Shifting Patterns : March 2014

Googology Wiki

the large number encyclopedia

How many counting numbers are there,
if there is an infinite number of them why are they all finite?
—Sbiis Saibian

Googology Wiki is a free online encyclopedia and community about numbers large and small.
(But mostly large.)

http://googology.wikia.com/wiki/Googology_Wiki

This is a great website to see what's going on in the large number community.

It is worth remembering that large numbers are not so much about magnitude but more about information patterns and colourful uses of language.

There is a surprising amount of information on the Googology Wikia.

Another place that has a lot of information, discussion,
comparison, discovery and invention is the forum game
on the xkcd website, known as My number is bigger!

So much creativity and thoughtful energy has gone into this enigmas and diversions forum game

So I just want to say a warm thank you to all the contributors and supporters.

It is a site I browse every now and then and it is fun to see the mixture of styles and approaches to the topic including some pretty serious and well informed contributions as well as some more light hearted forays into the topic, so many ideas, impossible to find the winners for this game.

On the Eretrandre website I have explored mostly the information patterns associated with large and complicated numbers, but they are only indirectly to do with the forum game, and are more an artistic and accurate idea (modulo well defined interpretations) about how to find a system of patterns, that can be used to understand generalised recursion, especially via COH expressions, where functional composition and hyperoperations come together. COH = Compositions Of Hyperoperations.

The quote above from Sbiis Saibian is actually quite profound for the truth about finite numbers and the concept of infinity, my understanding is, it is saying that considering, or if, there are an infinite number of finite numbers, isn't it a kind of common sense that to describe all of them as finite is glossing over the genuine variety of finite numbers that really exist in conceptual reality.

One of the important scientific contributions has been to clarify the notion of domains of discourse in mathematics. I have tried to elaborate this with my description of the four main realms or regions of the natural numbers or counting numbers (details on the Eretrandre website)

Briefly speaking, the first is the normal everyday realm, the second is the realm of most of number theory, large prime numbers, and combinatorics, the third realm are some of the non trivial stages of the Fast Growing Hierarchy, and the organic information patterns associated with COH expressions, the fourth realm being the numbers such as Graham's number.

Amateur and professional mathematicians can find this new distinction a useful and practical way to classify the natural numbers, complementary and supplementary to the important classifications by Robert Munafo.

www.mrob.com

Professionals and amateurs should mutually recognise each others ideas and let the quality and durability of the ideas be the characteristics to influence and inspire future mathematicians.

username MikeSmith

www.eretrandre.org