This is an archive of past discussions about Hindu–Arabic numeral system. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.
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.[1][2][3]
^Helaine Selin (2008). Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Springer Science & Business Media. p. 198. ISBN978-1-4020-4559-2.
Here is what these cited sources say:
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!"
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."
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.
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)
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."
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.
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)
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. ...
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)
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)
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)
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)
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)
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)
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 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)
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.
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)
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"?
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)
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
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)
"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"
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)
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)
