dev_history

Developmental History

The idea of a never-ending book about the ascent from one to infinity was first conceived by me as a kid as a thought experiment while trying to understand the magnitude of the infinite. To this end a small treatise was written called "One-to-Infinity" that detailed a way to get to some very large numbers by way of a series of polygonal notations I had devised. This web book is a spiritual successor to this long lost childhood treasure. Originally conceived as a website on large numbers that would serve as a vehicle for me to present some of my own research into the topic it eventually grew into a massive encyclopedia of large number history, lore and mathematics!

The seeds of the website were first sown on June 10th of 2008 on the new google pages service. For about 6 months from June to December of that year the website was developed privately outside of public view. Much of the work was scrapped in the process including an early list of large numbers (one of the first things created). Eventually the idea of turning it into a book that would cover the subject of large numbers exhaustively in the spirit of "one to infinity" emerged. To this end I began work on the introductory chapters, dubbed collectively as Section I. Originally I had intended to complete the entire book and then publish it, but when I realized the enormity of the task I opted instead to publish the web book in installments, perhaps a whole section at a time. This would give me the opportunity of exposure. Consequently on December 9th of 2008 I publicly launched my large numbers website to the world with an embryonic version of Section I available. Incidentally this was only 4 days after googology wiki was launched.

In the following month some developments of Section II were made behind the scenes. Small improvements were published for section I such as the expansion of the list of small primes to 200 on December 16th of the same year. The article "Number Survey" was added just 8 days later. As a way of closing out the year Section II Chapter 1 was released on December 31st 2008. A week later yet another enhancement was made to the "small primes" article.

Then on January 10th of 2009 events in my personal life conspired to interrupt my work on the website entirely. I needed to move to another state and events in the immediate future were uncertain. I therefore decided to make an announcement to the effect that the website was on hiatus, that I was uncertain that I'd be able to resume work, but that if I was unable to work on it any further I would simply release all unpublished work on an "as-is" basis. This was the earliest "no activity" period in the websites history. At this point my website was so new and so small it is doubtful that there were many people even paying attention though. Just 14 days later, after having moved and resituated myself I happily announced that I'd resume work on the website but that the site was still on "hiatus" until further notice.

On March 4th of 2009 I privately created the Section II Chapter 2 homepage. Then on march 28th the website was declared officially "reactivated", with a cryptic mention of more details later. On April 1st an article was released titled "Mathematicians Unveil largest Known Integer". This would be the first in a series of spoof articles that I'd write in celebration of "April fools day", a tradition that is kept up, somewhat irregularly, to this day. On April 7th a complete announcement was made about the status of the website. The website was officially put on "probationary status", which meant that updates wouldn't come as fast as they had initially. This status has never been officially removed, and for good reason: I have never been able to maintain any regular schedule of updates since then. While it's true that there is no regular update schedule I have usually had an update every few months since those early days (save for "The Great Divide"), and work on the site behind the scenes is an almost daily activity.

While this announcement was all well and good a true update did not come for many more months. Then on August 11th of 2009 after several months of behind the scenes work I was finally ready to publish the contents of Section II Chapter 2 - "The Tools of Science", a chapter completely devoted to the SI prefixes. This was the first major update since December 31st update release of Section II Chapter 1. This marks a period of about 8 months without updates, the first long dry spell in the websites history. But this update was followed by an even longer drought. In fact the website became all but abandoned for over a year after this last update. Oddly enough this time period also overlaps a long dryspell period for the googology wiki where it too looked like it might be abandoned to ravages of the internet. I hadn't forgotten about my site but I had completely stopped working on it all together throughout the rest of 2009 and most of 2010 in order to work on another massive project of mine: an as of yet incomplete pen and paper role playing game. This marked the longest stretch of complete inactivity for the site which I call "the great divide". The first anniversary of the websites public debut went uneventfully without even any fanfare...

After a while I began to feel disappointed by the sad incomplete state I had left my website in. A plan was hatched to make a major revitalization of the site. It was recognized by me that a major problem was the way I was releasing content: A chapter at a time. This made publication seem impossibly far away and consequently would ebb away my motivation. So part of the new regime would be that content would be released by the article instead of by the chapter. The next important part of the plan was to jump right to the good stuff and start talking about recursion and googological notations. This would be accomplished by launching the revitalization of my site with the release of Section III. I picked the auspicious date October 10th 2010 (10.10.10) to make my come back ( incidentally this was also the date chosen by Hasbro to launch their new my little pony series : Friendship is Magic. 10.10.10 was also a popular choice for "the end of the world" at the time, which might have had something to do with my choice). The first article for 3-1 (Section III Chapter 1) was released on this day. This was followed just one day later by a new article for chapter 2-3 (you may also notice the new use of abbreviated chapter names by section number followed by chapter number). One month later work began on revising Chapter 1, which I had felt was inadequate. The second anniversary of the website passed uneventfully. Two days later two new introductory articles were written for chapter 1-1 and for the book as a whole: "A Definition for the Counting Numbers" and "Jacob's Ladder". These did a much more thorough job of introducing the topic and giving the reader some background in basic set theoretic concepts of numbers. 2010 was closed out on December 27th with the release of one new article for chapter 2-4.

The website went largely inactive for a few months after that. Then on May 31st of 2011 a new article was released for 3-1: "Plexing and the Googol Series". Here at last was an article directly discussing the googol and the googolplex and their origin story. On June 14th of 2011 a new feature was added to the website: the Chapter Select. This was added so that navigation would be much more fluid. Previously it was necessary to return to the home page (called the "main hub" in current documentation), in order to jump to a new chapter. Now with the Chapter Select it would be possible to navigate entirely through the Chapter home pages (Now referred to as "Chapter Hubs"). On the same date a new article was released for 3-1: "The Fz, The Fuga & the megafuga", an article discussing the googological contributions of one Alistair Cockburn. At this point Section III was starting to take shape though still lacking much content. While I was padding out Section III, I was also working on completing the content for 2-4. Not long after on June 27th I released a new article for 2-4 on Russ Rowlett's Greek Based -illions. Just three days later an article on Professor Henkle's "million -illions" was released. 2-4 was now beginning to become one of the more interesting and complete chapters at this point.

The next 2 months was one of the most grueling periods of work on the website. I committed myself to the task of discussing a full development of Bowers' multi-tiered -illion system. I slavishly worked on this article for several hours at a time several days a week for the next two months. The work was so incredibly tedious that it actually started to wear away at me psychologically as I desperately tried to complete it while feeling that the goal just kept moving further and further away. I was also suffering from pretty severe depression due to personal issues. I eventually had a bit of a break down. After this however I felt better, especially since I was already near completion at that point. I decided just to keep trucking and finish. All and all it took some 50 hours of work to make that article a reality and it nearly took my sanity with it, but it was an incredible relief when it was done. The article was published on August 19th of 2011.

The next 3 months saw perhaps one of the most important developments of my website: the introduction of what would eventually become my Extensible-E System.

Interestingly, before the publication of "Hyper-E Notation", the first in a series of notations in the Extensible-E Series, I had all but abandoned my original childhood polygon notation. It seemed awkward and I had done little with since the days when I had first devised it. When I got back into large numbers in 2004 I went through a long phase of imitation and extension on other existing systems. The first system I made a massive extension on was Conway Chain Arrow Notation. At the time this was the furthest I had taken any system. Then I discovered Jonathan Bowers' work and BEAF. Naturally I asked myself how my Extended Chain Arrows compared. I was rather stunned to learn that they were only as strong as linear arrays, the weakest subsystem of BEAF! So BEAF appeared to be the best game in town. I endeavored to seriously study BEAF but was quickly confronted by the fact that Bowers' writings were all but incomprehensibly cryptic and terse. So I left off on large numbers for about 3 years. Then sometime in 2007 I discovered that Bowers' had a new website. For the first time a small window was opened on what BEAF was and how it worked. I began to understand what array-spaces were but not the details of their operation. So as a way to study BEAF I decided to devise my own variant array notation. This allowed me to understand what "spaces beyond spaces" and "spaces described by tetration" meant. This system sprawled on and on as I attempted to reached Bowers' fabled "Legion space". Not only was I not entirely sure how far I had gotten, but I got the sneaky suspicion that I wasn't even coming close! None the less I had made much progress in understanding BEAF and I wanted to relay this knowledge to the world. This is perhaps the real inception of my website because it was initially created to discuss my variant array notation and the insights I had gained into BEAF. An irony not lost on me is that to this day this web site has failed in both these objectives (one I hope to render someday soon however). In any case I had always thought my premiere notation would be this variant array notation.

So I didn't initially set out to expand upon my childhood notation. Instead I simply intended to write an article about it, after all, the website was meant to cover everything related to large numbers, every notation, so naturally I should discuss my own attempts. It also made sense since it played an important part in the writing of the web book. But as I began to prepare this material for discussing my polygon notation I was drawn to the idea of finding a way to notate a theoretical extension I had only imagined as a kid: the idea of sequences upon sequences built out of plugging the number of sides of the polygon back into itself repeatedly. This eventually evolved into a simple notation for Hyper-E Notation and Extended Hyper-E Notation. Furthermore it seemed only natural to also use this as an opportunity to debut myself as a googologist and introduce some googolism's of my own. After 3 months of building the article I finally published my work on Hyper-E and Extended Hyper-E on November 19th 2011. This system met with some initial resistance. I was told by a few members of the community that my system was essentially redundant as it closely mirrored Bowers' work. This was, of course, intentional. I meant my googolism's as direct parallels to Bowers', following in a tradition that he himself started. I had even adopted his trend of gathering googolism's into "Groups" ( now called "regiments") named after their most prominent members (now referred to as "Colonels". The military terminology is also an influence due to Bowers). Despite some initial negative reactions, googology wiki was quick to start adding my googolism's to its library and this helped to lend it legitimacy early on. Even at that point I had not decided to make Extensible-E my main system and figured that Extended Hyper-E would be as far as I would go with it. In any case this was a landmark article that I was very proud of at the time.

Soon after this I returned to the oft ignored task of improving earlier content (a problem that persists to this day). Just 5 days after the release of Hyper-E I broke chapter 1.1 into 1.1 and 1.2. At this point the use of the "dot" became the standard and it remains the standard to this day. The hyphen can still be found in the urls, but this is simply due to the fact that the urls due not allow for the use of the dot, and so hyphens have to be used instead. None the less, in all other forms of documentation the dot is always used.

The separation was created to separate the introduction of basic number concepts from the discussion of numeral systems. New improved articles on Number Sense and Tally marks were also released at the same time of the split up.

The 3rd Anniversary of the Large Number Site was the first to actually receive notice on the Updates & Announcements panel. In addition to this the website featured a special background and homepage image to commemorate the occasion. Celebrating the Anniversary became on of the annual "traditions" for the site from this point onward. One day after the anniversary Chapter 3.1 was broken into 3.1 and 3.2. 3.1 was meant to discuss basic recursive concepts while 3.2 would cover popular recursive notations, similar to the split between concept and notation in the split of 1.1 into 1.1 and 1.2.

On January 23rd of 2012 I released the article "Ascending with Up-arrows" for chapter 3.2, a long overdue article about Knuth's Up-arrow notation, a well known foundational notation in a lot of googology including Chain Arrows and BEAF.

On February 10th of 2012 I broke up what was called Announcements & Future Plans into the "Appendix" and "Communication Center". This change caused some resentment because it changed several urls in the process. The split was created however to provide a space for book content that was not easy to integrate into the narrative of the main sequence of chapters while also making a distinction between what was part of the book and what was part of the larger web site that contains it. The Appendix is part of the book. The Communication Center is not and is merely commentary on the development of the book. The Appendix was also created to introduce an important new feature: A Large Number List. This was something I had wanted to do since the early inception of the web site but had held off up to this point. Part of the reason for the hold off was because I only wanted to discuss numbers in the Large Number List that were already discussed in the rest of the book, but up until that point there was not enough content to put into the list. From this point on I planned to make periodic expansions on the Large Number List as the website was itself expanded.