Talk:Hindu–Arabic numeral system

Shang dynasty numerals

I do not believe that the cited sources support the assertion that:

According to various sources this number system has its origin in Chinese Shang numerals (1200 BC), which was also a decimal positional value system of base 10.

References

Here is what these cited sources say:

1. Campbell, p. 30: "an interesting hypothesis arises, namely that the numeration system commonly used in the modern world had its origins 34 centuries ago in Shang China!"
2. Lam, p. 101: "In 'The Conceptual origins of our numeral system and the symbolic form of algebra' and 'Linkages: Exploring the similarities between the Chinese rod numeral system and our numeral system', I advanced the following thesis—that China is the earliest civilization to possess the concept of our numeral system, also known as the Hindu-Arabic numeral system. In this paper, I summarize the main points that have been put forward and also examine fresh evidence to support a further claim—that our numeral system has its origins in the Chinese rod numeral system."
3. Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures, p. 198: I find no mention of Shang numerals. The only mention of Shang dynasty numerals or numeral system is on p. 1371, where Andrea Eberhard-Bréard writes: "Archaeologic finds from the Shang dynasty (fourteenth to eleventh century BCE) show the earliest number symbols inscribed on bones and tortoise shells. By then, different decimal and sexagesimal systems were in use. The use of rod-numerals is also attested on coins as early as from the Wang period (9-23 AD). These are related to instruments in use. For calculations, numbers were represented on a calculation surface by counting rods. The representation follows a decimal positional notation, where nine different signs for numbers ..."

None of these sources are asserting—as a fact—that the Shang dynasty numerals were the origin of the Hindu-Arabic numeral system. The most we can say, based on these sources, is that they might be.

Unless better sources are provided I'm going to delete this sentence. Paul August ☎ 17:26, 17 October 2023 (UTC)

The attribution (according to ...) means that we're not stating it as a fact. The third source, states among other things, "this fact together with other evidence supports the thesis that the Hindu—Arabic numeral system has its origins in the Chinese rod numeral system." M.Bitton (talk) 17:36, 17 October 2023 (UTC)

Yes, as you correctly point out, our article does not assert it as a fact. But it does assert that "various sources" do. However none of the cited sources assert this. 1) calls it "an interesting hypothesis", 2) says it provides "evidence to support" it, while the quote you give (by the same author as 2) simply mentions "evidence" which "supports the thesis". So none of these sources are asserting this as a fact, so our article can't say that anyone does assert this. Paul August ☎ 19:16, 17 October 2023 (UTC)

I have taken your concerns on board and changed it accordingly. Please let me know what you think. M.Bitton (talk) 21:37, 18 October 2023 (UTC)

The summary "According to some sources, this number system may have originated" does not accurately describe these sources. A more accurate one would be something along the lines of:

"While there is no concrete evidence linking the two systems, and there are fundamental structural and orthographic differences between them, a few Chinese scholars have speculated that the positional decimal numeral systems of ancient India might have been influenced by the Chinese rod numerals, which ultimately descend from the numerals used with the oracle bone script of the Shang Dynasty."

–jacobolus (t) 22:18, 18 October 2023 (UTC)

Alternately we could be more explicit and include direct (very strong) criticism of this theory. Here is what Chisomalis says:

Lam Lay-Yong (1986, 1987, 1988) hypothesizes that the rod-numerals were ancestral to the Hindu positional numerals. Her evidence for this hypothesis is that the rod-numerals are positional and decimal, and there was considerable cultural contact between China and India in the 6th century AD, around the time when positionality developed in India. Because the rod-numerals were used in computation and commerce, she asserts that it is inconceivable that the Indians would not have learned of this system from the Chinese, and, since it is so practical, they obviously would have borrowed it (Lam 1988:104). From this, she asserts that the rod-numerals are the ultimate ancestor of the Western numerals.

While Lam's hypothesis is plausible, I am deeply skeptical of its validity. Two immediate objections are that the Indian positional numeral-signs are those of the earlier Brahmi numerals, not of the rod-numerals, and that the rod-numerals have no zero-sign (whereas the Indian system does). To the first objection, Lam responds that "since six of the nine digits in rod numeral notation were strange to them, they would naturally have preferred their own numerals" (Lam 1986: 193). The notion that the rod-numerals were so foreign to the Indian mind as to require the total abandonment of its signs is unacceptable; who cannot comprehend the use of vertical and horizontal strokes? To the question of the zero, Lam replies that the abandonment of the alternating zong and heng positions required that the Indians develop a sign to fill the blank space (Lam 1986:194). I do not think this follows; a blank space would have served just as well as a zero-sign in either system, and if the abandonment of the alternating positions created such difficulty, why would the Indian mathematicians have done it? Even more damaging to Lam's argument are two structural differences between the rod-numerals and the Indian numerals that she ignores entirely: the rod-numerals have a quinary sub-base that the Indian numerals lack, and the rod-numerals are intraexponentially cumulative whereas the Indian positional numerals are ciphered. Moreover, no Indian texts of the period mention rod-numerals or any other Chinese numeration. Indeed, as I will discuss below, the Indian positional numerals were seen as remarkable in China in the early 8th century AD, suggesting that the Chinese traders who hypothetically transmitted the rod-numerals to India were entirely unaware of the result of their transmission. Lam's theory is so weak that it is equally plausible that the Greco-Roman counting board, which was also quinary-decimal, cumulative-positional, and used in the Middle East, was an ancestor of the Indian numerals - that is, it is not very plausible at all.

–jacobolus (t) 22:46, 18 October 2023 (UTC)

That's one criticism of Lam Lay-Yong's assertion that describes it as plausible. What about the other sources that support the theory/assertion/conjecture or whatever we want to call it? M.Bitton (talk) 22:49, 18 October 2023 (UTC)

In my opinion "fringe speculation unsupported by evidence" is a much fairer name than "conjecture". –jacobolus (t) 22:54, 18 October 2023 (UTC)

That's not how the RS describe it (listing another two). M.Bitton (talk) 22:59, 18 October 2023 (UTC)

Which is to say, after one author's rank speculation, later authors have repeated the same speculation, sometimes entirely uncritically, still without any evidence. –jacobolus (t) 23:02, 18 October 2023 (UTC)

Repeated means "used by others" which in this instance means other scholars. It's not our job to look for evidence or label the scholars' assertions and theories, all we can do is report what the RS say and leave it at that. M.Bitton (talk) 23:05, 18 October 2023 (UTC)

It's our job to serve readers by describing factually supported scholarly consensus, not trick them by exaggerating completely speculative and logically dubious claims, even if those claims happened to appear at some point in a peer reviewed paper. –jacobolus (t) 23:08, 18 October 2023 (UTC)

We already did that, but at the same time, we cannot hide what's out there (regardless of whether we agree with it or not). M.Bitton (talk) 23:10, 18 October 2023 (UTC)

Here's a review of the book Fleeting Footsteps coauthored by Lam, again criticizing the lack of evidence or serious analysis:

... In most recent times, this claim has been made most succinctly in the works of Wang Ling and Joseph Needham. In a 1958 paper delivered in Adelaide, Wang presented a detailed case for a Sino origin of the "Hindu-Arabic" numerals and pointed to the strong possibility of westward transmission to India. Wang's theory was further amplified in his collaborative work with Joseph Needham. Science and Civilization in China, vol. 3, devotes several pages (pp. 146-150) to this very issue and the phenomena of "stimulus diffusion". Needham's work clearly indicates the need for further research clarification as to the status of early Hindu mathematics and the possibility of cultural transmissions. It is exactly this research that must be undertaken to strengthen the claim for a Chinese genesis of our numeral system and, unfortunately, it is exactly this research that is lacking in Fleeting Footsteps. What was the status of ancient Indian mathematics during the Warring States period of (Chinese history? How were the numerals used in ancient India? Could the Chinese have obtained their mathematical knowledge from India? after all, Buddhism was an intellectual import from China's western neighbor. These are some of the issues and questions that must be addressed in positing a claim of a Chinese origin for the "Hindu-Arabic" numeral system and they remain missing footsteps in the path this book has taken.

Despite the inability to develop and strengthen its major premise, Fleeting Footsteps is a valuable resource for understanding early Chinese mathematics. ...

–jacobolus (t) 00:35, 19 October 2023 (UTC)

I pulled Needham's book off the shelf, and the analysis is basically: here's a list of mathematical developments that were seen in China a few centuries before they were seen anywhere else, and we have evidence of a decimal positional numeration system in China long before any extant Indian examples (Needham judges the Chinese system independent of Mesopotamian predecessors because there was no evidence of sexagesimal), therefore "could it be that the traveling monks exchanged mathematics for Indian metaphysics?" In other words, it's almost entirely speculative. –jacobolus (t) 00:46, 19 October 2023 (UTC)

References

The new language offered by M.Bitton is better than what was there before, but jacobolus's language is better still. Paul August ☎ 00:58, 19 October 2023 (UTC)

Unfortunately, jacobolus' language is WP:OR. I'm not exactly sure why they think that "conjecture" is not fair, but as luck would have it, that's exactly what "Frank Swetz" (whose 1994 review they cited above) used (in 2022) when describing the different theories.

Further, and perhaps more interesting, is the conjecture by historians of mathematics such as Wang Ling, Joseph Needham, and Lam Lay Yong and Ang Tian Se that our contemporary numeral system is derived from rod placements [Xu 2005]. They suggest that, as rod numerals were recorded and copied over centuries, scribes became complacent and hastened their writing process, gradually slipping into more cursive forms as illustrated below. What do you think? Perhaps our numeral system could more correctly be designated as the ‘Sino–Hindu–Arabic’ numeral system. Such a title might be more encompassing and historically revealing. M.Bitton (talk) 10:44, 19 October 2023 (UTC)

That what we are dealing with here is a "conjecture" is certainly true, but the question I take jacobolus to be raising, is just how "fringe" of a conjecture is it? (I further take his characterization of the conjecture as "fringe speculation unsupported by evidence" to be a bit of rhetorical hyperbole). I think something like what jacobolus has proposed above: "While there is no concrete evidence ..."—provided it can be adequately sourced—is a bit more nuanced and precise than what we have now. Paul August ☎ 12:34, 19 October 2023 (UTC)

I agree with M.Bitton. Hu741f4 (talk) 14:24, 19 October 2023 (UTC)

A conjecture that it put forward by various scholars and used by others is certainly not fringe. Describing as a such would solve the issue without delving into original research: something along the lines of Some historians of mathematics have conjectured that ... should do. M.Bitton (talk) 17:55, 19 October 2023 (UTC)

In my opinion the entire "origins" section of this article should be scrapped as largely a politically/ideologically motivated distraction from the primary focus of the page (based on edit wars between Indian vs. Arab nationalists), and the topic should be combined into the "history" section. The current scholarly consensus should be accurately described, ideally in substantially greater detail than we currently have done, prominently noting that our understanding is based on an extremely fragmentary record because few written documents survive from the times and places in question. After that, we can give room to this very weakly supported speculation about an origin in Chinese rod numerals, but only if we (a) directly state the basis for the claims [namely (1) both systems are positional and decimal, (2) various other mathematical ideas are attested in Chinese sources many centuries before they are attested in Indian sources, and (3) there was some cultural contact between India and China at the time, e.g. the spread of Buddhism.] and note that there is no direct evidence involved, and (b) mention the obvious criticisms [e.g. (1) the two systems are orthographically unrelated with the rod numeral system based, like Sumerian/Akkadian sexagesimal cuneiform numerals, on direct representation at each digit, while the Indian/Southeast Asian numerals are symbolic; (2) the Chinese system, like Roman numerals and Greek/Roman counting boards, is a bi-quinary representation, but the Indian numeral systems are not; (3) the Brahmi numerals are an obvious symbolic antecedent for the Indian numerals from which evolution is easy to imagine; (4) there is no mention of counting rods or rod numerals in any Indian source, or anything even vaguely similar] and possibly point out that they haven't really engaged seriously with them. –jacobolus (t) 14:47, 19 October 2023 (UTC)

By the way, someone should also probably try to redraw the figures showing the evolution of the numerals, as a few of them are illicitly copied without credit from published books. –jacobolus (t) 14:52, 19 October 2023 (UTC)

I think these are all good suggestions. Paul August ☎ 18:04, 19 October 2023 (UTC)

Addition of Hindu Numerals Image of Brahmi Script and its evolution

I bring to your notice that I insist on adding an image of the Hindu Numeral Image that has reference to the evolution from the Brahmi Script to Gwalior to Devanagari Script. I also insist on adding the names of the books of Al-Khwarizmi and Al-Kindi in their native language. I also insist on bringing the Evolution of the Number System Image to the top section. GurkhanofAsia (talk) 20:23, 7 January 2024 (UTC)

I see no reason why you shouldnt. adding images would be good for this. H20346 (talk) 22:49, 21 January 2024 (UTC)

Can you be specific about which image you mean? You also don't need to speak so formally ("bring to your notice" etc.). Note that File:Evolution_of_Hindu-Arabic_numerals.jpg is actually a copyright violation and should be removed from Wikipedia/Wikimedia commons; it was copied from Karl Menninger's 1969 book (page 418) without attribution. If you would be able to carefully draw a replacement image that conveys the same information without being a ripoff of Menninger's original diagram that would be a big help. –jacobolus (t) 23:26, 21 January 2024 (UTC)

Recent edit by Jacobolus

The recent edits by Jacoblus are factually incorrect and problematic

1) He claims that positional decimal system was invented in India around 1st Century AD, but the world's earliest positional decimal system was used by the Chinese in rod calculus. This system is older than the Indian positional decimal system.

2) He classified all those mathematicians, including Helaine Selin, who discussed the Chinese origin of number system as "scinologists"

3) He claims that the research of these "scinologists" are disputed, and are based on speculations, but he hasn't provided any reliable source for this. WP:OR

4) He has removed other sources like Campbell Douglas and J.C. Huggins without any explanation

Overall, he has edited this article in a way so as to give the reader a "purely Indian origin" while completely neglecting others as "scinologists" whose research, he described, is based on "speculations." Hu741f4 (talk) 12:34, 23 February 2024 (UTC)

I reverted back to the stable version (which has been discussed above). M.Bitton (talk) 13:07, 23 February 2024 (UTC)

On a cursory glance I think that many of the recent edits by Jacobolus are improvements. I'm going to take a closer look and add back any that I think are appropriate, while listing them here. Paul August ☎ 15:38, 23 February 2024 (UTC)

I disagree. In any case, you already made your position clear on this subject in the previous discussion, but what matters now is there is no consensus for this change. M.Bitton (talk) 15:40, 23 February 2024 (UTC)

There is no consensus because any time anyone tries to start improving this article in any way, you jump in to maintain the current incredibly mediocre and incomplete version, based apparently on some kind of political ideology. –jacobolus (t) 16:01, 23 February 2024 (UTC)

All POV with no exception is described as an improvement by those who want to inject it into the article. M.Bitton (talk) 16:02, 23 February 2024 (UTC)

Right now the article is a grossly incomplete and poorly written summary which does not link to the best available sources, does not accurately describe historical scholarship, and does horrendous injustice to a topic about which whole books can be (and have been) written. I'd like to see some collaborative effort to greatly expand and improve the article, but you, standing guard, won't let anyone even make the slightest change without reversion (cf. WP:OWN), which makes more significant improvement essentially impossible. –jacobolus (t) 16:52, 23 February 2024 (UTC)

In the meantime, at least two editors disagree with you. I also noticed that you tried the same tactic on the Arabic numerals and were reverted by a third editor (who also disagrees with you). M.Bitton (talk) 16:55, 23 February 2024 (UTC)

Going back through previous conversation, I didn't want to leave this hanging unanswered. This is not an accurate summary of what happened. What happened was I tried to make minor improvements to Arabic numerals, got instantly reverted which resulted in an edit war that hit a wall in discussion, and then I opened a discussion on the "Neutral Point of View Noticeboard" to attract a neutral third-party arbiter; this resulted in a small but significant improvement to that article (namely, adding links to this article and History of the Hindu–Arabic numeral system) which had previously been blocked for several years. Those changes didn't fully fix all of the problems with that article, which remains mediocre, but I'm hoping to get back to it in the future. –jacobolus (t) 19:57, 26 February 2024 (UTC)

You are grossly mischaracterizing the text I added. (1) The claim is not that the first ever positional system was invented in India (there were counting boards used in ancient Mesopotamia, Egypt, Greece, etc., possibly as much as millennia earlier), but only that the specific positional decimal system under discussion here developed in the Indian subcontinent. This is a widely accepted claim among scholars, and is not remotely controversial. (2) Nobody said that Selin is a sinologist; the sinologists (a word meaning China scholars) in question are Needham and Lam. (3) Two sources were provided for this claim, both of which are freely accessible. (4) The removed source is a derivative of Needham and Lam's claims, which doesn't accurately transmit their claims. –jacobolus (t) 15:45, 23 February 2024 (UTC)

You've been trying to downplay, if not erase the Chinese origin for months, so don't be surprised if some editors still don't agree with you. M.Bitton (talk) 15:50, 23 February 2024 (UTC)

This "Chinese origin" theory is fringe speculation by a couple of researchers which does not accurately reflect current scholarly consensus. The source I linked, a review in Historia Mathematica, disputing the claims in Lam's book, was written by an eminent historian of Chinese mathematics. –jacobolus (t) 16:04, 23 February 2024 (UTC)

That's your POV and you're more than welcome to stick to it. M.Bitton (talk) 16:05, 23 February 2024 (UTC)

No, it's the "point of view" of mainstream historians (for example Jean-Claude Martzloff who wrote A History of Chinese Mathematics, one of the best available books about the history of Chinese mathematics), which is why it should be reflected in Wikipedia. The current article text does not accurately reflect current scholarship, but gives undue weight to an unsubstantiated fringe theory, which it does not accurately describe or characterize, to readers' detriment. Wikipedia is supposed to give clear and fair summaries of current knowledge, not promote Arab-nationalist, Chinese-nationalist, or Indian-nationalist "my history is better than yours" contests. –jacobolus (t) 16:09, 23 February 2024 (UTC)

I see no point in repeating what was discussed in October 2023. M.Bitton (talk) 16:11, 23 February 2024 (UTC)

You didn't then, and won't now, actually engage with the content under discussion, because you don't actually have an argument beyond, more or less, "I like this version and nobody can change it because I said so". –jacobolus (t) 16:13, 23 February 2024 (UTC)

That's another baseless claim of yours that we can safely add to the list. M.Bitton (talk) 16:20, 23 February 2024 (UTC)

It doesn't matter what anyone's POV happens to be. All that matters is what the sources say. Could we all keep speculation about our fellow editor's points of view to ourselves? Paul August ☎ 16:13, 23 February 2024 (UTC)

The sources says a lot of things, so are we going to add everything they say or cherry pick what we want? M.Bitton (talk) 16:14, 23 February 2024 (UTC)

No of course not. What makes you assume I would ever think so? Paul August ☎ 16:29, 23 February 2024 (UTC)

What we should do is accurately reflect current scholarly consensus, which means finding the best survey sources we can written by mainstream mathematical historians, assigning each topic WP:DUE weight commensurate with its coverage in those sources, and pointing out for readers' benefit when specific claims are disputed by other scholars. The current version cherrypicks a small handful of fringe sources and describes their controversial speculations as fact. –jacobolus (t) 16:37, 23 February 2024 (UTC)

Actually, as it stands, the article is already downplaying the Chinese origin, What we should do is add more about it (for the benefit of the readers). M.Bitton (talk) 16:38, 23 February 2024 (UTC)

I would be happy to to add more about a Chinese origin, but I would need to see sources which characterize it in such a way that supports giving more emphasis to this theory. Paul August ☎ 16:46, 23 February 2024 (UTC)

I did add more about it (specifically, describing both the content of the theory and the reason it is disputed by other scholars), in the changes which you reverted. –jacobolus (t) 16:48, 23 February 2024 (UTC)

No, you tried to downplay it even more and that's not acceptable. M.Bitton (talk) 16:54, 23 February 2024 (UTC)

I've removed the image "Development of Hindu–Arabic numerals"

Development of Hindu–Arabic numerals

, since it seems to assert as a fact the descent from Shang numerals, also this is apparently a copyright violation. Paul August ☎ 15:44, 23 February 2024 (UTC)

The claim that the image is copyright violation is completely and utterly baseless. M.Bitton (talk) 15:46, 23 February 2024 (UTC)

That image seems to be derived from [1] which I assume is still under copyright, no? Paul August ☎ 15:53, 23 February 2024 (UTC)

No, it's not under copyright. M.Bitton (talk) 15:54, 23 February 2024 (UTC)

And what about that the image seems to assert as fact descent from Shang numerals? Paul August ☎ 15:54, 23 February 2024 (UTC)

Why remove it under false pretences? M.Bitton (talk) 15:56, 23 February 2024 (UTC)

It's not "false pretenses". The image is clearly copyright violation. It's useful to have an image of this style, but someone should make a better replacement image which (a) is more legible, e.g. using color, (b) isn't a copyright violation, and ideally (c) reflects current scholarly consensus. –jacobolus (t) 15:59, 23 February 2024 (UTC)

The only that is clear is the fact that you keep making baseless assertions. M.Bitton (talk) 16:00, 23 February 2024 (UTC)

It's not a "baseless assertion" that this was scanned from a book. It's blatantly obvious to anyone who compares the two that they are the same. –jacobolus (t) 16:02, 23 February 2024 (UTC)

I dare you to challenge its copyright status on Commons. M.Bitton (talk) 16:03, 23 February 2024 (UTC)

Do you still think the image is not under copyright? Paul August ☎ 16:03, 23 February 2024 (UTC)

I know so. M.Bitton (talk) 16:06, 23 February 2024 (UTC)

Could you please to explain to how you know so? Paul August ☎ 16:09, 23 February 2024 (UTC)

I checked the source and I suggest the others do the same before making baseless claims. M.Bitton (talk) 16:10, 23 February 2024 (UTC)

Where do you think the image came from, if not from Menninger's book (via Campbell and Higgins's book)? It's directly a scan of this page. –jacobolus (t) 16:11, 23 February 2024 (UTC)

Click on the image, go to Commons and read the source. More than this and I will have to read it for you. M.Bitton (talk) 16:13, 23 February 2024 (UTC)

I added the current attribution to Menninger to the Mediawiki commons image (before I realized it was via Campbell/Higgins's book). Previous the uploader (apparently user:Hu741f4, who is involved in this discussion) claimed it was their own work and did not include any attribution. While we have the uploader here we can directly ask: user:Hu741f4: Did you draw this image yourself or was it scanned from a copyrighted book? –jacobolus (t) 16:14, 23 February 2024 (UTC)

In other words, your claim of copyright infringement was baseless. M.Bitton (talk) 16:17, 23 February 2024 (UTC)

What? Do you know what copyright infringement means? –jacobolus (t) 16:25, 23 February 2024 (UTC)

No, I certainly don't and I usual wait for you to explain such complicated notions. M.Bitton (talk) 16:26, 23 February 2024 (UTC)

Your's talking about this page [2] right? It seems to me it saying that the image was derived from Karl Menninger (1969), Number Words and Number Symbols, page 418. Is that not correct? I would really appreciate it if you could try to treat me more politely. Paul August ☎ 16:26, 23 February 2024 (UTC)

That's because Jacobolus keeps messing around with it. I have always treated you with respect and if I said anything that could be construed otherwise, then I can assure you that there it is not meant that way. M.Bitton (talk) 16:30, 23 February 2024 (UTC)

I edited that page to credit Menninger, before I knew that the scan came from Swetz's paper (Swetz modified Menninger's diagram to paste the "Shang numerals" line on the top). Originally it said the image was user:Hu741f4's own work. –jacobolus (t) 16:31, 23 February 2024 (UTC)

If you keep edit warring on Commons (changing what was corrected by an admin there), you can guess what will happen next. M.Bitton (talk) 16:33, 23 February 2024 (UTC)

Are you saying that I removed it under false pretenses? Paul August ☎ 16:18, 23 February 2024 (UTC)

this is apparently a copyright violation this what you claimed after removing it. M.Bitton (talk) 16:22, 23 February 2024 (UTC)

Now you seem to be accusing me of lying!! Was that your intent?? I did not remove that image under "false pretenses". The reason I removed it was because it seemed to me (and still does) to be a copyright violation, there is nothing false about that, nor did I make any pretense about why I removed it. Paul August ☎ 16:42, 23 February 2024 (UTC)

Obviously not and "false pretences" was in hindsight the wrong choice of words (I certainly didn't mean anything by it). I will be creating a derivative that will make the discussion about the cso-called opyright irrelevant M.Bitton (talk) 16:46, 23 February 2024 (UTC)

Thankyou! But I have to point out that after you first chose those words, after which I asked you if you meant it: Are you saying that I removed it under false pretenses? you reasserted the same accusation: "this is apparently a copyright violation" this what you claimed after removing it. If the copyright issue could be resolved then I would be willing to consider adding the image back. But that would still leave the issue I've raised twice above, but you've yet to address, which is that that image seems to assert as a fact the descent from Shang numerals. Paul August ☎ 17:02, 23 February 2024 (UTC)

It's no more asserted as fact than everything else it shown. It's just an image that shows the possible theories that are discussed. M.Bitton (talk) 17:04, 23 February 2024 (UTC)

Without any other content the image seems to me to assert direct descent as a fact. Paul August ☎ 17:06, 23 February 2024 (UTC)

And thus is misleading at best. Paul August ☎ 17:07, 23 February 2024 (UTC)

It's not misleading and besides, it's sourced, isn't it? M.Bitton (talk) 17:09, 23 February 2024 (UTC)

Swetz's diagram is substantially misleading taken out of context. Here was the text accompanying it: "If one views a popular schematic of the evolution of our modern system of numeration and places the Chinese system in the appropriate chronological position, an interesting hypothesis arises, namely that the numeration system commonly used in the modern world had its origins 34 centuries ago in Shang China."

Note that the claim is explicitly speculative. But also, Needham and Lam, who made the original claims, don't say anything about "Shang numerals" influencing Indian numerals. What they claim instead is that the influence of counting rods might have put the idea of positional numbering into India, based on there being cross-cultural contact between India and China. The direct arrow from "Shang numerals" to "Brahmi numerals" is not actually something claimed even by the scholars who came up with this speculative theory. –jacobolus (t) 17:21, 23 February 2024 (UTC)

The arrow is claimed by Swetz (it's his diagram and he's placing the Chinese system in the appropriate chronological position). M.Bitton (talk) 17:24, 23 February 2024 (UTC)

Wait, now you agree it's Swetz's diagram? Why are you edit warring on the image description page to prevent me from adding a link to Swetz's book chapter then? –jacobolus (t) 17:28, 23 February 2024 (UTC)

Because the image that was uploaded is not his (it's clearly a derivative of an older source). M.Bitton (talk) 17:31, 23 February 2024 (UTC)

The image File:Evolution of Hindu-Arabic numerals.jpg that was originally uploaded by user:Hu741f4, without any attribution, is a scan of Swetz's 1984 diagram, which was itself a modified version of Menninger's 1969 diagram, a translation of Menninger's 1934 diagram. Please look at the images side by side; it is not at all hard to figure this out when you have them in front of you. I don't know why you are pretending not to be able to tell the difference between these. –jacobolus (t) 17:40, 23 February 2024 (UTC)

pretending Comment such as these tend to bring the discussion to a nice end. In any case, as soon as I have time, I will upload a derivative that will make any excuse about copyright look ridiculous. M.Bitton (talk) 17:42, 23 February 2024 (UTC)

It is a scan of a copyrighted book, which was originally added to Mediawiki commons without attribution. The original source is Karl Menninger's bok Number Words and Number Symbols, originally published in 1934 as Zahlwort und Ziffer (in German). Campbell and Higgins pasted Menninger's diagram into their 1984 book but tacked the "Shang numerals" box onto the top. –jacobolus (t) 15:57, 23 February 2024 (UTC)

The POV that you inserted on Commons was removed for a reason. M.Bitton (talk) 15:59, 23 February 2024 (UTC)

A sketch of Needham/Lam's theory and criticism thereof

@Paul August, let met try to give a summary for you. The original speculation comes from Joseph Needham (Science and Civilisation in China, vol. 3), and is pretty thin. Needham valuably piles up a lot of material related to China (it would be great if Wikipedia could cover some of this in greater detail), but in his eagerness to credit China with "more advanced and scientific" mathematics than other contemporary civilizations throughout history, unfortunately mischaracterizes the numerical systems and mathematical accomplishments of ancient Mesopotamia and the Mediterranean (and perhaps Egypt), and of medieval India and the Arab world, even as they were known 60 years ago; in the past half-century these have all been studied further, and his presentation is now quite dated. Needham is also pretty free mixing speculation with fact, which sometimes makes it hard to figure out precisely what he is claiming is known vs. conjectured. It makes a potential good starting point, but should be read with some healthy skepticism.

Here's most of the specifically relevant bit:

We are free to consider the possibility (or even probability) that the written zero symbol, and the more reliable calculations which it permitted, really originated in the eastern zone of Hindu culture where it met the southern zone of the culture of the Chinese. What ideographic stimulus could it have received at that interface? Could it have adopted an encircled vacancy from the empty blanks left for zeros on the Chinese counting-boards? The essential point is that the Chinese had possessed, long before the time of the Sun Tzu Suan Ching (late +3rd century) a fundamentally decimal place-value system. It may be, then, that the 'emptyness' of Taoist mysticism, no less than the 'void' of Indian philosophy, contributed to the invention of a symbol for sunya, i.e. the zero. It would seem, indeed, that the finding of the first appearance of the zero in dated inscriptions on the borderline of the Indian and Chinese culture-areas can hardly be a coincidence.

You can see that this doesn't present any particular evidence, and is explicitly speculative.

Lam Lay Yong, I believe at some point a student of Needham's, took the idea and elaborated it into a paper (or a few?) and a book Fleeting Footsteps with coauthor Ang Tian Se, which includes an English translation of the Sunzi Suanjing (a Chinese book of unknown original date and unknown original author, the main part of which probably dates from the 5th century or before and which was eventually included among the canon of "ten mathematical manuals" during the Tang dynasty in the 7th century). Lam analyses the counting-rod-based arithmetical procedures described in the available copy of the Sunzi Suanjing, and finds that a variety of arithmetical algorithms are similar to those found in medieval arithmetic sources written in Arabic. Noting that there was cultural contact between India and China at the time, e.g. the transmission of Buddhism from India to China, Lam therefore claims that Indian arithmetic must have come from China.

The problem with the book is that (a) Lam does not have any direct evidence whatsoever for her main theory, and (b) Lam does not address the several most obvious criticisms of her theory:

First, Chinese counting rods are in many ways similar to counting boards used in Egypt, Greece, Rome, and Mesopotamia, which were even older than Chinese counting rods, and used across a wide geographical area over long periods of time by civilizations with even more cultural contact with India. Unfortunately our knowledge of the precise methods used with these is somewhat scanty because we don't have any contemporary written manuals. I'm not enough of an expert to immediatly do it myself but I'd love to see improvement of our articles abacus and counting board, among others. Lam does not consider that Indian and/or Chinese arithmetic may have been influenced by these other tools/systems, a speculative conjecture which also has no direct evidence but is just as plausible as Lam's own. Positional numbering is also similar in many ways to the Mesopotamian positional (base sixty) system, to the Greek numeral system, etc.; the Chinese counting rod system is not particularly more similar to Indian arithmetic than these other previous systems, and there's nothing obvious about the relationship between Indian and Chinese systems.

Second, Lam doesn't consider, as Martzloff points out, that the copy of the Sunzi Suanjing she translated might have been modified or extended by copyists later than its original date. Indeed there is explicit historical documentation of such modification in the 7th century, not discussed by Lam's book ("the biography of Li Chunfeng (602-670) [...] states that Li Chunfeng and others reedited the SZSJ because 'the text was very erroneous (or contradictory) from the point of view of the principles'"). It is hard to firmly date the various pieces of the Sunzi Suanjing or figure out precisely when the methods described developed, but it is entirely plausible that methods described by Lam were even brought to China from outside. (It is also entirely plausible that they developed independently.) We have explicit evidence of the use of Indian numerals in China as early as the 8th century, and considering the cultural contact Lam stresses, it is entirely plausible that their influence was felt centuries earlier than that. But again this is all pure speculation, and any comments about it in Wikipedia should be described as such.

Third, Lam does not address the clear structural differences between Indian and counting-rod number systems. The counting-rod system uses a 5 × 2 structure also found in the Roman counting board but not found at all in the Indian arithmetic system. Lam puts great emphasis on the use of a blank space for zero in computing with counting rods, but this is a prominent feature of every kind of counting board. Lam hangs much of her theory on the claim that counting rods were used in a strictly positional way, unlike Greek, Mesopotamian, Egyptian, or other < 0 BCE written numeral systems, which involved various irregularities. She assumes that this purported feature couldn't have developed independently. But as Marzloff points out, this is not even an accurate summary of the actual use of counting rods, noting that for example blank spaces for "zeros" were not uniformly preserved, and that "irregular forms [...] were rather common in [Chinese] mathematical texts. [...] in practice, the counting-rod system was not as perfectly decimal and positional as the descriptions in Fleeting Footsteps would imply." The counting rod system is very concrete, almost identical in basic format to the Mayan (base twenty) or Sumerian (base sixty) systems, whereas Indian arithmetic uses symbols which are substantially abstract, more comparable to Greek alphabetic numerals. Neither counting rods nor Chinese written numbers of the time were discernably similar to the symbols adopted in India, which likely developed indigenously from earlier Indian symbols; nobody has even speculated that the symbols themselves originated in any Chinese system. Martzloff's summary is that "examples of Chinese written numerals from sources anterior to the tenth century do exist, and the structure of these militates against the idea of the Chinese origin of the Hindu-Arabic numerals."

Finally, Lam does not sufficiently address the lack of any direct or textual evidence, and does not surface any with her book. No numerically related words were adopted from Chinese into Indian languages (however, several were transmitted in the other direction). No extant Indian sources mention Chinese number systems. There are no examples of counting rods found in India. Etc. Etc.

Note again that Marzloff is one of the preeminent historians of Chinese mathematics; this is not some kind of politically motivated position. Indeed, I imagine the journal editors chose to have Martzloff write a review specifically to forestall any accusation of political motivation, as might arise if a scholar focusing on e.g. Greece, Persia, or Southeast Asia wrote a review. –jacobolus (t) 19:25, 23 February 2024 (UTC)

Thank's for this. I have a few questions but they'll have to wait. Paul August ☎ 19:54, 23 February 2024 (UTC)

Jacobolus edits, reverted by M.Bitton, and as restored by Paul August

I intend to restore certain edits as I see fit and I would like to discuss each such restored edit here in each in its own section. Paul August ☎

Image Evolution of Hindu-Arabic numerals.jpg

I've removed the image "Development of Hindu–Arabic numerals"

Development of Hindu–Arabic numerals

, since it seems to assert as a fact the descent from Shang numerals, also this is apparently a copyright violation. Paul August ☎ 17:44, 23 February 2024 (UTC)

[Note: I tried to move the discussion of this edit (see above) here but I was reverted by M.Bitton. Paul August ☎ 17:44, 23 February 2024 (UTC)]

@M.Bitton: Will you reconsider moving the apart of the discussion related to this image here? Do other editors think, this is a good idea? Paul August ☎ 17:48, 23 February 2024 (UTC)

It's part of the same discussion (the image was removed by them first before you removed it). I already said that I will upload a derivative of that image to put an end to the concerns about the copyright, so I'm not exactly sure why you're bringing it up again. As for your refactoring of the discussion, it was partially reverted because you moved comments around for no reason. M.Bitton (talk) 17:51, 23 February 2024 (UTC)

I was not trying to bring "it up again", I was simply trying to move the discussion from that section to here so readers could better focus on each editorial issue separately (and also ... sigh ... to help reduce comments about other editors and concentrate solely on content). And as I noted above the issue with the image for me is not just copyright. Paul August ☎ 18:18, 23 February 2024 (UTC)

The file https://en.m.wikipedia.org/wiki/Talk:Hindu–Arabic_numeral_system#/media/File%3AEvolution_of_Hindu-Arabic_numerals.jpg isn't a copyright violation because it is from 1960s publication. Check this out https://commons.m.wikimedia.org/wiki/Commons:Licensing Hu741f4 (talk) 18:23, 23 February 2024 (UTC)

the issue with the image for me is not just copyright in that case, I will wait until this is sorted before making a derivative. M.Bitton (talk) 19:28, 23 February 2024 (UTC)

The claim by some people in discussion at Wikimedia Commons was that image should not be copyrightable because it is a diagram based on glyph symbols which are not themselves copyrightable, and the commenters felt that the other features of the diagram (layout, style) were not sufficiently creative to merit copyright protection. I think this is a dubious reading of copyright law, albeit in practice it isn't likely to come up since Menninger is dead, this image is now quite old, and it has been spread around the internet for the past decade or two without any efforts at copyright enforcement by the rights-holders, who presumably don't care.

Nonetheless, I don't think it's a very good image for Wikipedia/Wikimedia to use for a variety of reasons:

• It's a crappy book scan, rather than a crisp newly made image, in black and white when we have full color available
• As typically rendered at thumbnail size the digits are too small to see clearly or compare
• The arrows give an oversimplified impression of the relationships between these systems
• Not enough different numeral sets are represented to give a global perspective
• The rows-of-10-digits format for each box takes up too much horizontal space and forces awkward layout of the arrows

I think we can draw a much better image with some effort, but we should try to base it on the best currently available survey source. The arrow connecting Shang -> Brahmi numerals is clearly inappropriate (there is no scholar claiming any direct link between these), but that's really the least of the problems with this diagram. –jacobolus (t) 19:43, 23 February 2024 (UTC)

The quality of the scan is not an issue (we can create a much better one). M.Bitton (talk) 19:56, 23 February 2024 (UTC)

What has changed since this discussion (see your comment there)? M.Bitton (talk) 13:48, 24 February 2024 (UTC)

Nothing has fundamentally changed since then. I think the Menninger image should not be included, but the general idea of a diagram indicating the evolution of numerals seems like a good idea, so it would be good for someone to draw one. I might even try to draw one myself at some point; possible layout improvements have been floating around in the back of my mind. –jacobolus (t) 15:30, 24 February 2024 (UTC)

You have changed your mind since then, so something has changed. I also see no reason whatsoever to replace a properly sourced image with someone's WP:OR. M.Bitton (talk) 17:35, 24 February 2024 (UTC)

No, I still think the scan is copyright infringement and should be removed (the logic "diagrams aren't creative enough to be copyrightable" seems clearly wrong to me, but I am not a lawyer and no lawyer has weighed in specifically here). I still think the image is somewhat outdated and poorly suited to the context of Wikipedia per se, and ideally any replacement should be improved in various ways, including layout, color scheme, content choices, aspect ratio, .... Any replacement should be based on the best available recent scholarly overview. Something that Frank Swetz hacked together in a few minutes in 1984 by gluing an extra box onto Meninger's 1934 diagram to illustrate his amateur speculations is not a good choice. –jacobolus (t) 17:39, 24 February 2024 (UTC)

We don't need a lawyer. If you still think that the image is copyvio, then you should try to have deleted from Commons. M.Bitton (talk) 17:44, 24 February 2024 (UTC)

I did recommend that these images all be deleted from commons as copyvio. A few random non-lawyers on Commons commented that they don't think diagrams are creative enough to be copyrighted, so the image is still preserved. I don't care enough about this to waste time escalating it and pressing the point, since I don't think there's really a practical lawsuit risk, but I still don't think we should use the images where we can avoid it. –jacobolus (t) 17:47, 24 February 2024 (UTC)

Either it's copyvio or it's not. At the moment and until proven otherwise, it's not copyvio, and therefore, there is no reason not to use it.

Also, when you change your comment after someone has replied to it, it is commonly best practice to indicate your changes. M.Bitton (talk) 17:50, 24 February 2024 (UTC)

I personally believe that it is a clear copyright violation, and should be removed from Wikimedia Commons; however, some other Wikimedians disagree, based on the claim that this type of diagram is ineligible for copyright. These kinds of legal questions are never completely unambiguous, but depend on legal interpretation and the whims of particular judges (at the trial court and possibly appellate levels). This particular example is never going to be litigated, so it maybe doesn't matter too much. –jacobolus (t) 19:45, 24 February 2024 (UTC)

In other words, the image is not copyvio (until proven otherwise) and therefore, there is no reason not to use it. M.Bitton (talk) 22:09, 24 February 2024 (UTC)

No, your "other words" are entirely different than my meaning. Please don't put words in people's mouths.

I have said clearly several times: I believe the image is a copyright violation and also not particularly appropriate in context on this article; we should not use it here but should make a better one instead.

However I don't care strongly enough about the copyright status to force the issue on Commons, since it would take a significant amount of effort for no real benefit; leaving it there (with attribution) isn't doing terribly much harm. (Aside: personally I think extremely long copyright terms should be abolished.) –jacobolus (t) 23:25, 24 February 2024 (UTC)

We don't base on our content on editor's unsubstantiated beliefs and I certainly see no reason to replace a perfectly sourced image with someone's WP:OR. M.Bitton (talk) 23:42, 24 February 2024 (UTC)

Actually, we base our content on consensus, see WP:CONSENSUS, which has certainly not been achieved with respect to the use of this image in this article. If you are going to put one of these diagram scans anywhere close to Wikipedia, it should be Menninger's original (the 1969 English translation), rather than Swetz's modified version. The latter is grossly misleading when taken out of the context of his article, and is frankly still substantially misleading even in the context of his article. However, the former is still 90 years out of date and not very well adapted to the context, having been drawn to meet the needs of a German book in the 1930s. –jacobolus (t) 00:27, 25 February 2024 (UTC)

Consensus only has meaning when it's based on what has been published by reliable sources. Swetz's version is reliable and covers what's cited in the article, therefore, I see no reason not to use it. M.Bitton (talk) 00:31, 25 February 2024 (UTC)

What you personally "see" is not the definition of consensus, which, to quote the lead of WP:CONSENSUS, "involves an effort to address editors' legitimate concerns through a process of compromise". The best recent scholarly source to use as a reference, if someone wants to redraw a better figure, is probably Chrisomalis (2002) Numerical Notation: A Comparative History, a survey by a career expert on this topic. Swetz was not an expert on this topic, his own article clearly explains why his diagram is not "reliable" out of context, and the presentation of "what's cited in the article" does not match scholarly consensus and indeed is sharply disputed by a range of experts in the field, as I have explained in my other comments. –jacobolus (t) 00:36, 25 February 2024 (UTC)

Your new "concerns" about not using the image are rather strange, given that you didn't have them last month. You also have failed to address the legitimate concerns of others (while consistently repeating what you "believe"). M.Bitton (talk) 00:46, 25 February 2024 (UTC)

I mentioned my most serious concern last month, namely that this image is a copyright violation. That remains my most serious concern with using this image now. I didn't comprehensively share my thoughts about this image, which I find problematic for several other reasons I have stated. If you want to start a new discussion about how best to draw a new non-copyright-infringing image about this topic, I'd be happy to participate; it's getting a bit cramped / out of scope for this particular subthread.

The whole point of having this conversation (instead of just e.g. edit-warring a preferred version back into the article) is to discuss editors' concerns. Which concern specifically do you think I am "failing to address"?

Aside: could you please try to be less aggressive? It comes across as extremely disrespectful. –jacobolus (t) 01:10, 25 February 2024 (UTC)

Please refrain from casting aspersions!

As I said previously, I will be more than happy to make a derivative of the map to address your most serious concern. As a matter of fact and to make this discussion shorter, I will start working on it straight away. M.Bitton (talk) 01:14, 25 February 2024 (UTC)

I don't know what you mean by casting aspersions, but the way your comments read to me, you have repeatedly put arbitrary key words in quotation marks implying a sarcastic air quotes, called my comments "strange", mischaracterized the content of my comments, impugned my motives, made demands that I should do one thing or another, and overall strongly personalized what could easily be a neutral content discussion. Could you try to stop doing that, whether or not it was intentional? It comes across as intentionally disrespectful. –jacobolus (t) 02:02, 25 February 2024 (UTC)

You know exactly what I mean (since you've been doing it for a while). As for the quotation marks, I suggest you take a leaf out of your own book.

Anyway, I am in the middle of creating the image to address your concern (it's time and energy consuming), so let's concentrate on that and get this over and done with. M.Bitton (talk) 02:20, 25 February 2024 (UTC)

@Hu741f4: your thoughts about restoring the sourced image that was removed would be appreciated. M.Bitton (talk) 22:12, 24 February 2024 (UTC)

As per the guidelines mentioned here, ( https://commons.m.wikimedia.org/wiki/Commons:Licensing ) the image can be used with or without attribution, but I can remake the image with clear texts. As for now, I agree with @M.Bitton that the image should be restored Hu741f4 (talk) 22:32, 24 February 2024 (UTC)

The image must absolutely not be used with the previous attribution as "Hu741f4's own work"; doing so intentionally would be grossly unethical plagiarism. –jacobolus (t) 23:26, 24 February 2024 (UTC)

Rewrite of first three sentences of the "Origin" section

I've restored a Jacobolus's rewrite to the first three sentences of the "Origins" section, which adds content, with what seem to me to be better sources, and which also does not change the current text concerning the Shang numerals. Does anyone have any issues with these edits? Paul August ☎ 18:08, 23 February 2024 (UTC)

Yes because the sentence is factually incorrect. The chinese were using the positional decimal system long before the Indians. The Chinese "Rod numeration" uses a positional ordering based on powers of ten and is obviously decimal. Rod numeration adheres to contemporary principles for positional ordering. Long before the Common Era, Chinese mathematicians were recording numbers using decimal-based place-value systems

https://maa.org/book/export/html/3403381#:~:text=Rod numeration is clearly decimal positional system, dates before the Common Era.

Also see

(Carl Boyer: page 178)

https://books.google.co.in/books?id=V6RUDwAAQBAJ&pg=PA178&dq=decimal+positional+system+ancient+china&hl=en&newbks=1&newbks_redir=0&source=gb_mobile_search&sa=X&ved=2ahUKEwi_qYaEi8KEAxUp-TgGHT52AeAQ6AF6BAgKEAM#v=onepage&q=decimal positional system ancient china&f=false

(Victor J Katz: page 8)

https://books.google.co.in/books?id=pWXxDwAAQBAJ&pg=RA6-PA8&dq=Victor+J+katz+Positional+decimal+chinese&hl=en&newbks=1&newbks_redir=0&source=gb_mobile_search&sa=X&ved=2ahUKEwixzYT1i8KEAxUW4zgGHSBgBrUQ6AF6BAgLEAM#v=onepage&q=Victor J katz Positional decimal chinese&f=false

( Hu741f4 (talk) 18:33, 23 February 2024 (UTC)

To be clear you are talking about this sentence:

"A positional decimal numeral system was developed in the Indian subcontinent sometime before the 1st century CE."

correct? Paul August ☎ 19:00, 23 February 2024 (UTC)

I want to be clear that I am not making any claim about the ultimate origin of these ideas; we're well into the realm of oral history at that point, and while there are sources in India from 500 BCE or before which have been described as possibly positional and decimal (and the Indus Valley Civilization even made impressively accurate decimally divided rulers before 2000 BCE, see Mohenjo-daro ruler), we simply don't have enough evidence to make remotely solid claims about what happened earlier than about the 1st century CE. They might have developed multiple times independently and indigenously in different places, or perhaps all ultimately trace to ancient Sumeria, who knows. I think RC Gupta's 1995 paper provides a pretty good survey of what is known about the concept of zero in particular (and to some extent about positional numbering in general) from different times/places around the world, including Mesoamerica, Mesopotamia, Egypt, China, Greece, ..., which is why I added it as a source. We should give a broader historical survey at History of ancient numeral systems, History of the Hindu–Arabic numeral system, Decimal#History, Positional notation#History, History of arithmetic, etc. –jacobolus (t) 19:47, 23 February 2024 (UTC)

That was my understanding of what you wrote. Paul August ☎ 19:55, 23 February 2024 (UTC)

"while there are sources in India from 500 BCE or before which have been described as possibly positional and decimal"

Please cite your sources that say these were "positional"

"we simply don't have enough evidence to make remotely solid claims about what happened earlier than about the 1st century CE."

Wikipedia isn't a place for pursuing original research and giving judgements. That is your personal opinion. We have multiple reliable sources by multiple authors (Victor J Katz, Carl Boyer, Lam lay young, Joseph Needham, Douglas A Campbell, Helaine Selin, Frank Swetz), all of them accept the Chinese origin of Decimal positional system.

"They might have developed multiple times independently and indigenously in different places, or perhaps all ultimately trace to ancient Sumeria, who knows."

This is again your personal opinion. Please don't use terms like "who knows" for something that is supported by multiple independent reliable sources.

"I think RC Gupta's 1995 paper provides a pretty good survey of what is known about the concept of zero in particular"

Your "thinking" doesn't matter. If RC Gupta is contradicting so many scholars then it is WP:Fringe Hu741f4 (talk) 20:14, 23 February 2024 (UTC)

Please cite your sources that say these were "positional"

I am not remotely an expert. Here's Gupta:

On the other hand the Sanskrit grammatic system of Pāṇini (c. 500 BC) has been claimed recently to contribute to the concept of zero in mathematical sense (i.e. involving positional analysis, operation of subtraction, process for going from maximum to minimum). It is even said that "he was the first man to use mathematical concept of 'zero' before mathematicians accepted it". His conception is presented in three forms, namely the linguistic zero, the it zero, and the anuvṛtti-zero, but his idea of 'absence' (lopa, etc.) cannot be truly compared with a zero in a place-value system.

According to Sadguru-śisya, the prosodist Piṅgala was a younger brother of Pāṇini, but usually Piṅgala is taken to flourish about 200 BC. For computing 2ⁿ, he gave a set of four sūtras one of which reads (VIII, 29 in his Chandah-śāstra), rūpe śūnyam, or "(Place) a zero (śūnya) when unity is subtracted (from index or power)". ¶ So it is believed that India possessed a zero symbol at that time (but śūnya may mean blank space.).

The word 'thibuga' used by Bhadrabāhu (c. 300 BC) has been found in a quoted gāthā and interpreted by Hemacandra to mean bindu. Some scholars try to see 'zero' of place-value notation in this. The Jaina canonical work Anuyogadvāra-sūtra (c. 100 BC) is said to provide the "earliest literary evidence" of the use of the word of place-value notation in this (see sūtra 142). Now credit for inventing the place-value system (with zero) is also being given of Kundakunda (between 100 BC and 100 AD) who may be the possible author of relevant works (Parikarma and Saṃta-kamma-paṃjiya) which are relevant.

That the decimal place-value system was in use then in India is clear from reference to it by Vasumitra (first century AD) to illustrate that ‘things are spoken in accordance with their states’. He says “When the clay counting-piece is placed in the place of Units, it is denominated 'one', when placed in the place of Hundreds, it is denominated 'hundred', and in place of Thousands it is denominated a 'thousand'. Vasumitra was a Buddhist. Similar counting process is mentioned in ancient Jaina works. In such positional process, the circular symbol (representing empty pit) would automatically denote zero. The use of zero symbol to fill the blank space66 is also found in Mahābandha (c. AD 100).

Retyping all of that just took me a lot of works since the diacritics are not easily available on my keyboard. For more see also my other source that you removed, doi:10.18732/H2XT07, and the sources it and Gupta cite. There are other books/articles about this general topic which we can try to hunt down, but I don't have too much more time today.

Wikipedia isn't a place for pursuing original research and giving judgements.

That's precisely my point. That's why I don't think we can really comment too much about what happened before the first century CE.

"Victor J Katz, Carl Boyer, Lam lay young, Joseph Needham, Douglas A Campbell, Helaine Selin, Frank Swetz"

You are conflating a wide range of different authors making radically different types of claims, attributing to the whole group the most extreme speculation by a couple of those authors, extrapolating beyond their original claims, and making their speculation sound more assured than these authors even claim themselves. For this kind of controversial speculative claim Wikipedia should be clear what is known, what is conjectured, and what level of certainty is involved, so that we don't mislead readers. –jacobolus (t) 20:40, 23 February 2024 (UTC)

@Paul August The first couple sentences of what I wrote should perhaps try to be more precise, and maybe add some discussion in footnotes. It's hard to disentangle the relation between a written numeral system per se and conceptual ideas about numbers described e.g. in verses. There are some clear bits of evidence about positional concepts appearing in Indian sources by the first century CE, but perhaps not yet reflected in the writing system per se.

I am decidedly not an expert (from what I can tell it doesn't seem like any professional experts have been involved in this or the several related Wikipedia articles, though I might be wrong about that), and still reading more about this topic to see if I can come up with a better summary of current scholarship. –jacobolus (t) 02:55, 25 February 2024 (UTC)

Ok. Paul August ☎ 11:55, 25 February 2024 (UTC)

Sources for a better glyph evolution image

Does anyone have recommended sources to examine while trying to draw a replacement for scans of Menninger's glyph evolution image? I mentioned Chrisomalis (2010) Numerical Notation: A Comparative History as one fairly comprehensive scholarly survey by a career expert. Are there other relatively recent surveys with decent coverage of this topic? –jacobolus (t) 02:10, 25 February 2024 (UTC)

Reason for reverting my edit

@Paul August has reverted my edit https://en.wikipedia.org/w/index.php?title=Hindu–Arabic_numeral_system&diff=prev&oldid=1209835548 because he has some issues with that edit. Please discuss your issues here, because I don't see any issue. All the contents were supported by multiple reliable sources. Hu741f4 (talk) 19:59, 23 February 2024 (UTC)

"The world's earliest positional decimal system was the Chinese rod calculus." – This is not an accurate statement. Decimal counting boards were used in Ancient Egypt many centuries before that. For example Herodotus in the 5th century BCE explicitly described how the (positional, decimal) counting boards used in Egypt and Greece were oriented in opposite directions; by that time this was an old technology firmly embedded in culture and language. –jacobolus (t) 20:09, 23 February 2024 (UTC)

Please show me a reliable source that says the decimal counting boards used in Ancient Egypt or by Herodotus were based on the "decimal positional system". Also If possible, please don't reply here, as I created this section only for Paul regarding removal of that particular edit. You can discuss your issues in the preceding section.Hu741f4 (talk) 20:18, 23 February 2024 (UTC)

Counting boards are inherently positional. That's the whole point. You have some counters or tokens (or in the Chinese case, rods) and depending on their position, the meaning changes. This comment directly addresses your edit, which I quoted directly. –jacobolus (t) 20:42, 23 February 2024 (UTC)

no! they aren't. If that is the case why no historian of Mathematics say that Ancient Egyptians were the first to have positional decimal system. Why all of them point towards ancient China? Please show me a reliable source that says the decimal counting boards used in Ancient Egypt or by Herodotus were based on the "decimal positional system" Hu741f4 (talk) 20:46, 23 February 2024 (UTC)

The Ancient Egyptian writing system was not positional (similarly, Attic and Roman numerals are not positional, and we might add, all of the historical Chinese written numeral systems were likewise not positional). However, these cultures used a positional decimal calculation tool, in the form of the counting board, which is structurally very similar to Chinese counting rods. One of the oldest remaining physical artifacts is the Salamis Tablet from ~300 BCE, but the idea is many centuries or possibly millennia older; there's circumstantial evidence that ancient Babylonians used some form of counting board to do sexagesimal calculations. I have to go for now, but I'll try to find you some good sources about ancient counting boards when I get the time. –jacobolus (t) 20:50, 23 February 2024 (UTC)

Very quickly before I run out the door, here's Reviel Netz (2002) "Counter Culture", explaining a bit of why it has been hard to find definite historical artifacts recognizable as Greek-style counting boards:

The only Greek scholar to have researched the subject is Lang, in a series of publications of fundamental value, published in the journal Hesperia between 1957 and 1968, to which I shall refer below. T. L. Heath, A history of Greek mathematicsP is still of some value. At any rate, while many questions on this issue are still open, there is no doubt that, in the ancient Mediter- ranean, calculations were frequently made by moving counters on a surface known as the 'abacus'. We therefore need to look at the ancient, or western abacus. In M. L. Lang's original publication in the field, "Herodotus and the abacus", 14 abaci were listed from the classical Aegean world. In a later publication, "Abaci from the Athenian Agora", the same author added two more from the Athenian Agora. A. Scharlig extends the list to 30 objects, with largely the same pattern of distribution: nearly all from the Aegean world, most from Attica. (The furthest afield seems to be SEG XXIII 620, a third-century B.C. abacus found in Cyprus.)

In her original publication from 1957, as well as two later articles, Lang went on to argue that some arithmetic features in calculations preserved in the literary tradi- tion of classical texts may be accounted for by assuming operations on the abacus. Finally, while no ancient source discusses the abacus as such, there are many passing references that take it for granted. Based on this archeological and literary evidence, a coherent picture of the physical shape of the ancient, western abacus and its usage may be suggested. [...]

Like Arabic numerals (and their Babylonian antecedents) the abacus is essentially positional: hence follows a certain abstraction. Just as it makes no difference, for pen-and-pencil operations, which absolute value the positions have (to add 1.345 and 1.678 is the same as to add 1345 and 1678), so it makes no difference, for the abacus, whether we move from 'fives' to 'tens' or from 'fifties' to 'hundreds'. If only for this reason, it makes clear sense to avoid marking the lines. It is true that the abacus is not as totally homogenous as are the positions of Arabic numerals: one must distinguish odd, 10ⁿ, from even, 5 × 10ⁿ positions. But such an alternate marking may easily be inserted on an ad hoc basis. We thus find that the western abacus has very little substance: really, no more than a row of scratches. The abaci listed by Lang were identified because, if not on the lines themselves, they had numbers marked at some other position of the abacus (perhaps to keep records during the operation). In the Greek world (unlike the Roman case) no counters were ever identified as "abacus counters", and there is no reason to suppose any existed. Ordinary pebbles would do and, as we shall note below, the Greek world had a profusion of other counters of all kinds, all useable on the abacus. Further, while the extant abaci (with a few exceptions, e.g. two abaci scratched hastily on roof-tiles) tend to be made with marble, in ordinary circumstances a mobile board would have been more useful. Most probably, abaci were mostly made with wood, but this is pure guesswork, as naturally none survives. Ultimately, indeed, the very notion of the abacus as a clearly defined artifact is misleading. While scratches are useful, the lines can very well be imag- ined, perhaps referring to whatever irregularity the surface at hand may have. Thus any surface will do. The abacus is not an artifact: it is a state of mind. The western abacus was wherever there were sufficiently flat surfaces - as well as sufficiently many objects that the thumb and fingers could grasp. Probably more designated abaci can be found if we look for them with more attention. But perhaps designated abaci are less important than the skills that make them so easy to construct and use on an ad hoc basis.

–jacobolus (t) 21:43, 23 February 2024 (UTC)

---

@Jacobolus: as I explained in the edit summary, the non-positional Brahmi numerals have their own article (that's what wikilinks are for), the origin of the ciphered-positional system is what matters here. What part of that do you disagree with? M.Bitton (talk) 16:24, 25 February 2024 (UTC)

If the topic for a section is the "origin" of the numeral system, then the section should clearly describe the origin of the numeral system. The history is not entirely clear since we primarily only have metal/stone inscriptions remaining with writing on other materials generally having deteriorated in the harsh conditions of the Indian subcontinent (desert landscapes are friendlier to preservation of plant materials), but there is a significant amount of remaining evidence which has been synthesized by the past century and a half of scholarship, and the scholarly consensus is that later Indian numerals evolved from various flavors of Brahmi numerals, in a relatively gradual process. It is essential context for readers to directly state that, with some dates giving an approximate chronology. We aren't writing an entire history of the Brahmi numerals here, only a couple sentences of essential context. If you are also interested in the origin of other features of the number system, it is important to explain what we know about where they came from; we also have some amount of evidence about that (especially textual evidence from sources composed in the 1st–6th century).

Please stop immediately reverting every attempted improvement to this article, and stop edit warring. It is impossible to improve collaborative living documents when one editor insists on reverting every change, even when the changes are appropriate and clearly sourced. –jacobolus (t) 16:42, 25 February 2024 (UTC)

The very source that you used makes it clear that the invention of ciphered-positional numerals (what matters here) likely occurred around 600 AD. Also, as someone who's fully aware of WP:BRD and WP:CONSENSUS, your edit summary and your explanation above make no sense, unless of course, you happen to think that the rules that you cite whenever it suits you don't apply to you. M.Bitton (talk) 16:45, 25 February 2024 (UTC)

Just to be clear: you think the origin of "ciphered-positional numerals" are "what matters here" (i.e. the only thing that matters). For the sake of argument, let's take your proposed scope and temporarily work through it:

You are insisting that we can't even mention the approximate date of the Brahmi numerals or their various proposed possible origins, because you claim it is out of scope. By that same standard, you are putting speculation about Chinese Shang numerals entirely out of that scope, as one (implausible, unsupported, disputed) theory among several for where Brahmi numerals might have come from.

You are insisting that we can't even mention descriptions of positional clay tokens used in India in the 1st century AD or positional number-naming used in Sanskrit verse in previous centuries, because you say it is out of scope. By that same standard, speculation about Chinese counting rods is even further out of scope, as just one entirely speculative theory (directly contraindicated by this other evidence) for where positional ideas may have come from.

Material about transmission to the Arab world and to Europe seems also out of scope for an "origin" section. So to take your standard, the origin section should be cut down to about 1–2 sentences. At that point we might as well just get rid of it, leave 1–2 sentences in the lead section, and merge more detailed material into sections about "history", "transmission", or similar. That sounds fine to me. Unless some convincing argument otherwise arises, I'll go ahead and merge the content you removed later into the article, ideally further extending it a bit, and scrap the "origin" section as unnecessary. –jacobolus (t) 17:36, 25 February 2024 (UTC)

There is a difference between what the sources state about the origin of the ciphered-positional numerals and your claims about the relevance of the non-positional numerals. The source that you cited mentions the likely date of the invention and then goes on about who invented the zero and the earliest surviving and unquestionable examples of ciphered-positional numerals with a zero derive.

Other Material about transmission of ciphered-positional numerals (again, this what the subject is about) is obviously relevant and if you can't see the difference, there there isn't much I can do about it.

Please respect the consensus building process and don't force your edit through the back door. M.Bitton (talk) 17:43, 25 February 2024 (UTC)

Which other material are you talking about. Counting rods (like the Mediterranean/Mesopotamian counting-board abacus) are not ciphered, nor are they numerals. Shang numerals are not really ciphered, and are not positional. These are just two among a wide variety of other similar systems including Semitic, Egyptian, Greek, etc., which are no less relevant than the Chinese examples (i.e. not really very).

The section as it currently exists gives an entirely distorted and misleading impression to readers. We can fix that either through removal of the misleading part (which you have rejected), or through addition of enough context to make it less misleading (which you have also rejected). That's not a tenable position to maintain.

transmission of ciphered-positional numerals (again, this what the subject is about) is obviously relevant – the section is explicitly titled "origin". Material about the later evolution and transmission of the system does not "obviously" belong there; indeed it is directly out of the scope implied by the title. –jacobolus (t) 18:19, 25 February 2024 (UTC)

I'm not going to repeat what was said in the previous discussion. We've been through that and if anything, we should highlight the possible Chinese origin even more than the flimsy mention at the end of the section. M.Bitton (talk) 18:24, 25 February 2024 (UTC)

It feels to me like every time I (or anyone else) tries to make an improvement to this currently mediocre article or other related articles, you revert the improvement and start edit warring to block it, and if someone starts a conversation about it you start rules lawyering instead of trying to understand their criticism or answer it.

My impression is that every time you are confronted with a concrete content discussion you quickly run away from it instead of explaining your thoughts or preferences or even answering direct questions. You won't explain your premises, your reasoning, or your preferred outcomes. Would you please try to address these points? Otherwise, my only assumption is that you don't actually have an argument. –jacobolus (t) 18:34, 25 February 2024 (UTC)

For the last time, PLEASE REFRAIN FROM CASTING ASPERSIONS!. M.Bitton (talk) 18:38, 25 February 2024 (UTC)

I am just telling you what my impressions and observations are about your, in my opinion disruptive, pattern of behavior, and trying to explain why they are frustrating. While this is indeed a criticism, I am trying hard not to speculate about why you are behaving this way. It feels quite hostile and insulting to me, but I'm open to the possibility that you don't intend it that way, and I am sorry if I am misunderstanding you.

I would appreciate it if you would attempt to switch to a more collegial, collaborative, and content-focused pattern, because edit warring, arguing about WP:POLICY abbreviations, repeatedly repeating "I won't repeat ..." about new questions that were never addressed, SHOUTING ABOUT THIS AND THAT, and so on are extremely unproductive and frustrating.

To get back to the content point, can you please explain, in detail, what you think the appropriate scope is for an "origin" section, and address the several direct questions I asked, instead of derailing yet another conversation by meta-discussion and ignoring the substance? –jacobolus (t) 18:49, 25 February 2024 (UTC)

One more time: PLEASE REFRAIN FROM CASTING ASPERSIONS!

I already explained what needed explaining, and as for the details, the ONUS to provide them for the inclusion is entirely on you. M.Bitton (talk) 18:53, 25 February 2024 (UTC)

In fact, this has gone on for a much longer than it has to and now it's time to ping some admins. @Drmies and Doug Weller: I'm sorry to have to ping you like this, but this editor has been casting aspersion on me for months and despite my numerous requests for them to stop, they only seem to double down on them to force me to reply in kind. You thoughts on this would be highly appreciated. Thanks. M.Bitton (talk) 19:05, 25 February 2024 (UTC)

Please stop SHOUTING. If my impressions are wrong, feel free to explain your intentions more clearly. Can you please try to understand why your behavior is frustrating, and try to adopt a more collaborative approach? I have explained my position in detail, immediately above. If you would like I can repeat it again to give you another chance to refocus on the content discussion. –jacobolus (t) 19:09, 25 February 2024 (UTC)

I also put a note at WikiProject Mathematics talk which can hopefully get some subject-matter experts or at least interested amateurs to come help us figure out a more productive way forward. –jacobolus (t) 19:25, 25 February 2024 (UTC)

Refocus on content disagreement: M.Bitton, can you please explain, clearly and in some detail, what you think the appropriate scope is for an "origin" section, and how you feel it fits with the rest of the article? My personal opinion is that any section under this title should clearly and somewhat completely discuss the origin of the Hindu–Arabic numeral system, as implied by the title. You clearly disagree, as evidenced by your removal of content directly addressing that question, and have by your editing behavior, edit summaries, and comments implied a scope which in my opinion does not match the section heading "Origin". I don't really understand what you think the scope should be. Under the scope you have set out as I best understand it currently, the section seems largely redundant and unnecessary, and I would also be happy to just merge it into the existing "history" section. –jacobolus (t) 19:09, 25 February 2024 (UTC)

Making me needlessly repeat myself while personally attacking me is beyond the pale. Enough is enough. I already pinged a couple of admins and will await their input. M.Bitton (talk) 19:12, 25 February 2024 (UTC)

I can't make you do anything, but the "discuss" step is an essential part of the "Bold, revert, discuss" process on which you based reverting my content additions. Otherwise, we end up with either an edit war or a stalled conversation. If you read that explanatory essay, you will find, "BRD is not a justification for imposing one's own view or for tendentious editing. ¶ BRD is not a valid excuse for reverting good-faith efforts to improve a page simply because you don't like the changes. ¶ BRD is never a reason for reverting. Unless the reversion is supported by policies, guidelines or common sense, the reversion is not part of BRD cycle". I'd really rather not derail this to further meta-discussion here though. Can you try to focus on the content? –jacobolus (t) 19:49, 25 February 2024 (UTC)

You already derailed the discussion with your persistent personal attacks that have been going on for months. M.Bitton (talk) 19:51, 25 February 2024 (UTC)

I have repeatedly tried to refocus the discussion on understanding the basis of concrete content disagreements, finding and describing relevant reliable sources, and working to establish some kind of working consensus. You can help that by remaining focused on the content discussion, rather than on my past frustrations with your patterns of editing behavior. –jacobolus (t) 19:54, 25 February 2024 (UTC)

your patterns of editing behavior Not only have you repeatedly attacked me personally for no reason other than to provoke me, but you're still doing it and doubling down on it. I will just ignore you until the admins that I pinged weigh in. M.Bitton (talk) 19:58, 25 February 2024 (UTC)

I have no desire to "provoke" you. Stating that in the past I was frustrated with your behavior is not a personal attack. If you like, we can start a separate discussion topic explaining the context about why I was frustrated last time; it's off topic here. –jacobolus (t) 20:01, 25 February 2024 (UTC)

You already have and despite my multiple requests to stop, you keep doing it and doubling down on the personal attacks. I couldn't care less about the reasons behind your attacks, but I will make sure that you will stop (one way or the other). M.Bitton (talk) 20:03, 25 February 2024 (UTC)

I am sorry: It has never been my intention to provoke you, and none of my comments are intended as a personal attack. If you have been "provoked" to anger, I hope you will return and refocus on content disputes when you are ready. Either way I intend to press the content point in the coming days. –jacobolus (t) 20:10, 25 February 2024 (UTC)

none of my comments are intended as a personal attack is that some kind of joke? I asked you repeatedly to refrain from casting aspersions and personally attacking me, but to no avail. In fact, you doubled down on them. In any case, I will await the admins' input (because this has been going on for months and it needs to stop, regardless of the intentions behind it). M.Bitton (talk) 20:24, 25 February 2024 (UTC)

I have tried very hard to be polite under what feels like a barrage of continuous disrespect from you, and I have pleaded with you over and over to please adopt a more collegial approach and refocus on concrete content disputes. –jacobolus (t) 21:02, 25 February 2024 (UTC)

@M.Bitton: I'm also not clear on why you think this content (which seems does seem relevant to me):

The Brāhmī numerals, a ciphered additive decimal numeral system, developed in the Indian subcontinent probably sometime around the 3rd century BCE, spreading through the Maurya Empire. The ultimate origin of the Brāhmī numerals is unresolved, but they have been theorized to have evolved from Greek, Chinese, or most plausibly Egyptian numerals, or to have developed indigenously. A decimal place-value system using clay tokens is mentioned by Indian texts composed in the 1st century CE, and by the 3rd century CE a positional number naming system developed for dates in Sanskrit verse.

does not belong here?

References

Paul August ☎ 19:17, 25 February 2024 (UTC)

Please read the explanation given above about the difference between the origin of the ciphered-positional numerals and the irrelevant origin of the non-positional Brahmi numerals. M.Bitton (talk) 19:25, 25 February 2024 (UTC)

@M.Bitton: I've read and I still don't understand the point you are trying to make. Are you saying that the origin of the Hindu–Arabic numeral system has nothing to do with the origin of the Brāhmī numeral system? Can you please cite a source for that assertion? Paul August ☎ 19:33, 25 February 2024 (UTC) P.S. In the future you should assume that I've read all of the previous discussion (doing otherwise seems rude). Paul August ☎ 19:38, 25 February 2024 (UTC)

I said what I'm saying and I won't provide a source to back your assumptions. This article is no more about the non-notational simple numerals than it is about the zero (though the zero is far more important), we have dedicated articles for those and wikilinks were created just for that purpose.

I will also ping Hu741f4 who may have something to say about this. M.Bitton (talk) 19:42, 25 February 2024 (UTC)

I agree with you @M.Bitton. None of the academic sources that discussed the Chinese origin of Hindu-Arabic numeral and base-10 decimal positional system (Joseph Needham, Frank J. Swetz, Lam Young, Campbell Douglas, Helain selin) have ever been questioned by other reputed scholars. @Jacobolus isn't providing any reliable review or other reliable scholarly source. Gupta is WP:Fringe if he contradicting all of them. Hu741f4 (talk) 20:29, 25 February 2024 (UTC)

@Hu741f4: would it be possible for you to also weigh in on the recent edit that I reverted? Thanks. M.Bitton (talk) 20:32, 25 February 2024 (UTC)

have ever been questioned by other reputed scholars – this statement is outright false. I recently linked to 2 very strong criticisms of Lam Lay Yong and Ang Tian Se's book by some of the worlds' foremost experts on this topic, and can find at least another 1–2 if you like. Campbell and Douglas are two separate people who have not weighed in on this topic; Frank Swetz's paper is a game-of-telephone repetition of Lam's claims which in my opinion does not accurately convey them and is thus not a great source. If you want to litigate either the counting rods -> positional Indian numbers or the Shang numerals -> Brahmi numerals theories (which are entirely distinct and should not be conflated), can we make a new discussion topic about it though? It's getting a bit cramped in this one. –jacobolus (t) 20:53, 25 February 2024 (UTC)

@Paul August I don't think this point can necessarily be settled by sources, or by a fight about which sources are better. It's really a question about high-level article organization and about the intended scope of each section.

As I understand it, a section titled Origin in an article titled Hindu–Arabic numeral system clearly implies its scope to be the origin of the Hindu–Arabic numeral system, which I take to mean the immediate context and the process whereby that system originally developed, in keeping with the plain meaning of the word origin, "the point or place where something begins, arises, or is derived", from Latin for "to rise".

Under this understanding of the scope, this material (both a brief mention of the additive system the Hindu–Arabic numeral system came from, and also some discussion of ideas about positional numeration present in the same cultural context) seems self evidently relevant. If other editors believe that not to be the correct interpretation of the scope of this section, they should explain clearly and completely what they imagine the scope to be, and why they think "Origin" is an appropriate title for that. –jacobolus (t) 20:21, 25 February 2024 (UTC)

OK perhaps. But (to me) M.Bitton seems to be saying that: "the origin of the Hindu–Arabic numeral system has nothing to do with the origin of the Brāhmī numeral system". Since otherwise it would, as you say, seem self-evident that the origin of the Brāhmī numeral system would belong in a section entitled "Origins".

@M.Bitton:} could you confirm or deny that that is in fact what you are saying? Thanks. ~~ Paul August ☎ 20:41, 25 February 2024 (UTC)

The origin of the non-notational Brahmi numerals is covered (or should be covered) in the article that is dedicated to the Brahmi numerals. The origin in this article refers to the origin of the Hindu-Arabic numerals (the primary subject). M.Bitton (talk) 20:44, 25 February 2024 (UTC)

Yes but that's no reason why it can't also be briefly discussed here. Wikipedia articles aren't disjoint. So does that mean that you agree that the origin of the Brāhmī numeral system does have relevance for the origin of this numeral system? Paul August ☎ 20:53, 25 February 2024 (UTC)

The source that they cited mentions the likely date of the invention and then goes on about who invented the zero (because of its importance in the Hindu-Arabic numerals) and the earliest surviving and unquestionable examples of ciphered-positional numerals with a zero derive. That's the kind of relevant content that belongs in the origin. M.Bitton (talk) 20:54, 25 February 2024 (UTC)

The edit made by @Jacobolus isn't neutral. It discusses one POV while completely ignoring the other authors. Hu741f4 (talk) 20:58, 25 February 2024 (UTC)

Which edit are you referring to? Are we talking about this text:

The Brāhmī numerals, a ciphered additive decimal numeral system, developed in the Indian subcontinent probably sometime around the 3rd century BCE, spreading through the Maurya Empire. The ultimate origin of the Brāhmī numerals is unresolved, but they have been theorized to have evolved from Greek, Chinese, or most plausibly Egyptian numerals, or to have developed indigenously.

Which part does not seem neutral / seems to be pushing a non-mainstream of view? –jacobolus (t) 21:04, 25 February 2024 (UTC)

Note: I don't at all mind linking to more primary and secondary sources about these various theories (we can start by following Chrisomalis's careful and reasonably thorough seeming list of references); we can elaborate in a footnote about the historiography, why one or another theory is considered more plausible, etc. Or if a footnote seems cramped, we can merge this whole section into a later part of the article where we can go on at slightly more leisure, or we can even put an extended discussion at History of the Hindu–Arabic numeral system and direct readers there for more information. –jacobolus (t) 21:14, 25 February 2024 (UTC)

That the Hindu–Arabic numeral system developed from the Brāhmī numeral system does not contradict the fact they both may ultimately have derived from the Shang dynasty numeral system. Paul August ☎ 21:13, 25 February 2024 (UTC)

Stephen Chrisomalis isn't a reputed authority in history of Mathematics. Hu741f4 (talk) 21:03, 25 February 2024 (UTC)

@Hu741f4: that aside, what do you think about the relevance of the history of the non-notational Brahmi numerals (which have their own article)? M.Bitton (talk) 21:05, 25 February 2024 (UTC)

It shouldn't be discussed here at such length, because this article is about Hindu-Arabic number system. The basic characteristic of Hindu-Arabic numeral is decimal positional system. It is unrelated in contrast to Chinese numerals Hu741f4 (talk) 21:15, 25 February 2024 (UTC)

@Hu741f4 Which proposed theory about Chinese numerals are you specifically interested in? Are you interested in (1) the theory that the Brahmi numerals may have arisen from Chinese written numerals / that both Chinese and Indian numeral systems may have developed from a common ancestor, or (2) the theory that the Brahmi numerals developed into a positional system under the influence of counting rods? These two are largely unrelated and distinct theories. We could plausibly mention both of these theories, so long as we also include (a) material about all of the equally plausible competing theories in either or both cases, as well as (b) some description of the amount of evidence available for the various possibilities, for context. –jacobolus (t) 21:19, 25 February 2024 (UTC)

"Stephen Chrisomalis isn't a reputed authority in history of Mathematics" – He wrote his PhD and later this book, published by Cambridge University Press, about the comparative history of numeral systems. His book has hundreds of citations in the scholarly literature. Here are some reviews:

• "Numerical Notation is a masterly work – comprehensive, authoritative and methodologically rigorous. It will be a cornerstone in the study number systems for years to come." (Alexander 2010, JSTOR 41428508)
• "Does Chrisomalis provide a methodological example to follow? I enthusiastically say yes. Numerical notation is a fine piece of analysis of cultural evolution. [...] He manages to recognize the many factors and contingent causes that are involved in the evolution of numerical notation systems, and, yet, to single out some important and pervasive constraints. It is quite an achievement in cultural evolutionary study." (Heintz 2013 JSTOR 42001652)
• "The great strength of this book lies rather in the detailed analyses it offers of the different numerical notations that are attested, their families and interactions, and their manifold paleographic variations. [...] within its defined remit, Numerical Notation: A Comparative History will remain a key reference text for years to come." (Lloyd 2010 JSTOR 10.1086/659672)
• "Prodigious in its theoretical scope, sweeping in the depth in which it probes and brings together a large number of seemingly diverse systems, Numerical Notation constitutes a well-informed quest for cultural universals in a subject usually left [...] to narrowly focused specialists. There is something of value in this work for all scholars, regardless of the subfields of anthropology and culture history with which they might identify." (Aveni 2010, JSTOR 20798881)
• "In not quite five hundred dense but exceptionally clearly written pages, the young anthropologist Stephen Chrisomalis has managed to produce what would be for most people a crowning achievement of a life in scholarship: a monograph that is both astonishing in its comprehensiveness and careful about detail; that is both a work of reference and somethingthat can be picked up and read, whether in whole or in part; that is both theoretical and data-driven; and that is simultaneously polemical in its attitudes and illuminating in its analyses. [...] it seems to me that all readers of this journal, regardless of specialty [...] are going to need to pay attention to this brilliant and original book. [...] this is a work for the ages [...]" (Katz 2011 JSTOR 41380727)

Can you suggest another survey source about Hindu–Arabic numerals or numeral systems more broadly from the past few decades which you think we should rely on instead? I don't at all mind finding more sources here; from what I can tell the relevant historical claims in Chrisomalis's book are not controversial. –jacobolus (t) 23:50, 25 February 2024 (UTC)

Citation style

@Jacobolus: Can you please explain why you chose to not use the short form cites I introduced into the "Origins" section? Paul August ☎ 15:22, 26 February 2024 (UTC)

This article has previously had a convention of putting citations to short articles/chapters into footnotes, and citations to full books which needed page numbers specified in multiple different places into a list at the end, with short references including the page numbers in footnotes. I don't see a clear reason for adopting a mishmash of mixed conventions. –jacobolus (t) 15:26, 26 February 2024 (UTC)

I could imagine adopting some other style convention though; this article is (and has been) generally mediocre and inconsistent in scope, organization, content, sourcing, and style, and the citation style is no exception, with lots of incomplete and poorly formatted references and lots of unsourced claims. If the defenders of this article would stop deleting every attempt at improvement (including the sources), it would be theoretically possible to substantially fix, expand, and improve the article, including adopting some different citation style. There are high-quality Wikipedia articles which adopt a variety of different styles for sources. –jacobolus (t) 15:33, 26 February 2024 (UTC)

I think it's very useful to have page numbers (with links) whenever possible, for all citations, with full bibliographic info in a separate section. So unless you object I would like to return to using short form cites. Paul August ☎ 15:45, 26 February 2024 (UTC)

I object to having an inconsistent mishmash of different citation styles within an article, and I don't think it's worth cleaning up and globally restyling the current citations in this article unless we're going to actually commit to making a substantial rewrite/improvement, since many of the current citations are not very good. Specific page numbers aren't really necessary for sources which are shorter than about 30 pages, though they can be fine to include also. One way to add both the full page numbers of a book chapter or paper and also a specific page number is to include a quotation along with the "quote page" parameter. It's also probably fine to specify the page number range and then explicitly call out one page, something like "pp. 45–75, specifically p. 62". –jacobolus (t) 16:03, 26 February 2024 (UTC)

Origins of non-positional numerals and of positional concepts

I added a "dubious" flag to the sentence about "Shang numerals". This sentence is currently inaccurate and also not reflective of the linked sources. The referenced ~1400 BCE numerals found on oracle bones are an interesting topic in their own right and it would be great if Wikipedia had an article about them, but they are not "positional" in the sense meant by this article. To the best of my understanding, Lam's claim in her papers and book is that the feature from Chinese arithmetic adopted in India was the positional idea (from counting rods), not anything about written numerals from more than a millennium year earlier. I'll try to re-read Lam's papers; it's been a few months since I looked at them. –jacobolus (t) 15:49, 26 February 2024 (UTC)

In that case, why did you revert my edit? M.Bitton (talk) 15:53, 26 February 2024 (UTC)

I reverted my own edit, as a polite gesture to @User:Paul August, who had said "Can we please not make any substantive changes to this section which are undiscussed on the talk page." –jacobolus (t) 15:57, 26 February 2024 (UTC)

There are 2 different subjects which may be worth addressing in this article, but if either or both is to be addressed, it should be accurate, moderately complete, and well sourced.

1. What was the origin of the Brahmi numerals. There are a wide range of theories about this, and if we mention any of them, we should flesh the topic out and describe all of the main contenders and the evidence presented for them.
2. What was the origin of positional concepts which eventually transformed Brahmi numerals into the modern positional system. If we want to discuss this topic, we should also describe the various theories about this, including evidence from within India and proposed influences from outside, again along with some notion of what evidence there is for each theory.

We should be clear to separate these two topics, since they are mostly unrelated.

–jacobolus (t) 15:57, 26 February 2024 (UTC)

Well the most recent edits regarding this article have to do with how we represent the relationship of the Shang numerals to this topic, can we focus on that for a moment? Paul August ☎ 16:03, 26 February 2024 (UTC)

There have been some scholars who have speculated that the Brāhmī numerals originated in Chinese numerals, or that Chinese numerals and Brāhmī numerals both descend from a common ancestor. Swetz's off-hand explicitly speculative remark in his paper about Chinese mathematics was not really a serious considered proposal, and shouldn't be considered as anything more than idle speculation. Here's what Chrisomalis (2010) says:

The Brāhmī script came to prominence in the mid third century BC [...]. Brāhmī script was probably derived from a Semitic prototype (Aramaic, South Semitic, or Phoenician), although many South Asian scholars still support the theory that the script was indigenously developed (Salomon 1996: 378–379). [...]

The question of the ultimate origin of the Brāhmī numerals – specifically, whether or not they constitute a case of independent invention, and if not, on which ancestor(s) they were modeled – is unresolved, and is made more complex by the politicization of the matter. [...]

One set of theories regarding the origin of the Brāhmī numerals derives them from existing representational systems used in South Asia. Borrowing from the letters of the Brāhmī script to create an alphabetic numeral-system, while once a popular theory, is not really sustainable (Prinsep 1838, Woepcke 1863, Indraji 1876, Datta and Singh 1962 [1935], Gokhale 1966, Verma 1971). [...] The derivation of the Brāhmī numerals from the Kharoṣṭhī letters is even more improbable [...]. Finally, a more recent set of theories derives the Brāhmī numerals from those of the Indus Valley civilization (Sen 1971, Kak 1994), but there are no examples of any writing from India between the latest Harappan inscriptions (around 1700 bc) and the first Brāhmī inscriptions [...].

If not derived from any South Asian system, the Brāhmī numerals could have developed independently. Woodruff (1994 [1909]: 53–60) speculated that both the Chinese and Brāhmī numerals derived from a hypothetical ancient set of cumulative tally signs for 1 through 9, which would then have spread to both China and India. [...]

Finally, a number of theories argue for a foreign origin of the Brāhmī numerals. Falk (1993: 175–176), noting structural and paleographic resemblances between the Brāhmī and the earliest Chinese (Chapter 8) numerical notations, argues for a Chinese origin. However, there is little evidence of contact between the two regions at this period, and the only paleographic similarity between the systems is the common use of horizontal strokes for 1, 2, and 3. It has occasionally been proposed that the Greek alphabetic numerals inspired the Brāhmī numerals, given their appearance following the Alexandrine period, the strong trade ties with the Greco-Iranian kingdoms of Parthia and Bactria, and the structural similarities between the two systems. However, the evidence for the “alphabeticity” of the Brāhmī numerals is weak at best (see the previous discussion), and there is no paleographic correspondence between the Greek and Brāhmī numerals.

It is most plausible that the Brāhmī numerals are derived from the Egyptian hieratic or demotic numerals. Burnell (1968 [1874]) argued for a demotic origin, while Bühler’s (1963 [1895]) much more prominent analysis argued for a hieratic origin. The three systems are structurally similar: they are all decimal, hybrid ciphered- additive/multiplicative-additive systems, and represent 200, 300, 2000, and 3000 by adding quasi-multiplicative strokes to the signs for 100 or 1000. There are resemblances in around one-third of the sign-forms, and very close resemblances for a few, such as 9 (Bühler 1963 [1895]: 115–119; Salomon 1995, 1998). While there was not tremendous Egypto-Indic cultural contact, Ptolemaic traders reached as far as the city of Muziris (modern Cranganore) on the Malabar Coast, and Aśoka is known to have sent Buddhist missionaries to Alexandria (Basham 1980: 187). Of the two Egyptian systems, I believe the demotic to be a more likely ancestor, because in the Ptolemaic period the use of hieratic numerals was very limited. Thus, although the demotic and Brāhmī systems differ in both the power at which multiplication is used and the direction of writing, I believe that a demotic origin should be adopted as a working hypothesis.

–jacobolus (t) 16:20, 26 February 2024 (UTC)

They have not speculated, they have stated what they believe in; that's why we are attributing what they stated to them and not stating it as a fact in Wikipedia'a voice. M.Bitton (talk) 16:25, 26 February 2024 (UTC)

You are missing my point. All of these theories about the origin of Brahmi numerals (descent from a Harappan system, independent origin, origin in Chinese, Greek, or Egyptian hieratic or demotic systems) are speculative, based on little direct evidence. But if we are going to mention any of them, we should mention them all, and at least in a footnote elaborate about the lack of available evidence. –jacobolus (t) 16:31, 26 February 2024 (UTC)

You are missing everyone's point. We're not talking about anything else but the part that you tried to tag. M.Bitton (talk) 16:33, 26 February 2024 (UTC)

We're talking about a mishmash of two distinct claims, which you keep improperly conflating. (1) Brahmi numerals may have evolved from Chinese numerals, among several possibilities, and (2) Brahmi numerals may have evolved into a positional system under influence from Chinese counting rods, among several possibilities. Paul August asked about claim #1, which is why I am discussing it in this subthread replying him; please stop changing the subject; claim #2 is better left to a different subthread. The "stable" text of this article and Swetz's off-hand remark and quickly sketched diagram are apparently addressed to claim No. 1, but there are people proposing this more seriously, e.g. Falk (1993) Schrift im alten Indien. If we want to include this claim, it should be in the context of competing theories. The statement as it was in the article is not accurate, and has nothing to do with Lam's two articles. –jacobolus (t) 16:44, 26 February 2024 (UTC)

See my previous comment and your first comment in this section. There will be no more replies to this. M.Bitton (talk) 16:53, 26 February 2024 (UTC)

To help facilitate discussion, here is the current text under discussion:

According to some sources, this number system may have originated in Chinese Shang numerals (1200 BC), which was also a decimal positional numeral system.

Here is some new text proposed here by jacobolus:

According to some scholars, the Hindu–Arabic number system originated in Chinese counting rods, also a positional decimal number representation.

Paul August ☎ 16:00, 26 February 2024 (UTC)

I obviously agree with the second since that's what the scholar have stated: "the Hindu-Arabic system could only have originated from the rod numeral system". M.Bitton (talk) 16:02, 26 February 2024 (UTC)

@Paul August: why did you strike the second statement? M.Bitton (talk) 16:07, 26 February 2024 (UTC)

Oops sorry, the proposed changes by jacobolus here were:

Some scholars have theorized that the positional concept in the Hindu–Arabic number system may have originated in Chinese counting rods, also a positional decimal number representation.

Paul August ☎ 16:11, 26 February 2024 (UTC)

Here's the proposed change:

According to some scholars, the Hindu–Arabic number system originated in Chinese rod numeral system, also a positional decimal number representation.

because I explained above, that's what the scholar have stated: "the Hindu-Arabic system could only have originated from the rod numeral system".

M.Bitton (talk) 16:12, 26 February 2024 (UTC)

Yes that was your new proposed change. Paul August ☎ 16:14, 26 February 2024 (UTC)

Who are you quoting here: "the Hindu-Arabic system could only have originated from the rod numeral system" Paul August ☎ 16:23, 26 February 2024 (UTC)

Lam. M.Bitton (talk) 16:25, 26 February 2024 (UTC)

Can you please say where? Paul August ☎ 16:39, 26 February 2024 (UTC)

Here's a link to the source. M.Bitton (talk) 16:44, 26 February 2024 (UTC)

Thanks Paul August ☎ 16:57, 26 February 2024 (UTC)

Proposed changes

• Current:

  According to some sources, this number system may have originated in Chinese Shang numerals (1200 BC), which was also a decimal positional numeral system.

• Proposed change by jacobolus here:

  Some scholars have theorized that the positional concept in the Hindu–Arabic number system may have originated in Chinese counting rods, also a positional decimal number representation.

• Proposed change by M.Bitton here:

  According to some scholars, the Hindu–Arabic number system originated in Chinese rod numeral system, also a positional decimal number representation.

Paul August ☎ 16:37, 26 February 2024‎ (UTC)

To be clear, my "proposed change" is what I consider the minimal change necessary to make this statement not outright false / grossly misleading; ideally the change should be much more substantial and should contextualize and explain these claims, possibly in a footnote. –jacobolus (t) 16:46, 26 February 2024 (UTC)

My minimal change would make the statement inline with what the scholars have stated: "the Hindu-Arabic system could only have originated from the rod numeral system". M.Bitton (talk) 16:51, 26 February 2024 (UTC)

Overall, a better solution in my opinion would be to either eliminate the "origin" section and merge the content downward into the "history" section, or else move it downwards next to the history section, leaving a short 2–3 sentence summary in the lead section.

We can then have one full subsection about the Brahmi numerals, and a separate subsection about the origins of a positional concept, each of which would have enough space (at least several sentences, possibly extended by explanatory footnotes) to describe the various theories relevant to each of those two topics:

1. we can mention the various theories about where Brahmi numerals may have come from, showing a picture of the symbols used in Brahmi numerals for 1–9, 10–90, etc., and maybe also showing a few pictures of the glyphs appearing in Egypt, China, Greece, and possibly others, for comparison; and
2. we can describe both foreign and local evidence about positional concepts c. 500 BCE – 700 CE, including textual evidence from India about Sanskrit verse numbers and clay-token counting boards, description of Greek counting boards, description of Chinese counting rods, and a more complete discussion about the evolution of Brahmi-descended numerals from an additive to a positional system.

The current article's organization doesn't give enough space to mention the Chinese origin theory without either (a) giving it "undue weight", or (b) ballooning the size of the section to a disproportionate size, distracting readers from other important topics such as the use and structure of the Hindu–Arabic numeral system. –jacobolus (t) 17:05, 26 February 2024 (UTC)

Can you please concentrate on what's being discussed? M.Bitton (talk) 17:08, 26 February 2024 (UTC)

I am concentrating on what is being discussed: the changes necessary to fairly and accurately cover this topic in an encyclopedic manner; I frankly do not think 1–2 sentences in the current "origin" section is an acceptable medium-term solution; but we can leave some version of it as an inadequate stopgap, with a 'dubious' tag preserved, pending a more complete solution. –jacobolus (t) 17:11, 26 February 2024 (UTC)

Here is what the sources currently cited in our article say:

1. Swetz, p. 30: "an interesting hypothesis arises, namely that the numeration system commonly used in the modern world had its origins 34 centuries ago in Shang China!"
2. Lam 1988, p. 101: "In 'The Conceptual origins of our numeral system and the symbolic form of algebra' and 'Linkages: Exploring the similarities between the Chinese rod numeral system and our numeral system', I advanced the following thesis—that China is the earliest civilization to possess the concept of our numeral system, also known as the Hindu-Arabic numeral system. In this paper, I summarize the main points that have been put forward and also examine fresh evidence to support a further claim—that our numeral system has its origins in the Chinese rod numeral system."
3. Lam 2008, p. 198: " ... This fact together with other evidence supports the thesis that The Hindu-Arabic numeral system has its origins in the Chinese rod numeral system".

Paul August ☎ 16:56, 26 February 2024 (UTC)

Here is another quote mentioned above by M.Bitton:

Ang and Lam 2004, p. 185: "the Hindu-Arabic system could only have originated from the rod numeral system".

Paul August ☎ 17:13, 26 February 2024 (UTC)

Here is how Chrisomalis (2010) diplomatically addresses Lam's claims (Chrisomalis's PhD thesis more aggressively rejects Lam's claims, as do multiple reviews of Lam's book):

Lam Lay-Yong (1986, 1987, 1988) hypothesizes that the rod-numerals were ancestral to the Hindu positional numerals, because the rod-numerals are positional and decimal, and because there was considerable cultural contact between China and India in the sixth century AD, when positionality developed in India. Because the rod-numerals were used in computation and commerce, she asserts that it is inconceivable that the Indians would not have learned of this system from the Chinese, and, since it is so practical, they obviously would have borrowed it (Lam 1988: 104). Yet the Indian positional numeral-signs are those of the earlier Brāhmī numerals, not of the rod-numerals, and the rod-numerals have no zero- sign (whereas the Indian system does). Moreover, the rod-numerals have a quinary sub-base that the Indian numerals lack, and the rod-numerals are intraexponentially cumulative, whereas the Indian positional numerals are ciphered. No Indian texts of the period mention rod-numerals or any other Chinese numeration.

The details here matter, and Lam's claims cannot be left as "according to some scholars" without more context. –jacobolus (t) 17:16, 26 February 2024 (UTC)

Adding two more quotes: #Helaine Selin, 2008, p. 198: "this fact, together with other evidence supports the thesis that the Hindu-Arabic system has its origin in the Chinese rod numeral system." this tertiary source is already mentioned above.

1. David E. Rowe, Wann-Sheng Horng 2015, p. 312: "Lam Lay Yong has pointed out that this system could only have originated from the rod numeral system, which was developed centuries earlier."

M.Bitton (talk) 17:16, 26 February 2024 (UTC)

Your first link is a chapter by Lam. –jacobolus (t) 17:18, 26 February 2024 (UTC)

Published by others, which makes it even more relevant and DUE. I will also ping Hu741f4 who may have something to say about and most probably other quotes to add. M.Bitton (talk) 17:19, 26 February 2024 (UTC)

Lam is an expert about counting rods, and was solicited to write a chapter about counting rods in the "Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures". I don't have any familiarity with this particular book, but Springer publishes a lot of similar large collections, often without too steep a filter on what is said inside or very extensive editing. Scholars make all sorts of claims without any explicit endorsement by their editors. –jacobolus (t) 17:27, 26 February 2024 (UTC)

That's right, she's an expert. M.Bitton (talk) 17:30, 26 February 2024 (UTC)

However, she is not any kind of expert about Indian numeral systems, cultural contact between India and China, etc., and people who are experts in those topics have strongly rejected her claims. If we are going to mention her claims, we should also directly mention that they are rejected by people with more direct and relevant experience. –jacobolus (t) 17:32, 26 February 2024 (UTC)

I have no problem with mentioning everyone's view in details, but it has to be everyone (quotes and all) with no cherry picking. That comes at a price: we'd have to create a whole section about the Chinese origin. M.Bitton (talk) 17:34, 26 February 2024 (UTC)

Okay great, we agree then: let's make the various possible theories more explicit and describe them more completely alongside criticisms. That was my goal all along.

Can we move/merge the "origin" section somewhere else then? I think an extended discussion will be distracting to readers at the very top of this article. –jacobolus (t) 17:36, 26 February 2024 (UTC)

I don't agree with you. If you think that there anything about the Chinese origin that needs extending, please mention it here so we can discuss it. M.Bitton (talk) 17:39, 26 February 2024 (UTC)

Why should we only consider possibly extending the Chinese origin? Paul August ☎ 17:41, 26 February 2024 (UTC)

First of all, we don't have to and second, that's what we're discussing here (the Chinese origin of the Hindu-Arabic numerals). M.Bitton (talk) 17:46, 26 February 2024 (UTC)

Whoops, you edited your comment (to add "That comes at a price ...") out from under my reply; the wiki software didn't show a conflict before I pressed "reply". Anyway, I think we should have a dedicated section about the possible origins of positional concepts, in which Lam's theory can be discussed alongside others, all described with a comparable level of detail. –jacobolus (t) 17:41, 26 February 2024 (UTC)

The sentence that you edited and then tried to tag is what's being discussed. Now, can we please concentrate on that? M.Bitton (talk) 17:43, 26 February 2024 (UTC)

I don't understand what this comment means. But what I am focused on is achieving some kind of consensus about a mutually acceptable path forward for organizing this article with a clear scope for various sections, so that hopefully every improvement I make doesn't get immediately reverted by you, since when that happens it is very difficult to make meaningful progress. –jacobolus (t) 17:47, 26 February 2024 (UTC)

Let me be precise: my proposed sentence above "Some scholars have theorized that the positional concept in the Hindu–Arabic number system may have originated in Chinese counting rods, also a positional decimal number representation." is nothing more than a temporary stopgap, and I do not consider it an acceptable medium-term solution to the problems with the current article. I would like to arrive at a mutually acceptable solution which we can build on without constant edit warring.

My current proposal is that we should try to merge the "origin" section into one or two subsections of the "history" section, expand the history section and add more sources, and more fully explain various theories about the origin of positional concepts, including Lam's theory, in a subsection called something like "Origin of positional concepts" or similar (I'd be open to suggestions of a better heading). –jacobolus (t) 17:54, 26 February 2024 (UTC)

I suggest you read my proposal above. M.Bitton (talk) 17:56, 26 February 2024 (UTC)

Can you please be explicit? I have read all of your comments, but I don't know which proposal you are referring to. –jacobolus (t) 17:57, 26 February 2024 (UTC)

I don't have to convince you, your position is clear and so is mine. M.Bitton (talk) 17:59, 26 February 2024 (UTC)

I am not asking you to "convince me", I am asking you to be explicit about what you are talking about, since I can't figure out which "proposal" you mean. –jacobolus (t) 18:00, 26 February 2024 (UTC)

I suggest you read the discussion again. M.Bitton (talk) 18:03, 26 February 2024 (UTC)

If we are not truing to convince each other then what is the point of all this? We might swell just take a vote! Paul August ☎ 18:02, 26 February 2024 (UTC)

We know each other's position (they haven't changed since the last discussion that took place months ago). M.Bitton (talk) 18:04, 26 February 2024 (UTC)

That's simply not true, mine have certainly evolved. Paul August ☎ 18:06, 26 February 2024 (UTC)

And are you saying that yours have been and will continue to be unchanged? Paul August ☎ 18:07, 26 February 2024 (UTC)

Mine has certainly evolved. M.Bitton (talk) 18:09, 26 February 2024 (UTC)

I agree Paul August ☎ 17:52, 26 February 2024 (UTC)

Unlike her, those people are not experts in the Chinese rod numeral system. M.Bitton (talk) 17:47, 26 February 2024 (UTC)

Yes, which is why they shouldn't (and as far as I understand, don't) emphatically speculate about rod numerals in ways that are not supported by expert scholarship. –jacobolus (t) 17:50, 26 February 2024 (UTC)

Yes and I'm an expert on topological functors so what? Paul August ☎ 17:39, 26 February 2024 (UTC)

Have reliable sources published anything of yours that links topological functors to the origin of the Hindu-Arabic numerals? M.Bitton (talk) 17:42, 26 February 2024 (UTC)

No ;-) But my point was that not every expert's opinion about everything ought to carry equal weight. Paul August ☎ 17:49, 26 February 2024 (UTC)

Right now, we're giving more weight to the Indian origin than we are to the Chinese one. M.Bitton (talk) 17:52, 26 February 2024 (UTC)

Right now we are not giving any space at all to descriptions of how positional concepts were used in India, because when I added those, with several sources, you immediately deleted them. –jacobolus (t) 17:56, 26 February 2024 (UTC)

I suggest (once again) that you read first comment in this discussion that you initiated after attempting to tag the Chinese origin (what this discussion is about). M.Bitton (talk) 17:58, 26 February 2024 (UTC)

That this numeral system is called the "Hindu-Arabic numeral system" should mean there would be a lot to say about Indian origins for it? No? Paul August ☎ 18:00, 26 February 2024 (UTC)

Are we talking about the origin or the names (including the Arabic)? M.Bitton (talk) 18:02, 26 February 2024 (UTC)

Huh?? Paul August ☎ 18:03, 26 February 2024 (UTC)

Your quote 1 is my quote 3. Paul August ☎ 17:24, 26 February 2024 (UTC)

I missed that (too much green text). In any case, the fact that it's a tertiary source is very important because that's we use to establish DUE. M.Bitton (talk) 17:26, 26 February 2024 (UTC)

Proposed reorganization

From what I can tell, M.Bitton and I can agree that the § Origins section in its current place at the very top of this article, isn't really enough space to flesh out possible theories about the origin/early evolution of the Hindu–Arabic number system. To quote M.Bitton: "I have no problem with mentioning everyone's view in details, but it has to be everyone (quotes and all) with no cherry picking. That comes at a price: we'd have to create a whole section about the Chinese origin." Paul August, does moving/merging the 'origins' section seem okay with you also?

If so, I'd like to propose, as a way forward, that I will try to write more text in the next few days about both Lam's counting rod theory and also other competing theories, in a draft page somewhere (e.g. in user space), and then will merge it in as a subsection of the § History section after discussion here. M.Bitton: if you would like to write your own competing draft for that section, that would be fine, then we can bring them together and compare. As a separate subsection, I'll try to flesh out the section § Predecessors, possibly retitled to "Brāhmī numerals", and include a few sentences inline about theorized origins for the Brāhmī numerals there, including a theorized Chinese origin. –jacobolus (t) 18:13, 26 February 2024 (UTC)

I said it and I will repeat it here: I don't agree with you!

This discussion that you initiated after trying to change the sentence about the Chinese origin is clearly about the Chinese origin, so please discuss the two possible alternatives that have been put forward (see the two possible sentences that have been quoted and the sources that go with them). M.Bitton (talk) 18:17, 26 February 2024 (UTC)

None of the possible alternative in the previous section is an acceptable solution to me. If we are going to have an § Origin section near the top, in my opinion it must discuss the topics I previously added in Special:diff/1210146115 which you then deleted in special:diff/1210217567.

If you don't think the topic of the origin of positional ideas deserves a whole separate section under the § History section, then can you please explain in detail what you think the appropriate scope is for the § Origins section? To me, all of the material you removed falls very clearly into the scope implied by the name "Origins", but at any rate is clearly relevant to this article and should be preserved somewhere. –jacobolus (t) 18:25, 26 February 2024 (UTC)

If you own proposal (and change) isn't acceptable to you, then I rest my case. M.Bitton (talk) 18:27, 26 February 2024 (UTC)

The edit summary was "make the least change necessary to make the sentence about Chinese counting rods minimally accurate" – this is a temporary stop-gap, not a "proposal". But I would appreciate it if you would address my proposal in this section and answer the several direct questions I have asked you, instead of derailing yet another conversation by aggressive off-topic rhetorical flourishes. –jacobolus (t) 18:32, 26 February 2024 (UTC)

@Hu741f4: here are the proposals that have been put forward (if jacobolus thinks that their edit isn't proposal, then there isn't much that could be said about that). M.Bitton (talk) 18:35, 26 February 2024 (UTC)

Your comments continue to be extremely rude. Can you please knock it off? –jacobolus (t) 18:36, 26 February 2024 (UTC)

Your persistent personal attacks are getting boring and therefore, I will simply ignore you from now on (you just made yourself irrelevant). M.Bitton (talk) 18:41, 26 February 2024 (UTC)

So you think that you've been perfectly polite here, and haven't being at all rude? Paul August ☎ 18:49, 26 February 2024 (UTC)

They have been persistently attacking me for months and you have never ever (not even once) said a thing to them. Care to explain why? M.Bitton (talk) 18:52, 26 February 2024 (UTC)

You are welcome to "ignore me" if discussion with me is so distressing to you. After all, Wikipedia is a volunteer project. However, in that case you should stop inappropriately reverting my well supported and clearly justified changes to the article. –jacobolus (t) 18:58, 26 February 2024 (UTC)

I suggest you read WP:CONSENSUS (you know, the policy that you quoted above after removing the sourced content that you disagree with). M.Bitton (talk) 19:00, 26 February 2024 (UTC)

Yes, finding consensus involves frank, clear, and polite discussion. Neither edit warring nor stating "I will simply ignore you" is an example of behavior leading toward consensus. –jacobolus (t) 19:02, 26 February 2024 (UTC)

Discussion doesn't mean repeating the same over and over again. Yes, I will ignore any repetition of yours because ultimately, that always lead to the same thing: personal attacks from you that are getting beyond boring. M.Bitton (talk) 19:04, 26 February 2024 (UTC)

Me asking you to knock it off with what reads to me like deliberate rudeness is not a "personal attack". If you didn't intend to be rude, then a simple "I'm sorry you read it that way, it was unintentional and I will try to be more careful in the future" would suffice. –jacobolus (t) 19:20, 26 February 2024 (UTC)

Ha ha ha. M.Bitton (talk) 19:21, 26 February 2024 (UTC)

Sarcastic laughter is an example of the kind of rudeness I would like you to stop. –jacobolus (t) 19:25, 26 February 2024 (UTC)

While we are at it, I have also asked you to stop SHOUTING! in your comments. Can you also commit to that please? –jacobolus (t) 19:21, 26 February 2024 (UTC)

I'm still awaiting the response from the admins that I pinged and this continue, I will ping others as well. M.Bitton (talk) 19:23, 26 February 2024 (UTC)

This all seems fine with me. Paul August ☎ 18:37, 26 February 2024 (UTC)

@M.Bitton: I also would like a clear statement from you about what you see as the proper scope of the "Origins" section. Paul August ☎ 18:44, 26 February 2024 (UTC)

I already explained that the discussions was initiated after the bold edits, so I see no reason not to discuss those, especially after spending time looking for the sources that you asked for.

To be clear, my "proposed change" is what I consider the minimal change necessary to make this statement not outright false / grossly misleading is also what you wrote after the bold edits. M.Bitton (talk) 18:46, 26 February 2024 (UTC)

You didn't answer my question, what should the scope of the "Origins" section be? Paul August ☎ 18:50, 26 February 2024 (UTC)

I did answer it. M.Bitton (talk) 18:53, 26 February 2024 (UTC)

I'm not talking about sections on this talk page, I'm talking about the section entitled "Origins" in our article. What should the scope be of that section? Paul August ☎ 19:04, 26 February 2024 (UTC)

I am talking about what initiated this discussion. M.Bitton (talk) 19:05, 26 February 2024 (UTC)

Fine, that's what your talking about, but my question was about what you think the scope should be for the "Origins" section, can you please respond to that? Paul August ☎ 19:14, 26 February 2024 (UTC)

Can you pleas respond to my question above (about their personal attacks)? M.Bitton (talk) 19:18, 26 February 2024 (UTC)

An article's talk page is about discussions concerning the content of the article. If you want to have a discussion about another editor's conduct you should bring it up elsewhere, such as that editor's talk page, or an administer's talk page (like mine), or at ANI. Paul August ☎ 19:31, 26 February 2024 (UTC)

If that;s the case, then why did you make a comment about "rudeness"? M.Bitton (talk) 19:38, 26 February 2024 (UTC)

@M.Bitton If you and Paul August would like to have a discussion about civility at user talk:jacobolus you are more than welcome to use that as a venue. I'm happy to explain where I was coming from with any of my specific past comments. –jacobolus (t) 19:39, 26 February 2024 (UTC)

You are in no position to dictate anything, so please do me a big favour and refrain from pinging me. M.Bitton (talk) 19:40, 26 February 2024 (UTC)

It could also be Paul August's talk page. Feel free to get specific about which comments of mine you felt were "personal attacks", and I will explain what the context was, why I made each comment, what I was thinking and feeling at the time, etc. It's off topic for this page though. I am sorry if you felt attacked, none of my comments has ever been intended as a personal attack, though I have indeed been frustrated with you. –jacobolus (t) 19:45, 26 February 2024 (UTC)

Your so-called frustration doesn't justify the persistent personal attacks. M.Bitton (talk) 19:48, 26 February 2024 (UTC)

Can you pick out some concrete examples, and start a new conversation at a better venue? In my opinion "persistent personal attacks" is a grossly inaccurate summary, but as I said, I am happy to address specific comments. –jacobolus (t) 19:50, 26 February 2024 (UTC)

As the instigator of the personal attacks who refuses to refrain from doing after being repeatedly asked to, your opinion is irrelevant to me. M.Bitton (talk) 19:53, 26 February 2024 (UTC)

Please be specific if you like, and I will go through my comments with you point by point, explaining them and apologizing for any that seem rude. However, please start that conversation somewhere else.

On this page, please stick to the subject of article content, and stop with the vague off-topic mischaracterizations of my comments and intentions. Thanks. –jacobolus (t) 20:10, 26 February 2024 (UTC)

As the instigator of the personal attacks who refuses to refrain from doing after being repeatedly asked to (see the bolded requests above), your opinion is irrelevant to me. M.Bitton (talk) 20:18, 26 February 2024 (UTC)

Would you mind if I {{collapse}} all of the subthreads consisting entirely off-topic meta discussion? These are very distracting to any new readers who might try to understand out the on-topic content discussion. –jacobolus (t) 20:28, 26 February 2024 (UTC)

Don't you date touch my comments. M.Bitton (talk) 20:29, 26 February 2024 (UTC)

It feels to me like the way you have been derailing thread after thread with off-topic meta discussion while repeatedly refusing to address point-blank content questions is a deliberate strategy to stonewall any concrete content progress on the article. Such a strategy feels like an abuse of the discussion page, which is not intended to be a general-purpose discussion forum.

If that's not your intention, I would be glad to be wrong about my inferences here, but it would help us if you could explain what your intentions and motives actually are, answer the direct content questions asked of you, and redirect off-topic concerns to a more appropriate venue. –jacobolus (t) 20:38, 26 February 2024 (UTC)

As the instigator of the personal attacks who refuses to refrain from doing after being repeatedly asked to (see the bolded requests above), your opinion is irrelevant to me. M.Bitton (talk) 20:40, 26 February 2024 (UTC)

This comment is inaccurate and defamatory. –jacobolus (t) 21:24, 26 February 2024 (UTC)

So can you now please answer my question? Paul August ☎ 19:32, 26 February 2024 (UTC)

So can you please answer my question? M.Bitton (talk) 19:35, 26 February 2024 (UTC)

I will answer your question if you ask it on my talk page. I don't think such a discussion would be fruitful here. Are you saying unless I answer the question here and now you won't answer mine? Paul August ☎ 19:44, 26 February 2024 (UTC)

You made your comment here, so I would appreciate if you could answer my question here. M.Bitton (talk) 19:45, 26 February 2024 (UTC)

What "comment" of mine are you referring to? If you are talking about my question to you: So you think that you've been perfectly polite here, and haven't being at all rude? That was a sincere question on my part. I think we could all be more polite. I was trying to see if you also thought you could have been more polite. Did you think my question was itself rude? I'm sorry if you did, that was certainly not my intension. But whatever, I will discuss all of this at length anywhere else but not here.

So again, I'm asking you to PLEASE help me understand your view about what the scope of the "Origins" section should be? I don't see how else we can arrive at a consensus concerning what should be in that section, or whether it ought to be merged with the "History" section. Paul August ☎ 20:06, 26 February 2024 (UTC)

My question is also very sincere, so I would really appreciate it if you could answer it here (where you made your comment). M.Bitton (talk) 20:14, 26 February 2024 (UTC)

I have repeatedly asked you what you think the appropriate scope is for the § Origins section, and every time you have changed the subject. I still do not understand what your position is about this. –jacobolus (t) 18:56, 26 February 2024 (UTC)

I haven't been able to understand the opposition to the (proposed) edits by jacobolus. Having read through much of the talk page, it seems to me that the contributions by M.Bitton here are of a disruptive nature. Gumshoe2 (talk) 21:35, 26 February 2024 (UTC)

Also, Kim Plofker's book "Mathematics in India" might be a useful reference for some material. Gumshoe2 (talk) 21:38, 26 February 2024 (UTC)

Plofker (2009) Mathematics in India is kinder to Lam's counting rod theory than some other expert sources are, but puts it in appropriate context as one of multiple theories and explicitly calls out the lack of evidence. The relevant section is § 3.1 Numbers and Numerals, pp. 43–48:

The earliest extant physical examples of decimal place value numerals are found in inscriptions from around the middle of the first millennium CE, written in scripts derived from Brāhmī. At present, the first such inscription known in an Indian source may be the one on a certain copper plate from Gujarat [... from] about 595 CE.⁷ Decimal place value numbers are also found in some inscriptions from Indianized cultures in Southeast Asia around the same time. [...] We can certainly infer that if the decimal place value system had been incorporated into epigraphic styles over much of South and Southeast Asia by this time, it must have originated quite a bit earlier.

footnote 7: However, it has been persuasively argued that this particular record is spurious and was actually inscribed at a later date; [...]

But we do not need to rely only on such inferences to push back the date of origin of decimal place value beyond the time of its earliest known inscriptional records. The content of some older textual sources includes hints about the writing of numbers that suggest a place value system, although of course the texts themselves are physically recorded only in much later manuscript copies. For example, a commentary from probably the fifth century CE on an ancient philosophical text, the famous Yoga-sūtra of Patañjali, employs the following simile about the superficial “changes of inherent characteristics” (Yoga-sūtra 3.13):

Just as a line in the hundreds place [means] a hundred, in the tens place ten, and one in the ones place, so one and the same woman is called mother, daughter, and sister [by different people].

Even earlier, the Buddhist philosopher Vasumitra in perhaps the first century CE used a similar analogy involving merchants’ counting pits, where clay markers were used to keep track of quantities in transactions. He says, “When [the same] clay counting-piece is in the place of units, it is denoted as one, when in hundreds, one hundred.” Such statements clearly expect the audience to be familiar with the concept of numerical symbols representing different powers of ten according to their relative positions. Due to the brevity of their allusions and the ambiguity of their dates, however, they do not solidly establish the chronology of the development of this concept.

A different representation of decimal place value is revealed by a verbal notation called by medieval authors bhūta-saṅkhyā or “object-numbers,” here designated the “concrete number system.” Its function is to provide synonyms for ordinary number words such as “three” or “twelve.” Recall that in Sanskrit, at least after the Vedic period, even technical treatises were most often composed in verse. [...]

The concrete number system, to judge from all its extant examples, has apparently always been a place value system, representing large numbers with strings of words that stand for its individual digits or groups of digits, in order from the least significant to the most significant. Thus, if we encounter, say, the verbally expressed concrete number “Veda/tooth/moon,” we translate it as “four [for the four Vedic collections]/thirty-two/one,” and write it as 1324. These concrete numbers are not combined with number words signifying powers or multiples of ten, so their only unambiguous interpretation is as pure decimal place value. Hence the idea of a positional system for numerals must have been commonplace by the time the concrete number system was invented.

A firm upper bound for the date of this invention is attested by a Sanskrit text of the mid-third century CE, the Yavana-jātaka or “Greek horoscopy” of one Sphujidhvaja, which is a versified form of a translated Greek work on astrology. Some numbers in this text appear in concrete number format, as in its final verse [...] So it corresponds to [269/270 CE]. Evidently, then, positional decimal numerals were a familiar concept at least by the middle of the third century, at least to the audience for astronomical and astrological texts.

Exactly how and when the Indian decimal place value system first developed, and how and when a zero symbol was incorporated into it, remain mysterious. One plausible hypothesis about its origin links it to the symbols used on Chinese counting boards as early as the mid-first millennium BCE. These counting boards, like the Indian counting pits mentioned above, had a decimal place value structure: they were divided into columns representing successive powers of ten, with units on the right. Small rods were arranged in regular patterns in the columns of the board to designate numbers from 1 to 9, and a column left blank signified a zero. Indians may well have learned of these decimal place value "rod numerals" from Chinese Buddhist pilgrims or other travelers, or they may have developed the same concept independently from their earlier non-place-value system; no documentary evidence survives to confirm either conclusion.

We will see in section 3.3 that there are textual indications of a written symbol for zero in India even before the start of the Common Era, but it is not clear whether the symbol was part of place value notation at that time. The use of zero in decimal numerals and its characteristic round shape may have been reinforced by the round zero markers in sexagesimal place value numerals introduced to India in Greek astronomical and astrological texts.

I would be more or less fine with something like this as a summary of the counting rod theory. Important features of this coverage: (1) it describes the repeated appearance of place-value concept in multiple contexts in India in 0–500 CE or perhaps before, including some kind of "counting pits" and Sanskrit verse "concrete numbers", (2) it doesn't make imply certainty about statements for which available evidence does not support firm conclusions (3) it explicitly describes the available evidence and mentions whether the evidence seems reliable, and also points out which parts are lacking evidence. –jacobolus (t) 22:52, 26 February 2024 (UTC)

Here' the relevant part that applies to the primary topic (the Hindu-Arabic numeral system):

Exactly how and when the Indian decimal place value system first developed, and how and when a zero symbol was incorporated into it, remain mysterious. One plausible hypothesis about its origin links it to the symbols used on Chinese counting boards as early as the mid-first millennium BCE. These counting boards, like the Indian counting pits mentioned above, had a decimal place value structure: they were divided into columns representing successive powers of ten, with units on the right. Small rods were arranged in regular patterns in the columns of the board to designate numbers from 1 to 9, and a column left blank signified a zero. Indians may well have learned of these decimal place value "rod numerals" from Chinese Buddhist pilgrims or other travellers, or they may have developed the same concept independently from their earlier non-place-value system; no documentary evidence survives to confirm either conclusion.

As far as I can see, this doesn't contradict what the other scholars have stated about the Chinese origin of the Hindu-Arabic numerals. M.Bitton (talk) 00:39, 27 February 2024 (UTC)

The entire part I quoted is directly relevant to addressing basic questions about the "Origins" of the numeral system, and all of the topics mentioned by Plofker must be discussed in the same place in this article (but shorter, with less detail than the book) to provide essential context and avoid putting undue emphasis; it's going to take at least 2–3 paragraphs, possibly extended by further detail in explanatory footnotes, which is why I recommend merging it into a subsection of the § History section. Even more detail, something more comparable in scope/detail to Plofker's book section, could be included at History of the Hindu–Arabic numeral system. –jacobolus (t) 02:42, 27 February 2024 (UTC)

I agree with the two above comments by jacobolus, although I think it could be possible to be briefer than 2-3 paragraphs. Gumshoe2 (talk) 03:26, 27 February 2024 (UTC)

Something like this seems reasonable to me. Paul August ☎ 11:07, 27 February 2024 (UTC)

IF that's what you truly believe, then ANI is thataway. M.Bitton (talk) 21:46, 26 February 2024 (UTC)

Not seeing any specific reasons claimed why this proposal wouldn't be an effective way of resolving this dispute, I am going to work on making those draft changes under the assumption that other editors will broadly support the reorganization once it's ready. If anyone would still like to see a different kind of organization, please make clear and concrete proposals now and we can discuss them: I'm not aiming for a fait accompli here. –jacobolus (t) 19:16, 26 February 2024 (UTC)