current status

Book's

Current Development

Status

(Last updated 2015.08.11)

Currently only the first 4 sections are available, along with an appendix and index. None of these sections are considered "complete", though they still offer plenty of content for visitors to comb through for hours on end. The books content is estimated at over 1500 pages when last checked ( 2013.10.25 ). Section I covers some basic numeric concepts (one-to-one correspondence), and briefly discusses some of the number systems that have been devised (egyptian numerals, roman numerals, and decimals). Section II discusses large numbers that crop up in astronomy and cosmology, scientific notation, the SI prefixes, and discusses some number naming systems that expand on basic -illions. Section III discusses a set theoretic way of looking at numbers, introduces the "fundamental functions" and how recursion can be used to build other simple functions such as addition, multiplication, and even exponents and factorials. It then goes on to introduce a long series of popular large number notations including Steinhaus-Moser Polygon notation, and Knuth Up-arrow notation. Section IV introduces more advanced systems such as the fast growing hierarchy, and my own Extensible-E System.

Despite the wealth of content however there is still much that is missing from the website. As of yet there is no discussion of Conway Chain Arrow notation, a popular large number notation. There is no article discussing Archimedes seminal work in googology, the "Sand Reckoner". There is as of yet no full discussion of BEAF, or the closely related Bird Array Notations. There is also no discussion of many latter day googological notations, such as Hollom's Hyperfactorials, for example. Harvey Friedmann's TREE function is also not discussed, nor any of the other very fast growing combinatorial functions, nor any of the uncomputable functions. Many numeration systems of interest are not discussed, such as the babylonian numerals, greek numerals, and chinese numerals to name just a few. All and all there is still a huge amount of work left for the book and this list is by no means exhaustive. Even assuming all this was added to the book there is no reason to think I would necessarily be done as googology is still a growing field and it is almost certain that by the time I implement all of these topics there will be yet new topics to discuss. It may even be the case that googology is growing so rapidly that I will never really catch up. If this is indeed the case than it is not a stretch to think that this book really isn't meant to be "completed" but is in fact a perpetual work in progress.