Talk:List of numeral systems

Names of numbers in languages

By definition, the verbal names of numbers in languages cannot be a numeral system (only if there is a system of written marks etc.). AnonMoos (talk) 14:06, 22 April 2011 (UTC)

You should also reference the base 3 system employed in the Han dynasty book on divination by Yang Hsiung the Tai Hsuan ching. I discovered this in the mid 1970's while an undergraduate at UCSB. Unfortunatly it has not been I mentioned this in letters to Nathan Sivin and Dr Joseph Needham. Dr Needham seemed to have recognized this in his Science and Civilization in China volume but kindly credited me with the discovery. I think it was also recognized in a Japanese translation. The key passage is in Chapter 8 "The Numbers of the Tai hsuan Ching.

推玄算：家，一置一，二置二，三置三；部，一勿增，二增三，三增六；州，一勿增，二增九，三增十八；方，一勿增，二增二十七，三增五十四。 Sunwukongmonkeygod (talk) 17:07, 1 April 2023 (UTC)

Undecimal

I wrote this in the table at the undecimal row:

"Jokingly proposed during the French revolution to settle a dispute between those proposing a shift to duodecimal and those who were content with decimal."

Can anyone help me with a source for that?Laelele (talk) 12:04, 8 November 2012 (UTC)

I'm not sure if it was a joke. Pages 69–70 of Glaser's History of Binary and Other Nondecimal Numeration has "The Metric Commission, consisting of Borda, Lagrange, Lavoisier, Tillet, and Concorcet, made a ‘Rapport’ on October 27, 1790 to the Academy of Science in Paris, indicating that the Commission had briefly considered proposing that the decimal arithmetic be replaced for common use by the duodecimal system and that the Metric System be duodecimalized to match. ... Any advantages of base 12 would be due to its being richer in divisors than 10 and certain common fractions such as 1/3 and 1/4 would have simpler equivalents in base 12 notation. As one can gather from a later paper by Delambre ..., at least one member of the Commission, namely Lagrange, refused to concede even such a slight theoretical advantage to base 12. He argued to the contrary, that poorness in divisors was an advantage, and that perhaps they should consider a prime number, such as 11, since then no proper fraction (with 11 as a denominator) would be reducible and each would neatly preserve 11 as a denominator." This just screams "bad idea" to me, though: imagine the recurring decimals that we would have to deal with on a daily basis! Double sharp (talk) 14:46, 29 January 2015 (UTC)

Positional numeral systems without own article

There are a number of positional numeral systems that do not have or no longer have their own article. Where there is not another page that covers such a system, i have linked the redirect to 'list of numeral systems' where there is at least mention of the system, and there is some context. Bcharles (talk) 14:23, 8 August 2013 (UTC)

On £sd and degrees

Do these really count as bases 240 and 360? They're more like a single place of that base (and for £sd, it's not even pure base 240; it's 20-on-12). (Yes, I did add degrees as base 360 some time ago, but I'm reconsidering it.) Double sharp (talk) 15:01, 29 January 2015 (UTC)

Standard positional numeral systems table

Imagine that! The most well-cited entry is the one stating decimal to be the most commonly used base! (Giggles.) Now to try to improve that situation... Double sharp (talk) 01:08, 19 March 2015 (UTC)

See also

I came across these two lists

• List of numeral systems
• List of types of numbers

and wondered if someone looking for information on one list might end up only finding and reading the other, so I thought they should at least be cross-linked. I am also wondering if both could use some cleanup. IveGoneAway (talk) 23:15, 13 April 2015 (UTC)

Maybe Roman numeral is misplaced in List of types of numbers.

Maybe List of types of numbers could be annotated to say that the list is generally in terms of the Hindu–Arabic numeral system. IveGoneAway (talk) 23:24, 13 April 2015 (UTC)

I agree that numeral systems do not strictly belong at List of types of numbers. On the other hand, the average reader probably does not understand the distinction between numerals and numbers. So if we relegate Roman numerals, binary numerals, etc. to a hatnote, then it has to be prominent and clear. Mgnbar (talk) 00:49, 14 April 2015 (UTC)

DNA - Quaternary but not

Earthly DNA has four nucleobases, or "values": A, C, G, and T. Thus, genetic sequences can be stored in pseudo-quaternary binary: 00, 01, 10, and 11. Also, DNA itself can store binary information in quaternary strings. However, since there is no inherent valuation of these "digits" from zero to three, DNA neucleobases do not count as an example of a quaternary number system. (There are also many nucleic acid analogues -- fake nucleobases -- but I won't go into that here.) --2601:0:580:47C3:7D1C:9CB3:5AAC:1FAE (talk) 20:38, 3 January 2016 (UTC)

I thought about this and came to the same conclusion. ACGT values were not defined perhaps some sort of analysis of the molecular structure might suggest a rational method. Sunwukongmonkeygod (talk) 17:16, 1 April 2023 (UTC)

Source of Wuvulu-Aua number

<ref> Hafford, James (2015). "Introduction". Wuvulu Grammar and Vocabulary. 72-76 JIAFU (talk) 19:09, 5 February 2017 (UTC)

Octodecimal

The Octodecimal page that the article links to in the section Standard positional numeral systems redirects back to the article. Ergo, it is a indirect self-link. I'm not quite sure how to fix that 😕. 24.111.140.218 (talk) 05:32, 24 September 2017 (UTC)

Telephone numbers as example of duodecimal

The article gives telephone numbers as a usage example of duodecimal. Is that true? Telephone numbers seem decimal to me -- I've never seen a working phone number with a pound or a star inside of it. I think this might be confusing duodecimal notation (which sometimes uses the pound and asterisk symbols) with actual usage. I recommend the removal of telephone numbers as a usage example.

123.231.111.255 (talk) 10:29, 14 October 2017 (UTC)

Base 1000

Anyone who knows the name of Base 1000 answers this question; What is the name of Base 1000? — Preceding unsigned comment added by 2600:1700:3A20:25B0:C9B0:AEED:57C7:E8DD (talk) 01:43, 23 August 2019 (UTC)

That doesn't sound very useful to me, but by the rules of Latin, its name would be "Millesimal"... AnonMoos (talk) 15:59, 23 August 2019 (UTC)

Pentatrigesimal (and a couple of others)

The text says "Using all numbers and all letters except O" - but https://www.translatorscafe.com/unit-converter/en-US/numbers/38-13/base-35-base-10/ (for example) uses 0-9A-Y instead of 0-9A-N,P-Z - so this may not be accurate in all understandings of base 35? likewise bases 34,33 have exceptions listed which seem to work for car numberplates but not for the general usage of the bases Simonalexander2005 (talk) 09:28, 7 August 2020 (UTC)

Sounds right. Perhaps "Using all numbers and all letters except one (usually excluding either O or Z)".--Nø (talk) 16:40, 7 August 2020 (UTC)

I think the idea is to list *why* the base might be used. There are a lot more reasons to exclude 'O' than 'Z'. That other page appears to be machine-generated and has many bases not in this table.Spitzak (talk) 20:41, 7 August 2020 (UTC)

Tangut

The Tangut system appears as a series of identical squares. Is this correct, or is this a computer glitch? These squares look like the ones I see when my computer can't read certain texts, which is why I ask.Kdammers (talk) 03:46, 12 November 2020 (UTC)

It just means that your computer (and mine) doesn't have a Tangut font installed. The bytes are correct (or at least plausible) in the wikitext, and anyone with software to display this extinct language should be able to read them. Certes (talk) 13:07, 12 November 2020 (UTC)

Then maybe the text should be replaced with an image of the text, since I doubt very many people coming to the article have Tangut-reading software, and those who do don't need this snippet of information about Tangut. Kdammers (talk) 02:21, 13 November 2020 (UTC)

I see characters on my machine (Linux running Chrome). Don't know if they are correct.Spitzak (talk) 03:40, 13 November 2020 (UTC)

The Ciphers of the Monks

The notational system described in The Ciphers of the Monks appears to be missing. Kdammers (talk) 03:49, 12 November 2020 (UTC)

This article is about numeral systems; writing systems for expressing numbers, not about ciphers, which are systems for making and numbers unreadable. The right place for The Ciphers of the Monks would appear to be our Encryption#Ancient article. --Guy Macon (talk) 05:49, 12 November 2020 (UTC)

Although the book's title says "cipher," the Wikipedia article about the book clearly names it a numeral system and describes it as such. It is a systematic system expressing numbers that is systematic, logical and easily readable without being decoded. Kdammers (talk) 02:18, 13 November 2020 (UTC)

Are you implying that the monks did not have access to any existing and well-known method of writing down integers from 1 to 9999? I would like to see a quote from the book that explains the purpose of using a different notation. --Guy Macon (talk) 04:39, 13 November 2020 (UTC)

The Speculum review cited at the The Ciphers of the Monks article seems to have good information. There doesn't seem to be any cryptographic intent. It's a numeral system pretty similar to other numeral systems. (I have a separate concern about the title and content of the article, which I have raised at Talk:The Ciphers of the Monks.) Mgnbar (talk) 12:46, 13 November 2020 (UTC)

We have an article on that number system at Cistercian numerals. It's not a cipher, it's an alternate base-10 numeral system that appeared at about the same time as Hindu-Arabic numerals (and was eventually replaced by that system). I am happy to see that we have included it. -- Netwalker3 (talk) 03:30, 26 January 2021 (UTC)

Roman numerals could get quite lengthy (1338=MCCCXXXVIII), and Europe was just learning of Arabic numerals. Cistercian could express from I to 9999 in ONE character, saving both ink and valuable parchment space.

Here the word "ciphers" had the sense of 'numbers', not of 'codes'. Jethro Clampett on The Beverly Hillbillies used to say he'd learned "readin', writin', and cipherin'" [arithmetic]. – .Raven  ^.talk 01:32, 16 May 2023 (UTC)

Cherokee numerals

@Carter: wrote on my talk page:

Hello Nø regarding this reversion on List of numeral systems, your parsing of Cherokee syllabary#Numerals is incorrect. Sequoyah developed a full numeral system; it's not a "system for writing Cherokee number words" any more than "64" is a way of writing "sixty four." The section of the Cherokee syllabary article could use expansion and additional detail, but I still don't understand your objection or how you're understanding what it says. Can you please help me in clearing this up? Carter (talk) 9:41 pm, Yesterday (UTC+2)

My reply is that the description on the linked page on those numerals should be amended to warrant the claim, before we link to it.--Nø (talk) 07:04, 18 May 2021 (UTC)

And my reply is that your objection is unclear, both here and previously on Talk:Cherokee syllabary. The system used is essentially the same as with Greek, Glagolitic, and Cyrillic numerals (separate glyphs for "ones" and "tens" and markers for larger numbers that are combined to create even larger numbers), which is described in the article and in this WP:RS article. If you have suggestions as to improve the text, please make them, but it clearly meets the definition of a numeral system. Carter (talk) 12:14, 18 May 2021 (UTC)

Explain to me - no, explain to everyone in the article Cherokee syllabary#Numerals - how the system works. What is a "ciphered-additive-structure"? 64 is 60 and 4 (fine!); 504 is 5, 100 and 4 (how?). Of course, it works fine in English (and possibly in Cherokee) number words, but if that is the logic implied, I think it is more properly described as a shorthand for Chrokee number words than as a numeral system. I don't think lists or templates of numeral systems should link to an article that doesn't describe a numeral system - whether it's because it isn't a numeral system, or because the description is lacking.--Nø (talk) 12:32, 18 May 2021 (UTC)

It is a system for representing numbers as strings, so it's a numeral system. It seems to be verifiable. This article (List of numeral systems) doesn't have to explain how it works. The fact that it's not obvious, how it works, tells us that it's not trivially a rendering of Arabic numerals with different digits. So it seems perfect for inclusion in this article. Mgnbar (talk) 13:24, 18 May 2021 (UTC)

Then, should - or at least could - we include written number words in English, French, Kiswahili and Nganasan (to mention a few) as numeral systems?--Nø (talk) 13:41, 18 May 2021 (UTC)

Sorry Nø, you're not making sense here; "ciphered-additive structure" is the source's description of the numeral system; the concept is discussed some at Alphabetic numeral system#Systems and perhaps a link to that article should be included. Cherokee numerals aren't encoded in a font as of yet, so it's hard to show here, but here's the description of the same principal from Greek numerals: "This alphabetic system operates on the additive principle in which the numeric values of the letters are added together to obtain the total. For example, 241 was represented as  (200 + 40 + 1)." Cherokee numerals use the same basic principal. The difference is that Sequoyah didn't create separate characters for 200 to 900, so the "ones" value preceding the 100 character is understood as multiplying, so 504 is written as "5 100 4", but is understood as "5 × 100 + 4". I should also note that Cherokee isn't an alphabetic numeral system because a seperate group of symbols was created for numbers instead of reusing the syllabary's letters. Carter (talk) 14:28, 18 May 2021 (UTC)

Nø, I would say yes. The difference between "sixty four" and "64" is superficial. So is the difference between "three score and four" and "34₂₀". However, I could understand if you wanted to exclude numerals written in plain text. Even then, the Cherokee numeral system seems to qualify, because it uses specialized glyphs not used elsewhere in Cherokee. Mgnbar (talk) 14:47, 18 May 2021 (UTC)

I'd think 5*100 + 4 is not an example of ciphered-additive structure. And, while "sixty four" and 64 may appear similar, three hundred and seventeen millions seven hundred and four thousand nine hundred and sixty nine is marekdly different (and not just longer than) from 317704969. Of course, a system needs not be positional to qualify, and needs not be able to represent arbitrarily large integers. There may be no clear-cut line between what we must include (like Mayan and Roman numerals) and what we shouldn't (like, imho, English number words such as three hundred and seventeen millions seven hundred and four thousand nine hundred and sixty nine). I still need to see a more clearcut definition of the Cherokee system, answering (implicitly, but unambiguously) e.g. the question: How does it represent 317704969, or how large integers can it represent?--Nø (talk) 16:16, 18 May 2021 (UTC)

Perhaps multiplicative-additive-cipher system would be more accurate, but it's not the term the source used. As for your requested number, it would be rendered as (3 × 100 + 17) million sign + (7 × 100 +4) thousand sign + (9 × 100 + 60 + 9). Carter (talk) 16:39, 18 May 2021 (UTC)

Here are images. In Cherokee, 504 is ᎯᏍᎩ ᏍᎪᎯᏥᏆ ᏅᎩ but in Sequoyah's numeral system it is , using the characters for 5 100 and 4. For the system to be a shorthand for spoken Cherokee, as Nø described it above, 20 would be as the word ᏔᎵᏍᎪᎯ (twenty) could literally be parsed as ᏔᎵ (two) ᏍᎪᎯ (ten). Instead, the numeral for 20 is . Carter (talk) 20:18, 18 May 2021 (UTC)

Unless I've mis-read the time-stamps, it has been two full days since the last comment on this topic. I have not seen any convincing argument that Cherokee numerals do not constitute a numeral system. So can we include them in this list? Mgnbar (talk) 00:53, 21 May 2021 (UTC)

I've tried to clarify, as best I can with the available sources, here and on Cherokee syllabary#Numerals in line with Nø's objections/questions. As far as I'm concerned, Cherokee numerals clearly belong in this list. Carter (talk) 23:59, 23 May 2021 (UTC)

@Tcr25: I do not have time to review your contributions right now; I will look at it at some later time. Clearly, wp:Be bold!--Nø (talk) 13:57, 24 May 2021 (UTC)

Please provide RSs (not fandom sites etc.) for these prefixes to -gesimal

@Kwamikagami: Your edit at 00:37, 15 April 2023, added 19 new compound "-gesimal" terms to this article. Google finds most of them on fandom sites, which are non-RS. What specifically is or are your reliable source(s) for these additions? (sexavigesimal, septemvigesimal, novemvigesimal, quitrigesimal [which Google finds only on this article!], sexatrigesimal, septentrigesimal, novemtrigesimal, quinquadragesimal, Septenquadragesimal [replacing Septaquadragesimal], novemoctogesimal, quinnonagesimal, sexanonagesimal, septennonagesimal, Viginticentesimal, Ducentesimal [replacing Duocentesimal] — all capitalized or not as in the original.) If in fact we have accepted fandom sites as RSs, please advise me of the page saying so. – .Raven  ^.talk 06:06, 15 April 2023 (UTC)

Try searching GBooks rather that fandom sites. Then search for the nonce words used in this article and see if you find any more.

"quitrigesimal" was a typo. Fixed. — kwami (talk) 06:09, 15 April 2023 (UTC)

I did not "search fandom sites"; I searched the Web with Google, and mostly fandom sites showed up... plus this Wikipedia article itself, and occasionally other wikis – which also are not RSs. That correction of your first sentence aside, your second sentence requires that *I* should search for RS cites to support your edit. This is not how it works. When you add a string of sourceless claims, that is sufficient reason to revert. Your refusal to name, cite, or link to any RS suggests that you don't know of one. So I'm reverting that edit, and the adjacent two that left redlinks throughout the page. Please don't repeat them until you can do it properly – sourced and leaving the page functional. – .Raven  ^.talk 07:08, 15 April 2023 (UTC)

A simple search of GBooks will turn most of these up, often in sources spanning over a century, except in cases where neither term is found. WP:SKYISBLUE. But it's not worth my time to engage in one of your play-debates, so I tagged the section as unreliable and will leave it to others to clean up. — kwami (talk) 07:27, 15 April 2023 (UTC)

Again, it's not anyone else's job to find reliable sources supporting your edits. If you don't already know of some, or even one, to properly cite, don't make that edit in mainspace. Work it as a draft or in your sandbox, put the words in there, then find sources for them. But wait until you have at least one reliable source for each fact-claim before adding it/them to an article. This is very stable Wikipedia practice, upheld by consensus. You should already have understood it by now. – .Raven  ^.talk 07:40, 15 April 2023 (UTC)

> "I tagged the section as unreliable...." – I note that you are not naming the sources you consider unreliable. Are other editors supposed to read your mind? Also, that you neither edited nor provided any sources yourself in those three edits, only posted unsourced claims of new words... then when asked for RSs, said to "search" for them. No, that's not a cite. Had your edits remained, they would have made the article more unreliable than before. – .Raven  ^.talk 07:52, 15 April 2023 (UTC)

Nonce terms

Apart from base 2–12 and the decades, which are standard, the names of the bases are not the traditional ones, but often nonce inventions by the author of the single source for them (who also created nonce digits that AFAICT no-one else uses). For example, base 25 is normally 'quinvigesimal', not 'penta-vigesimal', which is more commonly used for vigesimal with a sub-base of 5. If any of these nonce terms are actually in use, they should be given alongside the standard English terms.

Also, normal punctuation is needed. E.g. 'base-32 notation' and 'base 32', not 'Base32'; 'base' is not a proper noun and is not capitalized.

I started to fix myself but was reverted by an edit-warrior who is more interested in scoring points than in improving WP, so I'll let someone else handle it. — kwami (talk) 07:22, 15 April 2023 (UTC)

The problem is that the original terms on the page linked to other existing pages (blue-links), while your "corrections" did not (hence created red-links). Changing a link presumed that what you change it to has a referent, a linkable page. If you want to create redirects first, fine. Or if the pages' editors agree by consensus to having them moved, also fine. After that, you can change the links without them turning red and useless to the reader who wants to know more. You're not new here; you should know this already. – .Raven  ^.talk 07:34, 15 April 2023 (UTC)

I've gone through and performed some copyediting per Kwami's suggestion, above, as it seems like a valid change. I used piping to preserve the blue-links. I did not add in any of the alternative names, (See above section) as a google search for "sexavigesimal" on Google Books returns only two hits, by the same linguistics author, and none others. I'm not an expert on this field, so if this was wrong, feel free to revert. I hope this is an acceptable compromise on the punctuation issue. EducatedRedneck (talk) 11:50, 16 April 2023 (UTC)

Good solution! – .Raven  ^.talk 18:11, 16 April 2023 (UTC)

If we're excluding words that only get a few hits, then we'll need to remove quite a few of these words. — kwami (talk) 04:02, 17 April 2023 (UTC)

I got a few hits for "octovigesimal" and "octotrigesimal", but they're from mineralogy and mean 8x20 and 8x30, not 8+20 or 8+30. They are analogous to "octoduodecimal" (8x2x10), "quadrisexdesimal" (4x6x10), "octodecimal" (8x10), "sexduodecimal" (6x2x10), "quadrioctonal" (4x8).

Confirming the centuries, but they're e.g. "ducentesimal", not *duocentesimal.

Have found "tetrasexagesimal" for base 64.

Found one source on Chinese divination with "sexavigesimal" and "sexatrigesimal", and "hexavigesimal" in the index as a redirect to the former, but so far it's just one source.

Found "penta-vigesimal" and "quinquavigesimal" in multiple sources, but only as 5x20.

"Heptadecimal" was just by James Lovelock in Gaia; everyone else seems to use septendecimal, which is quite common in music. For 19, getting "undevisimal", again from music.

"Sexadecimal" and "sedecimal" are both reasonably common (e.g. Leibniz develops an algorithm for converting decimal numbers to sedecimal and offers two distinct ways of completing the sedecimal character set by identifying the six extra digits ...). Only one source for "trecentosexagesimal"; otherwise it's "tricentesimal", not *trecentesimal. — kwami (talk) 04:45, 17 April 2023 (UTC)

Personally I don't see a problem with just removing all the rarities. They are kind of like the names of the n-gons: except for the smallest values of n, the common names are usually just "base n" or "n-gon". Double sharp (talk) 06:44, 17 April 2023 (UTC)

RV'd the deletion of (most) -esimal names after base-21, e.g. "trivigesimal" – see here, or for numerous others here. – .Raven  ^.talk 07:44, 17 April 2023 (UTC)

I see you're back to playing stupid. Even if your online source counts as a RS, it contradicts your edits, e.g. Undenary, Quattuordecimal, Quindecimal, Nonadecimal, Unovigesimal. But of course it's not a RS. I tagged all the terms I didn't find RS sources for. It makes the article a mess, but it's not worth edit-warring over.

The problem is that people read this article and don't realize it's bullshit. For example, I'm in an argument with someone who claims that "penta-vigesimal" means base 25, rather than dual base 20 and base 5, because they read it here. I doubt most of these terms would even be accepted on Wiktionary, where they only require 3 attestations over at least a year. — kwami (talk) 07:49, 17 April 2023 (UTC)

I made no edits except to restore the status quo ante after your blanking. Your tagging the items "cn" is a more appropriate move.

As to "penta[-]vigesimal", does the hyphen change the meaning? What if the word is automatically broken after the "penta" at the end of a line, thus hyphenated anyway? How would we know which is meant?

Best see: Judith Elaine Hankes; Gerald R. Fast (2002). Perspectives on Indigenous People of North America. p. 347. ...the students and their teacher had collected a great deal of material about other Arctic and Native American counting systems. In a letter that they received, written by Robert Petersen from the University of Greenland, they learned that the Eskimo counting system is technically called a pentavigesimal... [italics added] – All subsequent discussion of the Iñupiaq Kaktovik numerals as "pentavigesimal" seems to have originated there, e.g. Iñupiatun Uqaluit Taniktun Sivuninit/Iñupiaq to English Dictionary. 2014. The Iñupiat have traditionally used a base-20-subbase-5 counting system, technically known as a 'pentavigesimal system.' This indicates that counting is based on groups of five "units," which are, in turn, combined into larger groups.... This book says so because that class said so, because a letter told them so. [N.b.: the late Peterson was a professor of Eskimology, not math.]

On any other topic, I keep finding the term defined as base-25, e.g. [1], [2], [3], [4] [5]. I don't have a dog in the race, kwami, I'm just saying what I saw. – .Raven  ^.talk 08:30, 17 April 2023 (UTC)

> "I'm in an argument with someone who claims that "penta-vigesimal" means base 25... because they read it here." — I've found that argument, and I see that as usual you misrepresent what the other actually said: "'Pentavigesimal' means base 25 according to most sources (including Wikipedia)." [emphasis added] That is not just "because they read it here." – .Raven  ^.talk 09:12, 17 April 2023 (UTC)

@Kwamikagami and Nosferattus: For your and others' ease of comparison, I put a table in my userspace comparing the current list of terms with five websites for base-conversion. Again, I have no dog in the race. You can click the site names at top to see their content for yourselves. I've marked with big asterisks those kwami gave on the mainspace list. – .Raven  ^.talk 16:05, 17 April 2023 (UTC)

Websites copying off each other are not a RS.

I notice that your last source, which contradicted your edits, is missing. — kwami (talk) 16:07, 17 April 2023 (UTC)

(1) calculator.name and calculatormind.com are copyright, respectively, 2021 and 2023. The earlier logically cannot have copied off the later. They might possibly both have copied off a third, still earlier, source – but I don't know that. Would you like me to remove calculatormind from the chart? You can, of course, simply ignore it if you so choose. I haven't made anything there compulsory (as if I could).

(2) Thank you for the reminder! That link wasn't on the page I'd been referring to. I've added number-reference.com in alphabetic order, before url-decode.com. It does have some unusual names. You'll notice I've boldfaced differences. – .Raven  ^.talk 20:43, 17 April 2023 (UTC)

@.Raven: Do you feel that having the long names has encyclopedic value? I know my opinion is that it does not; it just feels like an idle clicker game to me, but since this isn't my field, I fully accept that I might be missing important context.

If you don't feel they have particular encyclopedic value, I suggest we go with @Double sharp's suggestion, above. If there's a reliable source describing (not just using) the term, then it can stay. If there are no sources, or if the only sources simply use the word in passing but don't discuss or define it, then per WP:V, we can't verify and so won't publish it. Does this feel like a reasonable approach?

One final note I'd like to make. I don't calculator websites qualify as a WP:RS. However, if it's bluelinked, that seems reasonable to include.

Also, thanks to @Kwamikagami for fixing the grammar on my earlier edit.

Looking forward to hearing everyone's thoughts. EducatedRedneck (talk) 17:35, 17 April 2023 (UTC)

@EducatedRedneck: "Do you feel that having the long names has encyclopedic value?" I don't have any feeling, good or bad, about using long names at all; I'm happy saying either "base 3" or "ternary", "base 16" or "hexadecimal". (Disclosure: reading hexadecimal was a significant part of my pre-retirement life.) The issue is whether listing the terms is useful to some significant portion of our readers, as a reference to translate perhaps unfamiliar words back and forth from the base number, to read or write in contexts where that's appropriate. We're not the only kids in class; newbies arrive all the time, and may need to learn things we consider old hat or even useless for ourselves.

As to the calculator websites: they went to the effort of creating algorithms to convert between all those bases; I'm sure they also went to some effort to list the names they thought clearest and/or most useful to their user communities. (There's not much more to "define" about those names than the base number they refer to.) If you know of more reliable sources that list all the names, please let me know! – .Raven  ^.talk 20:54, 17 April 2023 (UTC)

@.Raven Re: Value to the readers: Agreed, and good point. I suppose I'm coming at it from the angle of, "It's better to not have information than to have information with a bad source." I suspect, if a term is used with any frequency, there will be a definition out there somewhere we can cite. And if there isn't a citation we can use, I don't think it's used frequently enough to worry about. (E.g., I get 0 book hits for "Octoquinquagesimal".) I also think that, as an encyclopedia, providing definitions for lists of words isn't exactly our job. That sounds to me like a job for a dictionary, perhaps Wiktionary.

Regarding the calculator sites, I think they qualify as WP:RSSELF, precisely because we have no clue who they are, where they got their information, or if they just populated their table of names by looking at a word and saying "yeah, that sounds right". I'd rather leave a reader to keep looking than give them potentially incorrect information.

That said, I do take your point that, especially for terms commonly used, (e.g. Tetrasexagesimal) it would have value to retain it. How about the following: if a term has 3 hits or fewer on Google Books and Google Scholar, it's removed. Otherwise, if it doesn't have a citation, retain the citation needed tag, with the argument that a source likely exists. Would this approach be more reasonable? EducatedRedneck (talk) 21:34, 17 April 2023 (UTC)

Tetrasexagesimal was one of the terms I left in, precisely because it could be verified. Definitely better to not provide false information. That's basic to WP. — kwami (talk) 01:48, 18 April 2023 (UTC)

Sure. If I might make one suggestion? Rather than simply delete entries for which few hits are found, <!-- comment them out -->, so other editors can later re-check for hits (e.g. times change; Google and Bing get different results) on the currently deprecated names. – .Raven  ^.talk 21:45, 17 April 2023 (UTC)

Are we going to continue to have a problem with adding terms which meet those conditions, because they are found in RS's? — kwami (talk) 00:47, 18 April 2023 (UTC)

If you recall, terms inserted were reverted precisely because RSs were not provided by their inserter, and also not found by their reverter after searching – which burden of proof belonged to the former, not the latter – for which the inserter accused the reverter of being "an edit-warrior who is more interested in scoring points than in improving WP". But, thank goodness, above you have demonstrated your understanding of what an RS is and isn't, so I'm sure you won't have such a problem providing them. – .Raven  ^.talk 05:44, 18 April 2023 (UTC)

@.Raven That's a good suggestion! I agree.

@Kwami As I see it, if you find a RS which describes or defines the base with the name (not merely mentions the name), and cite it with the addition, then its inclusion is desirable. I might ask you to help me understand why something is an RS (on account of me being unfamiliar with the subject area), but I think we all agree that if a term is added with a citation to an RS, it's a good edit.

If nobody objects, I intend to start commenting out the terms with few hits in a few days. I'd like to any other talk page watchers a change to weight in first, though. EducatedRedneck (talk) 22:20, 18 April 2023 (UTC)

Generally, self-published books and websites are not considered RS's. The exception is if it's something by a known expert in the field, such as a blog of field work.

Mentions in dictionaries are generally acceptable, assuming it's not self-published or online. (Unless it's an online version of a print dictionary, which is just a technicality.) — kwami (talk) 22:41, 18 April 2023 (UTC)

Long name clean-up

I started cleaning up the table of long form base names (i.e., "XXXXXimal"). I only reviewed bases 19-29 to start with. A summary of what I did, and the rationale, follows:

For each base long name, I did a search on Google Books for that term. If there were fewer than 3 hits using the term, I removed it on the presumption that no source exists. To determine the number of hits, I looked for sources that were, 1) in English, and 2) used the term in question. (Many hits returned didn't seem to use the term.) Per @.Raven's suggestion, I commented out, rather than deleting the removed entries.

• Enneadecimal - No hits. Removed.
• Unvigesimal - 4 hits, 3 of which were non-English. Removed.
• Duovigesimal - Multiple hits, but the only hits that I could see which contained the word were from before 1900. Removed.
• Trivigesimal - Multiple hits, but none which I could see contained the word. Removed.
• Tetravigesimal - 2 hits, no direct word use, Removed.
• Pentavigesimal - I left this one in. It only has 2 hits that mention the system, but that's enough to make me think it can be sourced. However, if others disagree, I wouldn't object to its removal.
• Hexavigesimal - Multiple hits; left in.
• Heptavigesimal - No hits which had the word. Removed.
• Octovigesimal - Many sources, but they seem to refer to Octovigesimal as an 8-sided prism, not a base. Removed.
• Enneavigesimal - No hits. Removed.

I intend to continue the clean-up later. I figured I should start small so if there are problems, we can address them without causing too much extra work. EducatedRedneck (talk) 14:42, 30 April 2023 (UTC)

Thank you for this diligent (and carefully explained) work! – .Raven  ^.talk 20:37, 30 April 2023 (UTC)

Hm, aren't you going to demand a RS that they did the search? This is OR! How do we know it actually happened? You're slipping, Raven, you're slipping. Soon anyone will be able to say anything on WP just because we can verify that it's supported by the preponderance of sources. And then where we be? — kwami (talk) 21:27, 30 April 2023 (UTC)

Searching for sources to cite is not what WP:OR means. That's replicable online -- and if need be ER could even link the search URLs they used -- so everyone else can verify the individual hits (or lack thereof)... if you feel that's necessary.

This is utterly unlike the WP:BECAUSEISAIDSO of "I contacted [organization name] who told me X." Who else can verify that source, now or later? How would anyone even know they'd reached the same person? – .Raven  ^.talk 02:24, 1 May 2023 (UTC)

That was my point. When I did a Gbooks search of these terms, you claimed that was not a valid approach. It's only valid if you do it.

As for the other, you can check whether two editions of a source differ by checking the two editions of that source. Not difficult. Why you're still claiming that verifying Unicode with their own documents is OR is beyond me.

However, since you've now decided that the work I did was valid after all (or at least it would be if someone else were to do it), I'll start restoring what you reverted. — kwami (talk) 06:33, 1 May 2023 (UTC)

Did the terms you added have the number of hits on actual discussions ER set as their standard? I had searched for them, as you may recall, without finding any reliable sources in support, after you had posted the entries with no citations at all. Merely asserting the sources' existence, without making that verifiable by others, doesn't justify an addition. Searching for such sources and NOT finding them, on the other hand, amply justifies the entries' removal. You yourself told me on Talk:Alchemical symbol#Manganese:

No more discussion: supply RS's or not, it's up to you -- but without RS's, all of your claims will be reverted. — kwami (talk) 06:33, 26 April 2023 (UTC)

I expect you to abide by the same standard you set. What's your RS for "sexatrigesimal"? Cite it in the article. – .Raven  ^.talk 02:48, 2 May 2023 (UTC)

Richard Cook (2006) Classical Chinese combinatorics: derivation of the Book of Changes hexagram sequence. Sino-Tibetan Etymological Dictionary and Thesaurus Project, UC Berkeley. Also 'sexavigesimal'. — kwami (talk) 05:24, 2 May 2023 (UTC)

Oh dear, Richard Sperling Cook is your "reliable source"? Have you read his colleagues' comments on that book?
• Shaughnessy, Edward Louis (2022). "11. The Hexagram Sequence" (PDF). The Origin and Early Development of the Zhou Changes. Brill. p. 430. ISBN 978-90-04-51394-5. Richard Sperling Cook, Classical Chinese Combinatorics: Derivation of the Book of Changes (Berkeley, Cal.: Sino-Tibetan Etymological Dictionary and Thesaurus Project, 2006) is a much more ambitious attempt to demonstrate a mathematical logic behind the traditional sequence of the hexagrams. Cook's analysis is based on treating the twenty-eight invertible hexagram pairs as single entities. Unfortunately, despite my best efforts to follow his analysis, which is clearly based on an impressive command of both traditional Chinese Yijing exegesis and also the history of Western theories of combinatorics, I am unable to follow the logic.
• Drasny, József (2019). "The solution of the King Wen sequence? Richard S Cook's Classical Chinese Combinatorics – a review article". Yijing Dao. ... I have to point out that, in the presentation of the theory, the author nowhere follows the usual method of logical reasoning: from premises to the conclusion. He does not use conditionals, arguments, or such words as supposition, assumption, hypothesis, guess, etc. It is not an exaggeration to say that the book only contains statements. These statements are, in many cases, without precedents and/or consequences, and so the reader does not know where they come from or what conclusion can be drawn from them. As a result, it is very difficult to follow the author's train of thought. It is not easy to accept the attitude that he believes in the validity of all his statements and takes them for granted without any reason. ...
At the end of the book, the author says:
This sequence derivation is not a formal mathematical proof of the kind to which modern mathematicians are accustomed. (p 505)
I can do nothing but agree with him. ...
Without independent evidence, readers do not get any new information. The process that Cook recounts is only one of the countless possibilities for arranging the hexagrams in this known order, and thus, his story remains only a fiction.
Unfortunately, the author also went astray in the field of mathematics. ... the mathematical operations, in many cases, seem to be strange and directly adapted to the actual task. ...
Moreover, there is no connection between this procedure and the ancient Chinese culture. ... The personal and objective conditions wherein these mathematical ideas might have been born are missing. ...
In sum, Cook's theory has remained unproved for me.
But Cook is your one and only citation? – .Raven  ^.talk 06:44, 2 May 2023 (UTC)

@EducatedRedneck: I found 3 hits that used hexavigesimal. One of those also used quadravigesimal for base-24, but I couldn't find any other hits for that word. 2 more hits were in an index as "see 'sexavigesimal'," which is what they actually used, so we've got 3 hits that use "hexavigesimal" and 2 that use "sexavigesimal". That's not a significant difference, so IMO we should list both.

For "pentavigesimal", I couldn't find a single source at Gbooks that used it for base-25. The only confirmed hits used it for base-20 with a subbase of 5. Can you link to your 2 hits?

For base-19, there are multiple hits for "undevicesimal". — kwami (talk) 21:44, 30 April 2023 (UTC)

Thank you for the checks; I'm far from an expert, so I appreciate having some quality control! I think I was not as clear as I could've been; I didn't examine the sources myself, just did a "low-hanging fruit" pass to eliminate any terms with zero English mentions. If you (or anyone else) does a more thorough search and finds that the hits don't constitute a RS, that sounds to me like excellent grounds for removal.

For Pentavigesimal, the two hits which seemed to be English language are this [6] and this [7]. It sounds like neither of those are RS, so if you think they should also go, I'd concur.

For Hexavigesimal, I think we're seeing the same hits. Four of the first five hits seem to use hexavigesimal to mean base-26. For the other terms (sexavigesimal, pentavigesimal) they seem to fall below the "3 hits" threshold discussed above, but if you think it's likely a reliable source exists, I've no objection to their inclusion.

(I realize that I'm the one who left pentavigesimal in; I'm happy to follow the lead of more experienced editors.)

EducatedRedneck (talk) 22:00, 30 April 2023 (UTC)

@EducatedRedneck: Those are RS's for pentavigesimal, but they're not for base-25. They're base-20 with a subbase of 5, so I'll comment that one out.

For base 35 and 36 that you left in, I'm finding no hits for 35, and for 36 I'm only getting sexatrigesimal.

To continue the list, apart from the decades themselves, there are no hits for any of the bases in the 40s though 90s apart from tetrasexagesimal, for which there are multiple hits. For bases over 100, there are no hits apart from a single one for 360. Thus apart from base-64 I am commenting them out. There are, however, hits for ducentesimal, tricentesimal and quadricentesimal. Could you verify and add those in? (I'd do it myself, but Raven would just start an edit-war claiming it's OR, so it's not worth it.)

— kwami (talk) 22:19, 30 April 2023 (UTC)

> "For base-19, there are multiple hits for 'undevicesimal'." — Alas, most appear to be on various pages of xen.wiki, not a WP:RS. What RSs have you found for it? – .Raven  ^.talk 07:29, 2 May 2023 (UTC)

What you describe as "base-20 with a subbase of 5" appears to be called "quinary/vigesimal" or "quinary-vigesimal" or even "quinary vigesimal" (with a space instead of punctuation) in many books and articles, e.g:

• Nykl, Alois Richard (September 1926). "The Quinary-Vigesimal System of Counting in Europe, Asia, and America". Language. 2 (3): 165–173. doi:10.2307/408742. JSTOR 408742. OCLC 50709582 – via Google Books. p. 165: A student of the American Indian languages is naturally led to investigate the wide-spread use of the quinary-vigesimal system of counting which he meets in the whole territory from Alaska along the Pacific Coast to the Orinoco and the Amazon.
• Eells, Walter Crosby (October 14, 2004). "Number Systems of the North American Indians". In Anderson, Marlow; Katz, Victor; Wilson, Robin (eds.). Sherlock Holmes in Babylon: And Other Tales of Mathematical History. Mathematical Association of America. p. 89. ISBN 978-0-88385-546-1 – via Google Books. Quinary-vigesimal. This is most frequent. The Greenland Eskimo says 'other hand two' for 7, 'first foot two' for 12, 'other foot two' for 17, and similar combinations to 20, 'man ended.' The Unalit is also quinary to twenty, which is 'man completed.' ...

I've added those two as sources for Quinary-Vigesimal (5+20). – .Raven  ^.talk 05:20, 8 May 2023 (UTC)

@Kwamikagami: if you look at Quinary#Usage, you see the statement, "Gumatj has been reported to be a true '5–25' language, in which 25 is the higher group of 5." (You'll note on following up that the Gumatj had, like other indigenous Australians, been subjected to the false assertion they were too 'primitive' to count past three.) This would be called "quinary-pentavigesimal", as the last line on the page indicates, in parallel to the much-used "quinary-vigesimal", befitting how numerous other websites use the term "pentavigesimal" (base-25), and by the parallel with "pentadecimal" (base-15), pentatrigesimal (base-35), pentaquadragesimal (base-45), all of those referring to a number ending in 5, not ending in 0 with a subbase of 5. You don't accept all those websites as RSs, but what websites, books, or articles anywhere say "pentadecimal" is base-10 with a subbase of 5, or "pentatrigesimal" is base-30 with a subbase of 5, etc.?

You're ultimately relying on Robert Petersen's inexpert advice to the Kaktovik students, which they trustingly repeated, as Hankes & Fast 2002 reported, and the Iñupiaq to English Dictionary 2014 took for gospel. (You do realize that means these are not two "independent" sources, right?)

So now you've put "pentavigesimal" in the 5+20 spot, it has two terms... leaving none for the Gumatj's 5+25. Is that an equitable division? – .Raven  ^.talk 10:31, 8 May 2023 (UTC)

I'm editing based on the sources that I have. Do you have RS's for 5+25? If so, add them to the article and stop playing stupid. — kwami (talk) 21:25, 8 May 2023 (UTC)

You're editing based on sources I cited above with the observation that they ultimately derived from a single source, an Eskimologist but not a mathematician. You have, by WP's rules as I understand them, ONE source (an unpublished letter from Petersen), who on this topic may not be reliable, particularly given the disagreement of all sources NOT derived from him.

Also, we were taking wikilinked terms as having been documented on their articles. You wikilinked 'pentavigesimal' at 5+20, although that wikilink redirects back to this same page (giving the false impression it had an article with documentation), and although that redirect's history indicated it went here as meaning base 25; meanwhile you left the same term on the '25' row commented out, not wikilinked. That's what New Englanders call "sharp dealing".

I'm attaching a 'cn' to that 5+20 'pentvigesimal' and commenting it out. – .Raven  ^.talk 05:47, 9 May 2023 (UTC)

Also, for "undevicesimal", if you had bothered to actually check you would have found Haluska (2003) Mathematical Theory of Tone Systems, Chisholm (1985) in Philosophie des Geistes / Philosophie der Psychologie, and Church & Langford (1981) in The Journal of Symbolic Logic, vol. 46. "Tredecimal", "quattuordecimal", "quindecimal" and "septendecimal" also have multiple hits. For some reason I'm not finding "octodecimal"; "duodevicesimal" seems to be more common, though still below our threshold.

I'm placing the new ad hoc terms in italics. They're used by a single author, below the limit we'd agreed on, and have odd forms such as "unodecimal" that contradict standard usage. — kwami (talk) 02:27, 9 May 2023 (UTC)

Actually, "unodecimal" also shows up in Ulrich, Werner (November 1957). "Non-binary error correction codes". Bell System Technical Journal. 36 (6): 1364–1365.

Also: Rawat, Saurabh; Sah, Anushree (May 2013). "Subtraction in Traditional and Strange Number System by r's and r-1's Compliments". International Journal of Computer Applications. 70 (23): 13–17. doi:10.5120/12206-7640. ... unodecimal, duodecimal, tridecimal, quadrodecimal, pentadecimal, heptadecimal, octodecimal, nona decimal, vigesimal and further are discussed... – .Raven  ^.talk 04:56, 9 May 2023 (UTC)

Hey, if you have adequate references, great. The problem with this article has been either making stuff up or using non-representative sources as if they were the norm. As long as the claims on WP reflect sources per RS and WEIGHT, then we're good. — kwami (talk) 07:47, 9 May 2023 (UTC)

Timekeeping etc.

In the table, there are many examples like hours being base 12 or 24, and months being base 12. Now, unless the base is applied to a number of consecutive positions, as in degrees-minutes-seconds or hours-minutes-seconds, does it really qualify? Or, even, should it be truly positional and hence apply to an arbitrary number of postions before it qualifies? Or ... should we at least make a clearer distinction between these "degrees of positionality"? (With hours and months, you could say it is really modulo 12 or 24, rather than base 12 or 24.) Nø (talk) 21:25, 14 May 2023 (UTC)

I agree. Unit-dozen-gross might qualify. But 12 hours in a half day, 12 months in a year, 12 inches in a foot, and 12 pennies in a shilling aren't really examples of standard positional systems in base 12. They smell of original research. Also the Chinese zodiac seems dubious as an example, as 12-year cycles are apparently bundled into 60-year cycles. Mgnbar (talk) 21:40, 14 May 2023 (UTC)

Use of "Also Known As"

Recent edits by User:Hazegrae have added "also known as" into some entries on the list of systems. (E.g., " Undecimal (also known as unodecimal, undenary)") I've removed it to keep the table consistent, as none of the other multi-name entries have that construction. However, I don't have an opinion on whether the list format ("Undecimal, unodecimal, undenary") or prose format ("Undecimal (also known as...)") is better. Either way, whichever there's consensus for, we should make it standard throughout the table. Thoughts? EducatedRedneck (talk) 11:47, 20 June 2023 (UTC)

My issue is standardizing the appearance if "also known as" labels are used in the table. Another editor had added unodecimal to undecimal without the convention; duodecimal didn't have it either, but decimal did (for denary). Happy to see all such alternatives captured on the pages applicable to each term. Hazegrae (talk) 12:15, 20 June 2023 (UTC)

> "whether the list format ("Undecimal, unodecimal, undenary") or prose format ("Undecimal (also known as...)") is better"

When IN a list or table where alternative names are listed, to have "also known as" is redundant, since there that is shown by the existence in one place of multiple names.

When NOT in such a list or table, but in body text, then "[W], also known as [X], [Y], or [Z]" would be appropriate... on the first mention. – .Raven  .talk 05:58, 21 June 2023 (UTC)

Problems with page previews for multiple articles linked from this page

Many of the articles linked in the main table on this page have an extremely incorrect image in the page preview. By "extremely incorrect", I mean articles about numerals and the page preview image is an open surgical wound, which is a bit disturbing to say the least. Anyone know how to fix this? it looks like purging a page makes fixes its preview, but there are a LOT of pages showing this image, and I can't purge every one, I have to go to sleep sometime... Marcus erronius (talk) 10:25, 7 September 2023 (UTC)

Sorry, I don't know how to fix it. But this page has never had such an image (in the past several years, at least). So I doubt that the problem actually has to do with this page. Contact some kind of Wikipedia tech support, or the editor who made the tool?

If you want me to help you test, then you could tell me a linking article where you still have this problem, and exactly what I could do, to try to reproduce it. Mgnbar (talk) 11:26, 7 September 2023 (UTC)

Looks like it's been fixed. It affected about 1 in 5 of the links on the right-hand side of the first main table on this page (which all now show no image in the hover preview), and the ones I checked had never had the image added to them. This made me think it wasn't vandalism, but a bug. I'm going to assume it was a transient error that showed up in the cache, since clearing the cache fixed it. Seems odd that the image was of gore, which made me immediately assume vandalism, but who knows. Marcus erronius (talk) 22:43, 8 September 2023 (UTC)

General Cleanup

There were a few old issues with uncited material from April of this year, so I went ahead and did a clean up. This was two parts:

• In the list of base names, I removed every entry which did not have a (non-commented) name or usage. There were around a dozen rows that just said "Base 29" with no other information. Given that other bases with neither name nor usage were already omitted, I did this to keep it consistent. I do note that all these entries had names that had been commented out for lack of citation back in April, so if someone thinks they can find a citation now for one or more of them, feel free to add them back in.
• There was a section on names for negative bases with a citation needed also back in April. That one has been visible in main space for six months with no citations, so I went ahead and removed it. Again, if someone thinks it CAN be verified, I've no objection to putting it back in. EducatedRedneck (talk) 00:08, 1 October 2023 (UTC)

I am surprised to see no mention of negative real integer bases (never mind their names), while -3/2 and -√2 are listed! —Tamfang (talk) 18:10, 1 July 2024 (UTC)

Baudot code as a usage example for base32

I recently cited Baudot code as a usage example for base32. My related edit was reverted. (For a clear explanation of the stateful part, see here.)
Stanford and Britannica make it clear Baudot code worked on the principle of encoding 32 combinations/characters, though they don't use the exact term of "base32". Good enough? —ReadOnlyAccount (talk) 11:59, 26 October 2023 (UTC)

PS: While it largely preceded current terminology, in terms of historical impact, Baudot code was far more influential than many other usage examples provided, though I suppose you'll say that's neither here nor there. — Preceding unsigned comment added by ReadOnlyAccount (talk • contribs)

Those sources look good enough to me. While they don't say it's base-32 verbatim, it does specify the number of combinations. Given the Britannica source, it may be worth specifying the original Baudot code, as the Britannica source talks about Base128 applications for modern Baudot.

It does seem that Baudot is stateful, but we'd need a more reliable source for that one, I think. Readthedocs.io does not strike me as a particularly reliable source. Also, please make sure you put your signature at the end of your message; I added a template to your post script, but if I hadn't, your post script would've had nothing identifying who wrote it.

Thank you for the prompt movement to the talk page, and your sources! I appreciate you helping to improve the article! EducatedRedneck (talk) 14:39, 26 October 2023 (UTC)

WP:FORUM lecture on Baudot, etc.

They're not actually talking about base128 applications for "modern Baudot", and I don't think such a thing exists, but I do think what you've hit upon with that is arguably a mistake in Britannica, or at the very least VERY dated and consequentially highly misleading phrasing. Remember, the Encyclopædia Britannica predates Baudot code by over a century, and the EB was already in its 7th edition before Émile Baudot was in his diapers. What I'm saying is, they haven't really gotten with the times in that paragraph, which by the look of things may well date back to some time in the sixties or seventies. Quoth Britannica: Modern versions of the Baudot Code usually use groups of seven or eight “on” and “off” signals. Groups of seven permit transmission of 128 characters; with groups of eight, one member may be used for error correction or other function. See also teleprinter. By «“on” and “off” signals» they mean bits. By "groups of seven or eight [bits]", they mean 7-bit bytes or 8-bit bytes. Yes, bytes weren't always 8-bit. That's how old this is. "Groups of seven" again means seven-bit code units (or 7-bit bytes), and indeed the original US-ASCII code was only seven bits, not eight, and guess how many original (NOT extended) ASCII characters there are? 128, which is all the combinations seven bits can give you. (Technically ASCII was only 95 printable characters, including the dubiously "printable" blank space character, plus 32 C0 control codes, plus delete, sometimes also deemed a control code. Original ASCII comprising 128 characters is a lie to children.) When ASCII was invented (mostly by Bob Bemer), just before the "early Internet" (read: ARPANET) got invented, they were hesitant to use all eight bits for their code, but they wanted more than six bits, so they compromised on seven, and indeed just like EB says, they sometimes used the eighth bit for parity or other uses, especially on MTAs, that's email servers to you and me, and that's where 7-bit bytes lasted the longest. In {{CURRENTYEAR}} it's still not clear if All The MTAs finally fully support 8-bit bytes for email. EB's reference to teleprinters once again is a dead give-away as to how old this prose is. But what has that to do with Baudot code, you cry! Well. They didn't strictly just say Baudot code, did they? They said "Modern versions of the Baudot Code", and yes, arguably, you could, in a sort of like this kind of way, call subsequent character encodings "Modern versions of the Baudot Code". They're not actually talking about literally new versions of actual Baudot code. They're talking about subsequent 7-bit and 8-bit codes, like ASCII – and EBCDIC, oh joy! And more codes besides; maybe KOI-7. There used to be quite a few variants. The EB's analogy is kind of reasonable, because if you go to Wikipedia's Baudot code article, you'll see how back in the day, some versions of Baudot code were standardised by the International Telecommunication Union (originally the International Telegraph Union) as versions of the International Telegraph Alphabet (ITA). But guess what also subsequently got standardised as a version of the ITA? That's right: ASCII. So there. Wiiiith regards to Baudot code's statefulness: I meant to point you to section 1.2 on page 3 (or PDF p.7) of this manual, only it turns out, that's essentially the same as the other source, only in a different format. But if that wasn't good enough for you, will this be (pp.3/4/6/7)? If not, just let me explain: Look at the Stanford source you accepted: In its table, to the right, it has a Figure column and Letter column. So those are two columns, showing different characters for (almost) all the codes, with very few exceptions. (Why H is an exception I'll never know.) But in these columns, among the exceptions, you'll find Letter Shift and Figure Shift. They do the same job the Shift Out and Shift In characters do in ASCII's C0 codes, which I've already whispered in your ear about, above. They signal to the party on the other end (maybe a man, maybe a machine) that it's time to switch to the respective column. Don't ask me what column they started out in by default when beginning a transmission. I would guess letter, but that'll just make you scream for MOAR SAUCE, so I won't. So anyway, that's all statefulness really means, and is. The statefulness allowed Baudot code to send and receive more than just 32 different characters while still only using 5-bit code units. So here, it's either in the letter(s) state or the figure(s) state. You can switch between more than two columns (or sets of characters, or states) if you have each machine keep track of where it is, and send possibly multiple shift-in or shift-out characters/codes, depending on what state it wants to switch to. That requires some kind of stack or a tiny amount of memory, just enough bits to store a big enough state-keeping variable in. You know how I snuck in KOI-7 earlier? Guess what KOI-7 is too: Stateful. It uses the same Shift-in and Shift-out C0 control codes as ASCII. And arguably the 800-pound gorilla of stateful encodings is ISO 2022, and his friends – hopefully all finally increasingly obsolete, but you never know. If none of that's good enough, then it would be a "fun" exercise to got though the Baudot code page, which repeatedly mentions statefulness, and see if you can find all the references to support that (honestly relatively obvious) conclusion. But I'm not going to be the one to do that, as I've done more than my fair share of make-work today. Finally, if you are so minded as to reinstate my reverted edit, you should do it, because I won't. That's because reportedly it's veeeery easy to be taken for an edit warrior at Wikipedia, and if I do it, that might look bad. It won't look bad if you do it. PS: It is a bit of a lark to look at Britannica's alleged history of their Baudot Code page. I don't believe for a second that they wrote that article anywhere near the date they recoded with "New article added". I do believe that's when they put that article online. But clearly their actual prose was written close to four decades before they finally put it online. Do you think we should tell them about this discussion? They do have a Contact Us page with actual street and email addresses and phone numbers, which is as old-school as it is sincerely seriously respectable – in an age when being given the run-around to the nth degree is the frequently infuriating default. Just seeing that made them grow on me. —ReadOnlyAccount (talk) 18:15, 26 October 2023 (UTC) There are a few things that you may wish to consider. The first is WP:WALLOFTEXT. I did skim your message, and will respond to it, but in the future you're more likely to influence others on this site if you stay short and to the point. The second is WP:OR and WP:SYNTH; what you've just said about modern Baudot code is one of the two, because here at Wikipedia, we don't report what we've found to be true, we report on what reliable sources say. Of which Encyclopedia Britannica very much is one; your argument that it was founded before Baudot was born makes about as much sense as saying we can't trust US Government webpages because it was founded before the internet. Which is why the third thing you may wish to consider is reading WP:RS. The two sources you gave for statefulness are (1) from the same source I doubted, above, and (2) a pdf with no provenance which may have been written as a middle school research project for all we can tell. I've also changed my mind on the Stanford source because, upon closer inspection, it's course materials, not anything published and peer reviewed. Regarding Baudot code, I took a look, and I see no references saying it's stateful. The word only seems to appear in infoboxes. If you felt like going through and adding {{cn}} tags, or better yet sources, that would be lovely. Finally, you should feel free to try the edit a second time if you've addressed the concern. In this case, I've gone ahead and done it for you, per your request, while omitting the unsourced claim of statefulness. I do very much appreciate that you're trying to avoid edit warring; that's an admirable trait, and will help you have a long editing career here, if you wish it! EducatedRedneck (talk) 18:46, 26 October 2023 (UTC)

Noting here below the collapse that the Britanica reference seems solid, and so was added to the article. No compelling source for statefulness has been presented, and so has not yet been added to the article. Further discussion on sources can resume here. EducatedRedneck (talk) 22:35, 27 October 2023 (UTC)

The way I understand Baudot, it is binary. Unless a string of Baudot letters is interpreted as a number base 32, or e.g. as encoding an element in a list of way more than 32 symbols, it is not base 32 in any meaningful way. Nø (talk) 11:49, 28 October 2023 (UTC)

That argument makes sense to me, but I've been unable to find a reliable source that says one way or the other. I've found some course learning materials which claim binary, but those aren't peer-reviewed. For now, I've taken mention of Baudot Code out of the article until we come to a consensus. Perhaps someone with more subject-area familiarity than me can find a good source.EducatedRedneck (talk) 12:48, 28 October 2023 (UTC)

Baudot code is stateful, there is a FIGs and LTRs codes that change the interpretation of all following codes. Spitzak (talk) 22:43, 28 October 2023 (UTC)

I don't think anyone here has disagreed. What we need is a reliable source saying so, however. Perhaps because this isn't my wheelhouse, I wasn't able to find one. I hope you'll be able to find one where I couldn't, so when we find a WP:RS saying which base Baudot code is, we can also add the Stateful descriptor to it. (And to the Baudot article itself, too!) EducatedRedneck (talk) 23:05, 28 October 2023 (UTC)

Removal of Base91-Base94

I noticed that @ReadOnlyAccount improved the phrasing on these bases (thank you!), but then also realized that they were all sourced to blogs or github. Beyond the lack of sourcing, their description boils down to, "It encodes all ASCII characters except..." which strikes me as trivia. Especially since we could keep expanding that list of exceptions to get descriptions all the day down to single-digit bases. If anyone disagrees, feel free to revert and discuss here. EducatedRedneck (talk) 11:42, 17 January 2024 (UTC)

Not only that, some of the descriptions seem to be wrong. Ones that exclude two characters are not 2 smaller than ones that don't, etc. I agree deleting all this is the correct thing to do. Spitzak (talk) 23:32, 17 January 2024 (UTC)

Missing samples

For the numerals above Egyptian there is no sample of the numerals as well as the Rumi numerals. Legendarycool (talk) 03:00, 2 June 2024 (UTC)

This has some number systems not mentioned here

https://www.afrikanistik-aegyptologie-online.de/archiv/2012/3553 Legendarycool (talk) 11:19, 9 July 2024 (UTC)

https://books.google.com.au/books?hl=en&lr=&id=kXZhBAAAQBAJ&oi=fnd&pg=PP2&dq=numerical+notation&ots=XtnGgEyFEk&sig=1LsnxHayK4sUH7WRw65f32h-Wm8&redir_esc=y#v=onepage&q&f=true Another good source Legendarycool (talk) 11:25, 18 July 2024 (UTC)

Base Column in List of Numeral Systems

I recently reverted an edit which ascribed Base "5&10" to Roman Numerals and realized that the article doesn't define base well. I'm a layperson, and I have no idea what "5&10" means in relation to base. I'm also not sure what we mean by base in the article, as the concept of Radix doesn't seem to apply when using an additive system.

Some of the entries in the table, particularly those with ten characters and that are decimal, are obvious enough I think we can leave them in under WP:BLUE. For the rest, I think we should have a citation that says the system is BaseX, and for the less obvious types (such as those with an ampersand) perhaps a note explaining what it means. EducatedRedneck (talk) 15:21, 14 July 2024 (UTC)

For power and base, I like Chrisomalis' (2010, p. 4) definitions: "All numerical notation systems (and most lexical numeral systems) are structured by means of powers of one or more bases. A power is a number X multiplied by itself some number of times (its power); 10^1 = 10, 10^2 = 100, 10^3 = 1000, etc. By mathematical definition, a number raised to the power 0 equals 1. A base is a natural number B in which powers of B are specially designated." It's worth noting that the Roman numerals share the same organization as the Mesopotamian proto-cuneiform numbers do; the difference is the base amounts (5 and 10 for Roman numerals; 10 and 6 for proto-cuneiform). Hazegrae (talk) 15:44, 14 July 2024 (UTC)

I do understand how bases and powers work, but within the context of numeral system, base usually means Radix. In a positional numbering system, the digit in position 0 is multiplied by BASE^0, the digit in position 1 is multiplied by BASE^1, and so on. This is not the case for roman numerals, so the concept of base (as radix) does not seem to apply. If there's another definition for base, it needs to be clarified and sourced. EducatedRedneck (talk) 15:49, 14 July 2024 (UTC)

Radix, as defined in the article, relates specifically to positional systems. Under this narrow definition, no numeral system has a base if it isn't positional. Number systems that are additive, like Roman numerals and proto-cuneiform, are widely understood as having a base organization, even if that notion of base is not identical to the radix notion. However you decide this, my point was that if Roman numerals are excluded, so too should other numeral systems with the same organization (e.g., proto-cuneiform and proto-Elamite). Hazegrae (talk) 16:04, 14 July 2024 (UTC)

I see; I think I missed your point above initially; my bad! I agree that if remove Roman numerals, the other nonpositional ones should likewise have the base entry removed for consistency. I get the feeling you know better than I do about whether or not they should have a base. (I have intermediate math proficiency, in the same way an engineer is proficient with physics but may have trouble following theoretical discussions.)

Number systems that are additive... are widely understood as having a base organization This may very well be true, in which case it should be trivial to find a source that says so. What I'm trying to get at is that, for a non-expert reader, the definition of base needs clarification, and the non-obvious entries supported with citations. Does that make sense? EducatedRedneck (talk) 16:12, 14 July 2024 (UTC)

Admittedly, the literature isn't really all that helpful in this regard because the more one tries to define concepts like "base" and "power," the more technical and the less intuitive they become (see Zhang & Norman's 1995 article for an example). The definition Chrisomalis (2010, p. 4) uses for numerical notation systems is fairly straightforward (and he applies the term "base" throughout his analysis of the five types as defined by his notions of inter- and intra-exponential organization, only two of which are positional). Comrie (2013) offers a fairly benign definition for numbers in natural language: "By the 'base' of a numeral system we mean the value n such that numeral expressions are constructed according to the pattern ... xn + y, i.e. some numeral x multiplied by the base plus some other numeral." Since this interface doesn't let me enter Comrie's italics, the original is found here: https://wals.info/chapter/131. Hammarstrom (2009, p, 5) defines base for numbers in natural language as follows (italics indicated with *): "Perhaps the most salient single characteristic of a numeral system its base, or more correctly speaking, its set of bases. The *set of bases* of a natural language numeral system may be defined as follows. ¶the number *n* is a base iff ¶1. the next higher base (or the end of the normed expressions) is a multiple of *n*; and ¶2. a proper majority of the expressions for numbers between *n* and the next higher base are formed by (a single) addition or subtraction of *n* or a multiple of *n* with expressions for numbers smaller than *n*." The sources cited here use the term 'base" for Roman numerals (an additive system; Zhang & Norman, 1995, p. 276 give a base of 10 and a sub-base of 5) and numbers in natural language (i.e., where written symbols and the idea of a radix don't apply). Hazegrae (talk) 16:25, 14 July 2024 (UTC)

Well this issue is partly based in philosophy but I think, due to the usage of bases in other additive systems indicates that the bases should be used for Roman numerals. Legendarycool (talk) 00:38, 15 July 2024 (UTC)

The linked source doesn't appear to discuss Roman Numerals in particular, or non-positional systems generally. If you have a source that specifies the Roman base, by all means, go ahead. I do feel that we should define, either in the body or a note, what we mean by "base", as common usage is equivalent to radix. If there's a better or more technical definition, we need to clarify it. So, no objection from me to re-adding the base with proper citations. If your source (Zhang & Norman 1995?) describes how/why Roman Numerals are Base 10 and 5, we could use their definition in the explanatory note as well. EducatedRedneck (talk) 00:42, 15 July 2024 (UTC)

"All numerical notation systems (and most lexical numeral systems are structured by means of one or more bases. A base is a natural number B whose powers (B multiplied by itself some number of times) are specially designated within a numerical system" (Chrisomalis 2004:38). That is, base is a property of most numerical notation systems (not just those with positionality where the term radix comes into play), as well as spoken numbers in natural language. The appendix to Chrisomalis' 2004 article (pp. 51-52) lists 100 numerical notations systems; this reference is an appropriate and comprehensive reference for base and sub-base assignments. The list includes additive systems like Roman numerals (base 10, sub-base 5), proto-cuneiform (base 60, sub-base 10), and proto-Elamite (base 10). On a related note, Zhang and Norman don't define base in their article, and their typology includes various dimensions and other qualities that make it less straightforward. I recommend Chrisomalis as the source of the definition for "base"; he's a linguist (so, he's well versed on the use of the term as applied to spoken numbers in linguistic circles) who specializes in numerical notation systems (so, he's a good source on the term as applied to numerical notation systems as found worldwide and throughout time). Hazegrae (talk) 10:27, 15 July 2024 (UTC)

I added the base/subbase for Roman numerals, a definition for base, and cited Chrisomalis 2004 for both. I also added a definition and example for subbase; thus far I haven't found a clear-cut definition in the literature but will add one once I find one. Hazegrae (talk) 11:30, 15 July 2024 (UTC)

What is a number system

What would be a reasonable line between adding every Hindu-Arabic system (maybe we should) and putting every base ten positional notation system in one box? Legendarycool (talk) 10:57, 12 August 2024 (UTC)

I mean this as, what should be a separate number system. Legendarycool (talk) 10:57, 12 August 2024 (UTC)

As much as I'd like to trim down the article, I think the subject is a list of Numeral systems, not a list of Number systems. To me, the focus of a numeral system is on how it's written. That includes, but is not limited to the base. I feel that, as long as a system uses different notation, (even to represent the same concepts,) it is within the scope of this article to include it as a distinct entry. EducatedRedneck (talk) 11:05, 12 August 2024 (UTC)

To clarify (I hope) the discussion so far: How many of the numeral systems listed here are identical to Hindu-Arabic numerals (base-ten, positional) but with different symbols than 0, 1, 2, 3, 4, 5, 6, 7, 8, 9? If there are many of them, then placing them in their own table would make that table very clean, help us clean up other sections, and emphasize what is common vs. uncommon. Mgnbar (talk) 15:29, 12 August 2024 (UTC)

@Mgnbar Ah, I see; that makes much more sense to me! I agree, then, that this would be a useful addition. In particular, I like your distinction: if it's base 10 and positional, I think having its own "Decimal Numeral Systems" table, and the other put into a table perhaps called "Non-Decimal Numeral Systems". I'd also argue that the systems with multiple bases (e.g., Roman numerals) should go into the non-decimal category. Sorry for misunderstanding you, Legendarycool, and thank you for clarifying, Mgnbar! EducatedRedneck (talk) 19:25, 12 August 2024 (UTC)

So to clarify what I meant.

What should be considered separate numeral systems this could mean having every number system as a separate box (all the Indian and Chinese numbers) or putting all of one base in one very large box (all the Hindu-Arabic numerals would be in a single box).

I think maybe a good decision would be to put all numerals systems to ensure all of the cultures and languages are represented equally to be more WP:NPOV and having all of these Indian numerals together might go against WP:Notability as some of the Indian numeral systems have more user than others have had in their lifetime yet their put in one box despite different dates of origin E.g. Devanāgari developed in 1200 ce and 600 million uses of the script (multiple languages), Gujarati developed in 1592 and used by probably a few million, &c. These systems have dates of creation and would have sources just as other ones on the list.

I say every system should be separate though I’m still unsure how to best balance briefness and encyclopaedic precision in this article.

P.S. Sorry if anything is badly worded I haven’t gotten enough sleep recently.

P.PS. Thanks for giving your thoughts on this so quickly. Legendarycool (talk) 07:03, 13 August 2024 (UTC)

We should also probably look through the changes to see why it was originally put like that so we can get a better understanding of the reasoning of all of the changes. Legendarycool (talk) 11:50, 13 August 2024 (UTC)

I don't understand how your proposal is different from what we currently have. It seems that you want a complete list of all distinct numerals systems, with dates and sources. That is what we have (albeit imperfectly, as a work in progress).

In your most recent post, I don't understand which changes you are talking about. This article has been evolving slowly over time, as Wikipedia articles typically do. Mgnbar (talk) 12:38, 13 August 2024 (UTC)

There are two different arrangement principles in the article: 1) by culture and time period, and 2) by type of notation (positional or otherwise). Can you explain what your proposal would mean vis-à-vis that. Are you looking to get away with the culture/time period aspect and replace it with decimal and non-decimal and then lump all the different decimal script/culture versions into one box? —Carter (Tcr25) (talk) 14:05, 13 August 2024 (UTC)

Not to speak for Legendarycool, but I was envisioning something like this:

Extended content
By Culture/Time Period Decimal Systems Name Sample Approx. First Appearance Example Entry Ipsum Lorem Sit dolorem Non-Decimal Systems Name Base Sample Approx. First Appearance Example Entry XX Ipsum Lorem Sit dolorem By type of notation Unchanged

If it's a decimal system, it goes in that table. Otherwise, it goes in the other. We ALSO have the "by notation", which is more exhaustive; it mostly lists bases and some uses, but doesn't show the digits, so we leave it unchanged. My thinking is that, by organizing the "By Culture" part, we make it easier for the reader to look up a system they've encountered or read about. If anyone has a different thought, don't let my over-enthusiasm deter you from sharing it! EducatedRedneck (talk) 18:05, 13 August 2024 (UTC)

So basically removing the base column for all the decimal ones and then grouping the remaining ones in a separate table? I don't have a strong objection, but to me the interesting thing is being able to see how systems compare based upon time (which the current table allows for) and by geography (which isn't included in the table). That would allow for a reader to see where influences from one culture or numeral system to another may come into play. Breaking them apart by decimal or non-decimal would make that sort of investigation harder. —Carter (Tcr25) (talk) 18:46, 13 August 2024 (UTC)

That's a good point. What if we use row highlighting to denote the decimal family within the table? I'm still struggling with the formatting, but the below should give you an idea.

Extended content

Name Base Sample Approx. First Appearance Proto-cuneiform numerals 10&60 c. 3500–2000 BCE Indus numerals c. 3500–1900 BCE Proto-Elamite numerals 10&60 3100 BCE Sumerian numerals 10&60 3100 BCE Egyptian numerals 10 3000 BCE Babylonian numerals 10&60 2000 BCE Aegean numerals 10 𐄇 𐄈 𐄉 𐄊 𐄋 𐄌 𐄍 𐄎 𐄏  ( ) 𐄐 𐄑 𐄒 𐄓 𐄔 𐄕 𐄖 𐄗 𐄘  ( ) 𐄙 𐄚 𐄛 𐄜 𐄝 𐄞 𐄟 𐄠 𐄡  ( ) 𐄢 𐄣 𐄤 𐄥 𐄦 𐄧 𐄨 𐄩 𐄪  ( ) 𐄫 𐄬 𐄭 𐄮 𐄯 𐄰 𐄱 𐄲 𐄳  ( ) 1500 BCE Chinese numerals Japanese numerals Korean numerals (Sino-Korean) Vietnamese numerals (Sino-Vietnamese) 10 零一二三四五六七八九十百千萬億 (Default, Traditional Chinese) 〇一二三四五六七八九十百千万亿 (Default, Simplified Chinese) 零壹貳參肆伍陸柒捌玖拾佰仟萬億 (Financial, T. Chinese) 零壹贰叁肆伍陆柒捌玖拾佰仟萬億 (Financial, S. Chinese) 1300 BCE Roman numerals 5&10 I V X L C D M 1000 BCE Hebrew numerals 10 א ב ג ד ה ו ז ח ט י כ ל מ נ ס ע פ צ ק ר ש ת ך ם ן ף ץ 800 BCE

We'd want to workshop the color to highlight, and which rows to highlight. We'd also need to add some prose explaining what it indicates. Legendarycool, would this work for what you were thinking? Tcr25, thanks for bringing this up! EducatedRedneck (talk) 21:19, 13 August 2024 (UTC)

Sorry, but I don't love this proposal. Organizing by time is admirable, but so is organizing by region. No one table can capture the subtle inter-cultural movements of these ideas across time and space. Many of the non-decimal numeral systems seem not to have bases at all; saying that they do is almost certainly original research. (This has been a long-standing issue in this article.) I think that the casual reader will not understand why some numeral systems are highlighted and some are not; it will seem like favoritism.

I guess I could get behind a sortable table with five columns: name, date, continent, positional or not, base if positional. Not highlighted. The sample glyphs, that are currently in the tables, seem less important to me. Mgnbar (talk) 22:17, 13 August 2024 (UTC)

Thank you for your input! I agree that allowing grouping without sacrificing the various sorting criteria (age, base, etc.) is a hard problem. If my proposal doesn't do it, then it's better we reach that conclusion here than try to force it into article space!

I could see a use for continent for the numeral system, but ironically I feel that'd be more likely to be used to find and compare dissimilar systems. I'd like to see the sample glyphs stay in the table; I've used it before when I find unfamiliar text and am trying to localize it.

Finally, thanks to y'all for a good and productive discussion. I appreciate y'all sharing your thoughts and making sure the article stays on the right track! EducatedRedneck (talk) 22:44, 13 August 2024 (UTC)