Emile. Жан-Жак Руссо
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the parts when he could not compare the whole; he must substitute his estimated aliquot parts for exact aliquot parts, and instead of always applying the measure by hand he must get used to applying it by eye alone. I would, however, have his first estimates tested by measurement, so that he may correct his errors, and if there is a false impression left upon the senses he may correct it by a better judgment. The same natural standards of measurement are in use almost everywhere, the man's foot, the extent of his outstretched arms, his height. When the child wants to measure the height of a room, his tutor may serve as a measuring rod; if he is estimating the height of a steeple let him measure it by the house; if he wants to know how many leagues of road there are, let him count the hours spent in walking along it. Above all, do not do this for him; let him do it himself.
One cannot learn to estimate the extent and size of bodies without at the same time learning to know and even to copy their shape; for at bottom this copying depends entirely on the laws of perspective, and one cannot estimate distance without some feeling for these laws. All children in the course of their endless imitation try to draw; and I would have Emile cultivate this art; not so much for art's sake, as to give him exactness of eye and flexibility of hand. Generally speaking, it matters little whether he is acquainted with this or that occupation, provided he gains clearness of sense—perception and the good bodily habits which belong to the exercise in question. So I shall take good care not to provide him with a drawing master, who would only set him to copy copies and draw from drawings. Nature should be his only teacher, and things his only models. He should have the real thing before his eyes, not its copy on paper. Let him draw a house from a house, a tree from a tree, a man from a man; so that he may train himself to observe objects and their appearance accurately and not to take false and conventional copies for truth. I would even train him to draw only from objects actually before him and not from memory, so that, by repeated observation, their exact form may be impressed on his imagination, for fear lest he should substitute absurd and fantastic forms for the real truth of things, and lose his sense of proportion and his taste for the beauties of nature.
Of course I know that in this way he will make any number of daubs before he produces anything recognisable, that it will be long before he attains to the graceful outline and light touch of the draughtsman; perhaps he will never have an eye for picturesque effect or a good taste in drawing. On the other hand, he will certainly get a truer eye, a surer hand, a knowledge of the real relations of form and size between animals, plants, and natural objects, together with a quicker sense of the effects of perspective. That is just what I wanted, and my purpose is rather that he should know things than copy them. I would rather he showed me a plant of acanthus even if he drew a capital with less accuracy.
Moreover, in this occupation as in others, I do not intend my pupil to play by himself; I mean to make it pleasanter for him by always sharing it with him. He shall have no other rival; but mine will be a continual rivalry, and there will be no risk attaching to it; it will give interest to his pursuits without awaking jealousy between us. I shall follow his example and take up a pencil; at first I shall use it as unskilfully as he. I should be an Apelles if I did not set myself daubing. To begin with, I shall draw a man such as lads draw on walls, a line for each arm, another for each leg, with the fingers longer than the arm. Long after, one or other of us will notice this lack of proportion; we shall observe that the leg is thick, that this thickness varies, that the length of the arm is proportionate to the body. In this improvement I shall either go side by side with my pupil, or so little in advance that he will always overtake me easily and sometimes get ahead of me. We shall get brushes and paints, we shall try to copy the colours of things and their whole appearance, not merely their shape. We shall colour prints, we shall paint, we shall daub; but in all our daubing we shall be searching out the secrets of nature, and whatever we do shall be done under the eye of that master.
We badly needed ornaments for our room, and now we have them ready to our hand. I will have our drawings framed and covered with good glass, so that no one will touch them, and thus seeing them where we put them, each of us has a motive for taking care of his own. I arrange them in order round the room, each drawing repeated some twenty or thirty times, thus showing the author's progress in each specimen, from the time when the house is merely a rude square, till its front view, its side view, its proportions, its light and shade are all exactly portrayed. These graduations will certainly furnish us with pictures, a source of interest to ourselves and of curiosity to others, which will spur us on to further emulation. The first and roughest drawings I put in very smart gilt frames to show them off; but as the copy becomes more accurate and the drawing really good, I only give it a very plain dark frame; it needs no other ornament than itself, and it would be a pity if the frame distracted the attention which the picture itself deserves. Thus we each aspire to a plain frame, and when we desire to pour scorn on each other's drawings, we condemn them to a gilded frame. Some day perhaps "the gilt frame" will become a proverb among us, and we shall be surprised to find how many people show what they are really made of by demanding a gilt frame.
I have said already that geometry is beyond the child's reach; but that is our own fault. We fail to perceive that their method is not ours, that what is for us the art of reasoning, should be for them the art of seeing. Instead of teaching them our way, we should do better to adopt theirs, for our way of learning geometry is quite as much a matter of imagination as of reasoning. When a proposition is enunciated you must imagine the proof; that is, you must discover on what proposition already learnt it depends, and of all the possible deductions from that proposition you must choose just the one required.
In this way the closest reasoner, if he is not inventive, may find himself at a loss. What is the result? Instead of making us discover proofs, they are dictated to us; instead of teaching us to reason, our memory only is employed.
Draw accurate figures, combine them together, put them one upon another, examine their relations, and you will discover the whole of elementary geometry in passing from one observation to another, without a word of definitions, problems, or any other form of demonstration but super-position. I do not profess to teach Emile geometry; he will teach me; I shall seek for relations, he will find them, for I shall seek in such a fashion as to make him find. For instance, instead of using a pair of compasses to draw a circle, I shall draw it with a pencil at the end of bit of string attached to a pivot. After that, when I want to compare the radii one with another, Emile will laugh at me and show me that the same thread at full stretch cannot have given distances of unequal length. If I wish to measure an angle of 60 degrees I describe from the apex of the angle, not an arc, but a complete circle, for with children nothing must be taken for granted. I find that the part of the circle contained between the two lines of the angle is the sixth part of a circle. Then I describe another and larger circle from the same centre, and I find the second arc is again the sixth part of its circle. I describe a third concentric circle with a similar result, and I continue with more and more circles till Emile, shocked at my stupidity, shows me that every arc, large or small, contained by the same angle will always be the sixth part of its circle. Now we are ready to use the protractor.
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