# Links

Additional Links

In this page, I will share links to anything online relating to large numbers. This page also serves as my own tracking page for all the good websites and information on large numbers out there, giving it a kind of twofold purpose.

**Large Number Websites**

*These are websites or sections of websites about or relating to large numbers.*

Sbiis Saibian's Large Number Site (One to Infinity: A Guide to the Finite) - This is Sbiis Saibian's large number site, by far the biggest inspiration for this website. It is a web-book under construction that gives a detailed and thorough review of numeral systems, large numbers in the real world, functions that generate googologically large numbers, and more, and like my site it's designed to be a googology resource for newcomers and "experts" alike. Perhaps the most notable thing there is his own Extensible-E notation for making large numbers, where he names literally *over 15,000* googolisms!

Googology Wiki - This is a wiki and forum dedicated to large numbers that anyone can contribute to, founded by Nathan Ho. It's how I myself discovered the wonderful world of googology. The wiki has pages about numbers, large number functions, people, and some concepts. It's also a great hub for people in the googology community to chat about googology, share their own large numbers, and analyze/formalize systems.

Notable Properties of Specific Numbers - A very long list of numbers sorted by size, made by Robert Munafo. It lists any and all kinds of numbers with interesting properties, ranging from purely numeric properties to numbers like 42 or 666 with huge significance to human culture. The list of numbers only goes up to Steinhaus's *mega*, but he discusses far larger numbers in his large numbers pages. It's a major part of the inspiration for my own list of numbers.

Robert Munafo's Large Numbers - This is the part of Robert Munafo's website where he describes various large numbers and ways to notate them. It is one of the very first serious coverages of large numbers ever created on the Internet! He goes over large numbers and ways to denote them in order of size in a way accessible to the layman. Unlike Sbiis Saibian's long articles, this website's information is presented quite concisely.

Bowers' Big Number Central - This is the large numbers section of Jonathan Bowers' website, where he defines his famous array notation, gives examples on how it works, and gives two lists for his googolisms, one for his extension to the -illion naming system, and one for his googolisms using array notation. It is significant because Bowers is the father of modern googology, the one who really turned googology into how we know it today.

Bird's Super Huge Numbers - This page on Robert Munafo's website links to PDFs where Chris Bird devises his own extensions to Bowers' array notation called Bird's Array Notation, a sibling of Bowers' notation, and compares it to other large numbers (particularly those of Bowers'). Bird has also assisted in the construction of Bowers' notation. This is not an easy read for beginners, as familiarity with the idea of googological notations (particularly the fast-growing hierarchy) is highly recommended.

Prime Curios! - This is a huge collection of interesting facts about numbers, sort of similar in spirit to my, Sbiis Saibian's, and Robert Munafo's number lists, with a specific focus on prime numbers. Although it's not directly relevant to googology, it's worth noting due to its massive size and facts given.

*Second Generation Large Number Sites*

These next few websites are some of the second-generation large number sites, sites made by members of the googology community from around 2012 to the present with heavy inspiration from other sites like Sbiis Saibian's and Robert Munafo's - my own large number site falls under this category. Many of the second-generation large number sites are unfortunately either abandoned, not very good, or both. Here I will list some of the better second-generation large number sites.

大數之旅 (Tour of Large Numbers) - This is a googology site written in Chinese (which I don't speak), which is heavily inspired by and strongly resembles large number sites like Sbiis Saibian's and my own. If the Google translations are of any indication, it's an awesome quality site, especially considering that the author is only 12 or 13 years old as of May 2015, and considering that other work made by people around that age range is pretty shabby.

Hollom's Extremely Big Numbers - This is a website (updated infrequently) by Lawrence Hollom where he presents his hyperfactorial array notation and the revised version, factorial array notation, the former of which is one of the most powerful large number systems ever created! He also presents some of his own research on uncomputable functions, including bounds for Adam Goucher's xi function and his own original doodle function.

Almost Infinite - A site by SuperJedi224 of Googology Wiki where he defines some googolisms with existing notations and several notations of his own, including an ordinal hierarchy of his invention.

Punching Reality - A website by Thomas Jones where he discusses various things in googology. It is a small website that is no longer active, but it does have some interesting content and it is of decently good quality.

Googology63556 - A googology site by Ikosarakt1 of Googology Wiki, which in his own words "posts anything he knows about it". He also presents some functions of his own devising, including a sibling of the fast-growing hierarchy called the "middle-growing hierarchy".

**Blog Posts on Large Numbers**

From 1 to 1,000,000 / From 1,000,000 to Graham's Number - These are two posts from the popular blog-style website "Wait But Why" that talk about large numbers, starting by capturing the immensity of numbers starting with 1 to a million with visualizations and examples in the human world. Then in the next post the author continues to giving examples of large numbers in each order of magnitude. After that the author continues with discussing the googol, some more large numbers in the universe, and googolplex, and then gives a thorough review of the enormity of Graham's number. The website has a lot of other great posts as well, about pretty much any subject; I highly recommend you check it out.

Adam Goucher's Fast Growing Functions - This is a page where you can access blog posts by Adam Goucher about fast-growing functions that can make large numbers, for example the Goodstein function or Harvey Friedman's famous TREE function. He also introduces the *xi function*, a function he devised which is one of the fastest-growing functions known!

Peter Hurford's Large Numbers - This web archive page is a page from which you can access Peter Hurford's blog posts on large numbers. He begins by talking about the classic large numbers including Graham's number and Conway chain arrows, devising his own original extension to chain arrows along the way. Then he goes on to introduce readers to the *fast-growing hierarchy*, the nigh universal benchmark notation for large numbers. He goes all the way up to the level of the *large Veblen ordinal*, which is quite far through the world of large numbers!

**Articles on Large Numbers**

Googology in Japan - exploring large numbers - This is the English version of a page where Kyodaisuu of Googology Wiki defines seven unusual googolisms he dubs the Fish numbers. One of these is an attempt at expanding on Rayo's number, the latter of which was for a while honored as the largest named number.

Googology - This is an unusual page on googology published by Michael Joseph Halm. It is said to be a translation of the works of a mysterious figure named Andre Joyce. Although much of its information is erroneous, it is a relevant work to googology as it's the origin of the word "googology".

Who can Name the Bigger Number? - An essay by Scott Aaronson that discusses the wonderful world of large numbers an how different it is from what you likely think. It's the source of what used to be the quote on the top of my homepage. It also was the inspiration for the "Big Number Duel" that gave birth to *Rayo's number*.

**Large Number Videos**

What is the Largest Number? - This is an awesome YouTube video by Sharkee that talks about very large numbers in order of size. It's a rare video that doesn't just end the large number discussion at Graham's number but goes way way beyond, introducing people to the monstrous numbers TREE(3), Loader's number, and Rayo's number. Although mostly explains the numbers larger than Graham's number only through words, the video still does a great job at popularizing large numbers beyond Graham's number. He even says that he wouldn't have been able to make the video if it weren't for Googology Wiki.

**Forums and Miscellany**

Googology Wiki's IRC chat - This is an open IRC chat set up by Nathan Ho for the googology community to discuss anything, whether or not related to googology.

Really Big Numbers - This is a forum page where Allstair Cockburn introduced the world to the fuga- family of prefixes. It's the origin of various googological functions devised by many different people like the Torian, the gag- prefix, and some others. It's also where Sbiis Saibian made his very first post on large numbers on the Internet, introducing people to the *promaxima*, his upper-bound on the number of possible different parallel universes.

http://hddb.teamikaria.com/forum/viewtopic.php?f=11&t=1903 - This is a thread about large numbers from a forum on the higher dimensions. It's most notable because Jonathan Bowers himself (under the screen name Polyhedron Dude) gave major clues at how his array notation works.

**My Own Links**

YouTube: https://www.youtube.com/cookiefonster

Twitter: https://twitter.com/cookie_fonster

Blog: https://cookiefonster.com/

Old blog: https://cookiefonster.blogspot.com/

SoundCloud: https://soundcloud.com/cookie-fonster/

Bandcamp: https://cookiefonster.bandcamp.com/

Discord server: discord.gg/PM6Zbrd

Tumblr (not used much): http://cookiefonster666.tumblr.com/

Another Google site of mine: https://sites.google.com/site/polyominosconway/

Another Google site of mine (2): https://sites.google.com/site/homestuckcommentaryabridged/