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This is a new, sourced, write-up of the reference to this term I happen to know. Eric Weisstein has inserted a a note in MathWorld about a (slightly different) generalization of the term, and the article on that was deleted, perhaps rightly. Septentrionalis 21:10, 13 July 2006 (UTC)
I don't think that Regular number is a good location for this article. I haven't ever seen that term used to mean a 5-smooth integer, although I have seen it used once or twice with other meanings. Further, the term Hamming number is used fairly widely. Although they will always be "5-smooth" to me (or perhaps {2, 3, 5}-smooth), I think that Hamming number is the right place for this article. Thoughts?
CRGreathouse ( t | c) 21:09, 2 March 2008 (UTC)
Why is this article not renamed yet? It seems it has also been voted to be deleted once: /info/en/?search=Wikipedia:Articles_for_deletion/Regular_number How about calling it "Babylonian regular numbers"? "Regular numbers" is clearly not a right name (show me a non-Babylonian who believes that these numbers are more regular than the others). -- Cokaban ( talk) 14:16, 13 October 2013 (UTC)
Should Wikipedia record (and mention in such a prominent place as the opening paragraph of the article) a nonce term apparently made up and only ever used in the context of some forgotten computing contest? And may I ask what reason was given for such a label by whoever coined it? The term "ugly number" strikes me as terribly POV, and moreover its strong pejorative character seems completely ludicrous and unwarranted given the high notability and usefulness of these numbers for all kinds of purposes (starting by their utmost importance in geometry and music). It seems as if whoever thought such a dismissive label as "ugly" was somehow befitting for these numbers, must have thought that "number beauty" is measured by arcanity and lack of pragmatic value, so that the quantities that govern myriad aspects of our daily lives would appear "ugly" because they are to be found all around. 213.37.6.23 ( talk) 09:57, 8 May 2008 (UTC)
I expanded a previous footnote into a paragraph about computing sexagesimals in order, after discovering the Knuth and Bruins references on the subject as well as the Gingerich citation we already had. I'd also like to add something like " Eppstein (2007) describes an algorithm for computing tables of this type in linear time for arbitrary values of k.", with a later bibliography entry Eppstein, David (2007), The range-restricted Hamming problem. But as you can see, that would be a little self-serving. If someone else thinks this would be an appropriate addition, please go ahead and add it. — David Eppstein ( talk) 18:22, 27 May 2008 (UTC)
The formula i use for calculating regulars in base 60 less than 60^N, is KN^2/2 - AN + B, where K=(ln60)^3/ln(2)ln(3)ln(5) = 56.002707, A = 4.7, and B = 2. For new entries, the formula is KN - C, where C = 32. This is for N places. In base 120, these are K=89.5324377, A=12.95, B=4, C=47. The error is less than 1 over a range of N=30. Wendy.krieger ( talk) 09:33, 19 February 2017 (UTC)
Is there a reason that this article keeps mentioning that these numbers can divide powers of 60? It seems strange, because that's just another way of saying that their prime factors are one of 2,3, or 5, isn't it? If there's anything more than that (that I'm missing), it probably should be clearly stated. Luminifer ( talk) 05:18, 1 June 2009 (UTC)
In an article about the Hamming problem it is nice to have the solution. Since the article discusses how non-trivial the solution of the problem in a non-lazy language is, it is a good idea to include the non-lazy solution itself, especially, since it is only 10-lines long. The language of implementation is irrelevant, Python was just an example. I propose to undo the removal of the solution. GrGBL ( talk) 11:58, 30 May 2010 (UTC)
The result of the move request was: Not moved. There is clearly no consensus in favour of moving to the proposed title of "Babylonian regular numbers". There is not enough information to determine if there is support for the "5-smooth numbers" alternative, so I suggest that the nominator or others should pursue that as a separate move request, if they are interested in doing so. ( non-admin closure) — Amakuru ( talk) 11:22, 21 October 2013 (UTC)
Regular number →
Babylonian regular numbers – The term "regular numbers" to designate numbers whose inverse in base-60 number system has finite number of digits seem to be obsolete by 2500 years. Base-60 number system is not used anymore. There may be specialists in other narrow fields (besides babylonian studies) who might like to have their favorite numbers called "regular"
Cokaban (
talk)
14:36, 13 October 2013 (UTC)
Since the discussion has become a little fragmented, I thought it might be helpful for me to outline what I see as the reasons for giving this article the title it now has, "regular number".
Do I thnk "regular number" was a good choice for the historians of mathematics to have made? No, I'm sad they didn't search for a modern cognate of a Babylonian word for finite or terminating and use that instead. "Sofic numbers" would make some sense (despite the Hebrew rather than Babylonian root), and is both more informative and less boring. But the historians made their choice, "regular number" is reasonably unambiguous (the only competing definition I know of is the one for having a terminating decimal reciprocal, which has been deemed non-notable), and it's not for us to try to push a better phrase. — David Eppstein ( talk) 16:24, 15 October 2013 (UTC)
The result of the proposal was no consensus. -- BDD ( talk) 17:40, 14 November 2013 (UTC)
Regular number → 5-smooth numbers – This page discusses properties and uses of 5-smooth numbers, but pretends to describe an ostensibly common term "Regular number". The term "regular number" does not exist in modern English or mathematics. All the references of the article that contain the term "regular number" are about "sexagesimal regular numbers" in ancient Babylonian mathematics (which apparently used base-60 number system). Now these numbers are called 5-smooth. For any prime p, there is the set of p-smooth numbers, which has properties similar to those of the set of 5-smooth numbers. This article is about historical appearances of 5-smooth numbers under different names, their uses in music terminology and notation, and mathematical properties of the set of all 5-smooth numbers (which are not substantially different from the properties of the set of all p-smooth numbers for any prime p) --Relisted. Steel1943 ( talk) 07:55, 4 November 2013 (UTC) Cokaban ( talk) 09:49, 27 October 2013 (UTC)
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Reviewing |
Reviewer: Shushugah ( talk · contribs) 21:51, 18 December 2021 (UTC)
Rate | Attribute | Review Comment |
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1. Well-written: | ||
![]() |
1a. the prose is clear, concise, and understandable to an appropriately broad audience; spelling and grammar are correct. | |
![]() |
1b. it complies with the Manual of Style guidelines for lead sections, layout, words to watch, fiction, and list incorporation. | |
2. Verifiable with no original research: | ||
![]() |
2a. it contains a list of all references (sources of information), presented in accordance with the layout style guideline. | |
![]() |
2b. reliable sources are cited inline. All content that could reasonably be challenged, except for plot summaries and that which summarizes cited content elsewhere in the article, must be cited no later than the end of the paragraph (or line if the content is not in prose). | Per discussion below, it's properly cited |
![]() |
2c. it contains no original research. | |
![]() |
2d. it contains no copyright violations or plagiarism. | |
3. Broad in its coverage: | ||
![]() |
3a. it addresses the main aspects of the topic. | |
![]() |
3b. it stays focused on the topic without going into unnecessary detail (see summary style). | |
![]() |
4. Neutral: it represents viewpoints fairly and without editorial bias, giving due weight to each. | |
![]() |
5. Stable: it does not change significantly from day to day because of an ongoing edit war or content dispute. | I believe so. There hasn't been any edit warring and an active talk page is a good thing. There's been recent edits, but that's Wikipedia for you. |
6. Illustrated, if possible, by media such as images, video, or audio: | ||
![]() |
6a. media are tagged with their copyright statuses, and valid non-free use rationales are provided for non-free content. | |
![]() |
6b. media are relevant to the topic, and have suitable captions. | |
![]() |
7. Overall assessment. | This article was a delight to read. It's neither too technical, nor too bare bones. Its diverse applications without resorting to trivia/hat collecting makes this a win for me. I mentioned the inline reference as main thing to change and would gladly do it myself if need be. |
@ Shushugah: This does NOT use a deprecated style for referencing. It uses footnotes for referencing. The use of parenthetical author (year) short references in footnotes, pointing to more complete references in a later section, is not deprecated, neither is the use of parenthetical author (year) forms in the text of the article, as part of sentences of the article rather than as references. The only thing that was deprecated was extra-textual references formatted parenthetically in article text rather than in other ways. There used to be some of these in the article; I removed what was I believe the last one in preparing for this nomination, in Special:Diff/1059406410. The only remaining parenthetically-formatted reference, to Stormer 1897, occurs within another footnote, so is not covered by that deprecation. — David Eppstein ( talk) 22:18, 18 December 2021 (UTC)
References
The result was: promoted by
Theleekycauldron (
talk)
20:04, 1 January 2022 (UTC)
Improved to Good Article status by David Eppstein ( talk). Self-nominated at 01:10, 25 December 2021 (UTC).
I tried to edit the article, pointing out that sometimes the term "regular number" is used for non-integers, and adding something in the section on Babylonian mathematics about reciprocal tables and the remarkable one containing all the six-place regular numbers. David Eppstein systematically reverts whatever I do, claiming that my reference doesn't say what it says and that it doesn't matter if it does, and that I don't do the reference in the right way. I claim that those are not sufficient reasons to revert what I do. Eric Kvaalen ( talk) 18:22, 14 January 2023 (UTC)
![]() |
Most of the discussion on this dispute has focused on the contention that the term is sometimes used for non-integers. For now, I agree with David Eppstein that we should exclude this content. My two issues with it are that (a) Fowler and Robson (arguably) use the term in this sense only briefly, and this one citation doesn't really justify that the term is "sometimes" used this way. Also, (b) their use of the term is so easily interpreted as shorthand for "a regular integer place-shifted into fractional from", with all of their examples fitting this case, and the shorthand is so expedient since the Babylonians so frequently treat the two numbers as synonymous. This interesting and useful synonymity is already explained well in the status quo ante article text.The rest of Eric Kvaalen's edit concerns the Seleucid six-place regular reciprocal table, but I haven't seen enough discussion on that part to be able to weigh arguments. I have this page watchlisted, and I'd be happy to answer follow-up or clarifying questions. Thanks for seeking out a third opinion. Firefangledfeathers ( talk / contribs) 02:57, 22 January 2023 (UTC) |
Thank you Firefangledfeathers. I certainly do object to his removal of what I wrote about the reciprocal table. And the fact that he systematically reverts everything I do. He doesn't like something about the format of the reference I gave (I don't understand what), so he uses that as one of his reasons for reverting the whole edit. As for the question of whether we should say that the term is sometimes used to mean certain fractions, I don't see what's so bad about mentioning this, perhaps with revised wording, like "can be used" or "has been used". That's a fact, and I don't see why we must prevent readers from being exposed to it. Eric Kvaalen ( talk) 06:02, 22 January 2023 (UTC)
On "I am not claiming ..."
, I didn't say you were! If something I said made it seem like that, it wasn't intentional. You've reiterated your argument, but it hasn't changed my mind.
Thanks for linking CotACM, which does include Knuth's correction. It's in the "Letters" segment, and here's a PDF link. It makes it clear that Knuth's opinion that Inaqibıt-Anu had collected all the up-to-six place regular reciprocals is just that: an opinion. Knuth owns up to misreading a source and quotes another researcher who thinks there was only one tablet. Sadly, it looks like the surviving tablet doesn't even include all the reciprocals starting with 1 or 2, only 136 of the 231. The line in §Algorithms needs to be updated, at the very least, to state that the extent of Inaqibıt-Anu's accomplishment is only hypothesized by Knuth, and that even he doesn't think the scribe got them all. Firefangledfeathers ( talk / contribs) 02:46, 4 February 2023 (UTC)
I was complaining that David Eppstein wouldn't let me mention how Fowler and Robson use the term because he disagrees with them. Anyway, I have now edited the article to include a correct description of the tablet of Inaqibıt-Anu. Thanks for the link to the correction of Knuth. Actually, the old version contains an interesting appendix which is not in the newer version. You know, he has offered a check to anyone who would find an error in one of his papers, and I wrote to him once about an error in a paper quoting him, but apparently it wasn't in his original! He wrote me a nice reply.
Eric Kvaalen (
talk)
11:00, 8 February 2023 (UTC)
![]() | Regular number has been listed as one of the Mathematics good articles under the good article criteria. If you can improve it further, please do so. If it no longer meets these criteria, you can reassess it. | |||||||||
| ||||||||||
![]() | A
fact from this article appeared on Wikipedia's
Main Page in the "
Did you know?" column on
January 6, 2022. The text of the entry was: Did you know ... that certain bamboo species
release large numbers of seeds in synchrony after numbers of years that
have only 2, 3, and 5 as their prime factors? |
![]() | This article was nominated for deletion on 2006 July 7. The result of the discussion was delete. |
![]() | This article is rated GA-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
|
This is a new, sourced, write-up of the reference to this term I happen to know. Eric Weisstein has inserted a a note in MathWorld about a (slightly different) generalization of the term, and the article on that was deleted, perhaps rightly. Septentrionalis 21:10, 13 July 2006 (UTC)
I don't think that Regular number is a good location for this article. I haven't ever seen that term used to mean a 5-smooth integer, although I have seen it used once or twice with other meanings. Further, the term Hamming number is used fairly widely. Although they will always be "5-smooth" to me (or perhaps {2, 3, 5}-smooth), I think that Hamming number is the right place for this article. Thoughts?
CRGreathouse ( t | c) 21:09, 2 March 2008 (UTC)
Why is this article not renamed yet? It seems it has also been voted to be deleted once: /info/en/?search=Wikipedia:Articles_for_deletion/Regular_number How about calling it "Babylonian regular numbers"? "Regular numbers" is clearly not a right name (show me a non-Babylonian who believes that these numbers are more regular than the others). -- Cokaban ( talk) 14:16, 13 October 2013 (UTC)
Should Wikipedia record (and mention in such a prominent place as the opening paragraph of the article) a nonce term apparently made up and only ever used in the context of some forgotten computing contest? And may I ask what reason was given for such a label by whoever coined it? The term "ugly number" strikes me as terribly POV, and moreover its strong pejorative character seems completely ludicrous and unwarranted given the high notability and usefulness of these numbers for all kinds of purposes (starting by their utmost importance in geometry and music). It seems as if whoever thought such a dismissive label as "ugly" was somehow befitting for these numbers, must have thought that "number beauty" is measured by arcanity and lack of pragmatic value, so that the quantities that govern myriad aspects of our daily lives would appear "ugly" because they are to be found all around. 213.37.6.23 ( talk) 09:57, 8 May 2008 (UTC)
I expanded a previous footnote into a paragraph about computing sexagesimals in order, after discovering the Knuth and Bruins references on the subject as well as the Gingerich citation we already had. I'd also like to add something like " Eppstein (2007) describes an algorithm for computing tables of this type in linear time for arbitrary values of k.", with a later bibliography entry Eppstein, David (2007), The range-restricted Hamming problem. But as you can see, that would be a little self-serving. If someone else thinks this would be an appropriate addition, please go ahead and add it. — David Eppstein ( talk) 18:22, 27 May 2008 (UTC)
The formula i use for calculating regulars in base 60 less than 60^N, is KN^2/2 - AN + B, where K=(ln60)^3/ln(2)ln(3)ln(5) = 56.002707, A = 4.7, and B = 2. For new entries, the formula is KN - C, where C = 32. This is for N places. In base 120, these are K=89.5324377, A=12.95, B=4, C=47. The error is less than 1 over a range of N=30. Wendy.krieger ( talk) 09:33, 19 February 2017 (UTC)
Is there a reason that this article keeps mentioning that these numbers can divide powers of 60? It seems strange, because that's just another way of saying that their prime factors are one of 2,3, or 5, isn't it? If there's anything more than that (that I'm missing), it probably should be clearly stated. Luminifer ( talk) 05:18, 1 June 2009 (UTC)
In an article about the Hamming problem it is nice to have the solution. Since the article discusses how non-trivial the solution of the problem in a non-lazy language is, it is a good idea to include the non-lazy solution itself, especially, since it is only 10-lines long. The language of implementation is irrelevant, Python was just an example. I propose to undo the removal of the solution. GrGBL ( talk) 11:58, 30 May 2010 (UTC)
The result of the move request was: Not moved. There is clearly no consensus in favour of moving to the proposed title of "Babylonian regular numbers". There is not enough information to determine if there is support for the "5-smooth numbers" alternative, so I suggest that the nominator or others should pursue that as a separate move request, if they are interested in doing so. ( non-admin closure) — Amakuru ( talk) 11:22, 21 October 2013 (UTC)
Regular number →
Babylonian regular numbers – The term "regular numbers" to designate numbers whose inverse in base-60 number system has finite number of digits seem to be obsolete by 2500 years. Base-60 number system is not used anymore. There may be specialists in other narrow fields (besides babylonian studies) who might like to have their favorite numbers called "regular"
Cokaban (
talk)
14:36, 13 October 2013 (UTC)
Since the discussion has become a little fragmented, I thought it might be helpful for me to outline what I see as the reasons for giving this article the title it now has, "regular number".
Do I thnk "regular number" was a good choice for the historians of mathematics to have made? No, I'm sad they didn't search for a modern cognate of a Babylonian word for finite or terminating and use that instead. "Sofic numbers" would make some sense (despite the Hebrew rather than Babylonian root), and is both more informative and less boring. But the historians made their choice, "regular number" is reasonably unambiguous (the only competing definition I know of is the one for having a terminating decimal reciprocal, which has been deemed non-notable), and it's not for us to try to push a better phrase. — David Eppstein ( talk) 16:24, 15 October 2013 (UTC)
The result of the proposal was no consensus. -- BDD ( talk) 17:40, 14 November 2013 (UTC)
Regular number → 5-smooth numbers – This page discusses properties and uses of 5-smooth numbers, but pretends to describe an ostensibly common term "Regular number". The term "regular number" does not exist in modern English or mathematics. All the references of the article that contain the term "regular number" are about "sexagesimal regular numbers" in ancient Babylonian mathematics (which apparently used base-60 number system). Now these numbers are called 5-smooth. For any prime p, there is the set of p-smooth numbers, which has properties similar to those of the set of 5-smooth numbers. This article is about historical appearances of 5-smooth numbers under different names, their uses in music terminology and notation, and mathematical properties of the set of all 5-smooth numbers (which are not substantially different from the properties of the set of all p-smooth numbers for any prime p) --Relisted. Steel1943 ( talk) 07:55, 4 November 2013 (UTC) Cokaban ( talk) 09:49, 27 October 2013 (UTC)
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GA toolbox |
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Reviewing |
Reviewer: Shushugah ( talk · contribs) 21:51, 18 December 2021 (UTC)
Rate | Attribute | Review Comment |
---|---|---|
1. Well-written: | ||
![]() |
1a. the prose is clear, concise, and understandable to an appropriately broad audience; spelling and grammar are correct. | |
![]() |
1b. it complies with the Manual of Style guidelines for lead sections, layout, words to watch, fiction, and list incorporation. | |
2. Verifiable with no original research: | ||
![]() |
2a. it contains a list of all references (sources of information), presented in accordance with the layout style guideline. | |
![]() |
2b. reliable sources are cited inline. All content that could reasonably be challenged, except for plot summaries and that which summarizes cited content elsewhere in the article, must be cited no later than the end of the paragraph (or line if the content is not in prose). | Per discussion below, it's properly cited |
![]() |
2c. it contains no original research. | |
![]() |
2d. it contains no copyright violations or plagiarism. | |
3. Broad in its coverage: | ||
![]() |
3a. it addresses the main aspects of the topic. | |
![]() |
3b. it stays focused on the topic without going into unnecessary detail (see summary style). | |
![]() |
4. Neutral: it represents viewpoints fairly and without editorial bias, giving due weight to each. | |
![]() |
5. Stable: it does not change significantly from day to day because of an ongoing edit war or content dispute. | I believe so. There hasn't been any edit warring and an active talk page is a good thing. There's been recent edits, but that's Wikipedia for you. |
6. Illustrated, if possible, by media such as images, video, or audio: | ||
![]() |
6a. media are tagged with their copyright statuses, and valid non-free use rationales are provided for non-free content. | |
![]() |
6b. media are relevant to the topic, and have suitable captions. | |
![]() |
7. Overall assessment. | This article was a delight to read. It's neither too technical, nor too bare bones. Its diverse applications without resorting to trivia/hat collecting makes this a win for me. I mentioned the inline reference as main thing to change and would gladly do it myself if need be. |
@ Shushugah: This does NOT use a deprecated style for referencing. It uses footnotes for referencing. The use of parenthetical author (year) short references in footnotes, pointing to more complete references in a later section, is not deprecated, neither is the use of parenthetical author (year) forms in the text of the article, as part of sentences of the article rather than as references. The only thing that was deprecated was extra-textual references formatted parenthetically in article text rather than in other ways. There used to be some of these in the article; I removed what was I believe the last one in preparing for this nomination, in Special:Diff/1059406410. The only remaining parenthetically-formatted reference, to Stormer 1897, occurs within another footnote, so is not covered by that deprecation. — David Eppstein ( talk) 22:18, 18 December 2021 (UTC)
References
The result was: promoted by
Theleekycauldron (
talk)
20:04, 1 January 2022 (UTC)
Improved to Good Article status by David Eppstein ( talk). Self-nominated at 01:10, 25 December 2021 (UTC).
I tried to edit the article, pointing out that sometimes the term "regular number" is used for non-integers, and adding something in the section on Babylonian mathematics about reciprocal tables and the remarkable one containing all the six-place regular numbers. David Eppstein systematically reverts whatever I do, claiming that my reference doesn't say what it says and that it doesn't matter if it does, and that I don't do the reference in the right way. I claim that those are not sufficient reasons to revert what I do. Eric Kvaalen ( talk) 18:22, 14 January 2023 (UTC)
![]() |
Most of the discussion on this dispute has focused on the contention that the term is sometimes used for non-integers. For now, I agree with David Eppstein that we should exclude this content. My two issues with it are that (a) Fowler and Robson (arguably) use the term in this sense only briefly, and this one citation doesn't really justify that the term is "sometimes" used this way. Also, (b) their use of the term is so easily interpreted as shorthand for "a regular integer place-shifted into fractional from", with all of their examples fitting this case, and the shorthand is so expedient since the Babylonians so frequently treat the two numbers as synonymous. This interesting and useful synonymity is already explained well in the status quo ante article text.The rest of Eric Kvaalen's edit concerns the Seleucid six-place regular reciprocal table, but I haven't seen enough discussion on that part to be able to weigh arguments. I have this page watchlisted, and I'd be happy to answer follow-up or clarifying questions. Thanks for seeking out a third opinion. Firefangledfeathers ( talk / contribs) 02:57, 22 January 2023 (UTC) |
Thank you Firefangledfeathers. I certainly do object to his removal of what I wrote about the reciprocal table. And the fact that he systematically reverts everything I do. He doesn't like something about the format of the reference I gave (I don't understand what), so he uses that as one of his reasons for reverting the whole edit. As for the question of whether we should say that the term is sometimes used to mean certain fractions, I don't see what's so bad about mentioning this, perhaps with revised wording, like "can be used" or "has been used". That's a fact, and I don't see why we must prevent readers from being exposed to it. Eric Kvaalen ( talk) 06:02, 22 January 2023 (UTC)
On "I am not claiming ..."
, I didn't say you were! If something I said made it seem like that, it wasn't intentional. You've reiterated your argument, but it hasn't changed my mind.
Thanks for linking CotACM, which does include Knuth's correction. It's in the "Letters" segment, and here's a PDF link. It makes it clear that Knuth's opinion that Inaqibıt-Anu had collected all the up-to-six place regular reciprocals is just that: an opinion. Knuth owns up to misreading a source and quotes another researcher who thinks there was only one tablet. Sadly, it looks like the surviving tablet doesn't even include all the reciprocals starting with 1 or 2, only 136 of the 231. The line in §Algorithms needs to be updated, at the very least, to state that the extent of Inaqibıt-Anu's accomplishment is only hypothesized by Knuth, and that even he doesn't think the scribe got them all. Firefangledfeathers ( talk / contribs) 02:46, 4 February 2023 (UTC)
I was complaining that David Eppstein wouldn't let me mention how Fowler and Robson use the term because he disagrees with them. Anyway, I have now edited the article to include a correct description of the tablet of Inaqibıt-Anu. Thanks for the link to the correction of Knuth. Actually, the old version contains an interesting appendix which is not in the newer version. You know, he has offered a check to anyone who would find an error in one of his papers, and I wrote to him once about an error in a paper quoting him, but apparently it wasn't in his original! He wrote me a nice reply.
Eric Kvaalen (
talk)
11:00, 8 February 2023 (UTC)