Is science formed by pure reason? No. No one can say what pure reason is, for the exercise of our thought is connected indissolubly with experience. But, without pausing at this consideration, let us ask what pure reason can do, if deprived of all objects of experience? One thing only, namely, take cognizance of itself. Now the reason, in taking cognizance of itself, only creates logic, that is to say, the theory of the laws of knowledge. Some philosophers, to be sure, have undertaken to prove that reason, by dint of self-contemplation, might arrive at the knowledge of all things. They have maintained that all the secrets of the universe are contained in our thought, and that by just reasoning one may form the science of astronomy without looking at the stars, and write the history of the human race without taking the trouble to search laboriously into the annals of the past. But these attempts to construct facts, instead of observing them, have succeeded too ill to merit very serious attention.
Science does not proceed therefore either from pure experience or from pure reason; whence does it really come? From the encounter of experience and of reason. Man observes, and he ascertains that facts are governed according to intelligent design. He creates mathematics, and discovers that the phenomena of the heavens and the earth are ruled according to the laws of the calculus. His thought meets in the facts with traces of a thought similar to his own. If any one of you doubts this, I once more appeal to the almanac. Science, then, has birth only from a meeting of experience with reason; how is this meeting effected? The whole question of the origin of science is here. This encounter is not necessary; it does not result simply from perseverance in observation. The encounter of mind and of facts constitutes a discovery. The thought which has governed nature may remain long veiled from our mind. All at once perhaps the veil is lifted, and the thought of man meets and recognizes itself in the phenomena which it is contemplating. We encounter in this case the exercise of a special faculty, which is neither the faculty of observing nor the faculty of reasoning, but the faculty of discovering. When a man possesses it to a certain degree, we call him a man of genius. Genius, or the faculty of discovering, is the generating principle of science. Still, strange to say, this principle is scarcely pointed out by a great number of logicians. They develop at length the rules of observation and the rules of reasoning; and it seems that, in their idea, the conjunction of reason and experience is effected all alone and of necessity. I taught logic myself in this way for twenty years, until one day, thinking better upon the subject, I was obliged to say to myself (forgive me this rather trivial quotation):
Tu n'avais oublié qu'un point:
C'était d'éclairer ta lanterne.[163]
The meeting together of the understanding and of facts is a discovery; and discovery depends upon a faculty sung by poets, admired by mankind, and too little noticed by logicians—genius. Genius has for its characteristic a sudden illumination of the mind, a gratuitous gift and one which cannot be purchased. But let us hasten to supply a necessary explanation. Genius is a primitive fact, a gift; but the work of genius has conditions, or rather a condition—labor. Labor does not replace genius, but genius does not dispense with labor; nature only delivers up her secrets to those who observe her with long patience. Newton was asked one day how he had found out the system of the universe. He replied with a sublime naïveté: "By thinking continually about it." He so pointed out the condition of every great discovery; but he forgot the cause—the peculiar nature of his own intellect. It was necessary to be always pondering the motions of the stars; but it was necessary moreover to be Isaac Newton. So many had thought on the subject, as long perhaps as he, and had not made the discovery.
Labor, the condition of discoveries, should have as its effect to recognize the methods really appropriate to the nature of the inquiries, and to keep the mind well informed in existing science. In fact, every scientific discovery supposes a series of previous discoveries which have brought the mind to the point at which it is possible to see something new. For this reason it is that a discovery often presents itself to two or three minds at once, when there are found, at the same epoch, two or three minds endowed with the same power. They see all together because the onward progress of science has brought them to the same summit: this is the condition; and because they have the same power of vision: this is the cause. There is therefore a method for putting ourselves on the road to discovery, but no method for making the discovery itself. The man of genius sees where others do not see; and when he has seen, everybody sees after him. If, furnished with Gyges' ring, you could gain access to the studies of savants at the moment when a great discovery has just been made, you would see more than one of them striking his forehead and exclaiming: "Fool that I was! how could I help seeing it? it was so simple." Truth appears simple when it has been discovered.
Discovery therefore, which has labor for its condition, is the principle of the progress of science. Under what form does a discovery present itself to the mind of its author? As a supposition, or, which is the same thing, as an hypothesis. Hypothesis is the sole process by which progress in science is effected. If we supposed nothing, we should know nothing. In vain should we look at the sky and the earth to all eternity, our eye would never read the laws of astronomy in the stars of heaven, nor the laws of life upon the bark of trees or in the entrails of animals. This is true even of mathematics. The contemplation, prolonged indefinitely, of the series of numbers, or of the forms of space, would produce neither arithmetic nor geometry, if the human mind did not suppose relations between the numbers and the lines, which it can only demonstrate after it has supposed them. The conditions are very clearly seen which have prepared and made possible a fruitful supposition, but the hypothesis does not itself follow of any necessity. It appears like a flash of light passing suddenly through the mind.
The carpenter's saw opens a plank from end to end on the sole conditions of labor and time; but the discovery of truth preserves always a sudden and unforeseen character. Archimedes leaps from a bath and rushes through the streets of Syracuse, crying out, "I have found it!" Why? The flash of genius has visited him unexpectedly. Pythagoras discovers a geometrical theorem; and he offers, it is said, a sacrifice to the gods, in testimony of his gratitude. He thought therefore, according to the fine remark of Malebranche, that labor and attention are a silent prayer which we address to the Master of truth: the labor is a prayer, and the discovery is an answer granted to it.
When this wholly spontaneous character of discovery is not recognized, and when it is thought that the observation of facts naturally produces their explanation, it must needs be granted that a discovery is confirmed by the very fact that it is made. But this is by no means the case. Hypothesis does not carry on its brow, at the moment of its birth, the certain sign of its truth. A flash of light crosses the mind of the savant; but he must enter on a course, often a long course, of study, in order to know whether it is a true light, or a momentary glare. Every supposition suggested by observation must be confirmed by its agreement with the data of experience. Let us listen to a great discoverer—Kepler. He is giving an account of the discovery of one of the laws which have immortalized his name.
"After I had found the real dimensions of the orbits, thanks to the observations of Brahe and the sustained effort of a long course of labor, I at length discovered the proportion of the periodic times to the extent of these orbits. And if you would like to know the precise date of the discovery,—it was on the eighth day of March in this year 1618 that,—first of all conceived in my mind, then awkwardly essayed by calculations, rejected in consequence as false, then reproduced on the fifteenth of May with fresh energy,—it rose at last above the darkness of my understanding, so fully confirmed by my labor of seventeen years upon Brahe's observations, and by my own meditations perfectly agreeing with them, that I thought at first I was dreaming, and making some petitio principii; but there is no more doubt about it: it is a very certain and very exact proposition."[164]