A1-2 : Notes on Future Development

My site has grown considerably over the last two years. Prior to 2010.10.10, I only had Section I and chapter 2.1 complete. After about a year of inactivity I decided to return to my site to reinvigorate it. Since then Chapter 2.4 on the -illion numbers has been partially completed, and I began work on Section III. My site has gained in popularity and now receives small but regular traffic. The quality of my writing has improved, and the complexity of the site has increased. The result is that the website is now somewhat lop-sided with earlier work not being on par with later work. It is therefore my intention to begin improving the overall quality of the site within the next year.

Firstly, I am planning to re-write most of Chapter 1.2. The chapter will be devoted to number systems. I'm planning on adding an article on Mayan Numbers, and Babylonian numbers (both really awesome systems), as well as rewriting the article on egyptian numbers. I also want to improve my introduction of the decimal numbers, and discuss the evolution of the arabic numerals.

I also want to begin work on Chapter 1.3. This will be a very important foundational chapter that will give people the background necessary to tackle the material in Section II and Section III. I plan to go over the basics of arithmetic up to 3rd degree operators and their inverses, and also introduce the various kinds of numbers: integers, rationals, reals, etc.

Besides this I also plan to add at least one more article to the -illions chapter, and revise the article on Conway&Guys -illions.

The main focus for 2012 however will be on Section III because of the importance of everything that's going to be covered there. I am planning on releasing Chapter 3.3 soon, which will go into even greater depth with the numbers introduced in Chapter 3.2. I haven't completely decided yet, but Section III may have as many as 4 chapters eventually.

This will be plenty to keep me busy for the new year. However, I also have something special planned for the near future. I am planning on releasing the first article of Section IV sometime in 2013. Yes, there will be a Section IV, and it will take the reader beyond the popular discussion of large numbers into the lesser known and more obscure facets of the subject. Prior to this however, I want the first 3 sections to be in decent condition.

A last note: I will be trying to update more frequently than in the past. The reason I declared my site on "probation" for as long as I have is because I couldn't commit to any kind of schedule for the site. However I now seem to be getting my life into a kind of routine in which I could conceivably have regular updates once every 1 to 2 months. In fact, I've been able to release an article for 3 consecutive months now. If I can keep this up for at least a year I'll officially declare my site as active.

I'm looking forward to great things for this site.

'til then, keep counting ...

Sincerely,

-- Sbiis Saibian, The Large Number Enthusiast

2010.12.11 22:37 Saturday

A New Approach and New Content for 2011

I have decided to revamp Chapter 1-1, the first chapter of my web book for two important reasons. 1. When my googlepages site got transfered to google sites, most of the pages in this chapter got partially scrambled, and not all the links work properly since the change. I have postponed correction of these problems mainly to work on new content in chapters 2-4 and 3-1. However I have decided to fix these problems to improve overall site functionality. 2. I was never very happy with my introduction of the counting numbers. I am trying to create an entirely new approach in introducing and developing the topic of large numbers.

Originally I took a more traditional approach to how to introduce the subject. In order to speak about large numbers it is usually a good idea to provide some background on numbers and mathematics to begin. The problem is that this can prove to be a daunting detour for some, and it only tangentially relates to large numbers. This is because we already possess an intuitve understanding of such concepts. Another important aspect of my original approach was to treat the development of large numbers as mainly historical; that as time progressed people were able to come up with larger and larger numbers. While this is certainly true it is not entirely inline with the main impetus of this site. I did not create this site to discuss historical developments alone. My main objective for this site is to show how large numbers can be generated and to develop methods and theory to extend further and further. The historical approach distracts from this main objective and also does not give the reader an "active" role in the development of large numbers. For these reasons I think that chapter 1-1 needs some revision to bring it more in line with the main purpose of this site.

Another impetus for the revision is that I always felt dissatified with the first article as an introduction to the subject. The use of "number sense" as foundational concept didn't seem to entirely work. It was based on the "historical approach" I had originally took. "Number Sense" would simply be the earliest conception of numbers in modern humans, before the development of language or even symbolism. However this fails to define number. Recently after some thought on foundational issues, and doing some reasoning, I came to what I feel is a much more intuitive and clear way to define counting numbers, that doesn't even require me to use tally marks, number names, formal set theories, functions, or sophisticated and subtle definitions ! The most straightforward way to define the counting numbers is as the size of all collections ( for simplicity sake I at first ignore a distinction between finite and infinite sets. I later use this to create a paradox related to the number of such numbers. Since such a paradox arrises it necessates the usual distinction. This seems the more logical approach since infinity is a derivative concept of the finite). I will admit that even this first article is somewhat technical in detail, but it tries to base things only on famaliar and intuitive concepts, rather than heavy formalism. In this sense it is relatively approachable, but it does require some thought, especially the section discussing the principle of equivalent orderings, and proving that (N) is greater than any counting number, yet is not itself a counting number. I still feel it is a much more clear and decisive introduction to the counting numbers. Better yet it provides the real impetus for an interest in large numbers: a desire to better understand the distinction between the finite and the infinite and how they are related. My original introduction "One-to-One" never even mentions infinity, and at the time that was intentional because I wanted to discuss the finite in isolation from the infinite. However I now am coming to the opinion that the infinite is an important motivator into large number research. Jonathan Bowers even refers to very large finite numbers as "Infinity Scrapers". Doesn't that suggest that we really are trying to reach for the infinite, even if we know such a task is futile?

I am also very pleased with the following article "Jacob's ladder". What better way to introduce large numbers than by generating some. Because I only use the most basic concepts I needn't set up so much foundational material before getting into large numbers. I can almost immediately start generating very large numbers with only the most basic ideas as a base. The difficulties in conceptualizing such large numbers also provides a motivation for the reader to gain a better understanding of numerical and mathematical concepts.

In any case, I plan to revamp chapter 1-1 and correct all the technical problems as well as improve the flow of the writing to better suit my new design goals. I also am considering the creation of new chapters for section I. I noticed when I started working on chapter 3-1 that I hadn't really provided an adaquate foundation for functions and operations in the previous two sections. I simply assume this is well understood. In Section II, I make extensive use of scientific notation and exponential concepts, but nowhere to I really provide good grounding in how these things work (especially the compounded versions of stacked exponentials) and I don't really provide a way to conceptualize just how large these numbers are. I came to the realization I would have to introduce the basic operations to provide some kind of foundation for my later discussion of recursive functions in Section III. I haven't entirely decided how to reorganize Section I, so it's still a work in progress. Most likely there will be an addition of at least one more chapter, and the last chapter "Encyclopedia of Numbers" is probably going to get restructured to better suit my new design goal.

I also plan to return to working on Chapter 2-4 in the near future, probably after most of Chapter 1-1 is properly corrected and enhanced. 2-4 is especially important because I think the -illion series is one of those very popular topics in large numbers circles (that and the googolplex series), and I have delayed it for so long. I had originally promised to complete it within a month of my websites first release, just over 2 years ago today, and I still have not completed it. I plan to remedy this soon.

I must admit that the time I have available to work on this site is quite limited. I am currently attending college and working part-time. However the semester will be ending soon and I will have about a month off of work and school. I am hoping this provides me at least alittle more time than usual to work on this website as well as my other personal projects.

In any case, you can expect new content, fixed links, and better flow of ideas in the coming months and year. Stay tuned and thanks for your interest and patience.

Sincerely,

-- Sbiis Saibian

2009.08.11 11:50 Tuesday

Future Plans for Section II

After many months of inactivity, I've finally added a new chapter ! I still want to try and finnish section II. I plan to have 2 more chapters.

Chapter 3 will be a bit of an excursion, a chance to take it easy. It will go over some of the more famous history in regards to large numbers. The emphasis here is that numbers are sometimes purely imaginitive, and strictly impractical. This is in constrast to the first 2 chapters which plant numbers squarely within reality. But ultimately this website is concerned with numbers as abstractions, and so this chapter is actually going to be more in line with my main points. Basically I want chapter 3 to get people interested.

Chapter 4, will be the long promised chapter on the -illion series , and it will also be the close of Section II. I want to show people that even counting has it's limits. Numbers go beyond anything we can number. Mainly Chapter 4 is an extension of the idea of a "naming convention".

Alot of the obessiveness with large numbers has to do with naming them. Many people seem to find this addictive. Type "googolplex" into a search engine and you'll see what I mean. However, it is not with naming the numbers that I am mainly concerned. All of this is really just a primer for what will follow.

I hope to finnish Section II before 2009 ends, but that might not happen the way things are going. In any case, Section I & II are really just primers for Section III. This section will be where the discussion of large numbers really begins...

--Sbiis Saibian

2008.12.31 12:03 Wednesday

Possible Relocation to Google Sites

I'm very happy that I have finally published my first chapter of Section II. I hope that it is well recieved and stimulating. Of coarse there still is plenty more to be written.

As I said before, I want to try to finnish section II. Section II will contain 3 more chapters ( 4 chapters total ) that will cover everything from scientific notation SI prefixes and the illion series. Given the amount of time that it took me to get this far, and assuming I am not unduly delayed, I might finnish Section II some time in april of 2009.

I intend to continue to support this site as much as I can, but there are considerable obstacles. One impending problem is that I am not entirely sure how permanent the very service I am using is. My website is part of the "Googlepages" service, which allows google users to create simple websites for free. A few months ago Google announced that it was going to discontinue "googlepages" sometime later this year in favor of another service "Googlesites". 2008 however is just about to close, and since that time google has not said much about it's plans. Their plans are rather ambiguous to me right now.

How might this effect this site ? If google did shutdown googlepages, my website would likely vanish. I would then be forced to reconstruct it elsewhere, which would take considerable time and effort. If you know of a good free service or someplace to find free webspace and would like to let me know you can email me. My email address is listed at the bottom of my homepage.

Regardless of what happens I want to try to construct a very comprehensive site on large numbers. It doesn't matter to me so much where it is.

-- Sbiis Saibian

2008.12.06. 12:31 Saturday

Future Plans for this Site

Unfortunately I'm going to be busy within the upcoming days, so I may have to postpone updates for at least a week. However it is my intention to update soon to revise old content, and provide new content.

Ideally my next update would be a month from now, and would include a completed Section II. I look forward to publishing section II because it is really going to get into the more interesting and popular large number topics. -illion numbers are a very popular topic amongst number enthusiasts, and they are mentioned almost as frequently as the Googol and Googolplex ( I don't think I'm going to go over the "Googol series" in section II, because I think it will fit better later on).

I want to make sense of the sometimes confusing world of -illion numbers. The fact is there is a lot of stuff out there that people have trouble sorting out. Besides the officially recognized illions, there are the latin based illions proposed by Conway, and an unusual set of "illions" coined by Jonathan Bowers which go much further than the usual attempts. Also there are many illions which mascerade as real numbers. Most people know that a "zillion" isn't an actual number but a very large indefinite one, but what about gijillion ? Wikipedia lists "gajillion" under "indefinite and fictious numbers", but the term "gijillion" was actually used to designate a well defined and actual number by Jonathan Bowers ! There are also a slew of ridiculous -illions coined everyday by ordinary people chatting in blogs and so forth. None of this are even remotely recognized by any official dictionary. Futher, the glut of these "amateur illions" are sometimes erronous, not well defined, or even meaningless, intentionally or unintentionally. In otherwords, one has to sift through the chaff to find the good grain ( well defined illions). For me it's more important that an illion number is well defined and part of a semi-logical naming system, than whether some scholars thinks it's usage is widespread enough to merit it with a stamp of approval. But I'll stop there before I give too much away !

Also I want to update and expand section I. Essentially Section I is there to go over the different ways we can notate numbers, while Section II assumes that the decimal notation is established and instead goes on from there. There are other notations I could explore in section I. For example, although I mention "bases" such as 12, 20 and 60, I don't actually have an article on "bases". Not everyone is familiar with them, so I think an article on them would be interesting, and would widen some peoples view on what "numerals" really are (ie. ideas).

I also have other plans, but I don't want to give too much away just yet. I hope people find my site interesting and want to learn more about large numbers. The problem is that few people truly devote serious attention to this subject. Most math sites will only contain a few choice pages on large numbers as a "diversionary topic". Few would devote a website to the topic. Also a lot of the information on large numbers is scattered across the web in small chunks. There are no websites, except a few rare exceptions , which gather all the information on large numbers into one place. This is my intention. I will try to actualize this, despite certain limitations.

Sincerely,

-- Sbiis Saibian

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