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Proposal for modification of policy in Googology Wiki:Policy#Analyses[]
The current wording of Googology Wiki:Policy#Analyses does not conform to many pages with approximations to numbers in other notations. For example, the policy does not specifically state that Hyperfactorial array notation is an allowed notation in analyses, which means that we would all have been warned/blocked adding HAN approximations to numbers, especially when the notation itself is quite confusing; and that we would technically only be allowed to add BAN, BMS and FGH (and HH and SGH) approximations, which is very boring and useless especially for milestone googolisms like a pentacthulhum.
Also, another example, the current policy states that we are not allowed to use BEAF beyond tetrational arrays in approximations. So many numbers beyond epsilon-zero have BEAF approximations on their number pages; additionally, BEAF is like a ballpark for understanding the true size of googolisms.
With the current wording of that section of the policy, many approximations in {{Approximations}} would be rendered useless and be limited to a few notations.
Therefore, I propose the following changes to the policy:
- Analyses should allow all well-defined notations as long as there is a Gwiki page describing the notation. An administrator/bureaucrat/P進大好きbot will decide whether a notation is sufficiently well-defined. I suggest putting an official list of which functions are well-defined on the policy and what functions we are allowed to use in number analyses in other notations.
- Only specific notable ill-defined notations should be allowed in analyses, for example BEAF beyond tetrational arrays, dollar function and strong array notation (UNAN possibly?). Such analyses must have an "(intended)" next to them to show that they are ill-defined. An administrator/bureaucrat/P進大好きbot will decide whether an ill-defined notation is notable enough. I can now immediately think of a nonnotable ill-defined function: Almighty Array Notation.
- FGH, HH and SGH approximations are allowed iff the user specifies what OCF they are using above \(f_{\alpha}(n)\) when \(\alpha > \omega\) (and possibly the system of fundamental sequences) (Exceptions could be Hyp cos' catching function and Bachmann's \(\psi\) which don't have wiki pages). This means that analysis using an unspecified \(\psi\) for example are disallowed.
I hope this is clear enough to you and that you take this into consideration when voting. If you have any changes you want to make to make this slightly clearer, please suggest down below.
Please tell us whether you agree or disagree with Redstonepillager's proposed changes to Googology Wiki:Policy#Analyses outlined above.
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Even if you agree (resp. disagree) with one of the topics, you can agree (resp. disagree) with another one. Also, the voting right in this community is just a right, but not a duty. Therefore we do not force you to vote (you can silently abstain from this voting, and you can express your decisions for the topic above).
Redstonepillager 14:41, 19 October 2023 (UTC)
- Thank you for the proposal. Although I disagree with some of them, I hope that good discussion will be held.
- Disagree. The reason why we have the rule is to ensure the notability. When we did not have the rule, many users added their own notations in analyses of well-known numbers in order to advertise them. Since it does not match the purpose to provide a helpful information for the reader, it is not welcomed.
- Disagree. The reason why we have the rule is to ensure the reproducibility and to avoid misleading. When we did not have the rule, many users added their own analyses using BEAF beyond tetration without any theoretic justification in analyses of higher computable level. This caused serious misunderstanding of many readers that BEAF is actually so strong, and is actually intended to work in that way, although there is no agreed upon definition in that level. As long as there is no actual official definition, no analysis makes mathematically sense, and hence is reproducible. Since this wiki is an academic wiki, personal guess without any theoretic justification or reproducibility should not be added.
- Agree, only when the system of fundamental sequences is required to be clarified, the exception allowing the ill-defined Catching function is removed, and analysis beyond Buchholz's OCF level requires a proof. There is no need to allow to use ill-defined function. Analysis written in an article should be sufficiently reproducible (and people wrote so many wrong analyses even for Buchholz's OCF level when I came to this community due to the tradition to ignore proofs and definitions). Therefore, it is better to allow only a proof-based analysis at least beyond Buchholz's OCF level.
- p-adic 22:02, 19 October 2023 (UTC)
- I agree with some of your points, but I will comment on each of your comments.
- So you are essentially suggesting that analysis using Hyperfactorial array notation is not allowed, just because it isn't explicitly specified on the wiki policy. It is a perfectly well-defined notation up to the Countable limit of Extended Buchholz's function. You are also suggesting that analysis using strong array notation is disallowed just because there is no proof of the well-foundedness of the notation, and SAN is, in my opinion, fully formalised at least below epsilon-zero. However, you are also suggesting that BEAF analysis using a separator not officially formalised by Bowers himself (the [] brackets) would not be allowed, which I agree with. I think that people used that unformalised separator just because of this video. So perhaps would it be a good idea to list all notations allowed in analyses?
- I disagree with your reasoning, but I do agree with some of your points. This blog post, this blog post and this blog post all by Hyp cos is probably why people put BEAF analyses beyond the well-defined level. The "serious misunderstanding" is more like community consensus, BEAF is indeed ill-defined beyond tetrational arrays but Bowers intended it to go much much further. Since there is no agreed upon definition, we could simply specify whether the intended approximation is using the non-climbing method or the climbing method (but both "meet" at the small veblen ordinal). If you think those BEAF analyses are incorrect, we could just nominate those blog posts for deletion simply because they are "misleading". Finally, although this wiki is indeed an academic wiki, there is also a community embedded within, and creators of individual notations have likely added analyses to their notations, which seem logical because every single array notation other than HAN have the same principle. Also, I highly doubt that any serious analyses of functions/array notations are personal guesses.
- So are you suggesting that we should all learn Taranovsky's C for analysis beyond Rathjen's \(\psi\)? Nah, too complicated. Not everyone here is a serious mathematician like you, Pbot. Rathjen's psi function is also tricky and challenging to learn and I believe that it doesn't even reach higher l-n-gion spaces in BEAF in what Bowers intended. Also, not everyone is gonna bother writing up an entire proof that the limit of BAN is \(\psi_0(\Omega_\Omega)\), if you see what I mean. The tradition to use wrong FGH approximations using undefined OCFs is possibly long gone too.
- I agree with some of your points, but I will comment on each of your comments.
Redstonepillager 23:35, 19 October 2023 (UTC)
- Thank you for the replies.
- > So you are essentially suggesting that analysis using Hyperfactorial array notation is not allowed, just because it isn't explicitly specified on the wiki policy.
- Not exactly. There are two points:
- Approximating a well-known notation by a less known notation causes the incident which I explain above. In order to avoid the trouble in a fair way, it is good to fix a sufficiently famous notations which can be officially used in this wiki. Since this is not a vote for adding Hyperfactorial array notation but for allowing all well-defined notations, Hyperfactorial array notation is not an exception for this purpose.
- Many of the functions are just believed to be well-defined and strong, even when there are no proof. For example, are you responsible for the well-definedness of Hyperfactorial array notation and the strength in your statement with reproducible proof? If no, then how do you get the truth that your statement is correct? (In order to clarify the point, please answer both. Thank you. For our convenience, I enumerate my questions. These are questions 1 and 2)
- > You are also suggesting that analysis using strong array notation is disallowed just because there is no proof of the well-foundedness of the notation
- Not exactly. SAN does not have an official formalisation, by the reason explained in the corresponding article.
- > So perhaps would it be a good idea to list all notations allowed in analyses?
- If I correctly understand, the policy has already listed all notations allowed in analyses.
- > If you think those BEAF analyses are incorrect, we could just nominate those blog posts for deletion simply because they are "misleading".
- Why...? Is there any policy to allow to delete misleading blog post? (Question 3)
- > Also, I highly doubt that any serious analyses of functions/array notations are personal guesses.
- Even if the authors of analyses are serious, the required property is the reproducibility in academic sense. For example, people used UNOCF "seriously" in there analyses, and they have rough consensus on their analyses. However, those did not mathematically make sense. (In order to make people understand, I showed a contradiction under the assumption that there analyses of UNOCF vs Buchholz's OCF and UNOCF vs PSS are correct.) I respect their serious trials, but results should be academically estimated. (I emphasise that I am not insisting that all of their results are incorrect. I understand that many experts have outstandingly great ability to analyse notations. However, they are not reproducible, and are based on many implicit assumptions. In order to be responsible as an academic wiki, we keep the position that we are collecting sourced information, rather than to spread statements just given by trusted members.)
- > So are you suggesting that we should all learn Taranovsky's C for analysis beyond Rathjen's?
- Not exactly. I suggested the use of OCFs with an explicit system of fundamental sequences. In the agreement, Stegertz's and so on can be used.
- > Not everyone here is a serious mathematician like you, Pbot.
- I know. I am not requiring for everyone to be a mathematician, but to be responsible for what they write in an academic sense. This is a wiki to collect first sources, and people, even if they are not mathematicians, can collect first sources appropriately. This is not a place to output new personal studies, and hence people should not write what they cannot be academically responsible.
- > Rathjen's psi function is also tricky
- Compared to what other well-defined function? (Question 4)
- > I believe that it doesn't even reach higher l-n-gion spaces in BEAF in what Bowers intended.
- It is the point. Since BEAF is unformalised, people can state anything on the intended value. I have ever discussed a similar estimation, but the one who insisted did not understand OCFs of that level at all. BEAF was traditionally considered to be the strongest and to be much stronger than OCFs, but the belief was made when few f them understood OCFs beyond EBOCF. (You know that there are lists of common mistakes in corresponding articles. When I came to this community, almost all understanding on OCFs were wrong.) Such an expectation based on estimation of actual well-defined works without referring to actual definitions causes serious misunderestimation, like UNOCF users did for Rathjen's OCFs.
- I doubt that Bowers understood OCFs of that level when he created BEAF, and hence guess that even an intended value is not so big as numbers of that level. However, I respect BEAF users pure belief in BEAF, because it is also an aspect of googolism. On the other hand, if we edit an article, we need to be academically responsible by giving a reproducible information. That is why it is not good to add analyses based on BEAF.
- p-adic 00:49, 20 October 2023 (UTC)
- 1. are you responsible for the well-definedness of Hyperfactorial array notation and the strength in your statement with reproducible proof?
- no.
- 2. If no, then how do you get the truth that your statement is correct?
- If I was adding a HAN approximation to a googolism for example, I would most likely use User blog:Cloudy176/Hyperfactorial array notation: Analysis part 1 which the creator of the notation has agreed to be an accurate analysis. For anything requiring dimensional and multidimensional arrays, it's just guesswork based on the FGH sizes of faxul numbers given by the community, but I have a 99% confidence that the approximation is correct. I like to tread very carefully with analyses.
- >If I correctly understand, the policy has already listed all notations allowed in analyses.
- I'm exactly trying to clarify the rules on what notations are allowed in analyses. The current wording does not represent the googological community in 2023. The current policy might have been true and useful in, say, 2014 (or whenever BMS was first formalised).
- 3. Why...? Is there any policy to allow to delete misleading blog post?
- There is no policy but the blog posts may have been misleading enough such that people add BEAF approximations beyond the well-defined level and confuse readers, as per your saying. I would not like to see those blog posts deleted but if that's what you want (not confusing readers), then I have nothing to say.
- 4. Compared to what other well-defined function?
- I didn't make any comparisons. I simply stated that it is a tricky one to learn, so some (or most) people are not going to bother learning it.
- 1. are you responsible for the well-definedness of Hyperfactorial array notation and the strength in your statement with reproducible proof?
- Redstonepillager 02:10, 20 October 2023 (UTC)
- Thank you for answers.
- > If I was adding a HAN approximation to a googolism for example,
- I am sorry, but this does not seem to answer my question. You clarified "It is a perfectly well-defined notation up to the Countable limit of Extended Buchholz's function.", and hence I asked how you are certain for the well-definedness. Since you clarified it as a fact, there is some academic evidence, right? (Question 1)
- > For anything requiring dimensional and multidimensional arrays, it's just guesswork based on the FGH sizes of faxul numbers given by the community, but I have a 99% confidence that the approximation is correct. I like to tread very carefully with analyses.
- As I said, trusting and confidence do not effect here. We need reproducibility of results, rather than confidence of personal works by experts. Indeed, "99% blah-blah" is not necessarily trustworthy in this community, because UNOCF was said to be "99% formalised" if I correctly understood.
- > There is no policy but the blog posts may have been misleading enough such that people add BEAF approximations beyond the well-defined level and confuse readers, as per your saying.
- It sounds strange. Since policy does not allow us to freely judge to delete personal page, we should not. Could you share an evidence that we are allowed to delete them? (Question 2)
- Also, my statements do not ensure any sort of justification of such decisions. Therefore I do not understand why you believe that we are allowed to do so. Possibly are you confounding the main space and the personal spaces?
- > I didn't make any comparisons. I simply stated that it is a tricky one to learn, so some (or most) people are not going to bother learning it.
- Then it is not a fair point of view. Rathjen's work is not tricky as one in that level. If people think that it is bothering to learn that level, it is ok. They can choose not to study that level, and contribute to a lower level in a responsible way. Therefore, this does not justify any use of ill-defined notations.
- p-adic 10:30, 20 October 2023 (UTC)
- Q1. Since you clarified it as a fact, there is some academic evidence, right?
- We have yet to see a proof of termination of HAN, but given that the nucleaxul numbers have a clear pattern in FGH order type, I suppose that HAN has a well-defined limit of \(\psi_0(\Lambda)\) with respect to EBOCF with the lambda is the omega fixed point.
- Q2. Could you share an evidence that we are allowed to delete them?
- I couldn't find any evidence, but we could put a notice on those blog posts that the analysis does not mathematically make sense.
- Also, why are we deviating from the original topic of proposing to add an official well-defined function list to the policy and the discussion of whether to allow ill-defined functions in approximations?
- Redstonepillager 11:06, 20 October 2023 (UTC)
- > We have yet to see a proof of termination of HAN, but given that the nucleaxul numbers have a clear pattern in FGH order type,
- Such a pattern does not give evidences... When you state that a given notation is well-defined as a fact, please be responsible for the statement. People claimed that PSS was obviously terminating by the clear pattern even before showing the termination, while the termination was non-trivial. Some analyst even claimed that the termination of "all" versions of BMS was clear due to the patern matching, while some of them is currently known to be non-terminating. People claimed that UNOCF was essentially well-defined up to at least of standard OCF level due to the patern matching, while it is even ill-defined at a very low level.
- Allowing "all well-defined notations" without giving any proof of well-definedness causes this problem. When somebody put analyses by some notation, and other rejected them by the lack of the well-definedness proof, the the one claims "All well-defined notations should be allowed. So, you have any proof of non-termination?" because he or she strongly believes the well-definedness. Like you, claiming that Hyperfactorial array notation should be allowed because it is "known" to be well-defined.
- > I couldn't find any evidence, but we could put a notice on those blog posts that the analysis does not mathematically make sense.
- If you have no evidence why you are certain that we could? (Question 1) Blog posts are given in personal spaces. We do not have right to disturb personal works unless we have reasonable justification in the policy. Since the policy does not forbit users to put uncertain contents in a blog post, such destruction should be avoid.
- > Also, why are we deviating from the original topic of proposing to add an official well-defined function list to the policy and the discussion of whether to allow ill-defined functions in approximations?
- This is because you claimed that my opinion leads to the conclusion that we can remove such blog posts. Since removing personal works is not allowed in the policy, it causes a simple abuse of admin right. So, you are essentially insisting that my opinion leads to the conclusion that we can let admin to abuse admin right. Therefore, you should be responsible for you statement.
- p-adic 22:47, 20 October 2023 (UTC)
- I didn't say I was "certain" those blog posts could be removed. Redstonepillager 05:25, 21 October 2023 (UTC)
- You mean that many of your statements are uncertain when you are not clarifying that they are certain, even when you clarified them as facts, right...? Please claim statements as facts which you are certain. For example, you are not supposed to state that we can remove blog posts when you are not certain, and are no tsupposed to state that HAN is well-defined when you are not certain. Such clarification as facts just makes discussion ambiguous.
- p-adic 09:57, 21 October 2023 (UTC)
- I didn't say I was "certain" those blog posts could be removed. Redstonepillager 05:25, 21 October 2023 (UTC)
- Agree per nom. I ensure that the proposed change will make the statement much clearer, especially for various well-defined notations, while it is currently unclear. DeepLineMadom (talk) 00:53, 20 October 2023 (UTC)
- For the first 2 points, I wait for the discussion to finish. For the 3rd point, I basically agree, except that I think Wainer hierarchy for \(f_{\alpha}(n)\) when \(\alpha < \varepsilon_0\) can be used without mentioning, as it is so popular and a kind of de facto standard. 🐟 Fish fish fish ... 🐠 07:20, 20 October 2023 (UTC)
- for fundamental sequences associated to Cantor normal form, you forgot to add. Redstonepillager 09:09, 20 October 2023 (UTC)
- I agree to all 3 statements, but I have 2 questions.
- If a notation is proven to be well-defined, then it should be mathematically make sense. Also, it's a good idea to allow all well-defined notations because this may encourage people to learn more googological notations.
- We should allow ill-defined notations iff the notation is relatively famous and they must be notable enough, for example BEAF beyond tetrational arrays, dollar function, strong array notation and maybe UNAN. Their analyses also must have either "(intended)" next to the name of the notation or "(debatable)" next to the expression to show that they are ill-defined. Also, unspecified extensions that are not in the wiki such as \(\{10,100([1]1)2\}\) should not be allowed. But I want to ask, why Almighty Array Notation is not notable?
- Specifying which OCF the user is using above \(f_{\alpha}(n)\) when \(\alpha > \omega\) (and possibly the system of fundamental sequences) are necessary because if we just provide a random OCF expression, e.g. \(\psi(\Omega^{\omega})\), it will have ambiguities and hence the expression will be ill-defined. Also, do we think we should allow OCFs that are from blog posts such as Hyp cos' catching function and Bachmann's \(\psi\) as a valid OCF?
- But still, I agree to all of the statements.
- HaydenTheGoogologist2009 13:36, 21 October 2023 (UTC)
- Directed to HaydenTheGoogologist2009.
- Pbot said that notations like hyperfactorial array notation have no proof of termination, and trio-sequence BMS has no proof of termination. Should we also formally allow trio- sequence BMS for stuff above \(\psi_0(\Omega_\omega)\) with respect to Buchholz's function?
- Should we allow reflection/stability as well for extremely large numbers? (For context, meameamealokkapoowa oompa is "around" \(\psi(min \Pi_1((^{++})\text{-}\Pi_1\cap\Pi_1((^{++})\text{-}\Pi_1))\) using reflection according to a discord message from Googology and Apeirology discord server, so this might be very wrong).
- Regarding the catching function, since it is based on FSes of Bachmann's \(\psi\), and since Bachmann's \(\psi\) is ill-defined probably from \(\psi(\varepsilon_{K+1})\), we need to have a bit more discussion.
- Fish pointed out that we don't necessarily need to mention Wainer hierarchy with CNF's FSes \(f_{\alpha}(n)\) when \(\alpha < \varepsilon_0\).
- Redstonepillager 14:06, 21 October 2023 (UTC)
- Directed to HaydenTheGoogologist2009.
- To Redstonepillager
- The ill-definedness of the catching function is more serious. It is unformalised even at a very low level. Therefore, I do not understand why you picked it up as an exception.
- p-adic 15:42, 21 October 2023 (UTC)
- I think we should allow Hyperfactorial array notation, strong array notation and Bashicu matrix system but only up to their well-defined levels. I think that Hyperfactorial array notation is well-defined up to at least \(200![200([200([200([200([...])200])200])200])200]\) (Large Veblen ordinal level), strong array notation is well defined up to \(\text{s}(3,3\{1`2\}2)\), and the Bashicu matrix system (with respect to version 2.3 = 4) is well defined up to \((0,0)(1,1)(2,2)(3,3)...[100]\). Also, you must specify which version of BMS you're using if you're not using either BM2.3 or BM4.
- I don't think we should allow reflection/stability for extremely large numbers, because they're usually ill-defined.
- I don't think we should allow Hyp cos' catching function or Bachmann's \(\psi\) (by Hyp cos) because the catching function is ill-defined even at the very first level, and Bachmann's \(\psi\) (by Hyp cos) is not formalised. However, the original version of Bachmann's \(\psi\) is allowed.
- On second thought I think we don't necessarily need to mention Wainer hierarchy with CNF's FSes \(f_{\alpha}(n)\) when \(\alpha < \varepsilon_0\) because I think it's the default function for all \(\alpha < \varepsilon_0\).
- By the way, I've summarized my opinions in https://sites.google.com/view/haydens-big-numbers/googology-wiki-related/proposal-for-modification-of-policy-in-googology-wikipolicyanalysis .
- HaydenTheGoogologist2009 06:04, 22 October 2023 (UTC)
- To Hayden. Holey cow.
- When using SAN and BEAF past Ε₀, HAN past the large veblen ordinal, D Shamlin Jr's extension of BAN, or trio sequence BMS, we need to label the notations as (intended) or the analysis as (debatable), as there is no proof of formalisation/termination.
- Also I guess that the ill-definedness of catching function makes sense, but I think that it's still a good idea to put (intended) and allow it to be used in analysis because we don't expect everyone to learn Taranovsky's C and that it reaches the limit of BEAF.
- Redstonepillager 07:22, 22 October 2023 (UTC)
- To Hayden. Holey cow.
- > D Shamlin Jr's extension of BAN
- Actually, that's BEAF.
- But anyways, I agree with the first statement, but I only partially agree with the second statement. According to the policy, we shouldn't add links to blog posts in articles.
- HaydenTheGoogologist2009 14:03, 22 October 2023 (UTC)
- > That's BEAF
- this video shows D Shamlin Jr going to extended BAN, no rules yet, just large numbers gradually increasing
- >We shouldn't add link to blog posts in articles
- Catching hierarchy...
- Redstonepillager 15:56, 22 October 2023 (UTC)
- Unfortunately, your page is marked as candidate for deletion, so looks like we can’t add it.
- HaydenTheGoogologist2009 23:30, 22 October 2023 (UTC)
- it no longer is though, for a good reason. Redstonepillager 07:05, 27 October 2023 (UTC)
- As I explained at your talk page several days ago, the cited sources are not valid sources for the coined work. I readded the deletion template. Also, please do not personally remove the template when discussion is not over.
- p-adic 09:16, 27 October 2023 (UTC)
- it no longer is though, for a good reason. Redstonepillager 07:05, 27 October 2023 (UTC)
Is there any more discussion? Because this "voting" should end on Nov 2nd (14 days). Redstonepillager 17:26, 31 October 2023 (UTC)
- Please reclarify that many of your claims were uncertain and actually wrong, because users believe what you wrote.
- You stated that Hyperfactorial array notation is well-defined and has some strength, but it is actually unknown to be well-defined and to have that strength.
- You stated that Catching function can be an exception, but it is actually ill-defined even at very low level.
- You stated that there is already an article on Catching function in the context referring to the original version, but you created it by yourself actually as an article on your own recast under the same name rather than the original version.
- You stated that we could remove blog posts if we follow the current policy on analysis, but the current policy does not allow such a deletion.
- Including uncertain information directly related to voting is unsound, and hence you should officially correct your mistakes.
- Also, when a user created an article on his or her own notation and used it in an analysis while it is unknown to be well-defined, should we first spend time to prove the well-definedness before judging the validity? It is not sound because this wiki is a place to collect first sources, but is not a place to add unsourced information and to make somebody have duty to prove the correctness. Say, will you be responsible for addition of such analyses? Or are you just trying to make other users (such as me, admins, and panels) have duty while you will not cost time? If so, since checking the well-definedness generally costs much time, the proposal is not based on careful thoughts on equal tasks on each user.
- p-adic 22:36, 31 October 2023 (UTC)
- There have been discussions based on the initial proposal, and the proposal was not updated since then. I share the concern by p進大好きbot about "who validates the well-defindedness of the notation", as I am one of the members of the responsibility (admin). For this reason, I disagree to the first 2 points, at least at the current state of the description. For the 3rd point, I already agreed. 🐟 Fish fish fish ... 🐠 07:07, 1 November 2023 (UTC)
- I propose an alternative proposal below based on discussion so far. —Preceding unsigned comment added by Redstonepillager (talk • contribs)
Alternative proposal 1[]
The old proposal has gone virtually nowhere and this new proposal has modifications to the original one to make it slightly more concise.
Since I propose an alternative proposal, this voting should be extended by seven days. Here are my updated proposals to change the rules in Googology Wiki:Policy#Analyses and I pretty much expect the rules said there to be crystal clear. This shall only apply to mainspace pages.
- Proposal 1. Allow all well-defined notations to be used in analyses, because it will encourage people to learn more notations. Gwiki administrators will decide whether a notation is well-founded or not as well as the limit of its well-foundedness if the notation continues beyond its well-founded limit (e.g. BEAF is well-founded up till tetrational arrays). We should list all gwiki admin panel-approved well-founded notations that can be used on analyses on the policy, and the list shall be decided and maintained by the admin panel.
- I propose a preliminary list of well-defined notations as below:
- Arrow notation
- BEAF up to tetrational arrays
- Bashicu matrix system version 2.3 = 4
- Bird's array notation
- Chained arrow notation
- Copy notation
- DeepLineMadom's Array Notation
- Extensible-E System (includes Collapsing-E Notation, excludes all interpretations of ##xE^ and /xE^)
- Graham Array Notation
- All maps defined by Fish used to construct the relevant Fish numbers
- Scientific notation
- Steinhaus-Moser Notation
- Taro's multivariable Ackermann function
- X-Sequence Hyper-Exponential Notation
- Fast-growing hierarchy, Hardy hierarchy, and Slow-growing hierarchy with respect to the following system of fundamental sequences:
- The fundamental sequences associated to iterated Cantor normal form, finitary Veblen function, Buchholz's function by Buchholz and Denis, Extended Buchholz's function, Rathjen's psi function and Taranovsky's C. This could also include my FGH to SGH catching function when I fix all issues to the article.
- I propose a preliminary list of well-defined notations as below:
- Proposal 2. Allow an notation with no proof of well-foundedness to be used in analyses iff it is sufficiently notable. Gwiki administrators will decide whether an ill-defined notation is sufficiently notable and a list shall be put on the policy on which ill-defined notations are sufficiently notable to be used in approximations. The list shall be decided and maintained by the admin panel.
- I propose a preliminary list of sufficiently notable ill-defined notations as below:
- BEAF beyond tetrational arrays
- Dollar function
- Hyperfactorial array notation (no proof of well-foundedness)
- All interpretations of ##xE^ (excludes /xE^)
- Strong array notation (no proof of well-foundedness)
- Username5243's Array Notation
- I propose a preliminary list of sufficiently notable ill-defined notations as below:
- Proposal 3. Using FGH HH or SGH in analyses is allowed iff one specifies the FS (or OCF) for \(f_\alpha (n)\), \(H_\alpha (n)\) and \(g_\alpha (n)\) when \(\alpha\) > \(\omega\).
- Proposal 3.1. Assume the use of a fundamental sequence iff they meet the requirement as written below.
- Wainer hierarchy/CNF is assumed when the user puts a valid Wainer/CNF expression in \(\alpha\).
- Veblen hierarchy is assumed when the user puts a valid Veblen function expression in \(\alpha\) as well as the following Greek characters used for shortening: \(\varepsilon_\alpha\), \(\zeta_\alpha\), \(\eta_\alpha\), and \(\Gamma_\alpha\).
- Proposal 3.1. Assume the use of a fundamental sequence iff they meet the requirement as written below.
Anyone can propose to make changes to any of the lists mentioned in the proposals via a section of the voting page. This must be voted on and ratified by the community.
This proposal takes all rights to the admin team. For example, they will decide whether hyperfactorial array notation is well-defined or not. This should leave no exceptions.
Please tell us whether you agree or disagree with Redstonepillager's first alternative proposition to Googology Wiki:Policy#Analyses outlined above.
From Googology Wiki:Policy#Voting, a single user cannot use two or more accounts in a voting. Only non-blocked users that were registered for at least 100 days, made at least 1 edit in the past 10 days, and have more than 100 edits in total, may vote to avoid abusing the voting system. This vote shall hold for \(n\) days. Please do not forget to add your signature by writing four tildes (~~~~).
Even if you agree (resp. disagree) with one of the topics, you can agree (resp. disagree) with another one. Also, the voting right in this community is just a right, but not a duty. Therefore we do not force you to vote (you can silently abstain from this voting, and you can express your decisions for the topic above).
Redstonepillager 11:14, 1 November 2023 (UTC)
- You mean that you propose writing these sentences in the policy? In the policy it is written "Additionally, we should specifically list all gwiki admin panel-approved well-founded notations that can be used on analyses on the policy." and "a list shall be put on the policy on which ill-defined notations are sufficiently notable to be used in approximations."? Then where is the list? If the list is not given, the policy is self-contradictory. Your proposal should be with a concrete list of such lists, otherwise the voting may not begin. 🐟 Fish fish fish ... 🐠 16:44, 1 November 2023 (UTC)
- I think that the current policy is clear enough and do not feel like rewriting the policy to the suggested one. It would be more constructive to discuss how we can update the list given in the analysis section. 🐟 Fish fish fish ... 🐠 16:51, 1 November 2023 (UTC)
- I must add that admins have no special right over the users for community decision. Maintaining such "lists" should be the work of all users in gwiki, not by admin group. 🐟 Fish fish fish ... 🐠 17:01, 1 November 2023 (UTC)
- Disagree.
- The duty "Gwiki administrators will decide whether a notation is well-founded or not as well as the limit of its well-foundedness" is absolutely heavy.
- The statement "This could also include my FGH to SGH catching function when I fix all issues to the article" is not validly judged because others do not know how the function will be changed. Please refrain from trying to make others use your own future work.
- Disagree.
- I have already explained that the problems on Hyperfactorial array notation and SAN are not just well-foundedness, but well-definedness as a system. Nobody has ever proved that the former one is well-defined as a possibly ill-founded notation, and the latter is known to be even unformalised. Since I have already pointed out the issues, please do not hide them. Others will misunderstand the level of the ill-definedness.
- Use of ill-defined notations in analyses is quite misleading. People might believe that they are well-defined, as people actually believed UNOCF, "normal OCF", BEAF, and SAN were well-defined.
- Agree under the following restrictions:
- The clarification of the assumption should be rewritten more precisely.
- The statement should be corrected because Veblen hierarchy is not applicable to \(\Gamma_{\alpha}\) for \(\alpha > 0\). Perhaps you intend a finitary extension. Or further extensions?
- What does "valid Wainer/CNF expression" precisely mean? People sometimes use non-normal expressions. The proposal forbids the implicit use of them, right? (I have no opinion on the choice, and this is just for clarification.) At any rate, please use non-ambiguous term for a proposal.
- What does "valid Veblen expression" precisely mean? People sometimes use non-normal expressions. The proposal forbids the implicit use of them, right? (I have no opinion on the choice, and this is just for clarification.) At any rate, please use non-ambiguous term for a proposal.
- Analysis beyond Buchholz's OCF level requires a proof.
- The clarification of the assumption should be rewritten more precisely.
- Disagree.
- p-adic 22:47, 1 November 2023 (UTC)
- Removed the statement as nobody seems to agree to it.
- Removed the reference to catching hierarchy.
- Can you please show that HAN lacks well-foundedness?
- I've added one more detail to clarify stuff if that helps. If you still think that using ill-defined notations in analyses is problematic, let me know.
- I've tried to rewrite everything in proposal 3 more precisely. —Preceding unsigned comment added by Redstonepillager (talk • contribs)
- In my decision, I partly agree to the whole proposal.
- For proposal 1, I agree to include the well-defined notations in the preliminary list, but I disagree to the statement "Gwiki administrators will decide whether a notation is well-founded or not as well as the limit of its well-foundedness if the notation continues beyond its well-founded limit" because this will just give more work to the admins. Also I disagree to include the Catching function in the list since it is ill-defined even at the very first level.
- For proposal 2, I agree to include the sufficiently notable ill-defined notations in the preliminary list iff their analysis have either "(intended)" next to the name of the notation or "(debatable)" next to the expression to show that they are ill-defined, but I disagree to the statement "Gwiki administrators will decide whether an ill-defined notation is sufficiently notable and a list shall be put on the policy on which ill-defined notations are sufficiently notable to be used in approximations" because this will just give more work to the admins, just like the statement in proposal 1.
- For proposals 3 and 3.1, I agree that using FGH HH or SGH in analyses is allowed iff one specifies the FS (or OCF) for \(f_\alpha (n)\), \(H_\alpha (n)\) and \(g_\alpha (n)\) when \(\alpha\) > \(\omega\). However, I recommend to rewrite proposal 3.1 as follows:
- Wainer hierarchy/CNF is assumed when the user puts a valid Wainer/CNF expression in \(\alpha\) where \(\omega < \alpha < \varepsilon_0\). For example, \(\omega\), \(\omega+1\), \(\omega2\), \(\omega^2\), \(\omega^{\omega}\), etc.
- Veblen hierarchy is assumed when the user puts a valid Veblen function expression in \(\alpha\), such as \(\varphi(1,0)\), \(\varphi(1,0,0)\), \(\varphi(1,0,0,0)\), etc., as well as the following Greek characters used for shortening: \(\varepsilon_\alpha\), \(\zeta_\alpha\), \(\eta_\alpha\), and \(\Gamma_\alpha\). For example: \(\varepsilon_0\), \(\zeta_0\), \(\eta_0\), and \(\Gamma_0\).
- HaydenTheGoogologist2009 07:05, 2 November 2023 (UTC)
- I think it is sufficient to note that the list can be updated after discussion in the community, for example at the talk page of the policy. 🐟 Fish fish fish ... 🐠 07:10, 2 November 2023 (UTC)
I have also added proposal 4 for the relevant warnings if anyone violates the proposals above assuming all passes. Redstonepillager 13:49, 2 November 2023 (UTC)
I personally think that it is not good to frequently change the proposals, because the repetition makes the disscussion essentially invisible or seriously misleading for future users. Could you revert the change, and simply add a new section instead? (Through the process, please move opinions for the updated proposal to the new section.)
Also, in order to avoid masssive rewriting, if you intend to update the proposals, please do it at least after you understand issues. Otherwise, other users need to cost much time whenever (for example, just giving a possible extreme case) you try to revert the discussion by the change so that agreement will win. If you intend to repeat to change the proposal so frequently before you understand the issues, I clarify that I disagree all changes of the policy in the current voting unless otherwise specified, in order to save my time.
In my personal point of views, the voting process is not a process to frequently change the target to vote after the beginning of the voting period. The change of the conclusions in each user is of course ok in sound discussions, but for voting, the target of the voting should be usually fixed after the beginning of the voting period. Only exceptions are serious mistakes in the descriptions. So, if you just intend to correct mistakes, please try to understand issues before rewriting the proposals. Namely, if you have something that you do not understand, then you should ask details until you fully understand responsibly or try not to include related information.
Also, your request "Can you please show that HAN lacks well-foundedness?" does not seem to be appropriate. Why should I owe this task, which I am not responsible for? You were responsible for your statement of the well-definedness and the well-foundedness of HAN because those were unproved, but other users are not responsible for the opposite statements.
p-adic 22:38, 2 November 2023 (UTC)
Alternative proposal 2[]
This is a revision of my first alternative proposal.
Since I propose a second alternative proposal, this voting shall be further extended by seven days. Here are my updated proposals to change the rules in Googology Wiki:Policy#Analyses and I pretty much expect the rules said there to be crystal clear. This shall only apply to mainspace pages.
- Proposal 1. Allow the list of well-defined notations below to be used in analyses, because it will encourage people to learn more notations. Anyone can propose to add notations or object to any notation on the list on a specific section of the voting page, which must be voted on and ratified by the community.
- I propose a preliminary list of well-defined notations as below:
- Arrow notation
- BEAF up to tetrational arrays
- Bashicu matrix system version 2.3 = 4, up to \((0,0)(1,1)(2,2)(3,3)(4,4)(5,5)\ldots \ldots\) (pair sequence limit)
- Bird's array notation (Bird's version)
- Chained arrow notation
- Copy notation
- DeepLineMadom's Array Notation
- Extensible-E System (includes Collapsing-E Notation, excludes all interpretations of ##xE^ and /xE^)
- Graham Array Notation
- All maps defined by Fish used to construct the relevant Fish numbers
- Scientific notation
- Steinhaus-Moser Notation
- Taro's multivariable Ackermann function
- X-Sequence Hyper-Exponential Notation
- Fast-growing hierarchy, Hardy hierarchy, and Slow-growing hierarchy with respect to the following system of fundamental sequences:
- The fundamental sequences associated to iterated Cantor normal form, finitary Veblen function, Buchholz's function by Buchholz and Denis, Extended Buchholz's function, Rathjen's psi function and Taranovsky's C. See proposal 3 and proposal 3.1 for more information.
- I propose a preliminary list of well-defined notations as below:
- Proposal 2. Allow an notation with no proof of well-foundedness to be used in analyses iff it is sufficiently notable. Anyone can propose to add notations or object to any notation on the list on a specific section of the voting page, which must be voted on and ratified by the community. Additionally, an analysis using the notations below are only allowed iff their analysis has either "(intended)" next to the name of the notation or "(debatable)" next to the expression to show that they are ill-defined.
- I propose a preliminary list of sufficiently notable ill-defined notations as below:
- BEAF beyond tetrational arrays
- Trio sequence system in Bashicu matrix system under version 2.3 = 4
- Dollar function
- D Shamlin Jr's extension of Bird's array notation up to \(\psi_0(\Lambda)\)
- Hyperfactorial array notation (no proof of well-foundedness)
- All interpretations of ##xE^ (excludes /xE^)
- Strong array notation (no proof of well-foundedness)
- Username5243's Array Notation
- I propose a preliminary list of sufficiently notable ill-defined notations as below:
- Proposal 3. Using FGH HH or SGH in analyses is allowed iff one specifies the FS (or OCF) for \(f_\alpha (n)\), \(H_\alpha (n)\) and \(g_\alpha (n)\) when \(\alpha\) > \(\omega\).
- Proposal 3.1. Assume the use of a fundamental sequence iff they meet the requirement as written below.
- Wainer hierarchy/CNF is assumed when the user puts a valid Wainer/CNF expression in \(\alpha\) where \(\omega < \alpha < \varepsilon_0\). For example, \(\omega\), \(\omega+1\), \(\omega2\), \(\omega^2\), \(\omega^{\omega}\), etc.
- Two-argument/finitary Veblen hierarchy is assumed when the user puts a valid Veblen function expression in \(\alpha\), such as \(\varphi(1,0)\), \(\varphi(1,0,0)\), \(\varphi(1,0,0,0)\), etc., as well as the following Greek characters used for shortening: \(\varepsilon_\alpha\), \(\zeta_\alpha\), \(\eta_\alpha\), and \(\Gamma_\alpha\). For example: \(\varepsilon_0\), \(\zeta_0\), \(\eta_0\), and \(\Gamma_0\).
- Proposal 3.1. Assume the use of a fundamental sequence iff they meet the requirement as written below.
- Proposal 4. Anyone who uses a notation not specified in policy (assuming the proposals above are vetted) in analyses in mainspace pages are liable for a warning, which follows the same three-tier system. More information will be reviewed if this proposal is vetted, including the draft contents of the warnings.
Please tell us whether you agree or disagree with Redstonepillager's second alternative proposition to Googology Wiki:Policy#Analyses outlined above.
From Googology Wiki:Policy#Voting, a single user cannot use two or more accounts in a voting. Only non-blocked users that were registered for at least 100 days and have more than 100 edits in total may vote to avoid abusing the voting system. This vote shall hold for \(n\) days. Please do not forget to add your signature by writing four tildes (~~~~).
Even if you agree (resp. disagree) with one of the topics, you can agree (resp. disagree) with another one. Also, the voting right in this community is just a right, but not a duty. Therefore we do not force you to vote (you can silently abstain from this voting, and you can express your decisions for the topic above).
Redstonepillager 21:22, 3 November 2023 (UTC)
- I changed my opinion. I disagree to all proposals.
- The last proposal did not include the claim "This proposal takes all rights to the admin team. For example, they will decide whether hyperfactorial array notation is well-defined or not. This should leave no exceptions.", but you silently added it as if it were there from the beginning when you created this new proposal. Such a silent change affecting the discussion history makes the whole discussion untrustworthy for future users.
- You continue to claim misleading statements which I have already pointed out. Namely, your explanation that HAN and SAN are just unknown to be well-founded simply leads to severe misunderstanding of other users.
- You cited "list of well-defined notations", i.e. you clarified that all the notations listed are well-defined, but you have never cited trustworthy sources of the statement for new notations (for example for DeepLineMadom's Array Notation), although I have already requested you to be responsible for you statements.
- The statement "Buchholz's function by Buchholz and Denis" is incorrect.
- There is no agreed upon definition of "the system of fundamental sequence associated to Rathjen's psi function" if I correctly understand, but you have never cted a specific one.
- your request "Can you please show that HAN lacks well-foundedness?" does not seem to be appropriate. Why should I owe this task, which I am not responsible for? You were responsible for your statement of the well-definedness and the well-foundedness of HAN because those were unproved, but other users are not responsible for the opposite statements.
- For those reasons, I judged that this voting is not sound. That is why I changed my opinion.
- p-adic 22:41, 3 November 2023 (UTC)
- >you silently added it
- Any evidence?
- >you clarified that all the notations listed are well-defined
- If you think that those notations are ill-defined, let this proposal get ratified and then you can propose to remove the notations you think are ill-defined (which would need a community vote). You can then propose to remove as many as you want. This list is simply preliminary.
- >You were responsible for your statement of the well-definedness and the well-foundedness of HAN
- Just because you made a paper about the proof of termination of pair sequence BMS does not mean you can tell us to make an entire rigorous proof of the termination of HAN. In fact, this applies to any notation. If the definition of notation A looks like as if there aren't any ambiguities, it is probably well-defined. Redstonepillager 19:48, 4 November 2023 (UTC)
- > Any evidence?
- Special:Diff/413829
- > If you think that those notations are ill-defined,
- Please stop the repetition of the wrong claim. My claim is that you are responsible for your statements. We are not responsible for disproving your statement.
- > Just because you made a paper about the proof of termination of pair sequence BMS does not mean you can tell us to make an entire rigorous proof of the termination of HAN.
- I am claiming that you are responsible for your statements. My ability is irrelevant. Continueing such a shifting goal post is not honest attitude in a discussion.
- > If the definition of notation A looks like as if there aren't any ambiguities, it is probably well-defined.
- This is not an academic thought at all. You should be responsible for your statements instead of silently assuming that all of your unproved expectations are correct. This is an academic wiki. We should not put uncertain descriptions.
- p-adic 23:01, 4 November 2023 (UTC)
- In my decision, I partly agree to the whole proposal.
- For proposal 1, I agree to include the well-defined notations in the preliminary list, as all well-defined notations mathematically makes sense. However, the statement "Buchholz's function by Buchholz and Denis" is wrong. It should be "Buchholz's function by Buchholz and Extended Buchholz's function by Denis".
- For proposal 2, I changed my opinion. I disagree to include the sufficiently notable ill-defined notations in the preliminary list even if their analysis have either "(intended)" next to the name of the notation or "(debatable)" next to the expression to show that they are ill-defined, because I think adding ill-defined notations may still leads to misunderstanding of other users.
- For proposals 3 and 3.1, I agree that using FGH HH or SGH in analyses is allowed iff one specifies the FS (or OCF) for \(f_{\alpha}(n)\), \(H_{\alpha}(n)\) and \(g_{\alpha}(n)\) when \(\alpha > \omega\), as this avoids unspecified and/or ill-defined OCFs.
- For proposal 4, I agree that anyone who uses a notation not specified in policy (assuming the proposals above are vetted) in analyses in mainspace pages are liable for a warning, which follows the same three-tier system, as this should be treated the same as the other rules in the policy. We already have the level 1 warning template: {{Unnotable}}, but we don't have the level 2 and 3 warning templates of it.
- HaydenTheGoogologist2009 05:20, 4 November 2023 (UTC)
- >may still leads to misunderstanding of other users.
- BEAF is supposed to be stronger than OCFs, if it was well-defined. SAN is supposed to be well-defined as well and be extremely strong. That's what the "intended" is for. The legion = LVO belief is long disproven so I really don't see how using ill-defined notations in analyses is misleading towards other users, especially the dollar function. Googology is an art, not really a rigorous division of maths. Redstonepillager 19:48, 4 November 2023 (UTC)
- > The legion = LVO belief is long disproven so I really don't see how using ill-defined notations in analyses is misleading towards other users, especially the dollar function.
- Several people actually thought that BEAF, "normal OCFs", UNOCF, and SAN are well-defined. The fact that you do not understand the history does not mean thatthere is no history.
- > Googology is an art, not really a rigorous division of maths.
- This is your personal point of views. At least this wiki is a place to collect sourced informations rather than to put mathematically incorrect/meaningless/uncertain descriptions.
- p-adic 23:01, 4 November 2023 (UTC)
- >Several people actually thought that BEAF, "normal OCFs", UNOCF, and SAN are well-defined. The fact that you do not understand the history does not mean thatthere is no history.
- You didn't answer my point at all. The point is that putting (intended) next to a SAN approximation for example is intended for people to give an idea of how SAN is supposed to approximate the value of googolism X. Same goes with BEAF beyond tetrational arrays and dollar function. If the point of approximations is to help a reader understand a number, I see no issue with using an ill-defined notation iff (intended) or (debatable) is used (see above).
- Therefore isn't it strictly your personal preference when you insist about the ill-definedness of notation A, when the gwiki community agrees on the well-foundedness of said notation? Now obviously this does not apply to UNOCF or BEAF beyond tetrational arrays, for example, where the community agrees that these are ill-defined. The notion of "several people" does not represent a majority therefore I don't know why you said that.
- For the "normal ocf", it's the same principle; you insist the lack of well-foundedness of this ocf (which you call "normal ocf"), and that the community considers that a well-founded OCF. It has fundamental sequences as well.
- This is just my opinion. Redstonepillager 11:07, 8 November 2023 (UTC)
- > If the point of approximations is to help a reader understand a number,
- The assumption is wrong. The past treatment of ill-defined notations in analyses made people misunderstand that many OCFs were very weak. The information given by ill-defined notations, whose "correctness" does not mathematically make sense, just prevents accurate estimation of existing notions. It does not matter whether you put (intended) or something like that.
- > Therefore isn't it strictly your personal preference when you insist about the ill-definedness of notation A, when the gwiki community agrees on the well-foundedness of said notation?
- > For the "normal ocf", it's the same principle; you insist the lack of well-foundedness of this ocf (which you call "normal ocf"), and that the community considers that a well-founded OCF. It has fundamental sequences as well.
- No. And unfortunately, according to your claims, you seem not to understand what "well-foundedness" rigorously means. Could you please answer the definition which is precisely applicable to this context? (Namely, I am not asking another meaning of the same word, which is irrelevant to the current topic.)
- Also, why do you persistently ignore the most important issue? I am claiming that you should be responsible for your statements, while you are insisting as if I were responsible for disproving your claim.
- I am waiting for your responsible attitude, e.g. to give a reliable source for your statement on the well-definedness of the new listed stuffs.
- p-adic 12:15, 8 November 2023 (UTC)
Placing a vote before this discussion closes.
- Agree for proposal 1.
- Neutral for proposal 2
- Agree for proposal 3
- Agree for proposal 3.1
- Agree for proposal 4
Redstonepillager 20:38, 10 November 2023 (UTC) Update 21:26, 10 November 2023 (UTC): vote closed.
- For proposal 1, there are 2 agrees and 1 disagree.
- For proposal 2, there are 2 disagrees and 1 neutral vote.
- For proposal 3, there are 2 agrees and 1 disagree.
- For proposal 3.1, there are 2 agrees and 1 disagree.
- For proposal 4, there are 2 agrees.
I shall wait for Kyodaisuu to ratify this proposal and apply changes proposed in this proposal to the policy.
Redstonepillager 21:26, 10 November 2023 (UTC)
Approval[]
I confirm that the proposals 1, 3, 3.1, 4 of "Alternative proposal 2" were approved. As it is written in a proposal style, I wrote a draft of the revised policy in the "Analyses" section. Note that \(\omega\) was also included in Wainer hierarchy. For proposal 4, the proposal was approved, so it is OK to write the warning template. However, the current policy does not mention each individual warning template. We just have policy on warning and blocking in general. Therefore, it is not suitable to write a policy about warning template of analysis in the policy. We just note that the proposal was approved here. So this is the policy of analyses section based on the approval of the proposal. I will update the section later after the sentence is confirmed.
Analyses should be based on comparison or approximation to well-defined notations below. Anyone can propose to add notations or object to any notation on the list on the voting page to get approval by the community.
- Arrow notation
- BEAF up to tetrational arrays
- Bashicu matrix system version 2.3 = 4, up to \((0,0)(1,1)(2,2)(3,3)(4,4)(5,5)\ldots \ldots\) (pair sequence limit)
- Bird's array notation (Bird's version)
- Chained arrow notation
- Copy notation
- DeepLineMadom's Array Notation
- Extensible-E System (includes Collapsing-E Notation, excludes all interpretations of ##xE^ and /xE^)
- Graham Array Notation
- All maps defined by Fish used to construct the relevant Fish numbers
- Scientific notation
- Steinhaus-Moser Notation
- Taro's multivariable Ackermann function
- X-Sequence Hyper-Exponential Notation
- Fast-growing hierarchy, Hardy hierarchy, and Slow-growing hierarchy with respect to the following system of fundamental sequences:
- The fundamental sequences associated to iterated Cantor normal form, finitary Veblen function, Buchholz's function, Extended Buchholz's function, Rathjen's psi function and Taranovsky's C. Using FGH HH or SGH in analyses is allowed iff one specifies the FS (or OCF) for \(f_\alpha (n)\), \(H_\alpha (n)\) and \(g_\alpha (n)\) when \(\alpha \ge \omega\). Assume the use of a fundamental sequence iff they meet the requirement as written below.
- Wainer hierarchy/CNF is assumed when the user puts a valid Wainer/CNF expression in \(\alpha\) where \(\omega \le \alpha < \varepsilon_0\). For example, \(\omega\), \(\omega+1\), \(\omega2\), \(\omega^2\), \(\omega^{\omega}\), etc.
- Two-argument/finitary Veblen hierarchy is assumed when the user puts a valid Veblen function expression in \(\alpha\), such as \(\varphi(1,0)\), \(\varphi(1,0,0)\), \(\varphi(1,0,0,0)\), etc., as well as the following Greek characters used for shortening: \(\varepsilon_\alpha\), \(\zeta_\alpha\), \(\eta_\alpha\), and \(\Gamma_\alpha\). For example: \(\varepsilon_0\), \(\zeta_0\), \(\eta_0\), and \(\Gamma_0\).
- The fundamental sequences associated to iterated Cantor normal form, finitary Veblen function, Buchholz's function, Extended Buchholz's function, Rathjen's psi function and Taranovsky's C. Using FGH HH or SGH in analyses is allowed iff one specifies the FS (or OCF) for \(f_\alpha (n)\), \(H_\alpha (n)\) and \(g_\alpha (n)\) when \(\alpha \ge \omega\). Assume the use of a fundamental sequence iff they meet the requirement as written below.
🐟 Fish fish fish ... 🐠 06:25, 12 November 2023 (UTC)
- "Buchholz's function by Buchholz and Denis" is incorrect. It was made by Buchholz. So I remove "by Buchholz and Denis". 🐟 Fish fish fish ... 🐠 07:02, 12 November 2023 (UTC)
- Thank you very much. Redstonepillager 07:52, 12 November 2023 (UTC)
- I removed the bold text for the examples of valid CNF and Veblen function expressions because it's unnecessary.
- Also, I think we should add the following notations to the list:
- Down-arrow notation
- Nested Cascading-E notation (as this is not created by Sbiis Saibian)
- Peter Hurford's extension of chained arrows
- And now, we need to start removing approximations of numbers that are using ill-defined notations.
- HaydenTheGoogologist2009 12:42, 12 November 2023 (UTC)
- Agreed. Down-arrow notation and Hurford's extension are proven to be well-defined, but Nested Cascading-E may be ill-defined because its definition is incomplete, and the source is dead.
- HaydenTheGoogologist2009 13:17, 12 November 2023 (UTC)
- Thank you for the change. Since Redstonepillager kept silence on showing the source of the well-definedness of the listed notations, how about adding to the policy a credit to the user as the one who is responsible for the statement of the well-definedness? Since this wiki is a place to collect sourced information, people will believe that the well-definedness has already been proved otherwise.
- p-adic 22:45, 12 November 2023 (UTC)
- Writing a credit does not prevent people from believing that the wel-defindedness has already been proved. If it is the purpose, we can add a sentence, something like "Please note that well-definedness has not been proven for all notations in the list." 🐟 Fish fish fish ... 🐠 03:27, 13 November 2023 (UTC)
- Good. Then in addition, isn't it good to also replace "well-defined notations" by "notations" or "notations expected to be well-defined"? Referring to "well-defined notations" with a warning that there is no source of the well-definedness is cofusing.
- p-adic 07:26, 13 November 2023 (UTC)
- Thank you.
- p-adic 11:59, 13 November 2023 (UTC)
Modification[]
The current paragraph
- Analyses should be based on comparison or approximation to well-defined notations below. Anyone can propose to add notations or object to any notation on the list on the voting page to get approval by the community.
is misleading, because "well-defined notations below" appears that the well-defindedness has already been proved. Therefore, I propose modifying this paragraph to
- Analyses should be based on comparison or approximation to notations expected to be well-defined as shown below. Anyone can propose to add notations or object to any notation on the list on the voting page to get approval by the community. Please note that well-definedness has not been proven for all notations in the list.
Please note that it is not a vote yet. Approval of community can be made by discussion or vote. I think that discussion has priority. When we cannot agree on discussion, we can move on to vote. I welcome suggestion to modification of the sentences, or objection to the rewriting. When the sentence is sufficiently brushed up and no one disagrees, and sufficient time (for example 7 days) has passed, we can judge that the discussion is over. If we cannot decide by discussion, we move on to vote. 🐟 Fish fish fish ... 🐠 09:55, 13 November 2023 (UTC)
- I think i can agree with this Redstonepillager 15:45, 14 November 2023 (UTC)
- As no one disagreed in 7 days, I update the policy as I proposed. 🐟 Fish fish fish ... 🐠 04:49, 20 November 2023 (UTC)
Modification 2[]
Given the ratification of the previous proposal, I propose to add Hyperfactorial array notation, strong array notation and H* function to the list of allowed notations, but I will create different proposals for the restriction of adding hyperfactorial array notation and strong array notation, since for both of these the set of valid expressions is not precisely defined but we don't care about that. This is just like how we can analyses BEAF up to tetrational arrays. This is because HAN and SAN are most likely well-defined but its well-definedness has not been proven, since I can exploit the statement "well-definedness has not been proved for all notations below". I also believe that there are extensive benefits to all of these notations getting added, albeit with restrictions as explained below.
When I say "[ordinal] is the limit of [x]", these bounds were shown by Hollom in a gwiki blog post.
When you vote for proposals 1 and 2 below, please specify which proposal you would like to be ratified.
- Proposal 1.1. Add HAN to the list of well-defined notations up to \(\varphi(\omega,0)\), the limit of linear arrays. This will prohibit the w/ operator in being used in analyses since it works in a slightly funny way.
- Proposal 1.2. Add HAN to the list of well-defined notations up to \(\psi_0(\Omega^{\Omega^{\Omega}})\) with respect to buchholz's function, the Large Veblen ordinal, which is the limit of dimensional and nested arrays.
- Proposal 1.3. Add HAN to the list of well-defined notations up to the Countable limit of Extended Buchholz's function, i.e. the limit of the nucleaquaxul series. This is where I suspect the "funny brackets" being used for the first time (wasn't shown by Hollom) (which doesn't have a definition so it can't be included in this vote).
- Proposal 1.4. Do not add HAN to all extent to the list of well-defined notations that are allowed to be used in analyses.
I seriously think that adding HAN to analyses is a good idea, since it works in a slightly different way compared to other notations and this will help beginners to understand how the notation works.
Okay, strong array notation. p-bot says that "there is no proof that a formalisation of SAN is well-founded", but he probably means the higher levels like pDAN and sDAN.
- Proposal 2.1. Add SAN to the list of well-defined notations up to the limit of extended array notation, i.e \(\varepsilon_0\). I remember Hayden saying that this is the best idea.
- Proposal 2.2. Add SAN to the list of well-defined notations up to the limit of multiple expanding array notation, i.e. Ψ 0(Ω ω).
- Proposal 2.3. Add SAN to the list of well-defined notations up to the limit of DAN, which is the community-decided well-defined limit.
- Proposal 2.4. Do not add SAN to all extent to the list of well-defined notations that are allowed to be used in analyses.
For the H* function, it is the only googological notation attempting to represent illions that has a useful growth rate, and I do still see it as a notable notation. For the following proposal you can agree or disagree to it.
- Proposal 3. Add H* function the the list of allowed notations in analyses.
However, I refrain from adding trio sequence BMS v4 to the list of well-founded notations.
Please tell us whether you agree or disagree with Redstonepillager's modification to Googology Wiki:Policy#Analyses outlined above.
From Googology Wiki:Policy#Voting, a single user cannot use two or more accounts in a voting. Only non-blocked users that were registered for at least 100 days and have more than 100 edits in total may vote to avoid abusing the voting system. This vote shall hold for 7 days. Please do not forget to add your signature by writing four tildes (~~~~).
Even if you agree (resp. disagree) with one of the topics, you can agree (resp. disagree) with another one. Also, the voting right in this community is just a right, but not a duty. Therefore we do not force you to vote (you can silently abstain from this voting, and you can express your decisions for the topic above).
If nobody votes on this proposal throughout the 7 day period, it will be is automatically ratified.
Redstonepillager 08:41, 20 November 2023 (UTC)
My personal opinion:
I proposal to ratify proposal 1.2 and 2.2, and i agree to proposal 3.
Redstonepillager 08:41, 20 November 2023 (UTC)
Could you promise the following, which you frequently ignore?
- You will not change the proposal after the discussion. (You directly edited the past discussion at least twice. The latter one was a serious manipulation by inserting a new proposal after the discussion was closed. Such a manipulation makes the precise discussion essentially inaccessible by the future users.)
- You will be responsible for your statement by showing sources. (You repeated the irresponsible attitude to spread unsourced information during the past voting, and such an inappropriate attitude prevents a sound discussion.)
- You will not use the precise terminology in discussion. (You used "well-founded" without understanding the precise meaning, and irresponsibly ignored my request to check the incorrect understanding. You can avoid to use incorrect terminology by simply using only what you know. The use of incorrect terminology makes a discussion absolutely misleading.)
At least, since you are continuing the inappropriate misdirection of the discussion, I disagree with all of the change proposed by you.
Seriously, please stop spreading unsourced information as if it were proved facts. This is not an honest attitude in an academic community at all.
p-adic 00:28, 21 November 2023 (UTC)
- Unfortunately I can only promise your first point (and maybe your third point).
- >I disagree with all of the change proposed by you
- Based on what you said before that, isn't this also dishonest attitude in a discussion? Digressing from the original topic and making "votes" based on that without looking at the proposal itself? Redstonepillager 20:22, 23 November 2023 (UTC)
- No. I have looked at all of them, and have sufficient reasons for disagreement, e.g. your wrong unsourced claims. If you change your irresponsible attitude, then I might change my opinion after sharing feedbacks. However, you clarified that you do not follow the promise, i.e. intentionally keep the inappropriate attitude such as trials to spread unsourced information even though you have already understood the fact that it is essentially deceiving others. Therefore, costing time for this irresponsible and unconstructive voting not based on innocent and honest will to make this commuinty better is simply wasting time.
- p-adic 21:54, 23 November 2023 (UTC)
- For the first 2 proposals, I propose to ratify proposals 1.2 and 2.1, as I think this is the limit of all well-founded functions for both notations. For proposal 3, I agree to add the H* function to the list of allowed notations in analyses, as it's like the only well-defined and notable notations that can represent -illion numbers.
- HaydenTheGoogologist2009 12:50, 25 November 2023 (UTC)
vote closed at 11:09, 28 November 2023 (UTC). For proposal 1, 1.2 has most votes; for proposal 2, 2.1 has most votes; for proposal 3, there are 2 agrees and 1 disagrees. So I wait for Fish to formally ratify this vote. Redstonepillager 11:09, 28 November 2023 (UTC)
- You should have written that proposal 1 and 2 also had 1 disagrees respectively. However they have 2 agrees respectively so I think 1.2, 2.1 and 3 were approved. You can edit the rule based on this approval. Just write in the edit summary that it was approved in this page. 🐟 Fish fish fish ... 🐠 11:22, 28 November 2023 (UTC)
- Why did you edit BEAF? 🐟 Fish fish fish ... 🐠 17:22, 28 November 2023 (UTC)
- I think a giving a certain representation of what is and isn't allowed in approximations in the policy is a good idea. Some people might not understand what a tetrational array in BEAF is, so I think replacing "tetrational arrays" with "\(X\uparrow\uparrow X \& n\)" would be slightly clearer. It's the same thing that some people might not understand or recognise "expanding array notation" in SAN so I write "s(a,b{1`2}2)" instead of "expanding array notation". Redstonepillager 07:54, 29 November 2023 (UTC)
- But rewriting BEAF was not included in the current proposal. It is reasonable to make an edit of the BEAF with the edit of current proposal. I think that you should just revert the edit to regarding the BEAF and also the expression of SAN to the original proposal. Then discuss your edit here. There needs to be vote, just ask opinion. It is unreasonable to edit a community-approved expression without discussion in the community. 🐟 Fish fish fish ... 🐠 08:29, 29 November 2023 (UTC)
- I think a giving a certain representation of what is and isn't allowed in approximations in the policy is a good idea. Some people might not understand what a tetrational array in BEAF is, so I think replacing "tetrational arrays" with "\(X\uparrow\uparrow X \& n\)" would be slightly clearer. It's the same thing that some people might not understand or recognise "expanding array notation" in SAN so I write "s(a,b{1`2}2)" instead of "expanding array notation". Redstonepillager 07:54, 29 November 2023 (UTC)
- Why did you edit BEAF? 🐟 Fish fish fish ... 🐠 17:22, 28 November 2023 (UTC)
Modification 3[]
I didn't know this before (yes, unfortunately, i am being honest), but apparently Rathjen's psi function does not have fundamental sequences associated to them (at least defined by Rathjen himself). Also, Rathjen's \(\psi\) is rather difficult for people to actually take into account some approximations.
Therefore, I propose adding Hyp cos' Inaccessible / Mahlo OCF along with fundamental sequences for the inaccessible OCF and the the Mahlo OCF, as a supplementary OCF to Rathjen's OCF. (Both of these are mentioned on Denis' website, so I would assume that they are at least semi-notable. In fact, all of Denis' numbers above Yottinommwil use that ordinal collapsing function and associated fundamental sequences, excluding the tar series)
I also propose adding Madore's function to the list of allowed ordinal collapsing functions. It has quite a small limit ordinal \(\psi(\varepsilon_{\Omega+1})\), but IMO it is the most useful for beginner googologists.
- Proposal 1. Add Hyp cos' Inaccessible/Mahlo OCF with associated fundamental sequences to the list of allowed OCFs used in analyses as a post-Countable limit of Extended Buchholz's function ocf.
- Proposal 2. Add Madore's \(\psi\) to the list of allowed OCFs used in analyses.
However, we must be careful to not add too many OCFs to the list, because one day, Hyp cos' catching function or UNOCF might be added to the list! /j
Please tell us whether you agree or disagree with Redstonepillager's modification to Googology Wiki:Policy#Analyses outlined above.
From Googology Wiki:Policy#Voting, a single user cannot use two or more accounts in a voting. Only non-blocked users that were registered for at least 100 days and have at least than 100 edits in total may vote to avoid abusing the voting system. This vote shall hold for 7 days. Please do not forget to add your signature by writing four tildes (~~~~).
Even if you agree (resp. disagree) with one of the topics, you can agree (resp. disagree) with another one. Also, the voting right in this community is just a right, but not a duty. Therefore we do not force you to vote (you can silently abstain from this voting, and you can express your decisions for the topic above).
If nobody votes on this proposal throughout the 7 day period, it will be automatically ratified.
Redstonepillager 13:41, 18 December 2023 (UTC)
- You say
- I didn't know this before, but apparently Rathjen's psi function does not have fundamental sequences associated to them (at least defined by Rathjen himself).
- but, according to the log of this page, p-adic said on 3 November 2023
- 5. There is no agreed upon definition of "the system of fundamental sequence associated to Rathjen's psi function" if I correctly understand, but you have never cited a specific one.
- and you did not specify definition of "the system of fundamental sequence associated to Rathjen's psi function" as the request by p-adic, and just ignored it. Why do you say that you didn't know it before? It means that you do not read p-adic's message carefully. It is not a sincere attitude. I request you to participate in discussion more sincerely, especially when it is a proposal that you started. 🐟 Fish fish fish ... 🐠 14:12, 18 December 2023 (UTC)
I would like any discussion here only being related to the proposals itself and no more. Thanks. Redstonepillager 14:57, 18 December 2023 (UTC)
- To begin with, do you agree with the following?
- You will not manipulate the proposal after the discussion, as you irresponsibly did. (When I pointed out this, you requested the source. However, when I showed a source, you simply ignored it in an irresponsible way.)
- You will add sources whenever you clarify a mathematical statement as if it were a fact. (You have spread many unsourced statements including wrong statements and refused to show sources in an irresponsible way.)
- You will sincerely read other users' comments. (You ignore many warnings and explanations of your incorrectness irresponsibly.)
- In order for us not to waste time for your repetitive proposals which do not follow the natural requests above, I ask you to promise to clarify to follow them.
- Also, I disagree with all the changes you proposed. Because of your repetitive proposals ignoring of the requests above, I do not cost time to repeat to add details on reasoning, as I have already explained.
- p-adic 23:06, 18 December 2023 (UTC)
- >You will not manipulate the proposal after the discussion
- ok
- >You will add sources whenever you clarify a mathematical statement as if it were a fact
- ok
- >You will sincerely read other users' comments
- ok
- also this isn't the best place to chat abt this, if you want to discuss more please use my talk page thx
- Redstonepillager 02:28, 19 December 2023 (UTC)
- This is not a discussion, but a natural request closely related to the voting. Namely, I asked these here because these information help other users to judge whether it is good to cost time to write detailed opinions. Also, it is really illogical to ask to write these to your talk page because you are simply ignoring warnings and requests at your talk page. Therefore, I will request these when you start voting here.
- p-adic 12:24, 19 December 2023 (UTC)
- Proposal 1: I disagree. Analyzing at this level is quite complex, and it appears that there isn't a single, well-established definition. The fact that a definition appears on a personal website doesn't make a significant difference. However, if it were presented in a peer-reviewed paper or published by a renowned mathematician, that might carry more weight. People can analyze anything in their blog posts, and these analyses can be referenced in articles as in "User A states that this number corresponds to ordinal... according to the definition found in..." by citing the blog post with a complete explanatory sentence. Nonetheless, it is inappropriate to include such an approximation in a table. Most "approximations" in current Gwiki articles merely show the approximated value without citing the source of the approximation. If we were to accept Proposal 1, the approximation would be presented in the same manner as in other articles. We do not include it in the "allowed list of analysis", and if we do decide to describe an approximation at this level by a specific individual, complete citation information is necessary for verification by others.
- Proposal 2: I disagree. We already have Buchholz's work at this level. Buchholz has defined OCF and ordinal notation in a published paper. In contrast, Madore's work lacks ordinal notation and has not been published in a peer-reviewed journal. Therefore, we have no reason to use Madore's system in the main article. Furthermore, their similar notation styles can cause confusion. As previously mentioned, anyone can use Madore's system in a blog post, but it is still preferable to clearly identify which system is being used even in a blog post. 🐟 Fish fish fish ... 🐠 16:37, 19 December 2023 (UTC)
Unfortunately, proposal 1 (with 2 disagrees) and proposal 2 (with 2 disagrees) were not ratified, and no changes will be made to the policy. Redstonepillager 05:52, 29 December 2023 (UTC)
Punishes add in Project:Policy[]
We should adding the policy for more punish. Example if against the "Can't add no source content", what punish it no said.Gongxiang01 (talk) 01:52, 26 November 2023 (UTC)
- We do not punish anyone in this community, or Fandom in general. I already explained you that blocking is not a punishement. In the "block" section, it is written that "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." Therefore, adding no source content can be a violation of rule and can be a reason of blocking. In https://community.fandom.com/wiki/Help:Blocking , it is also explained that "Breaking other policies." can be a reason for blocking. But just understand that it is to prevent damage or disruption of the community, and not a punishment. 🐟 Fish fish fish ... 🐠 05:01, 26 November 2023 (UTC)