Extremely Large Numbers

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We talk about TREE(3)


Chapter 1: The Universe Will Reset


Did you know that if you wait long enough, the universe will randomly reassemble itself into exactly this moment?


It's called the Poincaré recurrence time: roughly 10^10^10^120 years.


That's 10 to the power of (10 to the power of 10 billion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion trillion...)


After this time, every atom will randomly bounce back into the exact same position. 

You'll be reading this again. With the same memories. Same thoughts. Same everything.
And it'll happen again. And again. Forever.
Welcome to eternal recurrence. 🔄♾️


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Chapter 2: The Most Insane Number Ever Used in Math


Forget infinity. Let me introduce you to TREE(3).
TREE(1) = 1
TREE(2) = 3
TREE(3) = ... incomprehensibly, obscenely super hyper ultra  massive


How big? It makes the number of atoms in the universe (10^80) look like a joke.
It makes Graham's Number look like pocket change.


It's estimated to be around... well, we can't even really estimate it properly. 

It grows faster than almost any computable function.

TREE(3) isn't just a big number; it’s a number so vast that it makes "infinity" feel like it's right around the corner. 

If you tried to imagine it, your brain would literally collapse into a black hole from the information density.


Chapter 3: The Proof That Breaks Reality

Here's where it gets completely absurd:
TREE(3) emerges from a simple question about drawing trees with colored nodes. Simple rules. 

Elementary logic.
But the mathematical proof that TREE(3) exists requires roughly **2↑↑1000 symbols** (that's tower notation—insanely large).


If you wrote one symbol every Planck time (10^-43 seconds)—literally the fastest anything can happen in physics—you'd need more time than exists before the universe's heat death.

In fact, you'd need to write through multiple universal resets via Poincaré recurrence before finishing the proof.🤯🥸🤯😵‍💫😵‍💫🤯🥸🥸🧐🧐🧐


Math literally produces truths too big for physical reality to contain.


Let that sink in. 📜♾️🌌


Further Reading:



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