All right, I want you to just, for a second,
picture a scene with me. Okay. It's November.
The year is 1717, and it is a biting, freezing
cold night in Paris. Mm -hmm. But I don't want
you to think of the, you know, the romantic,
glowing Paris we see in movies. Right. This is
not the city of light yet, not by a long shot.
Exactly. This is 18th century Paris. It's dark.
It probably smells of wood smoke and... Well,
open sewers. It's quiet except for the wind rattling
the shutters. It's a setting that sounds like
the beginning of, I don't know, a Charles Dickens
novel, doesn't it? It really does. Yeah. Because
we're zooming in on a very specific place. The
steps of a church. Saint -Jean -Laurent. Okay.
And right there, on those cold stone steps exposed
to all the elements, someone has left a bundle.
No! It's a newborn baby. A foundling. Foundling.
And we have to be really honest about the reality
of that time. Abandoning a child on church steps
in November was, I mean, it was usually a death
sentence. A death sentence. Oh, absolutely. The
survival rate for foundlings in 18th century
France was terrifyingly low. You're talking about
the cold, hunger, disease. The odds were just
stacked entirely against this child. So by all
rights, that should have been the end of the
story. Just a tragic anonymous statistic in the
parish. Should have been. But it wasn't. This
shivering infant didn't just survive the night.
He grew up to become one of the most formidable
intellects of the entire Enlightenment. It's
an incredible story. We were talking about a
man who would basically rewrite the laws of physics,
co -edit the most important, maybe the most famous
book in human history. And he tried to turn music
into a math problem. And maybe the most surprising
thing of all, a man who had the integrity, or
maybe it was the skepticism, to tell a king he
didn't want a planet or a moon named after him.
Today we are diving deep into the life and mind
of Jean -Laurent d 'Alembert. A true polymath.
I mean, he was a mathematician, a physicist,
a philosopher, a music theorist, and a central
figure in what they called the Republic of Letters.
This deep dive is going to be a wild ride. We've
got a massive stack of sources here, biographies,
his own articles from the encyclopedia, historical
analyses of his physics, and even some... pretty
juicy letters from the salons of Paris. Our mission
today is to really unpack how this abandoned
child rose to the absolute top of European intellectual
society. We need to understand his massive contributions
to science because, spoiler alert, if you're
an engineer or a physicist listening to this
today, you are using his math. Absolutely. We're
going to have to look at the trite, the dynamique,
the wave equation. I mean, these are things that
genuinely revolutionized how we understand the
physical. world. But I also want to get into
the messy stuff. Oh, there's always messy stuff.
For a guy who is a genius of logic, he had some
serious blind spots. We're going to talk about
his feud with the most famous musician of the
era. And we absolutely have to talk about the
gambler's fallacy. Oh, the Dallin Bear system.
It's a classic. It's basically the reason casinos
make so much money. It proves that even the most
brilliant minds can get tripped up by, you know,
simple probability. I feel like that's going
to make me feel a lot better about my own struggles
with math. Fair enough. So let's go back to the
beginning. The church steps. Saint -Jean -Laurent,
who leaves a baby on a church step in November.
Do we even know who the parents were? We do.
And this is where the story immediately takes
a very sharp turn away from that sort of poverty
-stricken orphan narrative you might be picturing.
Okay. This wasn't a case of a poor family who
couldn't afford to feed another mouth. The mother
was Claudine Guérin de Tencin. Wait, hang on.
I've heard that name. The Tencin. As in the famous
writer and salon hostess. The very same. She
was an absolute force of nature in Parisian society.
She was a runaway nun who turned her home into
one of the most influential salons in Europe.
She was incredibly well connected. She was wealthy,
prominent. But she wasn't married. Exactly. In
1717, for a woman of her high social standing
to have an illegitimate child. It would have
been a catastrophic scandal. I mean, it would
have just ruined her reputation, her position,
everything. So she made a calculation. A very
cold calculation. She abandoned the child to
save her status. That is just, it's brutal. So
she leaves him there, assuming he'll be picked
up by the church. Well, let's not think about
the alternative. No. What about the father? Was
he in the picture at all? He was. The father
was the Chevalier Louis Camus de Touche. He was
an artillery officer, a military man. But the
crucial detail here is that he wasn't in Paris
when the birth happened. He was abroad on booty.
But, and this is the big twist in the story,
when he returned to Paris and found out what
Claudine had done, He didn't just wash his hands
of it. He actually cared. He did. He went looking
for the child. He cracked the baby down, probably
through church records or the foundling hospital
where the baby had been taken after being found.
He found his son. So, happy ending then. He takes
the boy home, raises him as the son of an artillery
officer. Not quite. You have to remember the
incredibly rigid social structures of the time.
Detouche was a chevalier, a nobleman. He couldn't
just bring an illegitimate child into his household
and raise him as his heir. The stigma was just
too strong. So what did he do? He orchestrated
the solution. He arranged for the boy who, by
the way, had been named Jean Laurent after the
patron saint of the church where he was found
to be fostered. Fostered by whom? Someone in
his circle? Not at all. He placed him with a
woman named Madame Rousseau. And it's an important
note. There is no relation to the famous philosopher
Jean -Jacques Rousseau. Okay, got it. So who
was this Madame Rousseau? She was the wife of
a glazier. A glassworker. A glazier. So we're
talking working class. Very much so. A humble,
artisan home. And this is the environment where
d 'Alembert... one of the greatest geniuses of
the century, would spend the next 50 years of
his life. Wait, did you just say 50 years? Five
zero? Rarely 50. He didn't just stay there until
he was 18 and then leave for college. He lived
with the glacier and his wife well into his adulthood,
long after he had become famous. You're telling
me he was writing for the encyclopedia, corresponding
with kings and emperors, and still coming home
to the glacier's house. That's exactly right.
It's this incredible paradox. That is amazing
stability for someone who... started life on
a doorstep yeah but i have to ask about the dynamic
there you have this brilliant child clearly a
prodigy living in a working -class home was madame
rousseau like the supportive mom in a feel -good
movie you know go get him tiger you're a genius
Quite the opposite, actually. And this is one
of those tragic comic elements of D 'Alembert's
life that I find so fascinating. She was a stable
mother figure. You know, she fed him and housed
him. She gave him a home. But she absolutely
did not get him. She didn't understand his intellect?
Not in the slightest. She didn't understand his
ambition, his drive, any of it. Can you give
me an example? Oh, there's a very famous anecdote
that historians always cite. Whenever D 'Alembert
would achieve something, you know, maybe he cracked
a new mathematical problem or... wrote a brilliant
paper he would run to her, all excited to share
his discovery. Like any kid would. And she would
just look at him, shake her head, and say, you
will never be anything but a philosopher, and
what is that but an ass who plagues himself all
his life that he may be talked about after he
is dead? An ass who plagues himself. Wow. Thanks
for the vote of confidence, Mom. That is just
scathing. It certainly must have kept his ego
in check. But here's the other side of the coin.
While he didn't get any intellectual encouragement
from her, he did have financial support coming
from the shadows. His biological father, Detutious.
Right. He never officially recognized him as
his son, so legally d 'Alembert remained a bastard.
But Laetitia secretly paid for his entire education.
He set up an annuity of 1 ,200 livres a year
for him. Which, in the early 18th century, is
not pocket change. That's a serious amount of
money. Oh no, it was enough to secure a top -tier
education. It's what allowed him to enter the
Jensenist College des Quatre Nations, also known
as College Mazere, when he was just 12 years
old. Okay, so he goes from the glazier's house
to this... prestigious college but it wasn't
a science academy or anything like that right
this was run by jansenists right and this is
absolutely crucial for understanding d 'alembert's
intellectual rebellion to understand what he
fought for you really have to understand what
he was fighting against and what was that the
jansenists were a very specific very rigorous
catholic sect the curriculum was heavy on theology
philosophy law and the arts but scientifically
They were still teaching Cartesian principles.
Cartesian as in Rene Descartes. I think therefore
I am. Yes. but also Descartes' physics. And this
is where it gets really sticky. In the early
18th century, France was still clinging to Descartes'
ideas about how the universe worked, specifically
the theory of vortices. Vortices. Vortices in
space. That's basically the idea. See, Descartes
couldn't get his head around gravity working
across empty space. He just hated the idea of
a force acting at a distance. It seemed like
magic to him. Okay. So he hypothesized that the
entire universe was filled with these invisible
particles swirling around in giant whirlpools
or vortices. And these swirling particles physically
pushed the planets around in their orbit. So
the planets are just like debris caught in a
cosmic drain. That's a pretty good way to put
it. Now, by the time d 'Alembert is in school,
Isaac Newton, over in England, has already published
his Principia. Newton has the math. He has universal
gravitation. It actually works. But the French
schools were stubborn. Incredibly stubborn. It
was a matter of national pride in a way. So they
were still teaching Descartes' innate ideas.
This notion that we are born knowing certain
truths in these swirling, invisible vortices.
D 'Alembert being the budding genius that he
is, he smells a rat. He scorned it. He absolutely
hated the curriculum. Later in life, he wrote
about how much he despised that education. He
called the theology he was forced to study unsubstantial
fodder. Unsubstantial fodder. I like that. He
was hungry for something concrete, something
provable. He wanted mathematical rigor, not swirling
invisible particles. It's a classic teenage rebellion,
isn't it? Yeah. But instead of sneaking out to
drink cheap wine, he's sneaking out to do calculus.
Essentially, yes. And the funny thing is... The
Jansenists actually recognized his brilliance.
They tried to recruit him. They really wanted
him to become a priest. They pushed him hard
toward theology. Wow. Imagine D 'Alembert as
a priest. That would have changed history a little
bit. He refused flat out. Said it was unsubstantial.
So then he pivoted. He went to law school for
a couple of years. He actually became an avocat,
a lawyer in 1738. But he was bored out of his
mind. So then he dabbled in medicine for a bit.
But he said he couldn't handle the imprecision
of it. It wasn't rigorous enough for him. He
sounds hard to please. He was. Finally, he just
couldn't deny it anymore. He fell completely
in love with mathematics. It was the only thing
that gave him the absolute certainty that he
craved. And somewhere during this transition,
he sort of of invents himself, right? He changes
his name. Yes. This is when he really forges
his own identity. He was enrolled in school under
the name Jean -Baptiste D 'Aremberg. But that
wasn't quite right. Eventually, he changed it
to d 'Alembert. Why d 'Alembert? Where did that
come from? The leading theory is simply euphony.
It just sounded better. It does have a ring to
it. Jean -Laurent d 'Alembert. It has a rhythm,
a certain dignity. It sounds like the name of
someone who is going to discover a theorem. It
really does. It sounds distinguished. So, OK,
he's rejected the priesthood. He's bored by law.
He's quit medicine and he's finally embracing
mathematics. He's living with his foster mom
who calls him an ass. How does he make his splash?
How does he get from, you know, obscurity to
the Academy of Sciences? He starts by punching
up way up. In 1739, he's 22 years old and he
sends a communication to the Académie de Science.
But he doesn't just send a polite introductory
letter. He points out a series of errors in a
standard, widely used mathematics textbook called
Analyse de Montreux by a man named Raynaud. That
is a power move. That's like a kid in college
emailing a publisher to say, hey, you know the
book everyone uses to learn math. It's wrong.
And here's why. It's incredibly confident, maybe
even bordering on arrogant. But the key is this.
He was right. And in the world of mathematics,
being right is the only currency that actually
matters. That got him noticed. I bet it did.
So the very next year, 1740, he submits a paper
on fluid mechanics, specifically on the refraction
of solid bodies. This work gets recognized by
Claro, who was a major mathematician of the time.
And this begins his big ascent. It does. It wasn't
overnight. He faced a few rejections along the
way. But in 1741, he was finally elected to the
Académie des Sciences. Later on, he'd be elected
to the Berlin Academy and become a fellow of
the Royal Society in London. He was networking
with the absolute best minds in Europe. OK, let's
unpack the science because we said this is a
deep dive and I really want to understand what
he actually did. He writes a book in 1743 called
the Touré de la Dynamique. The Treatise on Dynamics.
This is his masterpiece, right? It is. This is
the big one. And at the heart of it is what we
now call d 'Alembert's Principle. Okay, I've
read the Wikipedia summary of this, and I'll
be honest, my eyes glazed over. For those of
us who didn't spend 50 years studying calculus,
can you explain d 'Alembert's Principle? Why
is it such a big deal? Let's break it down. Think
about Isaac Newton. Newton gave us the fundamental
laws of motion, most famously five a dollar.
Force equals mass times acceleration. Right.
And that's great if you are calculating something
simple like how a planet moves through empty
space or a cannonball flying through the air.
Simple motion. But the real world is rarely that
simple. What if you have a system that is constrained
in some way? Constrained? What do you mean? Imagine
a bead sliding along a curved wire. Or a pendulum
swinging on a fixed rod. Or, maybe the best example,
a roller coaster car on a track. Okay, yeah,
I'm visualizing a roller coaster. The car can't
just go anywhere at once, it has to follow the
track. The track itself is exerting a force on
the car to keep it in line. Now, if you try to
calculate the motion of that car using just Newton's
simple Phamelotters, it gets really, really messy.
Because you have to constantly calculate the
force of the track pushing back against the car
at... every single millisecond, and that force
is always changing direction as the track curves
and dips. That sounds like a mathematical nightmare.
It was. It was a massive headache for physicists
and engineers. And this is where d 'Alembert
found a brilliant way around it. He realized
that you can just rewrite the equation. How?
Instead of FOMO, you can write $5 monics. Okay,
that looks like simple algebra. You just move
the mod to the other side of the equation. It
looks simple, but the conceptual shift is absolutely
profound. He introduced the idea of a new sh**.
forces, he said let's treat the acceleration
part, the ma, as if it were a force pushing back
against the motion. So he invented a fake force
to make the math work. A fictitious force, yes.
But by doing this, he converted a problem of
dynamics things moving and accelerating into
a problem of statics things in equilibrium, balanced.
Wait. So he turned a moving movie into a frozen
photograph so he could measure it more easily.
That is a perfect analogy, yes. He froze the
frame, mathematically speaking. By treating the
system as if it were in balance, the sum of the
real forces plus this new inertial force equals
zero, he could use the much simpler laws of statics,
a principle called virtual work, to solve these
incredibly complex problems. And it let him ignore
the messy parts. It allowed physicists to effectively
ignore the forces of constraint. like the track
pushing on the roller coaster car, and just focus
on the motion itself. That is fascinating. So
he basically hacked Newton's laws to make them
usable for complex machines and real -world systems?
Exactly. And this principle is still the foundation
of what we call analytical mechanics today. If
you study advanced physics or mechanical engineering,
you use something called the Lagrange equations,
which are directly derived from D 'Alembert's
work. It's fundamental. Okay, so that's the dynamics.
But he didn't stop there. He also did groundbreaking
work on something called the wave equation. Yes.
This is another massive, massive leap. D 'Alembert
was completely fascinated by vibrating strings,
like a violin string or a guitar string. Which
seems pretty simple, right? You pluck it, it
vibrates, wiggles back and forth. It seems simple
to our eyes, but mathematically, it's an absolute
beast. Think about it. A vibrating string is
changing in two ways at once. It changes in time
as it moves up and down, and it changes in space
because the curve of the string is different
at different points along its length. So you
have two variables changing at the same time.
Time, which we can call the dollar, and position
along the string, zix large. Exactly. And before
d 'Alembert, could they handle that? Not really.
Calculus was still young. They could handle functions
with one variable changing. d 'Alembert had to
essentially invent a new kind of math. to handle
both simultaneously. And that was... He developed
what we now call partial differential equations.
He was one of the very first to do it. And he
derived the formula, the equation that describes
how a wave propagates along that string. This
is the crazy looking thing with the curly leads.
Yeah. If I partial c do it, if I partial z do
it thing. That's the one. And what's so incredible
is that that equation doesn't just describe violin
strings. It describes sound waves moving through
the air, light waves, electromagnetic waves.
The mathematical object... in that equation,
the D 'Alembert operator, is absolutely critical
in modern theoretical physics, from acoustics
to quantum mechanics to special relativity. So
he basically gave us the language to talk about
how energy moves through space. In a very real
sense, yes. He wrote the grammar for waves. That
is just mind -blowing. So every time I hear a
sound or turn on a light, the fundamental physics
describing it goes back to this guy. Precisely.
But... And there's almost always a but with D
'Alembert. Sometimes his math was too perfect
for the real world. Are we talking about the
paradox now? We are. D 'Alembert's paradox. This
came about around 1752. I love a good paradox.
Lay it on me. Okay. So D 'Alembert was applying
his fancy new calculus to the flow of fluids.
liquids and gases he wanted to calculate the
drag force on an object moving through a fluid
like the wind resistance on a baseball or the
submarine moving through water exactly now to
make the math solvable with the tools he had
he had to make some simplifying assumptions he
assumed the fluid was ideal what does it mean
an ideal fluid It means it was inviscid. So it
had zero viscosity, no stickiness or internal
friction, and it was incompressible, meaning
its density never changes. So a perfect frictionless
fluid that doesn't really exist. Right. And when
he ran his equations for this ideal fluid equations,
which were, I should stress, mathematically flawless,
he proved that the total drag force on the object
would be zero. Zero. Zero. But, I mean, if I
stick my hand out of a moving car window, I feel
a lot of force. If I try to run through a swimming
pool, there's... definitely drag it's very much
not zero exactly that's the paradox his perfect
theory said there should be no resistance but
reality said there is a huge amount of resistance
he was stumped he famously scratched his head
and said he would have to leave the explanation
to future geometricians so was he stupid or was
his math just broken neither his math was correct
for the conditions he set the problem was that
a fluid with zero viscosity doesn't exist in
the real world He had idealized the problem so
much that he had idealized the answer right out
of existence. So what was he missing? He was
missing the effects of viscosity, especially
in a thin layer right next to the object surface,
what we call the boundary layer. That's where
all the friction happens. It took scientists
decades, really, until Ludwig Prandtl in the
early 20th century to fully figure out how to
mathematically account for that boundary layer
and resolve the paradox. It's so interesting
that he kept hitting this wall. where his beautiful
clean theory was just too clean for the messy
real world. That is a recurring theme with D
'Alembert. You're right. He loved the purity
of the logic. He was a Platonist in a way. He
loved the ideal form. But the world is dirty
and sticky and complicated. Speaking of dirty
and sticky, let's talk about politics. Let's
talk about the project that really defined the
entire era, the encyclopedia. The great project.
I mean, you cannot talk about the Enlightenment
without talking about the encyclopedia. For a
modern listener, the word encyclopedia just sounds
so boring. It sounds like that stack of dusty
books in the school library that nobody touches
anymore. But this wasn't just a reference book,
was it? Oh, no, not at all. It was a war machine.
It was a weapon disguised as a book. The encyclopedia,
edited by Denis Diderot and d 'Alembert, was
a revolutionary attempt to collect all human
knowledge, science, arts, crafts, history, and
present it all through the lens of reason. And
why was that so dangerous? Because up until that
point, knowledge was controlled by two entities,
the church and the monarchy. The church decided
what was true about the universe and God. The
king decided what was true about society and
politics. The encyclopedia came along and said,
no, we can figure this stuff out for ourselves
using logic, evidence and observation. It was
democratizing knowledge. Exactly. It was inherently
subversive. It was a direct challenge to the
authority of the throne and the altar. And D
'Alembert wasn't just some random contributor.
He was the co -pilot of this whole thing. He
was Diderot's right hand man. Diderot was the
visionary. He handled the arts, literature and
the philosophy. big picture. Dale and Bear was
the science guy. He was in charge of all the
articles on mathematics and physics. And that
is a huge responsibility. It was absolutely monumental.
He personally wrote over a thousand articles
for it. A thousand. Can you imagine the workload?
But his most famous and probably most important
contribution was the preliminary discourse. This
is the big introduction to the entire 35 volume
set. It's so much more than an introduction.
It's a manifesto for the Enlightenment. In it,
he mapped out this tree of knowledge showing
how all human knowledge is interconnected, growing
from the trunk of reason. It celebrated the progress
of the human mind. It was a declaration of intellectual
independence. But doing this kind of project
came with some very real risks. Diderot actually
went to prison for his writing, didn't he? He
did. He spent time locked up in the dungeons
of Vincennes. D 'Alembert managed to stay out
of jail, mostly because he was a bit more cautious,
a bit less confrontational than Diderot. But
the pressure was immense. The state censors were
constantly breathing down their necks. The Jesuits
were attacking them in pamphlets. And amidst
all this pressure, D 'Alembert undergoes a kind
of philosophical shift. He started out as a fairly
straightforward materialist, you know, believing
in just matter and motion. But he changed his
views. He did. I think working on these deep
philosophical questions forced him to question
the nature of reality itself. He moved from that
simple materialism toward a much more nuanced
position of skepticism and idealism. What does
that mean exactly? He famously wrote that he
doubted whether there exists outside us. anything
corresponding to what we suppose we see. Wait,
that's very, that's very Matrix. He's questioning
if the physical world is actually real. He is.
He's aligning himself with philosophers like
George Berkeley, and in many ways he's anticipating
Immanuel Kant. He's basically saying, look, all
we have is our perception of the world through
our senses, but we can't be 100 % certain that
the world is exactly as we perceive it. It's
a very sophisticated and I think humble position
for a top scientist to take. He's admitting the
limits of human perception. But his humility
didn't save him from controversy. We have to
talk about the Geneva incident. This seems to
be the moment where he really, really stumbled.
The Geneva controversy of 1757. Yes, this was
the beginning of the end for his involvement
with the encyclopedia. So what happened? So d
'Alembert writes an article for the seventh volume
about the city of Geneva. Now, Geneva at the
time was the international center of Calvinism,
very strict, rigorous Protestantism. The city
of Calvin. And in his article, D 'Alembert decides
he's going to compliment the clergymen of Geneva.
That sounds nice enough. Yeah. Hey, you guys
in Geneva are doing a great job. Well, it depends
on how you compliment them. He praised them for
being so enlightened and rational that they had
moved away from strict dogmatic Calvinism and
toward pure Socinianism. I have no idea what
Socinianism is, but I'm guessing the clergymen
did not take that as a compliment. Socinianism
is a specific Christian heresy. It denies the
doctrine. of the Trinity. It denies the divinity
of Christ. It basically says that Jesus was a
great moral teacher, but he wasn't God. Oh, oh
no. Exactly. D 'Alembert was essentially announcing
to the entire world, hey, these pastors in Geneva
are so smart, they don't even really believe
in Christianity anymore. They're basically deists,
like us enlightened philosophers. That is, wow.
He outed them as heretics in the most famous
and controversial book in Europe. It was an absolute
disaster. The pastors of Geneva were furious.
They were being accused of abandoning their faith
in public. It caused an international diplomatic
incident. Where did D 'Alembert even get this
idea? Did he just make it up? No, and that's
the real kicker. He got the information from
Voltaire. Voltaire. The satirist. The one and
only. Voltaire lived near Geneva at the time,
and he loved to stir the pot. He almost certainly
fed D 'Alembert this juicy insight. Oh yes, my
dear D 'Alembert, the pastors here are practically
atheists. You must put that in your book. Knowing
full well it would cause a massive firestorm.
But D 'Alembert got trolled by Voltaire. In a
huge way. The backlash was severe. Jean -Jacques
Rousseau, who is from Geneva and very proud of
it, publicly attacked D 'Alembert for slandering
his hometown. There were committees appointed
to answer the charges. D 'Alembert tried to backtrack.
He tried to excuse himself by saying he just
meant they didn't accept the authority of the
pope in Rome, but the damage was done. And the
stress just got to him. It did. He was tired
of the constant fighting. He was tired of the
threats of censorship. He was, I think, fundamentally
a more timid person than Diderot. He resigned
from his editorship of the Encyclopedia. He just
walked away. And left Diderot to finish the whole
project alone. Pretty much. He went back to a
safe place. He went back to his math. But he
didn't stop trying to apply that math to other
fields. Which brings us to a field where he really
ruffled some feathers. Music. Oh, yes. I love
this part of his story. Because we think of music
as art, as emotion, as soul. But de Lambert looked
at a violin and saw a calculus problem. He really
did. He was absolutely convinced that since sound
is just vibration and vibration is physics and
physics is described by math, then music must
be a branch of mathematics. It was that simple
to him. But at first he found a partner in this
line of thinking, the composer Jean -Philippe
Rameau. Rameau is a giant. He's the back of France,
basically, the most important French composer
of the 18th century. And what was the connection?
Well, Rameau had written his own highly influential
treatise on harmony that was very theoretical.
He was trying to explain why certain chords sound
good together using the physics of overtones
and harmonic series. d 'Alembert read it in 1749,
and he loved it. He praised Rameau's deductive
character. He saw a kindred spirit, someone else
who was trying to systematize art and find its
rational principles. If they were friends. At
first, yes. In 1752, d 'Alembert even wrote his
own book, Elements de Musique. which was an attempt
to summarize and simplify Rameau's complex theories
for the general public. He wanted to be Rameau's
popularizer. That sounds helpful. Here, let me
translate this genius work for the common man.
It was certainly meant to be, but here's the
problem. d 'Alembert wasn't a musician. He was
a mathematician. So when he encountered parts
of Rameau's theory that were a bit messy or complex
or relied on the musician's ear rather than pure
numbers, he, well, he fixed them. He fixed the
music theory. Without being a musician. He changed
certain concepts to make them fit his neat mathematical
equations better. He argued that Rameau's core
idea of the core sonore, the sounding body, wasn't
sufficient to explain everything. He tried to
impose a logical structure that the music itself
didn't necessarily support. I can just imagine
how Rameau felt about that. Thanks for explaining
my life's work to everyone, but you changed all
the important parts and you don't even play the
harpsichord. Romo was absolutely furious. He
felt d 'Alembert had completely misconstrued
the finer points. Plus, Romo was already angry
about the articles on music that Rousseau was
writing for the Encyclopédie, which he also thought
were nonsense. He felt surrounded by these philosophers
who couldn't compose a simple tune, but wanted
to tell him how music worked. So he turned on
d 'Alembert. Viciously. They had a series of
bitter public exchanges in the press. The friendship
was completely over. And it really reveals D
'Alembert's intellectual arrogance, doesn't it?
It does. He had this very Baroque bias. He believed
that the modern music of his own time was the
pinnacle of perfection. He actually argued that
the music of the ancients, the Greeks and Romans,
was worthless. Worthless. The foundation of Western
music. He claimed that because we don't have
their sheet music and because time had destroyed
their models, there was nothing to look back
to. He just dismissed the entire history of music
before his own era as irrelevant. That's an incredibly
harsh take. And it gets worse. He also claimed
that music couldn't imitate reality as well as
painting or poetry because musicians simply lacked
inventiveness. Wow. He really looked down on
the artist, didn't he? He valued the structure
of the music, the math of the frequencies, far
more than he valued the creative act of the musician.
It's a classic case of a specialist in one field
math trying to force another field music to play
by his own rigid rules. Speaking of forcing things
to play by rules, we absolutely have to talk
about the gambling. The gambler's fallacy. This
is one of the most famous things associated with
his name, but for all the wrong reasons. Yes.
It appears in his work, Quote We Peeler. which
means head or tail. So lay out the d 'Alembert
system for us. What was his big wrong idea? D
'Alembert argued quite seriously that if you
flip a coin and it comes up tails, the probability
of it landing on heads for the next flip actually
increases. Okay, stop right there. I have to
push back here. This is the man who invented
partial differential equations. He understands
calculus better than almost anyone alive at the
time. How on earth does he not understand that
a corn doesn't have a memory? Is he just being
stupid or are we missing something? It's not
stupidity. It's a philosophical blind spot. He
believed in what he called a maturity of chances.
He had this deep -seated feeling that nature,
or the universe, prefers balance. If there's
an excess of tails, he thought nature must provide
a head soon to balance the cosmic scales. But
that feels so intuitive. If I'm at a roulette
wheel and it lands on red ten times in a row,
every single bone in my body screams black as
dew. And that is exactly why casinos are rich
and gamblers are not. Because the roulette ball
doesn't know where it landed on the last spin.
The odds are 50 -50 or slightly less because
of the green zero every single time. They are
independent events. But d 'Alembert, the great
mathematician, he defended this fallacy. He did.
He argued passionately against the conventional
probability theory that had been developed by
Pascal and Fermat. And this mistaken belief led
directly to the betting system that still bears
his name, the Martingale system or d 'Alembert
system. How did the system work? The idea is
simple. Every time you lose a bet, you increase
your next spread, usually by doubling it. Why?
Because you believe you are due for a win. And
when that inevitable win finally comes, it will
be large enough to cover all your previous losses
plus a small profit. Then, if you win, you go
back to your original smaller bet. I mean, on
paper, if you have to win eventually, you'll
make your money back. On paper, with an infinite
amount of money and no table limits, yes, it
works. But in the real world, two things happen.
One, you hit a losing streak that is so long
you simply run out of money to double your bet
again. Or two. Or two, you hit the table limit.
The casino literally has a rule that says you
cannot bet more than a certain amount precisely
to stop systems like this. And then you lose
everything. You lose everything. Exponential
growth is a scary thing when it's working against
you. If you start with a $10 bet and you lose
just 10 times in a row, your 11th bet has to
be over $10 ,000. Ouch. The fact that d 'Alembert,
the man of pure reason, the man who scorned imprecision,
defended this system just shows that even in
the age of reason, human intuition is a powerful
and often misleading drug. He wanted the universe
to be fair and balanced, even when it's just
random. I find it so incredibly humanizing. He's
calculating the drag of fluids in an ideal frictionless
space, but he can't figure out a simple coin
toss. It makes him feel like a real person, not
just a historical figure. It does. And that brings
us to his personal life. He wasn't just a brain
in a jar. He was a socialite. He was a regular
in the Parisian salons. the great salons of Marie
-Thérèse Rodegefant and the Marquise du Deform.
These were the intellectual and social hubs of
Paris. You have to picture a living room filled
with the smartest, most influential people in
Europe. Writers, scientists, diplomats, aristocrats,
all drinking coffee, arguing about God and the
king, and of course, gossiping. And this is where
he met Julie de Lisbonasse. His great love story.
Julie was the paid companion, or reader, to the
Marquise du Défense. She was brilliant, she was
charming, she was witty, and d 'Alembert was
completely smitten. And it wasn't just a passing
crush, was it? It became a very serious partnership.
It did. When Julie had a major falling out with
the Marquise, marquees and was essentially kicked
out onto the street, D 'Alembert did something
very scandalous for the time. He moved in with
her. In the 18th century, an unmarried man and
woman living together. That's incredibly bold.
It was, but he didn't seem to care about the
gossip. He nursed her through a terrible bout
of smallpox. He was completely devoted to her.
They lived together until her death in 1776.
Did they ever marry? No, they never did. But
the bond was undeniable. Her death absolutely
devastated him. He spent the last years of his
life in a deep gloom, living in a small apartment
at the Louvre. At the Louvre. The museum. Yes,
because as the perpetual secretary of the Académie
Française, he was given official rooms there.
And Diderot, his old partner, even wrote a fictional
version of him, right? Le Rêve de D 'Alembert
or Alambert's Dream. Yes, although that was written
after Diderot and d 'Alembert had drifted apart.
Yeah. In the story, d 'Alembert is sick in bed,
muttering philosophy in his sleep. Diderot uses
the character of d 'Alembert to explore these
really radical materialist ideas, ideas that
the real d 'Alembert had arguably moved away
from by that point. And a fascinating literary
caricature. It is, and it shows how iconic he
had become. He was a character in other people's
fiction now. So we have the math, the music,
the love, the controversy. How does it all end
for him? He died in October of 1783 at the age
of 65. He had suffered from a urinary bladder
illness for years, most likely bladder stones.
It was, by all accounts, a very painful end.
And what about the burial? Was he honored as
a great mind of France? This is the final insult,
and it really brings us full circle back to his
birth. Because he was a known unbeliever, an
agnostic or a deist who had angered the church
his whole life with his writings, he was refused
a Christian burial. Just like Voltaire had been
a few years earlier. Exactly. The church did
not forgive. He was buried in a common, unmarked
grave in the Saint -Jean -Laurent district, ironically,
right near the church where he was first found
as a baby. The man who helped to find the Enlightenment,
buried in a pit with no name. Just like he was
found on the steps with no name. That is, it's
poetic and it's terrible at the same time. But
his legacy couldn't be buried. You can refuse
him a tombstone, but you can't erase the mathematics.
We still have the Delamere -Gauss theorem, which
you may know as the fundamental theorem of algebra.
We have the ratio test for determining if an
infinite series converges. We have the d 'Alembert
operator in physics. And there's even an island
named after him, isn't there? There is. Île d
'Alembert in South Australia, named by the French
explorer Nicolas Baudin. And what about the moon
of Venus? Or, almost. Ah, yes. The final great
anecdote. Frederick the Great of Prussia, who
was a huge admirer of d 'Alembert, he tried to
hire him to run the Berlin Academy many times,
proposed naming a suspected moon a Venus d 'Alembert.
A moon of Venus. But Venus doesn't have a moon.
We know that now. But back in the 18th century,
some astronomers thought they saw one. It was
a recurring observation, probably an optical
illusion or a distant star. And d 'Alembert was
offered the honor of having it named for him.
He was, and he turned it down. Maybe it was modesty.
Perhaps he knew the sighting was dubious. He
was a skeptic to his core, remember? Or maybe
he just didn't need his name in the sky to know
that he mattered. And it's a good thing he refused,
because the moon, of course, turned out not to
exist at all. That was a smart move. You definitely
don't want to be the namesake of a cosmic mistake.
Indeed. So, let's wrap all this up. What does
it all mean? When we look at this incredible
life, the foundling on the church steps, the
Glacier's foster son, the academic superstar,
the encyclopedist, what's the final takeaway?
For me, he was the ultimate connector. He tried
to connect physics to math, math to music, and
philosophy to the general public through the
encyclopedia. He truly believed that the world
was understandable, that it was rational. He
believed that if you just thought hard enough,
you could write an equation for everything, from
the drag of water on a ship to the melody of
a flute. Even if he sometimes had to oversimplify
the world to make it fit into his neat equations.
He had the courage to try. He lived in a time
of chaos and superstition and authority, and
he tried to build a scaffold of reason for people
to climb on. I just keep coming back to that
quote from his foster mother. You will never
be anything but a philosopher. And what is that
but an ass who plagues himself all his life?
That he may be talked about after he is dead.
She was wrong. He wasn't plaguing himself for
nothing. He was building the foundation of the
modern world. Every engineer calculating the
stress on a bridge, every physicist studying
wave mechanics, every single person who looks
up a fact in an encyclopedia, they are all standing
on his shoulders, whether they know it or not.
So here's my final question for you, listening
to this right now. We live in an age of incredible
information overload, maybe even more so than
the readers of the Encyclopedia did. And we have
specialists for everything. We have people who
spend their entire lives studying just one protein
or one type of coding language. But do we have
enough Dellen Bears? Do we have enough people
who are brave enough or maybe arrogant enough
to try to synthesize it all, to try to understand
music and fluid dynamics and philosophy? Even
if they get the coin flip wrong occasionally.
Exactly. Is the risk of being spectacularly wrong
in one field worth the attempt to try and understand
everything? I think D 'Alembert would say yes.
And looking back at his life, I have to say I
think he's right. Thanks for diving deep with
us today. It's been a real pleasure. We'll see
you next time.