Levels of Operation: HOLY CRAP THIS IS GONNA GET CRAZY.
So… this might help you understand what is coming up.
Math geeks, gather here.
Are you ready to have a nightmare about a new thing?
Something that is so crazy, even crazy would call it that?
First, we’ll start off with what you know. (Even the average person knows this, so it shouldn’t be that hard.)
LVL 1: COUNTING
We all know counting. If we want to get from 3 to 7, we just count up: 3, 4, 5, 6, 7. Super simple, but not efficient.
LVL 2: ADDITION (+)
So addition is more advanced than counting. It puts multiple counting steps into one number. to get from 3 to 7, you just add 4 (3+4) = 7.
LVL 3: MULTIPLICATION (*)
Multiplication is more advanced. You can now put multiple adding steps into one operation!!! to get to 12 counting by 3s, do 3*4.
LVL 4: Exponentiation (↑)
Exponentiation is multiple multiplying steps! Yeah! so, 5↑2 = 5*5 = 25. Simple!
Now, after Level 4, people don’t use the operations that we are going to further discuss. But the reason why is because these numbers get so… big and scary.
Now listen. Look at me. What we are about to enter is a realm beyond your own comprehension.
It’s called hyper operation.
Ready? Good.
LVL 5: Tetration (↑↑)
Tetration is iterated exponentiation. It’s like a… power tower, or a whole lot of powers stacked up on top of each other.
3↑↑3 = 3↑(3↑(3)) = 3↑27 = 7.6255975e+12. WHOAH.
3↑↑4 = 3↑(3↑(3↑(3))) = 3↑(7.6255975e+12) = a number MORE THAN A GOOGOLPLEX. WOW.
LVL 6: PENATION (not penetration)(↑↑↑)
Penation is iterated tetration. It’s a tower of power towers. It’s a super mega power tower.
3↑↑↑3 = 3↑↑(3↑↑(3)))=OH MY CRAP. THAT IS SOOO BIG. We’ll call that number WTF.
LVL 7: HEXATION(↑↑↑↑)
Okay, this is going to give you nightmares. It gave me some nightmares.
Hexation is iterated penation. HOLY CRAP THAT IS GONNA BE BIG. HOLY CRAP.
3↑↑↑↑3 = 3↑↑↑(3↑↑↑(3)) = WTF↑(WTF↑(3))). THIS IS FREAKIN’ BIG, AND IT IS SOOOO BIG THAT — THAT — THAT — WUT THE FREAKIN HELL?!!
Graham’s number
Okay, guys. I’m ‘bout to say some s*** that’s NOT okay. Like, SO NOT OKAY.
So we’ll call the first iteration of graham’s number g(1).
g(1) = 3↑↑↑↑3.
Got it?
Now, the number of arrows in g(2) is what g(1) equals.
Holy crap that’s a lotta arrows.
g(2) = 3↑↑↑…↑↑↑3
g(3) has the same amount of arrows as g(2) equals.
and so on.
g(64), which is officially graham’s number, has the same amount of arrows that g(63) does.
CRAP THAT’S A LOT OF ARROWS. LIKE, A LOT.
This image should help you understand better:
So there you have it.
Good luck on sleeping tonight.
P.S: If you want to learn more about the subject, I suggest you visit the link from Wait But Why here.
