11,018 Pages

## The big picture

Do unto others as you would have others do unto you. Most of the following rules are specific applications of that principle.

## Wiki philosophy

Googology Wiki is an encyclopedia and discussion forum about large numbers and fast-growing functions. Similar to the fact that wikipedia has no firm rules, we have no firm rules. Sometimes improving Googology wiki requires making exceptions. Be bold, but not reckless, in updating articles. And do not agonize over making mistakes: (almost) every past version of a page is saved, so mistakes can be easily corrected.

## Original work (READ THIS !)

Probably the single most common mistake made by newcomers to the wiki is to show up and dump their latest invention into the encyclopedia. The point of the encyclopedia is to document published googologisms and ultimately unite the scattered literature of large numbers. It's a mirror, not a publishing platform.

The recommended way to get your work on the wiki is to create a blog post. Blogs offer a free and easy way to broadcast your creations to the community, and you can get feedback from other googologists in the form of comments.

Original work on the wiki is allowed as long as it is cited from a good source (in compliance with Rule X), but if it is low-quality enough a poll will be posted in the talk section of the created page, and after three days the majority vote will decide whether the page stays or goes. (Note that copying text verbatim rarely counts as quality work.)

## User interactions

Be nice. Don't attack other users personally.

Be a decent human being. Don't make actions or statements discriminating against anyone based on race, class, ethnicity, gender, sexuality, disability, religion, etc.

### Don't bite the newbies

New GWikians may stumble a bit while learning the ropes. Don't bite them! Clean up after them and, if necessary, courteously let them know what was wrong. There's a lesson in every mistake.

### Assume good faith

A sufficiently bad mistake is hard to distinguish from malice. Whenever possible, assume good faith.

### Discord

There's a Googology Discord where you can talk with other users. Of course, the usual rules of employing common sense and being a decent person apply.

## Notability

On wikis, we have to be constantly deciding whether an article should be created or not for each number and concept. Numbers and functions should be mathematically well-defined, or at least an attempt at being mathematically well-defined. For example, a number defined as "infinity plus 42" is not acceptable unless it is significant enough in pop culture. The following are some general rules of thumb:

### Numbers

• Pretty much any number greater than 100 is fine. We allow integers 0 to 99, but any irrational constants less than 100 like e or $$\sqrt{2}$$ are generally not allowed. Note that some irrational constants on this wiki are greater than 100, such as Ramanujan constant.
• Named numbers are much preferred over unnamed ones. There are a good number of exceptions to this however.
• Commonly used numbers should have peer-reviewed sources, and uncommonly used numbers, e.g. numbers appeared purely in googology, should have the first sources. For more details, see #Clarification of creator.

### Transfinite numbers

• Even when they're only tangentially relevant to googology, ordinals, cardinals and related functions are fine.

### Functions

• They should grow fast enough to be related to googology. As a general rule of thumb, things that grow slower than factorial are not acceptable. Addition and multiplication are fine because they form the basis of the hyperoperators.
• Googologists are mostly concerned with functions mapping counting numbers to counting numbers. Functions like $$e^x$$ map naturals to irrationals and thus are not easily analyzable with standard googological tools. As usual, exceptions are common; use your own discretion and discuss in case of controversy.

### Analyses

• Pages such as articles and templates should not include links to non-existing pages.
• Links are used to help readers to access existing related articles and to grasp lists of other existing related concepts. If we allowed links to non-existing articles on numbers, we could not ensure the actual existence of the numbers, because no source is accessible for a reader. For example, we could freely add links to non-existing articles on non-existing fake numbers as if they existed.
• As an exception, we can use a link to a deleted page in talk pages, because it is helpful in discussions.
• Redirect pages are valid only when they redirect to relevant pages in the main space and the titles of the redirect pages are valid.
• Redirects to non-existing pages or blog posts are not allowed, because they are not relevant pages which actually exist in the main space. If we allowed redirects to blog posts, it would essentially allow users to put blog posts in the main space.
• The titles of redirect pages should be reasonable. For example, an alternative name of a number is allowed to be the title of a redirect page to the article on the number, but the article should include the alternative name with a valid source, because otherwise we cannot judge the validity of the alternative name. The same logic is applicable to a typo of the name of a number.
• As an exception, a shorthand is allowed to be the title of a redirect page, as long as it is commonly used in a googology community.
• Category pages for articles in the main space should not include a link to a blog post.
• It means that we should not add a blog post to a category for articles in the main space such as Category:Numbers, Category:Illion, Category:Up-arrow notation level, and so on. If we allowed to add blog posts to categories for articles in the main space, it would essentially allow users to put blog posts in the main space.
• Adding blog posts to categories which does not include articles in the main space is traditionally allowed to some extent as a humor. It does not mean that users can freely create off-topic categories.

### Other stuff

• Some articles don't directly describe large numbers or functions, but rather systems that give rise to them. Examples include Goodstein sequences and Latin squares.

### People

• Someone who has made a useful enough contribution to Googology and whose presence has been acknowledged by other members of the community may have an article written about them. However, a user must not write an article about themselves, and new users shouldn't have articles written about them.

## Citations

Googology Wiki is intended as a reflection of large number literature, online and offline. It is not the place to introduce new googology. The point of this rule is to make Googology Wiki a well-documented piece of work, not a place where people can dump their trivial salad numbers.

Good sources include:

• Blog posts (see below)
• Textbooks and other reliable print sources
• Articles from reputable websites
• Self-published books, papers, and websites. Googology Wiki doesn't have a conflict of interest policy, and it's acceptable to write articles about your own work.

• Wikipedia
• Forums and other wikis (sister wikis of Googology Wiki, nlab, and so on). There are some exceptions such as c2wiki's famous ReallyBigNumbers page, where many well-known googologisms come from.
• Private communications
• Other pages within Googology Wiki

All this said, there is some leeway with original content. While Wikipedia considers itself a tertiary source, Googology Wiki is a secondary source. Our articles frequently offer commentary, analysis, and explanations of the source material (although it should be neutral and objective if possible). It's acceptable and common to discuss and analyze existing googology. Readers should note that such commentaries are not subject to academic review, in contrast to some of our sources.

Note that some other wikis such as "Gugology Wiki" and "Googology-testing Wiki" may contain irrelevant sources.

### What can be a source?

If you want to add a source to a specific description, e.g. a definition or a statement, you need to cite the first source or a peer-reviewed source of the description. A personal website is not peer-reviewed, and hence can be a source of the definition of a number only when the website clarifies that the number is created by the author or the creator allows it as the first source. (See also: #Reliability of a source, #Personal website)

For example, Bowers' website can be the first source of the numbers created by Bowers himself. On the other hand, if it included a description like "Goooogoooool is a well-known number defined as 10000000", then it should not be dealt with as a source of Goooogoooool. Similarly, Denis's website can be the first source of Denis's numbers, and hyp cos's website can be the first source of hyp cos's numbers. One typical mistake is to refer to Bowers' website as a source of your own number. Since Bowers' website is not the first source or a peer-reviewed source of your own number, the citation is invalid.

Similarly, even if Bowers' website refers to a certain number, it cannot be a valid source of properties which are not written in the web site, because it is not the first source or a peer-reviewed source of such properties. Therefore the location to put the citation is quite important.

Further, even if Bowers' website refers to a certain property, e.g. well-definedness or growth rate, it cannot be a valid source of the property unless the website is the first source, i.e. the website includes a proof of the property, because it is not a peer-reviewed source. It can just be the first source of the fact that Bowers wrote the statement.

### How to cite a source

If you want to cite a source, you need to put a link to the website by using the <ref></ref> command right after the information of which the website is actually the first or a peer-reviewed source. Here is a list of elementary mistakes repeated by users:

1. To put a link to a website as a source of a name of a number written before the <ref></ref> command, while it does not include the name. (Even if the website includes names of a number, it might not be a source of the other name of the number.)
2. To put a link to a website as a source of a property of a number written before the <ref></ref> command, while it does not include the property. (Even if the website includes the name of a number, it might not be a source of properties of the number. Even if the website includes properties of a number, it might not be a source of the other property of the number.)
3. To put a link to a website as a source of a name or a property of a number written before the <ref></ref> command, while it is not the first or a peer-reviewed source of the information. (Even if the website includes the information, it might not be unreliable. In order to ensure the accuracy and the reproducibility of a source, you need to refer to the first or a peer-reviewed source.)

Some old pages use "External Links" sections to put sources. If you find a link which should be cited as a source, please move it to an appropriate location in an article, instead of marking it as a candidate of deletion. Of course, you can use "External Links" section to simply put an external link to a related page.

When we cite a long reference, e.g. a book with 10 or more pages and a video with 1 or more minutes, then we need to clarify the exact location in the reference where we can find the cited description.

### How to fix a link to an invalid source

If you find a cited description whose source does not include it, please fix the issue in the following ways

1. If the link to the source is alive and you know an alternative accessible source, please replace the original source by the alternative source. In order to find an actual source, it is good to look for the cited description at subpages or related pages of the original source.
3. If you do not know an alternative accessible source but the description is not doubtful, please remove the link, put {{citation needed}} template, and add a reason of the edit to the summary box. It is also good to ask other users (especially the one who added the description) an actual accessible source.
4. If you do not know an alternative accessible source and the description is doubtful, please remove the description and the link, and add a reason of the edit to the summary box.

If you do not know how to fix the issue, please feel free to ask other users at the corresponding talk page.

### Reliability of a source

As an exception, sufficiently "reliable" websites can be sources even if they are not the first sources or peer-reviewed sources. For example, Cantor's Attic was dealt with as a reliable website until it has gotten closed. Therefore we should clarify the borderline:

1. Allam's website was used by himself as a sources of his own numbers and his fake results on known numbers. It can be the first source of his own numbers, but can never be a source of those fake results unless he specifies reproducible explanations.
2. 2000 steps analysis was referred to as an evidence of several fake properties of functions in this community. It deals with unspecified functions and includes many errors. Therefore it can never be a source of results on actual (specified) functions.
3. Very big numbers is frequently used as a source of illion numbers. It just states that the website is based on the author's "knowledge", which is obviously unreliable. Since the author is not the creator of them, it should not be a source. For such traditional names of numbers, there is no "first source", but peer-reviewed publication can be a reliable source. For example, online encyclopedia which is freely editable is not appropriate, because it is not peer-reviewed by definition.
4. Numberpedia is used as a source of numbers by Garrett Wilkinson. Since the encyclopedia is not freely editable and is created by the person, it can be the first source. (But there is an issue on the notability. See its talk page.) Also, it includes many known numbers, but it can never be a source of them.

We clarify that we do not intend to blame those great websites. We are just mentioning to them as websites which cannot be reliable sources in an academic sense.

### Personal website

Several users create articles on their own numbers with citation to their own websites. It is allowed as we clarified above, because their own websites can be the first sources of their own numbers. However, they are not usually peer-reviewed, and hence might include many mathematical errors. Googology Wiki allows articles on ill-defined numbers in the current policy, and hence the existence of such errors cannot be a reason of the deletion. We can just explain the fact that they are ill-defined and the reason of the ill-definedness, instead of deleting the articles.

One problem is that the creators might silently change the definitions by updating their own websites as if those errors did not exist from the beginning and edit the corresponding articles to insist that they are well-defined. In that case, their own websites are not reliable sources, because quoted information might drastically vary. Therefore in order to avoid losing the reproducibility of a source, it is better to clarify the retrieval date if the users tend to update their own websites when other users point out errors. It is also good to make use of snap shots or web archives if the users continue to cheat.

Another problem is that statements such as the size of their own numbers in their own websites are not usually verified by others. We should always keep in mind that the reliability and the validity of a source depends on a description which we want to refer. Their own websites can be the first sources of their own numbers, but are not necessarily reliable sources of statements on them. Therefore when we refer to statements in their own websites, it is better to clarify that they are not peer-reviewed by writing something like "the creator intends/expects that the number is greater than Rayo's number" rather than "the number is greater than Rayo's number".

Note that although Cantor's Attic is a dead site, the raw source of any article is still accessible by appending "?action=raw" to the end of the URL of the article.

## Voting

The following users are members of the voting panel:

For voting-related policy, see #Blog_posts and #Clarification_of_creator.

## Blog posts

It is allowed to put content from blog post to the mainspace under the voting system. If somebody thinks that the blog post is well-qualified, it is possible to propose at Googology_Wiki:Voting to add info to the mainspace from it and add that post to the source. Only non-blocked users that were registered for at least 100 days (10 of them they were active) and 100 edits may vote to avoid abusing the voting system. Voting holds for 10 days.

For more details on the discussion about the voting system, see this blog post.

### Categories

It is allowed to put blog posts in categories, but not to mainspace categories - they should be placed on separate categories for blog posts.

### When posting

In line with this forum post, all counting blogs are banned. This does not include well-thought out competitions designed to spark serious thought, but rather posts which are quickly filled with comments which it doesn't take much thought to type.

### When commenting

Think before you comment. Comments which are entirely unrelated to the message of the blog post or are trivial salad extensions of the concepts discussed in the post are frowned upon.

## Clarification of creator

For an article on a number or a function, we have the following restrictions:

1. If the name is commonly used, then it should have a peer-reviewed source of the name.
2. If the name is uncommonly used and coined by non-anonymous one, then it should have the first source of the name.
3. If the name is uncommonly used and coined by anonymous one, then it should have the first source of the name and have been passed the voting system.

In particular, an article on an uncommon number should include information of the (anonymous or non-anonymous) creator of the number. If an article on a name includes no information of the (anonymous or non-anonymous) creator and refers to a non-eer-reviwed source, then it will be a candidate of deletion.

## Block

Admins will block harmful users. For example, vandalism, harassment, impersonation, racism, violation of rules or laws, and so on can be a reason of blocking. Also, users should sufficiently respect each other. When a user ignores other users in order to persist his or her personal preference, it will cause an edit war, which is not welcomed in this community.

### Vandalism

Vandalism is a deliberate attempt to harm the integrity of the encyclopedia. If you encounter vandalism, revert it and leave the owner a firm but respectful message to stop. If the vandalism persists, contact an administrator and they'll deal with it the way they see fit.

Examples of vandalism can include:

• Fake information
• Unconstructive edits
• Spam

If a user shows suspected attitudes, then admins will warn or block them. As we #assume good faith, we usually ask the user first not to repeat such suspected attitudes.

Fake information: As our purpose is to archive googology in the world as a secondary source, we are required to write information with first or peer-reviewed sources. Writing unsourced information (especially incorrect mathematical statements and non-existing notions) without any proof or reliable reasoning is discouraged. However, there are several examples of good information directly given by users. For example, there are many unsourced but reliable analyses, which help readers to understand numbers and functions. Therefore as long as the analyses are regarded as reliable descriptions, it is traditionally allowed in this community. In particular, we do not have to remove such a constructive description. Of course, if analyses are based on seriously unreliable assumptions or are obviously incorrect, we can remove them by clarifying the reason at the summary box. If a user repeats to add fake information, then admins might warn them.

Unconstructive edits: One of typical attitudes is the removal of information, which is strongly believed to be wrong in this community. For example, the removal of a correct and sourced information deeply related to the article in which it is written is against our purpose to archive googology. There are several unsourced information which is strongly believed to be correct. For example, as the #Deadlink section explains, there are several web pages whose links are dead. If an article referred to such a page while the link was alive, then the cited information is believed to be correct, although it is literally currently unsourced. Therefore in that case, it is discouraged to simply removed the cited information or put the deletion tag. It a user repeats such unconstructive edits, then admins might warn them.

Spam: Writing off-topic information, multi-posting to obtain other users' attention, creating irrelevant articles, and so on are not helpful to develop this wiki. It a user repeats to post spam contents, then admins might warn them.

One easiest way to deal with such suspected attitudes is to simply revert the edits. Generally speaking, it is believed not to be good to "feed" vandals, and hence we should just revert attacks without trying to "fight" vandals. Some vandals simultaneously write both correct information and incorrect information. In that case, it is really hard to check all edits by vandals during their vandalism. Therefore we are allowed to revert all of such edits without checking the correctness, in order to avoid spending more time than vandals. Of course, if we find appropriate information in the reverted edits, then we can simply restore them.

### Edit war

An edit war happens when two or more editors have a dispute, and instead of discussing things out, they revert back and forth between the revisions they want. Edit wars are not productive in any way, and generally just make people more angry. Instead of edit warring, talk it over and come to a decision.

In an effort to fight counterproductive edit warring, we will mirror the 3RR rule as found on Wikipedia:

Any editor who makes more than three reverts on the same page within a 24-hour period will be blocked for 24 hours. Self-reversion and reversion of obvious vandalism do not count towards this.

The purpose of 3RR blocks — and any other blocks, for that matter — are to prevent further disruption, not to punish misbehavior.

In order to avoid an edit war, it is good for you not to delete a correct description only due to your own preference. For example, if you think that it is better to remove spaces and blank likes or coversely add spaces and blank lines, it is just your preference, which is perhaps conflicting others' preference. If you feel that it is good to replace a correct description, you can discuss the topic in the corresponding talk page. Also, it is good to add a constructive description instead of deleting a correct description.

If two or more editors have distinct preferences which do not violate any other policy, then we should not persist our own preference. Instead, it is good to have a discussion at the corresponding talk page, before deciding to change the contents in a way following our own preference and ignoring other preferences. Even if your preference is not violating the policy, it does not mean that other preferences automatically violate the policy. Therefore stating something arrogant like "My preference should be respected, as it does not violate the policy" is non-sense. Similarly, we should not move articles with contributions by other users unless we have discussions at the talk page.

### How to warn users

Since it is hard for admins to check all vandalisms in this wiki everyday, normal users can help them by sending warnings to other users violating the policy. When you find someone violating the policy, you can warn the user by creating a new section for the warning and write

{{warning|<the precise rule in the policy>|<the precise source of the violation of the rule by the user>}}

at the user's talk page. The warned user can justify or apologise for the attitude below the warning, but must not remove or edit the warning by himself or herself. In that case, an admin will check the discussion, and clearly comment whether the justification or the apology is acceptable or not. Users can freely give opinions against the decision, and the admin can change the decision through the opinions. If the justification is judged to be acceptable and the user asks the admin to remove the warning, the admin will remove it. If the apology is judged to be acceptable, then the admin will add the status to the format. We regard a warning given in this way referring to a violation which has no accepted justification or apology as a valid warning. If you find a user satisfying either one of the following conditions, please report it to an admin:

1. The user has never been blocked and has been given three or more valid warnings.
2. The user has ever been blocked, is currently unblocked, and has been given three or more valid warnings since the last blocking of the user.

In that case, the admin will check the correctness of the sources in the format. If the sources of three or more of them actually show distinct violations, then the admin will block the user at least three months for the first time, and at least 99 years for the second time.

As a restriction of this rule, we should warn a user at most once for violations to a single rule given before the first warning related to the rule, in order to believe that the user just did not know the rule. This restriction does not prevent to warn violations to a single rule after the first warning related to the rule.

## Undefined notation

Undefined notation is when a wiki page introduces a notation but never specifies what it actually is. This is the most common with OCFs. You must specify the specific notation used, otherwise, your addition may be removed. The undefined notation template should be used whenever a notation isn't defined or it is different from the actual notation used in the article.