It has never yet been supposed, that all the facts of nature, and all the means of acquiring precision in the computation and analysis of those facts, and all the connections of objects with each other, and all the possible combinations of ideas, can be exhausted by the human mind. The mere relations of magnitude, the combinations, quantity and extent of this idea alone, form already a system too immense for the mind of man ever to grasp the whole of it; a portion, more vast than that which he may have penetrated, will always remain unknown to him. It has, however, been imagined, that, as man can know a part only of the objects which the nature of his intelligence permits him to investigate, he must at length reach the point at which, the number and complication of those he already knows having absorbed all his powers, farther progress will become absolutely impossible.
But, in proportion as facts are multiplied, man learns to class them, and reduce them to more general facts, at the same time that the instruments and methods for observing them, and registering them with exactness, acquire a new precision: in proportion as relations more multifarious between a greater number of objects are discovered, man continues to reduce them to relations of a wider denomination, to express them with greater simplicity, and to present them in a way which may enable a given strength of mind, with a given quantity of attention, to take in a greater number than before: in proportion as the understanding embraces more complicated combinations, a simple mode of announcing these combinations renders them more easy to be treated. Hence it follows that truths, the discovery of which was accompanied with the most laborious efforts, and which at first could not be comprehended but by men of the severest attention, will after a time be unfolded and proved in methods that are not above the efforts of an ordinary capacity. And thus should the methods that led to new combinations be exhausted, should their applications to questions, still unresolved, demand exertions greater than the time or the powers of the learned can bestow, more general methods, means more simple would soon come to their aid, and open a farther career to genius. The energy, the real extent of the human intellect may remain the same; but the instruments which it can employ will be multiplied and improved; but the language which fixes and determines the ideas will acquire more precision and compass; and it will not be here, as in the science of mechanics, where, to increase the force, we must diminish the velocity; on the contrary, the methods by which genius will arrive at the discovery of new truths, augment at once both the force and the rapidity of its operations.
In a word, these changes being themselves the necessary consequences of additional progress in the knowledge of truths of detail, and the cause which produces a demand for new resources, producing at the same time the means of supplying them, it follows that the actual mass of truths appertaining to the sciences of observation, calculation and experiment, may be perpetually augmented, and that without supposing the faculties of man to possess a force and activity, and a scope of action greater than before.
By applying these general reflections to the different sciences, we might exhibit, respecting each, examples of this progressive improvement, which would remove all possibility of doubt as to the certainty of the further improvement that may be expected. We might indicate particularly in those which prejudice considers as nearest to being exhausted, the marks of an almost certain and early advance. We might illustrate the extent, the precision, the unity which must be added to the system comprehending all human knowledge, by a more general and philosophical application of the science of calculation to the individual branches of which that system is composed. We might shew how favourable to our hopes a more universal instruction would prove, by which a greater number of individuals would acquire the elementary knowledge that might inspire them with a taste for a particular kind of study; and how much these hopes would be further heightened if this application to study were to be rendered still more extensive by a more general ease of circumstances. At present, in the most enlightened countries, scarcely do one in fifty of those whom nature has blessed with talents receive the necessary instruction for the developement of them: how different would be the proportion in the case we are supposing? and of consequence how different the number of men destined to extend the horizon of the sciences?
We might shew how much this equality of instruction, joined to the national equality we have supposed to take place, would accelerate those sciences, the advancement of which depends upon observations repeated in a greater number of instances, and extending over a larger portion of territory; how much benefit would be derived therefrom to mineralogy, botany, zoology, and the doctrine of meteors; in short, how infinite the difference between the feeble means hitherto enjoyed by these sciences, and which yet have led to useful and important truths, and the magnitude of those which man would then have it in his power to employ.
Lastly, we might prove that, from the advantage of being cultivated by a greater number of persons, even the progress of those sciences, in which discoveries are the fruit of individual meditation, would, also, be considerably advanced by means of minuter improvements, not requiring the strength of intellect, necessary for inventions, but that present themselves to the reflection of the least profound understandings.
The physicist is like someone who's watching people playing chess and, after watching a few games, he may have worked out what the moves in the game are. But understanding the rules is just a trivial preliminary on the long route from being a novice to being a grand master. So even if we understand all the laws of physics, then exploring their consequences in the everyday world where complex structures can exist is a far more daunting task, and that's an inexhaustible one I'm sure.
Suppose it were perfectly certain that the life and fortune of every one of us would, one day or other, depend upon his winning or losing a game of chess. Don't you think that we should all consider it to be a primary duty to learn at least the names and the moves of the pieces; to have a notion of a gambit, and a keen eye for all the means of giving and getting out of check? Do you not think that we should look with a disapprobation amounting to scorn upon the father who allowed his son, or the state which allowed its members, to grow up without knowing a pawn from a knight?
Yet, it is a very plain and elementary truth that the life, the fortune, and the happiness of every one of us, and, more or less, of those who are connected with us, do depend upon our knowing something of the rules of a game infinitely more difficult and complicated than chess. It is a game which has been played for untold ages, every man and woman of us being one of the two players in a game of his or her own. The chess-board is the world, the pieces are the phenomena of the universe, the rules of the game are what we call the laws of nature. The player on the other side is hidden from us. We know that his play is always fair, just, and patient. But also we know, to our cost, that he never overlooks a mistake, or makes the smallest allowance for ignorance. To the man who plays well the highest stakes are paid with that sort of overflowing generosity with which the strong shows delight in strength. And one who plays ill is checkmated—without haste, but without remorse.
People who are unused to learning, learn little, and that slowly, while those more accustomed do much more and do it more easily. The same thing also happens in connection with research. Those who are altogether unfamiliar with this become blinded and bewildered as soon as their minds begin to work: they readily withdraw from the inquiry, in a state of mental fatigue and exhaustion, much like people who attempt to race without having been trained. He, on the other hand, who is accustomed to research, seeks and penetrates everywhere mentally, passing constantly from one topic to another; nor does he ever give up his investigation; he pursues it not merely for a matter of days, but throughout his whole life. Also by transferring his mind to other ideas which are yet not foreign to the questions at issue, he persists till he reaches the solution.
Equations seem like treasures, spotted in the rough by some discerning individual, plucked and examined, placed in the grand storehouse of knowledge, passed on from generation to generation. This is so convenient a way to present scientific discovery, and so useful for textbooks, that it can be called the treasure-hunt picture of knowledge.
It is almost as difficult to make a man unlearn his errors, as his knowledge. Mal-information is more hopeless than non-information: for error is always more busy than ignorance. Ignorance is a blank sheet on which we may write; but error is a scribbled one on which we first erase. Ignorance is contented to stand still with her back to the truth; but error is more presumptuous, and proceeds, in the same direction. Ignorance has no light, but error follows a false one. The consequence is, that error, when she retraces her footsteps, has farther to go, before we can arrive at the truth, than ignorance.