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Blaise Pascal, 1623-1662

pascal.gif (11207 bytes)We run carelessly to the precipice, after we have put some thing before us to prevent us seeing it.

The French mathematician, theologian, physicist and man-of-letters, Blaise Pascal, was born June 19 at Clermont-Ferrand, the son of the local president of the court of exchequer. Pascal's mother died in 1630 and the family moved to Paris, where his father, a prominent mathematician, personally undertook his children's education. Unlike the famous education of John Stuart Mill, the young Pascal was not allowed to begin a subject until his father thought he could easily master it. Consequently it was discovered that the eleven year old boy had worked out for himself in secret the first twenty-three propositions of Euclid, calling straight lines "bars" and circles "rounds."

At sixteen he published a paper on solid geometry which Descartes refused refused to believe was the handiwork of a youth. Father an son collaborated in experiments to confirm Torricelli's theory, unpalatable the the Schoolmen, that nature does, after all, not abhor a vacuum. These experiments, carried out by Pascal's brother-in-law, Florin P�rier, consisted in carrying up the Puy de D�me two glass tubes containing mercury, inverted in a bath of mercury and noting the fall of the mercury columns with increased altitude. Again, Descartes disbelieved the principle, which Pascal fully described in three papers on the void published in 1647, when he also patented a calculating machine, later simplified by Leibniz, which he had built to assist his father in his accounts. Pascal was also led to invent the barometer, the hydraulic press and the syringe.

In 1648 Richelieu appointed Pascal senior to a post at Rouen, but the latter died died in 1651. Pascal's sister, Jacqueline, entered the Jansenist convent at Port-Royal, but Pascal divided his time between mathematics and the social round in Paris until November 23, 1654, near midnight, when he had the first of two revelations, according to a note found sewn into his clothes, and he came to see that his religious attitude had been too intellectual and remote. He joined his sister at her retreat at Port-Royal, gave up mathematics and social life almost completely and joined the battle of the Jansenists against the Jesuits of the Sorbonne who had publicly denounced Arnauld, the Jansenist mathematician, as a heretic. In eighteen brilliant pamphlets, the Provincial Letters (1656-57), Pascal attacked in superb prose, the Jesuits' meaningless jargon, casuistry and moral laxity. This early prose masterpiece in the French language, the model for Voltaire, failed to save Arnauld, but undermined for ever Jesuit authority and prestige.

Pascal's papers on the area of the cycloid (1661) heralded the invention of the differential calculus. Fragments jotted down for a case book of Christian truths were discovered after his death, August 19, 1662, and published as the Pens�es in 1669 in order of completeness. The groundwork for Pascal's intended Christian apology, they contain the most profound insight into religious truths coupled, however, with skepticism of rational thought and theology. For more biographical details, please see the entry for Blaise Pascal from A Short Account of the History of Mathematics, (4th ed., 1908) by W. W. Rouse Ball. See also entries at the Catholic Encyclopedia, and the MacTutor. Pascal's minor works and selected letters, all from Volume 14 of the Harvard Classics (1909), are available as well.

Excerpts from Pascal's Pens�es


When we do not know the truth of a thing, it is of advantage that there should exist a common error which determines the mind of man, as, for example, the moon, to which is attributed the change of seasons, the progress of diseases, etc., For the chief malady of man is restless curiosity about things which he cannot understand; and it is not so bad for him to be in error as to be curious to no purpose.


Do you wish people to believe good of you? Don't speak.


Man's Disproportion -- Behold! This is where natural reason brings us. If it is not true, there is no truth in man; if it is true, he finds in it a great cause of humiliation; either way, he is forced to abase himself.

And, since he cannot go on without this knowledge, I wish, before entering into larger studies of nature, that he consider nature for a serious and leisurely moment, as well as look on himself, and get to know the proportions between nature and man.

Let man contemplate Nature in its entirety, high and majestic; let him expand his gaze from the lowly objects which surround him. Let him look on this blazing light, placed like an eternal lamp in order to light up the universe; let him see that this earth is but a point compared to the vast circle which this star describes and let him marvel at the fact that this vast orbit itself is merely a tiny point compared to the stars which roll through the firmament.

But if our gaze stops there, let the imagination pass beyond this point; it will grow tired of conceiving of things before nature tires of producing them. The entire visible world is only an imperceptible speck in the ample bosom of nature. No idea can come close to imagining it. We might inflate our concepts to the most unimaginable expanses: we only produce atoms in relation to the reality of things. Nature is an infinite sphere in which the center is everywhere, the circumference is nowhere. Finally, it is the greatest sensible mark of God's omnipotence, that our imagination loses itself in that thought.

Let man, having returned to himself, consider what he is in comparison with all that is; let him see himself as if thrown out of the district of Nature; and, from this little prison cell in which he finds his lodging, I mean the universe, let him learn to judge the earth, its kingdoms, its villages, and himself with a proper estimation. What is man in the infinite?

But to offer him another astonishing prodigy, let him behold the tiniest things he knows of. Let a mite show him in the smallness of its body parts incomparably smaller, legs with joints, veins in the legs, blood in the veins, humours in the blood, drops in the humours, vapors in the drops, which, dividing to the smallest things, he wears out his imaginative power, and let the last object which he arrives at become now the subject of our discourse; he might think that this perhaps is the smallest thing in the universe. I wish now to make him see therein a new abyss. I want to paint for him not only the visible universe, but all the imaginable immensity of nature within the confines of an atom. Let him see an infinity of universes, in which each has its own firmament, planets, earth, in the same proportion as the visible world; within this earth, there are animals and finally, mites, in which he'll find again the same things as he found in the mite he started with; and finding again the same things without end, let him lose himself in these wonders, as shocking in their smallness as others are in their immensity; for who will not admire our body, which before was imperceptible within the universe, imperceptible itself within the bosom of nature, and which is now a colossus, a world, or rather a whole, in comparison to the nothing, the smallness, we can't arrive at?

Anyone who considers himself in this way will be seized with terror and, discovering that the mass nature has given him supports itself between two abysses of infinity and nothingness, he will tremble in the face of these marvels; and I believe that as his curiosity changes to admiration, he will be more disposed to contemplate them in silence then search them out with presumption.

For, finally, what is man in nature? He is nothing in comparison with the infinite, and everything in comparison with nothingness, a middle term between all and nothing. He is infinitely severed from comprehending the extremes; the end of things and their principle are for him invincibly hidden in an impenetrable secret; he is equally incapable of seeing the nothingness from which he arises and the infinity into which he is engulfed.

What else may he do except to perceive some appearance of the middle of things, eternally despairing to know their principles or ends? All things arise from nothingness and are carried to infinity. Who can follow these astonishing processes? The author of these marvels can comprehend them. All others cannot.

Failing to contemplate these infinities, men have recklessly taken it on themselves to study nature, as if it had the same proportions as they did. It is a mighty strange thing that they wished to comprehend the principles of things, and to arrive from there at a knowledge of everything, with a presumption as infinite as their object. For doubtless no-one could devise such a plan without a presumption or capacity as infinite as nature's. . . .

We naturally believe that we are more capable of arriving at the center of things rather than embracing their circumference. The visible extent of the world surpasses us visibly; but, since we surpass small things, we believe ourselves capable of possessing them, and yet it requires no less capacity to reach nothingness as it takes to reach everything; the one is just as infinite as the other; and it appears to me that anyone who comprehended one of these extreme principles of things would have also arrived at the knowledge of the other infinite. The one depends on the other, and the one leads to the other. These extremities touch each other and reunite by going in opposite directions and find themselves again in God, and in God alone.

Let us then know our limits; we are something, and we are not everything; such existence we have takes from us the knowledge of first principles, which arise from nothingness; and the smallness of our existence hides infinity from our view. . . .

Behold: this is our true state. It is this which renders us incapable of knowing anything for certain or from being absolutely ignorant. We wander in a vast medium, always uncertain and drifting, pushed by one wind and then another. Whenever we find a fixed point to attach and fix ourselves to, it shifts and leaves us and, if we follow it, it slips away from us and flees from us eternally. Nothing stops for us. This is our natural state, but the one most contrary to our inclination; we burn with desire to find a firm seat, and a final, constant base on which to build a tower which will lift us to the infinite; but all our foundations crack, and the earth opens up into an abyss.

Let us not then seek assurance or finality. Our reason is always deceived by the inconstancy of appearances; nothing can fix the finite which lies between the two infinities which enclose and flee from it. . . .


Weariness -- Nothing is so insufferable to man as to be completely at rest, without passions, without business, without diversion, without study. He then feels his nothingness, his forlornness, his insufficiency, his dependence, his weakness, his emptiness. There will immediately arise from the depth of his heart weariness, gloom, sadness, fretfulness, vexation, despair.


Man is obviously made to think. It is is his whole dignity an his whole merit; and his whole duty is to think as he ought. Now, the order of thought is to begin with self, and with its Author and its end.

Now, of what does the world think? Never of this, but of dancing, playing the lute, singing, making verses, running at the ring, etc., fighting, making oneself king, without thinking what it is to be a king and what to be a man.


We are so presumptuous that we would wish to be known by all the world, even by people who shall come after, when we shall be no more; and we are so vain that the esteem of five or six neighbors delights and contents us.


Man is but a reed, the most feeble thing in nature; but he is a thinking reed. The entire universe need not arm itself to crush him. A vapor, a drop of water suffices to kill him. But, if the universe were to crush him, man would still be more noble than that which killed him, because he knows that he dies and the advantage which the universe has over him; the universe knows nothing of this.

All our dignity consists, then, in thought. By it we must elevate ourselves, and not by space and time which we cannot fill. Let us endeavor, then, to think well; this is the principle of morality.

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