Googology as popularly understood, is a catch-all term for anything related to "large numbers" ... no matter how tangentially. Consequently this wiki has incorporated information from a variety of sources including mathematics, science, cosmology, computer science, number theory, among others. No matter how grand or mundane the topic, if it involves large numbers it will probably be considered of "googological interest". Googology itself is billed as "the study of large numbers". But does this really capture everything that googology is, or has come to represent?
One thing that I have noticed that seems to generally not be recognized in the discussion is googology as a cultural phenomenon, googology as a community, and googology as a tradition. In fact, many times these aspects have been dismissed and downplayed or out right denied. Instead anything involving large numbers, regardless of motivations, subject matter, relation to other work, or how the author self identifies is considered "googological", and the person is knowingly or unknowingly a "googologist" by default.
So for example we get such notions as "Harvey Friedmann is a googologist" and "googolism's are not a big or important part of googology". This makes sense only if we think of googology as a catch-all for anything involving large numbers, but when I speak of googology I am usually talking about a tradition, about how we got here and who "we" are. But who are "we"? Phrases like "googology is still playing catch-up with the mathematicians" make no sense if googology is just about large numbers, but makes perfect sense if googology is a tradition which borrows from academia but grew out from it, not within it.
Bottom line is we have been talking about two different things, two different uses for googology and this has lead to a difficultly in two halves of the community understanding each other. I think it's time to make this distinction clear: googology may be viewed as a topic that encompasses anything related to large numbers, but there is also a tradition , albeit small, that has repeatedly been downplayed and swept under the rug. There is a tacit lack of acknowledgement of where we came from. This wiki did not emerge in response to Harvey friedmann's work. Harvey friedmann's work was sought out and incorporated because this community existed. The same can be said for ordinal notations, FGH and many other things. These are borrowed from academia but googology existed before these things were standard here, and googology was not empty of content prior to them. There is a tacit assumption that what we do here , in the community, is "not important", that the work of community members is "secondary".That at best the googology community is redundant, and all the meaningful accomplishments exist in academia.
Googology is about large numbers and the best ways to get there? Right? Thats our received wisdom and basically almost every one here would agree with that statement without much question. But if this is true a lot of what we do here doesn't make sense. Why not have the community agree what's the most efficient way to get large numbers and have a universal notation or concept. Why have a dozen different notations by a dozen different authors with confusingly similar appearances? Why have at least 97 percent of the wiki be articles about the names of numbers, all from various different number systems again by several different authors applying a cornucopia of methodologies?
I'll put it simply: our community has a blind spot. We do things the way we do them without thinking to much about why. we tell ourselves googology is only about large numbers, yet there are many things we do that are not absolutely essential to that. Googology, as practiced is often whimsical. But why? It's not essential. We could treat it with the upmost seriousness, focusing purely on the math and finding the most efficient methods. Why the propensity of "googolisms", why does the word googolism even exist? We don't need to name any of these numbers, and generally the notations are more useful for expressing specific numbers. Then again why bother expressing anything smaller than the largest possible number we can for a given notation. Or better yet just mention notations but don't have any articles on specific numbers. For those who understand googology as a tradition none of these questions should be difficult to answer, but for those who still insist googology is just about large numbers , and doesn't contain anything that is arbitrary, incidental, and contingent these questions and what they imply will seem baffling.
So let me try to explain what I'm talking about: I'm talking about the series of events and individuals that lead to the existence of this wiki and of the very concept of "googology" and I will try to show you that it grew from academia not within. That those most central to its development were far from the world of academia.
A popular recount of our history usually begins with Archimedes and his sandreckoner. It's a work with many of the hallmarks of what would become googology, but the reason why it's not really where our story should begin is because Archimedes, as far as we know, did not inspire a community of followers in the tradition of the sandreckoner. Ditto for other key incidents. Chuquets illions inspired prof. Henkle to make more, and this in turn may have inspired people like Luis Epstein, but the trail goes cold. Few people in the community dabble in illions because they are precieved as too small and cumbersome to work with, and furthermore Luis Epstein himself disavowed any association with googology. This is why I have sometimes referred to him as illionist instead. In fact Epstein has made it clear that he considers the vast majority of nomenclature of googology to be completely erroneous, ostensibly because it is (1) arbitrary and unrelated to ordinary counting and (2) does not attempt to name all numbers , just subsets of them, ie. How do you correctly count from a googol to a googolplex in proper english? Epstein is not interested in presenting yet another system of naming numbers, but working out the system of naming numbers, the correct and most logical way. This expresses a completely different notion than that of the googology community: there is no right system. Everyone who wants to can make their own system. Is this difference of opinion strictly about large numbers , or is it about something more, like say the purpose and meaning of nomenclature. In academia the answer is clear and Epstein is in the right. The purpose of nomenclature is to have a general standard that can be used by a community of researchers for clear communication, and so it is in most areas of life. The googology community is different in that nomenclature isn't a means to an end, but an end in itself. It is a way for community members to express their creativity and have ownership of their creations. Hence there is no "standard" way to name numbers and in fact doing so would deprive them of their creative impulse. Is this about large numbers, or are these things that are just so natural to our community that we never think to examine them.
So if it's not Archimedes and it's not chuquet that started the wiki, what did? The answer is, fortunately, really simple in our case: Edward Kasner. Kasner was a mathematician, but he also wrote popular books of mathematics for the average person. For books in this genre the emphasis is not on rigorous proofs but on exploration and creativity, introducing people to ideas they would not likely have thought about without prompting. It is in one such book "mathematics and the imagination" published in 1940, that we get the googol and googolplex, the true starting point of something we can recognize as googology. Ironically Steinhaus beat kasner by a year publishing "mathematical snapshots" in 1939, introducing the mega and megiston. These numbers were both vastly larger than the googolplex, but they didn't catch on. Meanwhile the googol and googolplex became household words to the point that they were officially included in dictionaries, no small honor for any googolism. But this was not enough to get the ball rolling. It was an invitation to continue but nothing really took hold for another 60 years, and that's because coming up with weird number names was at best a passing personal amusement. Something you might do as a kid, never tell anyone and forget. The idea of a community around such a pass time was unthinkable and absurd. For that you needed the internet. And here we reach the real watershed moment. Someone finally did answer the call and didn't just continue it but completely transformed it by taking it to a completely different level. In fact sometwo answered the call. The twin pillars of googology: Jonathan Bowers and a mysterious Andre Joyce, established most of the conventions of googological practice. They were both directly inspired by Kasners work, and they both directly expanded upon the googol, Bowers creating the giggol, and joyce stranger things like the googoc. Their methodologies and idealogies differed greatly but I think both shaped the early direction of what being a "googologist" meant, or could mean at any rate. It is Joyce who gave us the word "googology" and was the first to self-identify as a "googologist". It was Bowers who gave us the notion of an ever expanding personal notation, and organizing numbers into "groups". Both contributed to different forms of "zaniness" in the early community. Both had hundreds of names seemingly continuing in the kasnerian tradition, something not really seen before. It was something new. It inspired a young Nathan Ho to create googology101, following in a Joycian tradition that emphasized the absurdity and impracticality of the "mathematical" creations. Bowers inspired me and changed the direction of my own work. I related to his work and recognizing that I had done something similar as a kid without having known it was even a thing. And lastly and most importantly the wiki got formed which served as a lightning rod bringing those who dabbled with silly names for ridiculously large numbers to one place.
The first things on the wiki were not Graham's Number, TREE (3), or finite promise games. To this day in fact there is no article for TREE (3) , just one for the TREE function. What first appeared on the wiki was a googol and a googolplex, Kasners work. What followed was Bower's and Joyce's work as well as googolism's from googology101. This is how it began, and the influence of Kasner, Bowers and Joyce is palpable.
Yet in recent years these creators have been underplayed and fallen from grace. Bowers notation was deemed "ill-defined" with an implication of it being completely ambiguous and undefinable. Joyce's work was discredited as broken and sloppy.
Attempts to define googology as something in the lines of a tradition and community have been met with great skepticism. The most common side step has been to say "why do we even need to define googology". The answer is to define ourselves, determine where we came from, and where we should go from here.
The very word "googology" has become devisive. It has become impossible to talk about the community in a way that talks only about what we have created, what standards we have, and what values and ideas we hold , outside of the confines and controls of academia. Therefore I think it's time we abandon the label. What I want to identify with a new label is those who follow in the traditions of the works of Kasner, Bowers, and Joyce and who recognize ourselves as a social phenomenon and community which has been spreading and growing. A word has a lot of power and it's when there is a word for something that it really begins to exist and becomes something you can become a part of. This wiki, by the very act of using the term "googology" made it into a thing where before it was not. Being a "googologist" is assuming a certain kind of identity, one not properly codified or understood by academia. I don't think our community is different than many other nerd/geek cultures that have emerged and have defined themselves through a term. Like the furries, the bronies, and the trekkies, bits and pieces of what would emerge can be seen throughout history. For example one might say furries began back in Egypt when the Egyptians would draw pictures of their gods as animal-human hybrids. One could say it began with cartoons and cartoon companies like Disney that employed anthropomorphic characters. One might call Walt Disney a furry, but that would only make sense if furry were a descriptive label rather than an associative one. If everything involving people-animals is furrdom, then you can make that case. But that ignores a very real objective phenomenon: that the ideas of what it means to be a furry, the activities and ideas it involves, did not become prevalent, did not become an "identity" until the word "furry" was invented and one could identify as such. That's the power of a word. It can create and invent a whole category, a whole community that previously didn't exist!
So how shall I disambiguate what is meant when the word "googology" is only meant to address this community of self-idenfiers and their conventional practices? I would say the people I am talking about are all, whether aware of it or not, followers of what Kasner started. Shall we call this the Kasnerian tradition, and those who practice it Kasnerites? I might say I'm one. I also feel that I am very much a disciple of Bower's. Does that make me a Bowerite?
Everyone is of course free to identify how they chose. We can neither force people to use a label, nor stop them from using a label even if we deem it incorrect. We can debate what the criteria are for fitting in a certain category, and we can discuss whether certain labels are meant to be descriptive, describing some feature and identifying it, or associative, how the person chooses to associate and identify. These are not issues to work out here as they are far a field of "large numbers", but what I can say is that this IS a discussion about whether "googologist" is a descriptive or associative label. If it is descriptive label then Archimedes and Friedmann are googologists, but if it is an associative label then Epstein or even Bowers might not be a googologists, as Epstein actively rejected the label and Bowers never took on that mantle to the best of my knowledge. But labels aside lets at least admit, what Kasner started has snowballed into something more. We at the wiki may not observe it directly here, but a community of kasnerites is growing every day. New people keep finding the wiki, and they start replicating the same patterns of behavior that were first seen in Bowers: Coming up with a personal notation, giving it a special name, coining hundreds or thousands of number names and organizing them into groups, and creating websites to host their content. And most importantly, this is unprecrented and of a different character than what academia is doing and is interested in. That's a real phenomenon and all the semantics in the world doesn't change that. If it has become impossible to isolate that strand of the narrative from googology then we need a new way to talk about it. I suggest calling it the Kasnerian-Bowerian-Joycian tradition.
I can't force anyone to embrace it, I can't say it will catch on, but at very least it gives me a way to make the distinction crystal clear with a single word without the baggage and ambiguity that "googology" had apparently acrued.
If it has become impossible to talk about common practices here and to speak of them positively instead of derisively then maybe I can no longer speak of googology and googologists. Instead I'll be the first to say unapologetically, I'm a Bowerite , and i'd like to see us, not academia, make something of our own. When we do that we can say that we are no longer redundant or merely basking in the shadow of our superiors, we can take ownership for what we have created and have contributed something new to the world. Maybe that day will never come, but its my hope, and I think other Bowerites here will know what I'm talking about ...
We must go where academia has not gone ... if we are not pushing the boundaries and reaching the frontier, what purpose do we serve? Are there numbers so large they are useless or unconsidered even by mathematicians? There must be! Have we thought of them yet ... I don't think so ... but that's where I envision us going someday. Perhaps then mathematicians will borrow from our work instead of the other way around ...
when they need a bigger number ... :p
'Til then keeping counting my brothers
Sbiis.ExE , a Disciple of Bowers