Physics and Metaphysics

Descartes was even less satisfied with the Physics and Metaphysics taught him the following year than he had been with Logic and Morality.

He was far from blaming his Masters—he who boasted of being at that time in one of the most celebrated schools of Europe, where learned men were bound to be found, if anywhere on earth; and where the Jesuits had probably assembled the best of their Company, to establish the new College in the reputation it afterwards attained. Nor could he lay the fault upon himself, since he lacked nothing for this study—whether in diligence, openness of mind, or inclination. For he loved Philosophy with even more passion than he had loved the Humanities, and esteemed all the exercises carried out both in private and in public within the College, though he already found himself beset by doubts and errors, instead of that clear and assured knowledge of everything useful to life, which he had been made to hope for from his studies.

The further he advanced, the more he discovered his own ignorance. By reading his books and attending his Masters’ lessons, he saw that Philosophy had always been cultivated by the most excellent minds that had ever appeared in the world, and yet that in it there was nothing which was not disputed, and which consequently was not doubtful. The esteem he had for his Masters did not make him presumptuous enough to hope that he could succeed better than others. Considering the diversity of opinions upheld by learned persons upon the same matter—when, after all, there could never be more than one true opinion—he already accustomed himself to regard as almost false whatever was only plausible.

Had he had but one Master, or had he not been aware of these different opinions among Philosophers, he declares that it would never have occurred to him to withdraw from the number of those who must be content to follow the opinions of others rather than to seek out better ones themselves. He would have been more docile, placing himself among those who, through reason or modesty, judge themselves less capable of discerning truth from falsehood than their Masters or other persons from whom they may learn. But having learned already at College (these are his own words) that nothing so strange and so little believable could be imagined, but that some philosopher had already advanced it, he could not choose any Guide whose opinions seemed preferable to those of others. This is what obliged him, in later times, to clear for himself a new path and to undertake to guide himself.

Despite the obstacles which hindered his mind during the whole course of his Philosophy, he was obliged to finish this career at the same time as the rest of his companions, who had found neither doubts to form, nor difficulties to resolve, in their Master’s notebooks. He was then made to pass on to the study of Mathematics, to which he devoted the last year of his stay at La Flèche. And it seems that this study was to be for him the reward of those he had pursued until then. The pleasure he found in it repaid him abundantly for the pains scholastic Philosophy had caused him; and the progress he made was so extraordinary that the College of La Flèche acquired, through him, the glory of having produced the greatest Mathematician that God had yet brought forth.

What particularly charmed him in Mathematics, above all in Arithmetic and Geometry, was the certainty and evidence of their reasoning. Yet he did not yet understand their true use; and thinking they served only for the mechanical arts, he was astonished that, their foundations being so firm and solid, nothing higher had been built upon them. Among the parts of Mathematics, he chose the Analysis of the Geometers and Algebra to make them the subject of his special application; and the dispensation he had obtained from the Principal Father of the College, freeing him from all the practices of scholastic discipline, provided him the means to plunge into this study as deeply as he wished.

Father Charlet, Rector of the House and his perpetual Director, had procured him, among other privileges, that of remaining long in bed in the mornings—both on account of his frail health, and because he observed in him a mind naturally inclined to meditation. Descartes, who upon awakening found all the powers of his mind gathered and all his senses refreshed by the rest of the night, profited by these favorable moments for meditation. This practice became so habitual that it made for him a manner of studying for the whole of his life; and one may say that it is to these mornings in bed that we owe what his mind has produced of greatest importance in Philosophy and in Mathematics.

Already in College he applied himself to purify and perfect the Analysis of the Ancients and the Algebra of the Moderns. Until then, these two sciences had extended only to extremely abstract matters, which seemed of no use. The first had always been so bound to the consideration of figures that it could not exercise the understanding without greatly fatiguing the imagination. The second had been so tied down to certain rules and symbols, that it had been made into a confused and obscure art, capable only of embarrassing the mind instead of cultivating it. He began then to discover wherein these two sciences were useful, and wherein they were defective. His design was not to learn all the particular sciences which bear the common name of Mathematics, but to examine in general the various relations or proportions that are found in their objects, supposing them only in such subjects as might render their knowledge easier to him.

He remarked that to know them, he would sometimes need to consider them each separately, and sometimes only to retain or comprehend several together. To consider them more distinctly one by one, he thought he should suppose them in lines, because he found nothing more simple, nor more proper to be distinctly represented to his imagination and senses: this was all the use he intended to make of Geometrical Analysis. To retain them, or to comprehend several together, he judged he must express them by the shortest and clearest symbols possible: this was the help he expected from Algebra. By this means, he promised himself to take all that was best in Analysis and Algebra, and to correct all the defects of the one by the other. His work succeeded so happily that later he found a way of employing Analysis continually, not only in Geometry, but in even the most common subjects, where one perceives everywhere this way of reasoning with the justness of mind which this method had acquired for him; and he knew how to make Algebra the key to his Geometry, which he did not wish to leave within the reach of vulgar minds.

It seems this is what may have led some persons to believe that the Geometry employed by Mr. Descartes, to solve an infinity of questions, was nothing else than the Analysis of the Ancients. But those very persons, acknowledging that no trace of this Analysis remained in the world since the Ancients, appear to grant Mr. Descartes the glory of invention in this branch of science, for having unearthed a method that had remained buried and almost unknown to Geometers for so long a time. At least it was not the use he made of Algebra that ought to make him lose the merit of novelty: otherwise, the newest and most unheard-of inventions will no longer have anything new or unheard-of, as soon as one makes use of the letters of the alphabet to express them and make them intelligible to others.

Those who make Mr. Descartes the author of this sort of Algebra, which they call the key of all the liberal arts and all the sciences, and which they esteem the best method that has ever appeared for discerning truth from falsehood, attribute the invention to him from his time at College, when his Master was explaining in class the vulgar Analysis, which in all likelihood was nothing but Algebra. The Sieur Lipstorp affirms that he left all his companions far behind him in this kind of study, and that he went infinitely beyond what his Master could have expected. But he adds an anecdote whose truth seems to rest upon a circumstance that is absolutely false. He says that his Master, unable any longer to propose questions to him to which he did not immediately give solutions, and himself embarrassed in resolving those which he allowed his pupil to pose to him, openly confessed that he was thenceforth of no use to him, and that he could teach him nothing more in Algebra that was unknown to him.

One day, having proposed to him the most difficult question he could find, he appeared so astonished at the novelty and subtlety with which Descartes had solved it by means of his new method, that he could not recover from his amazement except by saying that he believed Viète had written something on the subject. Descartes, delighted to learn that he had been anticipated in this invention, begged his Master earnestly to procure him a Viète.

Lipstorp adds that Descartes, finding something abstruse and difficult to decipher in that author, respectfully pressed his Master to help him; but the Master excused himself on the ground of the difficulty of the passage, saying he knew only one man capable of understanding Viète’s Analysis; but that, after all possible searches, this much-desired man was not to be found. This, he says, led Descartes to rest content with what he had himself invented in Analysis, independently of Viète’s invention, and to rely upon his own genius in whatever he might invent or discover thereafter.

But this might have been Lipstorp’s imagination.

Descartes wrote in a letter written from Holland to Father Mersenne in 1639 that he did not even remember ever having seen so much as the cover of Viète while he was in France.

He said this to convict of falsehood a Geometer he did not know, but who boasted of having studied Viète with him in Paris.

He was still less likely to have seen Viète himself than his writings, since that great mathematician, a native of Fontenay-le-Comte in Poitou, who held an office of maître des requêtes in Paris, had died as early as 1603.