Drawing.
All children, being natural imitators, try to draw. I would have my pupil cultivate this art, not exactly for the sake of the art itself, but to render the eye true and the hand flexible. In general, it matters little whether he understands this or that exercise, provided he acquires the mental insight, and the manual skill furnished by the exercise. I should take care, therefore, not to give him a drawing-master, who would give him only copies to imitate, and would make him draw from drawings only. He shall have no teacher but nature, no models but real things. He shall have before his eyes the originals, and not the paper which represents them. He shall draw a house from a real house, a tree from a tree, a human figure from the man himself. In this way he will accustom himself to observe bodies and their appearances, and not mistake for accurate mutations those that are false and conventional. I should even object to his drawing anything from memory, until by frequent observations the exact forms of the objects had clearly imprinted themselves on his imagination, lest, substituting odd and fantastic shapes for the real things, he might lose the knowledge of proportion and a taste for the beauties of nature. I know very well that he will go on daubing for a long time without making anything worth noticing, and will be long in mastering elegance of outline, and in acquiring the deft stroke of a skilled draughtsman. He may never learn to discern picturesque effects, or draw with superior skill. On the other hand, he will have a more correct eye, a truer hand, a knowledge of the real relations of size and shape in animals, plants, and natural bodies, and practical experience of the illusions of perspective. This is precisely what I intend; not so much that he shall imitate objects as that he shall know them. I would rather have him show me an acanthus than a finished drawing of the foliation of a capital.
Yet I would not allow my pupil to have the enjoyment of this or any other exercise all to himself. By sharing it with him I will make him enjoy it still more. He shall have no competitor but myself; but I will be that competitor continually, and without risk of jealousy between us. It will only interest him more deeply in his studies. Like him I will take up the pencil, and at first I will be as awkward as he. If I were an Apelles, even, I will make myself a mere dauber.
I will begin by sketching a man just as a boy would sketch one on a wall, with a dash for each arm, and with fingers larger than the arms. By and by one or the other of us will discover this disproportion. We shall observe that a leg has thickness, and that this thickness is not the same everywhere; that the length of the arm is determined by its proportion to the body; and so on. As we go on I will do no more than keep even step with him, or will excel him by so little that he can always easily overtake and even surpass me. We will get colors and brushes; we will try to imitate not only the outline but the coloring and all the other details of objects. We will color; we will paint; we will daub; but in all our daubing we shall be continually peering into nature, and all we do shall be done under the eye of that great teacher.
If we had difficulty in finding decorations for our room, we have now all we could desire. I will have our drawings framed, so that we can give them no finishing touches; and this will make us both careful to do no negligent work. I will arrange them in order around our room, each drawing repeated twenty or thirty times, and each repetition showing the author's progress, from the representation of a house by an almost shapeless attempt at a square, to the accurate copy of its front elevation, profile, proportions, and shading. The drawings thus graded must be interesting to ourselves, curious to others, and likely to stimulate further effort. I will inclose the first and rudest of these in showy gilded frames, to set them off well; but as the imitation improves, and when the drawing is really good, I will add only a very simple black frame. The picture needs no ornament but itself, and it would be a pity that the bordering should receive half the attention.
Both of us will aspire to the honor of a plain frame, and if either wishes to condemn the other's drawing, he will say it ought to have a gilt frame. Perhaps some day these gilded frames will pass into a proverb with us, and we shall be interested to observe how many men do justice to themselves by framing themselves in the very same way.
Geometry.
I have said that geometry is not intelligible to children; but it is our own fault. We do not observe that their method is different from ours, and that what is to us the art of reasoning should be to them only the art of seeing. Instead of giving them our method, we should do better to take theirs. For in our way of learning geometry, imagination really does as much as reason. When a proposition is stated, we have to imagine the demonstration; that is, we have to find upon what proposition already known the new one depends, and from all the consequences of this known principle select just the one required. According to this method the most exact reasoner, if not naturally inventive, must be at fault. And the result is that the teacher, instead of making us discover demonstrations, dictates them to us; instead of teaching us to reason, he reasons for us, and exercises only our memory.
Make the diagrams accurate; combine them, place them one upon another, examine their relations, and you will discover the whole of elementary geometry by proceeding from one observation to another, without using either definitions or problems, or any form of demonstration than simple superposition. For my part, I do not even pretend to teach Émile geometry; he shall teach it to me. I will look for relations, and he shall discover them. I will look for them in a way that will lead him to discover them. In drawing a circle, for instance, I will not use a compass, but a point at the end of a cord which turns on a pivot. Afterward, when I want to compare the radii of a semi-circle, Émile will laugh at me and tell me that the same cord, held with the same tension, cannot describe unequal distances.
When I want to measure an angle of sixty degrees, I will describe from the apex of the angle not an arc only, but an entire circle; for with children nothing must be taken for granted. I find that the portion intercepted by the two sides of the angle is one-sixth of the whole circumference. Afterward, from the same centre, I describe another and a larger circle, and find that this second arc is one-sixth of the new circumference. Describing a third concentric circle, I test it in the same way, and continue the process with other concentric circles, until Émile, vexed at my stupidity, informs me that every arc, great or small, intercepted by the sides of this angle, will be one-sixth of the circumference to which it belongs. You see we are almost ready to use the instruments intelligently.