewise. Chil- dren survive by being confined in an environment where they cannot exercise such ' ' misplaced ' ' tendencies; ani- 258 FIXATION OF ARCS IN HABIT mals by reason of the fact that they (where they have survived in numbers) live in an environment where harm- ful stimuli (to which they do not respond negatively) are, in the main, lacking. An equally strong case can be made out for misplaced negative tendencies. To call those stimuli pleasant to which the animal positively reacts and unpleasant those to which he negatively reacts, is making a wholesale gratuitous assumption on a par exactly with the assumption made by the unreflective individuals who maintain that the moth flies into the candle because he likes the light or because the light is pleasant to him. Unquestionably we utilize these strong biological tendencies in the formation of habit. I.e., the animal is so constructed that in the presence of " hunger " it moves about; it re- sponds positively (or negatively) to light, etc. The utiliza- tion of these and other biological tendencies insures us that our organism must move in certain w^ays, and if he does he usually forms habits. (2) In the second place we have assumed that only the successful act is always fixed. This assumption is not true to the empirical facts, as can be shown. As an illustration we cite two actual cases, one from the work of Ulrich and the other from the work of Basset. In the latch box Ulrich had one animal that al- ways ran completely around the box before coming to the latch. Basset had one which ran completely around the box on his first trip without striking the plane, but always struck it on his second trip, i.e., he ran swiftly in a spiral. The experiment was tried of gradually extending the num- ber of trials in the case of these animals. But since the useless movement occurred every time the successful move- ment occurred, no improvement was noticed. There was no evidence that even a very large number of trials would cause the error to be eliminated. In the same way we have found one student making two extra spacing strokes on the Burroughs adding machine before pushing in the ''total " key. These extra movements were thoroughly fixed and would never have been eliminated except by accident. If the unsuccessful acts were not fixed along with the success- ful ones, it is clear that we should be dwelling constantly CERTAIN MISCONCEPTIONS 259 in a world of virtuosi. (3) In the third place an assump- tion has been made concerning the neurological mechanism which, to our mind, has been productive of great con- fusion. It is assumed by a good many writers, as we saw above, that there is an " overflow " or " diffusion phe- nomenon " and that this diffusion or overflow can spread without having to pass through preformed Pleural chan- nels. In this way accidental connections are said to be made and bonds or associations to be established. But we have tried to point out in several places that the nervous system is not 'built to permit such functions. When a stimulus arises in a receptor there is just as orderly a progression of events then as later when the habit is formed, viz., the stimidus is carried off along preformed and definite arcs to the effectors in the order in which the arcs offer the least resistance to the passage of the current. This order may vary with variations in the sum of intra- and extra- organic stimidation. There is no formation of new path- ways.^ In order to define the problem with which we have to deal more clearly, we will take an actual illustration. Sup- pose we present the rat with box I. He exhibits on the first test movements as follows: Goes Digs to definite away place sawdust 20 Crawls Strikes under opening floor with vibrissse and enters, In this case movements 3, 7, 15, 20 are necessary in the act as a whole. While we have numbered these movements serially, it would have been much better to have employed symbols for the movements and to have placed them at the ends of radii running to the center of a circle. The prob- lem box (stimulus) would represent the center of the circle ® It is quite probable that the difficulty here is one luainly of terminology^ 260 FIXATION OF ARCS IN HABIT and the radii the arcs leading to the separate movements. They occur in any fashion depending upon the condition of tension in the conductors. What we call progress in learn- ing comes about through the disappearance (dropping out) of all movements not needed in opening the box, such as 1, 2, 4, etc. When all false movements have disappeared we have the separate acts released in the order 3, 7, 15, 20. Learning is then complete or perfect. Examination of most habits shows that only in rare instances do we ever reach the stage where only the successful movements appear and no others. Learning is usually a compromise. It is obvious that our problem concerns only the causes leading to the dis- appearance of all movements except 3, 7, 15, 20. It follows further that when the useless movements are eliminated the correct movements arise serially ivithout any chaining or linking in any material sense (bonds, connections, etc.). Movement 20 cannot be executed until movement 3 has been executed, etc. Stated in other terms, we find no necessity for speaking of " associations." The '' association " is given in heredity — the act by which the result is obtained is '' associated " with the stimulus in the first place.^^ Fur- thermore, there is no evidence for assuming that there is resolution of one physiological state into another. It will be remembered that Jennings and others have adopted the view that learning means the readier resolution of physio- logical states. However well the conception may work in the realm of organisms with no nervous systems, it will not work in that of the higher organisms. By physio- logical states we could mean nothing but the sum of arcs and effectors at work (including under effectors, of course, glands, etc.). The physiological state changes when a new set of arcs begins to function. To say that one re- solves into the other is unclear.
Enumeration of some of the problems. — If we glance for a moment at the temporal distribution of the success- ful movement or movements we find several situations which deserve mention. With regard to I, motor habits, we ^°In certain cases this apparently is not the case. The "asso- ciation" seems to be indirect. (See p. 273.)
ENUMERATION OF PROBLEIMS 261 find: (a) One in which the successful act is necessarily the final one of the series, as, e.g., the solution of boxes I, II, and III. (6) One in which several acts are necessary for the solution: but during the learning stage, the first necessary movements having been accomplished, there may follow any number of useless movements. Likewise the sec- ond and succeeding movements as they are successfully accomplished may each in turn be followed by useless movements. This type of distribution is the one discussed above, (c) One which must be looked upon as involving the formation of a succession of simple habits like (a), above. The maze problem best illustrates this type, the ctils de sac representing the series of problems, each one of which must be mastered before the problem as a whole is considered learned. It is necessary to say, though, that they do not have to be mastered in order, and furthermore, when they are mastered no separate account of the chaining process is required. The animal goes forward: having eliminated the culs de sac he necessarily goes straight from the entrance to the food box or exit. (It will be noted that h and c are not essentially different.) In addition to this type of learning in motor habits we have a similar group connected with sensory habits, (d) The animal must learn to go towards one directive stimulus or away from it, when there is no fixed instinctive tendency to react either posi- tively or negatively to it (in cases where we directly utilize the positive or negative reactions to a given stimulus no learning is involved). As an example we cite the experi- ments on the testing of the limits of the spectrum of the chick, p. 335. (e) The animal must learn to go towards one directive stimulus or to go away from one or more directive stimuli (depending upon the fact whether we are using two or multiple stimuli methods) where no tendency is present to react positively to the positive stimulus and negatively to the negative stimulus (or stimuli). (/) It may be seen that in both (d) and (e) it is possible, where preliminary tests are made and show a positive tendency to go to one or the other stimuli, to force the animal to go towards the stimulus to which it ordinarily responds 262 FIXATION OF ARCS IN HABIT in a negative way. There are various refinements and subdivisions possible in these various types, but these repre- sent, in the main, the important ones.
Factors involved in fixation. — We may confess at once that we have no new principles to offer in solving the problems involved in learning; but we hope that by stating our problems carefully and by clearing away the miscon- ceptions referred to, we shall be able to show in a convinc- ing way that the mechanical principles with which we are already familiar and which can experimentally be shown to act in the way we maintain are sufficient to yield the solutions of those problems. We shall call these principles (1) frequency and (2) recency}'^ Without claiming that they are the only ones operative, let us attempt to apply them in specific cases.
Application o£ the principle of frequency in motor habits. — Let us take the sim-plest case first, the solving of a problem like that of the latch box {a, above). We will suppose that the animal displays movements 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Ten is the final and successful movement. But movements 1 to 10 inclusive do not embrace all of the reper- toire of the animal (actual observation.) Hence on the next trial the movements would need to be numbered (at random) 1, 3, 11, 12, 13, 14, lo; the third trial, 1, 7, 13, lo; the fourth trial, 6, 11, 4, 8, lo, etc. It will be seen by actual count that movement lo is repeated more often than any of the other movements. The successful movement always ap- pears once in every trial. No other movement necessarily appears in every trial. It is obvious from this description ^^ As we ha\'e pointed out, it is evident that what most authors mean on the mechanical side by the use of such terms as satisfactory, advantageous, producing pleasure, etc., is that the physiological tone of the organism is raised, and by the opposites of these, that the tone is lowered. Now it is perfectly' obvious that heightening or lowering the tone of the organism may respectively increase or decrease the length of time required to form a given habit. So probably would the introduction of caffeine, strychnine or atropine or any other drug which will increase or decrease the reaction time, heighten or lower the irritability, but it is evident that this principle fixes useless as well as useful movements. It cannot be invoked as an eliminating agent.
THE PRINCIPLE OF FREQUENCY 263 that if any movement, e.g., 1 above, were repeated as often as lo it would become as fixed as lo. It is the principle of repetition operating so far.
Justification for the use of the principle. — Our right to use the principle of frequency as a cause rather than as an effect of habit formation may be c|uestioned. It may be argued with justice that movement lo has nothing to favor it: that there is no reason to suppose that breaking such a chance series of movements each time after the successful act is performed (i.e., by the experimenter taking the animal out at the end of the trial and starting it over again) will cause 10 to appear more frequently than any other move- ment. This may be admitted. However, we know from the general theory of probability that in any chance temporal arrangement of events the probabilities are equal that any one of them will precede or will follow any other, and that in a large number of such chance arrangements of the same events any given event will precede each of the others in just half of the arrangements and will follow in the other half. But if now each temporal series is interrupted at the occurrence of the given event and the occurrence of all that follow is prevented the given event will occur twice as often as any other. A concrete ex- ample will illustrate this point. If ten slips of paper, numbered consecutively from 1 to 10, are drawn at random from a box until a certain number, 5, is obtained, the chances are equal that the required number 5, will pre- cede or will follow any other number, 9, e.g. If the drawing is interrupted when 5 is obtained and all the slips are returned to the box, and this procedure is repeated a num- ber of times, 5 will be present in every series of drawings, the number 9 in only those in which it, by chance, was drawn out before 5. Since this condition is met by only half of the series of drawings, the number 9 will appear only half as often as 5. The required number will appear twice as often as any other. In applying this principle let us suppose that the animal is capable of only two activities, A and B, when subjected to the stimulus offered by the problem box. B is the successful activity and leads to a 264 FIXATION OF ARCS IN HABIT change in stimulation ivhich prevents the occurrence of either A or B (i.e., the animal is taken out by the experi- menter, or he eats food and goes to sleep, deposits the straw in the nest, etc.). Then if the order in which A and B occur is due to chance only, B will occur twice as often as A. The following schema illustrates the fact that B occurs in every trial, A in only half: St = situation offered by problem box: stimuli are present, leading either to reaction A or reaction E. But when B occurs ( the successful movement) the animal is taken out by the experimenter,^^ which pre- vents the occurrence of either A or B until it is reintroduced. Call the situation which follows upon B^ St': — Trials Sequences A occurs B occurs (6) St-B-St' 0 + For the operation of this principle of frequency it is necessary that the activities set oif by the situation of the problem box be diverse — that the animal tend to go to some new activity rather than to continue to react in a circular way — e.g., to spend all his time biting at the wire. For if the chances for the repetition of the act just exe- cuted are equal to the chances of proceeding to another act, breaking the series after any given activity will not affect its chance of repetition. This will be evident from the following diagram, where either of the acts A and B may be repeated in any given trial: *2 Under life conditions there is no " intervener." of course. But the same effect is obtained. The animal sets food, lies down and sleeps, etc., — i.e., becomes, from the standpoint of the stimuli which may affect it. a different animal. A further illustration follows: A bird in constructing its nest on the ground under a bush must needs pass through a narrow hole in the underbrush.iust before reaching the nest. In bringing straws he carries them crosswise: he pushes, flies away, tries again, drops the straw, passes through the hole, turns around, and asrain picks up the straw by tne middle and tries to pidl it through. Finally he catches the straw on the end and pulls it through (B). The straw is then deposited in the nest and the situation develops (Sf). which is exactly on a par with the one created by the experimenter when he removes the animal.
THE PRINCIPLE OF FREQUENCY 265 Trials Sequences A occurs B occurs St-A-A-B-St' St-B-[B-A]-St' The letters en- St-A-A-B-St' closed in brack- St-B-[B-A]-St' ets do not ap- St-A-A-B-St' pear, since B St-B-[B-A]-St' ends this series.
etc.
The behavior mechanism of the animal meets this re- quirement nicely. The animal's activity depends upon the immediate conditions of stimulation. The perform- ance of one act places the animal under neiv conditions of stimulation which lead to some other activity rather than the one just executed. ^^ A simple example is shown in the following diagram. The figure represents a maze con- sisting of two arms, a and h, a being a blind alley, while h leads to the nest box. The animal is placed between the arms of the maze, at the original position of stimula- tion, St. He may go to either a or 5 (activities A and B). If B is chosen A cannot follow. If A is chosen B is more apt to follow A than is A itself, since the proprio-ceptive stimuli would tend to force the animal forward, after turning at the end of the alley a unless rival stimuli (smell, etc.) were present. I.e., the animal is now oriented towards St' and would have to turn round in order again ^^ In order to keep the explanation in as simple a form as possible we have not brought out certain facts which every investigator knows he must take into account. When the animal is first released the problem box is net the only stimulating factor (complex in its stimulation though it is). Hunger is driving the animal, certain olfactory substances are calling out movements, contact stimulation is present and tending to call out movements, etc. Furthermore, the stimulating value of the problem box changes as the animal advances towards it and recedes from it, — i.e., the olfactory stimulation in- creases and decreases in intensity, the visual influences change like- wise. Oftentimes it is luhile executing responses to these I'arious and changing stimuli that the animal happens to 'be in the Jieighhor- hood ivhere the execution of movement 10 becomes effective. The animal has probably executed movement lO (raising head) several times during the course of the trial but never before in the right place. To attempt to trace out these processes in detail would be futile.
266 FIXATION OF ARCS IN HABIT to perform A.^* The situation in the ordinary maze of the type of the Hampton Court may readily be presented by the following diagram (Fig. 52): Let A and B represent the segments of the true pathway and X the entrance to any cul de sac (let the segments be chosen somewhere in the middle of the maze). We will suppose that the animal is on its way to the position A for the first time. The chances of entering B and X are equal in the long run when the animal is in the position A. If the animal goes into B the true pathway scores one in frequency as over against the cul de sac. If the animal ^*At first sight this argument would seem to militate against the second princ'ple involved in habit formation, viz., recency. That the principle of recency is not jeopardized in this case appears when we consider that in order to test recency we should have to arrange conditions in such a way that the animal before turning at the end of the alley was placed again immediately at St, and furthermore, that he was in approximately the same physiological condition. After the animal has turned and has become oriented towards St' additional factors have been. introduced which militate against the recurrence of activity, A. We have to qualify our statements by saying " other things being equal " recency is a factor. In our original example of the latch box this condition is realized. A se- rious criticism may be urged against the use of recency when we consider the fact that an animal learns a problem far more rapidly, from the standpoint of number of trials necessary, when given only one trial per day than when given five trials in immediate succession. It is of course possible to soften the force of this objection by main- taining that recency is operative in the five-trial method but that its effects are offset and masked by certain disturbing physiological conditions (as yet unknown) which occur when several trials are given in immediate succession.
THE PRINCIPLE OF FREQUENCY goes into the cul de sac X and follows it out to the bitter end it must return. ^^ When it reaches the position of the letter X on the return again the chances of entering B and A are equal. We thus see that there is a greater probability of the animal's remaining on the true pathway than of his leaving it. Possibly the case can be more definitely presented if we ask for the probability that the X B- 1 1 V < animal takes the wrong path. In order that this may occur it must (1) choose the wrong path from A to X and (2) choose the wrong path from X to A. The prob- ability of each wrong choice is %; the probability that hotJi wrong choices be made is % x % = ^A. The com- plementary probability or the probability that it takes the right path is %. I.e., the chances are three to one that the animal goes out through B rather than comes back to the starting point. ^® This factor (frequency) alone is ^^ It does not always return. Sometimes it goes to the end of the cul de sac and lies down. If this happens often enough the animal very quickly forms the habit of going to the end of the cul de sac and lying down and going to sleep. This is just as good and just as true a habit as if the maze had been completely traversed and learned.
^® A type problem is this: ^^Tiat is the probability that heads be thrown at least once in two throws of a coin? The equally probable cases are these: HH, HT, TH, TT. Only the last is unfavorable whence the probability is %. The argument that there are three cases HH, TH, TT, the last of which only is unfavorable (whence 268 FIXATION OF ARCS IN HABIT probably sufficient to account for the formation of the maze habit. ^" Apparently it is difficult to obtain any ex- planation based upon other factors. Even those who would maintain that the obtaining of food, or ' ' satisfiers, ' ' to use Thorndike's term, is the thing which stamps in move- ments, cannot apply that principle in these cases because of the fact that the " satisfier " is not obtained until the end of an extremely long series of movements is reached. Furthermore, actual observation shows that the culs de sac occurring early in the series are eliminated oftentimes before those occurring later and hence in closer proximity to satisfaction.^^ Hence there is no immediate connection between the obtaining of food and the elimination of errors, as must necessarily be called for on Thorndike's first law. This phenomenon in itself is enough to make us hesitate before applying it. In the case of the less restricted activity permitted by the problem box, it is more difficult to define the relation of successive activities, but this difficulty is due, not to any difference in principle, but only to the greater complexity of the conditions.
Application of the principle of recency in motor habits. — It should be clear that if there exist any factors which tend to influence the arrangement of the series of p=%), is fallacious unless we take account of the fact that the three cases are not equally prohahle. The probability of case TH is 1/2; of cases HH and TT each 14. This evaluation of the cases leads to the argument. We are indebted to our colleague, Professor Coble of the mathematics department, for this development of the problem.
^^ If it happens by chance that any cul de sac is entered as fre- quently as any segment of the true pathway, it becomes as firmly fixed as the true segment. We often find that certain culs de sac are favorably placed (position in the series) and it is these which are hardest to eliminate. Sometimes, indeed, they are never elimi- nated. It seems worth mentioning that the animal in the maze does not always choose the shorter of two pathways when a longer and a shorter are offered.
^« Miss Hubbert, who has been making an extensive study of this question, states that in the circular maze (p. 100) white rats elimi- nate the errors in alley 4 first, if we neglect 6, the alley nearest to the food box. The justification for neglecting 6 arises from the fact that it contains no stop. The animal upon entering it may turn either to the right or to the left— i.e., it must run completely around the food box in order to make an error. As it passes the entrance the smell stimuli of course become directive.
THE PRINCIPLE OF RECENCY 269 activities — to make one or another come earlier in the series — the progress of habit formation will be altered. Becency in problems, like that of opening boxes, seems to be such a factor. Its effect would tend to make the last act of the series (i.e., the successful one, lo in our illus- tration) appear earlier. This will tend to decrease the probability of the occurrence of all other activities and hence quicken the rate of the learning process. In apply- ing the principle in the particular case (problem above) we need to assume that on the first trial the initial resist- ance in arc lo has been overcome and its reaction threshold lowered. Since the stimulus originally tended to call out this reaction along with the others (was primitively or instinctively associated with it) and since there is no instinctive spacing (no instinctive order of release, as often is the case with instincts) of the separate acts, it is most natural to suppose, other things being equal, that movement lo will appear earlier on the second trial than on the first. We might go still further and maintain that if we could start with a case where the thresholds of stimulation in all the arcs involved in the whole ten acts were equal, lo, being the most recent, would be the only