Facts About This User


QuickLinks
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
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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 bth".
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 fastgrowing 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 mineshaft and not knowing what you'll face. (I use this analogy both in reference to a reallife 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.
About Myself
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 hyperintelligent 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 inprogress list here.
Here are some additional links, which serve as sources for the mathematical facts and "About Myself" portions of this page.
My Favorite Song
This is probably my favorite song, and I can never tire listening to it, (I've even made a playlist of over a dozen remixes of this song, and yet after hearing the entire playlist I still wouldn't mind hearing it again).
An Error ?
\(\color{#FF0000}{\text{Error 801:A Possible Error Detected}}\)
Also...
It struck me as a surprise one could actually use MathJax with the category labeling system.