User blog:Nayuta Ito/Googology Tale: Go Shopping

G is the googologist.

A: Could you buy me 9 eggs, 10 apples, 8 lettuces, and 6 bottles of milk at the grocery store? G: OK. I think I have enough time, so I can buy them.

(On their way)

G: I forgot the memo but I know what I need to buy. 9 eggs, 10 apples, 8 lettuces, and 6 milks.

G: When I need to remember multiple numbers, I can use prime factorization. It even has a name: Gödel number!

2^9*3^10*5^8*7^6=1389411160200000000

G: And it's possible to decode because of the uniqueness of factorization!

G: However, the number seems way too long to remember.

(G comes up with a good word: recursive.)

G: How about factoring recursively until you get a zero at the top? 1389411160200000000=2^(2^0*3^(2^(2^0)))*3^(2^(2^0)*3^0*5^(2^0))*5^(2^(2^0*3^(2^0)))*7^(2^(2^0)*3^(2^0))

G: Now let's turn this into a hydra.

x            x       |             | x  x   x   x x x x       |   |   |   | | | | x x  x x x   x-- x x     | |   | | |   |   | | x x-- x--  x-- |    |       |     | x--

G: It's a drawing, so much easier to remember than just a number.

G: Speaking of a hydra, it should be simpler when I write it in terms of ordinals...

$$ \omega^{1+\omega^{\omega}}+\omega^{\omega+1+\omega}+\omega^{\omega^{1+\omega}}+\omega^{\omega+\omega} $$

G: Well, now I am at the grocery store.

B: Hello, may I help you?

G: I want to buy $$ \omega^{\omega^{\omega}}2+\omega^{\omega2} $$.

B: I couldn't catch it. Could you say that again?

G: $$ \omega^{\omega^{\omega}}2+\omega^{\omega2} $$. I know you have them.

B: I have no idea what you are trying to buy...

Lesson: Never say numbers to googologists.

Reference: 巨大数たん幻想入り　その２　「初めてのお使いｷｮﾀﾞ」