Nietzsche said life repeats itself an infinite number of times.
Poincaré almost proved him right with a single theorem.
Imagine that one late night,
a demon creeps into your loneliest corner
and says to you: 'This life you are living,
you must live it again,
and again in infinite cycles.'
Nothing will be new.
Every pain, every thought, every sigh,
even this very second as you stare at this screen,
will all return in exactly the same sequence,
over and over again.
Hearing these words,
would you collapse to the ground,
gnashing your teeth and cursing the demon,
or would you answer him: 'Excellent,
let's do it again'?
These are Nietzsche's words.
And just eight years after he wrote them,
a French mathematician used a cold physical theorem
to come within a hair's breadth
of proving the demon's prophecy.
Hello,
everyone.
I am Wang Lijie.
The theorem we're discussing today
is called the Poincaré Recurrence Theorem.
It sounds very academic,
but what it asks
is actually an ancient and terrifying question: Will the world
ever repeat itself exactly as it is?
Let's clarify the mathematician's side of the story first.
In 1890,
while studying celestial motion, Henri Poincaré
proved a conclusion.
In plain English, it goes like this:
As long as a system meets two conditions,
then after a long enough period of time,
it will definitely return to a state
nearly identical to its initial one.
Note that
it's 'definitely,'
not 'possibly.'
What are the two conditions?
First,
the system is closed.
Energy is conserved;
it cannot escape.
Particles are confined in a finite space
and won't fly off to infinity.
Second,
its evolution neither increases nor decreases.
Physicists call this volume-preserving.
You don't need to worry about the terminology.
Just remember,
it's like a closed, finite box with no energy loss.
If these two conditions are met,
everything inside this box,
no matter how complex the current arrangement,
or how unique it seems,
will, if you wait long enough,
eventually return to its state today.
Let me give you a simple analogy.
Suppose you shuffle a deck of cards.
The 52 cards are arranged in a specific order.
Does that order seem unique and gone forever?
But in fact,
the ways 52 cards can be arranged,
though numerous,
is a finite number.
As long as you keep shuffling,
until the end of time,
that original order
will theoretically reappear.
It's not that it might appear;
mathematics guarantees it will.
Imagine another scene.
You open a bottle of perfume,
and the scent slowly diffuses throughout the room.
Common sense tells us
Once these perfume molecules disperse,
they can never return to the bottle on their own.
But Poincaré said,
"That's not right."
If this room is completely sealed,
then after an extremely long period of time,
these molecules, through their random collisions,
will by chance all gather back at the mouth of the bottle.
It must happen.
Hearing this,
you might feel a bit unsettled,
because it directly conflicts with another ironclad rule
we've been taught since childhood.
That rule is the Second Law of Thermodynamics,
which is about entropy increase.
Everything moves from order to chaos.
Spilled water cannot be gathered back;
a broken mirror cannot be mended.
The arrow of time flies in only one direction,
never to return.
Poincaré's theorem says: "Wait."
The arrow has flown out,
but if you wait long enough,
it will fly back on its own.
This contradiction
ignited a massive academic war in 1896.
A young mathematician at the time
named Zermelo
took Poincaré's theorem
and used it like a knife
to stab the defender of the Second Law: Boltzmann.
Zermelo said, "Look,
since a closed system must return to its initial state,
entropy cannot increase forever.
It must eventually decrease back."
"So your law of entropy increase
is not an absolute truth at all."
It was a precise and brutal strike.
How did Boltzmann respond?
Boltzmann didn't deny that Poincaré was right.
He admitted
that systems do indeed recur,
but he immediately countered Zermelo with a calculation.
He said,
"You're right.
It will return."
"But do you know how long you'd wait for it to happen once?"
This waiting time
was later named by physicists
as the 'Poincaré Recurrence Time.'
And how long is this time?
For the air molecules in a room
to all gather in a corner once,
the time required
far exceeds the current age of our entire universe.
Not just by a little,
but to an extent you simply cannot imagine.
Later physicists made even more extreme estimates.
If we treat the entire observable universe
as a closed box,
for it to recur to this exact state once,
the wait would be roughly 10 to the power of 10
to the power of 123 years.
I can't even read this number out loud,
because it's too big to even write down.
It's not a trillion years,
nor is it a trillion-trillion years.
It is a stacked tower of exponents
so vast that the age of the universe
doesn't even count as a speck of dust in comparison.
Boltzmann's point was: "Brother,
your recurrence is mathematically correct,
but physically,
it's equivalent to never happening."
You won't see it in your lifetime,
nor will the solar system,
nor will the entire universe,
even after it burns to ashes.
In this battle,
Boltzmann won with an astronomical number.
Poincaré recurrence was shelved,
becoming a mathematically correct but useless theorem.
At this point,
the story seems to end—
a mathematical truth that would never be fulfilled in reality.
But,
this episode isn't just about physics.
We need to return to that demon at the beginning,
back to Nietzsche.
Nietzsche wrote down the idea of Eternal Recurrence
in 1882,
eight whole years before Poincaré's theorem.
He wasn't a physicist;
he had no Phase Space,
no Liouville's theorem.
He relied on pure philosophical deduction:
If the matter that makes up the world is finite,
if energy is neither created nor destroyed,
and if time is infinite,
then finite states being reshuffled over infinite time
must inevitably repeat.
Everything will return—
including you,
including this moment.
You see,
Nietzsche and Poincaré,
one using the language of poetry,
the other the language of mathematics,
at nearly the same time,
from two completely different directions,
stumbled upon the same stone.
But what Nietzsche really wanted to ask
was never whether the universe would actually repeat.
He asked: If it really did repeat,
could you endure it?
This is what he called the 'Heaviest Burden.'
For Nietzsche, Eternal Recurrence
was not an astronomical prediction,
but a touchstone weighing on your chest.
He forces you to see clearly: this day you are living now,
if you were forced to live it forever, exactly as it is,
would you despair,
or would you be grateful?
If the thought of living today 10,000 more times sickens you,
then you aren't living it right.
Only if you can calmly say 'once more'
can it be said you have truly lived this day.
Speaking of this,
I want to add another twist to this ancient proposition,
one that this channel cares about most.
This twist
is about consciousness.
I want to ask a question neither Nietzsche nor Poincaré explored:
The 'you' in that repetition—
would you know you are repeating?
The answer is:
No.
Think about it.
The condition for Poincaré recurrence is returning to nearly the exact same state.
And your memory,
every thought in your head at this moment,
is itself part of that system's state.
When the universe returns to this exact frame,
your memory is reset along with it.
The 'you' that repeats
won't have an extra record in your head saying 'this is the second time'
or 'this is the 10,000th time.'
This leads to a very curious conclusion:
If this life repeats infinite times,
and each time you have no knowledge of what happened before,
then experientially,
infinite times and only once
are completely indistinguishable.
You can only ever live in your 'one' time.
Infinite recurrences,
viewed from within yourself,
is just this one clean, single experience of the 'now.'
And that's not even the most dizzying part.
Taking another step beyond Boltzmann's astronomical number,
later physicists thought of an even more terrifying possibility.
They call it the Boltzmann Brain.
Their logic follows: if the universe truly fluctuates infinitely,
then over an unimaginably long timescale,
the random fluctuation of an entire orderly universe
would be extremely, extremely rare.
In contrast,
the random fluctuation of a single, solitary brain,
complete with a full set of false memories and thoughts,
would be much easier to occur,
and much more common.
In other words,
out of all the conscious beings that might arise,
the vast majority are not people living in a real universe,
but brains that popped out of nowhere,
only to exist for a split second before vanishing.
They believe they had a childhood,
possess a story,
and have a very recent past,
but all of that was packed in during the fluctuation,
and never actually happened.
What's so terrifying about this inference?
It points the finger directly at you.
You are sitting here right now,
feeling like you've lived for decades,
with clear, vivid memories.
But how can you be sure
that you aren't one of those brains that just fluctuated into existence,
pre-loaded with a full set of memories?
Could your so-called past
just be a packet of data stuffed into your mind this very second?
Do you see it?
This is actually the same specter
as the "recurring you" we discussed earlier.
The recurring you doesn't know they've recurred
because their memory was reset.
The Boltzmann Brain thinks it has lived
because its memory was forged.
Both point to the same cold truth: memory
cannot be used as evidence that you have truly lived.
We have always believed
that who I am and where I come from
is supported by memory.
But it turns out memory
is the most unreliable pillar in the world.
So you see,
after going in such a huge circle,
from Poincaré's theorem
to Boltzmann's astronomical numbers,
to Nietzsche's demon,
we finally land back on
just two words: the present.
Whether or not the universe repeats,
or if that recurrence time of 10 to the power of 100-plus years ever finishes,
actually has nothing to do with you.
Because the only thing you can grasp, experience, or change
is always the single frame right in front of you.
So,
within this single frame,
what can you actually change?
Friends familiar with our channel know
that I love using two analogies to understand spiritual practice.
One is comparing the "seeds" in Buddhist Yogacara
to the parameters in an AI Large Language Model.
The other is comparing "awareness"
to "observation" in quantum mechanics.
Today's topic of Eternal Recurrence
happens to tie these two analogies together.
The initial state described by Poincaré recurrence,
the setting that makes the universe keep returning,
can be understood as the underlying code of the universe.
This set of code
is something you cannot change.
You can't change the laws of physics,
you can't change the era you were born in,
and you can't change the past that has already happened.
From this perspective,
humans are indeed pushed forward
by a pre-written program,
on autopilot,
frame by frame.
But
what you can modify
are the parameters of your own internal model.
Every time you truly become aware of yourself—
aware of a rising thought,
aware of an emotion taking you over,
aware that you are falling once again into that familiar,
auto-playing reaction—at the moment that awareness occurs,
you are no longer just an actor pushed by a script.
You become the person observing yourself.
And the very act of observing
is quietly rewriting your parameters.
This is why I say
awareness is much like observation in quantum mechanics.
When you are unaware,
your reaction patterns exist like a superposition,
running automatically based on default probabilities.
When someone says something harsh to you,
anger automatically flares up.
Precise,
exactly like yesterday,
exactly like every one of those ten thousand repetitions.
But when you begin to observe this anger,
this observation of yours
intervenes in its collapse.
The direction it takes
begins to change.
So, at its deepest level,
the idea of Eternal Recurrence
isn't meant to scare you with an infinite future.
It is a reminder: since this moment is all you can experience,
and since even memory won't cross that threshold of return—then this frame,
will you let it play out automatically in a daze,
or will you, with full clarity,
live through it yourself?
You cannot change the universe's script,
but within this automatically repeating script,
you can manually fine-tune your own current frame.
Once this frame is corrected,
even if you fall back into autopilot later,
the direction your model is heading
has already quietly shifted.
When that demon in the dead of night asks if you'd live it all again,
he is actually asking the wrong question.
You don't need to answer for an infinite future;
you only need to answer for this one moment—are you
awake?
I am Wang Lijie.
See you next time.