Googology

Googology is the study and nomenclature of large numbers.

One who studies and invents large numbers and large number names is known as a googologist, and a large number name is known as a googologism. Googology is known for the rather comic names given to the googologisms, such as "meameamealokkapoowa oompa", "a-ooga", and "wompogulus".

Googology is not to be confused with googlology, the study of the Google search engine and its various other services.

History
Although the term googology is modern, the subject has existed for as long as humans have been fascinated by large numbers.

The earliest known work by a "googologist" is probably the "sand reckoner" written by Archimedes, a greek polymath, sometime in the 3rd century B.C. In it he develops a system of numbers extending to. There is other examples in ancient history that illustrate mankind's fascination, and even adeptness, with large numbers. Some religious texts contain some very large numbers. Although the Bible contains no definite numbers greater than, it uses figurative language in many places to describe very large numbers such as "the stars in the sky" or "the sands of the sea."

With the advent of modern mathematics, and the impending invention of the computer, mathematicians of the 19th and 20th centuries had access to numbers larger than ever before. This fascination was relayed to the laymen through popular books on mathematics. "Googol," "googolplex," and "mega" were all introduced in books of popular mathematics, written by mathematicians who wanted to explain to the laymen what mathematicians meant when they invoked infinity.

Eventually, the fascination of large numbers spread to a class of amateurs who took it upon themselves to extend the ideas hinted at in these popular books on mathematics. These became the early googologists. This took on something of a form of a hobby, that still continues today, with amateurs writing papers claiming to have "invented the largest number ever". That being said, not everything produced is brilliant, nor is it all crank mathematics. There is a variety of skill levels, and some of googology actually comes from professional mathematicians, not amateurs. Examples of googology from professional mathematics includes, Graham's Number, Conway Chain Arrows, the fast growing hierarchy, the function TREE(n), etc.

During most of the 20th century, early googologists worked in isolation. Since the advent of the internet however, there has been a greater confluence of ideas, and websites, such as Googology Wiki and One to Infinity have sprung up, to gather the loose bits of information that form the body of knowledge, methodology and conventions known as googology.

Furthermore, within the last 10 years (2002 through 2012) a loosely knit community of large number enthusiasts, dubbing themselves googologists, has emerged, building websites, sharing information, and developing a culture with a unique approach to one particular challenge: "What is the largest number you can come up with?" Googologists generally avoid many of the common responses such as "infinity," "anything you can come up with plus 1," "the largest number that can be named in ten words," "the largest number imaginable," "a zillion," "a hundred billion trillion million googolplex" or other indefinite, infinite, ill-defined, or inelegant responses. Rather googologists are interested in defining definite numbers using efficient and far reaching structural schemes, and don't attempt to forestall the unending quest for larger numbers, but rather encourage it.

As far as mathematical fields go, googology is an oddball. It precariously teeters on the edge of what we call "science," becoming somewhat of an art form as opposed to a mathematical study.

Although googology remains, and will probably always be, an obscure, esoteric, and impractical study, it at least now has a name, a history, and a community.

Etymology
The term was coined by Andre Joyce, formed by combining googol (the classic large number) + -logos (Greek suffix, meaning "study"). Joyce's googology involved devising a system of names for numbers based on wordplay and whimsical extrapolation. Interestingly, few people in large number studies have used the term, including Jonathan Bowers, Chris Bird, and Harvey Friedman. The word "googology" was not associated with their work until Googology Wiki.