Welcome to the Deep Dives, where we take a monumental
stack of history, science, and philosophy and
distill it into the knowledge you need, fast.
Today, we're embarking on one of the most astonishing
journeys through 17th century intellectual history.
We are unpacking the life of Blaise Pascal. French
polymath who, well, fundamentally shaped the
modern world in mathematics, physics, computing,
and literature. And he did it all before his
life was tragically cut short at the age of 39.
39 years. I mean, it's barely enough time for
most of us to figure out a career path. And yet
Pascal was an inventor, a physicist who disproved
ancient philosophy, a profound religious writer,
and a literary revolutionary. all at once. So
our mission today with this huge stack of sources
is to unpack how one person could lay the groundwork
for modern calculus, probability theory, public
transit, and computer engineering. And then after
all that, pivot his immense genius entirely toward
theology. It's an incredible story. And what's
so fascinating is that his genius was never just
abstract, was it? Not at all. His origins were
very practical. His father, Etienne Pascal, was
part of the administrative class, the noblesse
de robe. He was a royal tax commissioner. Ah,
so that environment, that world of numbers and
administration. Exactly. It was steeped in the,
um... the excruciating reality of manual, often
chaotic calculations. And that's what directly
pushed Pascal toward finding a better way, a
radical automated solution. It really is the
ultimate example of necessity birthing invention.
We're going to see how financial chaos in 17th
century France literally drove him to invent
the mechanical calculator. And how a challenge
from an aristocratic gambler sparked the entire
field of propodacty. It's a recurring theme,
isn't it? intensely practical problems leading
to these huge world -changing abstract solutions.
We'll start with his astonishing beginnings as
a child prodigy, trace his path through his inventions,
then move to his foundational physics experiments
that really settled the centuries -old debate
over the vacuum. And finally, we'll get into
the dramatic religious conversion that birthed
two of the most influential literary and philosophical
masterpieces in the French language. Okay, so
let's start at the beginning. Pascal was born
in Clermont -Ferrand in 1623. His mother died
when he was just three, and his father, Etienne,
made this really pivotal decision. He decided
to educate Blaise and his two sisters himself
when they all moved to Paris in 1631. And the
sources are all very clear on this. Young Pascal
had an extraordinary, almost alarming intellectual
ability, especially for math. But the defining
anecdote of his childhood is the story of restriction.
His father... who was a decent mathematician
himself, actually tried to keep math away from
him. Which sounds completely counterintuitive.
Right. Why would you do that? Was he afraid his
son would become, I don't know, too specialized
too early? It seems to be a bit of that. Etienne
had this idea that a proper classical education
language as literature had to come first. So
he actually removed all the math textbooks from
the house. He locked them away. Locked them away
and refused to even discuss the subject. The
plan was he'd teach Blaise math when he turned
15. But a mind like that, well, it finds a way,
doesn't it? It absolutely does. The story goes
that Blaze, who was only about 12... just started
figuring it out on his own. He was using charcoal
on a tile floor. Drawing shapes. Drawing shapes,
making up his own names for them, like bar for
a line and round for a circle. And by the time
his father found him, he had independently rediscovered
Euclid's first 32 propositions. Without any books.
Without any books. He had essentially reverse
engineered the fundamentals of geometry up to
the point of proving that the angles in a triangle
add up to two right angles. All on his own. That
is just... It's a hallmark of a mind operating
on a completely different level. He didn't just
learn geometry. He recreated it. And that led
just four years later to his first serious mathematical
work, the essay on conics. In 1640, he was 16.
16 years old and publishing serious mathematics.
What was the core idea in that work? The cornerstone
was something he called the mystic hexagram.
We know it today as Pascal's theorem. And what
does that state? It's an incredibly elegant proof.
Basically, if you draw any random hexagon inside
a conic section, a circle, an ellipse, whatever,
the three points where the opposite sides intersect
will always lie on a single straight line. The
Pascal line. It's one of those things that sounds
complex, but is visually just... Yeah. perfect
once you see it drawn out. And the reaction at
the time tells you everything. The great Rene
Descartes. The father of modern philosophy. He
was so astounded he was convinced that Pascal's
father had written it. He simply couldn't believe
a 16 -year -old was capable of that kind of original
thought. So he basically accused him of fraud.
Pretty much. When he was assured it really was
the son's work. Descartes gave this backhanded
compliment, saying it was impressive, but that
other related topics would scarcely occur to
a 16 -year -old child. Incredible. So he's already
fighting for recognition just because he's so
far ahead of his age. And from this very abstract
theoretical brilliance, his journey takes a very
practical turn. And that brings us to the financial
crisis the Pascal family faced. Right, because
they were initially quite comfortable when they
moved to Paris. Very. Etienne had sold his official
position for over 65 ,000 livres, a huge sum.
But then, in 1638, Cardinal Richelieu, who was
desperate for money for the Thirty Years' War,
defaulted on government bonds. And that just
wiped them out. It wiped out most of their wealth.
Their fortune plummeted. It was a crippling blow.
So to recover, Etienne gets a new job. He's appointed
the king's commissioner of taxes in Rouen in
1639, and Rouen was a mess. Tax revolts, chaotic
records. And his job was to sort through it all.
We're talking endless, grueling calculations.
Just endless. He was completely overwhelmed.
And this is where Blaze, seeing his father struggling,
applies his mind to the problem. This is the
origin of the Pascaline, around 1642. He's not
even 19 yet. It's not. And he builds this mechanical
calculator. It was a box with a series of geared
wheels. You'd dial in the numbers, and the machine
would perform addition and subtraction, even
handling the carryover automatically. It's one
of the very first mechanical calculators in history.
The other was Wilhelm Schickard's, but his was
lost in a fire. So Pascal's is the one that survives
and evolves. He spent a decade perfecting it,
building about 20 finished machines. He even
presented one to Christina, queen of Sweden.
But here's the friction point. If it was such
a pioneering invention, why didn't it take off?
Well, it was a mix of things. First, it was mechanically
very complex. It could jam, especially if you
tried to use it too quickly. And the accountants
said they were already very fast with their manual
methods. Exactly. Second, it was a bit cumbersome
to use. The process wasn't as intuitive as, say,
an abacus for people who are already trained
experts. And the third factor, I'm guessing,
was cost. The cost. It was extraordinarily expensive
to build and maintain. You could hire a whole
room of clerks for less. So it failed as a commercial
product. It didn't become a widespread tool.
It became what? A status symbol. A sophisticated
toy and a status symbol for the wealthy elite.
It was a brilliant technological leap, but the
world just wasn't economically ready for it.
It's a classic story in the history of technology.
You could be right, but right too early. So after
this foray into mechanical engineering, Pascal's
work pivots back into abstract mathematics. But
again, it's triggered by a very practical problem.
And this time it's not taxes. It's gambling.
Gambling. In 1654, he starts this now famous
correspondence with Pierre de Fermat, another
giant of French mathematics. And the whole thing
gets started because a guy named Chevalier de
Marais, an aristocratic gambler, has a couple
of puzzles he can't solve. And one of them, the
one that really ignited this new field, was the
problem of points. OK, can you break down the
scenario for us? Certainly. Imagine you and I
are playing a game of coin flips. The first person
to win five rounds gets the whole prize pot.
OK. But let's say we have to stop early. I've
won four rounds and you've won three. The game's
not over. How do we divide the prize money fairly?
The old way was just to divide it based on the
rounds we'd already won, right? So like a four
to three ratio. Exactly. And that's wrong. Pascal
and Fermat's breakthrough was realizing the division
has to be based on the future. on the probability
each of us has of winning from that point forward.
So you calculate all the possible ways the rest
of the game could play out. Precisely. And that
correspondence, that back and forth, gave birth
to the mathematical theory of probability. The
impact of that is just. It's hard to overstate.
It goes so far beyond the gambling table. Oh,
absolutely. The core concept they developed,
what we call expected value, it's the foundation
for how we quantify risk and uncertainty. So
you're talking about insurance, financial markets,
modern economics. All of it. Actuarial science.
The roots trace directly back to Pascal and Fermat
trying to solve a gambler's dilemma in 1654.
And it also leads some of the groundwork for
Leibniz and the later development of calculus.
It did. The focus on infinitesimals and approaching
limits was a key step. So again, you have a mechanical
calculator leading towards computing and a gambling
problem leading towards higher analysis. And
that same year, 1654, was just incredibly productive
for him. That's also when he wrote his treatise
on the arithmetical triangle. Right, the work
that details what we all know as Pascal's triangle.
Now, he didn't invent the triangle itself, did
he? No, the pattern was known for centuries in
China, India, Persia. Pascal's contribution was
to systematically explore its properties and
apply them to his new work on probability. And
in that same treatise, he did something else.
something methodologically revolutionary. This
was the really huge leap. He provided the first
explicit, formalized statement of the principle
of mathematical induction. Okay, for those of
us who haven't thought about that since high
school, can you give us a simple analogy? Think
of it like a line of dominoes, an infinite line.
Mathematical induction is how you prove that
all the dominoes will fall. You only have to
do two things. Okay, what's the first? First
is the base case. You have to prove you can knock
over the very first domino. that the statement
is true for the first instance simple enough
and the second part that's the inductive step
you have to prove that if any given domino falls
it will always knock over the next one that if
the statement is true for some number k it must
be true for k plus one so If you can knock over
the first one, and you know each one knocks over
the next, you've proven it for the entire infinite
line. Exactly. It's a way to formalize absolute
certainty in mathematics, which is, as you said,
incredibly ironic given what else happens in
1654. Because right at this peak of his mathematical
powers, he just stops. That's the great pivot.
1654 is the year of his definitive religious
conversion, the Night of the Memorial. After
that, he mostly gave up work in mathematics.
But not entirely. There's one last kind of bizarre
mathematical episode a few years later. In 1658.
And it was prompted by a severe toothache. A
toothache? He was in agony. And to distract himself
from the pain, he started thinking about the
cycloid. That's the curve traced by a point on
a rolling circle. It was a huge mathematical
puzzle at the time. And as he's deep in thought...
His toothache just vanished. Completely. And
Pascal, being in this new religious frame of
mind, took it as a heavenly sign. Divine approval
to keep working on the math problem. Yes. He
worked furiously and wrote an entire essay on
the area and volume of the cycloid in just eight
days. He even proposed a public contest with
cash prizes to solve related problems. So even
a brief return to his first passion yielded significant
results. It did. It showed that the mind was
still there, even if his focus had shifted heavenward.
It's just staggering that this same person, at
the same time, was also revolutionizing our understanding
of the physical world. I mean, this is the work
that gave us the scientific unit, the Pascal.
His physics work was also incredibly practical.
It led to two inventions we still use every day,
the syringe and the hydraulic press. The hydraulic
press is based on Pascal's law, right? Can you
break that down? Sure. Pascal's law says that
if you apply pressure to a fluid in a closed
container, that pressure is transmitted equally
to every part of the fluid. More importantly,
the pressure depends on the height of the fluid
column, not its total weight. And that's how
you get force multiplication, like in a car jack.
That's the perfect modern analogy. You apply
a small force on a small piston, and that pressure
is transmitted to a much larger piston, which
magnifies the force and lets you lift a two -ton
car with ease. And he had this very dramatic
way of demonstrating this, the Pascal's barrel
experiment. A fantastic illustration. He took
a sturdy, water -filled barrel and attached a
very long, very thin tube to the top. A tube
that went all the way up to the third story of
a building? Right, and then he started pouring
water into just that tiny tube. The volume of
water he added was minuscule. But the height
of the water column created immense pressure.
So much pressure that the barrel burst. It proved
that pressure depends on height, not volume.
It was a spectacular way to shatter common sense
intuition. But his biggest contribution to physics
was settling a debate that had been raging since
ancient Greece. The vacuum. This was a battle
against dogma. The Aristotelian view, which Descartes
also held, was horror vacuum. Nature abhors a
vacuum. The belief was that true nothingness
couldn't exist. Any space had to be filled with
some kind of invisible matter. But then evangelists
of Torricelli's experiments with mercury barometers
started to suggest otherwise. Torricelli's work
was the spark. Pascal picked it up and ran with
it. In 1647, he published a paper arguing that
a true vacuum did exist above the mercury in
a barometer tube, and it was the weight of the
air pressing down that held the mercury up. But
the old guard, the Cartesians... They weren't
convinced. No, they argued that some invisible
vapor or substance was filling that space, so
Pascal needed definitive, irrefutable proof.
And his hypothesis was brilliantly simple. Just
beautiful. He reasoned that if air has weight,
then there must be less of it on top of a mountain
than at the bottom, so atmospheric pressure should
decrease as you go up. And he had the perfect
laboratory right there. The Puy -de -Dôme Mountain.
The only problem was his own health was terrible.
He was often too sick to do things himself. So
he recruited his brother -in -law, Florent Perrier,
to conduct the experiment in 1648. And the methodology
they used was so rigorous for its time. It really
was. Perrier gathered a bunch of credible witnesses,
prepared two identical barometers, and took a
baseline reading at the lowest point in town.
Critically, he left one barometer there as a
control. To make sure the weather didn't just
change during the day. Exactly. Then he and his
party climbed the mountain. Almost 5 ,000 feet.
And when they got to the summit? The result was
immediate and decisive. The Mercury column was
more than three inches lower than it was at the
base. A huge drop. A massive drop. He repeated
the experiment five times, all with the same
result. When he got back down, the Mercury was
back to its original height. It was conclusive
proof. The weight of the air was real and the
vacuum was real. It permanently settled the debate.
And Pascal immediately replicated it on a smaller
scale in Paris by carrying a barometer up the
bell tower of a church and seeing the mercury
drop. And his response to his critics from this
period is one of the clearest statements of the
modern scientific method. It's a fantastic quote
on falsifiability. He said essentially that for
a hypothesis to be true, it's not enough that
all the phenomena fit it. If it leads to something
that contradicts even a single phenomenon, that's
enough to prove it's false. Science progresses
by seeking disproof, not just confirmation. A
profound idea. And of course, the legacy of all
this work is the SI unit for pressure, the Pascal.
Which brings us to that great turning point.
The same rigorous mind that insisted on empirical
proof in the physical world is the one that would
soon turn away from reason in the realm of faith.
The seeds for that were planted a bit earlier,
weren't they, in 1646? Yes, during a family crisis.
His father broke his hip, and the two doctors
who treated him were devout followers of Jansenism.
Jansenism. That was a very austere, rigorous
movement within Catholicism, right? Very much
so. It stressed human sinfulness and the absolute
necessity of divine grace for salvation. Pascal
was deeply influenced by talking with these doctors
and reading Jansenist works. That was his first
conversion. But it didn't fully stick at first.
After his father died, he went through what's
called his worldly period. And this led to a
really intense conflict with his sister, Jacqueline,
who he was very close to. She wanted to join
the Jansenist convent at Port Royal. She was
resolute. But Pascal resisted fiercely. He relied
on her, and he was also deeply suspicious of
the convent. The sources suggest he felt that
it had begun to smell like a cult. And the fight
was over her inheritance, which she had signed
over to the convent. He eventually gave in, but
it caused him... immense turmoil and led to a
period of spiritual isolation which all builds
up to the main event november 23rd 1654. that
night between 10 .30 and 12 30 pascal had an
intense two -hour mystical experience that changed
him forever and we only know about it because
of the note he scribbled down the memorial it
starts with just one word fire and the key line
rejects the intellectualized god of philosophy
fire God of Abraham, God of Isaac, God of Jacob,
not of the philosophers and the scholars. It
was a direct, overwhelming experience of God.
And the personal detail of what he did with that
note is just mind -blowing. It is. He sewed it
into the lining of his coat. And every time he
got a new coat, he would unpick the stitches
and sew it into the new one. No one knew it existed.
It was a completely private covenant, a secret
he kept until a servant found it after he died.
From that point on, his work is almost entirely
religious. He immediately starts writing his
first great literary work, The Provincial Letters.
Which was a blistering attack on something called
casuistry. What exactly was that? Casuistry was
a method of moral reasoning, especially popular
with the Jesuits, that tried to resolve ethical
dilemmas by applying general principles to very
specific cases. And Pascal saw this as just a
way to create moral loopholes. He thought it
was using complex reasoning to justify moral
laxity, to excuse sin. and he attacked it with
devastating effect. The letters were published
under a pseudonym, and they were brilliant. He
used humor, mockery, vicious satire. They became
a masterpiece of French prose. They were so powerful
that King Louis IV ordered the book to be burned.
And yet, even the Pope... while publicly condemning
them, was supposedly privately convinced by Pascal's
arguments. That's what the sources say. They
were just that persuasive. And one of the most
famous quotes comes from these letters, his apology
for one of them being too long. I have made this
letter longer than usual only because I have
not had the time to make it shorter. Iconic line.
And that leads into his unfinished magnum opus,
the pensées, or thoughts. This was meant to be
his great defense of Christianity. An apology.
And he had a very specific philosophical strategy
to convert the unbeliever. A brilliant one. He
planned to trap the reader between two opposing
philosophies, Pyrrhonism, which is radical skepticism,
and Stoicism, which is radical self -sufficiency
through reason. So he would use one to dismantle
the other. Exactly. He'd use the skeptic Montaigne
to show the flaws in the Stoic's confidence and
use the Stoic Epictetus to show the contradictions
in the skeptic's position. The goal was to drive
the reader to despair. To show that human reason
on its own fails when it comes to the big questions.
And that failure creates the need for a divine
answer. And within this framework is his most
famous idea. Pascal's Wager. This is where his
work on probability theory crashes into his theology.
He argues that since reason can't prove or disprove
God's existence, you have to make a bet. You
bet that God exists or you bet that he doesn't.
And then you calculate the stakes. If you bet
on God and you're right, your gain is infinite
eternal salvation. If you're wrong, your loss
is finite. A few earthly pleasures. What if you
bet against God and you're wrong? Your loss is
infinite. Eternal damnation. So from a purely
probabilistic standpoint, the only rational bet
is to believe. The infinite payoff just dominates
the entire equation. It's a pragmatic argument.
He's not saying it will make you believe, but
it gives you a reason to start acting as if you
do. And this preference for faith over pure reason
is why he clashed so strongly with Descartes.
He famously wrote, I cannot forgive Descartes
because Descartes used God to get his system
started and then, you know, didn't need God anymore.
For Pascal. God wasn't a philosophical premise.
God had to be felt in the heart. Which is all
captured in that perfect, timeless quote, thought
number 200. Man is only a reed, the weakest in
nature, but he is a thinking reed. We are fragile
and mortal, but our consciousness, our ability
to think, gives us infinite dignity. It's the
ultimate summary of human misery and human greatness.
And even with all this going on, he had one last
practical invention left in him. One last one.
In 1661, less than a year before he died, he
inaugurated one of the world's first public transportation
systems. The Carousel Saint -Saul in Paris. Horse
-drawn carriages, like buses, that ran on fixed
routes for a fixed price of five souls. And he
established the core principles we still use.
Fixed route, fixed price, and crucially, a fixed
schedule. The carriages left on time, even if
they were empty. That reliability is key. Now,
like the Pascaline, it wasn't a long -term commercial
success. The lines closed down by 1675. But the
concept, the invention of the system of public
transit, is all his. It's a final testament to
the sheer breadth of his mind. But his time was
running out. His lifelong health problems were
getting much, much worse. And he embraced a severe
ascetic lifestyle. He came to believe that...
Sickness is the natural state of Christians and
often refuse doctors seeing suffering as something
to be endured. He died in Paris on August 19,
1662. He was only 39. His last words were, may
God never abandon me. The autopsy revealed just
how much he had suffered physically. Grave problems
with his stomach and other organs, along with
damage to his brain, which likely caused the
chronic, debilitating headaches he had his whole
life. An incredibly short life. But the legacy
is just immense. His name is everywhere. It really
is. In science, the Pascal unit of pressure.
In technology, the Pascal programming language,
NVIDIA's Pascal microarchitecture. And in culture,
too. The chameleon in the movie Tangled is named
Pascal, the otter in Animal Crossing. And just
last year, in 2023, Pope Francis dedicated an
entire apostolic letter to him. He remains this
towering figure, a scientific giant whose ultimate
conclusions were theological. The man who started
out trying to help his father with tax ledgers
ended up systematizing chaos itself with probability
and then arguing the greatest truths can't be
calculated at all. It's a remarkable story of
synthesis. Tax calculations gave us the calculator.
A gambler's problem gave us probability. A toothache
gave us a key insight into the psychoid. His
life was a relentless pursuit of truth wherever
it led. He truly was the great synthesizer of
math, science, and faith. We have to go back
to that quote. Man is only a reed, the weakest
in nature, but he is a thinking reed. His physical
form was weak, but his mind changed our world.
And that profound tension in his own life between
rational certainty and spiritual submission leaves
us with a final thought for you to consider.
Pascal. the brilliant mind who codified certainty
in math and science, ultimately conclude that
certainty in life's biggest questions can only
be grasped through intuition and a wager. So
what fundamental questions in your own life do
you rely on intuition or a wager to answer, knowing
that reason alone can't give you the proof you
might want? That's a deep dive for another day.
Thank you for joining us. We hope you feel thoroughly
informed and perhaps profoundly curious.