11,329
pages
$$\text{Click Me}!$$

 This userbox is for a user who likes self-referential humor.
 This user does not get why user boxes are always in the third person.
 This user uses no bots when editing.
 This user can click over 15 times a second.
 This user is intrigued by the fourth dimension.
 This user is intrigued by the fifth dimension.
 This user can recite Jabberwocky in under 30 seconds. See here.
 This user likes origami, in particular the geometric structures.
 $$\huge 2$$ This user may repeat himself sometimes.
 This user likes borrowing source code from other wikis.
 This user likes recursive functions.
 $$\huge 2$$ This user may repeat himself sometimes.
 This user likes classical music, especially from Alkan and Liszt.
 This user likes cubing and twisty puzzles.
 This user likes memorizing digits of pi, and is currently at over 200.
 This user has watched almost all of the first seven seasons of MLP:FiM.
 This user's favorite color is blue.
 This user likes watching Spongbob.
 This user likes Minecraft though he's only played it a few times.
 This user likes pictures of Romanesco broccoli.
 This user likes the cold.
 This user likes making long lists.

These are links I frequent often and thus it would be more efficient if they were contained all in one place.

### User Pages

An Algorithmic Analysis Of The 2x2x3 3x3x3 4x4x4 5x5x5 7x7x7 Megaminx

Sandbox I II III IV V VI VII VIII IX X

### Miscellaneous

(At one point or another, I used these sites a lot. Now I've discovered something called "Bookmarks" on my Chromebook.)

## Interesting Mathematical Facts

• The probability that a tree selected from an infinite forest of trees will be visible from your perspective is $$\frac{6}{\pi^2}$$.[1]
• The 2,000,000,000,000,000th digit of $$\pi$$ after the decimal in binary is 0.[2]
• A sphere can be continuously turned inside out, under the condition it's surface is allowed to pass through itself.[3]

## How I Got Into Googology

It began about four years ago while I was playing the game Cookie Clicker, and upon the Cookie Clicker wiki I found the names of numbers such as undecillion and trevigintillion. this made me curious about the names of numbers past a quadrillion, and so I found myself on this Wiki, where I learned about a googolduplex, googoltriplex, and a googolquadplex. At that time, I don't believe I understood any mathematical operations beyond exponentiation so I would often just click on numbers because they had cool sounding names. I would have fun doing this, and pursued this for a few months, until I presumably lost interest.

A few months ago though I decided to revisit this old pastime of mine, due to some confusion in trying to relate a problem to someone I knew. The problem was as follows:

Given that $$f(x)=x^{x^{x^{.^{.^.}}}}$$, what is the highest positive value x can be such that $$f(x)$$ is finite, or does not diverge ?

The confusion in trying to relate this problem to another person was that I knew of no way to mathematically represent an infinitely high power tower of x's. So I invented a symbol for it, $$\Delta_4$$, which represented the 4th "tier of operations", where the first tier was addition, the second multiplication, and the third exponentiation.

$$a\Delta_{4} b$$ means "a tetrated to the b-th".

I had a nagging thought though- hadn't this already been done ? I remembered the time I had spent on the Googology Wiki and recalled that there was operation identical to this. So I searched for it, and found tetration. This was all it took for my enthusiasm to double as I learned with renewed fervor the functions and numbers I could not understand when I was younger.

So now I'm here, in the present, with knowledge of the fast-growing hierarchy, and Veblen functions. It has been quite fun actually, because Googology combines the rigour of mathematics with a certain feeling of exploration, like going into a mine-shaft and not knowing what you'll face. (I use this analogy both in reference to a real-life scenario and in reference to a game I've only been able to play a few times, but nonetheless really like, and that's Minecraft.)

There's still plenty for me to learn though, like BEAF and the many array notations people have developed over the years.

Below is some miscellaneous material that relates to numbers or Googology in one way or another.

## Googological Memes

The following are some memes I've seen or created that I find funny. All credit for the first 1 belongs to Kochab1.

As this is the internet I won't divulge too much, but it may safely be assumed I'm a human. Or I could just be a sufficiently advanced automaton that passes the Turing test[4]. Or I could be a hyper-intelligent dog owning an underground crime ring that makes a profit off of selling missing pairs of socks to sock dealers around the world.* Or maybe I'm not actually here at all and you are just imagining you read this, or maybe...

In any case, I like mathematics and that's why I'm on this site, I have a site here which you can visit, (though it is very much in the making).

## For Reference

For convenience of reference, I have compiled a list of all the blog posts on this Wiki linked in chronological order. You can find the in-progress list here.