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Blaise Pascal's Fixed Point: A Mathematician's observations

By Charlotte B. Cerminaro
web posted June 21, 2021

Blaise PascalOver four-and-a-half centuries have passed since the French mathematician and philosopher Blaise Pascal walked the earth, but his ideas and predictions continue to be just as accurate as when they were first written. Some of his most influential works were seemingly not intended for publication; they were rather simple observations and profound remarks--on everything from human behavior to theology, economics and predictive geometry.

When Pascal's most famous and thought-provoking work was found posthumously, it was more of a collection of brief ideas and observations, very unique but typical of his brilliant and unconventional mind. Many associate the name Pascal with groundbreaking discoveries about air pressure, vacuum states and early calculators, but arguably his greatest works came nearer the end of his very short life of only 39 years. These writings were gathered and organized into a volume eventually titled, Penseés (thoughts).

Throughout Pascal's life he single-handedly took on the Catholic dogma and self-contradictory theology that was still ubiquitous in the early years of the reformation. A very deep, almost intuitive understanding of the most profound theological complexities earned him enemies very quickly. His rational, mathematical mind posited simple challenges and scientific axioms in order to provoke thinking instead of reflexive, knee-jerk reactions and thoughtless dogmatic ideology. One of his most famous challenges is now known as Pascal's wager. It is a simple arithmetical argument for the existence of, and belief in, God--and a direct refutation of the elder Frenchman Descarte's existential ramblings.

One of the most strikingly relevant ideas that beautifully illustrates our modern-day "group think" and herd mentality is Pascal's metaphorical Fixed Point. He states, "When everything is moving at once, nothing appears to be moving, as on board ship. When everyone is moving towards depravity, no one seems to be moving but if someone stops, he shows up the others who are rushing on, by acting as a fixed point." Penseés, vol. 33. While the world rushes headlong into the seductive philosophy of self-indulgent hedonism, it's extremely difficult to remember that the greatest impact on the world has been made by and through men and women of principle. It's easy to sail with the ship. It is a difficult thing to stop, and to become the fixed point on which the world can focus and rely.

An often-observed phenomenon in animals and humans is the flocking behavior of the masses--the leader suddenly banks one way and everyone follows; now, for the most part, no one really knows who's leading or where they're going. They are blindly and obediently following just a split second after, determined to keep up and questioning nothing. Every once in a while they see someone heading in the opposite direction, or standing still, and they try not to think about whether their course is correct. A momentary discomfort is replaced by the smug satisfaction that they seem to have sheer numbers on their side, they are "moving with the crowd" so they absolutely must be right. The flocking behavior continues even after it's discovered that one of the "leaders" was clearly going the wrong way, and knew it all along.

Probably the most remarkable thing about 17th century mathematician Blaise Pascal is that he seemed to have his finger on the very pulse of civilization: Human nature, psychology, power, corruption, lies and truth. Long before the psychoanalytic revolution Pascal was persuading, analyzing and understanding the power structure and those who wielded it. Though he couldn't have imagined such things as social media--its unthinkable power and influence even over the self-described skeptics of our day--he had a firm grasp of the striking speed and almost-unstoppable momentum of a false but appealing idea, a superstition, a threat, or a new take on an old philosophy. The birth of nihilism, socialism, emotional anti-theism and the death and depravity that followed is a singular example of the power of groupthink. If no one stops and reasons, wondering from where an idea sprung and what are the possible implications, both overt and covert, they will be swept out with the tide on a course not of their own choosing.

The power structure in place during Pascal's time was only a hint of what would come; with one of the most persuasive and unusually brilliant minds in history he could only loosen that ideology at its foundation, from which it would eventually topple. If one of the most unimaginably difficult things we can do is to simply stop, be still, then what must it take for one person to make such an impact on this world? ESR

Charlotte B. Cerminaro is a Juilliard-trained classical musician who, in addition to being a studio and orchestral musician, enjoys writing and has a degree in Molecular Biology. © 2021

 

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