A Call to Counting
It is generally accepted that our "community" has grown. But by how much? And in what way. In order to get a quantitative handle on the situation I suggest the taking of a census. I believe now is a good time for us as a community to take stock of what "googology" has become.
Initially there was only a handful of people who were responsible for the content that this wiki had become the depository for. The very first googolism's added to the wiki appear to be googol, followed a mere 12 minutes later by googolplex, the joint work of Mr. Kasner and his nephew Milton. Some of the earliest googolism's, added mere days after the inception of the wiki, was the work of one Jonathan Bowers, even though he has never identified himself as a "googologist". Andre Joyce served as an early source, providing the name "googology" for the "subject" as well as being the first person to self identify as a "googologist". Robert Munafo provided a website that served as one of the first compilations of information on large number names and notations, and early pioneers, such as myself and Chris Bird, began to expand upon the work of Bowers, albeit in different directions. (Chris Birds work was instrumental in providing formal notation that eventually inspired Bowers to create a explicit notation up to tetrational arrays, and my work provided a framework for what it meant to be a practicing "googologist"). At this early stage there was only a handful of "googological" websites, and self-proclaimed "googologists". In fact other than myself and Joyce I don't believe anyone else adopted the label at this point.
Then came the "2nd wave", so to speak. Now people began rushing in, fully embracing the "googologist" moniker, creating systems and then names within those systems, following the tradition established by Bowers and worked and expanded upon by myself. A series of new notations, new number names and new googologists showed up. A handful of these were great additions to the googological databanks, and the creators created the second wave of googology sites. This 2nd wave never really stopped. It continued to grow, and new "googology sites" began to pop up at an increasing rate until there was a bit of a saturation point at which the wiki no longer reflected the entirety of available information on the internet. This is kind of where we stand today, with the exact number of googology websites and individuals claiming to be "googologists" unknown, but which could easily number in the dozens.
With the proliferation of "googologists" and "notations" it was inevitable that the discussion would eventually turn to what was "notable" enough to be included in the wiki. This has already begun to happen with certain notations being so poorly designed and of so little significance to the overall development of googology that their non-inclusion or deletion is being seriously considered and a community debate has begun: this is despite the tongue-in-cheek "goal" of the wiki to "reach 10^100 articles". Certainly we could include every absurdity of all humanity for all known history and still not even approach this goal. However, for practical considerations this is going to be generally undesirable both at a user-end side and administration side. On the user-end side, if the wiki were to be entirely unfiltered the law of averages would be that the majority of content would be poorly created and redundant and it would be hard to pin point what the "good stuff" is. On the administration side the up-keep and management of such a place in which anyone could easily create an account, offsite source, and add their own work freely to the wiki would open us up to vandalism, spamming, and flooding of low quality work and it would become nearly impossible to police in any way. So we are perhaps reaching a critical juncture here.
I believe it is time for the community to take some stock of itself and making an accounting of just what is the body of "googological knowledge and craft" at this point. This must be done somewhat outside of the purview of this wiki for this census to be of any general use. We need to know "what's out there" without considerations as to whether it is "notable" or meets a certain "quality standard". We can not begin to manage this content without first better understanding it, and for that we need to pull out all the breaks. This is the purpose the present census.
Whether the wiki can truly accommodate all of this content, and to what extent it is in any way obligated to host content remains open to debate, but at least we can have some cataloging of the existing material that is pending for inclusion.
To this end I suggest a very informal "census". In its most general definition a census is simply an "official count or survey of a population which may or may not include more detailed information on sub-groups or individuals within that population". Here "population" doesn't necessarily refer to "people" but rather to any set. For example the "set of all coined googolisms" is the "population of googolisms". There are several ways we could go about collecting census information on googology, from counting googolisms, to notations, to websites, etc. A later series of censuses may be conducted to address these issues (possibly to be counted all together as a single "2016 Census" for googology). For the present census however we want the simplest means to gain a rough order of magnitude of the available data supply. After giving this some thought I've come to the conclusion that the best way to achieve this is actually to count individuals rather than ideas. Individual googologists may create dozens of notations and thousands of googologisms over several platforms, but generally each work can be traced to a specific individual. Immediately however we run into the sticky issue that people who contribute willingly or unwillingly to the endevour of googology do not always identify themselves as googologist's, even within our humble community. Although for the most part these individuals may be treated as the exception rather than the rule, the "googology" trend growing rapidly on the internet, none the less it behooves this census to broaden its horizons beyond both our community and the emmerging "googology-inc" that was inspired by Andre Joyce and planted its seeds through this very wiki. If we only remain within the safe confines of community, we will not really expand our knowledge very far. However it is a good question to ask: how many people who contribute to googology identify as "googologists" or consider themselves part of the "googology community". To accommodate these secondary concerns the census data can provide additional information on individuals that puts them into important subcategories. The main "population" however that we wish to study is the "body of individuals who have contributed to googology". Hence forth we will refer to these individuals as "Contributors to the Spirit of Googology" or simply "Contributors" for short. Within this population we are also interested in the sub-population of people who identify as "googologists" (practicing or retired) or as "community members". Of course in order to study any population we have to actually define that population. Hence we need a very specific defintion for what a "contributor", "googologist", and "community member" even is. Undoubtably there will be those who disagree with my choice of definition, but we can add the proviso here that this definition exists purely for the sake of the census in question and that its scope should not be construed to extend beyond that. Others are of course free to come to their own conclusions about what qualifies as "googology" or a "googologist" and conduct their own investigations based on those assumptions.With that being said I kindly ask that the comments section not be entirely be dominated by discussion of definitions and rather be primarily focused on the data collection proposed. For the purposes of such a community discussion it might be advisable for someone to host either a blog or community meeting to discuss the issue at length and with as many people involved as possible, preferably in a moderated fashion.
Before I proceed to a definition I'd like to describe my design goals in order to justify my particular choices and avoid misunderstandings as to the nature and purpose of this survey. The very idea of what constitutes a "googologist" or "googology" has been a subject of some controversy in our community. The main contention involves whether people whose work is presented on the wiki, are ispo facto googologists by the mere fact of their works inclusion. This mainly comes up in connection with professional works recognized as "googological" in nature while the participants do not identify as "googologists" and are in no way affliated or even aware of our "community" (to be defined shortly). Of course even the notion of what our "community" is, is a subject of debate for the same reason. Technically any work which involves "positive real numbers" that might be deemed "suffiently large" (low barrier to entry) are certainly candidates for inclusion on the wiki and googology-lore. Those who produce such relevant content may be considered willing or unwilling, knowing or unknowing, "contributors" to googology. This should hopefully be in full agreement. However the purpose of this survey is also to gauge the growth of the phenomena specifically born on the internet and inspired by what we might call the core of googological tradition.
Politics aside what I'm about to say can not be denied: the "growth" of available content for inclusion on the wiki is not coming out of professional circles, but rather from people of all walks of life who have found this very wiki, or googology websites that has lead them to this wiki, and has motivated them to make user accounts and don the "googologist" moniker and make it their own. It's a seemingly ever growing web of interconnected inspiration that may at its root contain works from professional mathematics but is definitely a distinct phenomena from it. The most key distinction is that for this contingent math is merely a "tool" to try and "craft" googolisms and large numbers in general, for mathematicians "googology" is merely a trivial consequence of the nature of mathematics and is merely "diversionary" at best and a distraction and wasteful at worst. Its the intended aim and general behavior that distinguishes these sub-groups within what we might call the "population of content contributors". It should also be noted that for those professionals whose work is included, it is not them who is including their work here, but it seems to be a growing trend of these self styled "googologists" to submit their own work to the wiki itself. These distinctions have been repeatedly swept under the rug by certain community members, but I feel this distinction is very important if "we", those who primary users and followers of this wiki, are to move forward as a community.
So to clarify the googology community refers to those people who are either registered users of the googology wiki, or who are aware of the wiki and consider themselves members of this wiki community or the "googology community" in general, or whose inspiration for their work can eventually be traced back to the wiki. This definition is necessarily narrow for pragmatic considerations and to avoid any ambiguity. This leaves open the question of whether or not there are other "communities" which do very much what this wiki-community does and whether or not they are aware of us. In fact there is at least one confirmed case of an independently developed googology movement. So called Japanese Googology, much like its english speaking counter-part, was primarily inspired by the works of Edward Kasner, Ronald Graham, and John Conway, but was not directly aware of our own "movement" until a later date. The "googology" moniker was then recognized and appropriated. The two independently emerging communities have since had some communication with each other, mainly through our Fish, our own "mediator" of sorts at this very wiki. For the time being I believe it might be fair to consider this a separate "community" with its own roll call. The present census, hosted by myself, may not be prepared to perform such a task exhaustively. I would encourage any other "communities" out there to attempt their own in house censuses, as they would be in the best position to "call in their troops" so to speak. It might then be possible to combine the various community censuses to form a super-census that would determine the number of "internet googologists" worldwide. In addition is also the possibility of ennumerable "independents" whose work is fundamentally googological in nature, and yet who are unaware of any community of such individuals or even other googologists. There may be people who reinvent googology and yet never present their work on the internet. I myself sort of "independently" discovered "googology" long before internet access was even a general thing. The point however is that, pragmatically speaking, we need to focus on what we can know, not what we might not or never know. That being said the definition for the googology community is admittedly and purposefully incomplete and no offense to those excluded is intended. Later censuses may address these more difficult issues of extending the definition of what constitutes the larger "community" of googologists.
With that issue hopefully clarified lets discuss what is meant by a googologist within the community. Not every member of the community is ipso facto a googologist. Many are enthusiasts who, while making no contributions of their own, are none the less fans who are aware of and avid readers of the content of this wiki. What percentage of community members are googologists remains to be seen.
Here is my proposed 5-prong approach to what defines a "googologist" for the puposes of this census:
(1) Must be a member of a googology community. This is a group of individuals who have adopted the banner of "googology" and who work collectively towards its intended aims, namely, the purposeful search for ever better methods of number generation for the sake of making larger and larger numbers for its own sake.
(2) Must either self-identify as a googologist, or failing that see themselves as a practioner of large number studies (as opposed to a passive observer), who may or may not use another term to identify their practice. Not everyone whose work is googological in nature identifies with or is aware of the moniker. In order to meet this requirement it is sufficient to demonstrate that the work is an ongoing hobby with distinctly googological, rather than purely mathematical, aims.
(3) Must have actually created something googological in nature, either a notation for large numbers, a function for the purpose of generating large numbers, or names for specific large numbers. In short, produced some work with the aim of inclusion in googology-lore or wiki content, or failing that, as an attempt to invent or explore large numbers for personal interest or to share with others as a "discovery" or "achievement". Pseudo-quantifiers, for example a "zillion", are not considered googological because they lack any mathematical content and do not represent specific quantities. This should be considered a related but fundamentally distinct type of "work".
(4) Must have some documented proof of this work on the internet, either via inclusion of works on the wiki proper, in a blog post or personal page on the wiki, or on some offsite source.
(5) Must be working in "good faith". That is, there must be a sincere attempt to have their work taken seriously, as opposed to a public display not meant to be included in googology-lore or simply meant to lampoon or mock the practice in general. This includes purposely created "nonsense words" and "math" intended to make fun without having any actual mathematical content.
The quality of the work is not a criteria for inclusion, only a consideration of the sincerity of the participant. Knowingly produced nonsense is not googology. Nonsense which is unknowingly such to the creator in a sincere attempt at inclusion is still technically googology.
My choice of definition will undoubtably draw ire from some. I believe the disagreement ultimately boils down to semantics: whether by "googologist" we mean a set of characteristics that may be identified within individuals and applied categorically (just like we catalog and identify species), or do we mean an individual who identifies themselves as part of a certain community with certain proscribed but mutual attributes. Although this issue has come up here, there is nothing particularly special about this debate within the googology community. This issue has always been a contentious one within practically EVERY fandom. To give an example, the term "brony" is usually indicative of the person donning the label willingly and considering themselves part of the larger brony fandom. In this way it serves as a way to identify with a community and give a general indication of interest, not a clinical category. This can clearly be seen by the fact that some individuals choose NOT to identify as bronies even if their interests and behaviors align with the broader brony culture, and these individuals may be considered not as bronies, but simply "fans of the show". Furthermore people who, for whatever reason, end up liking "my little pony" but not being aware of the fandom would not call themselves bronies and the community would recognize that this is a distinct phenomena. This strongly suggests that the term "brony" is a social category, a form of self-appointed group inclusion. Of course there will be those who say that regardless of whether someone identifies with the community of bronies or not, they are one if they have the necessary attributes, and even community members might not be "real bronies" if they do not possess these traits. These arguments tend to end in flame wars on both sides. The more level headed ones in the community generally recognize that ultimately the social category and clinical category are distinct ideas and mustn't be confused with each other. The same is the case with the term "googologist". It clearly functions as a social category for people to identify with the "community of googologists" but not everyone who does work that is categorically googological in nature, necessarily identifies or even appreciates the label. Perhaps one of the most pronounced cases in our own community of Luis Epstein who does not identify with the term googologist and is in fact openly hostile to the whole host of nomenclature stemming from the work of Edward&Milton (The Miltonian tradition is I may coin a phrase).
My conclusion is simply this: googology is obviously a social phenomena at this point, and people adopt the googologist moniker to be included in the community in the same way that people adopt the "brony" label to be included in that community. This is what will be meant by "googologist" for the remainder of this census. For those individuals whose work is clearly "googological in nature", whether they recognize it or not, they may be considered by the more cumbersome but hopefully more neutral term "practitioner of the large number arts".
What makes a work "googological". The criteria is simple:
'(1) It' is written and produced clearly with the aim of producing the largest numbers possible, either that the creator can imagine, or to somehow "beat" or compete with numbers anyone else has ever thought of, regardless of the degree of success met at such an aim
(2) It is an ongoing hobby, with the prospective aim of constant improvement, not merely a "testing the waters" kind of thing. There is an element of "insatiable" present. "Practical" is not in its blood. It's aim is not to produce "a mildly useful or interesting notation" but rather to simply push boundaries and feed curiousity
This will no doubt also draw skepticism, but I will need these definitions to properly conduct my census.
A definition for "contributor" is also needed. Unlike the qualifications for a "googologist" these are not nearly as strigent. These conditions are designed to be accurate but still broad enough to capture all the work that has been deemed the purview of googology. A Contributor must:
'(1) Produce a googologically relevant work that deals with "large numbers"', even while its aims and methods may not be googological in nature
(2) that is accessible and known, preferably through the internet
As far as I can tell, this design should capture everyone who has done something for googology either as a "contributor" or "googologist".
Honest attempts at "clarification" on these points is welcome with the proviso that these definitions are not intended to be completely and totally unambiguous and some degree of interpretation is necessary, though I believe such absolute precision is not possible and that a lack of such precision does not mean useful information can not be gained. It may be better to contact me personally through my user page or email rather than in the comments section in order to make your concerns known.
Method of Data Collection
In order to be included in the Census either as an acknowledged "contributor" or "googologist" simply post a comment and affirm that you meet the relevent criteria and consider yourself a googologist or practioner of large number studies in some shape or form. Please provide proof with a link to some of your googological work. Even if you are not currently a participating googologist/contributor, if you at any previous point in time considered yourself a practioner, I encourage your participation in the census. For those wishing to "nominate" another as a candidate, I would prefer that individuals only nominate themselves and that you can let those wanting to be included know that they should make the submission themselves. Obviously a nomination will be rejected if it does not meet the 5-pronged approach, or if I can find no evidence of the person or the work you are claiming nomination for.
Lastly major contributors may be added to the list without their needing to personally "register", for the sake of completeness. Those whose work are clearly indicative of "googologist" status via there presense of community inspired tendencies observed in the nature of the work will be presumed to be "googologists" unless this is either contested or is in any way ambiguous. If it is unclear whether a work is clearly "inspired by" the googology movement or whether the creator is comfortable or identifies with the label, they will be listed as a contributor rather than a googologist. I will ebb on the side of caution except in cases where it is all but certain but a "word of god" has not been forthcoming from the creator and their personal identification is not explicitly stated. If you would like to contest your inclusion in either cateogry you must make your objections known and demonstrate either (1) why you should not be included or (2) explain why the inclusion is simply in error by failing to properly meet the criteria listed above.
For those who are not participating I just make a general request not to flood the comment sections with non-submission comments. Thank you in advanced for your cooperation and participation.
Presentation of Data
Those who get included will be among a list of "unofficial registered" googologists and contributors, and a tally of the total number of such individuals will be made. This information is correctly made public via another blog post which can be found here . The participation window will be 2016, no inclusions past that year. The Census data will be updated as my own time allows.
As a necessity I have to claim the final authority on who is and is not included on the "list" since I have no commitee at my disposal for making such decisions. I will say however that I will try to be honest and fair within the best of my ability, but that ultimately its the communities call to either accept or reject my list and decide whether it was conducted in a fair and non-biased manner.
Nominations will be rejected if no information is included and I can not find any information on the nominee or their googological work.
What you get out of Participation
Regardless of whether or not your work becomes part of the wiki "canon" record, participation will be a way for you to register yourself for recognition as a googologist or contributor within the community regardless of the merit of your work (although for those intending to derail the census through spaming, the sincerity-clause will exclude those participants whose work is not in "good faith" as previously defined).
Secondly the aggragation of participation will become general community knowledge, allowing us all to guage the amount of current participation in the community, and to have a concrete number representing the current "population of googologists and contributors".
I look forward to the results of the census. While there may be those who disagree with the design of the census and its implications for what googology is or should be, I want to say that this census is made in good faith towards the "community" however you choose to look at it. I love googology and I want to see it grow and flourish. I am an avid contributor and supporter of the googological community and am committed to seeing it succeed. Lets not let politics get in the way of a healthly community atmosphere.
'k, have at it!!!
To See the Census Results so far
Due to the length of this post the "registry" or Census results have been moved to a second blog post. Click here to jump to The Registry. You can make your "claim" here or at the "registry", though the registry would probably be more convenient.