Thirdly, we stir the surface of the water, and see the stick bend itself into several curves, move in a zig-zag direction, and follow the undulations of the water. Has the motion we gave the water been enough thus to break, to soften, and to melt the stick?
Fourth, we draw off the water and see the stick straighten itself as fast as the water is lowered. Is not this more than enough to illustrate the fact and to find out the refraction? It is not then true that the eye deceives us, since by its aid alone we can correct the mistakes we ascribe to it.
Suppose the child so dull as not to understand the result of these experiments. Then we must call touch to the aid of sight. Instead of taking the stick out of the water, leave it there, and let him pass his hand from one end of it to the other. He will feel no angle; the stick, therefore, is not broken.
You will tell me that these are not only judgments but formal reasonings. True; but do you not see that, as soon as the mind has attained to ideas, all judgment is reasoning? The consciousness of any sensation is a proposition, a judgment. As soon, therefore, as we compare one sensation with another, we reason. The art of judging and the art of reasoning are precisely the same.
If, from the lesson of this stick, Émile does not understand the idea of refraction, he will never understand it at all. He shall never dissect insects, or count the spots on the sun; he shall not even know what a microscope or a telescope is.
Your learned pupils will laugh at his ignorance, and will not be very far wrong. For before he uses these instruments, I intend he shall invent them; and you may well suppose that this will not be soon done.
This shall be the spirit of all my methods of teaching during this period. If the child rolls a bullet between two crossed fingers, I will not let him look at it till he is otherwise convinced that there is only one bullet there.
Result. The Pupil at the Age of Fifteen.
I think these explanations will suffice to mark distinctly the advance my pupil's mind has hitherto made, and the route by which he has advanced. You are probably alarmed at the number of subjects I have brought to his notice. You are afraid I will overwhelm his mind with all this knowledge. But I teach him rather not to know them than to know them. I am showing him a path to knowledge not indeed difficult, but without limit, slowly measured, long, or rather endless, and tedious to follow. I am showing him how to take the first steps, so that he may know its beginning, but allow him to go no farther.
Obliged to learn by his own effort, he employs his own reason, not that of another. Most of our mistakes arise less within ourselves than from others; so that if he is not to be ruled by opinion, he must receive nothing upon authority. Such continual exercise must invigorate the mind as labor and fatigue strengthen the body.