User blog:Nayuta Ito/Tale: A long name

Note: This tale is not completely original. The original story is entitled "Jugemu," a classical Japanese joke (rakugo). I just made it go wrong with googology.

Once upon a time, there was an old couple who have just got a son. It's the seventh day of the son, so they have to give him a name. Since they can't come up with a good name, the grandpa went to his friend to get an advice for the name. The friend agreed to give him some idea.

"OK. Now, what kind of boy do you want him to grow up to?"

"I just want him to live a long life."

"A 'long' life?"

Unfortunately, the friend was a googologist!

"Now, let's start with a googol. It is one followed by 100 zeroes."

"Googol Smith. This is a good name. I'll keep it."

"How about googolplex? It's one followed by googol zeroes."

"That's great. But do you have a bigger number?"

"Yes, of course. How about Bentley? It's from a story Forever Endeavor. In this story, Bentley is going to live for $$ 10 \uparrow \uparrow 10 $$ years."

"For what?"

"Ten tetrated to ten years. It's longer than the age of our universe, even longer than [the age of our universe in Planck seconds] to the [the age of our universe in Planck seconds] years... Our universe is too small to express this number."

"Wow, that's impressive!"

"But we are just the start of googology. 'Real' googology starts at Graham's number."

"What is that?"

"Well, it's way bigger than Bentley's life. First, iterated addition is multiplication, and iterated multiplication is exponentiation. Now imagine an iterated exponentiation..."

"What are you talking about?"

"I'm talking about Arrow notation."

"Stop doing mathematics. Just give me names."

"OK. Meameamealokkapoowa Oompa. Loader. Rayo."

"Great. Anything else?"

"Yes. Now we go to infinities. Omega, the smallest infinite ordinal."

"There seems no difference between way too large numbers and infinity!"

"There is a big difference. Finite numbers are just finite. Infinity can never be finite."

"OK. I understand the greatness of infinity. And please just give me some names related to infinity."

"It will be too long to explain, so I will just list names. Veblen. Bachmann. Uncountable. Inaccessible. Mahlo. Compact. Stage. Metastage. Huge."

"Is that all infinity?"

"Yes. Really big infinities."

"Now I've got a plenty of names. Please write all the names on paper so that I don't forget it."

Googol Googolplex Bentley Graham Meameamealokkapoowa Oompa Loader Rayo Omega Veblen Bachmann Uncountable Inaccessible Mahlo Compact Stage Metastage Huge

"Pick one you like."

Now the grandpa gets home. He needed to pick one, but he thought, "If each of these is super big, everything combined will be really big!" And he gave all the name to the son.

Time has passed and the son went to an elementary school. The boy is a bit wild, and one day he injured his classmate. The injured classmate's parents came to the couple.

"Your Googol Googolplex Bentley Graham Meameamealokkapoowa Oompa Loader Rayo Omega Veblen Bachmann Uncountable Inaccessible Mahlo Compact Stage Metastage Huge has injured our son!"

"Our Googol Googolplex Bentley Graham Meameamealokkapoowa Oompa Loader Rayo Omega Veblen Bachmann Uncountable Inaccessible Mahlo Compact Stage Metastage Huge injured your son!?"

"Yes! Your Googol Googolplex Bentley Graham Meameamealokkapoowa Oompa Loader Rayo Omega Veblen Bachmann Uncountable Inaccessible Mahlo Compact Stage Metastage Huge hit my son and my son was sent to the hospital! Do you see this injur... Wait. his injury is already cured."

"The name is so long, so I guess it has cured while you saying the name."