About proof[]
is there proofs that this is stronger than any nth-order arithmetic? :V
Fluoroantimonic Acid (talk) 17:35, January 8, 2016 (UTC)
- No. It is stronger than just a "special type of" nth-order logic. 🐟 Fish fish fish ... 🐠 22:56, January 8, 2016 (UTC)
- And what is this "special type of" nth-order logic we talk about? LittlePeng9 (talk) 08:07, January 9, 2016 (UTC)
- It is a written in the proof of calculation termination (it is written in special terminology and it is difficult to translate into English... I hope some Japanese can translate it into English). For example, calculation of 2-row matrix can be expressed with 2nd order logic. Bashicu matrix does not cover "all of" 2nd order logic (it means that it does not diagonize over the entire 2nd order logic), but special "kind" or "type" of 2nd order logic, as defined in the algorithm. 🐟 Fish fish fish ... 🐠 08:37, January 9, 2016 (UTC)
- In the proof it is written "n行でn階述語論理のある体系（n階のカインド）を対角化した強さとなる。" Literally it says n-row matrix diagonizes a special type of n-th order logic (n-th order kind). I am not sure if the word "n-th order kind" is a familiar usage of terminology, but anyway in the proof the word "hight of kind" is used. 🐟 Fish fish fish ... 🐠 08:46, January 9, 2016 (UTC)
- ja:ユーザー:黒羽カフカ "バシク行列の計算可能性の証明はもうしばらくお待ちください。" means "Please wait for a while until I rewrite the proof of computability of Bashicu matrix" 🐟 Fish fish fish ... 🐠 17:02, January 18, 2016 (UTC)
L and m[]
In Rule 3-2, what are \(L\) and what is \(m\)? While editing I have added "by choice of \(L\)" as I believe that is the case, but I want that clarified. Also, how is \(\Delta\) ever used? It is defined in Rule 3-3, but doesn't appear elsewhere. LittlePeng9 (talk) 20:23, January 8, 2016 (UTC)
- From the example, it appears that Rule 3-3 is meant to specify \(\Delta\), not \(N\). I'm assuming that this is correct, and changing it. ~εmli 22:37, January 8, 2016 (UTC)
- Looks like \(L\) is \(S_1\). Deedlit11 (talk) 02:16, January 9, 2016 (UTC)
- Also, \(m\) is the number of rows in the matrix, or in other words the length of each vector. Deedlit11 (talk) 02:22, January 9, 2016 (UTC)
Limit[]
I don't think \(\begin{pmatrix}0&1&2&3&2&3 \\ 0&1&2&3&2&3 \\ 0&1&1&1&1&1\end{pmatrix}\) reach the limit of Taranovsky's notation. Maybe it just reach the limit of the "Degree of reflection" one. {hyp/^,cos} (talk) 14:32, April 12, 2016 (UTC)
Column comparison[]
Is the "<" relationship on columns a strict total order? {hyp/^,cos} (talk) 10:59, April 12, 2016 (UTC)
- This order isn't total - for example, \((1,2)\) and \((2,1)\) are incomparable. LittlePeng9 (talk) 20:07, April 12, 2016 (UTC)
Something wrong happens[]
Something wrong happens at (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,1,0)(3,1,0)[n]. When we attemp to solve \(\begin{pmatrix} 0&1&2&1&2&3&2&3&\cdots&2&3&2&3 \\ 0&1&0&1&1&0&1&0&\cdots&1&0&1&1 \\ 0&1&0&0&0&0&0&0&\cdots&0&0&0&0 \end{pmatrix}[n]\) where there are m \(\begin{matrix}2&3 \\ 1&0 \\ 0&0\end{matrix}\)'s, the sequence for the next step will start from \(\begin{pmatrix} 0&1&2&1&2&3&2&3&\cdots&2&3&2&3 \\ 0&1&0&1&1&0&1&0&\cdots&1&0&1&1 \\ 0&1&0&0&0&0&0&0&\cdots&0&0&0&0 \end{pmatrix}\) where there are m+1 \(\begin{matrix}2&3 \\ 1&0 \\ 0&0\end{matrix}\)'s, and the "(3,0,0)(2,1,0)(3,1,0)" is a part of \(B(1)\).
So (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,1,0)(3,1,0)[n] reduces to (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,1,0)(3,0,0)(2,1,0)(3,1,0)...[n], where (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,1,0)(3,0,0)(2,1,0)(3,1,0)[n1] reduces to (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,1,0)(3,0,0)(2,1,0)(3,0,0)(2,1,0)(3,1,0)...[n1], where (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,1,0)(3,0,0)(2,1,0)(3,0,0)(2,1,0)(3,1,0)[n2] reduces to (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,1,0)(3,0,0)(2,1,0)(3,0,0)(2,1,0)(3,0,0)(2,1,0)(3,1,0)...[n2], and so on (n < n1 < n2 < ...).
So we can never solve (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,1,0)(3,1,0), and the same as (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,0), (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1), (0,0,0)(1,1,1)(2,0,0)(1,1,1), (0,0,0)(1,1,1)(2,0,0)(2,0,0), (0,0,0)(1,1,1)(2,0,0)(3,0,0), (0,0,0)(1,1,1)(2,0,0)(3,1,0), (0,0,0)(1,1,1)(2,0,0)(3,1,1), (0,0,0)(1,1,1)(2,1,0), (0,0,0)(1,1,1)(2,1,1), (0,0,0)(1,1,1)(2,2,0), (0,0,0)(1,1,1)(2,2,1) and (0,0,0)(1,1,1)(2,2,2). {hyp/^,cos} (talk) 10:53, April 28, 2016 (UTC)
- Yes, it does appear that some of the possible notations do not reduce. However, the system may still be worthwhile googologically; it does seem that some of the notations do reduce, and can get quite large (e.g. (0,0)(1,1)...(n,n)). It would be very useful to find a condition or conditions such that notations that satisfied the condition always reduced. Unfortunately, there is a language barrier between us and the Japanese folks working on the problem. Deedlit11 (talk) 07:19, April 29, 2016 (UTC)
The definition was changed.
For a maximal j which hold \(\forall i<j(y_i<x_i)\), \(x_i\quad i<j\) of sequence N replace \(y_i\quad i<j\) for each i.
For example
(0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,1,0)<(3,1,0)> N=(3,1,0) Δ=(0,0,0)
(0,0,0)(1,1,1)(2,0,0)(1,1,0)<(2,1,0)>(3,1,0) N=(2,1,0) Δ=(1,0,0)
(0,0,0)(1,1,1)(2,0,0)<(1,1,0)>(2,1,0)(3,1,0) N=(1,1,0) Δ=(2,0,0)
(0,0,0)(1,1,1)<(2,0,0)>(1,1,0)(2,1,0)(3,1,0) N=(1,1,0) Δ=(2,0,0)
(0,0,0)<(1,1,1)>(2,0,0)(1,1,0)(2,1,0)(3,1,0) N=(1,1,0) Δ=(2,0,0)
<(0,0,0)>(1,1,1)(2,0,0)(1,1,0)(2,1,0)(3,1,0) N=(0,0,0) Δ=(3,0,0)
If \(x_j=0\) , a matrix continued from the sequence is a bad part.
Thank you for point out mistake, and sorry for my poor English. --KurohaKafka (talk) 22:16, May 12, 2016 (UTC)
Another interpret
\(x_1\) of sequence N replace \(y_1\)
(0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,1,0)<(3,1,0)> N=(3,1,0) Δ=(0,0,0)
...
<(0,0,0)>(1,1,1)(2,0,0)(1,1,0)(2,1,0)(3,1,0) N=(0,1,0) Δ=(3,0,0)
--KurohaKafka (talk) 03:39, May 13, 2016 (UTC)
Oh...what's the new definition of the \(<\) relation on columns? I didn't get it from your words above. {hyp/^,cos} (talk) 15:47, May 13, 2016 (UTC)
Another interpretation is mistake.
The new definition doesn't use the \(<\) on columns, make sure that \(x_j=0\) or not instead. --KurohaKafka (talk) 12:09, May 14, 2016 (UTC)
Okey...but what's the new definition of Rule 3-1 and Rule 3-2? {hyp/^,cos} (talk) 15:09, May 14, 2016 (UTC)
Yes, I would like to understand the new rule but we need to see how to compute the next matrix. Deedlit11 (talk) 16:42, May 16, 2016 (UTC)
New Rule 3-1 and Rule 3-2
Firstly, \(N=S_n\) and \(\Delta=Z\).
\(i\) and \(j\) are as mentioned above.
Compare \(N\) with \(S_{n-1}\), and replace \(x_i\) with \(y_i\). If there is no possible value of \(i\) (\(j=0\)), \(N\) does not change.
Add \(x_i-y_i\) to \(\Delta_i\).
If \(x_j=0\), bad part is \(S_{n-1}\). Otherwise, compare new \(N\) with \(S_{n-2}\).
Repeat this until you find \(x_j\) which equal to 0. If not found, replace \(S_n\) with \(Z\).
If \(x_j=0\) when you calculate in \(S_k\), bad part is \(S_k\frown S_{k+1}\frown\cdots\frown S_{n-1}\).
Rule 3-3 and Rule 3-4 are unchanged.
e.g.
(0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,1,0)(3,1,0)
Bad part is (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,1,0).
\(\Delta\)=(3,0,0)
B(1)=(3,0,0)(4,1,1)(5,0,0)(4,1,0)(5,1,0)
B(2)=(6,0,0)(7,1,1)(8,0,0)(7,1,0)(8,1,0)
……
So (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,1,0)(3,1,0) is expanded to
(0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,1,0)(3,0,0)(4,1,1)(5,0,0)(4,1,0)(5,1,0)...
--KurohaKafka (talk) 12:26, May 17, 2016 (UTC)
- Ahh...still unclear for me. What's \(i\), \(j\), \(x_i\) and \(y_i\)? {hyp/^,cos} (talk) 23:07, May 17, 2016 (UTC)
- \(S_k=(y_0,y_1,\cdots,y_n)\quad N=(x_0,x_1,\cdots,x_n)\)
- e.g.
- \(S_k=(1,1,1)\quad N=(2,2,1)\)
- \(y_0=1\quad y_1=1\quad y_2=1\) and \(x_0=2\quad x_1=2\quad x_2=1\)
- \(j=2\ i=0\ \text{or}\ 1\) and \(x_j=1\)
- Program is here. バシク行列数(Bashicu matrix number)
- --KurohaKafka (talk) 12:36, May 20, 2016 (UTC)
- But why the final \(\Delta=(3,0,0)\) in the (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,1,0)(3,1,0) example?
- After 4 steps we've scan to the (1,1,1) in matrix (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,1,0)(3,1,0), and now \(N=(1,1,0)\) and \(\Delta=(2,0,0)\).
- The next step is comparing (0,0,0) with N. We get \(y_0<x_0\) and \(y_1<x_1\) but \(y_2=x_2\), so j = 2, and i can be 0 or 1. The next step is adding \(x_i-y_i\)'s to \(\Delta\), so the new \(\Delta=(3,1,0)\), not (3,0,0). {hyp/^,cos} (talk) 16:26, May 20, 2016 (UTC)
- I'm sorry that my explanation was not enough.
- \(x_h\) is the bottom value not being 0 in \(S_n\), and \(\Delta=(\Delta_0,\Delta_1,\cdots,\Delta_{h-1})\)--KurohaKafka (talk) 21:45, May 20, 2016 (UTC)
- Now I see. Given \(S_k\) (the beginning of the bad part), the definition of \(\Delta\) is unchanged. {hyp/^,cos} (talk) 00:44, May 21, 2016 (UTC)
Still with problems[]
Using the new definition, we take a look at (0,0,0)(1,1,1)(2,0,0)(1,1,1)[n].
- (0,0,0)(1,1,1)(2,0,0)(1,1,1) reduces to (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,1,0)... (Bad part is (0,0,0)(1,1,1)(2,0,0))
- (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,1,0) reduces to (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)(4,1,1)... (Bad part is (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1))
- (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)(4,1,1) reduces to (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)(4,1,0)... (Bad part is (3,0,0))
- (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)(4,1,0) reduces to (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)(4,0,0)... (Bad part is (3,0,0))
- (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)(4,0,0) reduces to (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)(3,0,0)... (Bad part is (3,0,0))
- (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)(3,0,0) reduces to (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)(2,2,1)... (Bad part is (2,2,1)(3,0,0))
That's the first "period".
- (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)(2,2,1) reduces to (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)(2,2,0)(3,3,1)(4,1,0)... (Bad part is (1,1,0)(2,2,1)(3,0,0))
- (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)(2,2,0)(3,3,1)(4,1,0) reduces to (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)(2,2,0)(3,3,1)(4,0,0)(5,1,1)... (Bad part is (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)(2,2,0)(3,3,1))
- (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)(2,2,0)(3,3,1)(4,0,0)(5,1,1) reduces to (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)(2,2,0)(3,3,1)(4,0,0)(5,1,0)... (Bad part is (4,0,0))
- (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)(2,2,0)(3,3,1)(4,0,0)(5,1,0) reduces to (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)(2,2,0)(3,3,1)(4,0,0)(5,0,0)... (Bad part is (4,0,0))
- (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)(2,2,0)(3,3,1)(4,0,0)(5,0,0) reduces to (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)(2,2,0)(3,3,1)(4,0,0)(4,0,0)... (Bad part is (4,0,0))
- (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)(2,2,0)(3,3,1)(4,0,0)(4,0,0) reduces to (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)(2,2,0)(3,3,1)(4,0,0)(3,3,1)... (Bad part is (3,3,1)(4,0,0))
That's the second "period".
Continue upward, we get (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)...(k,k,0)(k+1,k+1,1)(k+2,0,0)(k+1,k+1,1), and we can never solve (0,0,0)(1,1,1)(2,0,0)(1,1,1)[n]. {hyp/^,cos} (talk) 09:24, May 23, 2016 (UTC)
My current rule
If a value at the first line of N is n+1, then go to left from the right end until we find a sequence T_0 that value at first line is n-1. In T_0T_1...S_{n-1}, S'_0 is a right-hand sequence which is the biggest sequence by lexicographic order and that first line has n. Worse part denotes S'_0S'_1...S_{n-1}.
In worse part, put a restriction on each sequence that first line has a bigger value than n+1 and that value not being 0 doesn't continue as N; in the same line, we don't add a value of Δ to the sequence U that value is not bigger than N's one or each sequences subsequent to the right and that value of first line is bigger than U's one at first line.
example
(0,0,0)(1,1,1)(2,1,0)(1,1,1)→...(1,1,0)(2,2,1)(3,1,0)...
(0,0,0)(1,1,1)(2,1,0)(3,1,0)(1,1,1)→...(1,1,0)(2,2,1)(3,1,0)(4,1,0)...
(0,0,0)(1,1,1)(2,1,0)(3,2,0)(1,1,1)→...(1,1,0)(2,2,1)(3,1,0)(4,2,0)...
(0,0,0)(1,1,1)(2,1,1)(1,1,1)→...(1,1,0)(2,2,1)(3,2,1)...
(0,0,0)(1,1,1)(2,2,1)(3,2,0)(1,1,1)→...(1,1,0)(2,2,1)(3,3,1)(4,3,0)...
(0,0,0)(1,1,1)(2,2,1)(3,2,0)(1,1,1)(2,2,1)→...(2,2,0)(3,3,1)(4,4,1)(5,4,0)(3,3,1)...
(0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,1)→...(2,2,0)(3,3,1)(4,4,1)(5,2,0)...
(0,0,0,0)(1,1,1,1)(2,2,1,0)(3,2,0,0)(1,1,1,0)(2,2,1,0)→...(2,2,0,0)(3,3,1,1)(4,4,1,0)(5,2,0,0)(3,3,1,0)...
If N=(1,...), T_0 is rightmost Z.
example
\((0,0,0)(1,1,1)(2,2,2)(0,0,0)(1,1,1)(2,1,0)(1,1,1)\)
- then \(T_0T_1...S_{n-1}=S_4S_5S_6=(0,0,0)(1,1,1)(2,1,0)\)
BashicuHyudora's rule
1.We change the string N to a string of a bad part left.
2.S denotes a string that is found first to left from N, comparing these first line, S has a lessor value than N's one.
3.We don't add a value of Δ each line of N iff the line has a lessor value than the same line value of S or S's one is not added a value of Δ.
example
(0,0,0)(1,1,1)(2,1,0)(3,2,0)(1,1,1)→...(1,1,0)(2,2,1)(3,2,0)(4,3,0)...
(0,0,0)(1,1,1)(2,2,0)(3,1,0)(4,2,0)(1,1,1)→...(1,1,0)(2,2,1)(3,3,0)(4,1,0)(5,2,0)... --KurohaKafka (talk) 09:44, October 20, 2016 (UTC)
"Limit of Taranovsky's C"[]
Erm,I am not sure about that.I don't see any proof for that so it may be an estimate but there is no reason we should believe it.Boboris02 (talk) 16:26, March 17, 2017 (UTC)
Very outdated[]
BM1 is nonterminating during pair sequences, BM2 is nonterminating in quad sequences, and there are many more versions now.CatIsFluffy (talk) 03:29, June 6, 2019 (UTC)
- Although you might have already noticed, Koteitan updated the description in the main article.
- p-adic 04:44, June 7, 2019 (UTC)
- How do you think BM1 definition should be kept or not in this article? It is easier to understand than BM4, however, It is old rule already fixed and it is not indicate the true power of the BMS now. Koteitan (talk) 03:31, June 10, 2019 (UTC)
- I personally think that it is good to keep the description of BM1, because BM1 is historically important. On the other hand, it might be also good to create a new article on BM2.3, under the assumption that it is the final version of accepted BMS except other variants, e.g. TBMS, IBMS, B-function, and so on, which are given distinct names.
- p-adic 12:03, June 10, 2019 (UTC)
- I was thinking about rewriting the non-mathematical description of how BM works, using the most current version, BM4. I think it would help people understand the rules more intuitively. Would that be ok? QuasarBooster (talk) 03:38, February 2, 2020 (UTC)
- I think that it is good if we have articles for each official version of BMS, because Bashicu will perhaps create BM5, BM6, and so on in the future. For example, how about having this article to play a role similar to the article of Fish numbers together with overviews based on the current descriptions? Anyway, you can start to add explanations on BM4, because we can move them to a new article if we create a specialised article on BM4 in the future.
- p-adic 07:14, February 2, 2020 (UTC)
- Welcome. Try everything.
- Koteitan (talk) 07:56, February 2, 2020 (UTC)
- I agree that splitting the versions of BM into different articles would probably be a good idea. Ok, I'll work on the description for BM4 in a day or two.
- QuasarBooster (talk) 20:44, February 2, 2020 (UTC)
Column encoding?[]
I wondered if it was possible to encode the matrix columns as simple numbers so I tried doing that. One thing I realized was that the encoding would have to somehow preserve the "<" relation using some other relation between two numbers. I naively tried the normal < but that one is transitive while "<" is intransitive. I tried coprime but the relation is symmetric and "<" is asymmetric. Now I'm starting to think this encoding might not be possible. Is this already known or is there still a possibility that an encoding could exist? QuasarBooster (talk) 01:03, September 11, 2019 (UTC)
- There are several known methods to encode a Bashicu matrix into a sequence of simple numbers. Although they are not exactly encodings of a column into a number, but might be helpful for you as alternatives. The most famous systems are N-primitive system and Y-sequence system in Japanese googology, but there is no article explaining them. Instead, there is an article on difference sequence, which explains a common strategy to encode a Bashicu matrix into a sequence of numbers. You can find a link to the earliest application, i.e. hyper primitive sequence system, which will help you how difference sequence system actually works. Also, a variant of Y-sequence called F-sequence introduced here by Syst3ms is also helpful. Please be careful that there is another attempt to interprete Y-sequence here by Ubersketch, but it is ill-defined.
- p-adic 01:23, September 11, 2019 (UTC)
- How about giving a simple indices which are the ascending order of the size? For example, let (X) be Bashicu Matrix and [Y] is new notation,
(0)=(0,0)=(0,0,0) = [0] (0)(0) = [0,0] (0)(1) = [0,1] (0,0)(1,1) = [0,2] (0,0,0)(1,1,1) = [0,3] (0)(1)(0) = [0,1,0] (0)(1)(1) = [0,1,1] (0,0)(1,1)(0,0) = [0,2,0] (0,0)(1,1)(1,0) = [0,2,1] (0,0)(1,1)(1,1) = [0,2,2] (0,0)(1,1)(2,0) = [0,2,3] (0,0)(1,1)(2,1) = [0,2,4] (0,0)(1,1)(2,2) = [0,2,5] (0,0,0)(1,1,1)(0,0,0) = [0,3,0] ...
something like that.
- It does not solve the problem on the "<" relation, especially when the bottom entry of the corresponding column is zero, does it?
- p-adic 03:48, September 11, 2019 (UTC)
(Vote) Remove some unnecessary stuff from the page[]
I propose a vote on this edit: https://googology.fandom.com/wiki/Bashicu_matrix_system?diff=389959&oldid=389958 The individual who reverted my changes said that I removed "important details on actual problems", but these "problems" were unspecified, and I do not believe that I removed any important details on any actual problems. Ecl1psed276 (talk) 04:44, 4 July 2023 (UTC)
- You removed the sentences which appear in the difference page which you cited. You can see that you actually removed them. Could you share a link to the discussion log where this community confirmed the removal of those sentences, following Googology WIki:Policy#Wiki philosophy? You know a removal of contents (except nonsense ones written by vandals) without any discussion can be treated as a vandalism, and the fact that what you silently removed were written by others and kept for a long time explains that it is illogical for you to conclude that those are nonsense descriptions which can be freely removed without discussion. So, under the assumption that you are trying to follow the policy, I assume that you simply forgot to put a link to the discussion. Please show the link where the community agreed the removal, instead of simply state that you only removed unnecessary stuffs. Also, next time, please put a link before others' asking you to do so, in order to make everyone understand the actual dicussion. Thank you.
- p-adic 05:02, 4 July 2023 (UTC)
- I read the Wiki Policy page that you linked, and none of the things in that section seem to apply to my edit, so I don't think a discussion is necessary in order to do it. It sounds like you are coming very close to accusing me of vandalism, which I absolutely did not do. I assume that you believe my edit was "unconstructive", as specified in the policy? Is that the reason you undid it? I do not think my edit was unconstructive at all. The policy page says that the removal of information in an article is considered inappropriate, and they say that things like correct and sourced information deeply related to the article in which it is written are against the wiki's purpose. The stuff I removed certainly does not fall under that description:
- I removed this bit of the article: Most claims about the strength and well-foundedness of BMS have so far not been formally defined, or they haven't been proven. I heavily dislike the wording of that sentence, because it gives more focus to claims about the strength of BMS, rather than, well, the strength of BMS. Instead of saying "Most claims are incorrect/are not well-defined/are informal/etc", we should instead say "BMS is known to terminate up to at least (0,0,0)(1,1,1), but it is not known to terminate in the general case." Along with removing the aforementioned bit, I also added multiple sentences to the article that specify that BMS is not known to terminate (which obviously implies that any claim that BMS is well-founded must be unproven.)
- I also removed an unnecessary paragraph talking about people's various analyses and how they are undefined for various reasons, because there is already a section specifically for talking about analyses of BMS. In that section, I edited it to make it succinctly (and correctly) say that the analyses should not be taken as fact, as they are informal. This doesn't need to be repeated multiple times throughout the entire article, and we especially don't have to waste multiple paragraphs on it. There was a mention of Bashicu's comparison of the matrix (0,0,0,0)(1,1,1,1) to his OCF, only for the article to say that it's undefined. Is there any reason for the article to talk about specific undefined analyses at all? I can sort of understand including this one, since it was made by the creator of BMS himself, but that does not detract from my general point. We can simply say that to date, nobody has performed any formalized analysis of BMS past a certain point (that "point" would be the matrix (0,0,0)(1,1,1) which corresponds to the limit of pair sequence system), and any analysis that goes past that point is not expected to be correct or formal.
- Ecl1psed276 (talk) 06:40, 4 July 2023 (UTC)
- > I read the Wiki Policy page that you linked, and none of the things in that section seem to apply to my edit
- How could your edits be exceptions of "In order to make discussions about decisions on this wiki (e.g. creating new rules, removing descriptions from articles, renaming or moving articles, blocking and unblocking users, and so on) visible and available, those should be held inside this wiki."? As long as you ignore the policy by removing descriptions from articles without discussion inside this wiki and the FANDOM's guide line to clarify that every user has the same user right to decide anything on articles, it is obvious that your removal is unconstructive.
- > so I don't think a discussion is necessary in order to do it.
- Why do you think that you can freely remove what others wrote without discussion?
- > I removed this bit of the article: Most claims about the strength and well-foundedness of BMS have so far not been formally defined, or they haven't been proven. I heavily dislike the wording of that sentence, because it gives more focus to claims about the strength of BMS, rather than, well, the strength of BMS.
- Why do you think that your personal preference should be reflected in a non-equivalent way amobg other users, by ignoring the intention of others who wrote what you want to silently remove without discussion?
- > Instead of saying "Most claims are incorrect/are not well-defined/are informal/etc", we should instead say "BMS is known to terminate up to at least (0,0,0)(1,1,1), but it is not known to terminate in the general case."
- Why? We can write both, and you have never explained why the information on incorrectness/ill-definedness/informality/etc should be immediately removed without discussion.
- > I also removed an unnecessary paragraph talking about people's various analyses and how they are undefined for various reasons, because there is already a section specifically for talking about analyses of BMS.
- Please specify what paragraph which you insist that is unnecessary.
- > There was a mention of Bashicu's comparison of the matrix (0,0,0,0)(1,1,1,1) to his OCF, only for the article to say that it's undefined. Is there any reason for the article to talk about specific undefined analyses at all?
- It is simply because it is actually an important history of the analysis of BMS. Again, why do you think that it is worth nothing and hence can be freely removed before asking discussion, even though you can easily imagine that the ones who wrote them have intentions?
- As long as you disagree with the wiki policy to have discussions inside this wiki before removals and FANDOM's guideline to clarify that every use has the same user right in decisions, any discussion will not be sound. Couldn't you stop to ignore the wiki policy and the FANDOM's guideline?
- p-adic 09:04, 4 July 2023 (UTC)
Clarification that BMS is not an ordinal notation[]
I propose rewriting
- Although Bashicu matrix system is not an ordinal notation system,
to
- Bashicu matrix system is not an ordinal notation system, because a recursive well-ordering on the system is not defined. However,
and add a footnote of
- Sometimes the termination of BMS is identified with the claim that BMS is an ordinal notation system, but it is based on confusion of the well-foundedness of BMS with the well-definedness of the lexicographic order and confusion of a recursive relation with a relation related to an algorithm in some sense.
p進大好きbot wrote this sentence. 🐟 Fish fish fish ... 🐠 06:57, 6 September 2023 (UTC)
- Thank you.
- p-adic 08:05, 6 September 2023 (UTC)
Moving paragraphs[]
I think that the paragraphs before "contents" are too long and detailed, and most of them should go to "Analysis of Growth Rate" section. Then we can briefly introduce BMS as a leading paragraph of this article. 🐟 Fish fish fish ... 🐠 11:23, 7 September 2023 (UTC)
- Does it the same as "目次" in Japanese system? (There is no "contents" found in my environment.) Reordering might be good. I note that there was also a proposal to separate this article into two in order to make it easier to read (cf. several comments in #Very outdated).
- p-adic 12:05, 7 September 2023 (UTC)
- I see. Thank you.
- p-adic 13:02, 7 September 2023 (UTC)
- I moved the leading paragraphs to the analysis section, and moved explanation of basic notation in the leading paragraph, as this must be the first thing to be understood. I also added some short description as an introduction. 🐟 Fish fish fish ... 🐠 19:50, 7 September 2023 (UTC)
Difficult[]
rt. It very difficult, because it define so many let people forgeting.—Preceding unsigned comment added by Gongxiang01 (talk • contribs)