CHAPTER II
The Preparation of the Unconscious Mind[1].
It is a common mistake to suppose that no preparation for science is needful or possible, except early teaching of what are called scientific subjects. Early attitude is far more important than early teaching.
Medical authorities have told us that consciousness resides in but a small portion of the total machinery by means of which we think and learn, and that it is dangerous and futile to over-feed and over-exercise that small portion, while neglecting that larger portion the action of which does not immediately cause consciousness. And, indeed, there is much reason to believe that the amount learned by children might be very much increased without the least injury to their health of body or mind, and with much less exertion than is now imposed on them and on their teachers, if the cultivation of the unconscious and that of the conscious portions of the organism were kept properly balanced and adjusted to each other. In the old days of classical education the training of the unconscious mind was necessarily little connected with school subjects; one can learn nothing about a dead language except by reading books or being told things. Children learned Latin in school; and the unconscious informing of the mind was done in haphazard fashion and by means of quite other subjects. Much of it was called 'idling,' or 'mischief,' or 'naughtiness.' The educational profession has not quite shaken off the influence of this old state of things; it should not be blamed if it has not yet realized what needs doing in the direction of informing the unconscious mind. For the present generation, at least, it will be wise of parents to assume that teachers, on the whole, err in the direction of attending too exclusively to the conscious mental action, and that they, the parents, must compensate what is lacking.
The first thing we must do is to resolve seriously that a good deal of time before the age of ten, and of the vacations afterwards, shall be resolutely dedicated to the training of the unconscious mind. We must not only discourage the setting of holiday lessons by masters; we must also check in ourselves the tendency to overflow into being amateur professionals, so to speak, spoiling the future work of the professional teacher by premature and amateurish teaching.
Many parents seem to think that all the time is wasted for their children which is not spent in taking in consciously some special idea which some adult already understands. We must get rid of this notion entirely. A writer on education[2] has said that a human being comes into the world not chiefly to acquire knowledge or to develop his faculties, but to establish relations; and I would add that a child comes into science, not only to learn facts and to develop the faculty for doing things, but primarily to establish relations with the laws of nature, by which we mean—if we truly mean anything—the laws according to which the world is governed. And in order that relations may be properly established, the adults who are directing the child must, at proper times, keep silence even from good words.
I fear we are in some danger of forgetting, in the rush of modern education, that conscious mental effort rather interferes with the work of establishing relations. The time for establishing relations is the Sabbath of the I Am, the Jubilee when the land is lying fallow. Sabbath does not mean any sort of conscious exertion. But on the other hand it does not mean useless idleness. A mathematical writer on logic[3] of the nineteenth century wrote, that to listen to the voice of the Eternal Teacher we must make silence from conscious learning or even thinking; and adds, 'In these days we need repose far more than we need work. Repose is the brother of silence. We are sterile for lack of repose far more than for lack of work. The wise man acquires wisdom during the time of his repose.' A mathematician of the eighteenth century said that Sabbath and Jubilee mean, not mere cessation from work, but renewal. Sabbath, Jubilee, Holy Days, Holidays, mean, in fact, time to renew our force for future work by getting our relations with unseen forces, with nature, with man, and even with tools, more true, more perfectly harmonious, more elastic and easy than is possible while the conscious mind is acting on the relation. Begin therefore as early as you can to set up in the child's mind what one may call a Sabbatical rhythm in science; a clear distinction between the time when he is being taught by man and the time when he is free to investigate or experiment as he pleases. Give him limits of time and place, lay down certain necessary negative conditions for safety and health, and to avoid annoying other people; and let the child realize that during that time, in the allotted place, provided he conforms to the prescribed conditions, no one will interfere with his experimenting exactly as he pleases.
It is curious and painful to observe how many things have been proposed by true educationalists, simply for the purpose of ministering to the action of the unconscious mind, and afterwards perverted, by persons possessed with the teaching mania, to the purpose of stuffing into children's minds some idea which is in the teacher's mind. This is especially the case in regard to early kindergarten work. Each object is catalogued as intended to teach this, or to prove that, or to illustrate so-and-so; many parents seem to have no idea that it may be well to let a child have things and handle them, without any one talking, and find out what the things have to say.
We have now to consider three points connected with science:
(1) What kind of teacher is likely to err least in the matter of neglecting the unconscious cerebration?
(2) Assuming that many teachers will err in that direction, and that the parents wish to utilize the time before school age, and the holidays later on, for the purpose of compensating this one-sided action of the school; how shall they decide, in any given case, on the kind of subject most likely to be useful in this respect?
(3) How does one set about to direct the action of unconscious cerebration, in science? First. What kind of teachers do least harm in the way of neglecting to provide material for unconscious cerebration in science? Those are most neglectful of it who have 'got up' the elements of several sciences, simply in order to be free to advertise themselves as able to teach, and who have no other connexion with, or interest in, science than that. The best science teacher is usually a thorough-going enthusiast in the science itself, who, in the intervals of regular teaching, gets his pupils to assist him in his own investigations or pursuits. But that supposes an ideal condition of things; and ideal conditions can seldom be secured. As I said, the responsibility for unconscious preparation for science lies with the parents at present.
This brings us to the second question:—How shall the parents decide for any given family what subjects can be most usefully employed as food for the unconscious brain? Choose for this purpose some subject to which you see the child attracted; and one the materials for which are at hand or can be procured without effort, or strain, or fuss. The means used for feeding the unconscious brain should be as far as possible dissociated in the children's minds from any notion of doing things for their own instruction. Whatever you set children to do for this purpose should be done either to amuse themselves, or, better, to amuse some one else; or by way of helping some one else; and by means of objects which you can introduce into the house for purposes of play, or use, or ornament. If there is any one about, a relative or intimate friend, who knows some science subject well and is not a professional teacher—an uncle electrician or photographer, a friend who owns a star telescope, an aunt with a hobby for collecting seaweeds or growing ferns, a nice friendly carpenter or blacksmith in the place where you go for holidays, let the children spend as much of their spare time with this person as they and the person wish. Lay no stress on their learning any special thing from him or her; leave the children to absorb whatever impressions they can gather. A country-bred girl who in her own childhood went nutting and blackberrying, or worked in a little garden, may be a better holiday companion for children than the town-bred, school-trained governess, however much the latter may know about 'ovaries' and 'stipules,' and the names of classes and orders.
Thirdly, when you have decided on your subject, how shall you proceed to direct the action of the children's unconscious brain towards it?
We will begin with the preparation for Natural History. Choose as pets animals to whom you can give some sort of real natural life. Give the children something to do in connexion with the animals. If you cannot entrust the feeding or cleaning of the pets to the children, you can at least make it their business to give the horse his daily treat of fruit or sugar or bread, the dog his bath or swim. If you have birds in cages—a thing which I cannot believe is right where there are children, as I think it gives them a false start as to the rationale of our power over the lower creatures; but still, if you do—let the children accustom the birds to fly about the room and perch on their hands and heads. Let them make a garden for the cage-birds by sowing bird-seed and chickweed in pots, so that they may watch the birds picking green shoots as they grow. But it is far better to let them feed and tame wild birds.
I am not going to join in Michelet's protest against accustoming children to masses of cut flowers; but I will say that there is no use in trusting to cut flowers and exotics raised by gardeners as preparation for understanding Nature. Let the children have such homely plants as thrive without very skilled care, and attend to them themselves. Let them also grow such things as mustard and cress for the family use. I wish to call special attention to the advisability of children doing such things as a contribution to the family's resources. It is advisable, not only on moral grounds, as tending to promote unselfishness, but because it makes it easier to secure repeated performance of the same task, with slight variations. Incessant novelty stimulates the conscious brain too much; monotony tends to dull the whole brain; but a duty which has to be done under varying circumstances, a uniform result which has to be properly attained under varying conditions, does much to furnish with material the unconscious brain. A child who supplies the family with small salad at stated intervals has to water it in dry weather, shelter it from very scorching sun, grow it in pots in town, and in the hardest frosts on a flannel near, but not too near, the stove; he thus becomes accustomed to the feeling that Nature's unvarying laws of growth present multifold difficulties to finite man.
We come now to preparation for the physical sciences.
If there is a seltzogene in the house, let the children see it made up; not once only, with an elaborate explanation of the action of acids on alkalies—that appeals to consciousness; let them see it done as often as they wish, till they become saturated with the sense of the invariableness of the action; till they are sure that, though mother can make mistakes, the chemicals never do, and that when anything goes wrong it is because the human agent has been wrong.
The habit of using tools quite experimentally on a variety of material will be useful. The science of mechanics deals largely with resistances and strains. When the teacher begins talking of these things it is advisable that his class should have ready a basis of subconscious experience of the resistance of various woods to the hammer and saw. If you turn the children loose in company of some nice person of the artisan class, you may wish to make some compensation for any waste of his time the children may cause; let it take the shape of an informal present at the end of vacation, not of a weekly wage. The man who is hired to teach at a fixed wage feels bound to teach; he is sometimes tempted to treat pupils as if the business on hand were learning a lesson; to give them the right kind of wood to make each object of, cut ready into the right-shaped block to begin upon; to tell them in what order to do the various portions of the work, and which tool to use for each operation and how to handle each. It is desirable that children should sometimes be free to experiment under varied and accidental conditions, to use the wrong kind of wood and the tool which is not quite the best for the purpose, and hurt their fingers a little, and learn by making mistakes, with some one about who will protect them from seriously wounding themselves, will quietly prevent their making overmuch use of tools too heavy for their small hands and therefore likely to injure the flexibility of their muscles, and to whom they can apply when puzzled or discouraged.
There is some connexion between the due feeding of the unconscious brain and the process of going wrong; by which I mean going at first some way which is not the ultimately right way. The nature of this connexion is as yet obscure, but it evidently exists, and we have to deal with it. Parents are given to children in order to prevent their going wrong in ways which will compromise their future; we must not, more than we can help, let them permanently injure their health, or acquire habits which will handicap them physically, mentally, or socially, or grow up ignorant of things which they ought to know. But the more careful we are in these respects, the more, not the less, we need to compensate the lack of wrongness in serious matters by providing abundantly safe opportunities for going wrong, and learning by experience, in matters of no consequence. For among all the habits which science requires us to form, none is more important than the habit of learning when there is no man to teach us, of profiting by our own past errors, of rising on stepping-stones of our mistaken selves to correcter judgements. Now there are few places in which a child can do so many things wrong, without injury to himself or annoyance to anyone else, as in a carpenter's shop. He can begin to make something out of wood that has a flaw, or that is too soft for his purpose; or he can try to gouge out a piece that is too hard for anything but a very sharp chisel to bite into. He can begin on too small a piece; he can begin without taking proper measurements and put his centre-bit in the wrong place; and, when he finds himself baffled, he can try again another way. And when he is tired of failures he can ask the carpenter how he begins; and that is a useful lesson in modesty. And he can get so delightfully dirty without any real soil or filth. But, if not in the carpenter's shop, then elsewhere, provide somewhere, somehow, opportunities for children to go wrong and make mistakes, under the protection of some one who will not interfere with them till they ask for guidance, unless serious mischief is threatening.
As preparation for hydrostatics, let the child dabble in water, with hands and feet, in warm water and cold, in salt water and fresh, as much as is safe from the health point of view. Let the baby have things to float in his bath, sticks, shells, toys of wood and china. Let him turn the water-tap on and hold his hands under it and experiment on making splashes of many shapes and kinds. I do not mean that you should tolerate such disorderly mischief as turning taps on the sly and flooding the house; that is bad training for the child as well as inconvenient for the household. But when you are by to see that no harm is done, let the child turn the water-tap when he wishes; not once in order that you may show him something that you can see happen, but habitually. Let him play with falling water. What is wanted is to get his finger tips, so to speak, quivering in response to the tremor of water at various temperatures and densities, and moving in various ways. All these physical experiences pass up to the brain and produce some impression there. They do not constitute knowledge; a man may dabble in water all his life and remain ignorant of hydrostatics as a fish; but they do form the unconscious material which, when he comes to study hydrostatics later on, will make his knowledge living and real, not shadowy.
When a child's attention is attracted by any unfamiliar occurrence, especially by any such sound as that of a singing flame, or by a moving light on the ceiling, do not unnecessarily distract him. As long as he is interested and happy, leave him alone. Let him acquire the habit of quiet and silent observation.
As preparation for learning electricity, do not be satisfied with once showing the child that sealing-wax rubbed on flannel will attract bits of paper, but let him have a stick of wax, or better, a common vulcanite comb and a piece of flannel, and keep them, and try all the experiments he wants to try. Let him learn by experience that after a time the comb discharges and needs to be rubbed again; that if he touches the table with the charged comb it discharges at once and he has the labour of rubbing over again. As soon as he can be trusted to handle a glass rod without cutting himself, let him have one and an old silk handkerchief. Do not attempt to explain why the comb must be rubbed with wool and the rod with silk; but let him find out that so it is. I have seen a charming set of toys made (from receipts published by Tyndal, for poor boys) out of paper and pith, wire and scraps of sheet tin, some sealing-wax and a few needles, with which two children, aged three and a half and five, played the whole afternoon. The habit of using them seemed to have evoked in the small mites a deftness of touch on apparatus, and a sort of personal acquaintance with what scientific people call the 'behaviour' of electric force, its manners and customs under a variety of conditions, quite different from any knowledge that would be imparted by any kind of teaching.
Of course the child has a magnet; but he too often uses it only for attracting the regulation ducks and fish; he should be provided with a box of iron filings and some small nails. A second magnet increases the range of free experimentation.
Most children delight in machinery which moves with a slow, steady, rocking motion. Let them waste as much time as they like in watching it. A hayband twister such as is still in use in remote country places, the spinner of an old-fashioned rope-walk, the rocking piston of a steam ferry-boat, becomes quite a familiar friend of children who have the opportunity of cultivating its acquaintance. They might have many worse friends. But a better one still is the Sympalmograph or Harmonograph, especially the old-fashioned kind, made of two pendulums swinging different ways, and holding between them a pen, which traces exquisite curves that suggest wings, and flames, and strange unknown flower-forms. If you know where lives one of these old harmonographs, cultivate the acquaintance of the owner, and get leave to let the little ones see the big, ugly, lumbering monster creating the most fairy-like beauty by simple obedience to rhythmic law. Do not preach or try to explain; let the motion itself lay its spell on their souls and preach a sermon too eloquent to be translated into human speech.
I said that children can have worse friends than a steam piston. One of these worse friends is the person who interrupts their fascinated contemplation by saying, 'It is waste of time to watch this old slow-coach affair; if you want to see machines, I'll take you to see one that will turn out a gross of diagrams while this lumbering old thing makes one. a mile of rope while this makes a yard.' If a child is left to his natural instincts he will prefer to be able to follow what is going on. The love of very rapidly whirring machinery is an acquired taste, and, for a child, an essentially unhealthy one. It is bad for nerves and eyesight; and if a child does like it, it is in the kind of mood in which, if he got into the same later on, he would not be likely to make a scientific discovery; he would be more likely to take to drink, or gambling, or sensationalism in politics, or to startling the public with violent attacks on sacred things, or, in short, to anything in the world which is most emphatically not science.
A modern child must of course acquire some sympathy with the desire for rapid achievement; but there are better ways of introducing him to it than stunning him with the racket of rapidly whirring wheels. Choose, if possible, some machine which makes little whirr, bustle, or dust; which causes no vicious tremor to eyes or nerves; and in which the large amount of work got through in proportion to the amount of force exerted by the operator is due not to any piece of the machine moving quickly, but to the fact that every touch of the operator's finger sets a great variety of parts moving, each one at a moderate pace but exactly in harmony with all the rest. The Linotype composing machine is admirable in all these respects; and the amount of work done for one movement of the compositor's finger might fairly be called miraculous.
There is at South Kensington a selection of machines well chosen for educational purposes. Some of the models are only set working hy special request made beforehand; but several work at stated hours daily. The most attractive to children are those which they can turn on themselves by touching an electric button. When you are at the Gallery, do not be in a hurry to explain; do not talk unless the children ask questions; and do not imaginethat the afternoon has been wasted because you have no proof that any special thing has been learned. The sensation of putting one's finger on a button and seeing a whole army of wheels, cogs, levers, and hammers respond, as if by enchantment, to one's touch, is a tremendous revelation to a child's sub-conscious mind: and, until the sensation is quite familiar, it ought to be undisturbed by any conscious teaching. The day when a child receives any great new revelation of his own relation to unseen forces should be treated as a Sabbath, a Holy-day, and no work of mental effort should be imposed on him that day.
There are three volumes, called La Science, Amusante, written in French—easy and very beautiful French—by some one whose nom de plume is 'Tom Tit' They supply suggestions for a great variety of experiments which can be carried on at home, and which seem to be admirably selected for the purpose of training the fingers, and through them the unconscious brain, into harmony with natural law.
Real and repeated experimentation with commonplace objects has a far more educative influence than a constant variety of so-called 'mechanical' toys. The common peg-top is a valuable teacher, and, like other teachers, should be allowed to speak to its pupil in its own language. When a top is asleep (i. e. when its rotation is perfect) it can be picked up from the ground and made to jump from hand to hand without its rotary motion being interfered with; whereas the same action stops the rotation of a top which has not yet settled into its spin or which has nearly exhausted its impulsion. There are some conceptions in physical science which present no difficulty to one who, years before he hearis any discussion about matter and force, has made a long series of experiments with the same object rotating under varied conditions. A useful toy for illustrating the interaction of opposing forces is the sling, which suddenly exhibits tangential motion at the moment when the stone escapes from the counteracting force of the string. A small weight fastened to an elastic string represents the dual force under which the planets move, the force of attraction alternately yielding a little to the tangential impulse and slightly overcoming it.
The practice of playing with such toys as the sling and stone, the sucking-valve, the old-fashioned rope-maker's wheel, and the bandalore, may be made a means of accustoming children's nerves to the feeling of Nature's opposing tendencies, and may prepare the organization for receiving knowledge, later on, into the conscious brain. By training the hand to trace out Nature s action, we train the unconscious mind to act spontaneously in accordance with Natural Law; and the unconscious mind, so trained, is the best teacher of the conscious mind.
The delight that most children take in swinging is the outcome of natural physical craving to be in line with Natures forces. This purpose is best served by the pace at which and the height to which the child is swung being regulated according to his own instincts. If we excite him to allow himself to be swung higher than he likes, either by competition with other children or by the injudicious comments of adults, we do something to turn what should be a preparation for future revelation into a preparation for future vice or brain-disease. The element of competition has its place, and a very important one, in education; but its function is to stimulate to active exertion among known facts. Children may legitimately run races for a prize, or compete together as to speed and accuracy in working out sums by methods already quite familiar; but whenever the business on hand is revelation, whether by learning to understand a mental process, observing a natural fact, or tuning the nervous system into harmony with Nature's rhythmic law, the idea and feeling of competition should be entirely absent. Too much stress cannot be laid upon this point. The false crossing of influences, the applying of stimulus inappropriate to the particular function, especially the dragging of the element of competition into the wrong portions both of the educational life and the professional life, are responsible for more of insanity and vice than any one dreams of who has not given very special attention to the subject.
Of arithmetic and algebra I shall say little here, as they are treated in another chapter. Only one point I will lay stress on. Many a life of intellectual muddle and intellectual dishonesty begins at the point where some teacher explains the rule for Greatest Common Measure to a child who has not had the proper basis of sub-conscious knowledge laid in actual experiences. Therefore, if you value your child's future clearness in science, trust no teacher to tell him anything about G. C. M. or L. C. M. till you have ascertained that he is able[4] to find, easily and accurately, by means of compasses, the longest length that will repeat exactly into each of two unequal given lengths, and the shortest length into which each of two given unequal lengths will fit.
We now come to the subject of geometry, the condition of which affords, it seems to me, a standing warning against directing educational care too exclusively to the conscious mind, and neglecting to provide food for unconscious mental action.
There seems to be evidence that, in ancient times, all people in good society were expected to know simple truths about geometric forms, in the same way as we all know simple facts in natural history. The elementary properties of the triangle, parallelogram, circle, ellipse, and spiral seem to have been familiar to ordinary people. They were not expected to know much about geometry, but they were expected to have and to use ordinary faculties of observation on facts within every one's reach. Euclid was, in his day, a sort of Darwin of geometry. He wrote not a geometry for beginners, but a book about the logical concatenation of geometric facts for men already geometers; just as our Darwin wrote a book about the concatenation of biologic forms for people already biologists, to the extent at least of knowing that horses prance and dogs bark and wag tails; that worms creep and birds fly; that some flowers have scent; that some fruits are sweet and others are sour.
Euclid's book was a type and model of all that a good book on logical concatenation should be. The use which was made of it till lately is the type and model of how such a book should not be used. Teachers assumed that the excellence of the book gave them the right to use it in defiance of all the laws of psychology. The result of such misuse is always the same: loss of natural instinct. Textbooks are written expressly on purpose to inform the consciousness. A good textbook should explain everything step by step, and should assume nothing which it does not actually state. Euclid does this in perfection. He wrote, as I have said, for men for whom the words triangle, circle, parallelogram were already charged with associations; and he gave definitions intended for the purpose, not of telling something fresh, but of clearing up and settling conceptions which were hazy from long familiarity.
Now when it became customary to give to boys of ten or twelve what Euclid wrote for grown men, that was not far wrong; boys now can quite well assimilate what was grown-up food two thousand years ago. But if children of twelve are to learn what Euclid wrote for advanced men, children of three should be acquiring the sub-conscious physical experiences which lads in Greece picked up in the course of nature and by the accidental help of architecture and statuary. This precaution our grandfathers entirely omitted. The effect was somewhat similar to that which would be produced if it ever became the fashion to make children learn theoretic natural history from books illustrated by flat diagrams, before allowing them to see any real animal or plant. Europe has lost geometric instinct and the habit of geometric observation. All of us at this time are in a condition of artificially paralysed geometric faculty; and now the aim and study of all true mathematicians is to restore the vitality of geometric instinct.
One partial remedy that has been suggested, by Spencer among others, is to substitute for Euclid some book of similar kind but less perfect of that kind; some book which mixes up a little real geometry with Euclid's idea of logical concatenation. This does not go to the root of the matter. The remedy is not to substitute for Euclid some inferior and less thorough textbook, but to precede and supplement the use of textbooks by some gymnastic calculated to restore normal vitality to the paralysed natural faculty. A very great deal has been done of late years, by mathematicians, in the way of suggestions towards the creation of such a preparation. The misfortune is that our mathematicians do not yet know how to explain their ideas intelligibly to non-mathematical mothers and lady nurses.
What is emphatically not wanted is that unscientific mothers and nurses should learn something about geometry and teach it before the school age; what is wanted is that we should deal with those type-forms which are the subjects of geometry on the same principles as we ought to deal, and to a great extent do deal, with the other classes of form: the living forms evolved by nature, and the artificial forms created by man for his use, such as furniture, domestic appliances, and ornaments.
First comes the education of the senses From the time when an infant begins to stroke the cat, to smell flowers, and to handle a spoon, have geometric solids as ornaments or toys, so that the senses of sight and touch may actually develop in contact with true type-form.
Next, the training of associated ideas. When you purchase type-forms, have the correct names written on each, and take care to call each by its name, so that the children may grow up with well-formed groups of associated ideas clustered round the words which mathematical teachers will use. Be as careful as possible not to misuse mathematical terminology in daily talk; either use it accurately or not at all. For instance, do not talk about the 'centre' of a long table, nor say 'ellipse' when you mean the oval suggested by two intersecting circles.
Then comes the training of the executive faculty. When the child can handle a pencil firmly and has outgrown the stage of mere scrawling, when he begins brush-drawing of flowers, or the drawing in pencil of boats and houses, give the hand also some training in the production of type-forms and the use of geometric tools. A violin, by the fact of being played on repeatedly, ripens and mellows into fitness for making music, because a relation is gradually established between the wood and the musical scale; and so it is with a child's brain; when he is generating type-form, some relation is being established between the brain and the laws which govern the generating of curves.
Lastly—and this is probably the most important preparation for future living comprehension of mathematical ideas—there is the cultivation of the geometric imagination. At the same age at which the child begins to realize that a tadpole grows into a frog, a boy into a man, a seedling into a flowering plant, let him have the opportunity of watching also how one geometrical type-form grows out of, or flows into, another. A common night-light placed in the bottom of a deep round jar in a dark room throws on a sheet of cardboard held over it patterns of conic sections, which pass into each other as you change the position of the card-board. Children very early learn to love watching figures thrown in light; and there is no age at which this amusement can hurt them, provided that the motion is slow, and that no one excites them by trying to explain things. A variety of other methods for training the geometric imagination at a later stage will be dealt with in a future chapter.
I am happy to be able to inform busy mothers that at early stages the needle and thread has many advantages over any other implement yet devised; a child can ornament cards by setting long straight stitches in a way which causes beautiful curves to grow under his hands without his knowing why or how, and without any pattern being set for him.
In the kindergarten attached to Bedales School the children generate designs suitable for tiles or carpets by the grouping and intersection of parabolas, curves of pursuit, &c. In many of these designs lines are first drawn which represent the ribs of some natural leaf; and these are then used as co-ordinates, by means of which a leaf-outline is evoked as the envelope of a system of tangents drawn in silk. Some of these designs have been noticed in the Inspector's report that he had 'found that the teaching of the calculus was leading to a most interesting evolution of design.'
The beauty of some of the designs is unquestionable; and there can be no second opinion about the value of the method, as training, from the point of view of geometry as well as from that of art. What is not quite so obvious at first sight is its bearing on the training of the unconscious mind for science. Without the slightest intellectual strain it puts the children through that normal sequence of orderly attention to classification and detail, interspersed with nodal points of synthesis, which may be called the very breathing-rhythm of the scientific discoverer.
But to make this exercise of any use there must be no copying from diagrams; the value of it depends on the child evoking a curve, watching it growing, under his fingers, from mere obedience to a law.
When children are introduced by any such method as the foregoing into the laboratory of the great creators of scientific thought, three classes of comments are made by adults who do not quite understand what is going on. The first takes the form of a congratulation on the cleverness of children at the present day. 'I did not know what a conic section was when I was sixteen.' The second, of alarmed remonstrance. 'Isn't it dangerous to worry little children's brains with such learned subjects? It is far better for a child of seven to be stitching round the outline of an animal or a house on the ordinary kindergarten cards, or even working a sampler as our grandmothers did, than to be stimulating his brain with abstract mathematics.' The third comment is one of scornful incredulity. 'Now, do you believe those children understand what a parabola is? Somebody must have shown them how to work it; the teachers are only showing off.'
I will answer these comments in order:—
There is no more cleverness in a child drawing a curve than in the pendulum of the harmonograph doing so; in both cases alike an implement has heen set moving according to a certain law, and beauty has resulted, not from understanding but from obedience. As for any strain to the brain, stitching a curve from its tangents is not more straining to the brain and nerves than stitching round a printed outline, not nearly as much so as working the fine cross-stitch samplers of our grandmothers. The difference is that working a sampler and following a ready-drawn outline cultivate only neatness and dexterity, but the act of evoking a curve 'out of the everywhere into here,' by simple obedience to a rhythmic law, lodges an impression on the unconscious mind which will be ready to surge up in ten years' time, and perhaps make some class-teacher at College wonder why this boy or girl, though not very studious and full of all sorts of interests outside the curriculum, never had the least difficulty in grasping the idea of the differential calculus. As for the implied suggestion that there can be no other alternative except either conscious understanding or else dishonest 'show-off,' let us notice this: If the child had grown some cress in his garden, no one would have asked whether he really understood the laws of evolution, or whether he was only 'showing off'; every one would know that he neither made the cress, nor thought he made it, nor pretended to make it; by sowing seeds as directed and watering them at due times he summoned to his aid forces of growth which he could not understand, and they responded to his call and they made the cress grow. Why had he not as good a right to summon to his aid the forces which make a curve? The cress grew even while he slept; and the curve grew while his conscious brain slept. And if the one thing is not as simple, as restful, and as unpretentious as the other, it must be because some one is making a needless muddle about what might be a perfectly normal element of child life.