Depictions of two of Pascal's most significant contributions to mathematics and society
Mytour.comMathematician, physicist, religious thinker, and master of language: Blaise Pascal truly embodied the essence of a Renaissance man by any measure.
Born on June 19, 1623, in Clermont-Ferrand, France, Pascal emerged as a self-taught mathematical genius during his early teenage years [source: Britannica; "Prodigy"]. At just 16 years old, he conceived Pascal's theorem, which states that if any hexagon is inscribed within a conic section (the curve formed by a plane intersecting a cone) and the opposite sides are extended, their intersections will lie on a single straight line.
Shifting focus, Pascal created one of the earliest digital calculators in 1642 to assist his father, a mathematician and tax collector, modestly naming it the pascaline. This device employed gears and pins to perform addition with integers. With a few clever mathematical techniques, it could also be used for subtraction, multiplication, and division. Various models were capable of handling five-, six-, and eight-digit numbers. The true challenge, however, was managing the nondecimal French currency system, where 20 sols equaled a livre and 12 deniers made up a sol.
As an offshoot of his research into perpetual motion, which he pursued to enhance the pascaline, Pascal also developed the foundational technology behind the roulette machine [source: MIT].
Even today, students in elementary school study Pascal's triangle, a triangular array of numbers where each number is the sum of the two diagonally above it, as shown in the accompanying illustration. While Pascal didn't create this configuration (it was used by Chinese and Persian mathematicians over 500 years earlier), he discovered innovative applications for it, such as computing probabilities.
In 1654, at the age of 31, Pascal applied his talent for formalization and analysis once more, collaborating with Pierre de Fermat to develop the calculus of probabilities. While exchanging ideas to solve a gambling problem, they introduced the concept of equally probable outcomes, a foundational idea that had previously escaped other thinkers. Examples include a coin landing on heads or tails, or a die showing any number from 1 to 6. Pascal systematized their discoveries into a universal rule for probability calculation, utilizing his triangle to streamline the process [source: Fermat and Pascal].
True to the spirit of a Renaissance man, Pascal's expertise spanned multiple disciplines. Next, we'll explore how his work in physics, metaphysics, and literature left a lasting impact for generations.
Pascal Tackles Physics and Metaphysics
As Pascal aged, he increasingly immersed himself in the study of physical sciences and Christian philosophy.
In 1646, Pascal initiated a series of experiments on atmospheric pressure to validate the theories of Galileo and his student Evangelista Torricelli, the Italian physicist behind the barometer's principle. By constructing his own mercury barometers, Pascal expanded on his predecessors' work, contributing foundational insights to hydrodynamics and hydrostatics [source: Britannica; "Blaise Pascal"]. His contributions were so significant that a unit of pressure, the Pascal, was named in his honor.
Pascal's work on pressure led to the invention of the syringe and the hydraulic press. The latter was based on Pascal's Law, which states that pressure applied to a confined fluid is transmitted equally in all directions, regardless of where the force is applied.
Hydraulic presses utilize this principle to generate mechanical advantage: A small force applied to a small piston over a long distance in an incompressible fluid (like water or oil) results in a larger piston moving a shorter distance. This concept, akin to liquid leverage, explains how hydraulic lifts raise cars and how hydraulic brakes can stop massive airplanes weighing hundreds of tons.
While his technical innovations and scientific research were groundbreaking, Pascal is perhaps best remembered for his profound impact on philosophy and Christian theology. His most famous philosophical contribution, Pascal's Wager, posits that it is pragmatic to live as though God exists. The reasoning is simple: if God is a myth, the loss is minimal, but if God is real, the potential gain—eternal life—is immeasurable [source: Honderich; "Pascal's Wager"].
As a religious philosopher and defender of Christianity, Pascal approached the arguments for God's existence and the Christian faith through psychology and historical evidence, rather than traditional metaphysical reasoning [source: Honderich; "Blaise Pascal"]. Much of his reasoning is encapsulated in his unfinished work, Apologie de la religion chrétienne, which, along with other notes, was later compiled into the renowned collection Pensées (Thoughts) [source: Britannica; "Blaise Pascal"].
Pascal's creativity also shone in the realm of literature. His work Provincales—a critique of the Jesuits in defense of Antoine Arnauld, a Jansenist on trial—remains influential. Nicolas Boileau, the pioneer of French literary criticism, hailed Pascal's writings as the dawn of modern French prose [source: Britannica; "Blaise Pascal"].
Like Archimedes and Galileo, Pascal was a genuine polymath, the result of a disciplined, inquisitive, and analytical intellect.
