Blaise Pascal

Based on Wikipedia: Blaise Pascal

In 1654, a French mathematician sat down to solve a gambling problem. The question seemed simple enough: if two players must abandon a dice game early, how should they fairly divide the pot based on their current scores? From this modest inquiry about splitting betting stakes, Blaise Pascal and his correspondent Pierre de Fermat accidentally invented probability theory—a mathematical framework that would eventually reshape economics, insurance, medicine, and our entire understanding of uncertainty.

Pascal was thirty-one years old at the time. He had already built the world's first commercial calculator, proved that vacuums exist despite Aristotle's insistence to the contrary, and invented public transportation. Within months of solving the gambling problem, he would have a mystical religious experience that would consume the rest of his short life. He died at thirty-nine, leaving behind a scattered collection of notes that would become one of the most influential works of Christian philosophy ever written.

His life reads like several extraordinary lives compressed into one.

The Prodigy Who Taught Himself Geometry

Blaise Pascal was born in 1623 in Clermont-Ferrand, a city in south-central France nestled against the volcanic mountains of the Massif Central. His mother died when he was three. His father Étienne, a tax collector and amateur mathematician, never remarried. Instead, he devoted himself to educating his three children—Blaise and his two sisters, Gilberte and Jacqueline.

Étienne had unconventional ideas about education. He decided his son should master Latin and Greek before touching mathematics, believing the latter would prove too seductive. He was right about the seduction, but wrong about the containment.

By age twelve, Blaise had independently rediscovered the first thirty-two propositions of Euclid's Elements—the foundational theorems of geometry that had taken ancient Greeks generations to develop. He worked them out on his own, drawing figures with charcoal on the tile floor of his room. When Étienne discovered what his son had done, he abandoned his curriculum and handed over a copy of Euclid.

At sixteen, Pascal produced his first significant mathematical work. He had been studying the ideas of Girard Desargues, a French architect and mathematician who was developing new ways to understand curves and shapes. Pascal wrote a short treatise on conic sections—the family of curves you get when you slice a cone at various angles, including circles, ellipses, parabolas, and hyperbolas. The central result, now called Pascal's theorem, describes a remarkable property of hexagons inscribed in these curves.

The work was so sophisticated that René Descartes, already one of the most famous thinkers in Europe, refused to believe a teenager had written it. Descartes assumed Étienne was the real author. When mutual friends assured him the work was genuinely the son's, Descartes sniffed dismissively: "I do not find it strange that he has offered demonstrations about conics more appropriate than those of the ancients," he wrote, "but other matters related to this subject can be proposed that would scarcely occur to a sixteen-year-old child."

History would prove Descartes wrong about Pascal's potential.

The First Calculator

In 1639, the Pascal family's fortunes shifted dramatically. Étienne had fallen out of favor with Cardinal Richelieu over tax policy and fled Paris, leaving his children in the care of a neighbor. But young Jacqueline's performance in a children's play attended by Richelieu charmed the powerful Cardinal, and Étienne was pardoned. More than pardoned—he was appointed the king's commissioner of taxes in Rouen, a city whose tax records had been thrown into chaos by local uprisings.

The job involved endless calculations. Étienne spent his evenings hunched over columns of figures, adding and subtracting taxes owed and paid, cross-checking totals, hunting for errors. Young Blaise was conscripted to help.

In 1642, not yet nineteen, Pascal decided to build a machine that could do the arithmetic automatically. He designed and constructed a mechanical calculator—a box containing a series of interlocking gears and wheels that could add and subtract numbers up to six digits. You entered numbers by rotating small wheels on the front; the gears carried tens automatically, the way we do mentally when adding 7 + 5 and getting 12.

This was the Pascaline, one of the first mechanical calculators in history. Pascal spent the next decade refining his design, eventually building around fifty machines. Eight survive today, scattered across museums in Paris and Dresden.

The Pascaline was a technical marvel but a commercial failure. The machines were extraordinarily expensive to manufacture, each one requiring precision metalwork that few craftsmen could execute reliably. They were also somewhat cumbersome to operate—faster than mental arithmetic for long calculations, but not dramatically so for simple sums. The Pascaline became, essentially, a luxury toy for wealthy aristocrats rather than a practical tool for accountants.

Still, Pascal had demonstrated something profound: arithmetic, that most human of mental activities, could be mechanized. The gears didn't understand addition—they just moved in precise patterns that happened to produce correct answers. This separation of calculation from understanding would echo through centuries of computing history.

Nature Abhors a Vacuum (Or Does It?)

The ancient Greek philosopher Aristotle had declared that nature abhors a vacuum—that empty space is impossible, that the universe is filled entirely with matter. For nearly two thousand years, this remained the accepted view. If you sucked air out of a container, something else must rush in to fill it. The idea of truly empty space seemed not just wrong but philosophically incoherent.

In 1643, an Italian physicist named Evangelista Torricelli made a troubling discovery. He filled a long glass tube with mercury, sealed one end, inverted it, and placed the open end in a bowl of mercury. The mercury in the tube dropped partway, leaving a gap at the sealed top. What was in that gap? Torricelli suspected it was nothing—a true vacuum.

Most scientists, including Descartes, refused to accept this. They proposed that some invisible substance—perhaps an extremely thin fluid called aether—filled the apparently empty space. After all, light passed through the tube, and surely light needed something to travel through.

Pascal, characteristically, decided to test the question experimentally rather than argue about it philosophically.

He replicated Torricelli's experiments and extended them. He tried different liquids—water, wine, oil—and found they rose to different heights based on their density. He sealed barometers inside other barometers, creating nested vacuums. He published his results in 1647 under the title "New Experiments with the Vacuum," laying out detailed rules for how atmospheric pressure supports columns of liquid.

But Pascal's most elegant experiment came from a simple insight. If the mercury in a barometer is held up by the pressure of the atmosphere—by the weight of all the air above it—then the mercury should drop at higher altitudes, where there's less air pressing down.

Pascal lived near the Puy de Dôme, a volcanic peak rising nearly 5,000 feet above the surrounding countryside. His health was too poor to climb it himself, so he recruited his brother-in-law Florin Périer for the expedition.

On September 19, 1648, Périer carried mercury, glass tubes, and measuring equipment to the summit. At the base of the mountain, the mercury stood at 26 inches and 3½ lines (lines being a small unit of measure, about a twelfth of an inch). At the top, it had dropped to 23 inches and 2 lines—a difference of over three inches. The experiment was repeated five times at different points on the summit, always with the same result.

Pascal replicated the finding in Paris by carrying a barometer to the top of the bell tower at Saint-Jacques-de-la-Boucherie, about 160 feet high. The mercury dropped two lines.

The implications were clear. The atmosphere had a definite height and a measurable weight. And at the top of Torricelli's tube, there really was nothing—a true vacuum, despite Aristotle's ancient objections.

Today, the standard unit of pressure bears Pascal's name. One pascal equals one newton of force per square meter. Atmospheric pressure at sea level is about 101,325 pascals. Every weather report, every tire gauge, every blood pressure reading uses units derived from the work of this seventeenth-century Frenchman who refused to accept ancient authority over experimental evidence.

Pascal's Law and Hydraulic Power

Pascal's work on fluids extended beyond barometers. He discovered a fundamental principle now called Pascal's law: pressure applied to a confined fluid is transmitted equally in all directions throughout the fluid.

This sounds abstract, but its applications are everywhere. Push down on one end of a closed system of fluid, and the pressure appears at the other end. More importantly, if the other end has a larger area, the force multiplies. A small force on a small piston can become a large force on a large piston—the principle behind every hydraulic car jack, every hydraulic brake system, every hydraulic excavator.

Pascal demonstrated this principle with characteristic flair. He attached a thin tube to a barrel full of water and ran the tube up three stories. Then he filled the tube with water. The tiny weight of water in the narrow tube, multiplied by the height, created enough pressure to burst the barrel. It became known as Pascal's barrel experiment—a vivid demonstration that pressure depends on height, not on the total amount of fluid.

He also invented the syringe, which works on the same principle: pressure applied by a plunger transmits through fluid to push it out through a needle.

The Birth of Probability

In 1654, a French nobleman named the Chevalier de Méré posed a puzzle to Pascal. Two players are engaged in a game of chance—say, rolling dice—and must stop before either has won. Given the current score, how should they divide the stakes fairly?

This problem—called the problem of points—had puzzled mathematicians for centuries. It appeared simple but resisted solution. The answer couldn't just be based on current scores, because a player who was behind might have a reasonable chance of coming back to win.

Pascal began corresponding with Pierre de Fermat, a lawyer and amateur mathematician who would later become famous for Fermat's Last Theorem. Through their exchange of letters, they worked out the first systematic approach to calculating probabilities.

The key insight was the concept of expected value. Instead of asking who would win, you ask: if we played this game thousands of times from this exact position, what would each player win on average? That expected value determines the fair division of stakes.

From this practical problem about gambling came the mathematical framework that would transform how humans think about uncertainty. Insurance companies calculate premiums using expected values of potential losses. Investors evaluate stocks by weighing expected returns against variance. Medical researchers design clinical trials to distinguish real effects from random chance. Weather forecasters express predictions as probabilities. All of this descends from letters exchanged between a French physicist and a French lawyer about splitting gambling stakes.

The correspondence also led Pascal to develop what we now call Pascal's triangle—a triangular array of numbers where each entry is the sum of the two entries above it. The triangle had been discovered earlier by Chinese and Persian mathematicians, but Pascal analyzed it systematically, proving numerous properties and showing its connection to the binomial coefficients that appear when you expand expressions like (a + b) raised to various powers.

In the same treatise, Pascal gave one of the earliest explicit statements of mathematical induction—the proof technique where you show something works for the first case and prove that if it works for any case, it works for the next, thereby establishing it works for all cases.

The Night of Fire

On November 23, 1654, something happened to Pascal. The nature of the event is unclear—he left no detailed account—but he experienced it as a direct encounter with God.

After his death, a servant found a piece of parchment sewn into the lining of Pascal's coat. He had carried it with him constantly for the remaining eight years of his life. The document, known as the Memorial, records fragments of what he experienced:

Fire. God of Abraham, God of Isaac, God of Jacob, not of the philosophers and of the learned. Certitude. Certitude. Feeling. Joy. Peace. God of Jesus Christ... Forgetfulness of the world and of everything, except God... Joy, joy, joy, tears of joy.

Pascal had been raised Catholic, and in 1646 he and his sister Jacqueline had been drawn to Jansenism, a movement within Catholicism that emphasized predestination and the inability of human will to achieve salvation without divine grace. The Jansenists were theological rigorists, suspicious of the more relaxed moral theology of the Jesuits.

After the night of November 23, Pascal largely abandoned mathematics and physics. He devoted himself to religious writing and to defending Jansenism against its critics.

The Provincial Letters

The conflict between Jansenists and Jesuits came to a head in the 1650s. The Jesuits, the most powerful religious order in the Catholic Church, had developed a sophisticated approach to moral theology called casuistry—the practice of resolving moral dilemmas by analyzing specific cases. Critics charged that Jesuit casuists found ways to excuse almost any sin, provided you could construct the right circumstances or mental reservations.

In 1656 and 1657, Pascal published a series of eighteen letters, the Lettres provinciales (Provincial Letters), attacking Jesuit moral theology. Writing under a pseudonym and with biting wit, Pascal portrayed the Jesuits as intellectually dishonest, willing to twist logic to excuse the sins of their wealthy patrons.

The letters were sensational. They circulated widely, were translated into multiple languages, and established Pascal as a master of French prose. They also got him in trouble—the letters were officially condemned, and he had to write the later ones while moving from hiding place to hiding place.

The Provincial Letters didn't resolve the Jansenist controversy—that would drag on for another century—but they demonstrated that theological arguments could be made accessible to general readers through clarity, humor, and vivid examples.

The Pensées and Pascal's Wager

In his final years, Pascal planned a comprehensive defense of Christianity. He never finished it. What survived was a collection of notes, fragments, and partial drafts that were published after his death under the title Pensées (Thoughts).

The Pensées is a strange and powerful book—not a systematic argument but a collection of observations, some polished and some barely sketched. Pascal reflects on human nature, on the miseries and greatness of humanity, on the search for meaning in a seemingly indifferent universe.

His most famous argument appears here: Pascal's wager. Pascal frames the question of God's existence not as a matter of philosophical proof but as a practical bet. Either God exists or he doesn't. Either you believe or you don't. You must wager—refusing to choose is itself a choice, since you'll live your life as if God doesn't exist.

Now consider the payoffs. If you believe and God exists, you gain eternal happiness—infinite reward. If you believe and God doesn't exist, you lose some worldly pleasures—finite cost. If you disbelieve and God exists, you face eternal damnation—infinite loss. If you disbelieve and God doesn't exist, you gain some worldly pleasures—finite benefit.

Pascal argues that any rational gambler, facing infinite potential gain against finite cost, should bet on God. Even if you think God's existence is unlikely, the expected value calculation favors belief.

The wager has been endlessly criticized. Critics point out that you can't choose to believe by willpower—belief isn't voluntary. They note that the argument applies to any possible God, not specifically the Christian one. They question whether a God worth worshiping would reward calculated belief based on self-interest.

But Pascal anticipated some objections. He didn't claim the wager would produce instant belief. Rather, he suggested that acting as if you believe—going to church, taking the sacraments, living as believers do—would gradually produce genuine faith. "This will naturally make you believe, and deaden your acuteness," he wrote. The phrasing is jarring to modern ears, but Pascal's point was that belief often follows practice rather than preceding it.

The wager also represents something historically significant: the first formal application of probability and expected value to a philosophical question. The gambling problem that led Pascal to develop probability theory found its way into his theology.

Public Transportation and Final Years

Pascal's practical mind kept working even during his religious period. In 1662, just months before his death, he established something remarkably modern: a public transportation system for Paris.

The carrosses à cinq sols (five-sol carriages) were horse-drawn coaches that ran along fixed routes at fixed times for a fixed price—five sols, a small coin. Before this, transportation in Paris meant either walking, hiring an expensive private carriage, or knowing someone with horses. Pascal's service was public, scheduled, and affordable.

The system operated successfully for about fifteen years before declining. But Pascal had established the template: fixed routes, fixed schedules, fixed fares, open to all. Every bus, tram, and metro system in the world descends from those five-sol carriages.

Pascal's health, never robust, deteriorated through his thirties. He suffered from chronic pain, possibly from stomach cancer or tuberculosis. In the summer of 1662, he moved in with his sister Gilberte. He died on August 19, 1662, at age thirty-nine.

The Man in His Contradictions

Pascal remains a difficult figure to categorize. He was a rigorous mathematician who became a fideist—someone who holds that faith operates in a realm beyond reason's reach. He was a fierce defender of scientific method who wrote that "the heart has its reasons which reason does not know." He designed calculating machines while insisting that humans are more than machines.

His scientific work was impeccably empirical. When he wanted to know about vacuums, he performed experiments. When he wanted to know about atmospheric pressure, he sent his brother-in-law up a mountain with measuring equipment. He dismissed Aristotle's ancient authority with the observation that nature doesn't consult philosophical texts before deciding what to do.

Yet his religious writings are full of paradox and mystery. He describes humans as simultaneously wretched and magnificent, capable of recognizing their own wretchedness in a way that demonstrates their greatness. He finds evidence for God not in philosophical proofs but in the human experience of seeking meaning.

Perhaps there's less contradiction than appears. Pascal's probabilistic wager treats religious faith the way his scientific work treated hypotheses—as something to be evaluated by consequences and evidence, even when certainty is impossible. His mathematical work on infinity prepared him to think about infinite rewards and punishments. His invention of the mechanical calculator taught him that some human activities could be reduced to mechanism while others could not.

He was, above all, someone who took ideas seriously enough to change his life for them. When probability theory suggested that betting on God was rational, he reorganized his existence around that bet. When experiments showed that vacuums were possible, he announced it despite contradicting the greatest philosopher in Western history. When he believed Jesuit theology was dangerous, he wrote eighteen letters attacking it while hiding from authorities.

The notes sewn into his coat, carried from the night of fire until his death, remind us that this consummate rationalist found his deepest truth in an experience beyond words: "Fire. God of Abraham, God of Isaac, God of Jacob, not of the philosophers and of the learned."

He was thirty-nine when he died—young enough that we can only wonder what he might have accomplished. The scattered notes of the Pensées, never organized into the book he planned, suggest a mind still grappling with the largest questions. The probability theory he co-invented was left for later mathematicians to develop fully. The mechanical calculator he built wouldn't find practical success for another two centuries.

But the questions he asked continue to matter. What can reason tell us, and where must it yield to other ways of knowing? How should we make decisions under uncertainty? What is the relationship between the physical world we can measure and the meanings we seek within it? Pascal didn't answer these questions definitively—perhaps they can't be answered definitively—but he asked them with unusual clarity and lived with unusual honesty about how hard they are.

The SI unit of pressure, the programming language PASCAL, the probability distributions, the triangle of binomial coefficients—these bear his name and mark his contributions to science and mathematics. But his more lasting legacy may be the example of a mind that refused to separate the technical from the philosophical, the mathematical from the spiritual, the rigorous from the passionate. He was, as he might have put it, thinking with both the mind and the heart.