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Nietzsche said life repeats itself an infinite number of times.

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Poincaré almost proved him right with a single theorem.

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Imagine that one late night,

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a demon creeps into your loneliest corner

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and says to you: 'This life you are living,

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you must live it again,

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and again in infinite cycles.'

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Nothing will be new.

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Every pain, every thought, every sigh,

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even this very second as you stare at this screen,

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will all return in exactly the same sequence,

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over and over again.

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Hearing these words,

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would you collapse to the ground,

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gnashing your teeth and cursing the demon,

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or would you answer him: 'Excellent,

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let's do it again'?

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These are Nietzsche's words.

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And just eight years after he wrote them,

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a French mathematician used a cold physical theorem

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to come within a hair's breadth

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of proving the demon's prophecy.

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Hello,

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everyone.

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I am Wang Lijie.

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The theorem we're discussing today

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is called the Poincaré Recurrence Theorem.

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It sounds very academic,

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but what it asks

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is actually an ancient and terrifying question: Will the world

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ever repeat itself exactly as it is?

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Let's clarify the mathematician's side of the story first.

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In 1890,

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while studying celestial motion, Henri Poincaré

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proved a conclusion.

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In plain English, it goes like this:

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As long as a system meets two conditions,

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then after a long enough period of time,

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it will definitely return to a state

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nearly identical to its initial one.

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Note that

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it's 'definitely,'

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not 'possibly.'

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What are the two conditions?

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First,

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the system is closed.

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Energy is conserved;

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it cannot escape.

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Particles are confined in a finite space

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and won't fly off to infinity.

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Second,

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its evolution neither increases nor decreases.

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Physicists call this volume-preserving.

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You don't need to worry about the terminology.

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Just remember,

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it's like a closed, finite box with no energy loss.

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If these two conditions are met,

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everything inside this box,

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no matter how complex the current arrangement,

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or how unique it seems,

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will, if you wait long enough,

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eventually return to its state today.

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Let me give you a simple analogy.

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Suppose you shuffle a deck of cards.

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The 52 cards are arranged in a specific order.

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Does that order seem unique and gone forever?

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But in fact,

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the ways 52 cards can be arranged,

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though numerous,

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is a finite number.

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As long as you keep shuffling,

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until the end of time,

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that original order

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will theoretically reappear.

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It's not that it might appear;

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mathematics guarantees it will.

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Imagine another scene.

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You open a bottle of perfume,

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and the scent slowly diffuses throughout the room.

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Common sense tells us

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Once these perfume molecules disperse,

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they can never return to the bottle on their own.

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But Poincaré said,

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"That's not right."

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If this room is completely sealed,

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then after an extremely long period of time,

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these molecules, through their random collisions,

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will by chance all gather back at the mouth of the bottle.

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It must happen.

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Hearing this,

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you might feel a bit unsettled,

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because it directly conflicts with another ironclad rule

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we've been taught since childhood.

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That rule is the Second Law of Thermodynamics,

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which is about entropy increase.

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Everything moves from order to chaos.

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Spilled water cannot be gathered back;

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a broken mirror cannot be mended.

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The arrow of time flies in only one direction,

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never to return.

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Poincaré's theorem says: "Wait."

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The arrow has flown out,

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but if you wait long enough,

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it will fly back on its own.

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This contradiction

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ignited a massive academic war in 1896.

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A young mathematician at the time

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named Zermelo

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took Poincaré's theorem

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and used it like a knife

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to stab the defender of the Second Law: Boltzmann.

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Zermelo said, "Look,

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since a closed system must return to its initial state,

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entropy cannot increase forever.

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It must eventually decrease back."

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"So your law of entropy increase

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is not an absolute truth at all."

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It was a precise and brutal strike.

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How did Boltzmann respond?

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Boltzmann didn't deny that Poincaré was right.

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He admitted

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that systems do indeed recur,

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but he immediately countered Zermelo with a calculation.

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He said,

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"You're right.

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It will return."

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"But do you know how long you'd wait for it to happen once?"

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This waiting time

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was later named by physicists

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as the 'Poincaré Recurrence Time.'

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And how long is this time?

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For the air molecules in a room

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to all gather in a corner once,

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the time required

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far exceeds the current age of our entire universe.

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Not just by a little,

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but to an extent you simply cannot imagine.

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Later physicists made even more extreme estimates.

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If we treat the entire observable universe

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as a closed box,

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for it to recur to this exact state once,

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the wait would be roughly 10 to the power of 10

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to the power of 123 years.

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I can't even read this number out loud,

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because it's too big to even write down.

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It's not a trillion years,

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nor is it a trillion-trillion years.

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It is a stacked tower of exponents

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so vast that the age of the universe

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doesn't even count as a speck of dust in comparison.

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Boltzmann's point was: "Brother,

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your recurrence is mathematically correct,

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but physically,

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it's equivalent to never happening."

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You won't see it in your lifetime,

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nor will the solar system,

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nor will the entire universe,

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even after it burns to ashes.

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In this battle,

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Boltzmann won with an astronomical number.

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Poincaré recurrence was shelved,

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becoming a mathematically correct but useless theorem.

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At this point,

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the story seems to end—

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a mathematical truth that would never be fulfilled in reality.

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But,

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this episode isn't just about physics.

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We need to return to that demon at the beginning,

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back to Nietzsche.

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Nietzsche wrote down the idea of Eternal Recurrence

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in 1882,

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eight whole years before Poincaré's theorem.

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He wasn't a physicist;

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he had no Phase Space,

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no Liouville's theorem.

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He relied on pure philosophical deduction:

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If the matter that makes up the world is finite,

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if energy is neither created nor destroyed,

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and if time is infinite,

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then finite states being reshuffled over infinite time

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must inevitably repeat.

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Everything will return—

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including you,

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including this moment.

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You see,

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Nietzsche and Poincaré,

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one using the language of poetry,

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the other the language of mathematics,

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at nearly the same time,

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from two completely different directions,

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stumbled upon the same stone.

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But what Nietzsche really wanted to ask

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was never whether the universe would actually repeat.

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He asked: If it really did repeat,

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could you endure it?

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This is what he called the 'Heaviest Burden.'

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For Nietzsche, Eternal Recurrence

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was not an astronomical prediction,

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but a touchstone weighing on your chest.

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He forces you to see clearly: this day you are living now,

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if you were forced to live it forever, exactly as it is,

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would you despair,

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or would you be grateful?

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If the thought of living today 10,000 more times sickens you,

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then you aren't living it right.

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Only if you can calmly say 'once more'

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can it be said you have truly lived this day.

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Speaking of this,

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I want to add another twist to this ancient proposition,

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one that this channel cares about most.

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This twist

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is about consciousness.

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I want to ask a question neither Nietzsche nor Poincaré explored:

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The 'you' in that repetition—

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would you know you are repeating?

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The answer is:

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No.

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Think about it.

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The condition for Poincaré recurrence is returning to nearly the exact same state.

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And your memory,

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every thought in your head at this moment,

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is itself part of that system's state.

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When the universe returns to this exact frame,

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your memory is reset along with it.

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The 'you' that repeats

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won't have an extra record in your head saying 'this is the second time'

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or 'this is the 10,000th time.'

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This leads to a very curious conclusion:

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If this life repeats infinite times,

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and each time you have no knowledge of what happened before,

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then experientially,

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infinite times and only once

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are completely indistinguishable.

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You can only ever live in your 'one' time.

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Infinite recurrences,

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viewed from within yourself,

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is just this one clean, single experience of the 'now.'

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And that's not even the most dizzying part.

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Taking another step beyond Boltzmann's astronomical number,

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later physicists thought of an even more terrifying possibility.

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They call it the Boltzmann Brain.

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Their logic follows: if the universe truly fluctuates infinitely,

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then over an unimaginably long timescale,

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the random fluctuation of an entire orderly universe

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would be extremely, extremely rare.

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In contrast,

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the random fluctuation of a single, solitary brain,

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complete with a full set of false memories and thoughts,

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would be much easier to occur,

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and much more common.

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In other words,

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out of all the conscious beings that might arise,

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the vast majority are not people living in a real universe,

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but brains that popped out of nowhere,

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only to exist for a split second before vanishing.

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They believe they had a childhood,

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possess a story,

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and have a very recent past,

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but all of that was packed in during the fluctuation,

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and never actually happened.

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What's so terrifying about this inference?

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It points the finger directly at you.

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You are sitting here right now,

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feeling like you've lived for decades,

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with clear, vivid memories.

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But how can you be sure

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that you aren't one of those brains that just fluctuated into existence,

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pre-loaded with a full set of memories?

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Could your so-called past

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just be a packet of data stuffed into your mind this very second?

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Do you see it?

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This is actually the same specter

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as the "recurring you" we discussed earlier.

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The recurring you doesn't know they've recurred

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because their memory was reset.

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The Boltzmann Brain thinks it has lived

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because its memory was forged.

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Both point to the same cold truth: memory

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cannot be used as evidence that you have truly lived.

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We have always believed

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that who I am and where I come from

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is supported by memory.

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But it turns out memory

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is the most unreliable pillar in the world.

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So you see,

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after going in such a huge circle,

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from Poincaré's theorem

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to Boltzmann's astronomical numbers,

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to Nietzsche's demon,

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we finally land back on

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just two words: the present.

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Whether or not the universe repeats,

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or if that recurrence time of 10 to the power of 100-plus years ever finishes,

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actually has nothing to do with you.

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Because the only thing you can grasp, experience, or change

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is always the single frame right in front of you.

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So,

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within this single frame,

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what can you actually change?

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Friends familiar with our channel know

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that I love using two analogies to understand spiritual practice.

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One is comparing the "seeds" in Buddhist Yogacara

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to the parameters in an AI Large Language Model.

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The other is comparing "awareness"

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to "observation" in quantum mechanics.

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Today's topic of Eternal Recurrence

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happens to tie these two analogies together.

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The initial state described by Poincaré recurrence,

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the setting that makes the universe keep returning,

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can be understood as the underlying code of the universe.

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This set of code

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is something you cannot change.

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You can't change the laws of physics,

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you can't change the era you were born in,

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and you can't change the past that has already happened.

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From this perspective,

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humans are indeed pushed forward

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by a pre-written program,

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on autopilot,

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frame by frame.

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But

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what you can modify

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are the parameters of your own internal model.

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Every time you truly become aware of yourself—

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aware of a rising thought,

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aware of an emotion taking you over,

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aware that you are falling once again into that familiar,

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auto-playing reaction—at the moment that awareness occurs,

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you are no longer just an actor pushed by a script.

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You become the person observing yourself.

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And the very act of observing

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is quietly rewriting your parameters.

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This is why I say

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awareness is much like observation in quantum mechanics.

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When you are unaware,

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your reaction patterns exist like a superposition,

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running automatically based on default probabilities.

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When someone says something harsh to you,

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anger automatically flares up.

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Precise,

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exactly like yesterday,

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exactly like every one of those ten thousand repetitions.

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But when you begin to observe this anger,

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this observation of yours

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intervenes in its collapse.

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The direction it takes

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begins to change.

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So, at its deepest level,

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the idea of Eternal Recurrence

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isn't meant to scare you with an infinite future.

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It is a reminder: since this moment is all you can experience,

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and since even memory won't cross that threshold of return—then this frame,

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will you let it play out automatically in a daze,

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or will you, with full clarity,

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live through it yourself?

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You cannot change the universe's script,

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but within this automatically repeating script,

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you can manually fine-tune your own current frame.

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Once this frame is corrected,

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even if you fall back into autopilot later,

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the direction your model is heading

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has already quietly shifted.

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When that demon in the dead of night asks if you'd live it all again,

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he is actually asking the wrong question.

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You don't need to answer for an infinite future;

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you only need to answer for this one moment—are you

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awake?

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I am Wang Lijie.

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See you next time.