Making the Most of One's Mind/Chapter 5
MODE OF STUDY
WHEN you go into your study you intend to work with your mind, but you must bring your body along, and the problem is how to deal with it during the study period. The least you can do, one would think, is to treat it as you would any other visitor, and offer it a chair. But not every one is of this opinion. There are those who point out that it is more profitable to stand than to sit while studying, and there are others who go still further, and maintain that a certain amount of gentle motion stimulates the brain. Some students walk up and down the room as they study, while others content themselves with some nervous motion or other, such as fidgeting with their hands, resting now on the right leg, now on the left, moving the head from side to side, twirling a pencil between the fingers—there is no end to the vagaries.
Now this is one of those cases in which it is dangerous to lay down hard and fast rules. What is excellent for one, may be disastrous for another. All that we can do is to consider the matter as a whole, indicate what suits the greater number of persons, and leave you to make your own applications.
A good deal depends upon whether you have a room of your own. If you have to study along with some one else, or worse still, have to study while there are other people in the room doing the ordinary things that people who are not students are in the habit of doing, your problem is greatly complicated. If you are with another student you must make a treaty with him offensive and defensive, by which certain fixed study periods are to be regarded as sacred from all interruptions, and during which nothing less than sudden illness or an alarm of fire will justify the opening of a conversation. Your time-table must be the result of agreement with your fellow, and must be made the basis of the treaty. How far you should enter upon coöperative work is a matter for serious consideration. A partnership in study almost invariably resolves itself into one of the partners becoming the teacher, and the other the pupil. This is not so serious a drawback as it looks, for the student who turns out to be the tutor does not really lose: he proves the truth of the Latin tag discimus docendo, for by teaching he learns: while the student who becomes pupil has obviously no right to complain. A partnership is inadvisable in the case of great inequality in ability or attainments between the two students. Here the pupil-partner becomes an unfair drag upon the teacher-partner.
A studying partnership has to be carefully manipulated. There is a strong tendency to an unwise division of labour. One partner will keep the text in his hand and try to worry out the meaning, while his friend attends to the dictionary and looks up all the necessary words. The result is that by and by each becomes a specialist, and does his part of the work exceptionally well, while he is all at sea in the work of the other. In a case like this, the two become a kind of compound unit, a sort of social molecule made up of two formerly independent atoms. If the object of the partnership were the production of good translations in the shortest time, then the partnership would be justified; but since the purpose is that each should become a well-developed all-around scholar, the plan of working must be modified. There must be alternation in the distribution of work, so that each acquires facility in all branches.
There is sometimes a very real advantage in cooperative study between fairly well matched students, even if they do not have to work together because of the necessity of using the same room. This is particularly the case with private students. There are many points on which mutual criticism is of the utmost value, even though neither is an authority on the subjects studied. The value of a fresh eye on our difficulties is great. We have seen the value of a co-worker in the chapter on Memory, and we shall find other cases under Reading and elsewhere. Further there are many occasions on which we require to get an outsider to state a case, or to suggest a datum for a problem. The private student is sometimes in the position of those pitiable people who play games against themselves—left hand against right—in which the whole process is vitiated by the fact that the plans of both sides are known to both players. A study partner may be as welcome to a student as an opponent to an enthusiastic chess-player eager for a game. Not the least of the functions of the student-partner is the service he renders as a sort of external conscience. We are much more easily satisfied with our own excuses for slackness than our partner is likely to be. Just as a man's wife is often an objective conscience to him, so a student's partner may do much to keep him up to a high level of endeavour.
But while we can thus turn to a positive advantage the presence of a fellow student in our room, it is a case of making the best of a bad job when we have to share a room with other people who have no special concern with our studies. If you have to work in the common living room at home, you will at least have the advantage of some degree of sympathy with your work. If there are other members of the family who have to be studying at the same time, you will probably be in a position to demand a fair degree of quietness from those who are not studying. A common room of this kind is a useful arena for struggles in self-sacrifice. But it also offers many opportunities for intelligent manipulation. You have to examine very carefully all the conditions of the case—especially the times and needs of the other members of the family. There is one outlet that is nearly always available unless the family is very poor indeed. This is the somewhat unpalatable expedient of early rising. If you have to work along with younger brothers and sisters, and find that you cannot make real progress, you will find that by going early to bed and getting up very early in the morning you are likely to find all the solitude you want. The one condition is the cost of a fire on the winter mornings—the kindling of the fire would be of course your contribution.
Coming now, however, to the case of the student who has a little room for his own use, we have to settle the question of the disposal of the body. Speaking generally it is better to sit than to stand. To be sure it is highly desirable to have the means of standing for a little now and then to relieve the weariness resulting from long continued sitting. If you can afford a sloping desk-table that is just breast high you will find it a great boon for general reading, but particularly for consulting dictionaries and other heavy volumes. The table need consist of nothing but four legs and a sloping board, but the board should have a rim at the lower end to prevent books from slipping off.
With regard to the kind of seat you ought to have, there is a difference of opinion. The first view is that we ought to treat our body severely. People do not put the matter quite so plainly as this, but what is clearly at the back of their minds is that for sound study the body ought to be a little uncomfortable. The opposite view naturally is that the body ought to be made as comfortable as possible, so that the mind may be left perfectly free to do its hard work. But neither view can be pushed to extremity. No one nowadays would maintain that the body should be made positively uncomfortable so as to help in study, though there was a time when such a view would not have been considered unreasonable. On the other hand, no one would recommend that the body should be pampered. The truth naturally lies between the two. We must not be positively comfortable: that is we must not be so comfortable as to be tempted to think about how comfortable we are. You may be quite comfortable sitting in an ordinary armchair, but if it is so deliciously padded that you want to snuggle into it, so as to enjoy it the more, it has passed the stage of respectable comfort. As a matter of fact the chair in which you do your ordinary study should have no cushion at all, unless you find the lack of a cushion positively uncomfortable. For, after all, it is your body that has got to be considered, not the body of any one who comes along to give you advice. He may prefer a hard chair when engaged in serious work. You may find such a chair a hindrance. The principle to determine the matter is that everything should be done to secure that the body does not make its presence felt at all, either by discomfort or by comfort so exuberant as to call attention to itself.
The attitude adopted during study is of some consequence. There is a subtle connection between the attitude of the body and that of the mind. Edward Thring, the distinguished Head Master of Uppingham, used to speak often about "the potency of attitude," and pointed out that a boy who came up to the blackboard with his hands in his pockets did not attack a problem in geometry with anything like the same effectiveness as his fellow who held himself erect, and looked as if he meant business. Probably Buffon, the celebrated French naturalist, carried this theory too far when he made a point of always doing his writing in full court dress, sword and all. Yet there is a certain connection between the official dress, and the stately style of this writer. There is said to be a sort of dressing-gown frame of mind that is apt to be put on along with that soothing garment. Naturally it is out of the question to lay down any hard and fast rules for the dress of students. The days of sumptuary laws are gone for ever: but there is no harm in calling attention to possible dangers. If your temperament is such as to be greatly modified by your immediate surroundings, it will be to your interest to keep an eye on your attitude as you set about your studies. Better study has been done in old clothes than was ever done in court dress, but a slovenly attitude is not necessarily an accompaniment of old clothes, and such an attitude is apt to induce a slovenly mental attitude to match. Besides, slovenly attitudes in over-easy arm-chairs are apt to have an unwholesome effect even from a purely hygienic point of view. You must be allowed to adopt whatever attitude you find from intelligent experiment to be the best for your particular case. But you will be well advised to give a long trial to an attitude that suggests as well as accompanies alertness of mind.
Assuming that you have hit upon the happy mean between discomfort and luxury, your next problem is how to carry on the actual process of study. You have your books, your papers, and your prescribed work. You have planned out your time, and you know that you have forty minutes to master a particular bit of work. Let us assume that this is a case of study that is mainly assimilative. You have to "get up" the reign of Henry VII of England in such a way as will justify the statement that "Modern History in England begins with the reign of Henry VII." You have read the reign in a general way during a previous course, so your present study takes the form of revision, with the additional incentive of a definite thesis to be maintained. You will first glance over the various paragraphs to revive your general impression of the whole, then you will select certain paragraphs for special attention. You pass rapidly over everything that treats merely of local and temporary interests—revolts, personations and what not—and fix your attention on the big things. You note that America was discovered in 1492, that the Renaissance which may be said to have begun in the middle of the fifteenth century was producing its fruit when Henry came to the throne, that the Reformation was making headway on the Continent, greatly aided by the spread of books resulting from the development of printing, that the increased use of artillery had brought the knight down almost to the level of the ordinary man-at-arms on the battle field. But all this you feel does not specially concern England, so you continue the search for something that brings this material to bear upon English life, and you find it in the decay of the power of the old nobility, through the general cause of the new conditions of warfare, and the cause, special to England, of the decimation of the noble families through the sanguinary struggles of the Wars of the Roses. You give a fresh revision to the paragraphs that deal with the enforcement of the Statute of Liveries, and the revival of the criminal jurisdiction of the Crown, the New Learning, the Oxford Reformers; and now you feel that you have enough matter to sustain the thesis that with Henry VII began such a set of new problems as entitles us to say that modern history begins in England with his reign.
In all this your mind has moved backwards and forwards over the whole field, pausing sometimes here and sometimes there. Some paragraphs have had much more of your forty minutes than the others, some have been passed over almost unread. The dominating purpose of the study has been to select the proper material and deal with its different elements in the order of their importance.
If your purpose had been to master the reign of Henry VII as a whole and for the first time, you would have proceeded differently, since this would have been a case of purely assimilative study. In such a case you would read over the whole rapidly, but of course not carelessly, in order to get a general idea of it. Then you would select certain paragraphs for a second reading because of their difficulty, or because your first reading showed them to be important. Next you would read the whole over again, giving as before special attention to the important paragraphs and noting anything that seemed to call for special treatment. Then you would proceed to ask yourself certain questions about the whole, and test whether you could answer them. Usually as you advance in a lesson of this kind you have to concentrate more and more on the uninteresting. Much of the striking material you master in the first reading. It is a very common mistake in preparing such a lesson as this to re-read the whole reign several times in succession, giving the same attention to all the parts, the easy getting the same attention as the difficult. The secret of study is to seize upon the important and the difficult parts, and concentrate upon them.
You must of course realize that your work will be judged by your success in mastering your subject. The test of study is not how long or how hard you have studied, but what you have attained by your study. There is nothing that a half-conscientious schoolboy likes better than to get a definite ruling from his teacher about the amount of time to be given to a particular lesson. He will innocently ask how often he ought to read over his history lesson, or how frequently he should repeat his multiplication table in order to satisfy the demands of the school. The wise teacher never gives a definite numerical answer to such questions. If he does, the boy will in all probability accept his decision and loyally go over the lesson the exact number of times recommended. But the chances are that the number of repetitions bulks too largely in his mind. The responsibility is somehow shifted on to the teacher, if only the required number of repetitions is given. If next day the boy breaks down, he may not make any open complaint to the teacher, but in his heart he thinks that he has been badly treated. Accordingly the wise teacher answers all such demands for a numerical prescription by telling the pupil that he will have to go over the lesson often enough to master it. The responsibility must be left with the pupil.
The interesting thing is that the intelligent pupil does know when he has mastered a particular bit of work. Without doubt you have felt this in your own experience. You have been working at a particular matter—not necessarily a problem with a definite "solution" that is recognized as right the moment it has been reached—for half an hour; almost suddenly you realize that you have mastered the position: you "know" the lesson. A few minutes before, you were quite well aware that you did not know it, but now the conviction has come to you that you do know it. No one can help you in such things. You must learn to know your own processes by experience. To some extent this applies also to the way in which you set about learning anything. It appears that we all differ in our mode of learning. and our teachers cannot lay down any very definite directions that we ought all to follow. In some cases, however, they can give definite instruction about how to carry out a particular bit of work.
On one occasion a teacher told his class that had just begun the study of formal Geography to "Draw a map of England." This was not a very wise proceeding. The pupils had never drawn. a map before; most of them were quite at sea, and had no idea how to begin. I can tell you exactly how one of them began. He examined the map in his atlas, and noticed that it was made up of a great number of little rectangles. He did not know that these were made by the crossing of the meridians and the parallels of latitude. So he carefully measured off each of these little rectangles, and completed as much of England as lay within each. In other words he proceeded to make a map of England as if it were a sort of geographical crazy quilt. The teacher told the class afterwards that he could not understand how any boy could be so stupid as to do such a thing. But this complaint was not very sensible. It is a teacher's business to understand how pupils can do stupid things. But it is also your business, so far as you take yourself in hand, to learn to avoid foolish beginnings like this little boy's. He did not really face the problem as a whole. A careful examination of his atlas would have shown him that England was not made up of separate segments: that there was a continuity of outline: that the thin lines making up the rectangles were continuous, and that these lines could be most comfortably drawn by measuring the spaces between them at the top and at the bottom of the map, and then joining by straight lines the marks made at the top with the corresponding marks at the bottom. The same thing being done with the horizontal lines, he would have found the little rectangles very useful as guiding lines in his drawing out the contour.
We shall have other examples of the folly of beginning a problem with no knowledge of what is really wanted. The teacher cannot be expected to state every detail of a problem, but the problem itself must be made quite clear, and the pupil should never be in the least doubt about what is required of him. Though the teacher cannot be expected to give detailed instructions about the working out of problems, he can at least give some very general directions that are applicable to all cases of study. For example, he can warn his pupils against the most dangerous habit of all—the habit of inattention. When we say that a person's wits are wool-gathering, we mean that his mind has wandered away from the matters in hand. No human being will ever succeed in study or in anything else who allows this habit to grow upon him. This does not mean that we must be on the stretch all the time, that we must never allow the mind to wander at ease among the things of the past and the distant. There is a place for reverie; and even day-dreaming is not altogether to be condemned. The important thing is that during the period that you profess to be studying you must study. Wool-gathering during study-time is fatal to all chance of success. One hour's strenuous study is worth three during which there are occasional lapses into reverie or day-dreaming. Students are very apt to point out how many hours they study per day. But this is meaningless unless we understand what kind of study it has been. It is quite possible to read a book and to turn over the pages systematically as you reach the bottom of each, and yet to know nothing of what you are reading. A student of the wool-gathering type may be reading a textbook in preparation for an examination. He is actually following the words on the page, for the observer can note how his eyes move backwards and forwards. Yet if a sheet of paper be thrust between his eyes and the book, and he is asked some question on the text, it will be found that he does not in the least know what he has been reading about. His attention has been elsewhere all the time. This kind of study is not only useless; it is worse than useless, for it actually cultivates the lack of power to concentrate our attention at will.
Those who write on such matters quarrel a good deal about the naming and nature of the different kinds of attention. They talk about voluntary attention, involuntary attention, non-voluntary attention, spontaneous attention. But for our purposes it is enough to have two kinds of attention—one that implies effort and one that does not. Many things we attend to naturally, easily, and without the least effort. This kind of attention may be called spontaneous. But there are many things that we find it necessary to attend to that are not in themselves attractive. If they are to get a fair share of our attention we must make an effort, we must exercise our will. That is why this kind of effortful attention is commonly called voluntary. This adjective does not mean that we attend willingly: we would much more willingly attend to more attractive things. It means rather that we attend by force of will: we compel ourselves by sheer willpower to attend to things that are in themselves unattractive, because we realize that these unattractive things are very important for us.
It is sometimes said that voluntary attention is a higher form than spontaneous, and that therefore the student should seek to rise from spontaneous attention to the voluntary form. But it might be more truly said that the object of education is to enable the pupil to pass from the voluntary form of attention to the spontaneous. Surely it cannot be the aim of either teacher or pupil to do something that will make attention more difficult. The better educated the student, the more easily ought he to be able to direct his attention wherever he chooses.
The relation between spontaneous and voluntary attention will be better understood when we consider the meaning and place of what is called interest. Certain things appeal to us, draw out our sympathy, rouse us to pursue then, all because in some way they concern us. Interest literally means being mixed up with or connected with something. What- ever in any way affects our activities is of interest to us. We are not to suppose that to be interesting is the same as to be pleasing. We are interested in a great many things that are extremely unpleasant. There is probably no place in the world more interesting than the dentist's chair. There you have no difficulty in maintaining attention. No effort of will is required. Your attention is perfectly spontaneous. As a matter of fact things go farther than that. Not only do you need no effort of the will to attend, but you are made to attend practically against your will. Very gladly would you attend to something else, but the circumstances of this case compel you to attend to what the dentist is doing. This kind of attention you may call, if you like, involuntary attention, or attention against the will. Still, there are only the two kinds of attention that are important so far as we are concerned. For in spontaneous attention there is no exercise of the will at all, whereas in voluntary attention the will is always making an effort. In what is called involuntary attention the will desires to attend to something, say a, and is compelled to attend to something else, say b. It implies effort, though unsuccessful effort. It is therefore of fundamental importance to learn what help we can get in our struggles to keep our attention fixed in whatever direction we may desire.
Experiments have been made to determine how long we can maintain attention by the sheer exercise of the will, that is how long we can attend to something that has no interest whatever for us. Suppose you concentrate your attention on some totally uninteresting thing, say the point of a needle, how long do you think you can maintain this voluntary attention? Remember you are to attend to nothing else but the point of the needle. You are not to think, for example, of the use of the needle, or the pain that the point would produce if you pricked your finger with it, or of the owner of the needle, or its maker, or its price, or its material—but merely of the point of the needle. You will find that even by a violent effort you are able to maintain this sort of unnatural attention for only a few seconds at a time. After that, either your mind wanders around the subject, seeking for points of interest, or you become dazed and find yourself attending to nothing at all.
If, then, you can use pure voluntary attention for only a few seconds at a time, it is surely impossible to carry on your studies by this means. The truth is that unless spontaneous attention comes to the aid of voluntary attention, steady study is impossible. It is certainly true that voluntary attention marks a higher level than spontaneous. Unless we are able to exercise voluntary attention we can hardly claim to be the captains of our own souls, and we are not to think that the very limited time during which we can maintain pure voluntary attention in any way diminishes the importance of this form. Its function is to give direction to the activities of the mind. The helm is not the most imposing part of a ship, and yet it controls all the rest. Voluntary attention plays the part of helm. It turns our activities in this way and in that, but it depends upon other forces to supply the motive power. Interest is the driving power that corresponds to the wind in the case of a sailing ship, and to steam or electricity in the case of the other kinds. The moment interest is introduced the attention ceases to be purely voluntary and becomes to some extent at least spontaneous. The more interest the greater the degree of spontaneity.
When you sit down to a disagreeable subject, you are unable to get up much interest, and in consequence you have to depend largely upon voluntary attention. You work for a minute or two, and then find that your attention has wandered. You pull yourself together, and compel yourself once again to attend. The less interesting the subject the more frequently you must use the whip of voluntary attention. Any little interest that you can get up in the subject is of the greatest possible help. Unfortunately interest is a treacherous ally: it works on both sides. It distracts as well as helps to concentrate. If in working at your textbook in Physics you find yourself reading the advertisements at the end, or if in dealing with an arithmetical problem about the cost of papering a room you find yourself wondering about the colour of the paper and the sort of man who is going to live in that room, interest has played you false. But of the two it is noteworthy that the first lapse is much worse than the second. There is less connexion between Physics and the advertisements than between the colour of the paper and the wall space of the room. There is less hope for the student who listlessly turns the pages of the book than for the one who only allows his imagination a little too free scope in playing around his problem.
Fortunately for the student, interest has a tendency to rise out of the very material studied, whenever enough time is allowed for it to develop. It is the function of the voluntary attention to secure this opportunity for interest to develop. At the beginning of a period of study in a disagreeable subject the appeal to the voluntary attention is rather frequent. The mind is continually letting itself wander and needs repeated calls to order. But as the work goes on the periods of spontaneous attention increase in length, and by and by there is need for only an occasional appeal to the voluntary attention.
There is a fact in natural history that is often used to encourage young people to face disagreeable work. At least I hope it is a fact, for I cannot say that I have ever verified it on its literal side. We are told that if we deal with a nettle gingerly we get badly stung, but if we "grip it like a man of metile" we escape all disagreeable consequences. However it may be with nettles, it is undoubtedly true that firm treatment of disagreeable subjects leads quite rapidly to an amelioration in the disagreeableness. It is probably the swing effect more than anything else that eases our way, and it is obvious that the fewer relapses into other matters the greater the chance of the swing to establish itself. The effort at the beginning is great—there is no sense in blinking the disagreeable fact—but the reward is in proportion. There are few joys to surpass the satisfaction we experience when we wake up to discover that we have been absorbed for half an hour in a subject that we dislike. Yet this absorption is the almost inevitable result of the resolute struggle against distraction during the first quarter of an hour of a three-quarters of an hour period of dealing with an unattractive subject.
Talking of being absorbed in a subject raises the question of the possibility of maintaining attention at the same level all the time. Experiments in psychological laboratories have shown that attention is rhythmic, it has a regular rise and fall. There are beats of attention just as there are beats of the heart. As we have the alternation between inspiration and expiration in breathing, so we have an alternation between concentration and diffusion in the process of attention. In fact some psychologists maintain that there is a definite connexion between the beats of attention and the rhythm of breathing. That there is some connexion between breathing and attention is plain to all, and is acknowledged by the very words we use in describing attention. Do we not speak of "breathless attention"? Are we not all familiar with the gasp that the crowd gives on the finish of a particularly striking display of fireworks? The brilliant lights command such concentrated attention that we all hold our breath till the lights die down, and our attention is once more set free. But this more or less physical side of attention, though interesting to us, cannot be manipulated to our advantage. It is little good to say to ourselves, "Now I want to attend: so I shall hold my breath." It is rather the attention that causes the holding of the breath than the holding of the breath the attention; though perhaps the best way of putting it is to say that the two form part of one whole, and cannot be dealt with separately.
There is, however, another form of rhythm of attention in which the rhythm is not quite so regular, but in which we have greater power of control. When we are studying a subject we are apt to think that the concentration beats are what really matter, and that the diffusion beats are really periods of rest. When we watch a painter at work we observe him going up to his canvas and putting in some fine touches with a delicate brush. This is his concentration beat, and we are inclined to say to ourselves, "Ah, now this is working, this is the real thing!" By and by he strolls back a bit from the canvas and takes in the general effect. "This," we say, "is the diffusion beat, no doubt. He is having a rest. We don't grudge him the relaxation. But of course it isn't work." But this is where we go wrong. The artist may be working just as hard, and may be using up quite as much grey matter in the brain when he estimates the general effect from a little distance as when he is working at close quarters and peering into the canvas. When we say that attention has two beats, we must not forget that both beats are beats of attention. We are not to suppose that the concentration beat means the presence of attention and the diffusion beat its absence. To be sure, we do have this alternation between attention and distraction. When, for example, we are beginning a disagreeable subject, we have already seen that every now and again we have wandered off to something else. This implies a real loss of attention to the subject we are studying, and we have to depend upon voluntary attention to bring us back to the point at which we strayed away from our subject. But in a case in which we are attending to the same subject throughout a whole lesson period, and have no strayings away from the subject in hand, we have yet a more or less regular alternation of the concentration and diffusion beats.
The word concentration is perhaps a little misleading here. We are too apt to think that attention always means concentration on a small area. A geologist has two main kinds of work: one is done in the field, the other in the laboratory. When you meet a geologist at work in the field, you are very likely to make the mistake of thinking that he is out merely for a stroll. He may have his hands in his pockets, he may be leaning over a gate and apparently doing nothing but taking in the beauty of the scenery. Ile may even be smoking as he goes along. If, however, you visit him in his laboratory, you may quite likely find him poring over a microscope, or at the very least busy with little specimens of minerals to which he is giving his close attention. This you feel to be work. This is what you understand by concentration. But you have to realize that concentration is a matter of the mind, and not of the area over which the mind is working. A man's mind may be as concentrated in trying to take in the meaning of a whole landscape, as in seeking to identify a particular mineral under the microscope. Indeed even in connexion with the microscope students are sometimes misled into thinking that there is greater attention implied in using the high powers than the low. But in using the seventy power, the observer may be attending quite as intently as when using the eleven hundred power. No doubt the higher power may imply a greater. amount of physical strain on account of the diminished quantity of light. But this is a matter of physical conditions rather than mental.
Concentration, then, we are to regard as referring to the whole subject we are studying at any time. To understand that subject we may have to take now a wide, now a narrow view. But so long as we do not lose sight of the main object we have before us we can claim to be attending all the time. Attention may be diffused as to its area but concentrated as to its purpose. With this explanation we may be perhaps permitted to use the terms concentration beat and diffusion beat, to indicate the narrower or wider area to which attention is applied.
In spite of all that has been said, it is probable that you have at the back of your mind the feeling that after all real attention is the kind that is marked by a screwing up of your forehead and a severe limitation of the area within which you restrict your thoughts. On your side is the evidence of a French savant who maintains that the broad muscle that forms the brow is the special muscle set apart to give expression to the state of attention. But you can pucker your brow over a wide arca as well as over a narrow one, and you may get some justification for respecting the diffusion beat by considering that we must know not only the details of anything that we are studying, but we must know that thing in its relations to other things. In our thinking we pass through three stages, the thing stage, the law stage, and the system stage. Children and savages are mainly at the thing stage. They examine each thing by itself and think of it as something by itself apart from all its surroundings. More mature thinking demands to know the relations between individual things and their surroundings. We concentrate on each thing no doubt, but immediately thereafter we let our minds play around it and try to find out how the thing stands in relation to other things. It is this playing around a subject that forms the diffusion beat. When Shakespeare is giving an account of the various qualities that make up man's excellence, he includes "looking before and after," and Shelley in his turn makes use of the same expression to emphasize man's superiority. It is because we can look before and after that we are able to understand our surroundings. We do not live from mere moment to moment. We let our minds play around all that is submitted to them, and in this way get to a truer knowledge. The concentration beat gives us the details of an individual fact, but when we start looking before and after in order to understand the true meaning of the fact, we find ourselves in the diffusion beat.
Obviously both beats are essential to intelligent study. We must get up thoroughly each detail that is of importance, but we must also learn what the importance of this detail is, and how it fits in with the other details that make up the whole subject of study. In learning grammar, for example, it is not uncommon for the pupil to get up all about the substantive, then all about the adjective, then all about the pronoun, and so on, without bringing all this knowledge together. Successful teachers never allow this to happen. They are continually referring backwards and forwards and showing the relation of all the facts that have been learned. This is why revision, that you are apt to find so dreary, is so very valuable. It is a systematic looking before and after, a deliberate organization of the facts that we have mastered.
Certainly there must be no paltering with thoroughness. But it is absolutely essential that we should realize exactly what we mean by this term. There is great danger that by misunderstanding its true meaning we may make serious mistakes in the conduct of our studies.
To begin with, there are occasions when we have no doubt at all in the matter. Certain facts have to be mastered. That is they have to be so thoroughly studied that they become parts of our very being. Facts that have to be turned into faculty are of this kind. The multiplication table, the declensions of nouns and the paradigms of verbs, the exact memorizing of verses or other verbal formulæ that are admitted to be worth memorizing—all these exemplify material that has to be thoroughly assimilated. In dealing with them we are not specially called upon to look before and after. They have to be mastered. Thoroughness demands this.
But some things are not worth getting up in this thorough fashion. Certain details in history, for example, are very valuable, since they give a clear idea of the conditions under which important events have happened. But they are not so important as those important events themselves. The terms of Magna Charta, or of the Constitutions of Clarendon, have to be mastered because of their intrinsic importance. But a great many details have to be considered in order to enable us to understand the conditions under which these documents were drawn up. In studying history, therefore, the student will naturally discriminate between what is essential and what is merely scaffolding.
It is dangerous to say anything that even seems to depreciate thoroughness. Poor human nature is only too willing to take advantage of anything that gives it the slightest encouragement to adopt the easiest course. In what follows you will please keep clearly in mind that what you are being warned against is not thoroughness, but a pseudo-thoroughness, a thoroughness that is out of place. In an admirable but now out-of-date book for the use of students (The Student's Manual) the Rev. John Todd has the following passage in a chapter entitled Study:
"Passing over a field of study has been compared graphically to conquering a country. If you thoroughly conquer everything you meet, you will pass on from victory to victory; but if you leave here and there a fort or a garrison not subdued, you will soon have an army hanging on your rear, and your ground will soon need reconquering. Never pass over a single thing, however minute or apparently of little consequence, without understanding all that can be known about it. He who accustoms himself to pass over a word or sentence, or a single point of mathematical inquiry, without thoroughly understanding everything that can be known about it, will soon be known as an inaccurate scholar."
The application is that no difficulty should be left till it is thoroughly mastered. Instead of pressing on to new matter the student is recommended to sit down before a difficulty, as a general would lay siege to a fortress. The difficulty must be mastered or the fortress taken before any advance is made. Even in warfare it is doubtful whether this policy is always a wise one. To the lay mind at any rate it appears as if the experience of the English generals during the great Boer War rather damages the claims of the principle. But in any case in respect of study the Rev. John Todd was wrong.
It is easy to understand what he really meant. He was so afraid of students shirking genuinely hard work that he laid down his severe rule. It is only a variant of the usual warning that there is no royal road to learning. Todd is right in not giving way to those who hold out hopes of a primrose path. Difficulties must be faced: the nettle must be grasped. But the question arises: Must it be now? To the man who knows human nature, such a question will be recognized as the most dangerous form in which the problem could be put. There is nothing so insidiously undermining to strength of character as this plea of justifiable procrastination. We are all so willing to postpone the evil hour that we welcome with something like enthusiasm the recommendation of any one who ventures to advise delay. But here I have no claim to deserve such an enthusiastic reception. I have no comforting advice in the way of avoiding difficulties. I admit that they must be faced, faced promptly, faced dourly. But we must not be foolishly dour. "Dogged does it," no doubt, but it does not always do it intelligently. There may be other ways. There may be a way round. We must not make the mistake of the English officers at the beginning of the Boer War, and sacrifice our energies by an heroic but unprofitable frontal attack. Our object is success in our studies, success, no doubt, in overcoming any particular difficulty, but more important still, success in our study as a whole. We must husband our resources, and use them to the best advantage. If we have faced a difficulty squarely, worked our way all round it, looked at it from every point of view, and can still make nothing of it, we are not well advised to sit down before it, and wait for something to turn up. Yet if we are to follow the advice of the Rev. John Todd, that is all that is left for us to do.
It has to be admitted that up to a certain point he is entirely in the right. We must not pass over any element of the problem as unimportant; we must see that we understand all the details, and we must realize which are the points that we do not understand. It is one thing not to understand a detail, it is another to know that there is a detail that we do not understand. It is not always possible to follow the counsel never to pass over a detail "without thoroughly understanding everything that can be known about it," but it is always a point gained when we are able to note that there is something that we do not understand. We have made no inconsiderable advance when we know that we have a difficulty to face. For it is sometimes possible to know and understand all the details of a problem without realizing that there is a problem at all.
Granted that we know that we are face to face with a serious difficulty, we want to know how to face it. I find that the great d'Alembert, the editor of the famous French Encyclopédie, gave this advice to young mathematical students when they come up against the disheartening wall that so often rears itself up before them: "Have faith, and go ahead!" It is pleasant to find that M. Fabre, the distinguished naturalist already quoted in our first chapter, has followed his countryman's advice, with a result that strengthens our view as against that of the Rev. John Todd. Speaking of the serious difficulties in his mathematical studies, M. Fabre says:
"Faith I had, and I went on pluckily. And it was well for me that I did, for I often found behind the wall the enlightenment that I was seeking in front of it. Giving up the bad Making to patch as hopeless, I would go on and, after I had left it behind, discover the dynamite capable of blasting it. 'Twas a tiny grain at first, an insignificant ball, rolling and increasing as it went. From one slope to another of the theorems it grew to a heavy mass; and the mass became a mighty projectile which, flung backwards and retracing its course, split the darkness and spread it into one vast sheet of light.
"D'Alembert's precept is good and very good, provided you do not abuse it. Too much precipitation in turning over the intractable page might expose you to many a disappointment. You must have fought the difficulty tooth and nail before abandoning it. This rough skirmishing leads. to intellectual vigour."[1]
In order to avoid abusing d'Alembert's advice, we must ask ourselves the question: "How long must I wrestle with an apparently insoluble problem before I can give it up with honour?" The answer is that we are never entitled to give it up at all, unless, as in the case of perpetual motion or the squaring of the circle, it can be proved that a solution of the problem is impossible. I have no comfort to give the lover of ease. There is no good saying Peace, when there is no peace. But while we must make up our minds never to give up a soluble problem, it does not follow that we should spend time unprofitably over it. Attack the problem as vigorously as you can, but do not suspend all your other operations merely to lay siege to it. A time comes when it is advantageous to make a note of our temporary failure, and move on. What we want to learn in each case is when that time for raising the siege has arrived. Now in dealing with a problem, we may be said to pass through three stages, marked by the degree of freedom with which we can manipulate the materials at our disposal.
At the first stage we bring forward a great deal of matter with which we are quite familiar. We know exactly what each bit of it means: our mind moves easily among the elements and we do not have to reason about it at all. We are here in the region of observation. We note certain things and know exactly what the bearings of those things are. As you get into the hall on returning home you say, "I see Jack's got back." As a matter of fact you see nothing of the kind. What you do see is a hat and a walking-stick. But they speak so plainly that you do not need to think about their meaning. You really infer from the hat and stick, that Jack must be in the house, but, as the conclusion is so easily drawn, the whole process is regarded as a matter of observation, and we say that we see or observe that Jack is at home. This stage may then be called the observation stage.
The second stage is marked by conscious inference, and may therefore be called the inference stage. Here we are dealing with things that we understand, but do not know intimately. We have to consider each fact and draw conclusions from it, and in this way make progress. The work may be slow, but we know where we are. We may not be successful at first, but if one way of dealing with the problem fails us, we try something else. We at least know what to do next. This inference stage is the most usual and interesting one in our studies. Sometimes the inference is easy, sometimes it is difficult. But we know when we are making progress. We know when we encounter a gap in our knowledge, and we know how to fill that gap. We keep our eyes and ears open, we ask questions, we read books, we use all the means in our power to reach the end we have in view. For at this stage we always do know definitely the precise object of our study.
In some cases, however, the problem becomes so difficult that we begin to lose our way altogether. It may arrive at that point at which it is beyond the reach of the materials at our disposal. When a Frenchman comes to this stage he says that he is at the end of his Latin. He has done all he can think of, and does not know what to do next. So long as we can go on asking questions and making intelligent experiments, we are still at the stage of inference, though we may be getting into the upper regions of inference where the air is very rare and it is difficult to breathe. But when we have no more definite questions to ask, and no specific experiments to suggest, we have reached what I like to call "the gaping point." People often find themselves at the gaping point in dealing with a very badly written letter they have received. After making all manner of inferences based upon the post-mark, and the signature, and whatever words they are able to make out, there comes a time when there is nothing more to be done than gape at the letter, turn it upside down, look at it sideways, carry it about in the pocket, and occasionally pull it out quickly to see if by any chance it is possible to take it by surprise, and get at the meaning. It is when we have reached the gaping point that the time has come for making a move away from the problem. When we have reached the stage at which we do not know what to do next, we have obviously come to a point at which further study of the problem is only a waste of time. By and by, no doubt, something will turn up that may throw light on the subject and suggest a new line of investigation, but in the meantime we are merely wasting time by gaping.
As a young teacher I had a class in technical drawing for skilled artisans. My pupils used to bring me drawings, that had been given them for their guidance, and get me to explain them. As a rule I found the drawings easy enough to interpret, but on one occasion a huge drawing in Perspective was handed to me as I left the class in the evening, for explanation next day. After supper I laid out the drawing on my table, and in twenty minutes I understood it all except one little three-quarters of a circle at one of the vision points. I could not understand what part it played in the whole scheme: it appeared absolutely useless. But experience in drawings of this kind had taught me that everything has a meaning, and I had read the Rev. John Todd. Accordingly I settled myself down to the siege of this difficulty. Hour after hour passed without bringing any enlightenment, and at length in the early morning, with an internal apology to the Rev. John Todd, I capitulated and started to roll up the sheet. To my surprise the tiny three-quarters of a circle moved. It turned out to be a hair from my moustache. It was then that my suspicions were aroused about the siege system of learning.
Take the case of a passage in a foreign language. At first you move easily enough among the nouns and verbs and adjectives. You know what most of them mean, and you know their ordinary agreements among themselves. You find, however, that there are some words that you do not know. The dictionary is at hand and this difficulty disappears. There may still be some little trouble about a concord or an inflection, but in general terms you fcel that you know the run of the passage. By and by, however, you observe that there is a combination of words that do not make sense. You look at each individual word, and find that you know them all. The grammatical details seem all in order. Yet there remains a persistent lack of meaning: the passage has no sense. But you are not yet reduced to extremity. You look up in your dictionary all the words, however familiar, that appear in the troublesome part, for experience has shown you that common words have sometimes a special meaning that the dictionary is good enough to disclose. For example, in a French passage, the word Monsieur is so commonplace as to rouse no suspicion. It is the last word in the passage that you would look for trouble about. Yet when every other word has established its bona fides and you turn this up in hopeless depression, you get the key to the whole passage when the dictionary tells you that this word was formerly used (with a capital—but you had paid no attention to this trifling peculiarity in your search after meaning) to denote the eldest of the King's brothers. But suppose you have no luck in the dictionary, and after all your efforts you remain baffled, and do not know what to do next, you have reached your gaping point. It is time to move on.
You have made a note of your defeat. You are depressed about it, and probably a little angry. All this is to the good. You are in a fighting mood, and determined sooner or later to get the better of the recalcitrant passage. Not infrequently you will find consolation sooner than you expect. It is not uncommon to find on the next page some remark or other that makes quite plain what formerly was unintelligible. When you are dealing with the individual passage you have of course done a good deal of looking before and after, but you have been limited by your ignorance of what is to come in the text. Your making an advance after you have recognized that you have reached your gaping point is in fact only an extension of the process of looking before and after. You are taking a wider view, and sooner or later this wider view will include something that throws light upon the difficulty you have temporarily abandoned.
Since you who read this book have taken your own education in hand you have become an educator, and therefore ought to be interested in the methods of teaching that are presented to teachers at their colleges. Unfortunately most of these methods demand two persons that are separate from one another. They are not usually such as can be applied by a person like yourself combining the two characters of educator and educand. But there are two special methods that have something to teach you, even though you cannot apply them to perfection.
The first of these is named the Socratic Method, after a Greek philosopher who flourished in Athens at the end of the fifth century в. с. You remember that I pointed out already that it is often the teacher's business to make his pupils take trouble. Socrates realized this with special clearness, and spent most of his time trying to get his fellow citizens in Athens to think for themselves. His plan was to get into conversation with some of them, and ask them the meaning of words that they used glibly enough but did not fully understand. His view was that as soon as we clearly understand the terms we use, we are on the direct way to right thinking. Accordingly he made them see by his conversation that they did not know exactly the meaning of the terms they were using, and then set them about finding out the true meaning. He would ask his friends what justice was, or temperance, or truth. They would answer easily enough at first, but he would go on to raise difficulties and could easily show that their meanings were not quite accurate. They would change one meaning for another, and with that too he had some fault to find, and by and by, after many trials, they would discover that they really did not know what the meaning of the word was. When they had reached this stage he would go on asking more and more questions, till at last he led them to find out for themselves the true meaning of the word.
You will thus see that in the Socratic method there are three stages in the experience of the pupil. He begins by being quite confident, though he has no cause to be confident. By and by he becomes confused, and reaches a state of doubt. After that he comes to the third stage, which again is one of confidence, but this time it is a confidence that has a good foundation. A peculiarity that marked the teaching of Socrates was that he always professed that he never really taught anybody anything. All that he did was to enable people to find out things for themselves. Obviously to carry out this method properly it is essential to have a teacher who stands outside of us altogether, and by his questions gets us to think in a particular way. The teacher is supposed to know beforehand all that the pupil is afterwards to learn. For Socrates' affectation of ignorance was only a pose. He knew quite well whither his teaching was tending, but for dramatic effect he proclaimed that he himself did not know, he just asked for information. This is what is called the Socratic irony. It was used because he had to deal with the very intelligent and rather conceited Athenians, and much of his teaching had no higher aim than to make these Athenians realize the possibility that they might be wrong. Now to some extent it is possible for us to use the Socratic method with ourselves. On a famous occasion Cromwell made the appeal to certain persons:
"I beseech you, in the bowels of Christ, think it possible you may be mistaken."
Is it too much to hope that the readers of this book have no need to have such a prayer addressed to them? Assuming then that we do not need to be convinced of our fallibility, we may be able to use the method of asking ourselves questions with the honest purpose of finding out how matters stand in relation to what we are studying. This plan of putting questions to ourselves is only a way of expressing what is always going on in our minds when we are dealing with a problem. Young pupils when set to write a short essay are often quite at a loss what to say. Teachers of junior forms in school sometimes hit upon the plan of telling their pupils to put internal questions to themselves, and then write out the answers. The answers when written down do make up some sort of essay. The arrangement is usually rather bad. But so soon as the youngsters have written down a sheet of answers, they find that they have some material to go upon. They acquire confidence, and by rearranging what they have written down and adding what occurs to them in the process, they are generally able to produce passable work.
You have seen that Socrates did his best to minimize his work as a teacher. But there is another method of teaching that urges the teacher to do still less for the pupil than Socrates did. After all he set the problem, and kept up a running fire of questions. The method known as Heuristic recommends the teacher to leave everything to the pupils after the problem has been clearly stated. The word heuristic means literally finding out, and the method has been described as the method of causing children to find out things for themselves. In schools this method is applied mainly in science teaching, but it need not be confined to science subjects. What makes it specially interesting to readers of this book is that it throws the whole responsibility of investigation upon the pupil. The method is not a new one, and has been associated with very distinguished names, among them Rousseau and Burke. But in recent years it has been brilliantly advocated by Professor Henry E. Armstrong.[2] He tells me that on one occasion his daughter, then a little girl, had been reading Professor Drummond's book called The Monkey That Would not Kill. Among the wonderful escapes of this monkey was one from drowning. He had been cast into the sea with a stone tied round his neck, and thought it was all over with him; but to his surprise he found that the stone was not nearly so heavy in the sea as it was on land, so he was able to get ashore. The little girl asked her father if it was true that a stone was not so heavy in the water as it is outside the water. This is a question that Professor Armstrong regards it as "criminal" to answer, since to do so wastes an excellent opportunity of applying the heuristic method. So his reply was, "Suppose we try to find out." Thereupon began a series of experiments, made by the little girl and recorded by her in an exercise book that I am in hopes to see published one day.
Here we have a very definite case in which we know exactly what the problem is. We may not be able to answer the question we have set ourselves, but at any rate we are in no doubt about what the question means. There is nothing more hopeless or more futile than to put in a period of study without knowing exactly what we are aiming at. In such a case we do not reach the gaping point, after a series of efforts to solve a problem. We start at the gaping point. Some teachers are very punctilious in stating at the beginning of every lesson what the exact aim of the lesson is. Obviously this is not always essential. Not much good is done by announcing at the beginning of a lesson on the Latin verb volo, "The purpose of this lesson is to master all the irritating peculiarities of the irregular verb volo." It is clear that the heuristic method is applicable only to constructive study. There is nothing to find out in a purely assimilative lesson. But in constructive study it is hardly possible to overestimate the importance of setting before yourself the definite end or purpose you have in view.
Very frequently time is wasted by the student in merely fumbling with a problem. Unless we have a clearly imaged end, there is great danger of merely fiddling about with the elements of a problem. Some students feel that when they are studying they must be doing something. In one particular school with which I was acquainted, it was counted an offence "not to have something on your paper." The effect of this was that even if a pupil had no idea how to work a particular problem, he had to write down something—a most pernicious habit. Writing nonsense is necessarily bad for any one. No doubt it is very unpleasant to sit at your desk and gnaw the end of your pen, but you do not improve matters by scribbling down meaningless words. This criticism naturally does not apply so long as you have the least idea of getting at a result by a series of trials. Your attempts may be far from hopeful, but so long as they have a definite object they are justifiable. So soon, however, as you have no definite purpose in what you do, you can no longer be said to study in any real sense.
- ↑ The Life of the Fly, p. 332.
- ↑ The Teaching of Scientific Method, Chap. xv.